arcee-ai/nuclear_patents · Datasets at Hugging Face

patent_number stringlengths 0 9	section stringclasses 4 values	raw_text stringlengths 0 954k
	claims	1. A system comprising:a laser source adapted to provide a laser beam directed along an optical path, wherein the laser beam is characterized by an output power in the range of 1 petawatt or higher; anda target positioned along the optical path and including:a laser incidence area for receiving the laser beam;an electron generation region adapted to absorb a portion of the laser energy associated with the laser beam and generate a plurality of electrons along an electron path;a compression region disposed along the electron path; anda capsule embedded within the compression region and including deuterium tritium (DT) gas. 2. The system of claim 1 wherein the target further includes a shock absorption region disposed between the electron generation region and the compression region, the shock absorption region configured to absorb a shock wave generated by the laser beam. 3. The system of claim 1 wherein the laser source comprises a Titanium Sapphire laser. 4. The system of claim 1 wherein the compression region includes a high Z material comprising one of gold, lead, tungsten, or silver. 5. The system of claim 1 wherein the electron generation region includes a first material and the compression region includes a second material different from the first material. 6. The system of claim 1 wherein the capsule includes an outer shell comprising a low Z material, wherein the low Z material comprises one of silicon dioxide, aluminum oxide, or carbon. 7. The system of claim 6 wherein the outer shell includes a plurality of layers. 8. The system of claim 6 wherein the outer shell comprises a porous material. 9. The system of claim 8 wherein the porous material includes aerogel. 10. The system of claim 1 wherein the capsule is characterized by a diameter of between 50 μm and 100 μm. 11. The system of claim 1 wherein the target further includes an electron transport region disposed along the electron path between the electron generation region and the capsule. 12. The system of claim 11 wherein the electron transport region comprises at least one of a high Z material or a low Z material, wherein the high Z material comprises one of gold, tungsten, lead or silver and the low Z material comprises one of silicon, beryllium, boron, or carbon. 13. A target comprising:a laser incidence area for receiving a laser beam;an electron generation region adapted to absorb a portion of laser energy associated with the laser beam and generate a plurality of electrons along an electron path;a compression region disposed along the electron path, the compression region configured to interact with the plurality of electrons and heat up to a first temperature of between 100 electron volts and 1000 electron volts; anda capsule embedded within the compression region and including deuterium tritium (DT) gas, wherein the capsule is configured to absorb radiated heat from the compression region and heat up to the first temperature. 14. The target of claim 13 further comprising a shock absorption region disposed between the electron generation region and the compression region, the shock absorption region configured to absorb a shock wave generated by the laser beam. 15. The target of claim 13 wherein the compression region includes a high Z material comprising one of gold, lead, tungsten, or silver. 16. The target of claim 13 wherein the electron generation region includes a first material and the compression region includes a second material different from the first material. 17. The target of claim 13 wherein the capsule includes an outer shell comprising a low Z material and wherein the low Z material includes at least one of silicon dioxide, aluminum oxide, or carbon. 18. The target of claim 17 wherein the outer shell includes a plurality of layers. 19. The target of claim 17 wherein the outer shell comprises a porous material and wherein the porous material includes aerogel. 20. The target of claim 13 further comprising an electron transport region disposed along the electron path between the electron generation region and the capsule, the electron transport region comprising at least one of a high Z material or a low Z material, wherein the high Z material comprises one of gold, tungsten, lead or silver and the low Z material comprises one of silicon, beryllium, boron, or carbon.
	abstract	The present invention makes it possible to obtain a multilayer film reflective mirror 61 comprising a first multilayer film 67 which is formed by alternately laminating Mo layers 671 and Si layers 673 on a substrate 63, and a second multilayer film 65 which is formed on top of the first multilayer film 67, and which is formed by alternately laminating Mo layers 651 and Si layers 653, wherein the thickness of the Mo layers in the first multilayer film is substantially equal to or smaller than the thickness of the Mo layers in the second multilayer film, and the ratio of the thickness of the Mo layers to the thickness of the Si layers in the first multilayer film is different from the ratio of these thicknesses in the second multilayer film. As a result, a multilayer film reflective mirror with a low internal stress in which a drop in the reflectivity is suppressed can be obtained.
043409709	claims	1. A nuclear power wheel comprising a stationary side gear having a central substantially horizontal axis and mounted on a frame means, a shaft having first and second ends, said shaft being mounted on said axis, means for rotating said shaft solely in one direction, a satellite gear fixed to said first end of said shaft, a wheel fixedly mounted between the first and second ends of said shaft, said wheel having an outer perimeter, a plurality of expansion valves mounted on said outer perimeter on radial axes, each of said expansion valves including a drive gear for delivering useful work output mounted on the second end of said shaft, 2. The nuclear power wheel of claim 1 wherein the nuclear heat element includes two fixed distinct masses of uranium-235, and a freely moveable cadmium means which is moveable solely by means of gravity which separates said two masses when inserted therebetween at the uppermost vertical point of the wheel and which is completely withdrawn at the lowermost vertical point of the wheel. 3. The nuclear power wheel of claim 1 wherein the frame means is secured to the sea floor and the drive gear is joined to a plural section drill means. 4. The nuclear power wheel of claim 3 including a hose extending from the sea floor to a sea surface means, said sea surface means having an air compressor means which injects air in at least one point in said hose in an upwardly flowing direction to assist in the movement of the contents of said hose.
	description	The present application is a divisional of U.S. patent application Ser. No. 11/296,438, filed on Dec. 8, 2005, which claims priority to Japanese patent application JP 2004-357319, filed on Dec. 9, 2004. 1. Field of the Invention The present invention relates to a technology for suppressing corrosion of metal components, such as nuclear power plant's structural components, in contact with high-temperature water, and more particularly, relates to a nuclear power plant having a corrosion-resistant coating, a method of making such a corrosion-resistant coating and a method of operating the nuclear power plant. 2. Related Art Metal components exposed to high temperature environment are found in almost all of the modern industrial and commercial plants. For example, in the course of steam reforming in a hydrogen production chemical plant, the reaction is carried out at high temperatures and pressures. Inside a boiler or a metal pipe connected to the boiler, hot water and steam move or travel while causing corrosion. The conventional preventive measures against corrosion of metal components have involved use of expensive, special corrosion-resistant materials, improvements on the environment to which the metal components are exposed, etc. For example, in a thermal power plant, a pH control reagent, a deoxidizer, or the like is added to control water chemistry and to thereby reduce the corrosion. In a boiling-water nuclear power plant, oxygen, hydrogen peroxide, and the like produced by radiolysis of water in the radiation field exist in a state dissolved in the reactor water. It is a well-known fact that stainless steel and nickel-based alloys, which are used for reactor structural components of the nuclear power plant, generate stress corrosion cracking in the presence of oxygen and hydrogen peroxide in a high-temperature environment such as a nuclear reactor. Hydrogen injection of injecting hydrogen into the reactor water has applied to some BWR plants in the world to reduce oxygen and hydrogen peroxide dissolved in the reactor water (refer to GENSHIRO MIZU-KAGAKU HANDBOOK [Handbook of Water Chemistry of Nuclear Reactor System], edited by Atomic Energy Society of Japan, published by Corona Publishing Co., Ltd., on Dec. 27, 2000, p. 210). The effect of the oxygen and hydrogen peroxide reduction by the hydrogen injection is confirmed as the decrease in corrosion potential of the metal components. The generation of stress corrosion cracking and the crack growth rate depends on the corrosion potential. The lower the corrosion potential, more suppressed the generation of stress corrosion cracking and development of cracks. As a result, the lifetime of the metal components can be extended. Other nuclear power plants in and outside Japan employ noble metal injection technology of conducting hydrogen injection after deposition of a noble metal, such as platinum (Pt) or rhodium (Rh), on surfaces of reactor structural components to accelerate reaction with hydrogen, increase the anode current to thereby decrease the corrosion potential (see the specification of Japanese Patent No. 2624906). The meaning of the corrosion potential of the metal components is as follows. When a metal is immersed in an electrolyte, the metal shows a potential inherent to that metal. This potential is called “spontaneous potential” of that metal. A corroded metal material shows a potential different (polarized) from its spontaneous potential due to the corrosion reaction. This difference in potential is referred to as the “corrosion potential”. A continuous measurement of the potential difference will estimate the progression of the corrosion. In a uniformly corroded metal material, the cathode reaction (reduction reaction) and the anode reaction (oxidization reaction) reach an equilibrium at the intersection of the cathode reaction polarization curve and the anode reaction polarization curve. This intersection corresponds to the corrosion potential. Another approach that has recently drawn much attention for decreasing the corrosion potential is to utilize the photocatalytic reaction. By coating surfaces of the metal components with a photocatalyst and irradiating the photocatalyst with light having wavelength near ultraviolet, electrons activated by the photoexcitation reaction cause the corrosion potential to decrease. The photoexcitation reaction can be accelerated with a noble metal disposed nearby. Accordingly, by depositing a photocatalyst or a high-efficiency photocatalyst containing a noble metal onto surfaces of the reactor structural components and inducing photoexcitation reaction by Cerenkov radiation generated in the reactor core, the corrosion potential during operation can be reduced (for example, refer to Japanese Patent Laid-open Publication Nos. 2001-4789 and 2001-276628). As the method of preventing parts of the metal components from corrosion in the absence of light, a technology for decreasing the potential difference by generating thermostimulated current utilizing thermal energy instead of light energy has been suggested (refer to Japanese Patent Laid-open Publication No. 2003-232886). Another corrosion reduction method proposed is to alternately laminate N-type semiconductor coatings and P-type semiconductor coatings onto surfaces of metal components (refer to Japanese Patent Laid-open Publication No. 9-125283). Yet another corrosion method proposed is to provide a coating consisting of three or more alternately stacked layers of an anion-permselective substance and a cation-permselective substance (refer to Japanese Patent Laid-open Publication No. 11-12719). According to the technology disclosed in Japanese Unexamined Patent Application Publication No. 2001-4789, electrons irradiated with light are activated by the photoexcitation reaction, thereby generating electrical current that decreases the corrosion potential. The corrosion prevention effect is, however, rarely expected in parts not exposed to light. In contrast to the corrosion prevention technology utilizing photoexcitation, a technology of decreasing the corrosion potential by utilizing electrical current produced by thermostimulated electrons is disclosed in Japanese Patent Laid-open Publication No. 2003-232886. According to this technology of producing the thermostimulated current, holes generated by thermostimulation cause anode reaction to occur and thereby increase the current. In an actual cases, however, the electrons stimulated by heat recombine with holes generated by the same thermostimulation, and the electric current does not easily flow. In order to efficiently convert the stimulated electrons and holes into a flow of electrical current, charge separation needs to be reliably carried out. Furthermore, the state that allows charge separation needs to be constantly maintained, and the ambient environmental conditions to which the metal components are exposed must be taken into consideration. In addition, nuclear power plants have inside a substantially large number of narrowed parts and parts with complicated shapes. Thus, the corrosion prevention methods utilizing the semiconductor properties disclosed in Japanese Patent Laid-open Publication Nos. 9-125283 and 11-12719 would face difficulty in application. The present invention was conceived in consideration of the circumstances in the prior art mentioned above and has an object to provide a nuclear power plant having a corrosion-resistant coating that can ensure suppression of corrosion due to stress corrosion cracking in various locations of reactor structural components not exposed to light and that can effectively maintain the effect of corrosion suppression for a long time. Another object of the present invention is to provide a method of forming such a corrosion-resistant coating and a method of operating the nuclear power plant at an improved efficiency. These and other objects can be achieved according to the present invention by providing, in one aspect, a nuclear power plant, wherein a corrosion-resistant oxide film is formed on a surface of a metal component of a reactor structure exposed to high-temperature water, the corrosion-resistant oxide film containing an oxide having a property of a P-type semiconductor, and a catalytic substance having an N-type semiconductor is deposited on the corrosion resistant oxide film so that the oxide film maintains the property of the P-type semiconductor. In another aspect, there is also provided a method of forming a corrosion-resistant coating on a surface of a metal component of a reactor structure exposed to high-temperature water, the method comprising: an oxide film forming step of controlling a water chemistry inside a reactor using a hydrogen injection device to deposit and/or form an oxide having a property of a P-type semiconductor in a reducing atmosphere or converting an existing oxide film; and a catalytic substance deposition step of depositing a catalytic substance on the oxide film, the catalytic substance having a property of an N-type semiconductor while retaining the property of the P-type semiconductor. In a further aspect of the present invention, there is also provided a method of operating a nuclear reactor in which a corrosion-resistant coating is formed on a surface of a metal component of a reactor structure exposed to high-temperature water, the method comprising the steps of: monitoring a corrosion potential at the surface of the metal component to examine a property of the oxide film; and controlling a water chemistry in the reactor to maintain and restore a corrosion-resistant oxide film. According to the above aspects of the present invention, the corrosion-resistant oxide film can be formed so as to achieve the functions and effects of the property or performance of the N-type semiconductor while maintaining or retaining the property of the P-type semiconductor. The suppression of corrosion due to stress corrosion cracking of metal components of a reactor structure can be ensured, and the effect of suppressing corrosion of metal components can be maintained for a long period of time. The nature and further characteristic features of the present invention will be made more clear from the following descriptions made with reference to the accompanying drawings. The preferred embodiments of the nuclear power plant, method of forming a corrosion-resistant coating for the nuclear power plant, and method of operating the nuclear power plant according to the present invention will be described hereunder with reference to the attached drawings. Further, it is to be noted that terms “upper”, “lower”, “right’, “left” and the likes terms are used herein with reference to the illustrations on the drawings or actually installing state of a reactor power plant. FIG. 1 is a schematic diagram showing a boiling water reactor (BWR, hereinafter) 11 and a Reactor Water Clean-up system 12 of a nuclear power plant 10 according to the present invention. The BWR 11 includes a reactor pressure vessel 13 and a cylindrical shroud 14 inside the reactor pressure vessel 13. A reactor core 15 is disposed inside the cylindrical shroud 14. A lower plenum 16 is disposed below the reactor core 15, and the reactor water inside the reactor pressure vessel 13 is introduced into the lower plenum 16 through a plurality of jet pumps 17, for example, ten jet pumps 17. The jet pumps 17 operate by tracking the operation of recirculation pumps 19 of a pair of reactor recirculation systems 18. Each recirculation pump 19 is provided to a recirculation pipe 20 for recirculating the reactor water inside the reactor pressure vessel 13. The ejection (pump-out) side of the recirculation pipe 20 is opposed to the inlet side of the jet pump 17. In each reactor recirculation system 18, the recirculation pump 19 is driven to discharge recirculation water from the ejection side of the recirculation pipe 20, and the flow of the discharged recirculation water merges with the reactor water around the jet pump 17 to thereby guide the reactor water into the lower plenum 16. The flow of the reactor water is reversed in the lower plenum 16 and heated by means of nuclear reaction as it passes over the reactor core 15, thereby forming a steam-liquid two-phase flow. The steam-liquid two-phase flow is separated by a steam separator, not shown, into a steam component and a liquid component above the reactor core 15. The liquid component returns to reactor water and re-enters a downcomer portion 21 of the reactor pressure vessel 13. The steam component is dried in a steam drier (not shown), and the resulting dry steam (main steam) is fed to a main steam system 25. The main steam fed into the main steam system 25 is then introduced into a steam turbine 27 through a main steam pipe 26 to drive a generator 28. The expanded steam that had been used to drive the steam turbine 27 is led to a condenser 29 where the steam is cooled and condensed to give a steam condensate. The condensate passes through a condensate water supply system 30 and flows back into the reactor pressure vessel 13 via a water supply pipe 31 serving as a water supply line so as to combine with the reactor water inside the reactor pressure vessel 13. A water supply pump 32 and a multistage water supply heater (not shown) are provided to the water supply pipe 31. The water fed into the reactor pressure vessel 13 via the condensate water supply system 30 partially circulates in the recirculation pipes 20 of the reactor recirculation systems 18 by the operation of the recirculation pumps 19. Part of the recirculation water in the recirculation pipe 20 is circulated in a residual heat removal (RHR) system 35 with an RHR-system pump 36 or in a reactor water cleanup (CUW or RWCU) system 40 with a CUW-system pump 41. The RHR-system pump 36 has an RHR pipe 37 diverging from the recirculation pipe 20 of the reactor recirculation system 18. The RHR pipe 37 has the RHR-system pump 36 and a heat exchanger 38. The downstream end of the RHR pipe 37 is connected to the reactor pressure vessel 13 so that part of the recirculation water can be circulated and returned to the reactor pressure vessel 13. The pipe configuration of the RHR system 35 is designed to suit the most typical operation mode for removing decay heat after the reactor shutdown. The circulation water cooled in the RHR system 35 is sprayed from the upper portion or the top of the reactor pressure vessel 13 to cool the head unit of the reactor pressure vessel 13. The pipe arrangement of the RHR system 35 is designed to operate in five modes, namely, a reactor shutdown cooling mode, a low-pressure water injection mode, a reactor container cooling mode, a pressure suppression pool water cooling mode, and a fuel pool cooling mode. The reactor water cleanup (CUW) system 40 has a CUW-system pipe 42 diverging from the recirculation pipe 20 of the reactor recirculation system 18. The CUW-system pipe 42 has a heat exchanger 43, the CUW-system pump 41 and a filter demineralizer 44, and is connected to the water supply pipe 31 of the condensate water supply system 30. The CUW system 40, the RHR system 35, a reactor auxiliary cooling system (not shown), a high-pressure reactor core spray system (not shown), and a fuel pool cooling and cleanup system (not shown) constitute the cooling water circulation system 12. The reactor pressure vessel (RPV) 13, the reactor recirculation systems 18, the main steam system 25, and the condensate water supply system 30 constitute a reactor primary cooling system 45. The nuclear power plant 10 has the reactor primary cooling system 45 and the cooling water circulation system 12, in each of which an austenitic stainless steel, such as SUS304 (18Cr-8Ni-0.06C), SUS304L containing 0.03% or less of C, SUS316 (18Cr-12Ni-2.5Mo) having improved corrosion and acid resistance, or SUS316L containing Mo, having excellent corrosion resistance, workability, formability and weldability, is widely used. The nuclear power plant 10 also has injection points P for connecting with a hydrogen injection system 46. The hydrogen injection system 46 is provided to form corrosion-resistant oxide films having properties of a P-type semiconductor onto surfaces of reactor structural metal components, such as pipes, various devices, and structural materials inside the reactor. The hydrogen injection system 46 can be connected to one or more injection points P located in the water supply pipe 31 of the condensate water supply system 30, the recirculation pipe 20 of the reactor recirculation system 18, the RHR pipe 37, of the RHR system 35, the CUW-system pipe 42 of the CUW system 40, and the like. The amount of injection hydrogen can be controlled from these injection points P. The water chemistry in the reactor can be controlled by adjusting the amount of the injection hydrogen. By controlling the water chemistry inside the reactor as mentioned above, oxide films having the properties of a P-type semiconductor can be formed on the surfaces (inner and outer surfaces) of the reactor structural metal components, such as various pipes, devices, and internal structural materials. These oxide films are corrosion resistant. Referring to FIG. 1, the reactor is also provided with a corrosion potential analyzer 47 including a test piece for monitoring the corrosion potential and shut-off valves 48. The corrosion potential analyzer 47 is installed onto the recirculation pipe 20 of the reactor recirculation system 18. Hereunder, preferred embodiments of the present invention will be described more specifically. A first embodiment of the present invention will be described with reference to FIGS. 2 to 4. In the first embodiment, the austenitic stainless steel widely used in the reactor structural materials of the reactor primary cooling system 45 and the cooling water circulation system 12 of the nuclear power plant 10 is provided with corrosion-resistant oxide films. FIG. 2 is a schematic diagram showing a surface of a metal component having a corrosion-resistant coating on the surface of SUS316L stainless steel, which is one example of the austenitic stainless steel. In this embodiment, a corrosion-resistant, corrosion-protective oxide film (film) 51 composed of an oxide, such as Fe3O4, having the properties of a P-type semiconductor is formed on a metal base material 50 composed of SUS316L stainless steel, and titanium oxide serving as a catalytic substance 52 having the properties of a N-type semiconductor is deposited on the oxide film 51. The catalytic substance 52 may be deposited on the oxide film 51 by forming a layer. The form of the catalytic substance 52 is not limited to the layer form. The catalytic substance 52 may be scattered into a matrix form or may be deposited as lines. The metal base material 50 is exposed to high-temperature water of 150° C. or higher, in particular, to reactor water of about 280° C. Although FIG. 2 shows an example that uses the SUS316L stainless steel as the austenitic stainless steel for the metal base material 50, the metal base material 50 may be made of a stainless steel alloy, iron steel, a non-steel material, or a non-ferrous metal. Although the oxide film for the metal base material 50 described above is composed of Fe3O4, the oxide film may instead be formed of an oxide such as FeO, NiO, PdO, UO2, WO2, Cr2O3, NiCr2O4, ZnCr2O4, CoCr2O4, FeCr2O4, MnO, Mn2O3, Mn3O4, Co3O4, CoO, Cu2O, Ag2O, CoAl2O4, MgCr2O4, NiAl2O4, or PbO, or at least one of them. The oxide film 51 having the properties of a P-type semiconductor should be formed on the surface of the metal base material 50 exposed to high-temperature water. In an actual nuclear power plant, the thickness of the oxide film 51 is preferably 0.01 μm to 5 μm, for example. Titanium oxide (TiO2) having the properties of a N-type semiconductor and serving as the catalytic substance 52 is deposited on the oxide film 51 having the properties of a P-type semiconductor. Instead of the titanium oxide (TiO2), BaTiO3, Bi2O3, ZnO, WO3, SrTiO3, Fe2O3, FeTiO3, KTaO3, MnTiO3, SnO2, ZrO2, CeO2, In2O3, Al2O3, MgO, MgFe2O4, NiFe2O4, MnO2, MoO3, Nb2O5, SnO2, SiO2, PbO2, V2O5, ZnFe2O4, ZnAl2O4, ZnCo2O4, or Ta2O5, or at least one of them may be used as the catalytic substance 52 that serves as the N-type semiconductor. A pn-junction is formed at the junction face between the P-type semiconductor and the N-type semiconductor, as shown in FIG. 3, by depositing the oxide film 51 composed on an oxide having the properties of a P-type semiconductor on the surface of the metal base material 50 and by depositing the catalytic substance 52 having the properties of an N-type semiconductor on the oxide film 51. The change in energy level causes a band 55 to contain a bandgap G. Since the band 55 contains a gap, an electron 56 and a hole 57 produced by thermal excitation E respectively migrate to a conduction band 58 of the N-type semiconductor and a valence band 59 of the P-type semiconductor. The migration of the electron 56 and the hole 57 can suppress recombination of the electron 56 and the hole 57 and allows charge separation to proceed. The electron 56 and the hole 57 contribute to the oxidation-reduction reaction in high-temperature water and thereby change the corrosion potential. FIG. 4 is a graph showing dependence of the corrosion potential on the water chemistry of high-temperature water of, for example, 280° C. In the graph, the corrosion potential of a case in which the oxide film 51 composed of Fe3O4, which is a P-type semiconductor, is disposed onto the surface of the austenitic stainless steel, 316L (metal base material 50) and 10 μg/cm2 or more, in particular, about 50 μg/cm2, of the catalytic substance 52, which is titanium oxide (TiO2) and is an N-type semiconductor, is deposited on the oxide film 51 is plotted (solid line A), and the corrosion potential of a case in which no titanium oxide is deposited is plotted (dotted line B). In the case of the BWR 11, due to the presence of titanium oxide, the corrosion potential does not exceed −0.1 V(SHE) and is about −0.5 V when the circulation water in the recirculation pipe 20 of the reactor recirculation system 18 has a feedwater hydrogen concentration of 0.3 ppm. As is described above, the formation of the pn-junction in the oxide film 51 causes charge separation, decreases the corrosion potential and suppresses corrosion of the metal base material 50. The lower the corrosion potential, the greater the corrosion resistance achieved by the oxide film 51. A second embodiment of the present invention will be described hereunder with reference to FIGS. 5 and 6. In this second embodiment, the structures identical to those of the first embodiment are referred to by adding the same reference numerals and explanation thereof is omitted herein, and the effects identical to those of the first embodiment are also attained, which are not described to avoid redundancy. FIG. 5 is a graph showing the influence of the particle diameter of the oxide having the properties of the P-type semiconductor deposited on the surface of the metal base material 50 on the corrosion potential V. The graph shows results of a case in which an Fe3O4 oxide film 51 is formed on the metal component made of austenitic stainless steel, SUS316L, and a case in which an NiO oxide film 51 is formed on the metal base material 50 made of stainless steel alloy, i.e., an Ni-based corrosion-resistant alloy, Alloy 600 (Inconel 600). A solid line C shows the corrosion potential curve of the case in which the Fe3O4 oxide film 51 is formed on the austenitic stainless steel, SUS316L, and a dotted line D shows the corrosion potential curve of the case in which the NiO oxide film 51 is formed on the surface of the Ni—Cr—Fe alloy, i.e., Alloy 600. The catalytic substance 52 deposited on the oxide film 51 is titanium oxide, and the amount of the titanium oxide is 50 μg/cm2 in both the cases. The corrosion potential V is measured under water chemistry conditions of the recirculation water of the reactor recirculation system 18 having a feedwater hydrogen concentration of 0.3 ppm. As is apparent from the results of the test in FIG. 5, the corrosion potential V shows a tendency to decrease as the particle diameter of the oxide having the properties of the P-type semiconductor decreases. As the particle diameter of the oxide (Fe3O4 or NiO) decreases, the area of the pn-junction formed between the oxide and titanium oxide, which is the N-type semiconductor, increases. Presumably, this is advantageous for the charge separation and thus decreases the corrosion potential. The results show that, since the corrosion potential needs to be −0.05 V(SHE) or less for SUS316L and 0.0 V(SHE) or less for Alloy 600, the particle diameter of the oxide needs to be 1 μm or less. FIG. 6 is a graph showing the influence of the thickness of the oxide film 51 having the properties of the P-type semiconductor on the corrosion potential V(SHE). The graph shows the results of a case in which an Fe3O4 oxide film 51 is formed on the metal component made of austenitic stainless steel, SUS316L, and a case in which a NiO oxide film 51 is formed on the metal base material 50 made of stainless steel alloy, i.e., a Ni-based corrosion-resistant alloy, Alloy 600 (Inconel 600). A solid line C1 is a corrosion potential curve of the case in which the Fe3O4 oxide film 51 is formed on the austenitic stainless steel, SUS316L, and a dotted line D1 shows the corrosion potential curve of the case in which the NiO oxide film 51 is formed on the surface of the Ni-based stainless steel alloy of Alloy 600. The corrosion potential curve C1 for SUS316L shows that the corrosion potential does not exceed −0.05 V(SHE) with the oxide film 51 having a thickness of 0.001 to 1 μm. The corrosion potential curve D1 for the Ni-based stainless steel alloy of Alloy 600 shows that the corrosion potential is maintained at 0.0 V or less with an oxide film 51 having a thickness of 0.001 μm to 1 μm. The curves C1 and D1 indicate that the corrosion potential is maintained at a negative value with the oxide film 51 having the properties of a P-type semiconductor and a thickness of 0.001 to 1 μm and that the interaction between the oxide, e.g., titanium oxide, and the P-type semiconductor decreases the corrosion potential. In an actual nuclear power plant 10, deposition of an oxide film in a thickness of 0.01 to 0.05 μm is confirmed. Thus, the corrosion resistance of the oxide film can be expected even in an actual plant. The particles of the Fe3O4 oxide film 51 are small and maintained to about 0.01 μm to about 0.1 μm diameter. The thickness of the oxide film 51 is not likely to decrease to less than 0.01 μm even when the thin film of the oxide particles is formed as a single layer. Thus, the oxide film 51 will have a thickness of at least 0.01 μm. In an actual plant, the substantial application range of the thickness of the oxide film 51 is from about 0.01 μm to about 5 μm. The longevity of the nuclear power plant 10 is determined by the lifetimes of the metal components (metal materials) used in reactor structural components such as various devices and pipes of the reactor primary cooling system 45 and the cooling water circulation system 12. The corrosion potential is set according to the longevity of the nuclear power plant 10 by adjusting the oxide film 51 deposited onto the surface of the metal base material 50. When a nuclear power plant 10 has a typical longevity, the corrosion potential of the metal components such as various devices and pipes of the reactor primary cooling system 45 and the cooling water circulation system 12 is maintained within regions F and H respectively shown in FIGS. 7A and 7B. When a longer lifetime of the nuclear power plant 10 is needed, the corrosion potential of the metal components of the reactor structural materials is set within regions F1 and H1 respectively shown in FIGS. 8A and 8B. FIG. 7A and FIG. 8A respectively show curves L and L1 each indicating the relationship between the thickness of the oxide film 51 having the properties of the P-type semiconductor and the amount of the deposited catalytic substance 52, i.e., titanium oxide (TiO2) when austenitic stainless steel, SUS316L, is used as the metal base material 50. The solid line L in FIG. 7A is a corrosion potential curve that yields a corrosion potential of −0.05 V(SHE), and the solid line L1 in FIG. 8A is a corrosion potential curve that yields a corrosion potential of −0.01 V(SHE). When the metal base material 50 is composed of stainless steel such as SUS316L, the use in a region G for a normal lifetime and a region G1 for extended lifetime is avoided. FIG. 7B and FIG. 8B respectively show curves M and M1 each indicating the relationship between the thickness of the oxide film 51 composed of an oxide having the properties of a P-type semiconductor and the amount of the deposited catalytic substance 52, i.e., titanium oxide (TiO2) when a Ni-based stainless steel alloy, Alloy 600, is used in the metal base material 50. Substantially the same results are yielded by using nickel oxide (NiO) instead of titanium oxide (TiO2). Alloy 600 is a Ni-based corrosion-resistant alloy having 0.05C-16Cr-8Fe as the main component. The solid line M in FIG. 7B is a corrosion potential curve that yields a corrosion potential of 0.0 V(SHE), and the solid line M1 in FIG. 8B is a corrosion potential curve that yields a corrosion potential of −0.05 V(SHE). When the metal base material 50 is composed of a Ni-based stainless steel alloy, Alloy 600 (Inconel 600), the use in a region I for a normal lifetime and in a region I1 for an extended lifetime is avoided. FIG. 9 is a graph related to a third embodiment of the present invention. In the description of the third embodiment, the structures identical to those of the first embodiment are referred to by the same reference numerals to omit repeated explanation, and the effects identical to those of the first embodiment are also attained, but omitted in description to avoid redundancy. The graph in FIG. 9 shows the corrosion potential characteristics observed from a test piece in which the metal base material 50 composed of SUS316L is coated with an Fe3O4 oxide film 51 having the properties of a P-type semiconductor and a thickness of 0.05 μm, and from a test piece in which the metal base material 50 composed of a Ni-based stainless steel alloy, i.e., Alloy 600, is coated with a NiO oxide film 51 having a thickness of 0.05 μm, while varying the amount of titanium oxide serving as the catalytic substance 52 deposited on the oxide film 51. The graph shows that as the amount of titanium oxide deposited on the oxide film 51 increases, the corrosion potential of the metal base material 50 decreases. A solid line N is a characteristic curve showing the relationship between the corrosion potential of the metal base material 50 composed of SUS316L and the amount of titanium oxide deposited. A dotted line O is a characteristic curve showing the relationship between the corrosion potential of the metal base material 50 composed of Alloy 600 and the amount of titanium oxide deposited. The curves N and O show that when 10 μg/cm2 of titanium oxide serving as the catalytic substance 52 is deposited, the corrosion potential of the metal base material 50 composed of SUS316L is lower or less than −0.05 V(SHE) and that of the metal base material 50 composed of Alloy 600 is lower or less than 0.0 V(SHE) due to the interaction with the P-type semiconductor. This result shows that stress corrosion cracking can be sufficiently suppressed by depositing the titanium oxide of the amount of 10 μg/cm2 or more serving as the catalytic substance 52. A fourth embodiment of the present invention will now be described with reference to FIGS. 1, 2, and 10 to 17. The fourth embodiments represents a method of forming a corrosion-resistant coating, including a step of oxide film formation of forming an oxide film 51 having the properties of a P-type semiconductor on the surface of the nuclear power plant 10 shown in FIG. 1 and the metal base material 50, which is a structural component of the nuclear power plant 10, and a step of catalytic substance deposition of depositing the catalytic substance 52 on the oxide film 51. There are provided methods possible to form a corrosion-resistant coating having the properties of a P-type semiconductor on the surface of the metal base material 50, the method including a method of preliminarily forming the coating before the metal base material 50 is processed and shipped as the reactor structural materials, a method of forming the coating during a trial run or operation after the structural materials are installed in the nuclear power plant 10, and a method of forming the coating during the operation of the nuclear power plant 10 by controlling the water chemistry. A method of forming the oxide film on the surface of the metal base material 50 according to any one of the timings may be employed. The oxide film formed on the surface of the metal base material 50 is known to undergo a significant change due to ambient aquatic environment. In this embodiment, a method of forming an oxide film that takes into account the water chemistry controllable in the BWR 11 and a real plant is described from the viewpoint of preventing the corrosion of peripheral structural components such as those inside the BWR 11 and the recirculation pipe 20. [First Method of Forming the Oxide Film] A first method of forming the oxide film includes an oxide film forming step of forming the oxide film 51 having the properties of a P-type semiconductor directly from the metal base material 50. This first method is used when a new metal component is installed in the nuclear power plant 10. The oxide film 51 is deposited by controlling the ambient aquatic conditions. The oxide film forming step for forming the oxide film 51 on the surface of the metal base material 50 in a real plant will be described hereunder. For example, in order to improve the reactor water chemistry of an actual plant in which hydrogen injection operation is already carried out, dissolved hydrogen and dissolved oxygen are controlled at an injection amount of 0.4 ppm, and the surfaces of an austenitic stainless steel, SUS316L are oxidized with high-temperature water of 280° C. The dissolved oxygen concentration is about 10 ppb, and the dissolved hydrogen concentration is 30 ppb or more, i.e., about 80 ppb. The hydrogen injection is carried out by connecting the hydrogen injection system 46 to the injection points P of the reactor primary cooling system 45 and the cooling water circulation system 12 of the nuclear power plant 10. In general, there are a large number of methods for forming an oxide film having the properties of a P-type semiconductor conducted in water having reducing properties, in which the reactor water is maintained at a reducing state by hydrogen injection. As far as the water chemistry of an actual plant is concerned, the hydrogen concentration in the feedwater is preferably 1.0 ppm or less, in particular, about 0.3 ppm during the operation of the nuclear power plant 10 since high-concentration hydrogen injection disadvantageously increases the turbine-system dose rate during the operation. In a reducing atmosphere, the corrosion potential of the metal surface is maintained at a low level. As shown in FIG. 10, the pH morphology of the ferrous oxide greatly changes with the change in corrosion potential brought about by controlling the water chemistry. By controlling the chemistry of the reactor water as mentioned above, an oxide film having the properties of a P-type semiconductor can be formed. With respect to the temperature for forming the oxide film, it is possible to choose one from a method forming an oxide film at room temperature which takes a longer time and a method of forming an oxide film at a temperature of reactor water, e.g., about 280° C., which takes into account the actual operation of the reactor. It is possible to choose the timing by taking into account the status of the actual plant, e.g., whether the plant is under inspection or in operation. FIG. 11 is a graph showing the corrosion potential observed under the water chemistry of the recirculation water in the reactor recirculation system 18 in which the hydrogen concentration in the feedwater is 1.0 ppm or less, in particular, about 0.3 ppm. In the observation, a test piece in which an oxide having properties of a P-type semiconductor was formed on the metal surface of SUS316L according to the first method of forming the oxide film was used. Before the corrosion potential testing, the test piece was exposed to high-temperature of 280° C. under the water chemistry of the reactor water at the reactor bottom (lower plenum), i.e., a feedwater hydrogen concentration of 0.4 ppm, for 500 hours. The surface of the resulting test piece was subjected to Raman analysis. The crystal morphology was confirmed to be Fe3O4. Titanium oxide of an amount of 200 μg/cm2 was deposited on the Fe3O4 oxide film 51 by using a sprayer 60 such as shown in FIG. 12. The sprayer 60 has a spray main unit 61 equipped with a solution tank 62 for storing titanium oxide, i.e., the catalytic substance. Deposition of an adequate amount of titanium oxide on the test piece can be carried out by rotating an adjustor knob 64 to adjust the nozzle opening of a spray nozzle 63 attached to the front end of the spray main unit 61, connecting the spray main unit 61 to a gas supply (gas cylinder) 67 containing nitrogen gas or inert gas via a gas feed pipe 66 equipped with a flow adjustor valve 65, and then pulling a spray switch 68 which functions as a control lever. Titanium oxide, which is the catalytic substance, is sucked out by the flow of the inert or nitrogen gas and is sprayed toward the test piece from the nozzle opening of the spray nozzle 63. Using this sprayer 60, titanium oxide serving as the catalytic substance was deposited onto the SUS316L test piece having the Fe3O4 oxide film 51. The test piece provided with a required amount of titanium oxide was subjected to corrosion potential testing in water having recirculation water chemistry in the reactor recirculation system 18, as shown in FIG. 11. FIG. 11 shows that, in corrosion potential analysis of the test piece, a temperature elevation process (heating process) of recirculation water was conducted up to 200 minutes after initiation of the analysis and that the corrosion potential was measured at a constant recirculation water temperature after the temperature elevation process. The recirculation water had a dissolved oxygen concentration of about 10 ppb, a dissolved hydrogen concentration of 30 ppb or more, in particular 31 ppb, and a hydrogen peroxide concentration of 65 ppb. The operation conditions, such as 280° C. high-temperature water and a pressure of 8.5 MPa, applicable to an actual plant were satisfied. As is apparent from the observed results of the corrosion potential, the corrosion potential of the test piece having titanium oxide deposited on the Fe3O4 oxide film 51 could be decreased to −0.1 V(SHE) or less, i.e., about −0.15 V(SHE), under the water chemistry of the recirculation water having a feedwater hydrogen concentration of 0.3 ppm, thereby improving the corrosion resistance. The test piece having no titanium oxide deposited on the Fe3O4 oxide film exhibited a corrosion potential increasing with time. The corrosion potential in this case is expected to further increase if the test is carried out for a longer time. [Second Method of Forming the Oxide Film] A second method of forming the oxide film includes a step of depositing atoms that constitute a P-type semiconductor onto the surface of the metal base material 50 and allowing an oxide having the properties of the P-type semiconductor to form by controlling the ambient aquatic conditions. Although FIG. 1 shows the cooling water circulation system 12 of the nuclear power plant 10 in which the hydrogen injection system 46 is connected through the injection points P. In this method, a solution injection system 70 (shown in FIG. 13) including atoms which constitute the P-type semiconductor should be connected to the injection points P (Pa and Pb) to replace the hydrogen injection system 46. The solution injection system 70 containing atoms constituting the P-type semiconductor has a structure shown in FIG. 13 and is connected to the injection points P of the cooling water circulation system 12. As shown in FIG. 13, the solution injection system 70 includes a hydrogen tank 71 which is connected to the injection point Pa of the cooling water circulation system 12 via a hydrogen feeding pipe 73 equipped with a flow adjustor valve 72. Hydrogen gas inside the hydrogen tank 71 is injected into the cooling water circulation system 12 from the injection point Pa. A solution 75 containing atoms which constitute the P-type semiconductor is stored in a solution tank 76, and the solution tank 76 is connected to the injection point Pb of the cooling water circulation system 12 via a solution injection pipe 78 having an injection pump 77. In this second method of forming the oxide film, the injection pump 77 shown in FIG. 13 is operated to inject atoms constituting the P-type semiconductor into the cooling water circulation system 12. The atoms circulate inside the cooling water circulation system 12 with cooling water and are deposited onto the surface of the metal base material 50 constituting the reactor structural components. The deposition of the atoms constituting the P-type semiconductor may be conducted during the shutdown or running operation of the reactor. In order to form an oxide having properties of a P-type semiconductor from the deposited atoms, the hydrogen gas controlled with the flow adjustor valve 72 in FIG. 13 is injected to change the chemistry of the reactor water. In this manner, the ambient aquatic environment and potential can be controlled, and the atoms deposited on the metal surface can be grown into an oxide having the properties of the P-type semiconductor. As the deposited atoms form an oxide, an oxide film functioning as a corrosion-resistant coating is formed on the surfaces (including inner surfaces) of the metal base material 50. FIG. 14 is a graph showing the corrosion potential of a test piece observed under the water chemistry of the recirculation water having a feedwater hydrogen concentration of 0.3 ppm. The test piece includes an oxide having the properties of the P-type semiconductor formed on the surface of an austenitic stainless steel, SUS316L by the second method of forming the oxide film. In this corrosion potential test, a Zn solution is injected to form the oxide film 51 on the surface of SUS316L. An oxide of ZnCr2O4 is formed on the surface of SUS316L by injecting the Zn solution. Titanium oxide serving as the catalytic substance is deposited in an amount of 70 μg/cm2 on the oxide film 51 on SUS316L of this test piece by using a plasma spraying equipment (not shown in the drawing) in a catalytic substance deposition step. By depositing a required amount of titanium oxide on the ZnCr2O4 oxide film 51, the corrosion potential can be decreased to −0.1 V(SHE) or less under the water chemistry of the recirculation water having a feedwater hydrogen concentration of 0.3 ppm. [Third Method of Forming an Oxide Film] A third method of forming an oxide film includes a step of changing the properties of the existing oxide film 51 on the metal base material 50 by controlling the ambient aquatic environment and a catalytic substance deposition step of depositing a catalytic substance on the oxide film. In an actual plant, the operation is conducted under various water qualities or chemistries, such as those required for operation of a reactor without hydrogen injection or for ultra-low iron operation, depending the type of the nuclear power plant 10. Thus, the properties of the oxide film 51 formed on the metal base material 50 are also different. By converting the oxide film 51 of the metal base material 50 through the controlling of the chemistry of the reactor water and potential, an oxide having the properties of a P-type semiconductor is produced. Alternatively, the metal base material 50 may be, for example, chemically decontaminated to expose the surface, and then an oxide having the properties of a P-type semiconductor may be deposited thereon by the first or second method of forming the oxide film so that a desired oxide film 51 can be formed on the surface of the metal base material 50. FIG. 15 shows corrosion potential of a test piece observed under the water chemistry of recirculation water having a feedwater hydrogen concentration of 0.3 ppm. The test piece had an oxide having the properties of a P-type semiconductor deposited on the surface of an austenitic stainless steel, SUS304L. In this corrosion potential test, a test piece having an Fe2O3 oxide film was treated in water at 280° C. having a dissolved oxygen concentration of about 10 ppb and a dissolved hydrogen concentration of 30 ppb or more, in particular, about 80 ppb, for 100 hours. Subsequently, the test piece was subjected to surface analysis. The results showed that the oxide film was changed to an oxide film mainly composed of Fe3O4. Subsequently, in the catalytic substance deposition step, a required amount, for example, 120 μg/cm2, of titanium oxide was deposited using a titanium oxide water chemistry deposition device 80 shown in FIG. 16. The water chemistry deposition is a method of injecting a titanium oxide solution of a particular concentration into high-temperature water and controlling the temperature, flow rate, titanium oxide concentration, and duration to deposit titanium oxide on the metal surfaces. This corrosion potential test was conducted at 200° C., a flow rate of 9.6 m/s, and a titanium oxide concentration of 10 ppm for 24 hours. The water chemistry was controlled to that of the core bottom water having a feedwater hydrogen concentration of 0.4 ppm. The water chemistry deposition device 80 is an experimental device having a structure shown in FIG. 16. The water chemistry deposition device 80 has a water chemistry (chemistry) control system 82 for maintaining and controlling the chemistry of water inside a water tank 81 and a catalytic substance deposition controlling system 83 for controlling the amount of the catalytic substance deposited on the test piece. Using a resin 86, such as an ion exchange resin, and a hollow fiber membrane filter 87, the water chemistry control system 82 purifies the water fed from the catalytic substance deposition controlling system 83 to the water tank 81 via a heat exchanger 84 and a cooling tower 85 to thereby produce pure water. The property of the resulting water is analyzed with a dissolved hydrogen meter 88, a dissolved oxygen meter 89, and a conductivity meter 90 to control the properties of the water inside the water tank 81 to the target levels. The water (pure water) having its chemistry controlled through the resin 86 and the hollow fiber membrane filter 87 is temporarily stored in the water tank 81 and fed to the catalytic substance deposition controlling system 83 using a high-pressure pump 91 via the heat exchanger 84. The catalytic substance deposition controlling system 83 is a closed circulation cycle 95. An example of injecting a titanium oxide (TiO2) solution as the catalytic substance into the closed circulation cycle 95 will be described below. The closed circulation cycle 95 includes a test piece deposition section 96 containing the test piece, a circulation pump 97 for controlling the amount and flow rate of water circulated, and a heat exchanger 98. These three devices are provided sequentially in this order. The suction side of the circulation pump 97 can in-take pure water fed from the water chemistry control system 82. The discharge side of the circulation pump 97 can discharge the pumped-out water to the water chemistry control system 82. FIG. 17 is a graph showing the change in amount of deposited titanium oxide over time when titanium oxide serving as the catalytic substance 52 is deposited on the oxide film 51 of the test piece using the water chemistry deposition device 80. The graph shows that the amount of the titanium oxide deposited increases with an increase in flow rate in the closed circulation cycle 95. The time required for depositing a target amount of titanium oxide can be easily estimated by controlling the concentration of the titanium oxide injected and the temperature. By converting the test piece deposition section 96, it becomes possible to deposit the catalytic substance, i.e., titanium oxide, onto surfaces of a reactor structural metal component having a different shape. In a case of installing a new reactor structural component, such as replacement of the recirculation pipe 20, it is possible to deposit an adequate amount of titanium oxide serving as the catalytic substance 52 on an existing oxide film 51 exhibiting the properties of a P-type semiconductor. In an actual plant, the deposition of the catalytic substance 52 can be conducted by connecting a titanium oxide injection device, not shown, to the injection points P shown in FIG. 1. The deposition is possible during the reactor shutdown operation or during the running operation. As is apparent from the graph of FIG. 15, titanium oxide deposited on the oxide film 51 by water chemistry deposition using the water chemistry deposition device 80 can decrease the corrosion potential to −0.1 V(SHE) or less, and sufficient corrosion prevention effects can be efficiently exhibited. A method of driving a reactor according to a fifth embodiment of the present invention will be further described hereunder with reference to FIGS. 18 to 21. In consideration of the fact that measurement of the corrosion potential of the structural component surface of the reactor primary cooling system 45 and the cooling water circulation system 12 is difficult in an actual plant, in this embodiment, as shown in FIG. 1, the corrosion potential analyzer 47 accommodating a corrosion potential monitoring test piece 100 is provided to the nuclear power plant 10 so that the corrosion potential of the structural components in the reactor water can be simulated and that the safety of the structural components can be monitored. The corrosion potential monitoring test piece 100 is exposed to high-temperature water from the BWR 11. As shown in FIG. 18, the corrosion potential analyzer 47 is a unit including a main device 101, the corrosion potential monitoring test piece 100, and a reference electrode 102 that can withstand high pressure. The corrosion potential monitoring test piece 100 and the reference electrode 102 are connected to an electrometer 104 via a cable 103. The corrosion potential of the corrosion potential monitoring test piece 100 measured with the electrometer 104 is input to a computer, i.e., a personal computer 105, either via a data cable 106 or by radio transmission, stored, and processed. By monitoring the processed data, the durability of the structural components and the properties of the oxide film can be monitored. The main device 101 having the corrosion potential monitoring test piece 100 and the reference electrode 102 of the corrosion potential analyzer 47 is detachably attached to the recirculation pipe 20 of the reactor recirculation system 18, as shown in FIG. 1. Alternatively, the main device 101 may be attached to the cooling water circulation system 12 or the reactor primary cooling system 45. FIGS. 19 to 21 are graphs showing the change in corrosion potential of the structural component of the nuclear power plant 10 in time elapsing due to changes in water chemistry. The graph in FIG. 19 shows the corrosion potential of a test piece in which an Fe3O4 oxide film 51 is formed on the surface of SUS316L under the water chemistry corresponding to that of the recirculation water having a feedwater hydrogen concentration of 0.3 ppm and in which 70 μg/cm2 of titanium oxide serving as the catalytic substance 52 is deposited onto the oxide film 51 by spraying. The first 200 minutes from the start of corrosion potential testing was spent for adjusting the water chemistry and measurement conditions under elevating temperature. Under the water chemistry corresponding to that of recirculation water having a feedwater hydrogen concentration of 0.3 ppm, a low corrosion potential was maintained due to the presence of titanium oxide, and the corrosion potential of the test piece was not more than −0.1 V(SHE). On the next day, the water chemistry was controlled to that of the recirculation water having a feedwater hydrogen concentration of 0.1 ppm. The results of the corrosion potential measurement are shown in FIG. 20. Under the water chemistry corresponding to a feedwater hydrogen concentration of 0.1 ppm, the corrosion potential increased to a level 0.0 V(SHE) or higher despite the deposition of titanium oxide. These results show that under an oxidizing atmosphere corresponding to a feedwater hydrogen concentration of 0.1 ppm, the metal surface cannot maintain the properties or performances of the P-type semiconductor, and the pn-junction face cannot be utilized. In other words, the effect of suppressing recombination of an electron and a hole is no longer exhibited, and the thermally excited electron recombines with the hole. Two days after, the water chemistry was changed to that of PLR (Primary Loop Recirculation) with a feedwater hydrogen concentration of 0.7 ppm or more, e.g., 0.7 ppm, to monitor the change in corrosion potential. In FIG. 21, the objective is to restore the P-type semiconductor properties in the oxide film in a reducing atmosphere corresponding to a feedwater hydrogen concentration of 0.7 ppm until up to about 450 minutes. As shown in the graph, the corrosion potential of the test piece with titanium oxide deposited thereon significantly decreased to about −0.55 V(SHE). As shown in FIG. 10, it can be assumed that the oxide film 51 changed from Fe2O3 to Fe3O4 due to the change in corrosion potential. After 500 minutes, the water chemistry was controlled to that corresponding to a feedwater hydrogen concentration of 0.3 ppm, thereby decreasing the reducing atmosphere, and the corrosion potential was measured under a steady state. The results shown in FIG. 21 show that a corrosion potential not exceeding −0.1 V(SHE) is maintained even after 1,000 minutes. This shows that even when the oxide film 51 has experienced the oxidizing atmosphere and changed in properties, the P-type semiconductor properties can be restored in the oxide film 51 by decreasing the corrosion potential to, for example, −0.5 V(SHE) or less in a reducing atmosphere, and that this oxide film 51 can still maintain a low potential in a moderately reducing atmosphere corresponding to a feedwater hydrogen concentration of 0.3 ppm. In an actual plant, it is possible to maintain and restore the corrosion-resistant coating and to thereby suppress corrosion of the metals of the reactor structural components by using the hydrogen injection system 46 (see FIG. 1) to change the reactor water chemistry and by monitoring the corrosion potential to set the corrosion potential of the material to the target level. FIG. 22 is a graph for explaining a sixth embodiment of the present invention. The graph shows the relationship between the corrosion potential of the structural components used in the nuclear power plant 10 and the rate at which cracks are developed. The crack development rate indicated by the longitudinal axis is logarithmically plotted. As the corrosion potential decreases, the crack development rate is largely decreased, showing that the development of the cracks is significantly suppressed. It is a well-known fact that the corrosion potential under normal water chemistry (NWC) of a typical BWR 11 is about +100 mV(SHE). The results of the monitoring of the corrosion potential of the reactor structural component indicate that the crack development rate can be reduced by about one order of magnitude by maintaining the oxide film 51 such that the corrosion potential of the austenitic stainless steel (SUS304SS) is −50 mV(SHE) or less. This also shows that sufficient corrosion suppressing effect is exhibited. The corrosion suppressing potential for the Ni-based stainless steel alloy, such as Alloy 600, is also evaluated based on the same concept. In the graph shown in FIG. 22, “K” represents a stress intensity factor indicating susceptibility of reactor structural components to crack, and “μS/cm” is a value indicating the purity of water, such as reactor water. In a typical reactor 11, a purity of about 1.0 μS/cm is observed during the inspection. FIG. 22 shows that the crack development rate observed with reactor water having a purity as high as 0.1 μS/cm is significantly lower than that with reactor water having a purity of 0.3 μS/cm even when the corrosion potentials of the reactor structural components are the same. Note that although the embodiments above concern application of the reactor recirculation system to boiling water reactors having circulation pumps outside the reactor, application to improved boiling water reactors having reactor recirculation pumps inside the reactor pressure vessels is also possible. The present invention can also be applied to nuclear power plants having pressurized-water reactors and CANDU reactors (Canadian deuterium uranium reactors).
039403122	summary	The invention relates to nuclear fuel comprised of particles of fuel carbide in which vanadium carbide is dissolved. By fuel carbide is meant within the scope of the invention, any carbide which may be used as fuel in a nuclear reactor. Said fuel carbide will thus mostly be uranium carbide or uranium-plutonium carbide. The use of carbide as fuel for nuclear reactors comes up against two main difficulties. There should first be taken into account the problem of joinability of the fuel carbide and of the stainless steel used as case material. When carbon migrates from the carbide to the case material, the mechanical properties of the steel deteriorate, which may cause a breaking of the case. The fuel carbide has moreover the property to swell strongly during the irradiating. Such swelling is caused by gaseous fission products which are insoluble in the carbide and which collect mostly on the boundaries of the grain-like particles, in the shape of gas bubbles. Due to the growing of such gas bubbles there occurs an undesirable volume increase. It is already known to obviate the chemical incompatibility between the fuel carbide and the case material, to add small amounts of metals or metal carbides, for example vanadium carbide. Due to such an addition, the chemical carbon potential is stabilized to a level where carbon migration to the case becomes thermodynamically impossible. To the contrary the problem of swelling of the fuel due to the formation of gaseous fission products during irradiating has not yet been solved. To oppose the fuel swelling, empty space has already been provided both between the case and the carbide and inside the carbide itself, as a porosity. This arrangement is but partly successful and causes further disadvantages. It has also already been proposed to precipitate finely-divided tungsten during the irradiating, because the elementary gas bubbles would be retained on the precipitate, in such a way that they will not coalesce and thus swelling of the aggregate will not take place. This measure also is not completely successful. The invention now provides a successful and economical solution, both to the fuel carbide swelling and to the incompatibility between said fuel and the stainless steel of the case material, without bringing substantial new disadvantages. For this purpose vanadium carbide is present in the particules as supersaturated solid solution and the particles are coated with a thin porous layer of vanadium carbide. It is also very important that the particles be monocrystalline. In an advantageous embodiment, the thin layer of vanadium carbide is comprised of vanadium monocarbide and vanadium hemicarbide. Preferably the density of the thin layer is low. In a particular embodiment of the invention, the thin layer has a density of about 65 percent of the theoretical density. The invention does not only relate to the above-described fuel, but also to a method for preparing a nuclear fuel. According to the invention, the method comprises preparing a supersaturated solid solution of vanadium carbide in fuel carbide, comminuting the material thus obtained down to a maximum size of the resulting grains of about 400 .mu., sieving out the particles with a maximum size lying between 20 and 400 .mu., coating the resulting particles with a thin layer of vanadium carbide having a maximum thickness of 10 .mu., and pressing together the coated particles. The particles pressed in a mold are preferably sintered. In an advantageous embodiment, the particles are coated with a thin layer of vanadium monocarbide and vanadium hemicarbide. In an useful embodiment, the supersaturated solid solution is prepared with approximately 1.5 atoms % vanadium carbide. In a preferred embodiment, to prepare the supersaturated solid solution, the fuel carbide is molten with the vanadium carbide, the resulting product is left to solidify, the product is annealed and it is very rapidly cooled. In a very particular embodiment, the particles are coated with a thin layer of vanadium monocarbide-vanadium hemicarbide with a maximum thickness of 10 .mu. by slightly moistening the particles and then bringing same in a mixer together with powder-like vanadium monocarbide-vanadium hemicarbide.
052001393	summary	FIELD OF THE INVENTION The present invention relates to protecting nuclear reactors, i.e. to controlling such reactors in such a manner as to enable them at all times to deliver the power that is required for satisfying varying needs, while avoiding as much as possible both unnecessary burning of fuel and any risk of an accident. Very strict safety criteria are defined for limiting such risks, in particular with respect to the boilers constituted by such reactors. The present invention relates more particularly to pressurized water nuclear boilers. BACKGROUND OF THE INVENTION In a power station including such a boiler, it is necessary to exercise accurate monitoring on the three-dimensional distribution of power within the core of the reactor. Such monitoring makes it possible both under normal operation and during accidental transients to make sure that safety criteria for the boiler are satisfied. Thus, an authorized operating range for the core is defined by a network of straight line limits plotted in a plane (see FIG. 1) in which the coordinates are nuclear power and axial power difference. The axial power difference parameter, referred to below by the letters DI, is defined as being the difference between the power PH measured at the top of the core and the power PB measured at the bottom of the core. EQU DI=PH-PB This parameter is representative of the axial distribution of power within the core. By keeping the operating point of the core within the domain delimited in this manner, it is possible to ensure, inter alia that safety criteria are satisfied in the event of accidental loss of primary cooling fluid. In addition, in order to avoid excessive variations in the temperature of the primary heat exchange fluid which cools the core, a program is defined for a reference temperature as a function of power level. When there is a difference between the measured temperature and the reference temperature, a regulation system is capable of acting automatically on the core control clusters in such a manner as to correct the difference. When this temperature regulation system is in action, the clusters are said to be in automatic mode. A cooling transient causes clusters to be extracted, and a heating transient causes them to be inserted. A problem arises with respect to this regulation: During certain accidental transients that cause the primary fluid to cool down suddenly, the temperature regulation system will cause the control clusters to be raised quickly if they are in automatic mode. However, such sudden extraction of the absorbent clusters has two consequences which are shown in one particular case by two curve segments C1 (solid line) and C2 (dashed line) in FIG. 1: firstly, core reactivity increases, thereby raising the nuclear power DT as plotted up the Y axis of FIG. 1; and secondly, power distribution rises towards the top of the core, thereby increasing the axial power difference DI which is plotted along the X axis. In FIG. 1, the authorized operating domain is represented by an outer limit FA which is constituted by straight line segments. In the event of a pre-accidental situation of the core represented by a point situated to the right of this operating domain, the nuclear power and axial power difference excursion may give rise to the operating point moving a considerable distance outside the domain. The characteristic evolution of such a cooling transient is shown by segments C1 and C2. A detailed analysis of this type of transient has shown that the core safety limits are approached and even exceeded without intervention of one of the reactor protection systems necessarily being guaranteed. A particular object of the present invention is to limit the risk that may result from an uncontrolled excursion of the reactor operating point outside said operating domain in the event that said excursion is related to a rapid extraction of the temperature regulating group of clusters. The invention is based on creating an inhibit signal for inhibiting instructions to extract the temperature regulation group whenever the reactor operating point leaves the operating domain dangerously. With conventional reactors, leaving the operating domain dangerously is equivalent to leaving it to the right in FIG. 1. SUMMARY OF THE INVENTION In the method of the invention, the reactor temperature regulation system is inhibited whenever a combination of the nuclear power and the axial power difference exceeds a predetermined inhibit threshold.
	description	The present invention relates to a fluoride sintered body and a method for producing the same, and more particularly, to a fluoride sintered body for a neutron moderator having a compact structure suitable for a moderator to restrict the radiation velocity of radioactive rays of every kind such as neutrons and a method for producing the same. Among fluorides, a calcium fluoride (CaF2) single crystal body, a magnesium fluoride (MgF2) single crystal body and the like have been relatively widely used in the optical field. There are very few cases where a fluoride is used in other than the optical field. The CaF2 single crystal body, having the advantage of a high plasma resistance, has been rarely used in a semiconductor manufacturing process. An application thereof to a member which is required to have the highest plasma resistance within a plasma etching furnace of silicon wafers, such as a ring boat or a ceiling board, has been considered. However, the CaF2 single crystal body is extremely expensive, and there has been no report that it was used in the actual manufacturing line. The CaF2 single crystal body, and a lithium fluoride (LiF) or an aluminum fluoride (AlF3) single crystal body have been rarely used as a shield to neutrons, one of radioactive rays. Large quantities of radioactive rays exist in the space, but most of them are cut off due to the earth's magnetic field and the influence of the atmosphere, resulting in the presence of just a trace quantity of them on the earth. Artificially, for example, radioactive rays such as neutrons are generated by nuclear reaction within a nuclear reactor. The radioactive rays are classified into alpha (α)-rays, beta (β)-rays, gamma (γ)-rays. X-rays, neutrons and the like. The power passing through a substance (penetrability) gradually increases in this order. The neutrons which are said to have the highest penetrability among the radioactive rays are further classified into small groups according to energy level. One example thereof is shown below. The energy level each type of neutrons has is shown in parentheses, and the larger the value is, the higher the penetrability is. In the order of the lowest penetrability, they are classified into cold neutrons (up to 0.002 eV), thermal neutrons (up to 0.025 eV), epithermal neutrons (up to 1 eV), slow neutrons (0.03-100 eV), immediate neutrons (0.1-500 keV) and fast neutrons (500 keV or more). Here, the energy values in the parentheses are not precise, and there are various views concerning the classification of neutrons. For example, there is a view which mentions 40 KeV or less, which is within the above energy region of intermediate neutrons, as the energy of epithermal neutrons. The typical effective utilization of neutrons is an application to the medical care field. The radiation therapy in which malignant tumor cells are irradiated with neutrons so as to be broken has been rapidly coming into general use in recent years. In order to obtain sufficient medical effects in the present radiation therapy, neutrons of a certain high energy must be used. In irradiation with high-energy neutrons, the influence on a part (a healthy part) other than an affected part of a patient cannot be avoided, leading to side effects. Therefore, in the present situation, the application of the radiation therapy is limited to severe patients. When a normal cell is exposed to high-energy radiation, its DNA is damaged, leading to side effects such as dermatitis, anemia due to radiation and leukopenia. Furthermore, in some cases, a late injury may be caused some time after treatment, and a tumor may be formed and bleed in the rectum or the urinary bladder. In order not to cause such side effects and late injuries, methods of pinpoint irradiation on a tumor have been studied. Examples thereof are: ‘Intensity Modulated Radiation Therapy (IMRT)’ in which only a tumor portion is three-dimensionally irradiated accurately with a high radiation dose; ‘Motion Tracking Radiation Therapy’ in which radiation is emitted to motions in the body of a patient such as breathing or heartbeat; and ‘Particle Beam Radiation Therapy’ in which a baryon beam or a proton beam each having a high remedial value is intensively emitted. The half-life of a neutron which is often used in such radiation therapies is short. 887.0±2.0 sec (about 15 min). The neutron decays in a short period of time, releases electrons and neutrinos, and turns into protons. The neutron has no charge, and therefore, it is easily absorbed when it collides with a nucleus. The absorption of neutrons in such a manner is called neutron capture, and one example of an application of neutrons to the medical care field by use of this feature is ‘Boron Neutron Capture Therapy (hereinafter, referred to as BNCT)’, which is recently gaining attention. In this method, by causing malignant tumor cells of a patient to react with boron, a reaction product (a boron compound) is formed in the tumor portion, and the reaction product is then irradiated with neutrons (comprising mainly epithermal neutrons and thermal neutrons) which have less influences on a healthy portion. And a nuclear reaction is caused only within the very small range where the boron compound has been formed, resulting in making only the tumor cells extinct. This method was proposed about 60 years ago. Because of small influences on a healthy portion of a patient, it has been attracting attention as an excellent radiation therapy since quite long before and has been studied in varied countries. However, there are wide-ranging problems on the development such as a neutron generator, a device for a choice and selection of neutrons to be remedially effective (a moderation system device), and avoidance of influences on a healthy portion of a patient (one of the requirements is to form a boron compound only in a tumor portion). At the present time, many of these problems cannot be said to have been sufficiently solved, and the method has not come into wide use as a general therapy. One of significant factors why it has not come into wide use is that in most of the past cases, a neutron generator was attached to an existing nuclear reactor and that all of the studies, developments and medical practices were conducted at the site, that is, the situation suitable for medical use could not be realized. In order to radically improve such situation, a neutron generator for medical use only must be developed and be put to practical use, and in Japan, a few device manufacturers are promoting the development of a neutron generator of this kind, in order to meet the expectations. In addition to the development of a small-sized high-performance neutron generator, another significant factor why it has not come into wide use is that a moderation system device must be also made high-performance and downsized. This is another major problem in aiming at practical use of the method. In order to effectively utilize neutrons as a particle beam for medical treatment, the selection of neutron types is important, and one example is shown below. From the point of view of medical effects, by removing high-energy neutrons which adversely influence healthy bodily tissues and reducing extremely-low-energy neutrons having little medical effect (such as thermal neutrons and cold neutrons), leading to a higher ratio of neutrons having high medical effects (such as a low-energy part of intermediate neutrons and epithermal neutrons), a desirable particle beam for medical treatment can be formed. The epithermal neutrons and the low-energy part of intermediate neutrons have a high invasive depth to the internal tissues of a patient. Therefore, for example, without craniotomy required in the case of brain tumor, or without an abdominal operation required even if the abdominal operation on another important internal organ cannot be easily performed, it is possible to carry out effective irradiation on an affected part. On the other hand, when the extremely-low-energy neutrons such as thermal neutrons are used, because of their low invasive depth, craniotomy or an abdominal operation is required, resulting in a significant burden on the patient. In order to safely and effectively utilize radiation, it is necessary to suitably select and arrange moderators. In order to effectively use neutrons having the highest penetrability among radioactive rays, it is important to know the moderation performance of materials of every kind to neutrons, leading to effective moderation. Most of neutrons generated by an accelerator such as a cyclotron are high-energy neutrons, and by using a moderator, high-energy neutrons whose energy level adversely influences a body (such as fast neutrons and a high-energy part of intermediate neutrons) should be removed as many as possible. In order to secure a required dose of the above-mentioned neutrons having high medical effects as well as cut off the high-energy neutrons which adversely influence the body to non-existent, highly difficult moderation control is required. Generally, when trying to secure a required dose of neutrons having high medical effects, high-energy neutrons are inevitably included. Therefore, the high-energy neutrons need be removed as many as possible in the next moderation step. There is one system of the above-mentioned Boron Neutron Capture Therapy (BNCT), which a group with Kyoto University as the central figure has been recently promoting (Non-Patent Document 1 and Non-Patent Document 2). In this system, without being attached to an existing nuclear reactor, a cyclotron accelerator as a neutron generator is exclusively installed. The neutron generator for medical use only is adopted. However, the cyclotron accelerator is large due to insufficient downsizing. And as a moderator selected for a radiation shield in order to safely and effectively utilize radiation (mainly neutrons) generated by this cyclotron accelerator, polyethylene containing calcium fluoride (CaF2) and lithium fluoride (LiF) is used, as well as lead (Pb), iron (Fe), aluminum (Al) and polyethylene. It cannot be said that the moderation performance of these moderators is sufficient. Though the details are described below, on condition that a required dose of epithermal neutrons most suitable for treatment by BNCT should be obtained, the neutrons obtained after moderation with the combination of these moderators are mixed with a large quantity of last neutrons having an adverse influence on healthy tissues. In order to conduct required moderation, the moderator becomes quite thick. In other words, the moderation system device becomes large. Therefore, there is a problem that the whole apparatus cannot be sufficiently downsized. In order to allow this BNCT to come into wide use in general hospitals, downsizing of the whole apparatus is a necessary condition. In order to downsize both of the accelerator and the moderation system device, the development of a moderator excellent in moderation performance is an urgent necessity. The selection of a moderator which is important for improving remedial values and downsizing a BNCT apparatus is described below in detail. In the BNCT, it is required to remove high-energy neutrons such as fast neutrons and to irradiate an affected part with neutrons comprising mainly epithermal neutrons and a small quantity of thermal neutrons. Specifically, an estimated dose of epithermal neutrons and thermal neutrons required in cases where the irradiation time is in the order of one hour, is said to be about 1×109 [n/cm2/sec]. In order to secure the dose, it is said that as the energy of an outgoing beam from an accelerator being a source of neutrons, about 5 MeV-10 MeV is required when beryllium (Be) is used as a target for the formation of neutrons. The selection of particle beam types through moderators of every kind in a neutron radiation field for BNCT using an accelerator is described below. A beam emitted from the accelerator collides with a target (Be), and by nuclear reaction, high-energy neutrons, mainly fast neutrons and the like are generated. As a method for moderating the fast neutrons, using Pb and Fe each having a large inelastic scattering cross section, the neutrons are moderated while suppressing the attenuation thereof. They are moderated to some extent (up to the order of 1 MeV) using these two kinds of moderators, and then moderated/optimized according to the neutron energy required in the radiation field. As a moderator to the neutrons moderated to some extent, aluminum oxide (Al2O3), aluminum fluoride (AlF3), CaF2, graphite, heavy water (D2O) or the like is used. By injecting the neutrons moderated nearly to 1 MeV into these moderators, it is required to moderate them to the epithermal neutron energy region (4 keV-40 keV) suitable for BNCT. In the case of the above group with Kyoto University as the central figure, as moderators, Pb, Fe, Al, CaF2, polyethylene and polyethylene containing LiF are used. The polyethylene and polyethylene containing LiF among them are moderators for shielding arranged in a manner that cover the outside portion of the apparatus in order to prevent leakage of high-energy neutrons out of the radiation field. To moderate the high-energy neutrons to some extent using Pb and Fe among these moderators (the first half of a moderation stage) is desirable, but it cannot be said that the second half of the moderation stage using Al and CaF2 after the moderation to some extent is very desirable. In this type of neutrons moderated to some extent, a quite large quantity of high-energy neutrons harmful to healthy cells is left. It is required to remove these high-energy neutrons to non-existent while allowing a required dose of intermediate-energy-level neutrons such as epithermal neutrons having high medical effects to remain, but it cannot be said that this point has been sufficiently achieved. That is, in the case of the moderators (Al and CaF2) used in the second half of the stage, many of the high-energy neutrons left through the moderation in the first half of the stage pass through them without cutoff. If such neutrons are used in a therapy as they are, a bad influence on healthy tissues of a patient cannot be avoided. That is because CaF2 in the moderators used in the second half of the stage does not have sufficient cutoff performance to the high-energy neutrons, and part of them passes without cutoff. The polyethylene containing LiF as well as CaF2 used in the second half of the stage is used in a manner that covers over the entire surface except an outlet of neutrons on the treatment room side. It is arranged so as to prevent whole-body exposure of a patient to the fast neutrons, and is not used as a moderator on the outlet. The polyethylene as a moderator in the first half of the stage is used in a manner that covers over the entire surface of the periphery of the apparatus except the treatment room side, like the polyethylene containing LiF in the second half of the stage, and it is arranged so as to prevent the fast neutrons from leaking to the surroundings of the apparatus. Therefore, instead of CaF2 in the second half of the stage, the development of an excellent moderator which can cut off and moderate high-energy neutrons while suppressing the attenuation of intermediate-energy-level neutrons required for treatment has been desired. From various kinds of researches/studies, the present inventors paid attention to MgF2 system sintered bodies as a moderator for obtaining neutrons having an energy distribution optimal to treatment (4 keV-40 keV), mainly comprising epithermal neutrons in anticipation of the highest remedial value, from the above neutrons moderated to some extent (up to 1 MeV). The MgF2 system sintered bodies include a MgF2 sintered body as well as a MgF2—CaF2 binary system sintered body, a MgF2—LiF binary system sintered body, a MgF2—CaF2—LiF ternary system sintered body, and the like. Until now, there is no report that MgF2 was used as a moderator to neutrons. There is no report of an example in which MgF2 system sintered bodies, including a MgF2 sintered body and a MgF2—CaF2 binary system sintered body, were adopted as neutron moderators. In the present application, an invention concerning a sintered body of MgF2 simple (equivalent to single) (hereinafter, referred to as a MgF2 sintered body) is described below. MgF2 is a colorless crystal, having a melting point of 1248° C., a boiling point of 2260° C. a density of 3.15 g/cm3, a cubic system and a rutile structure according to a science and chemistry dictionary. A single crystal body thereof has a high transparency, and since a high light transmittance is obtained within a wide range of wavelength of about 0.2 μm-7 μm and it has a wide band gap and a high laser resistance, it has been mainly used as a window material for eximer laser. Or MgF2 is deposited on the surface of a lens to be used for protection of the inner parts thereof or prevention of irregular reflection, both of them for optical use. Though in either case, a MgF2 single crystal body is used for optical use, the single crystal body is extremely expensive since the single crystal growth thereof takes long time and control of the crystal growth is highly difficult. Therefore, the use thereof is limited from the point of view of economical efficiency. On the other hand, since the MgF2 sintered body has a poor light transmittance and a low transparency because of its polycrystalline structure, it is not suitable for optical use. There are very few cases where MgF2 in the form of a single crystal body as well as a sintered body was used for other than optical use. There are just a few cases where a sintered body thereof was used for a plasma-resistant member, which are described below. As one example of an application of a sintered body mainly containing MgF2 to a plasma-resistant member, Japanese Patent Application Laid-Open Publication No. 2000-86344 (the below-mentioned Patent Document 1) is cited. In the scope of claims concerned, a sintered body comprises a fluoride of at least one kind of alkaline earth metals selected from the group of Mg, Ca, Sr and Ba, in which the total amount of metallic elements other than the alkaline earth metals is 100 ppm or less on a metal basis, a mean diameter of crystal grains of the fluoride is 30 μm or less, and the relative density is 95% or more. However, the substances in the list of examples of this publication were obtained by firing a metal fluoride of each single kind of the above four alkaline earth metals (i.e. MgF2, CaF2, SrF2 and BaF2) as a raw material, and there is no description that a mixture of those raw materials was fired. In firing of MgF2 and CaF2 as raw materials according to the examples shown in Table 1, the firing temperatures in the cases evaluated as appropriate (shown with ⊚ or ◯ in the Table) are 850° C., 950° C. and 1050° C. with MgF2, and any relative density of the sintered bodies is 95% or more. Likewise, with CaF2, the appropriate firing temperatures are 950° C., 1040° C. and 1130° C., and any relative density of the sintered bodies is 97% or more. On this point, according to the studies/experiments by the present inventors, MgF2 and CaF2 each presented a sublimation phenomenon at temperatures equal to these firing temperatures or lower than these, and a violent foaming phenomenon occurred at the above firing temperatures. Therefore, it was found that it was impossible to obtain a sintered body of MgF2 with a relative density of 95% or more, and a sintered body of CaF2 with a relative density of 97% or more. The present inventors ascertained prior to such firing experiments through differential thermal analysis of raw material powders that the sublimation of MgF2 starts at about 800° C. and becomes brisk at 850° C. or more, and that the sublimation of CaF2 starts at about 850° C. and becomes brisk at 900° C. or more. The results of this differential thermal analysis show that all of the firing temperatures in three cases of MgF2 and CaF2 each indicated as ‘appropriate’ in the examples of the Patent Document 1 are temperature conditions wherein a sublimation phenomenon briskly occurs in the firing process, and that it is actually difficult to make the sintered bodies compact. The inventors of this Patent Document 1 indicate in the description “since AlF3 starts to sublimate at a relatively low temperature, resulting in a necessity of firing while suppressing sublimation, it was difficult to obtain a compact sintered body”. They appear to have known ‘a sublimation phenomenon revealed in firing’, that is, ‘foaming of a sintered body’, that is. ‘it is difficult to obtain a compact sintered body’. However, for reasons unclear, as mentioned above, in either case of MgF2 and CaF2, it is described that the sintered bodies were produced at firing temperatures higher than the above temperatures at which the sublimation phenomenon starts. This means that sintering was conducted under the conditions difficult to obtain a compact sintered body due to the occurrence of brisk foaming within the sintered body in the firing process to promote sintering of a raw material powder. The present inventors grabbed such phenomenon and studied a method for minimizing the influence of the sublimation phenomenon in the sintering process, and developed an excellent sintering method by which compact sintered bodies can be stably obtained. Another example of an application of a sintered body mainly containing MgF2 to a plasma-resistant member is the Japanese Patent Application Laid-Open Publication No. 2012-206913 (the below-mentioned Patent Document 2). This invention discloses a method wherein, since a sintered body of MgF2 simple has a defect of low mechanical strength, by mixing at least one kind of non-alkaline metallic substance having a lower mean linear thermal expansion coefficient than MgF2 such as Al2O3, AlN, SiC or MgO, the defect of low mechanical strength of a MgF2 simple sintered body is compensated for. When a sintered body of such mixture is used as the above moderator to neutrons, the moderation performance thereof is greatly different from that of MgF2 simple because of the influence of the non-alkaline metal mixed with MgF2. Therefore, it was predicted that it was difficult to apply a sintered body of this kind of mixture to use as a moderator. As an invention related to a MgF2 sintered body, the Japanese Patent Application Laid-Open Publication No. 2000-302553 (the below-mentioned Patent Document 3) is cited. The greatest defect of sintered bodies of fluoride ceramics such as MgF2, CaF_, YF3 and LiF is low mechanical strength, and in order to solve this problem, invented was a sintered body made by compounding these fluorides and Al2O3 at a predetermined ratio. However, as the corrosion resistance and mechanical strength of the sintered body produced by this method, in any combination, a sintered body having just an intermediate characteristic between both of the characteristics of those fluorides and Al2O3 was obtained. A sintered body having a characteristic exceeding both of the characteristics was not obtained by compounding. As described above, in order to use a sintered body obtained by firing a mixture of MgF2 sintered by a conventional method with other substances for use other than plasma-resistant members, specifically, for new use such as a moderator to neutrons, one of radiation, there were a lot of problems left to be solved. Patent Document 1: Japanese Patent Application Laid-Open Publication No. 2000-86344 Patent Document 2: Japanese Patent Application Laid-Open Publication No. 2012-206913 Patent Document 3: Japanese Patent Application Laid-Open Publication No. 2000-302553 Non-Patent Document 1: H. Tanaka et al., Applied Radiation and Isotopes 69 (2011) 1642-1645 Non-Patent Document 2: H. Tanaka et al., Applied Radiation and Isotopes 69 (2011) 1646-1648 Non-Patent Document 3: Hiroaki Kumada et al., Health Physics, 42 (2007) 23-37 The present invention was developed in order to solve the above problems, and it is an object of the present invention to provide a fluoride sintered body for a neutron moderator, which is used in order to moderate the energy of neutrons in the good use of the neutrons, a kind of radiation, and is inexpensive unlike a high-purity single crystal body, and with which effective moderation effects can be obtained, resulting in capability of enhancing remedial values while downsizing an apparatus for therapy, and a method for producing the same. The present inventors first gave basic consideration to the selection of substances (metals or compounds) having a sufficient moderation effect on high-energy neutrons. In the BNCT, as described above, it is important to irradiate an affected part with neutrons comprising mainly epithermal neutrons and a trace quantity of thermal neutrons in order to minimize high-energy neutrons which are harmful in therapy while obtaining a large remedial value. Specifically, an estimated dose of epithermal neutrons and thermal neutrons required in the case of the order of one hour of irradiation time is about 1×10° [n/cm2/sec]. It is said that the energy of an outgoing beam from an accelerator being a source of neutrons required for that is about 5 MeV-10 MeV when beryllium (Be) is used as a target for the formation of neutrons. The selection of particle beam types by moderators of every kind in a neutron radiation field for BNCT using an accelerator is described below. A beam emitted from the accelerator collides with a target (Be), and by nuclear reaction, mainly high-energy neutrons (fast neutrons) are generated. As a method for moderating the fast neutrons, using Pb, Fe or the like having a large inelastic scattering cross section, the neutrons are moderated to some extent while suppressing the attenuation thereof. The moderator to the neutrons moderated to some extent (up to 1 MeV) is optimized according to the quantity of neutron energy required in the radiation field. As a moderator to the neutrons moderated to some extent, generally, aluminum oxide (Al2O3), aluminum fluoride (AlF3), CaF2, graphite, heavy water (D2O) or the like is used. By injecting the neutrons moderated nearly to 1 MeV into these moderators, the neutrons are moderated to the range of epithermal neutrons having energy (4 keV-40 keV) suitable for BNCT. However, by the method using the above moderators, the removal of fast neutrons which adversely influence healthy tissues of a patient in therapy tends to be insufficient. Then, if priority is given to this removal of fast neutrons, the neutrons are contrarily moderated too much and further moderated below the range of epithermal neutrons, and the ratio of thermal neutrons having a smaller remedial value than epithermal neutrons becomes large. Therefore, the present inventors selected two kinds of fluorides, MgF2 and CaF2, as candidates of hopeful moderators to the neutrons moderated to some extent from among compounds of every kind, and examined the below-described moderation effects. As a result (FIG. 4), it was ascertained that by injecting the neutrons moderated nearly to 1 MeV into a moderator made of MgF2, fast neutrons harmful in BNCT could be almost perfectly removed, and that epithermal neutrons in the energy range (4 keV-40 keV) optimal to the therapy could be obtained. There were various kinds of problems in producing a moderator made of MgF2, and what should have been thought first of all was a method for producing it. As a method for producing it, a crystal method, a single crystal method, a polycrystal method (i.e. a sintering method) and the like may be exemplified. A crystal produced by a crystal method generally has segregation in crystal orientation and impurities also easily result in segregation. When it is used as a moderator, variation easily arises in moderation performance depending on the part. Therefore, it appears to be unsuitable for a moderator. A single crystal produced by a single crystal method requires a high control accuracy in production, the stability of its quality is poor, and the cost thereof is extremely high. Therefore, it must be said that it is unsuitable for a moderator. Then, this time, the present invention was completed by studying and developing a method for producing a moderator through a polycrystal method (hereinafter, referred to as a sintering method). (1) Securing the purity of products in order to secure the performance as a moderator In order to secure the performance as a MgF2 moderator, first of all, securing the purity of products is important. In order to secure the purity thereof, it was thought that securing the purity on the raw material level, and keeping impurities from getting mixed in the manufacturing process were important, and taking these into consideration, the moderation performance was secured. There are three purity levels of MgF2 raw materials on the market such as 2N (99.0%), 3N (99.9%) and 4N (99.99%), and in a preliminary small-scale test, using these three purity levels of raw materials, the states of sintering characteristics were evaluated. (2) Relaxing sintering conditions by pulverizing the raw materials By pulverizing the raw material grains, reaction interfaces between grains in the sintering process were increased, so as to promote the progress of defoaming and make the progress of sintering reaction of every sintering part uniform. (3) Making the sintering reaction uniform by dividing the sintering step The sintering step was divided into preliminary sintering and main sintering (when the main sintering is further divided, the effects tend to increase). In the preliminary sintering step, the sintering reaction was mainly caused by grain growth by solid phase reaction (hereinafter, referred to as solid-phase sintering), while in the main sintering step, the sintering reaction was caused in the solid solution formation temperature region mainly by sintering body formation through solid solution formation reaction (hereinafter, referred to as solid solution sintering), or by sintering body formation through melt formation reaction (hereinafter, referred to as melting sintering). As a result, combined with the effect of pulverizing the raw materials in the above paragraph (2), the progress of the sintering reaction of every sintering part could be made uniform, and the sintered body could be allowed to have strong cohesion between particles. In addition to the moderation performance, the moderator needs to have a resistance to damage occurrence in handling such as the installation thereof in a moderation system device and a resistance to dust generation caused by neutron irradiation impacts. That is, it is required to have a characteristic excellent in mechanical strength. The mechanical strength of a sintered body is determined by micro strength of bonding parts between particles and the defoaming state such as the size, shape, distribution and number of bubbles, in other words, the shape such as the width and length of the bonding parts and a bound body (parent) of ex-particles (the compactness of the sintered body), and moreover, the brittleness originated from a crystal structure (such as single crystal or polycrystal) of the parent. (4) MgF2, a raw material for forming a high-density sintered body by foaming restriction and reduction of large-sized residual bubbles in the sintering process, easily causes a vaporization (sublimation) phenomenon in the sintering process, generates fluorine gas and easily causes a large number of fine bubbles within the sintered body. This foaming by vaporization and the decrease of voids essentially with the progress of the sintering process are contrary to each other. Therefore, it was decided to minimize the foaming. When a fluoride system raw material is heated at a high temperature, part of the material vaporizes. The temperature of the starting of vaporization depends on the composition. In the case of a composition chiefly comprising MgF2, vaporization starts at about 800° C. and becomes very brisk at about 850° C. Since the vaporization causes fluorine gas, fine bubbles are formed in the sintered body. The shapes of the formed bubbles are almost spherical, and when observing the broken-out section of the sintered body with an electron microscope (SEM), the sections of the bubbles look circular close to a perfect circle. The sizes of the bubbles are in the order between several μm of smaller ones and 20 μm-40 μm of larger ones described in diameter seen in the broken-out section. The shapes of the smaller bubbles of several μm in diameter are almost circular, while the shapes of the larger ones are rarely circular. Most of them are long and narrow, or angular, or irregular. From these shapes, it is considered that the smaller bubbles are freshly formed, and that the larger ones are aggregates of some of the formed bubbles. Therefore, it was decided to avoid the formation of small bubbles (foaming) as much as possible by means of sintering by heating at a low temperature, and also to avoid gathering of small bubbles through the process of heating as much as possible so as to make the sintered body compact. Combining the ideas of the above paragraphs (1)-(3), it was decided to produce a fluoride sintered body for a neutron moderator having a characteristic excellent in mechanical strength which is a required characteristic other than moderation performance as a member of a neutron moderation system device. In order to achieve the above object, a fluoride sintered body for a neutron moderator according to a first aspect of the present invention is characterized by comprising MgF2 of a compact polycrystalline structure, having a bulk density of 2.90 g/cm3 or more. Since the fluoride sintered body for a neutron moderator according to the first aspect of the present invention is a sintered body of MgF2 of a compact polycrystalline structure having a bulk density of 2.90 g/cm3 or more, the organizational structure of the sintered body is uniform, the difference between the internal and external parts is small, and by restricting the generated quantity of solid solution, the crystal growth is suppressed, leading to reducing the formation of brittle portions, resulting in enhancing the strength of the sintered body. Therefore, in the processing steps in producing the sintered body, or in handling between the steps, cracks or chips are not easily caused. A sintered body having a mechanical strength with which no damage such as cracks or chips may be caused when it is set in a BNCT apparatus, or even when neutron irradiation impacts are given thereto during operation of the apparatus, can be obtained. As a result, a fluoride sintered body for a neutron moderator having a good moderation performance and mechanical strength leading to easy handling can be provided. The fluoride sintered body for a neutron moderator according to a second aspect of the present invention is characterized by having a bending strength of 10 MPa or more and a Vickers hardness of 71 or more as regards mechanical strengths in the fluoride sintered body for a neutron moderator according to the first aspect of the present invention. The fluoride sintered body for a neutron moderator according to the second aspect of the present invention has extremely excellent mechanical strengths. Therefore, no crack or the like is caused in mechanical processing for finishing it as a moderator, and it can be a moderator having a sufficient impact resistance to neutron irradiation impacts given during use as a moderator. In order to achieve the above object, a method fir producing a fluoride sintered body for a neutron moderator according to a first aspect of the present invention is characterized by comprising the steps of: pulverizing a high-purity MgF2 raw material to the order of 1 μm-2 μm in median diameter and adding 0.1-1% by weight of a sintering aid thereto to mix; molding said mixed raw material as a starting raw material using a uniaxial press molding device at a molding pressure of 5 MPa or more; molding said uniaxially molded article using a cold isostatic pressing (CIP) device at a molding pressure of 5 MPa or more; conducting preliminary sintering by heating said CIP molded article to 550° C.-600° C. in an air atmosphere; and conducting main sintering by heating the same in the temperature range just below the starting temperature of foaming for 4-16 hours in an inert gas atmosphere to allow the sintering to make progress more uniformly, and then heating the same in the vicinity of the temperature limits in which a solid solution starts to be formed for 0.5-3 hours so as to form a MgF2 sintered body having a compact structure. Here, the CIP is a method for pressure molding wherein a uniaxially molded article is put into a bag sealed with a vinyl bag or the like in order not to directly touch clean water. The bag after deairing, is put within a pressure vessel, and the vessel is filled with clean water to apply a prescribed hydraulic pressure. Here, the starting temperature of foaming is a temperature at which part of a fluoride compound starts to decompose and fluorine gas is generated so as to start to form fine bubbles. A preliminary sintered body formed by heating a MgF2 raw material at 550° C. for 6 hours in an air atmosphere was grinded, and using the grinded substance as a sample of a differential thermal analyzer, alterations in weight and in endothermic and exothermic amount of the sample were examined while heating. A minute quantity of weight decrease was found at approximately 800° C. but it appeared that this was because, for example, fluorine attached to a parent of the preliminary sintered body or boron fluorine resolving in the parent, with a weak bonding property, dissociated and decomposed first of all. After further heating, a point of inflection of the weight decrease curve appeared at approximately 850° C., and the weight decrease became noticeable. It was anticipated that in the temperature limits above that, part of bonded boron fluorine in MgF2 would start to decompose, which would cause the generation of fluorine gas and the formation of fine bubbles. Therefore, the temperature corresponding to this point of inflection, that is, about 850° C. is referred to as the starting temperature of foaming. Here, the temperature range just below the starting temperature of foaming is specifically a temperature range of 750° C.-840° C. Here, the temperature limits in which a solid solution starts to be formed are temperature limits in the vicinity of 980° C. in which a solid solution starts to be formed in a phase diagram of the MgF2—CaF2 binary system shown in FIG. 1. The sintered body produced by the method for producing a fluoride sintered body for a neutron moderator according to the first aspect of the present invention has a strong bonding power between particles, leading to a high mechanical strength (micro strength) of the bonding parts. The bending strength and impact resistance which were problems to be solved are remarkably improved, and a sintered body which can be used as a neutron moderator without problems for actual use can be obtained. A sintered body to be produced has a higher degree of compactness according to the selection of the purity of MgF2, heating atmosphere, heating temperature pattern and the like. Since the body is sintered, the crystalline structure thereof is polycrystalline, resulting in remarkable improvement of the brittleness compared with a single crystal. Therefore, since the sintered body produced by the method for producing a fluoride sintered body for a neutron moderator according to the first aspect of the present invention has sufficient mechanical strengths in processing such as cutting-off, grinding and polishing as a moderator in a moderation system device for BNCT, and further in handling such as the installation thereof in the moderation system device, it can be installed without problems. Even if it is irradiated with neutrons, it can be used without problems to irradiation impacts thereof: and the moderation performance to neutrons is also extremely excellent. The method for producing a fluoride sintered body for a neutron moderator according to a second aspect of the present invention is characterized by the inert gas atmosphere in the main sintering step comprising one kind of gas or a mixture of plural kinds of gases, selected from among nitrogen, helium, argon and neon, in the method for producing a fluoride sintered body for a neutron moderator according to the first aspect of the present invention. Thus, as the inert gas, nitrogen (N2), helium (He), argon (Ar) or neon (Ne) may be used. The preferred embodiments of the fluoride sintered body for a neutron moderator and the method for producing the same according to the present invention are described below by reference to the Figures. In order to produce a fluoride sintered body suitable for a neutron moderator according to the preferred embodiments, a high-purity (purity of 99.9% by weight or more) MgF2 powder was used, and as a sintering aid, for example, a carboxymethyl cellulose (CMC) solution was added in the proportion of 0.03-0.5% by weight (not included in 100) to 100 of the powder. The mixture was used as a starting raw material. After filling the raw material into a mold form of a prescribed size, it was compressed at a molding pressure of 5 MPa or more using a uniaxial press molding device, and the molded article was further molded at a molding pressure of 5 MPa or more using a cold isostatic pressing (CIP) device. Preliminary sintering was conducted by heating this CIP molded article in the temperature range between 550° C. and 600° C. in an air atmosphere, and the preliminary sintered article was heated in the temperature range just below the starting temperature of foaming (the temperature defined through the measurement using a differential thermal analyzer, about 850° C.) (750° C.-840° C.) for 4-16 hours in an air atmosphere or an inert gas atmosphere. By this heating, sintering was more uniformly promoted, and thereafter, the same was heated in the vicinity of the temperature limits in which a solid solution starts to be formed, that is, in the temperature range of 900° C.-1100° C. for 0.5-3 hours, and then cooled so as to produce a MgF2 sintered body having a compact structure. As described above, in the phase diagram of the MgF2—CaF2 binary system shown in FIG. 1, the temperature at which a solid solution starts to be formed is in the temperature limits in the vicinity of 980° C. However, the present inventors presumed from the observation of the sections of actually sintered bodies, that there was a high possibility that a solid solution would be formed at a temperature dozens lower than 980° C., the temperature indicated in this phase diagram in the case of MgF2 simple. Therefore, they considered that the vicinity of the temperature limits in which a solid solution starts to be formed should be 900° C. or more, and guessed that a solid solution would be formed even in the case of heating at a temperature less than 980° C. Concerning the pulverization of MgF2 being a raw material, balls for ball mill were filled into a pot mill, 3 kg of the raw material was filled therein and mixed for one week so as to be pulverized. The pot mill made of alumina, having an inside diameter of 200 mm and a length of 250 mm was used. As the filled balls made of alumina, ϕ5: 1800 g, ϕ10: 1700 g, ϕ20: 3000 g and ϕ30: 2800 g were used. The particle sizes of the raw material after pulverization were measured using a laser diffraction/scattering particle size distribution analyzer LA-920 made by HORIBA. Ltd. The median diameters were approximately 1.2 μm-1.3 μm. As the sintering aid, two kinds, the CMC and calcium stearate, were selected. With various addition proportions of each of them, the tests for examining the effects thereof were conducted. For comparison, a test with no sintering aid was also conducted. Concerning mixing of the sintering aid, the two kinds of sintering aids were added in the proportion of 0-2% by weight, respectively. As is the case with the pulverization of the raw material, after filling the balls for ball mill into the pot mill, the sintering aid was mixed a whole day and night. This mixed raw material was filled into a mold form of a uniaxial press molding device (mold size 220 mm×220 mm×H150 mm) and compression molding thereof was conducted at a press pressure of 20 MPa. Then, this press molded body was put into a vinyl bag and sealed, and it was put into a molding part of a CIP device (inside size: inside diameter 350 mm×height 120 mm). The space in said molding part was filled with clean water, and cool isostatic pressing (CIP) was conducted with variations of isostatic pressures by hydraulic pressure at room temperature. Preliminary sintering was conducted on this CIP molded body in an air atmosphere with various kinds of heating conditions in the temperature range between 500° C. and 700° C. and in the time range of 3 to 18 hours. After observing the appearance of this preliminary sintered body, in a nitrogen gas atmosphere, the temperature was raised from room temperature to 550° C. at a fixed rate for 6 hours, and held there for 8 hours. Then, it was raised to 950° C. at a fixed rate for 2 hours and held there for 1 hour, and then lowered for 20 hours to 100° C. By observing the appearance of the taken-out sintered body and the compact state of the inside thereof, proper compositions, processing conditions and preliminary sintering conditions were investigated. As a result, there was no big difference between the effects of the two kinds of sintering aids, but in the case of no sintering aid, the shape keeping performance of the uniaxial press molded body was poor, so that loss of shape frequently occurred in handling to the following CIP molding step. When the mix proportion of the sintering aid was 0.03% by weight or more, the loss of shape was not noticed, while coloring which appeared to be a residual of the sintering aid was sometimes noticed on the preliminary sintered body or sintered body when the mix proportion thereof exceeded 0.6% by weight. Accordingly, the proper range of the mix proportion of the sintering aid was decided to be 0.03-0.5% by weight. When the molding pressure of the CIP device was less than 5 MPa, the bulk density of the sintered body in any of optimizing tests of the heating conditions of preliminary sintering and main sintering was lower by 2% or more than the case of the molding pressure of 5 MPa or more. For example, in the case of a molding pressure of 10 MPa, the bulk density of a sintered body sintered with the same sintering conditions was 2.95 g/cm3, while in the case of a molding pressure of 4.8 MPa, the bulk density of a sintered body was 2.86 g/cm3, 3% lower than the former. When the molding pressure was increased gradually from 5 MPa to 20 MPa, it was recognized that the bulk density of a sintered body after sintering tended to increase little by little. The tests were conducted until the molding pressure was gradually increased further to 50 MPa. The increase of the bulk density of a preliminary sintered body or a sintered body in the case of a molding pressure of 20 MPa or more was just slight, and a linear improvement like between 5 MPa and 20 MPa was not recognized. Accordingly, the proper value of the molding pressure was decided to be 5 MPa or more, preferably 20 MPa or more. Concerning the preliminary sintering conditions of a molded body in an air atmosphere, as shown in FIG. 2, at a heating temperature of less than 550° C. shrinkage was small compared with the size of the molded body, while at a heating temperature of 610° C. or more, the shrinkage was large and difficult to control. Accordingly, the proper range of the preliminary sintering temperature was decided to be between 550° C. and 600° C. Concerning the proper value of the heating time, as shown in FIG. 2, at 550° C. 8-9 hours were optimal from the evaluation of the shrinkage rate, and it could be judged that 4-10 hours were proper. At 600° C., 6-8 hours were optimal, and it could be judged that 4-10 hours were proper. From these results, the heating condition of the preliminary sintering was decided to be at 550° C.-600° C. 4-10 hours in an air atmosphere. The main sintering step important in producing a MgF2 sintered body suitable for a neutron moderator and the sintering mechanism thereof are described below. The definition of ‘primary flocculation process’ and ‘secondary flocculation process’ which are the terms expressing the degree of progress of the sintering step, is described below. The ‘primary flocculation process’ is the first half of the stage of sintering, and at the initial stage thereof, the intervals between particles gradually become narrower and the voids among particles also become smaller. Furthermore, the particle-to-particle contact portions become thick and the voids among them become small. Here, the majority of the voids are open pores connecting to the surrounding atmosphere. Such whole stage is called ‘primary flocculation process’. After the end of the primary flocculation process, with further progress of sintering, the open pores gradually decrease and turn into closed pores. Roughly the stage of turning into closed pores and the following stage of defoaming and compacting are called ‘secondary flocculation process’. In the present invention, due to pulverization of raw materials, particle size control, mixing of a sintering aid, uniaxial press molding, CIP molding, preliminary sintering and the like, it was recognized that the voids among particles of the preliminary sintered body were small, and that the voids almost uniformly scattered without gathering (the first half stage of the primary flocculation process). In the heating process of the next main sintering step, the heating temperature is gradually raised. Around the preliminary sintering temperature limits (550° C.-600° C.), particles start to gather, and thereafter, solid phase reaction starts in the temperature limits far lower than 980° C. at which a solid solution starts to be formed. With that, flocculation of particles makes progress, the particle-to-particle distances become short and the voids become small. Here, in the case of heating at a relatively low temperature (in the vicinity of 550° C.) like preliminary sintering for a short period of time, most of the voids remain in the open pore state (the second half stage of the primary flocculation process). It is generally said that the solid phase reaction starts in the temperature limits lower by the order of 10% or further lower than 980° C. From the observation of the sections of the sintered bodies in the preliminary test by the present inventors, it was considered that the solid phase reaction started in further lower temperature limits than generally said, at approximately 500° C. Its grounding is that at 550° C. the lowest limit of the proper preliminary sintering temperature, sintering had already made progress considerably and that the preliminary sintered body considerably shrunk compared with the molded body. In this preliminary test, the bulk volume shrunk in the order of 10-20% by volume. It was considered that the reaction made progress at a slow reaction rate in the temperature limits and that it made progress at a quite high reaction rate in the temperature limits in the vicinity of approximately 700° C. or more up to 980° C. What attention should be paid to is behavior of fine bubbles (foaming gas) generated through vaporization of part of a raw material in the temperature limits of about 8500° C. or more. In the case of heating at about 850° C. or more, it was considered that the heating time should be as short as possible, since this formation of bubbles became noticeable. Micro behavior of raw material particles is described below. Around a temperature exceeding 980° C. at which a solid solution starts to be formed, melting starts in the vicinity of a particle interface where fine particles of MgF2 are present, and a solid solution of MgF2 starts to be formed. As described by reference to FIG. 1, the present inventors presumed from the observation of the sections of the sintered bodies in the preliminary test that in the case of MgF2 simple, a solid solution would start to be formed in the temperature limits in the order of dozens of degrees lower than 980° C. as the true state. It was presumed that this solid solution filled the voids among particles and that in some parts, more fine voids were also filled in through capillary phenomenon. On the other hand, even if the heating temperature is lower than 980° C. by heating at about 700° C. or more for a long period of time as described above, the solid phase reaction makes progress, the voids gradually decrease with the elapse of time so as to be closed pores. Parallel with that, a gas component within the closed pores scatters within the bulk (parent) of the sintered body, leading to the progress of defoaming so as to make the sintered body compact with few bubbles (secondary flocculation process). Here, in order to make it compact by heating in the relatively low temperature limits of the order of 700° C., heating for a quite long period of time is required, resulting in low productivity and being uneconomical. Also here, in heating at about 850° C. or more, attention should be paid to the presence of line bubbles (foaming gas) generated through vaporization of a raw material. It is presumed that the bubbles contain fluorine gas. Fluorine, the atomic number of 9, having an atomic weight of 18.998, is heavier than the air, and a relatively heavy element among light elements. The diffusion velocity thereof within the bulk (equivalent for the parent) of the sintered body is slow (it is difficult to diffuse), and it is considered that once formed bubbles do not easily disappear. As measures for suppressing foaming, to avoid heating in the temperature limits of foaming as much as possible, and to hold heating in the temperature limits thereof to a short period of time are exemplified. The difference in appearance between such foaming gases and bubbles left after pores became closed but could not be defoamed in the sintering step (hereinafter, referred to as residual bubbles) is described below. The sizes of the foaming gases generated by general heating for a relatively short period of time are approximately several μm diameter, and the shapes thereof are almost perfect spheres. On the other hand, the sizes of the residual bubbles are all mixed up, large, medium and small, and the shapes thereof are not perfect spheres but irregular. Therefore, it is possible to distinguish the both according to the difference in shape. Here, in the case of heating at a high temperature far exceeding 980° C., or heating in the temperature limits exceeding 980° C. for a long period of time, a foaming gas and a foaming gas, or a residual bubble and a foaming gas gather and grow to a large irregular bubble, resulting in difficulty in judging its origin. With the progress of the secondary flocculation process, the voids among particles become smaller, all or most of the voids are surrounded by particles or a bridge portion of the sintered body so as to be closed pores (bubbles). Depending on the conditions, gases are released through the voids (open pores), or gas components within the bubbles permeate into the bulk such as the particles or the bridge portion of the sintered body to degas, resulting in extinction of the bubbles (defoaming phenomenon). Whether the voids among particles are left as closed pores (bubbles) or by degassing, they do not remain as bubbles so as to disappear, is a significant element for deciding the degree of achievement of compactness of the sintered body, leading to the characteristics of the sintered body. Particularly in the case of sintering in an inert gas atmosphere (a light element gas such as Hie or Ne), it was considered that the lighter element easily diffused within the pores or bulk of the sintered body, leading to promoting the capillary phenomenon and defoaming phenomenon, and that bubbles were difficult to remain, leading to easy compacting. Thus, in order to make the whole compact, it is important to advance the primary flocculation process and the secondary flocculation process continuously with good balance. In the present invention, the preliminary sintering step chiefly corresponding to the first half stage of the primary flocculation process and the main sintering step chiefly corresponding to the second half stage of the primary flocculation process and the secondary flocculation process are separately conducted, so as to make the two flocculation processes easy to make progress uniformly throughout the sintered body. However, it is meaningless to divide the sintering step into two steps of preliminary sintering and main sintering like this, if the heating conditions are not proper. For example, in the case of heating at a high temperature exceeding the proper limits in the preliminary sintering step, in the case of rapidly heating at the temperature raising stage of the main sintering step, or in cases where the holding temperature in the main sintering step is a high temperature exceeding the proper limits, a remarkable difference in the degree of compactness is caused between the periphery portion of the sintered body and the inside thereof. When such situation is caused, degassing becomes difficult in the process of compacting the inside of the sintered body, resulting in insufficient compactness of the inside thereof. Therefore, it is important to make the heating temperature pattern in the sintering step according to the size proper. As described above, the proper conditions till just before the main sintering step are disclosed. The preliminary sintered body provided to this main sintering step is in a state that the whole body has already advanced to the first half stage of the primary flocculation. What is important here is the whole of the preliminary sintered body has already advanced uniformly to the middle of the primary flocculation. In order to find a method for producing a fluoride sintered body suitable for a neutron moderator, various kinds of main sintering steps were conducted. Preliminary sintered bodies obtained by conducting uniaxial press molding and CIP molding on a compound material made of MgF2 being a pulverized raw material with CMC of 0.2% by weight as a sintering aid added thereto and conducting preliminary sintering thereon at 550° C. for 6 hours were used. In any case, the heating time was set to be 6 hours. In each case of a sintering temperature varying between 600° C. and 1200° C., at an interval of every 50° C., the bulk density of the sintered body was measured. In the case of a range approximately between 900° C. and 1100° C., the bulk densities exceeded 2.90 g/cm3, which were high, but in either case of a sintering temperature of 850° C. or less, and that of 1150° C. or more, the bulk densities were lower than 2.90 g/cm3. When observing the sections of those sintered bodies, in the case of those sintered at 800° C. or less, the bridge widths of the sintering portions were narrow, so that it could be judged as absolutely insufficient progress of sintering. In the case of a body sintered at 850° C. a few open pores were noticed. In the case of a body sintered at 1100° C., some irregular bubbles were found inside, and in the case of those sintered at 1150° C. or more, those had a porous pumiceous structure as if irregular bubbles were innumerably formed inside. Fine bubbles which were almost perfect spheres of several to dozen μm in diameter were observed all over the sintered body and innumerable irregular bubbles of 10 μm or more in diameter were found all over the sections observed. It could be judged that these perfect sphere bubbles were foaming gases from their shapes, and that these irregular bubbles were bubbles in clusters similarly from their shapes. On the other hand, from the examination by the present inventors, it was found out that in the process of heating the MgF2 raw material obtained by pulverizing those as measured by a differential thermal analyzer, the weight clearly started to decrease at about 800° C., and that the weight started to drastically decrease at about 850° C. This means that a sublimation phenomenon in which MgF2 starts to dissolve/vaporize to generate fluorine gas starts at about 800° C., and that this phenomenon becomes brisk at about 850° C. (what is called presenting a foaming phenomenon). Through this sublimation, as described above, fine bubbles are formed all over the sintered body. The behavior of the formed fine bubbles (foaming gases) such as defoaming or remaining as bubbles is decided according to the degree of progress of the sintering step, in which portion of the sintered body they were formed and the like. In the primary flocculation process, for example, since the whole sintered body contains mainly open pores, the majority of bubbles are defoamed through the open pores, leading to few bubbles left. In the secondary flocculation process, since the sintered body contains mainly closed pores, a lot of foaming gases cannot be defoamed, leading to bubbles left. Basically it can be said that to swiftly complete the sintering in the secondary flocculation process is a course to be taken to reduce residual bubbles. Thus, it is preferable that the transition from the primary flocculation process to the secondary flocculation process should be advanced in the whole sintered body with as small a time lag as possible. However, it is not easy to undergo the transition from the primary flocculation process to the secondary flocculation process in the whole sintered body without time lag. Then, the present inventors decided to complete the primary flocculation process and the first half of the secondary flocculation process by heating at a rather low temperature in the temperature limits just below the starting temperature of foaming (about 850° C.) for a relatively long period of time, and then, to complete the second half of the secondary flocculation process by heating at a temperature in the vicinity of the temperature at which a solid solution starts to be formed (980° C.) for a relatively short period of time. They found out that this was an excellent sintering method by which the degree of progress of sintering in the whole sintered body could be made uniform with formation of few foaming gases. The proper range of the sintering conditions is described below. As preliminary sintering, a molded body was held at 600° C. for (hours in an air atmosphere. The preliminary sintered body was about 212 mm×212 mm×t72 mm in size and a cuboid shape with two square surfaces on the top and bottom. The heating atmosphere was set to be a nitrogen gas atmosphere. Preliminary tests concerning each of heating and cooling conditions in the heating pattern were conducted in three cases of the required time of 3, 6 and 9 hours. As a result, in the case of 3 hours, small cracks occurred in the sintered body, while in the other cases, the results were good. Therefore, the required time was set to be 6 hours. The heating atmosphere was continuously set to be the nitrogen gas atmosphere. The heating temperature was varied in the range of 700° C. to 1250° C., and in eleven cases of the holding time of 2, 3, 4, 5, 6, 8, 10, 12, 14, 16 and 18 hours, the tests were conducted. As shown in FIG. 3, in the case of 750° C. or less, the compactness was insufficient, regardless of the holding time. In the case of a holding time of 4 hours or less, the compactness was insufficient in any case other than 1100° C. On the other hand, in the case of a heating temperature exceeding 1150° C., a large number of bubbles were generated due to too fast sintering speed, regardless of the holding time, while in the case of a holding time of 16 hours or more, foaming occurred in part of the periphery of the sintered body, leading to getting out of shape in appearance. Reviewing the results in FIG. 3 in detail, in the case of heating at 850° C., the sintering state was good with a holding time of 8 hours or more, while slightly insufficient with 6 hours or less. In the case of 900° C., the sintering state was good with a holding time of 5 hours or more, while slightly insufficient with 4 hours or less, and beyond decision of quality with 16 hours or more. In the case of 950° C., the sintering state was good with a holding time of 5 to 14 hours, while slightly insufficient with 4 hours or less, and beyond decision of quality with 15 hours or more. In the case of 1000° C. the sintering state was good with a holding time of 5 to 12 hours, while slightly insufficient with 4 hours or less, and much foaming with 14 hours or more. In the case of 1100° C., the sintering state was good with a holding time of 3 to 8 hours, while much foaming with 10 hours or more. In the case of 1150° C., much foaming was seen with any holding time. In the case of 1200° C., the sintering was insufficient with a holding time of 3 hours or less, while beyond decision of quality or poor because of too much melting with 4 hours or more. When the heating temperature was a comparatively low temperature of 800° C. to 850° C., the sintering was slightly insufficient when the holding time was between 4 and 8 hours. However, since the main sintering step was divided into two, the first main sintering step and the following second main sintering step in the present invention, that was regarded as being good as the evaluation in the first main sintering step. In order to examine the relationship among the heating temperature, the bulk density of the sintered body and the mass decrease TG thereof corresponding to a yield, using the same preliminary sintered body as the above, the holding time was set to be 6 hours, and the heating temperature was varied within the range of 600° C. to 1300° C. As a result, in the case of a heating temperature of 900° C., the bulk density was approximately 2.90 g/cm3. Like the results shown in FIG. 3, the sintered body having a bulk density of that or more could be judged to have sufficient compactness without troubles such as losing its shape in the treatment of the second step. On the other hand, in the case of a heating temperature of 1150° C. or more, the mass decrease TG was −0.8% or more, and the decrease of the yield was remarkable. When the heating temperature was more than that, foaming occurred in part of the periphery of the sintered body, resulting in a trouble such as getting out of shape in appearance. From the results shown in FIG. 3, it could be judged that, if the sintering step was one of the heating steps, the heating temperature of 850° C. to 1100° C. and the holding time of 3 to 14 hours (high-temperature short-time heating, or low-temperature relatively-long-time heating within these ranges) were proper conditions. What was clarified here is, when relatively long time heating, such as at 900° C. for 16 hours or more, at 1000° C. for 14 hours or more, or at 1100° C. for 10 hours or more, was conducted, the quantity of bubbles was large and part of those gathered and was growing to a large bubble. It was confirmed that such sintered body involved defects which would cause cracks to occur from a large bubble portion or cause splitting in the next mechanical processing step. From these situations, the present inventors decided as a fundamental plan of the main sintering step that foaming should be suppressed as much as possible, as well as the sintering reaction should be allowed to sufficiently make progress, leading to producing a sintered body having a good processability in the subsequent mechanical processing step. The fundamental plan at the beginning of the main sintering step was that forming should be tried not to occur as much as possible, that the sintering should be allowed to make slow progress, and that the difference between the degree of progress of the inner portion of the sintered body and that of the periphery portion thereof should be kept as small as possible. The heating temperature limits were decided to be within the range of 800° C. to 1100° C. as described above. Since the temperature at which foaming became noticeable was about 850° C., the heating temperature at the beginning of the main sintering step was set to be below 850° C., 840° C. or less, that is, from 750° C. to 840° C., and the holding time was set to be 5 to 12 hours. Heating at the next stage of enhancing the sintering reaction of the sintered body was decided to be conducted in the temperature limits in the vicinity of 980° C. at which a solid solution started to be formed, that is, 900° C. to 1100° C. within the above proper conditions. The holding time was decided to be made as short as possible in order to enhance the sintering reaction and suppress foaming. Judging from the results in FIG. 3 and the below-described examples and comparative examples, the holding time was decided to be 0.5 to 3 hours, since the enhancement of the sintering reaction was poor in the case of less than 0.5 hour, and too many bubbles were formed in the case of 4 hours or more. When the atmospheric gas was changed to helium, the results were not different from those in the case of nitrogen gas. At less than 800° C., the compactness was not sufficient regardless of the holding time, and in the case of a holding time of 4 hours or less, the compactness was insufficient. In the case of 1110° C. or more, the sintering speed was too fast regardless of the holding time as is the case with the nitrogen gas, resulting in occurrence of many bubbles, and in the case of a holding time of 4 hours or more, because of foaming, the appearance got out of shape in some cases. In order to examine the relationship among the heating temperature, the bulk density of the sintered body and the mass decrease TG thereof corresponding to a yield, using the same preliminary sintered body as the above, the holding time was set to be 6 hours, and the heating temperature was varied within the range of 600° C. to 1300° C. As a result, as is the case with the nitrogen gas, the bulk density was approximately 2.90 g/cm3 at a heating temperature of 900° C. It was judged that the sintered body having a bulk density of that or more would not lose its shape in the treatment of the subsequent step, as is the case with the nitrogen gas, resulting in having sufficient compactness. On the other hand, at a heating temperature of 1110° C. or more, the mass decrease TG was −0.8% or more and the yield decrease was remarkable. And foaming occurred in part of the periphery of the sintered body, resulting in a trouble such as getting out of shape in appearance. Therefore, it was judged that the heating temperature of 900° C. to 1100° C. and the holding time of 0.5 to 2.5 hours were proper conditions. Furthermore, since in the case of a heating temperature of 950° C. to 1050° C. and a holding time of 0.5 to 3 hours, defects such as cracks were difficult to occur when providing the sintered body to the mechanical processing, resulting in good mechanical processability, it was judged that the heating temperature of 950° C. to 1050° C. and the holding time of 0.5 to 3 hours were desirable. Therefore, as proper heating conditions of the main sintering step in a helium gas atmosphere, as is the case with the above nitrogen gas atmosphere, the proper condition of the first heating of the main sintering step was at 750° C. to 840° C. for a holding time of 5 to 12 hours, while that of the second heating thereof was at 900° C. to 1100° C. for a holding time of 0.5 to 3 hours. The inert gas is not limited to nitrogen and helium. In the case of argon or neon, the same effects can be obtained. Since neon is expected to have a high resolution degree or a scattering characteristic in the parent of this sintered body, like helium, the defoaming phenomenon can be further promoted and an improvement thereby equal to or more than that by helium can be expected. When the heating conditions of the main sintering step were within the proper range, the state of the completed sintered body was wholly compact in any case, and no clearly defective portion such as a locally large void or a crack seen in a general ceramic sintered body could be found. The present invention is more specifically described below by reference to Examples, but the present invention is not limited to these Examples. First, a typical characteristic evaluation test conducted on sintered bodies in the Examples is described. In order to evaluate the neutron moderation performance, a beam emitted from an accelerator is allowed to collide with Be being a target, and by nuclear reaction, high-energy neutrons (fast neutrons) are mainly generated. Using Pb and Fe each having a large inelastic scattering cross section as a moderator in the first half of moderation, the neutrons are moderated to some extent (approximately up to 1 MeV) while suppressing the attenuation of the number of neutrons. These are irradiated to a moderator to be evaluated (a moderator in the second half of moderation), and by examining the neutrons after moderation, the moderator is evaluated. The measurement of the contents of the neutrons (hereinafter, referred to as a ‘neutron flux’) was conducted according to the method devised by the present inventors (the above Non-Patent Document 3). The total thickness of each moderator in the second half to be evaluated was set to be 320 mm, and two kinds of moderators, MgF2 and CaF2 were selected. Furthermore, the case wherein MgF1 and CaF2 were superposed on each other (the total thickness was set to be 320 mm) was also evaluated. What was evaluated here is how many fast neutrons having high possibilities of adversely influencing a patient remained in the neutrons moderated by the moderator. The results are shown in FIG. 4. Here, as MgF2 and CaF2, compact sintered bodies thereof each having a relative density (100×(actual density)/(true density), unit %) of 95±2% were used. From FIG. 4, as the layer thickness of MgF2 increases as a moderator, (goes in a right direction on the axis of abscissas), the number of fast neutrons having possibilities of adversely influencing a patient decreases. In the case of MgF2 only, compared with the case of CaF2 only, the number thereof could be reduced to about ⅓ to ¼. It can be known that MgF2 is superior as a moderator. Using the above evaluation device, in the same manner, how the relative density (i.e. the compactness) of MgF2 influences the moderation performance was examined. As a moderator, only MgF2 sintered bodies, having a relative density of 90% to 97% were used. The results are shown in Table 1. The higher relative density the sintered body had, the less the quantity of mixed fast neutrons was, leading to obtaining excellent performance as a moderator. The sintered bodies having a relative density of less than 92% were varied in moderation performance. Some unstable cases, wherein the quantity of mixed fast neutrons suddenly increased, or the epithermal neutron dose drastically increased, were noticed. This appears to be because insufficient compactness resulted in insufficient moderation performance, or with the formation of open pores, impurities were mixed in the sintered body in molding thereof, resulting in irregular influence on the moderation performance. In order to allow the sintered body to present stable moderation performance, it was found that the relative density of 92% or more, that is, the bulk density of 2.90 g/cm3 or more was required. As evaluation indexes of mechanical strength, bending strength and Vickers hardness were adopted. The samples for bending strength, having a size of 4 mm×46 mm×t3 mm with the upper and lower surfaces optically polished were prepared according to JIS C2141, and tested according to the three-point bending test JIS R1601. To obtain the Vickers hardness, using ‘Micro Hardness Tester’ made by Shimadzu Corporation, an indenter having a load of 100 g was pressed for 5 seconds of loading time so as to measure the diagonal length of the impression, which was converted into hardness.Hardness=0.18909×P/(d)2 Here, P: load (N) and d: diagonal length of impression (mm) A high-purity MgF2 raw material (mean particle diameter of 20 μm and purity of 99.9% by weight or more) was pulverized using the pot mill and alumina balls described in the ‘Mode for Carrying Out the Invention’, to a high-purity MgF2 powder (mean particle diameter of 1.2 μm and purity of 99.9% by weight or more). To the powder, a carboxymethyl cellulose (CMC) solution was added as a sintering aid in the proportion of 0.2% by weight to 100 of the MgF2 powder, and mixed in the pot mill for 12 hours so as to be a starting raw material. This starting raw material was filled into a mold form (mold size of 220 mm×220 mm×H150 mm) using a uniaxial press device and compressed at a uniaxial press pressure of 10 MPa to be molded. This press molded body (size of about 220 mm×220 mm×t85 mm), which was put into a thick vinyl bag and sealed after deairing, was put into a molding part (inside size: inside diameter 350 mm×H120 mm) of a cold isostatic pressing (CIP) device. Clean water was filled into the space between the vinyl bag with this press molded body therein and the molding part of the CIP device, and isostatic pressing was conducted at a molding pressure of 20 MPa, resulting in a CIP molded body (size of about 215 mm×215 mm×t75 mm). Preliminary sintering at 600° C. for 5 hours in an air atmosphere was conducted on this molded body, resulting in a preliminary sintered body having a size of about 208 mm×208 mm t72 mm. This preliminary sintered body was heated from room temperature to 830° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 6 hours. It was then raised to 1000° C. at a fixed rate for 2 hours and held there for 1 hour. Heating was then stopped, and the temperature was lowered by self-cooling (furnace cooling) for about 20 hours to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The bulk density of the sintered body was calculated at 3.05 g/cm3 (relative density of 96.8%) from the rough size (193 mm×193 mm×t62 mm) and the weight thereof. The sintering state was good. Since the appearance of the sintered body was a square form in a plan view, the ‘bulk density’ here was obtained by a method wherein the bulk volume was calculated from the measured two sides of the square and thickness, and the weight separately measured was divided by the bulk volume. This also applied to the following. Using samples taken from this sintered body, by the method shown in the Non-Patent Document 3, evaluation tests of neutron moderation performance and characteristics of every kind were conducted. The results are shown in Table 1. This also applied to the following Examples and Comparative Examples. Concerning the neutron moderation performance, the decrease of epithermal neutron dose was slightly small compared with CaF2 as a comparative material, but the dose of fast neutrons having high possibilities of adversely influencing a patient was reduced to about ¼, so that it was found that MgF2 had an excellent moderation performance. As shown in Table 2, the other mechanical strengths were also good without problems. Using the same starting raw material as in the above Example 1, preliminary sintering at 550° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 208 mm×208 mm×t73 mm. This preliminary sintered body was heated from room temperature to 750° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 9 hours. It was then raised to 920° C. at a fixed rate for 2 hours and held there for 2 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 195 mm×195 mm×t64 mm, the bulk density thereof was 2.90 g/cm3 (relative density of 92.1%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 600° C. for 8 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 206.5 mm×207 mm×t71 mm. This preliminary sintered body was heated from room temperature to 840° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 12 hours. It was then raised to 1080° C. at a fixed rate for 2 hours and held there for 1 hour. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 192 mm×192 mm×t61 mm, the bulk density thereof was 3.00 g/cm3 (relative density of 95.2%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, this raw material was filled into the mold form of uniaxial press molding and compressed at a uniaxial press pressure of 70 MPa to be molded. Then, molding was conducted using the cold isostatic pressing (CIP) device at a molding pressure of 40 MPa, so as to obtain a molded body (size of about 213 mm×214 mm×t74 mm). Preliminary sintering at 600° for 10 hours in an air atmosphere was conducted on this molded body to obtain a preliminary sintered body of 204.5 mm×205 mm×t70 mm. This preliminary sintered body was heated from room temperature to 830° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 12 hours. It was then raised to 1080° C. at a fixed rate for 2 hours and held there for 1 hour. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 190.5 mm×191 mm×t60 mm, the bulk density thereof was 3.07 g/cm3 (relative density of 97.5%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 580° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 206 mm×206 mm×t70.5 mm. This preliminary sintered body was heated from room temperature to 800° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 12 hours. It was then raised to 920° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 191.0 mm×191.5 mm×t62 mm, the bulk density thereof was 3.02 g/cm3 (relative density of 95.9%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 580° C. for 7 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 207 mm×207 mm×t71.5 mm. This preliminary sintered body was heated from room temperature to 830° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 12 hours. It was then raised to 1000° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 192.5 mm×192.5 mm×t63 mm, the bulk density thereof was 2.99 g/cm3 (relative density of 94.9%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 580° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 206 mm×206 mm×t70.5 mm. This preliminary sintered body was heated from room temperature to 840° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 8 hours. It was then raised to 980° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 193 mm 193.5 mm×t62.5 mm, the bulk density thereof was 2.96 g/cm3 (relative density of 94.0%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 560° C. for 8 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 207 mm×206 mm×t70.5 mm. This preliminary sintered body was heated from room temperature to 8409° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 5 hours. It was then raised to 920° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 194.5 mm×194.5 mm×t64 mm, the bulk density thereof was 2.91 g/cm3 (relative density of 92.4%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 580° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 205 mm×205 mm×170.5 mm. This preliminary sintered body was heated from room temperature to 840 t at a fixed rate for 6 hours in a helium gas atmosphere, and the temperature was held there for 8 hours. It was then raised to 980° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 192.5 mm×192.5 mm×t62 mm, the bulk density thereof was 3.00 g/cm3 (relative density of 95.2%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics oft every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 560° C. for 6 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 207 mm×207 mm×t70.5 mm. This preliminary sintered body was heated from room temperature to 770° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 10 hours. It was then raised to 900° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 194.5 mm×194.5 mm×t64 mm, the bulk density thereof was 2.90 g/cm3 (relative density of 92.1%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 550° C. for 8 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 207 mm×207 mm×t70 mm. This preliminary sintered body was heated from room temperature to 790° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 6 hours. It was then raised to 940° C. at a fixed rate for 2 hours and held there for 1.5 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 194.5 mm×194.5 mm×t64 mm, the bulk density thereof was 2.91 g/cm (relative density of 92.4%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 550° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 208 mm×208 mm×t73 mm. This preliminary sintered body was heated from room temperature to 750° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 9 hours. It was then raised to 920° C. at a fixed rate for 2 hours and held there for 2 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 195 mm×195 mm×t64 mm, the bulk density thereof was 2.90 g/cm3 (relative density of 92.1%), and the sintering state was good. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of low mechanical strength. Using the same starting raw material as in the above Example 1, preliminary sintering at 530° C. for 5 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 209 mm×209 mm×t76 mm. This preliminary sintered body was heated from room temperature to 740° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 4 hours. It was then raised to 890° C. at a fixed rate for 2 hours and held there for 2 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 198 mm×198 mm×t68 mm, the bulk density thereof was 2.80 g/cm3 (relative density of 88.9%), and the sintering state was obviously porous and inconvenient, leading to a problem in handling. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of unmeasurably low mechanical strength. Using the same starting raw material as in the above Example 1, preliminary sintering at 550° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 208 mm×208 mm×t73 mm. This preliminary sintered body was heated from room temperature to 750° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 9 hours. It was then raised to 880° C. at a fixed rate for 2 hours and held there for 1.5 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 197 mm×196 mm×t67 mm and the bulk density thereof was 2.88 g/cm3 (relative density of 91.4%). The sintering state was good in appearance, but at the stage of grinding wherein the sintered body was finished using a grinder, a phenomenon that a grinding fluid was absorbed into the sintered body was recognized. Therefore, the microstructure of the inside of the sintered body was examined in detail. As a result, it was clarified that a large number of open pores were formed, resulting in insufficient sintering. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of low mechanical strength. Using the same starting raw material as in the above Example 1, preliminary sintering at 600° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 208 mm×208 mm×t73 mm. This preliminary sintered body was heated from room temperature to 840° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 8 hours. It was then raised to 1150° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 196.5 mm×197 mm×t68 mm and the bulk density thereof was 2.87 g/cm3 (relative density of 91.1%). The sintering state was porous. When examining the microstructure of the inside of the sintered body, the structure was not compact and a trace of violent foaming resulting in porosity was observed. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of low mechanical strength. Using the same starting raw material as in the above Example 1, this raw material was filled into a mold form (mold size of 220 mm×220 mm×H150 mm) using a uniaxial press device, and compressed at a uniaxial press pressure of 4 MPa to be molded. This press molded body (size of about 220 mm×220 mm×t85 mm) was put into a thick vinyl bag, and sealed after deairing. That was put into a molding part (inside size: inside diameter 350 mm×H120 mm) of a cold isostatic pressing (CIP) device. Clean water was filled into the space between the vinyl bag with this press molded body therein and the molding part of the CIP device and isostatic pressing was conducted at a molding pressure of 4 MPa, resulting in a CIP molded body (size of about 218 mm×218 mm×t75 mm). Preliminary sintering at 550° C. for 5 hours in an air atmosphere was conducted on this molded body, so as to obtain a preliminary sintered body of about 211 mm×211 mm×t73 mm. This preliminary sintered body was heated from room temperature to 740° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 6 hours. It was then raised to 900° C. at a fixed rate for 2 hours and held there for 1 hour. Heating was then stopped, and the temperature was lowered by self-cooling (furnace cooling) for about 20 hours to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The bulk density of the sintered body calculated from the rough size (199 mm×199 mm×t68 mm) and the weight thereof was 2.86 g/cm3 (relative density of 90.8%). The sintering state was slightly porous. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of low mechanical strength. Using the same starting raw material as in the above Example 1, this raw material was filled into a mold form (mold size of 220 mm×220 mm×H150 mm) using a uniaxial press device, and compressed at a uniaxial press pressure of 10 MPa to be molded. This press molded body (size of about 220 mm×220 mm×t851 nm) was put into a thick vinyl bag, and sealed after deairing. That was put into a molding part (inside size: inside diameter 350 mm×H120 mm) of a cold isostatic pressing (CIP) device. Clean water was filled into the space between the vinyl bag with this press molded body therein and the molding part of the CIP device and isostatic pressing was conducted at a molding pressure of 20 MPa, resulting in a CIP molded body (size of about 215 mm×215 mm×t75 mm). Preliminary sintering at 500° C. for 4 hours in an air atmosphere was conducted on this molded body so as to obtain a preliminary sintered body of about 211 mm×211 mm×t72 mm. This preliminary sintered body was heated from room temperature to 730° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 5 hours. It was then raised to 900° C. at a fixed rate for 2 hours and held there for 1 hour. Heating was then stopped, and the temperature was lowered by self-cooling (furnace cooling) for about 20 hours to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The bulk density of the sintered body calculated from the rough size (198 mm×198 mm×t68 mm) and the weight thereof was 2.85 g/cm3 (relative density of 90.5%). The sintering state was insufficient and slightly porous. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of low mechanical strength. Using the same starting raw material as in the above Example 1, this raw material was filled into a mold form (mold size of 220 mm×220 mm×H150 mm) using a uniaxial press device, and compressed at a uniaxial press pressure of 4 MPa to be molded. This press molded body (size of about 220 mm×220 mm×t85 mm) was put into a thick vinyl bag, and sealed after deairing. That was put into a molding part (inside size: inside diameter 350 mm×H120 mm) of a cold isostatic pressing (CIP) device. Clean water was filled into the space between the vinyl bag with this press molded body therein and the molding part of the CIP device and isostatic pressing was conducted at a molding pressure of 4 MPa, resulting in a CIP molded body (size of about 218 mm×218 mm×t75 mm). Preliminary sintering at 550° C. for 5 hours in an air atmosphere was conducted on this molded body, so as to obtain a preliminary sintered body of 211 mm×211 mm×t72.5 mm. This preliminary sintered body was heated from room temperature to 740° C. at a fixed rate for 6 hours in a helium gas atmosphere, and the temperature was held there for 6 hours. It was then raised to 900° C. at a fixed rate for 2 hours and held there for 1 hour. Heating was then stopped, and the temperature was lowered by self-cooling (furnace cooling) for about 20 hours to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The bulk density of the sintered body calculated from the rough size (198 mm×198.5 mm×t67.5 mm) and the weight thereof was 2.89 g/cm3 (relative density of 91.7%). The sintering state was slightly porous. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of low mechanical strength. [Comparative Material: CaF2] A high-purity CaF2 raw material (mean particle diameter of 20 μm and purity of 99.9% by weight or more) was pulverized using the pot mill and alumina balls to a high-purity CaF2 powder (mean particle diameter of 1.4 μm and purity of 99.9% by weight or more). To the powder, a carboxymethyl cellulose (CMC) solution was added as a sintering aid in the proportion of 0.2% by weight to 100 of the CaF2 powder, and mixed in the pot mill for 12 hours to be a starting raw material. This raw material was filled into a mold form (mold size of 220 mm×220 mm×H150 mm) using a uniaxial press device and compressed at a uniaxial press pressure of 10 MPa to be molded. This press molded body (size of about 220 mm×220 mm×t85 mm), which was put into a thick vinyl bag and sealed after deairing, was put into a molding part (inside size: inside diameter 350 mm×H120 mm) of a cold isostatic pressing (CIP) device. Clean water was filled into the space between the vinyl bag with this press molded body therein and the molding part of the CIP device, and isostatic pressing was conducted at a molding pressure of 20 MPa, leading to a CIP molded body (size of about 215 mm×215 mm×t75 mm). Preliminary sintering at 600° C. for 6 hours in an air atmosphere was conducted on the molded body, so as to obtain a preliminary sintered body having a size of about 208 mm×28 mm×t72 mm. This preliminary sintered body was heated from room temperature to 870° C. at a fixed rate for 6 hours in a nitrogen atmosphere, and the temperature was held there for 6 hours. It was then raised to 1100° C. at a fixed rate for 2 hours and held there for 1 hour. Heating was then stopped, and the temperature was lowered by self-cooling (furnace cooling) for about 20 hours to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The bulk density of the CaF2 sintered body was calculated at 3.05 g/cm3 (relative density of 95.9%, and the true density of CaF2 is 3.18 g/cm3) from the rough size (193 mm×193 mm×t62 mm) and the weight thereof. The sintering state was good. As the evaluation results, a sintered body in a compact sintering state could be obtained and the mechanical strength was sufficient as shown in Table 2. However, since a large quantity of fast neutrons remained, there was a big problem of the moderation performance to neutrons left. This result indicated that a CaF2 sintered body was inferior to a MgF2 sintered body in characteristics as a moderator even if the CaF2 sintered body was sufficiently compact. It is possible to be used as a moderator to restrict the radiation velocity of radioactive rays of every kind such as neutrons.
	abstract	A support grid for a nuclear fuel assembly, the fuel rod assembly having a generally cylindrical fuel rod with a diameter, wherein the support grid includes a frame assembly having a plurality of generally uniform cells, each the cell having at least one wall and a width and at least one generally cylindrical tubular member having a cell contact portion with a greater diameter and at least one helical fuel rod contact portion with a lesser diameter, the cell contact portion and the fuel rod contact portion joined by a transition portion, the greater diameter being generally equivalent to the cell width, and the lesser diameter being generally equivalent to the fuel rod diameter such that a fuel rod disposed in the tubular member would engage the inner diameter. Wherein the least one tubular member disposed in one cell of the plurality of generally square cells so that the cell contact portion engages the at least one cell sidewall.
050376012	summary	BACKGROUND OF THE INVENTION The glass-pool, air-cycle nuclear power plant of this invention is designed as an isolated system that requires minimal monitoring and is of a "walk-away" type, that is, one that can be shut down and decommissioned without any external intervention other then the poisoning of the nuclear reaction. In such event, the containment structure that contains the glass matrix pool and reaction core solidifies into a glass solid that can remain in place or be removed to a storage site. Recent disasters and near disasters in the operation of existing nuclear power plants of large size have required a reevaluation of the technology of nuclear power plant design. Far greater attention has been placed on power plants that are considered "passively-safe," that is, which do not require the intervention of an operator during a nuclear crisis in order to return the plant to a safe operating condition. The expense and complexity of current and future designs of light water reactor plants have required the nuclear industry to rethink its nuclear energy goals and have generated renewed interest in smaller, modular type plants that operate without the use of water as a coolant or as a steam generating medium. Renewed interest in more inherently safe designs such as liquid sodium systems, including static designs that do not require sodium pumps, such as that proposed in my prior patent, entitled "Nuclear Power Plant With On-Site Storage Capabilities," U.S. Pat. No. 4,313,795, issued Feb. 2, 1982. In that patent there is disclosed a nuclear reactor power plant having a gas cycle that utilizes superheated steam in its superheated state throughout the cycle. The use of a gas cycle reactor avoids a motive substance that must undergo a phase change. The use of a substance that has a phase change between liquid and gas, can typically result in emergency conditions. For example, when quantities of water contact high temperature core material the explosive reaction releases large volumes of contaminated steam. This is the heart of the traditional disaster scenario. Operating the reactor core in the very material that is to constitute its entombment on decommissioning, provides an attractive safety feature that other plants of advanced design appear to lack. This feature can provide a attractive solution to the problem of decommissioning and disposal of reactor cores. The use of new reactor fuel sources utilizing thorium/uranium.sup.233 in encapsulated fuel pellets with neutron moderation and containment by graphite shells and casings, provides the basis for advanced designs of walk-away nuclear power plants that require little or no monitoring during the life of operation of the plants. By use of smaller modular systems that are standardized with lower power goals which do not include failure prone internal or external liquid circulation pumps, the goal of a passively-safe or a walk-away nuclear power plant can realistically be achieved. One of the crucial problems facing the nuclear power industry in the United States is the fact that, all of the nuclear plants that have been constructed to date are different from one another. In addition to the huge capital cost, large scale, custom power plants cause difficulty in staffing and safe monitoring of plant operation. Furthermore, at the time of decommissioning, each plant must be considered as a separate entity for which a decommissioning plan must be devised that in many cases can result in decommissioning costs that exceed the original cost of construction. With a lower ultimate power goal for each plant, the system design can be standardized. By simply multiplying the number of identical plants, any desired greater power capacity can be obtained. Given a substantial flexibility in power rating and design, small inexpensive plants under one megawatt can be placed in operation to test operating parameters over a larger number of units at minimal financial and safety risk. The glass-pool, aircycle, nuclear power plant described and claimed herein resolves many of the current problems in the design of a safe power plant that utilizes fissionable nuclear materials that will not adversely impact the environment during operation or after shut-down. SUMMARY OF THE INVENTION This invention relates to a nuclear power plant and in particular to a glass-pool, gas-cycle plant having a thorium/uranium.sup.233 reactor in a glass matrix that is designed to constitute the heat dissipating core during operation, and, the inert tomb upon deactivation. The nuclear power plant of this invention couples a safe thermal source with a safe conversion means for converting thermal energy of a nuclear reaction to useful power, for example, electricity. Because the design of the power plant is directed to lower power goals, the thermal energy can also be converted directly to mechanical work useable on-site, for example, in pumping irrigation water. The design concept is such that the plant can be operated in an isolated environment as a self-contained system that requires no external support to either monitor operations or respond to an emergency situation. Key to the isolated system concept is the combination of an energy core that is immersed in a glass matrix that provides a heat sink to allow operation of the core at maximum temperature with the molten pool becoming the entombment matrix on solidification. The glass matrix includes in its composition fertile thorium material that is reduced in proportion to inert silicates as the distance from the central fissile core increases. During nuclear reaction, the glass matrix is in a molten state with a viscosity that increases as the distance from the core increases. The core and glass pool are encapsulated in a containment structure that is of a neutron reflecting substance such as graphite. The containment structure has a thermally conductive casing that provides a heat exchange from the glass-pool, thermal sink to a closed-cycle gas system. The other primary feature that insures the safety of the device is the use of a power extraction system that has a drive medium that does not undergo a phase change from liquid to gas. The use of a liquid to gas drive medium has been a significant contributor to the safety problems of prior art devices. In the preferred embodiment the gas is simply air. A unique divided cycle enables the effective use of air to comprise the motive force in an enclosed system. The unique, dual-path, air-cycle system utilizes a common compressor for each of two paths, with the compressor outlet coupled to a first path that communicates with the nuclear thermal source and a second path that communicates with an intercooler before being supplied to a turbine. Preferably, the compressed air from both sources drives a common turbine with the air from both sources combining in a common collector where the divergent temperatures are effectively moderated for return to the compressor. The nuclear reaction is preferably accomplished by utilizing a thorium/U.sup.233 breeding reaction in a glass matrix that on activation provides both a starting fissile material and a fertile feed material to continue a long term nuclear reaction preferably without the addition of more fuel. The life of the reaction can be determined at the time the plant is commissioned. At the time of decommissioning, when the fuel reaction is diminishing to the point that adversely affects the thermodynamic efficiency of the plant, the reduced-level, nuclear reaction is finally poisoned with a probe of a neutron absorbing material such as boron, allowing the glass matrix and core to cease reaction and gradually cool to a solid glass block. The entire core and encapsulation structure can either be removed for easy transportation as a vitrified solid to a central storage location, or can be entombed on site. If entombed on site, the volume of open space in the heat exchange area, between the pressure vessel and the encapsulation structure can be filled with a solidifying substance such as concrete, doped with a neutron absorber such that the outer containment structure totally entombs the decommissioned reactor capsule and shields any low level residual radiation that may be emitted from the core. These and other features of the preferred embodiment of this invention will be considered in greater detail in the detailed description of the preferred embodiments that follows.
	claims	1. An optical element comprising a substrate and at least a pair of alternate layers provided on the substrate, the alternate layers each having an Mo layer and an Si layer,wherein the Mo layer contains 90% or more of 98Mo and the Si layer contains 99% or more of 23Si. 2. An optical element comprising a substrate and at least a pair of multilayer films of a four-layer structure provided on the substrate, each of the at least the pair of the multilayer films having an Si/B4C/Mo/B4C structure in this order from the substrate,wherein the Mo layer contains 90% or more of 98Mo, the Si layer contains 99% or more of 23Si and the B4C layer contains 99% or more of 11B. 3. An X-ray mirror comprising the optical element according to claim 1. 4. An X-ray mirror comprising the optical element according to claim 2.
047479949	description	DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention is illustrated in FIG. 1 which utilizes a switchgear mechanism 10 as a reactor trip breaker RTB. The switchgear mechanism 10 receives power from an AC power bus 12 in a reactor control system and supplies power to a rod positioner 14 which controls the position of control rods in a pressurized light water nuclear reactor. The switchgear 10 can be a conventional switchgear mechanism, such as Westinghouse Part No. DS206 or DS4l6. Such a switchgear mechanism 10 conventionally includes an undervoltage trip coil 16 which is de-energized while the shunt trip coil 18 is energized, when an undesirable condition is detected in the nuclear reactor. According to the present invention, the shunt trip coil 18 in the switchgear 10 is provided power via a potential transformer 20, such as a Westinghouse type PXA, style No. 592A78lG0A, and a rectifier 22 which may comprise diodes 28, each diode may be a 1N3990, available from Westinghouse Electric Corporation. The shunt trip coil 18 is energized by activation of either a manual trip switch 24 or an automatic trip switch 26 connected to an automatic protection system. Since the potential transformer 20 is supplied with power by the switchgear 10, when the shunt trip coil 18 is energized to interrupt the supply of power to the rod positioner 14, the supply of power to the potential transformer 20 is also interrupted, thereby de-energizing the shunt trip coil 18. The rectifier 22 outputs a DC voltage which can be monitored to determine the ability of the trip coil control system to activate the shunt trip coil 18 and the condition of the power supplied to the rod positioner 14. The DC voltage will have a ripple, as illustrated in FIG. 1, if just three diodes 28 are used in the rectifier 22. One embodiment of the present invention includes a power monitoring device 30 to monitor the DC voltage output by the rectifier 22. The power monitoring device 30 comprises a voltage/optical converter 32, such as a Hewlett-Packard # HFBR-1201, which provides isolation between the trip coil control system and monitoring devices in the reactor control system. The voltage/optical converter 32 outputs a light signal which can be tranmitted over an optical cable 34, such as a Hewlett-Packard # HFBR-300. The light signal generated by a simple voltage/optical converter 32 is sufficient to transmit information regarding whether the rectifier 22 is outputting a DC voltage and further provides an indication regarding the condition of the power supply to the rod positioner 14, such as missing phases in the AC power. If additional information, such as voltage level, is desired, an analog/digital converter 36 can be added to the monitoring device 30. The monitoring device 30 may also include additional components at a remote distance from the switchgear 10. Such components are illustrated in FIG. 2 as receiving the light signal via the optical cable 34. An optical/voltage converter 40, such as a Hewlett-Packard # HFBR-2201, converts the light signal back into a DC voltage which is supplied to a microprocessor board 42, such as an Intel 88/40. The microprocessor board 42 includes a signal conditioner 44, microprocessor 46 and an output interface 48 for interfacing with other devices 50 in the reactor control system. Each reactor trip breaker 10 in a conventional reactor control system may be connected to several signal processing units such as the microprocessor board 42 illustrated in FIG. 2. With the addition of more voltage optical voltage/converters 32 to receive the output of the rectifier 22, several microprocessor boards 42 can be connected to monitor a single reactor trip breaker 10. The many features and advantages of the present invention are apparent from the detailed specification, and thus it is intended by the appended claims to cover all such features and advantages of the control system which fall within the true spirit and scope of the invention. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation illustrated and described, accordingly, all suitable modifications and equivalents may be resorted to, falling within the scope and spirit of the invention.
	claims	1. A segmented waste rod comprising:a plurality of burnt rod segments,the rod segments being removably mated to each other in an axial direction,the rod segments being individually cladded, andthe rod segments forming a continuous multi-segment waste rod; andat least one of the rod segments being a waste rod segment containing at least one piece of non-fuel waste sealed within the waste rod segment after harvesting isotopes produced in the waste rod segment in a nuclear reactor from the waste rod. 2. The segmented waste rod of claim 1, wherein the at least one piece of waste includes material from a harvested burnt rod segment. 3. The segmented waste rod of claim 2, wherein the at least one piece of waste is selected from the group consisting of a cladding, a container assembly, a male end plug, and a female end plug. 4. The segmented waste rod of claim 2, wherein the segmented waste rod has a length and outer diameter substantially similar to the burnt segmented rod. 5. The segmented waste rod of claim 1, wherein at least one of the rod segments not containing waste contains spent nuclear fuel. 6. The segmented waste rod of claim 1, further comprising:a lower extension removably mated to a first rod segment of the plurality of rod segments at a first end of the segmented waste rod; andan upper extension removably mated to a second rod segment of the plurality of rod segments at a second end of the segmented waste rod, the upper extension and the lower extension being recycled from a burnt segmented rod. 7. The segmented waste rod of claim 1, wherein the rod segments are removably mated via a male end plug and a female end plug. 8. A method for handling nuclear waste, the method comprising:harvesting isotopes produced in a rod segment in a nuclear reactor from the rod segment;placing the waste into the rod segment so as to form a waste rod segment;sealing the waste rod segment; andplacing the waste rod segment into a segmented waste rod by axially mating the waste rod segment to at least one of an upper extension, a lower extension, a rod segment containing spent nuclear fuel, and another waste rod segment. 9. The method of claim 8, further comprising:preparing the waste for placement into the waste rod segment before placing the waste into the waste rod segment. 10. The method of claim 8, wherein the waste includes material from a harvested burnt rod segment. 11. The method of claim 10, wherein the waste includes at least one of a cladding, a container assembly, a male end plug, and a female end plug of the harvested burnt rod segment. 12. The method of claim 8, further comprising:placing the segmented waste rod into a fuel bundle. 13. The method of claim 8, wherein placing the waste into the waste rod segment includes compressing the waste into the waste rod segment. 14. The method of claim 8, wherein the sealing the waste rod segment includes welding one of a female end plug and a male end plug to an open end of the waste rod segment. 15. A method of handling waste generated from a process of harvesting isotopes from a burnt segmented fuel rod, the method comprising:rolling, cutting, and curling cladding from a rod segment harvested for isotopes;crushing at least one end plug removed from the rod segment harvested for isotopes;placing the cladding, at least one end plug, a container assembly removed from the rod segment harvested for isotopes, and a cap of the container assembly into a waste rod segment;sealing the waste rod segment; andplacing the waste rod segment in the burnt segmented fuel rod in a location from which the rod segment harvested for isotopes was taken so as to form a segmented waste rod. 16. The method of claim 15, further comprising:inserting the segmented waste rod into a burnt fuel bundle in a location from which the burnt segmented fuel rod was taken.
	description	The present invention generally relates to a debris mitigation system and a lithographic apparatus that includes the debris mitigation system. More specifically, the invention relates to a debris mitigation system for trapping contaminant material coming from a debris-generating radiation source. A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. comprising part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate. In addition to EUV radiation, radiation sources used in EUV lithography tend to generate contaminant material that may be harmful for the optics and the working environment in which the lithographic process is carried out. Hence, in EUV lithography, a desire exists to limit the contamination of the optical system that is arranged to condition the beams of radiation coming from an EUV source. To this end, it is known to use a so-called rotating foil trap, for instance, as disclosed in U.S. Pat. No. 6,838,684. A typical foil trap uses a high number of closely packed foils that are aligned generally parallel to the direction of the radiation generated by the EUV source. Contaminant debris, such as micro-particles, nano-particles and ions can be trapped in walls provided by foil plates. Thus, the foil trap may function as a contamination barrier that traps contaminant material from the source. Generally, these foil traps are designed to have a sufficiently large dimension to trap virtually any contaminant particle traveling through the trap. Indeed, a large fraction of debris is captured since the velocity directions are mostly non-parallel to the foil plates so that impact of the contaminant material follows eventually. Also, smaller particles travel in typical random diffusion-like paths in which most of the particles are trapped eventually. However, a small fraction of particles travel in a direction and at a velocity that allows the particles to travel through the foil trap, which may cause undesired contamination of the optics. These are mostly micro and nanometer sized particles traveling at speeds <1000 m/s. Such particles may be stopped using a rotating foil trap. However, some of these particles have a velocity that is too high to be stopped by the rotating foil trap (typically this is the case for nanometer sized particles and for ions/fast neutrals). To improve the debris mitigating function of the foil trap, electromagnetic deflecting fields have been proposed. However, a rotating foil trap functions as a rotor in a static electromagnetic field, which may impede the function thereof and cause undesired inhibiting of the foil trap rotation. It is an aspect of the present invention to reduce the inhibiting effect of an electromagnetic field while improving the debris mitigating effect of the rotating foil trap. According to an embodiment of the invention, a debris mitigation system for trapping contaminant material coming from a debris-generating radiation source is provided. The system includes a contamination barrier constructed and arranged to rotate about an axis, and a magnet structure constructed and arranged to provide a magnetic field for deflecting charged debris from the radiation source. The magnet structure is constructed and arranged to provide a magnetic field through the contamination barrier. The magnetic field, when passing through the contamination barrier, is oriented along planes generally coinciding with the axis of rotation of the contamination barrier. According to an embodiment of the invention, a lithographic apparatus is provided. The apparatus includes a patterning device constructed and arranged to pattern a beam of radiation, a projection system constructed and arranged to project the patterned beam of radiation onto a substrate, and a debris mitigation system constructed and arranged to trap contaminant material generated by a debris-generating radiation source. The debris mitigation system includes a contamination barrier constructed and arranged to rotate about an axis, and a magnet structure constructed and arranged to provide a magnetic field for deflecting charged debris from the radiation source. The magnet structure is constructed and arranged to provide a magnetic field through the contamination barrier. The magnetic field, when passing through the contamination barrier, is oriented along planes generally coinciding with the axis of rotation of the contamination barrier. FIG. 1 schematically depicts a lithographic apparatus according to one embodiment of the invention. The apparatus comprises: an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. UV radiation or EUV radiation); a support structure (e.g. a mask table) MT constructed to support a patterning device (e.g. a mask) MA and connected to a first positioner PM configured to accurately position the patterning device in accordance with certain parameters; a substrate table (e.g. a wafer table) WT constructed to hold a substrate (e.g. a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate in accordance with certain parameters; and a projection system (e.g. a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g. comprising one or more dies) of the substrate W. The illumination system may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof, for directing, shaping, or controlling radiation. The support structure supports, i.e. bears the weight of, the patterning device. It holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions, such as for example whether or not the patterning device is held in a vacuum environment. The support structure can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The support structure may be a frame or a table, for example, which may be fixed or movable as required. The support structure may ensure that the patterning device is at a desired position, for example with respect to the projection system. Any use of the terms “reticle” or “mask” herein may be considered synonymous with the more general term “patterning device.” The term “patterning device” used herein should be broadly interpreted as referring to any device that can be used to impart a radiation beam with a pattern in its cross-section such as to create a pattern in a target portion of the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so called assist features. Generally, the pattern imparted to the radiation beam will correspond to a particular functional layer in a device being created in the target portion, such as an integrated circuit. The patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography, and include mask types such as binary, alternating phase-shift, and attenuated phase-shift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted so as to reflect an incoming radiation beam in different directions. The tilted mirrors impart a pattern in a radiation beam which is reflected by the mirror matrix. The term “projection system” used herein should be broadly interpreted as encompassing any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system”. As here depicted, the apparatus is of a reflective type (e.g. employing a reflective mask). Alternatively, the apparatus may be of a transmissive type (e.g. employing a transmissive mask). The lithographic apparatus may be of a type having two (dual stage) or more substrate tables (and/or two or more mask tables). In such “multiple stage” machines the additional tables may be used in parallel, or preparatory steps may be carried out on one or more tables while one or more other tables are being used for exposure. The lithographic apparatus may also be of a type wherein at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, e.g. water, so as to fill a space between the projection system and the substrate. An immersion liquid may also be applied to other spaces in the lithographic apparatus, for example, between the mask and the projection system. Immersion techniques are well known in the art for increasing the numerical aperture of projection systems. The term “immersion” as used herein does not mean that a structure, such as a substrate, must be submerged in liquid, but rather only means that liquid is located between the projection system and the substrate during exposure. Referring to FIG. 1, the illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus may be separate entities, for example when the source is an excimer laser. In such cases, the source is not considered to form part of the lithographic apparatus and the radiation beam is passed from the source SO to the illuminator IL with the aid of a beam delivery system comprising, for example, suitable directing mirrors and/or a beam expander. In other cases the source may be an integral part of the lithographic apparatus, for example when the source is a mercury lamp. The source SO and the illuminator IL, together with the beam delivery system if needed, may be referred to as a radiation system. The illuminator IL may comprise an adjuster for adjusting the angular intensity distribution of the radiation beam. Generally, at least the outer and/or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may comprise various other components, such as an integrator and a condenser. The illuminator may be used to condition the radiation beam, to have a desired uniformity and intensity distribution in its cross-section. The radiation beam B is incident on the patterning device (e.g., mask MA), which is held on the support structure (e.g., mask table MT), and is patterned by the patterning device. Having traversed the mask MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and position sensor IF2 (e.g. an interferometric device, linear encoder or capacitive sensor), the substrate table WT can be moved accurately, e.g. so as to position different target portions C in the path of the radiation beam B. Similarly, the first positioner PM and another position sensor IF1 can be used to accurately position the mask MA with respect to the path of the radiation beam B, e.g. after mechanical retrieval from a mask library, or during a scan. In general, movement of the mask table MT may be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which form part of the first positioner PM. Similarly, movement of the substrate table WT may be realized using a long-stroke module and a short-stroke module, which form part of the second positioner PW. In the case of a stepper (as opposed to a scanner) the mask table MT may be connected to a short-stroke actuator only, or may be fixed. Mask MA and substrate W may be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks as illustrated occupy dedicated target portions, they may be located in spaces between target portions (these are known as scribe-lane alignment marks). Similarly, in situations in which more than one die is provided on the mask MA, the mask alignment marks may be located between the dies. The depicted apparatus could be used in at least one of the following modes: 1. In step mode, the mask table MT and the substrate table WT are kept essentially stationary, while an entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e. a single static exposure). The substrate table WT is then shifted in the X and/or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C imaged in a single static exposure. 2. In scan mode, the mask table MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The velocity and direction of the substrate table WT relative to the mask table MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width (in the non-scanning direction) of the target portion in a single dynamic exposure, whereas the length of the scanning motion determines the height (in the scanning direction) of the target portion. 3. In another mode, the mask table MT is kept essentially stationary holding a programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, generally a pulsed radiation source is employed and the programmable patterning device is updated as required after each movement of the substrate table WT or in between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography that utilizes programmable patterning device, such as a programmable mirror array of a type as referred to above. Combinations and/or variations on the above described modes of use or entirely different modes of use may also be employed. FIG. 2 shows a basic configuration for a radiation system according to embodiments of the invention. In the Figure, the dashed lines represent EUV radiation 1 coming from an EUV source 2, which may be a discharge produced or a laser induced plasma source such as a tin, lithium or xenon source, which are known per se. The foil trap 3 functions as a contamination barrier for trapping contaminant material coming from the radiation source 2. To this end, the foil trap 3 is provided with a plurality of closely packed foil plates 4, typically about 100 arranged at a distance of about 0.3-5 mm (depending on radial distance). The foil plates 4 may have a length dimension in substantially the radial direction from the source 2 of about a few cm, for example. Preferably, the foil plates 4 lengths ranging from about 1.5-5 cm. Along a central axis, the source 2 may be shielded by a heat shield 5. The foil trap, also referenced as a contamination barrier, comprises a plurality of foil plates 4 positioned in respective planes which are parallel to a propagation direction of radiation 9. As is schematically indicated in FIG. 2, in the downstream direction of the radiation, a collector element 6 is present and has a converging power for collecting and converging the EUV radiation from the EUV source 2 to further EUV optics. Such a collector element 6 may generally be cylinder symmetric along a central axial direction and comprises concentrically curved shell formed reflective surfaces 7 that are stacked at a distance ranging between about 1 and 7 cm. As illustrated in FIG. 2, a magnetic field 8 may be arranged in the area between the source 2 and a foil trap 3. The magnetic field 8 may function to deflect charged particles from a trajectory that would leave the particles unhindered through the foil trap 3. However, when rotating the foil trap 3 through the magnetic field 8, the flux of magnetic field lines on the platelets 4 will change. As a result, a current may be induced, which in turn will induce a magnetic field that results in a force opposite to the force driving the foil trap 3. This may make it difficult to rotate the foil trap 3 at the desired speed. According to an aspect of the invention, a magnet structure is used to provide the magnetic field 8 through the contamination barrier 3. When passing through the contamination barrier 3 (see FIG. 3), the magnet field is oriented along planes generally coinciding with the axis of rotation 10 of the foil trap 3. Although the foil trap 3 can have any form and a magnetic flux through the foil trap 3 can be defined as a sum of fluxes passing through all constituent parts of the foil trap, in the embodiment of FIG. 2, the plates 4 are preferably oriented parallel to the magnetic field 8. In this respect, the magnetic field 8 is created so that magnetic field lines traverse the plates 4 in an axial direction, relative to the axis of rotation of the foil trap 3. In another respect, the magnetic field 8 may be provided to have magnetic field lines traversing the plates 4 in a radial direction, relative to the axis of rotation. According to another aspect of the invention, an outer magnet structure 11 is arranged providing a passage to the radiation, in addition to provide a magnetic field 8 for deflecting charged debris. The magnet structure 11 is preferably arranged to provide a magnetic field having a symmetry axis generally coinciding with the axis of rotation. In particular, the symmetry can be rotational symmetry about the symmetry axis and/or reflection symmetry in one or more planes passing through the symmetry axis. Preferably, the magnetic field 8 is provided generally invariant for a rotation of the rotating contamination barrier, that is, a rotation, less than 360° over a specified number of angles. More preferably, the magnetic field is provided generally invariant for any rotation angle of the rotating contamination barrier. In addition, another debris mitigation system may be present in this area between the source 2 and the foil trap 3, or between foil trap 3 and collector 6, for instance, using a buffer gas for thermalizing the ions coming from the EUV source. Then, the ions may be stopped by a stationary foil trap, in the same way as normal atomic debris is stopped. The magnetic field may rotate along with the foil trap 3 or may be stationary relative to that trap 3. FIG. 3 shows a further detailing of the magnetic structure 9, 11 for the magnetic field 8 shown in FIG. 2. The embodiment uses an outer magnet structure 11 and a central magnet structure 9 opposed relative to each other to provide a generally radially oriented magnetic field. In the current example, the outer magnet structure 11 is a hollow structure comprising axially opposed magnetic poles, that is, having a magnetic axis substantially parallel to the axis of rotation 10. A central magnet structure 9 is provided having magnetic poles for providing a magnetic axis generally parallel to the rotation axis 10, and having poles opposite to the poles of the hollow structure. Accordingly, at least on the axial outer ends of the magnetic structure, a generally radially oriented magnetic field is provided. The first magnet structure 9 is incorporated into the rotation axis 10 of the foil trap 3 and therefore it will rotate along with the foil trap 3. It should be noted that it is also possible to keep the magnet 9 stationary, and have a rotating foil trap 3 surrounding the axial magnet. The advantage of this is that it may be easier to equip the magnet with cooling. For the same reason, the magnet structure 9 is preferably stationary, but it may also be incorporated into the rotating part of the rotating foil trap 3, for example, to increase the structural strength. The second magnet structure 11 may be placed at a distance from the foil trap 3, but surrounding it and causing magnetic field lines to run in radial directions. FIG. 4 shows a cross-sectional view, in the viewing direction of the rotation axis, for an alternative embodiment. Here, the magnetic field is not fully rotation symmetric, but the magnetic field is provided generally invariant for a rotation of the rotating contamination barrier over an angle of 180°. The magnetic structure comprises an outer hollow magnet structure 11 that comprise semicircular radially opposed poles, and a central magnet structure 9 is provided that comprises radially opposed magnetic poles opposite to the poles of the hollow structure 11. The outer structure 11 is preferably an integral structure of radially aligned oppositely arranged curved magnetic structures 10 and 11 to produce a magnetic field that is radially aligned relative to the central axis of rotation. Due to limited rotational symmetry of the magnetic field, components surrounding the rotating foil trap may to some extent be exposed to a varying magnetic field, if the magnetic structures 10 and 11 rotate along with the foil trap. If structures 10 and 11 are stationary, the rotating foil trap may to some extent be exposed to a varying magnetic field. In another embodiment depicted in FIG. 5, a magnetic structure is shown for incorporation into the rotating foil trap 3 or for providing stationary relative thereto. The structure 11 is arranged concentrically relative to an axis of rotation, for example, as a static ring provided around the contamination barrier. The structure comprises a plurality of linear magnets having a magnetic axis aligned and arranged radially relative to a center axis of the contamination barrier. By increasing the number of magnets provided on the rotation axis and provided in a ring 12 concentric thereto at a distance, the magnetic field can be made more rotationally invariant. Typically, the number of magnets on the rotation axis and in the ring 12 may differ; for example, the number of magnets arranged in the ring 12 may be larger. Also, one of the magnetic structures 9, 11, respectively arranged axially or on a ring surrounding the rotational axis may be omitted. In the embodiment illustrated in FIG. 5, the radially aligned magnets may be provided fixed relative to the center axis. Also, the magnets may be provided as a static ring provided around the rotating foil trap 3. FIG. 6 shows an embodiment wherein a magnetic deflecting field is formed by two opposing linear magnets 13 that have a magnetic axis located on the rotation axis. Thus, in this embodiment, the magnet structure may comprise linear magnets having a magnetic axis oriented concentric with the axis of rotation of the rotating contamination barrier. This magnetic field may be perfectly rotationally symmetric around the rotation axis of the rotational foil trap 3. Similarly, a symmetric magnetic field may be formed using two opposing hollow cylindrical magnets surrounding the rotating foil trap 3, or even using a single magnet instead of two opposing magnets. FIG. 7 shows calculation results for magnetic field strengths in an embodiment that includes a rotating foil trap having an axial length of 30 mm; and FIG. 8 shows the results in combination with a stationary foil trap serially aligned respective to the optical axis having a length of 40 mm. A foil spacing was taken to be about 2 mm and an average ionization degree of high energy ions (E/Z=2.5 kV and E/Z=3 kV) is taken to be about 8+. It is shown in FIG. 8 that using a magnetic field strength of about 0.15 T, ions with energy up to Ekin of about 400 keV can be stopped using a combined rotating foil trap and stationary foil trap. Without the stationary foil trap, ions with energy up to Ekin of about 10 keV can be stopped, as shown in FIG. 7; based on deflection of ions with minimum charge Z=6. In FIG. 7, a vertical deflection x(L) is given for a given magnetic field strength B and ion charge Z. The bold horizontal line indicates the foil trap spacing b. For values of x(L)>b, the ion will have a collision with the foil. In FIG. 8, a vertical deflection y(L) is given for a given magnetic field strength B and ion charge Z. The bold horizontal line indicates the foil trap spacing b. For values of y(L)>b, the ion will have a collision with the foil. Although the embodiment of FIG. 2 shows a rotating foil trap having a rotation axis directed towards the pinch of the radiation source, that is, in line with an optical axis, the rotation axis may also have a certain angle relative to a line of sight coming from the radiation source. Although specific reference may be made in this text to the use of lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein may have other applications, such as the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, liquid-crystal displays (LCDs), thin-film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “wafer” or “die” herein may be considered as synonymous with the more general terms “substrate” or “target portion”, respectively. The substrate referred to herein may be processed, before or after exposure, in for example a track (a tool that typically applies a layer of resist to a substrate and develops the exposed resist), a metrology tool and/or an inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. Further, the substrate may be processed more than once, for example in order to create a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers. Although specific reference may have been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention may be used in other applications, for example imprint lithography, and where the context allows, is not limited to optical lithography. In imprint lithography a topography in a patterning device defines the pattern created on a substrate. The topography of the patterning device may be pressed into a layer of resist supplied to the substrate whereupon the resist is cured by applying electromagnetic radiation, heat, pressure or a combination thereof. The patterning device is moved out of the resist leaving a pattern in it after the resist is cured. The terms “radiation” and “beam” used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g. having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) and extreme ultra-violet (EUV) radiation (e.g. having a wavelength in the range of 5-20 nm), as well as particle beams, such as ion beams or electron beams. The term “lens”, where the context allows, may refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic and electrostatic optical components. While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described. For example, the invention may take the form of a computer program containing one or more sequences of machine-readable instructions describing a method as disclosed above, or a data storage medium (e.g. semiconductor memory, magnetic or optical disk) having such a computer program stored therein. The descriptions above are intended to be illustrative, not limiting. Thus, it will be apparent to one skilled in the art that modifications may be made to the invention as described without departing from the scope of the claims set out below.
050080709	description	DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The inventors have studied the fuel assembly shown in U.S. Pat. No. 4,587,090, i.e., the fuel assembly in which not only an enrichment but also an amount of a burnable poison in the upper region is larger than that in the lower region, and then found that the conventional fuel assembly suffers from the following new problems. Namely, the conventional fuel assembly suffers from a problem such that, in the case where it is desired to increase the spectral shift effect, as the burnable poison in the lower region of the fuel assembly is decreased, a maximum linear heat rating of fuel rods is considerably increased. If the number of the fuel rods that contains the burnable poison in the lower region or the concentration of the burnable poison contained in the fuel rods would be reduced, a neutron infinite multiplication factor would be increased in the lower region, so that the reactivity difference between the upper and lower portions of the reactor core becomes large. In addition, the thermal neutron flux density would be increased in the lower region of the reactor core so that the burning of the burnable poison would be hastened to further increase the reactivity difference between the upper and lower regions. For that reason, there would be a fear that the operational limit for the maximum linear heat rating would be exceeded because of the lower region peak in the axial power distribution at a certain period during the operational cycle. A variety of arrangements of the fuel assembly for overcoming the above-described new problems have been studies. The results of such studies will be explained hereinunder. The inherent function of the burnable poison is to control the excess reactivity at the initial stage of the operational cycle. Since the burnable poison is a strong neutron absorption material, the material should be prevented from being unburnt at the final stage of the operational cycle. Also, in the burnable poison such as gadolinia, the undue absorption of the neutron by the nuclides after the neutron absorption is not negligible. It is, therefore, important to reduce the burnable poison within the range where the reactivity at the initial stage of the cycle can be moderated in view of the economical point of the neutron. In view of the above-described point, it is very effective to reduce the amount of the burnable poison in the lower region of the fuel assembly. FIGS. 1A to 1D show the differences of operation changes, respectively, in the case (1) where the amount of gadolinia (Gd.sub.2 O.sub.3), i.e., the burnable poison is decreased in the upper region of the fuel assembly, in the case (2) where the amount of gadolinia is kept constant between the upper and lower regions of the fuel assembly, and in the case (3) where the amount of gadolinia is decreased in the lower region of the fuel assembly. In the case (1) where the amount of gadolinia in the lower region is decreased, the reactivity increment in the final stage of the operational cycle is remarkable due to the spectral shift effect as described above and shown in FIG. 1A. Since the void fraction in the initial stage in the operational cycle is increased, the excess reactivity is rather suppressed to a low level irrespective of the small amount of gadolinia (FIG. 1B). Also, since the reactivity increment in the reactor core is decreased when the operation state is in the transient stage from the operation state to the cold condition, the shutdown margin of the reactor is increased as shown in FIG. 1C. As described above, it is possible to enhance the fuel utilization without degradation of the shutdown margin of the reactor or the excess reactivity by reducing the amount of the gadolinia in the lower region of the fuel assembly. However, if the reduction of the amount of the gadolinia in the lower region of the fuel assembly is performed simply by decreasing the concentration of the gadolinia in the lower region or by decreasing the number of the fuel rods containing in the lower region thereof the gadolinia, the maximum linear heat rating is considerably increased as shown in FIG. 1D. The above-mentioned features of the present invention can be achieved on the basis of the concept to optimize the change in burning of power distribution in the reactor core axial direction power and of the burnable poison amount in the lower region of the fuel assembly in which the maximum spectral shift effect may be obtained without remarkably increasing the maximum linear heat rating. FIG. 2 shows a typical burning change at the axial power peaking. FIG. 3 shows the power distribution in the axial direction of the reactor core with respect to each burnup at the points A to E shown in FIG. 2. In FIG. 2, the lower peak of the axial power distribution at the initial of the operational cycle (point A) is weakened once at the point B and again strengthened most at the point C. Thereafter, the axial power distribution is rapidly flattened and weakened, and past the point D, the upward peaked power distribution is provided. With respect to such a change, as shown in FIG. 4, the peaking of the lower region is kept at a high level before the middle of the operational cycle while the axial power peaking maximum is being kept constant (in the right side condition of FIG. 4). As a result it is possible to increase the spectral shift effect without increasing the maximum linear heat rating. A plurality of groups of fuel assemblies that have different operational cycles are installed in the reactor core. According to the inventors' analyses, the action of the axial power peaking in the initial stage of the operational cycle mainly depends upon the burnup change in reactivity ratio between the upper region and lower region of the fuel assemblies in the first and the second operational cycles, and depends upon a relative power ratio of the fuel assemblies in the first and the second operational cycles. The local maximum peaking value of the axial output in the intermediate stage of the operational cycle depends upon the maximum value of the reactivity ratio between the upper and the lower regions of the fuel assemblies in the first operational cycle. Therefore, if the change of the neutron infinite multiplication factor in the initial burnup stage is adjusted by the amount of gadolinia of the fuel assemblies to suitably set the burnup change of the reactivity ratio of the upper and the lower regions of the first cycle fuel assemblies, a desired axial power peaking change as shown in the right portion of FIG. 4 may be obtained. The reactivity value of the strong neutron absorption material such as gadolinia depends upon a surface area thereof. The more the number of the fuel rods containing the gadolinia becomes, the more the reactivity moderating effect becomes. FIG. 5 shows the relationship between the number of the fuel rods containing the gadolinia and the neutron infinit multiplication factor. The neutron infinite multiplication factor of a fuel assembly composed of twelve fuel rods containing gadolinia by 4.5 wt% and four fuel rods containing gadolinia by 3.5 wt% is, in the initial state of the operational cycle, smaller by 3.3% .DELTA.k than that of a fuel assembly in which the number of the fuel rods containing gadolinia by 3.5 wt% is less by two than that of the former case. However, at the final stage when gadolinia is burnt up, there is only difference in maximum value of the neutron initiate multiplication factor only by 0.3% .DELTA.k because the value does not have a direct relationship with the number of the fuel rods containing the gadolinia in the case where the gadolinia concentration is kept constant in the fuel rods. When the number of the fuel rods containing the gadolinia in the lower portion of the fuel assembly is decreased, the lower region power peaking of the fuel assembly is raised, as shown in FIG. 6A, in particular at the initial stage of the operational cycle. In accordance with this phenomenon, the burnup rate difference between the upper and the lower regions of the fuel assembly is more enlarged, so that the lower region power peaking will be somewhat raised during the intermediate stage of the operational cycle. The concentration of the gadolinia contained in a single fuel rod will affect the burnup period of gadolinia. As shown in FIG. 7, the neutron infinite multiplication factor at the initial burnup stage may be kept within a short range of about 1.2% .DELTA.k according to the gadolinia concentration. However, if the concentration of gadolinia is low, the gadolinia will quickly be burnt up, so that the burnup reaching the maximum value of the infinite multiplication factor will be accelerated to provide a difference of 1.8% .DELTA.k in the maximum value of the neutron infinite multiplication factor. Therefore, the concentration of the gadolinia will affect the magnitude of the lower region peaking in particular in the intermediate stage of the operational cycle. When the concentration of gadolinia in the lower region of the fuel rod is increased, as shown in FIG. 6B, the power peaking in the lower region of the fuel assembly may be lowered mainly in the intermediate stage of the operational cycle. The solid line in FIG. 7 indicates the characteristics of the fuel assembly composed of twelve fuel rods containing gadolinia by 4.5 wt% and four fuel rods containing gadolinia by 3.5 wt%. The dotted line indicates the characteristics of the fuel assembly composed of sixteen fuel rods containing the gadolinia by 3.5 wt%. The dot and dash line indicates the characteristics of the fuel assembly composed of twelve fuel rods containing gadolinia by 5.5 wt% and four fuel rods containing gadolinia by 3.5 wt%. The axial power peaking control effect may be ensured by the combination of the number of the fuel rods containing the gadolinia and the gadolinia concentration to obtain the axial power peaking change close to the right portion shown in FIG. 4. Namely, the number of the fuel rods containing the gadolinia is decreased in the lower region of the fuel assembly, and the gadolinia concentration in that region is increased, so that the portion corresponding to the trough in the axial power peaking change may be raised in the initial stage in the operational cycle and the portion corresponding to the crest in the axial power peaking change may be lowered in the intermediate stage of the operational cycle. The adjustment of the gadolinia amount at which such characteristics may be obtained corresponds to the case where the gadolinia concentration which is lowest in the lower region of the fuel rods is kept at zero. However, the above-described fuel assembly is not constructed so as to control the axial power peaking at the very initial stage of the operational cycle. Namely, since the number of the fuel rods containing the gadolinia in the lower region of the fuel assembly is reduced, the power distribution in the transverse cross-section of the fuel assembly is made uniform to reduce the local power peaking. Therefore, the increment of the linear heat rating is small relative to the increment of the power peaking in the lower region of the fuel assembly. However, as the number of the fuel rods containing the gadolinia in the lower region of the fuel assembly is decreased, the peaking of the power in the lower region in the initial stage of the operational cycle is rapidly increased. For that reason, if the number of the fuel rods containing the gadolinia in the lower region of the fuel assembly is decreased to exceed some lower limit, the linear heat rating will be at maximum in the initial stage of the operational cycle. In order to improve this, it is preferable to reduce the lowest gadolinia concentration in the lower region to a rather small level that is not zero. Namely, the gadolinia at the lowest concentration (but not zero) in the lower region of the fuel rods only functions to suppress the power in the lower region at the very initial stage of the operational cycle. Thus, it is possible to shift the change of the axial power peaking relative to the burnup further to an ideal one. Subsequently, the fuel rods containing the gadolinia at minimum concentration in the lower region among the gadolinia containing fuel rods should be located as follows. (i) The reactivity in the lower region of the fuel assembly should be effectively reduced in the very initial stage of the operational cycle. (ii) Where the neutron spectrum is soft and the neutron importance is high, the amount of the burnable poison should be decreased as much as possible. Namely, it is preferable that the concentration of gadolinia should be low in the region close to the saturated water region such as locations adjacent to the water rods. In a region where the neutron flux density is high and the spectrum is soft, the reactivity moderating effect at the initial stage of burnup is remarkable even with a small amount of gadolinia. The small amount of gadolinia will be burnt rapidly, so that it is possible to readily attain an object to moderate the reactivity at the very initial stage of the operational cycle. Also, in view of the neutron absorption by the gadolinia nuclides after the neutron has been absorbed thereby, it is possible to enhance the reactivity after the burnup of the gadolinia by decreasing the amount of the gadolinia in the region adjacent to the saturated water region. In order to make, among the fuel assemblies, a wide region where the neutron spectrum is soft as described above, available is the fuel assembly where the water rod region is increased (that is, the number of the water rods is increased or the outer diameter of the water rods is increased). Incidentally, with respect to the enrichment of the upper and lower regions of the fuel assembly, if the upper region enrichment is higher than the lower region enrichment as shown in U.S. Pat. No. 4,229,258, the axial power distribution is made uniform to reduce the lower region power peaking. Since such a decreased amount of the power peaking in the lower region of the fuel assembly is not substantially related to the burnup of the operational cycle, it is effective to keep the axial power peaking substantially in a uniform state over the entire period of the operational cycle without largely changing the burnup of the axial power peaking. An embodiment which is obtained on the basis of the above mentioned inventors' study will be explained hereinunder. The preferred embodiment of the invention applied to a boiling water reactor will now be described with reference to FIGS. 8 and 9. A fuel assembly 10 according to the embodiment comprises an upper tie plate 11, a lower tie plate 12, a plurality of fuel rods 13, a plurality of fuel spacers 14 and two water rod WR. Each of the fuel rods 13 and the water rods WR are supported at its upper end portion to the upper tie plate 11 and at its lower end portion to the lower tie plate 12, respectively. Dioxide uranium pellets are filled in the fuel rods 13. The fuel spacers 14 are used to support the respective fuel rods 13 so that a space between the adjacent fuel rods 13 is kept at a predetermined distance. A channel box 15 is mounted on the upper tie plate 11 to surround the periphery of the fuel rod bundle supported by the fuel spacer 14. Six kinds of fuel rods 1 to 4, G1 and G2 are used as the fuel rods 13. The fuel rods are arranged in a regular square matrix of 9 rows and 9 columns. The two water rods WR are located in the central portion of the transverse cross-section of the fuel assembly and close to each other on a straight line connecting a pair of opposite corners of the channel box 15. An outer diameter of the water rod WR is larger than a pitch of the fuel rods. The two water rods WR occupies an area corresponding to the seven fuel rods 13 arranged at the same fuel rod pitch. Namely, seven fuel rods 13 are replaced by the two water rods WR. The fuel assembly having such an arrangement is shown in FIGS. 1, 7 and 8 of Japanese Patent Unexamined Publication No. 62-217186. The enrichment in the axial direction of the fuel rods 1 to 4, G1 and G2 and the gadolinia concentration distribution are shown in FIG. 10. Each fuel rod is filled with natural uranium in a range between a lower end of the effective length portion of the fuel and 1/24 of the effective length thereof, and in a range between 22/24 and 24/24 of the effective length portion with reference to the lower end of the effective length portion. The hatched regions of each fuel rod in FIG. 10 show the natural uranium filled portion. The fuel effective length portion means the region in which the fuel pellets are filled. None of the fuel rods 1 to 4 contain gadolinia. The fuel rods G1 and G2 contain gadolinia to be used as the gadolinia containing fuel rods. The average gadolinia concentration of the fuel rod G2 is lower than that of the fuel rod G1. The enriched uranium filling region of the fuel rods 1 to 4, G1 and G2 are in the range of 1/24 to 22/24 of the axial entire length of the fuel effective length portion with reference to the lower end of the fuel effective length. In the fuel rods 1, 3, 4, G1 and G2, the enrichment in the axial direction is uniformed in the enriched uranium filling region. The enrichments in the enriched uranium filling region of the fuel rods 1, 3, 4, G1 and G2 are as follows. The enrichment of the fuel rod 1 is at 4.85 %, the enrichment of the fuel rod 3 is at 3.90 %, the enrichment of the fuel rod 4 is at 3.20 wt%, the enrichment of the fuel rod G1 is at 4.20 wt% and the enrichment of the fuel rod G2 is at 3.8 wt%. The enrichment in the enriched uranium region of the fuel rod 2 is at 4.20 wt% in the range of 1/24 to 11/24 of the axial entire length of the fuel effective length portion with reference to the lower end of the fuel effective length portion, and at 4.85 % in the range of 11/24 to 22/24 of the axial entire length of the fuel effective length portion. The gadolinia concentration distributions of the fuel rods G1 and G2 are as follows. The gadolinia concentration of the fuel rod G1 is at 5.0 wt% in the range of 1/24 to 11/24 of the axial entire length of the fuel effective length portion with reference to the lower end of the fuel effective length portion, and the gadolinia concentration thereof is at 4.5 wt% in the range of 11/24 to 22/24 of the axial entire length of the fuel effective length portion. The gadolinia concentration of the fuel rod G2 is at 0.0 % in the range of 1/24 to 11/24 of the entire axial length of the fuel effective length portion, and the gadolinia concentration thereof is at 3.5 wt% in the range of 11/24 to 22/24 of the entire axial length of the fuel effective length portion. It is unnecessary to fill the natural uranium filling region with gadolinia since the power thereat is inherently small. If the gadolinia would be filled in this region, the gadolinia would be left after the completion of the operational cycle. The upper region is located above the position of 11/24 of the axial entire length of the fuel effective length portion from the lower end of the fuel effective length portion, whereas the lower region is located below that position. In the embodiment, twelve fuel rods G1 and four fuel rods G2 are used. The four fuel rods G2 are arranged at the position adjacent to the water rods WR that form the saturated water region therebetween. The twelve fuel rods G1 are arranged radially inward from the outermost periphery but are not arranged close to the water rods WR or the channel box 15. The channel box 15 is used to define the cooling water flow path within the fuel assembly 10 and to define a water gap (saturated water region) formed between the fuel assembly 10 when the fuel assembly 10 is installed within the reactor core. Namely, the fuel rods G1 are not arranged close to the saturated water region which is formed when the fuel assembly 10 is installed within the reactor core. With respect to the gadolinia within the fuel assembly 10, the amount of the gadolinia in the upper region of the fuel assembly 10 is expressed by the equation, 4.5 wt%.times.12+3.5 wt%.times.4=68, whereas the amount in the lower region of the fuel assembly 10 is smaller and expressed by the equation, 5.0 wt%.times.12+0.0 wt%.times.4=60. When the fuel rods G1 and G2 are divided into upper and lower regions, the maximum gadolinia concentration (5 %) portion and the minimum gadolinia concentration (0.0 %) portion are both present in the lower region in the gadolinia containing fuel rods. The above-described maximum and minimum gadolinia concentration portions are not present in the enriched uranium filling region in the upper region of the fuel assembly 10. Further, the fuel rods G2 containing the gadolinia at the minimum concentration are arranged in the vicinity of the water rods WR for enhancing the reactivity moderating effect by the converted nuclear seeds from the gadolinia after the burnup of the gadolinia, thereby keep the reactivity moderation at a minimum level. In the embodiment, to reduce the maximum heat rating, the average enrichment of the lower region of the fuel assembly is lower by 0.2 wt% than that of the upper region. FIG. shows the fuel assembly used for illustrating the effect of the embodiment, which fuel assembly is shown in Japanese Patent Unexamined Publication 62-217186, the gadolinia concentration and the enrichment distribution are kept uniform in both of regions. The fuel rods 1, 22, 23, 4, G3 and G4 shown in FIG. 12 are arranged to form a fuel assembly 16. The enrichments of the fuel rods 1, 22, 23, 4, G3 and G4 are at 4.85, 4.40, 3.80, 3.20, 4.40 and 3.80 wt%, respectively in the regions in the natural uranium filling region between the upper and the lower end portions thereof. The fuel rods G3 and G4 contain gadolinia with gadolinia concentrations of 4.50 and 3.50 wt%, respectively. FIG. 13 shows a change, relative to the burnup, of the maximum linear heat rating of the reactor core to which each of the fuel assemblies 10 and 16 is loaded. FIG. 14 shows a change, relative to the burnup, of the reactor average void fraction. In the fuel assembly 10 according to this embodiment, the amount of gadolinia in the upper region in the axial direction is larger than that in the lower region. Within the gadolinia containing fuel rods, the maximum and minimum gadolinia concentration portions are present only in the lower regions. Therefore, it is possible to keep the power peaking in the lower region at a high level in comparison with the fuel assembly 16 before the middle stage of the operational cycle. It is possible to keep the reactor core average void fraction in the first half of the operational cycle at a constant level that is larger than that of the fuel assembly 16, as shown in FIG. 14 in solid line. Thus, the spectral shift effect in the fuel assembly 10 is increased. The neutron effective multiplication factor at the final stage of the cycle according to this embodiment is higher than that of the fuel assembly 16 by 0.3% .DELTA.k. This shows the effect of 1% reduction of the necessary natural uranium amount. In the fuel assembly 10, it is possible to make the maximum linear heat rating smaller than the maximum linear heat rating ML that is at maximum in the fuel assembly 16. The case will be explained where the concept is applied to the fuel assembly 16, in which the fuel rods G2 with the gadolinia concentration of 4.5 wt% in the lower region and the gadolinia concentration of 3.5 wt% in the upper region and the fuel rods G3 with the gadolinia concentration of 0.0 % in the lower region and the gadolinia concentration of 4.5 wt% in the upper region are used as shown in FIG. 3B of U.S. Pat. No. 4,587,090. Namely, assume that, in the fuel assembly 16, the distribution of the gadolinia concentration of the fuel rods G3 is changed as the fuel rod G3 of U.S. Pat. No. 4,587,090, and the distribution of the gadolinia concentration of the fuel rod G4 is changed as the fuel rod G3 of U.S. Pat. No. 4,587,090. On the basis of this as the assumption, if the operation is started with the thus assumed fuel assembly being loaded on the reactor core, the maximum linear heat rating and the average void fraction are changed as follows. Namely, the maximum linear heat rating is changed between the solid line and the dotted line until reaching the position of about 6GWd/t (the intersection P between the solid line and the dotted line) in FIG. 13 and is changed along the dotted line after the point P. The reactor average void fraction of the assumed fuel assembly is changed in the same manner as the maximum linear heat rating. The reason why such characteristics are obtained in the assumed fuel assembly is that the maximum gadolinia concentration (4.5 wt%) within the gadolinia containing fuel rods is present in the lower region of the fuel rod G2 and the upper region of the fuel rod G3. In the fuel assembly 10 according to the embodiment, the maximum gadolinia concentration portion Gmax (for example, 5.0 wt%) within the gadolinia containing fuel rod is present in the lower portion of the fuel rod G1 (more exactly in the enriched uranium filling region within the lower region), the minimum gadolinia concentration Gmin portion (for example, 0.0 %) within the gadolinia containing fuel rod is present in the lower region of the fuel rod G2 (more exactly in the enriched uranium filling region of the lower region) and none of the maximum gadolinia concentration Gmax portion and the minimum gadolinia concentration Gmin portion within the gadolinia containing fuel rods are present in the upper region of the fuel rods G1 and G2 (more exactly in the enriched uranium filling region within the upper region). Accordingly, it is possible for the fuel assembly 10 to lower the maximum linear heat rating having the largest value exceeding that of the above-described fuel assembly assumed on the basis on FIG. 3B of U.S. Pat. No. 4,587,090. Also, since it is also possible for the fuel assembly 10 to keep the power peaking in the lower region of the first half of the operational cycle and the reactor void fraction at high levels than those of the assumed fuel assembly, the spectral shift effect is more enhanced than that of the assumed fuel assembly. Incidentally, the gadolinia concentration of the upper region (in particular in the enriched uranium filling region in the upper region) of each gadolinia containing fuel rod (G1 and G2) in the embodiment is between the maximum gadolinia concentration Gmax and the minimum gadolinia concentration Gmin. Since the fuel rods G1 having the maximum gadolinia concentration Gmax in the lower region thereof are disposed in the radial inner region from the outer periphery of the fuel assembly and away from the saturated water region, in which the neutron spectrum is hard, it is possible to effect the function of the gadolinia within the fuel rods G1 until the final stage of the operational cycle. The gadolinia in the upper and the lower regions of the fuel rods G1 is consumed in the final stage of the operational cycle. In the case where, as in the embodiment, the fuel rods G2 having the gadolinia concentration lower than that of the fuel rods G1 and having the gadolinia concentration in the upper region rather higher than in the lower region are disposed adjacent to the water rods WR, it is possible to enhance the shutdown margin of the reactor and effect the spectral shift at a maximum level. The fuel rods G2 have the function to increase the gadolinia amount in the upper region of the fuel assembly higher than that of the lower region. The function to generate the spectral shift is imparted to the fuel assembly 10. The natural uranium region located in the upper and the lower ends of each fuel rod has an effect to reduce the amount of neutron leaked downwardly and outwardly of the reactor core to enhance the economical aspect. In the embodiment, the fuel rods 13 are arranged in triplex closed loops from the outermost periphery of the fuel assembly to surround the two water rods WR. The two water rods WR are arranged in the central portion of the transverse cross-section of the fuel assembly and occupy an area corresponding to the area of the fuel rods 13 in a matrix of 3 rows and 3 columns. A diameter of the water rod WR is selected so that the water rods may be arranged in the above-described area. Thus, although the two water rods WR are disposed in such area, two fuel rods 13 may be further disposed besides the two water rods WR in the direction perpendicular to the straight line connecting the centers of the two water rods WR in the area where the fuel rods of 3 rows and 3 columns may be disposed. Therefore, the number of the replaced fuel rods 13 is reduced to seven (7=9-2). Also, since the two water rods WR are disposed in the central portion of the fuel assembly, it is possible to well moderate the fission neutron generated in the central portion of the fuel assembly 10 to enlarge the thermal neutron flux. Therefore, the thermal neutron flux in the central portion of the fuel assembly is enhanced and the thermal neutron flux distribution is flatted in the fuel assembly 10. Also, the fuel rods 13 and the water rods WR within the fuel assembly 10 are not considerably displaced from the symmetric arrangement thereof with respect to the center of the fuel assembly 10, so that it is possible to arrange the fuel rods having the same enrichment in a substantial symmetric arrangement. Another embodiment will be explained with reference to FIGS. 15 and 16, which is applied to the boiling water reactor. The fuel assembly 17 is substantially identical to the fuel assembly 10 with respect to the arrangement thereof. The differences therebetween reside in that the fuel rods 2 of the fuel assembly 10 are replaced by fuel rods 22 in which the enrichment of the enriched uranium filling region is uniform in the axial direction at 4.40 wt%, and the fuel rods G1 are replaced by fuel rods G5 that have a higher enrichment of 4.40 wt%. The other structure of the fuel assembly 17 is the same as the fuel assembly 10. The fuel assembly 17 has the same effect as that of the fuel assembly 10. Since the fuel assembly 17 uses the fuel rods 22, the maximum linear heat rating is increased by 2% in comparison with the fuel assembly 10. Also, the spectral shift effect is increased to enhance the effective multiplication in the final stage of the operational cycle by 0.05% .DELTA.k. Also, the shutdown margin of the reactor is enhanced according to the fuel assembly 17 rather than the fuel assembly 10. The reason for this is that since the enrichment of the upper region of the fuel assembly 17 is lower than that of the fuel assembly 10, the reactivity increment during the cold stop state becomes small. It should be noted that, according to this embodiment, the shutdown margin of the reactor is enhanced over the case where the enrichment and the gadolinia distribution are kept uniform in the axial direction in the fuel assembly 10. Under the condition that the enrichment distribution is kept constant in the axial direction and the gadolinia distribution in the upper region is kept constant, if the amount of the gadolinia in the lower region is decreased, the reactivity of the lower region is enhanced, so that the shutdown margin of the reactor is ensured. Still another embodiment of the invention will now be described hereinunder with reference to FIGS. 17 and 18. In this fuel assembly 18, the minimum gadolinia concentration Gmin is changed from 0.0 % to 1.0 wt%. Namely, in the fuel assembly 18, the fuel rods G6 are used instead of the fuel rods G2, the gadolinia concentration of the lower region of which is kept at 1.0 wt%. The four fuel rods G6 are arranged in the vicinity of the water rods WR in the same manner as the fuel assembly 10, that is, are confronted with the saturated water region. Thus, the thermal neutron flux density is kept at a high level. Therefore, it is possible to ensure the relatively large reactivity moderating effect even with a small amount of gadolinia. Also, the gadolinia concentration of the upper region of the fuel rods G6 is smaller than the gadolinia concentration of the upper region of the other gadolinia containing, fuel rods (G1) so that the gadolinia is fully burnt and is not left in the final stage of the operational cycle. An object of the arrangement of the plurality of water rods WR is to make uniform the power distribution within the fuel assembly. To this end, the gadolinia within the fuel rods G6 in the vicinity of the water rods WR is adapted to be burnt up fully when almost gadolinia is burnt up to increase the power. As a result, it is possible to increase the reactivity moderating effect at the initial stage of the operational cycle without sacrificing the effect on the power distribution uniformity. In this embodiment, the gadolinia amount in the upper region of the fuel assembly 18 is expressed by the equation, 4.5 wt%.times.12+3.5 wt%.times.4=68 and the gadolinia amount in the lower region thereof is expressed by the equation, 5.0 wt%.times. 12+1.0 wt%.times.4=64. The gadolinia amount in the lower portion is smaller than that in the upper portion. The fuel assembly 18 has the same effect as the fuel assembly 10. In particular, it is possible for the fuel assembly 18 to moderate the axial power peaking in the initial stage of the operational cycle by means of the fuel rods G6 in comparison with the fuel assembly 10. The linear heat rating of the fuel assembly 18 is then lowered. As a result, the maximum linear heat rating is lower by 3% than the fuel assembly 10 throughout the operational cycle. On the other hand the spectral shift effect is weakened since the gadolinia of the lower region of the fuel assembly 18 is somewhat increased, and the power distribution is made uniform as a whole. Therefore, the effective multiplication in the final stage of the operational cycle is lowered by about 0.1% .DELTA.k. However, on the basis of the fuel assembly 16 in which the enrichment is kept constant in the axial direction as shown in FIG. 11, although the maximum linear heat rating is lowered by 3%, the effective multiplication at the final stage of the operational cycle is increased by 0.2% k. Still another embodiment of the invention will now be described with reference to FIGS. 19 and 20. In this fuel assembly 19, a water rod WR1 having a cruciform cross section is arranged in the central portion of the fuel assembly 19. The fuel rods 1, 2, 23, 4, G1 and G7 are arranged in the fuel assembly 19 so as to surround the water rod WR1. The water rod WR1 sufficiently occupy a space corresponding to the space of the five fuel rods to keep the same water area as the fuel assembly 18. The number of the gadolinia containing fuel rods of G1 and G7 is sixteen. The twelve fuel rods G1 contains 4.5 wt% gadolinia in the upper region and 5.0 wt% gadolinia in the lower region. The other four fuel rods G7 are disposed close to the water rod WR1 and contain only in the upper region thereof the gadolinia of 3.5 wt%. The maximum gadolinia concentration 5.0 wt% portion and the minimum gadolinia concentration 0.0 % portion are present in the lower region of the fuel assembly 19 but not present in the upper region of the fuel assembly 19. Also, the gadolinia amount is smaller in the lower region of the fuel assembly 19. The enrichment of the lower region is lower than the upper region. However, the average of the enrichment difference between the upper and lower regions is at 0.2 wt% and is the same as the fuel assembly 10. The fuel assembly 19 has the same effect as the fuel assembly 10. However, in this embodiment, since the number of the fuel rods is larger by two than that of the fuel assembly 10, the average linear heat rating is lowered by about 2%. For that reason, it is possible to suppress the maximum linear heat rating relative to the fuel assembly 10. The characteristics of the reactor core on which the fuel assembly 19 is loaded are substantially the same as those of the fuel assembly 10. The improved effect of the characteristics relative to the uniform axial distribution and the enrichment in the fuel assembly 19 is also substantially the same as those of the fuel assembly 10. In the case where a large amount of recycle fuel may be used in a commercial light water reactor, it is possible to obtain the same effect with the plutonium instead of the uranium fuel. Further another embodiment of the invention will be described hereinunder with reference to FIGS. 21 and 22. This fuel assembly 20 is constituted by replacing all of fuel rods in the fuel assembly 10 with new set of fuel rods 31 to 35, and G8 to G11 shown in FIG. 22. These nine kinds of fuel rods are arranged in the fuel assembly as shown in FIG. 21. Each fuel rods is filled with natural uranium in a range between a lower end of the effective length portion and 1/24 of an entire effective length thereof. Further, in the fuel rods except for the fuel rods 32, natural uranium is further filled in a range between 22/24 of the entire effective length of the effective length portion and an upper end thereof. These upper and lower ends of the fuel rods 31, 34, 35, and G8 to G11 are the enriched uranium filling regions. The enrichments in the enriched uranium filling regions in the fuel rods 31, 34, 35 and G8 to G11 are 4.8 wt%, 3.7 wt%, 3.0 wt%, 3.7 wt% 3.9 wt%, 3.9 wt% and 3.9 wt%, respectively. The enrichment in each of the fuel rods is uniform in an axial direction thereof. The enriched uranium filling region in the fuel rod 33 is divided into an upper region and a lower region at a separating point of 11/24 of the axial entire length of the fuel effective length portion from the lower end thereof. The enrichment in the upper region of the enriched uranium filling region is 4.8 wt% and that in the lower region thereof is 4.1 wt%. The fuel rods G8 to G11 contain gadolinia in the enriched uranium filling regions. The fuel rod G9 contains gadolinia of 3.5 wt% allower the enriched uranium filling region thereof. The enriched uranium filling region of each of the fuel rods G8, G10 and G11 is divided into an upper region and a lower region at the same separating point as the fuel rod 33. The fuel rod G8 contains gadolinia of 4.5 wt% in the upper region thereof and gadolinia of 5.5 wt% in the lower region thereof. The fuel rod G10 contains gadolinia of 3.5 wt% in the upper region thereof and gadolinia of 1.0 wt% in the lower region thereof. The fuel rod G11 contains gadolinia of 4.5 wt% in the upper region thereof and no gadolinia in the lower region thereof. The fuel rod 32 has an upper end of the effective length portion which is located in 15/24 of the axial entire length of the fuel effective length portion from the lower end of another fuel rod. The fuel rod 32 has an axial length which is smaller than that of the other fuel rods. All of fuel rods 32 are located in an inner closed loop adjacent the outermost periphery of the fuel assembly 20. The use of the short length fuel rods are disclosed in Japanese Unexamined Publication Nos. 52-50498 and 60-2240092. This embodiment has the same effect as that of the fuel assembly 10, because a region of upper and lower regions in the fuel rods containing a maximum gadolinia concentration and a region of upper and lower regions in the fuel rods containing a minimum gadolinia concentration are located in the lower region in the fuel assembly, and the amount of gadolinia in the upper region in the fuel assembly is larger that in the lower region in the fuel assembly. Further, the short length fuel rod can lower the pressure loss in the upper region in the fuel assembly and improve the shutdown margin of the reactor.
	description	This application is a national phase of International Application No. PCT/EP2006/066710 entitled “Sealing Means, Transfer Device Comprising Such a Sealing Means, Arrangement Comprising Such a Transfer Device and a Method for Producing Said Sealing Means”, which was filed on Sep. 25, 2006, and which claims priority of French Patent Application No. 05 52938, filed Sep. 28, 2005. This invention mainly concerns a sealing means, in particular between two radioactive environments, a transfer device in a nuclear fuel production plant comprising means of tight insulation, a production plant comprising such a device and a method for producing such a sealing means. It is known, for example in document FR-1364102, a revolving or barrel door to transfer a radioactive object from one enclosed area to another, with the door providing when operating and when at rest, a tight seal between the two spaces. The seal is obtained thanks to an inflatable seal mounted on a wall partially surrounding the drum. The sealing means must resist hot gases and flames in the event of fire, in order to limit the propagation of contaminated gases and flames. However, the seals that are currently in use which are fixed on the door, or on the wall separating the two confined areas, do not ensure sufficient resistance to hot gases and flames or a tight seal against contamination during a long period. In addition these seals are fragile and quickly become brittle since they are solicited with each rotation of the barrel door. Thus major problems appear in terms of maintaining this type of transfer device, which can cause stoppages of installations for a long duration. It is consequently a purpose of this invention to provide a sealing means that offers the guarantees of safety that are required for this type of device. It is also a purpose of this invention to provide a transfer device that can operate in conditions that are safe for the environment and for people working in this type of installation. It is also a purpose of this invention to offer a method for producing said sealing means. The previously mentioned purposes are attained by a means making it possible to tightly insulate two chambers, formed by a seal and a seal carrier, with the seal able to insulate flames and hot gases and is sufficiently resistant to radiation to be suitable for such devices. The seal carrier is easily removable, thus making it possible to replace the seal easily when the latter shows signs of deterioration. By seal is meant the property of confining for a determined length of time flames and hot gases in a first chamber in order to avoid them passing into a second chamber. Thus, it is not necessary to have a seal that is resistant to flames, hot gases and radiation over a long period of time, since the latter can be changed quickly and easily. This replacement does not impose a prolonged stoppage of the device. The subject-matter of the present invention is mainly a sealing means for a transfer device of a nuclear installation comprising a seal carrier and a seal connected thereto, wherein the seal carrier is removably fixable between two areas insulated from each other. The seal carrier comprises for example a T groove receiving the seal. Advantageously, the seal carrier is made of stainless steel. The seal is made of a material that resists flames, hot gases and radiation, and advantageously intumescent material. In an embodiment, the seal carrier is made of several parts, for example three parts. The invention also relates to a transfer device of a nuclear installation between two chambers separated by a wall, wherein said transfer device comprises a transfer mechanism and at least one sealing means according to the invention, said sealing means being positioned between the wall and the transfer mechanism. Furthermore, the seal carrier and the seal are arranged substantially along the wall according to a generatrix of a cylinder forming the outer periphery of the transfer mechanism. In an embodiment, the transfer mechanism is of the barrel door type mobile around an axis, comprising a cylindrical body defining an inner space wherein an object can be positioned, with this space being accessible by an opening that can be oriented either on the side of a first chamber or on the side of a second chamber. Advantageously, the transfer device according to the invention comprises a first pressure drop means able to increase the travel of the gases between the chambers, said first means being mounted on an upper end of the door substantially according to a plane orthogonal to the axis of rotation of the door. The first pressure drop means is, for example, formed by a steel angle assembly and, advantageously, by several arcs of a circle placed end to end. The transfer device can also comprise a second pressure drop means positioned along a generatrix of the outer periphery of the transfer mechanism. This second means comprises for example an elongated element made of steel, with a substantially circular transversal section. In an embodiment, the door comprises a first axis projecting from an upper side and a second axis projecting from a lower side around which the door is able to rotate. The door can be driven in rotation by an electric motor. The subject-matter of the present invention is also a production or treatment installation, for example of nuclear fuel, for example of the MOX-type (mixture of uranium oxide and plutonium oxide) comprising a main chamber and at least one secondary chamber separated by the wall, an opening for communication between the chambers arranged in the wall, a transfer device according to the invention, insulating the chambers. The seal carrier is fixed by screw-bolt connection on the wall separating the two chambers. The production installation according to the invention can comprise a first curved recess with inner radius substantially equal to the outer radius of the door and receiving a portion of this door. The second pressure drop means is for example welded in a groove defined by the wall and a safety caisson defining the first recess, a second curved recess surrounding the door, over approximately 180°. The subject-matter of the present invention is also a method of producing the sealing means according to the invention, comprising the steps: installing shutters on the longitudinal and transversal ends of the groove of the seal carrier, injecting a flame- and hot gas-resistant material into the groove, removing shutters. In the description that follows, the invention is applied to a nuclear fuel production installation, but it also applies to an installation that uses said fuel or that treats it. Furthermore, the transfer device according to the invention can be used in any installation requiring a transfer between two areas between which a tight seal is expected. In FIG. 9, a workshop is shown schematically wherein a nuclear fuel is produced. This workshop comprises a main chamber 2 equipped for example with a means of transporting or conveying materials intended for the production of the nuclear fuel, and secondary chambers 4 wherein the different operations of transforming the basic materials of the nuclear fuel are executed. The basic operations are for example the proportioning of the primary mixture, milling, the proportioning of the final mixture, homogenisation, granulation and the production of nuclear fuel pellets which will then be placed in ducts in order to form fuel rods. The main chamber 2 has the shape of a rectangular corridor and the secondary chambers 4 are distributed on either side of the main chamber 2. Openings 18 allow for communication between chamber 2 and chambers 4. In order to provide maximum protection in use and in operation, the main chamber 2 and the secondary chambers 4 are insulated from each other in order to reduce the risk of propagation of flames and hot gases in the event of fire in one of the chambers. However, in order to allow for the transfer of the materials between the secondary chambers by the intermediary of the main chamber 2, transfer devices 6 are disposed between the main chamber 2 and the secondary chambers 4, at openings 18. In FIG. 1, this transfer device can be seen, comprising a barrel door 8 rotatable about the axis X of rotation and making it possible to transfer objects from the main chamber 2 to secondary chambers 4 and vice versa. The main chamber 2 is separated from secondary chambers 4 by an insulation wall 10. Since all of the transfer devices of the installation are substantially the same, only a transfer device 6 and a secondary chamber 4 will be described. The barrel door 8 substantially has the form of a regular cylinder, defining an inner space 12, communicating with the outside via an opening 14 that is substantially rectangular in the example shown. The barrel door 8 comprises a body 9 formed, for example, of a jacket 11 made of stainless steel filled with a material comprising cast iron and binders of the resin type, such as MP2. The jacket comprises, advantageously arms penetrating into the fill material in such a way as to ensure proper fixation of the shell 11 in the material. The wall 10 is made from, for example, concrete and covered with a shielding 16 in such a way as to form a fire-proof seal. The opening 18 is of substantially likewise dimension as that of opening 14 arranged in barrel door 8, in such a way that when the opening 14 of the barrel door is facing the opening 18 of the wall, openings 14 and 18 match up. The wall 10 comprises a recess 20 defined by a curved surface, with an inner radius that is substantially equal to the outer radius of barrel door 8, and receiving a portion of said barrel door 8. The barrel door penetrates into wall 10 and sealing means 22 are provided between the cylindrical periphery of the door and the curved surface of wall 10, in such a way as to provide a seal between the barrel door and the wall, and thus between the main chamber 2 and the secondary chamber 4. A sealing means 22 according to the invention is positioned along a generatrix (FIG. 1) of the cylindrical body 9 in such a way that it is in contact with the outer periphery of barrel door 8. Means 22 is, for example fixed to the wall 10, in particular to an end of the curved recess 20. This sealing means 22 comprises, according to this invention and as shown in FIGS. 3 and 4, a seal carrier 24 and a seal 26, with seal carrier 24 being fixed on the wall 10, and the seal being in contact with the outer periphery of barrel door 8. The seal carrier 24 has a substantially trapezoidal form, with the large base comprising a groove 25 wherein is placed seal 26. The particular form of the seal carrier ensures guidance for the mounting of the seal carrier, facilitating its accurate installation and the alignment of the seal with the outside cylindrical wall of the barrel door. The groove 25 advantageously has a T-shaped section in order to improve the holding of the seal 26. Advantageously, the seal carrier is provided with a handgrip handle 31 for the installation and mounting of the seal carrier on the wall 10 and the element 27. This handle 31 can be removable, it is used to mount the seal carrier, and for this it is fixed on the seal carrier. After the mounting of the seal carrier on the barrel door 8, it is removed for the operation of the barrel door. For the removal of the seal carrier, the handle 31 is again fixed to the latter. Advantageously, the seal carrier 24 is made from stainless steel by casting, and the groove 25 wherein is injected the material of the seal, is machine tooled. The seal is advantageously made from an intumescent material, which has the property of inflating when heated thus providing a tight seal for hot and flammable gases. Advantageously, it also provides heat insulation. For example the material of the seal can be chosen in order to provide its sealing function for more than 2 hours. The seal is for example made from bi-component mastic, such as a 335s of the Mécatiss® brand. The groove can have any other form that retains the seal in the groove, for example a trapezium form, with the large base corresponding to the bottom of the groove 25. The seal carrier 24 is fixed to the wall 10 in a removable way, for example by screw-bolt connection. Bolts 29 are for example welded on the shielding 16 (FIG. 2) wherein the seal carrier can be fixed using nuts. Any other means of removable fixation can be used to attach the seal carrier 24 to the wall 10. In the example shown, the seal carrier 24 is made from several pieces which are placed end to end in order to form the seal between the wall 10 and the barrel door 8 across the entire height of the barrel door 8. The transfer device 6 according to the invention comprises also, advantageously, a first means 28 shown in FIGS. 6A and 6B, able to provoke a pressure drop for hot gases. This first means 28 is positioned at an upper end of the barrel door 8. This means 28 is carried out in the form of an angle assembly or annular ring. The ring 28 as a cross-section in FIG. 6B, comprises a first 41 and a second 43 sides substantially at a right angle, the first side 41 being flush with an upper surface 36 of the drum 8 and the second side 43 being in line with the outer periphery of the drum 8, thus extending towards the top of drum 8. The angle assembly 28 is for example made of steel, comprising several arcs of a circle, for example six, placed end to end via welding. The arcs of a circle have an inner radius substantially equal to that of the barrel door. These sectors are advantageously non-jointed. The angle assembly 28 is, for example, fixed by its first side 41 on the barrel door 8 by a welded pin, washer and nut assembly 47. Advantageously, means (not shown) to adjust the position of the angle assembly can be provided on the angle assembly 28. The latter make it possible to fix a defined spacing between the recess 20 and the second side 43 of the angle assembly 28. These means of adjustment are advantageously removable and are mounted on the angle assembly 28 only for its positioning. The angle assembly 28 forms a baffle system, which makes it possible to substantially improve the seal by creating a pressure drop for hot gases. Furthermore, the addition of this angle assembly 28 on the barrel door 8 increases the total height of the barrel door, lengthening the travel of the hot gases to emerge on the upper side of the barrel door 8. The device according to the invention also comprises, more preferably, a second pressure drop means 30, positioned substantially along a generatrix of the cylindrical body 9, between the wall 10 and a safety caisson 32. The safety caisson 32 comprises a recess 34 of substantially curved form, with inner radius substantially equal to the outer radius of the barrel door 8 and defining with the recess 20 of the wall 10, a housing extending substantially at 180° around the barrel door 8. The caisson 32 avoids communication between chambers 2 and 4 during the rotation of the door 8 by providing a minimum overlap between the opening 14 of the door 8 and the caisson 32. As such it avoids the propagation of the fire during the rotation of the door. The caisson 32 is for example formed of a stainless steel jacket filled with MP2 as mentioned previously. The second pressure drop means 30, shown in FIG. 5, is disposed between the safety caisson 32 and the wall 10. In the example shown, the second pressure drop means 30 is formed of an elongated element, for example made of steel and of circular transversal section, of the round steel type, welded in a groove 34 arranged between the wall 10 and the caisson 32. Advantageously, the second means 30 is made of several sections, for example two, advantageously welded in a housing defined between the shielding covering the wall 10 and the caisson 32, for example via intermittent point weld. In the example shown, the upper and lower ends of the round steel (not shown) are folded to 90° towards the wall by moving the barrel door away, which makes it possible to remove the spacing of the emerging groove 34. The round steel is adjusted so as to guarantee a maximum spacing, for example of about 2 mm, with the outer periphery of the door. This makes it possible to obtain a pressure drop sufficient to limit a propagation of hot gases. In FIG. 10, a door 8 can be seen for a transfer device according to this invention, comprising a first upper surface 36 and a second lower surface 38, and first 40 and second 42 axes respectively projecting from surfaces 36 and 38, arranged according to the direction X and forming the axis of rotation of the door 8. In the example shown, the arms are maintained axially in relation to the wall 10 using a lower support 44 projecting transversally from the wall in the secondary chamber 2 and an upper support 46 also projecting transversally from the wall 10. The first axis 40 is fixed in rotation in relation to the door and mobile in rotation in relation to the upper support 46 by means of a bearing 48. The second axis is, in the example shown, fixed in rotation on the lower support 44 and mobile by means of a bearing 50 in relation to the door 8. The door is driven in rotation by an electric motor positioned at one end of the axis 40. The motor can be controlled from the exterior of the installation. The motor can also be positioned on the second axis 42. Several motors can also be provided. The operation of said transfer device shall now be explained. In FIG. 1, the drum can be seen, especially the inner space 12 open onto the main chamber 2. In this position, an object for example a bottle (not shown) containing one or several materials in order to produce nuclear fuel is introduced into space 12. The barrel door 8 is then driven in rotation around the X axis. After having completed a 180° rotation, the interior volume 12 is open onto the secondary chamber 4. The bottle contained in space 12 can thus be transferred into the secondary chamber 4. The transfer device can also be provided so that the rotation in one direction of the barrel door is less than 180°. We shall now describe a method of producing the seal and seal carrier unit according to this invention, in relation to FIGS. 7 and 8. Such a method comprises the following steps: installing shutters on the longitudinal and transversal ends of the groove (25) of the seal carrier, injecting a flame- and hot gas-resistant material into the groove, removing shutters. In the FIGS. 7 and 8, the step of injecting the material forming the seal in the seal carrier can be seen. In order to carry out the injection, the longitudinal ends 60, 62 of the groove, as well as its open end 64 are shut by plates 66, 68, 70 respectively, in such a way as to define the location and the form of the seal 26. The plates 66, 68 are maintained attached to the seal carrier, for example by screwing on the ends of the seal carrier. The plate 70 is, in the example shown, maintained by tightening between transversal elements 72 connected by the tightening elements 74, such as threaded rods and nuts. An orifice 76 is provided in plate 70 for the injection of the material of the seal via a nozzle 78 in the groove 25. When the material has the desired texture, the plates 66, 68 and 70 are removed. The seal carrier provided with the seal is ready to be mounted. At the transversal end 64 of the groove 25, a knitted sheet of Kevlar® and a sheet of Milard® can be provided in order to provide the seal of the mould when the material is injected. The latter are removed during demoulding.
045129215	description	DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT In order to decontaminate the coolant system of a water cooled nuclear power reactor, the reactor must first be shut down and the coolant allowed to cool below 100.degree. C. The decontamination solution is prepared by adding concentrated solutions to the coolant to make the coolant about 0.01M in oxalic acid and about 0.005M in citric acid, by adjusting the pH to about 3 with ammonia, and by adding and maintaining about 0.75 ppm dissolved oxygen in the coolant. The decontamination solution is then circulated at a temperature of about 90.degree. C., throughout the coolant system. As the decontamination solution circulates, the metal oxide films on the surface of the system dissolve and are complexed by the oxalic acid and to a lesser extent by the citric acid. In addition to the complexed metal ions, other particulate matter may be loosened and swept along by the decontamination solution. As the decontamination process proceeds, the dissolved metallic ions are continuously removed and the complexing power of the reagents renewed by passing a portion of the coolant containing the metal-ion complexes through a strong-base anion-exchange resin bed which has been presaturated with oxalic and citric acids in about the same ratio and about the same pH as these reagents are present in the circulating coolant. As the contaminated decontamination solution, which contains a mixture of unutilized or metal-ion-free organic anions and complexed divalent and trivalent metal ions, is passed through the presaturated anion-exchange resin bed wherein the metallic-ion complexes are exchanged for the metal-ion-free organic anions on the resin while any unutilized, metal-ion-free organic anions pass through the resin bed unaffected, whereby this portion of the decontamination solution is renewed and is ready for recirculation throughout the cooling system. The coolant may be made from 0.005 to 0.02M in oxalic acid with about 0.01M being the preferred concentration; lower concentrations result in much slower dissolution rates. Citric acid concentration may vary from about 0.002 to 0.01M with 0.005M being the preferred concentration. The ratio of oxalic acid to citric acid may vary from 1:1 to 10:1 with a ratio of about 2:1 preferred. The citric acid acts as a pH buffer and to retard the formation of ferrous oxalate which may otherwise precipitate and may be difficult to resolubilize. The citric acid may also act as a minor complexing agent. The oxalic and citric acids may be injected together or separately into the coolant as concentrated solutions. The pH of the coolant may vary from about 2.5 to 4.0, preferably 2.8 to 3.5 and most preferably about 3.0 and may be controlled by adjusting the pH with ammonia. Control of pH is important to obtain the highest dissolution rate with the minimum amount of corrosion. Coolant temperature during decontamination may vary from about 60.degree. to 100.degree. C. with 90.degree. C. being preferred. Temperatures above 100.degree. C. cause the organic reagents to decompose while below about 60.degree. C. the dissolution rate is very slow. A small amount of dissolved oxygen should also be added to the circulating coolant during decontamination to ensure complete oxidation of the Fe.sup.+2 to Fe.sup.+3. This is important to prevent formation of ferrous oxalate precipitate. The concentration of oxygen may vary from about 0.2 to 4.0 ppm, preferably about 0.5 to 1.0 ppm. The oxygen may be added by any convenient method, such as the addition of hydrogen peroxide to the coolant, or preferably, by gas injection into one of the flowing coolant systems. The anion-exchange resin may be any commercially available strong base anion exchange resin such as Bio Rad AG-1 or Amberlite IR-400. The resin, which is generally received in hydroxide form must be loaded with oxalate and citrate anions so that the anions on the resin are in chemical equilibrium with the reagents in the decontamination solution. This can best be accomplished by first loading the organic anion on the resin bed from a concentrated solution of the reagents. The resin can then be equilibrated in a stepwise matter with a dilute flushing solution of the same composition as the decontamination solution until the effluent from the bed has about the same concentration of reagents and pH as the decontamination solution. For example, a concentrated oxalic acid-citric acid solution is prepared in which the oxalate-citrate ratio is the desired ratio of the two reagents on the resin when it is in chemical equilibrium with the decontamination solution. This concentrated solution is added to the resin at a controlled rate until the pH is about that desired for the decontamination solution. A dilute oxalic acid-citric acid flushing solution is prepared having the same composition and pH as the decontamination solution. The resin is then flushed in a column with large quantities of the flushing solution until the effluent is the same pH as the decontamination solution. At this time the resin is presaturated and ready for use in regenerating the reagents in the coolant. When the coolant decontamination solution, containing a mixture of the unutilized metal-ion free organic anions and the metallic-ion complexes, is passed through the presaturated anion-exchange resin, the metallic-ion complexes are exchanged for the metal-ion-free organic ions in the resin. The unutilized reagents pass through the resin bed unaffected. Using oxalic acid as an example, the exchange reactions for the Fe.sup.+3 oxalate and Co.sup.+2 oxalic complexes are: EQU Fe(C.sub.2 O.sub.4).sub.3.sup.-3 +3RHC.sub.2 O.sub.4 .fwdarw.R.sub.3 Fe(C.sub.2 O.sub.4).sub.3 +3HC.sub.2 O.sub.4.sup.-, and EQU Co(C.sub.2 O.sub.4).sub.2.sup.-2 +2RHC.sub.2 O.sub.4 .fwdarw.R.sub.2 Co(C.sub.2 O.sub.4).sub.2 +2HC.sub.2 O.sub.4.sup.-, where R stands for the cationic species affixed to molecular structure of the resin. Although these are reversible, equilibirum reactions, they are driven to the right by the thermodynamic preference of the resin for the multicharged metallic-complex ion over the single-charged binoxalate anion and by the multistage sorption effect of the anion-exchange column. The decontamination reagents can be easily removed from the reactor coolant system by passing the coolant containing the reagents, either complexed or uncomplexed through a mixed ion-exchage resin bed, i.e. both anion- and cation-exchange resins, until the conductivity of the solution drops to about 1 .mu.mho. At this point, the coolant is essentially free of reagent and reactor start-up can be commenced. While the method of the invention as described, is applied only to the regeneration of oxalic acid and citric acid systems, the technology could potentially be applied to the regeneration of solutions of a variety of other metal complexing organic chemicals which might be used as decontaminating agents. These include nitrilotriacetic acid (NTA) and hydroxyethylethylenediaminetriacetic acid (HEDTA). The addition of a small amount (5 to 10% by volume) of cation-exchange resin to the presaturated anion-exchange resin could potentially provide a margin of additional capacity for the removal of divalent ions. Since the cation-exchange resin does not sorb appreciable amounts of Fe.sup.+3 from oxalate and citrate solutions, its capacity for removing the divalent metallic ions from the decontaminating solution is essentially independent of the Fe.sup.+3 concentration. Thus, even though it is less efficient initially than the anion-exchange resin for the removal of divalent ions, the cation-exchange resin may become more efficient as the anion-exchange resin reaches saturation with the Fe.sup.+3 complexes. EXAMPLE I To compare the effectiveness of the anion- and cation-exchange resins on the removal of iron and cobalt from a decontamination solution, a typical laboratory ion-exchange column (1 cm.times.30 cm) was loaded with strong-base anion-exchange resin (Bio Rad AG-1) to a height of 20 cm. To presaturate the resin, a solution of 0.02M oxalic acid, adjusted to a pH of 3.0 with NH.sub.4 OH, was passed through the column until the column effluent had the same concentration and pH as the feed. A simulated decontamination solution, consisting of 0.02M oxalic acid with 1.51.times.10.sup.-3 M Fe.sup.+3 and 4.0.times.10.sup.-5 M Co.sup.+2 (6.8.times.10.sup.-3 .mu.Ci/ml Co-60), was passed through the column, and the effluent was sampled periodically. The effluent samples were analyzed for the concentrations of Fe.sup.+3 and Co-60. The Fe.sup.+3 and Co-60 concentrations in the effluent are shown in FIG. I. The anion-exchange resin, presaturated with binoxalate anions, was essentially 100% efficient at removing Co-60 for about 500 bed-void volumes and at removing Fe.sup.+3 for about 550 bed-void volumes. This demonstrates the efficiency of the anion-exchange process for removing the metallic-ion complexes from the solution. Similar experiments to evaluate the cation regeneration process were conducted with hydrogen-ion-form cation-exchange resin and a pH 3 solution of 0.02M oxalic acid with 1.55.times.10.sup.-3 M Fe.sup.+3 and 5.7.times.10.sup.-5 M Co.sup.+2 (7.7.times.10.sup.-3 .mu.Ci/ml Co-60). The results of the Fe.sup.+3 and Co-60 are plotted in FIG. II. These data readily indicate that the Fe.sup.+3 -oxalate complex is not efficiently removed by cation-exchange resin (breakthrough after about one bed-void volume) and efficiency of the cation-exchange resin for removal of Co.sup.+2 decreases after only about 150 bed-void volumes of solution is passed through the column. This premature cobalt breakthrough occurred even though the ion-exchange column was not saturated with the metallic ions. EXAMPLE II An anion exchange resin was presaturated with oxalate and citrate anion in the following manner: A concentrated solution of oxalic acid and citric acid was prepared by dissolving 83.6 g oxalic acid and 33.5 g in citric acid in 1070 ml H.sub.2 O to form a solution 0.62M in oxalate and 0.149M in citrate. The concentrated solution was added to a beaker containing 780 ml of a strong base anion resin in the OH.sup.- form at a controlled rate of 12 ml/min and stirred, until a pH of 3 was achieved. This required about 625 ml of solution. The resin was then loaded into a standard ion exchange column and flushed with a solution of 0.012M oxalic acid and 0.005M citric acid at pH3 until the column effluent had about the same pH and oxalate-citrate concentration as the flushing solution. Table I below shows the correlation between solution volume and oxalate-citrate concentration. TABLE I ______________________________________ Total Solution Oxalate-Citrate Volume ml pH Concentration ______________________________________ 800 4.11 Not Determined 6200 4.10 Not Determined 18200 3.43 Oxalate-0.0085 M Citrate-0.008 M 29900 3.19 Not Determined 40900 2.98 Oxalate-0.0116 M Citrate 0.0049 M ______________________________________ The resin was then presaturated and ready for regeneration of the decontamination solution. EXAMPLE III An ion-exchange column breakthrough experiment was conducted to evaluate the elution sequence and the capacity of a mixed-bed of cation and presaturated anion resin used for the regeneration process. A solution of 0.01M oxalic acid and 0.005M citric acid at pH 3 containing 0.003M Fe.sup.+3 and 0.0001M Cr.sup.+3, Ni.sup.+2, Co.sup.+2, Zn.sup.+2, Mn.sup.+2, Cu.sup.+2, and Fe.sup.+2 was passed through a 90/10 mixture of anion and cation resins until the effluent and feed concentrations were similar. The effluent was sampled periodically and analyzed for metal ion concentrations by plasma spectrometry; the Fe.sup.+2 concentrations were determined spectrophotometrically. The elution sequence was (Fe.sup.+3,Cr.sup.+3), Cu.sup.+2, (Ni.sup.+2, Zn.sup.+2, Co.sup.+2), Mn.sup.+2 and Fe.sup.+2, which is in agreement with the oxalate complex stabilities for the various ions. These data indicate the quantity of cation resin added to the pre-saturated anion resin to provide back-up Co-60 capacity for the regeneration process must have sufficient capacity to adsorb all of the divalent corrosion products except Cu. In addition, these data indicated the Fe.sup.+3 and Cr.sup.+3 oxalate complexes have similar affinities for the anion-exchange resin since their breakthroughs occurred simultaneously and their final concentrations on the resin were proportional to their solution concentrations. The capacity of the presaturated anion-exchange resin for trivalent ions was determined to be 0.47 moles/liter, which is equivalent to the theoretical capacity. The capacity of the cation-exchange resin for divalent-ions was determined to be 0.33 moles/liter, which is approximately 40% of the theoretical capacity. EXAMPLE IV A circulating test loop was prepared to study the effects of the decontamination reagents on the removal of iron oxides and cobalt from reactor coolant system piping and to determine the efficiency of the reagent regeneration. A solvent consisting of 0.01M oxalic acid and 0.005M citric acid at pH3 was circulated through the loop. The dissolved oxygen content of the solvent was maintained within the specification of 0.75.+-.0.25 ppm. No ferrous oxalate precipitation was observed. Approximately 85% of the Co-60 activity was removed over the 12-hour dissolution cycle. Within a few minutes after the initial injection of the reagents, the loop chemistry and operating conditions were stabilized. All of the operating parameters were maintained within specification for the remainder of the run. The Co-60 activity in solution increased to a maximum during the first few hours of the test and then it decreased as the oxide film dissolution rate decreased and was exceeded by the solvent regeneration rate. The maximum Co-60 concentration obtained was equal to approximately 6.7% of the total Co-60 dissolved during the test. The oxalic acid and citric acid concentrations were maintained within specification during the decontamination cycle. The iron concentration in solution was maintained below 6% of the total iron dissolved. As can be seen from the preceeding discussion and Examples, the process of this invention provides an effective method for the decontamination of the coolant systems of water cooled nuclear power reactors by providing an efficient and effective method for continuously regenerating the reagents used for the decontamination process.
	summary
046831142	description	DETAILED DESCRIPTION According to the present invention, a composition and method are provided for combining a boron-containing burnable absorber with a nuclear fuel pellet, with the burnable absorber coated on the pellet, encased in a boron-containing glass. The nuclear fuel pellets are preferably comprised of uranium dioxide which is enriched in U-235 isotope. Other such nuclear fuels, however, may be used in the formation of the pellets, such as a mixture of uranium-plutonium dioxide. The fuel pellets are generally formed by enriching the uranium dioxide and, either alone or in mixture with plutonium dioxide, compacting the material to the desired shape and size, and sintering the same to produce dense pellets for use in a nuclear fuel rod. The sintered pellets are then coated according to the present invention. The coating formed on the nuclear fuel pellets is a boron-containing burnable absorber encased in a boron-containing glass, which coating is resistant to peeling and exhibits exceptionally low moisture or hydrogen adsorption. The boron-containing burnable absorber is preferably boron carbide (B.sub.4 C) but other known boron-containing absorbers such as zirconium diboride (ZrB.sub.2), and the like, which are stable at temperatures in excess of about 1000.degree. C. may also be used. The second component of the coating composition of the present invention is a specially developed boron-containing glass composition. The boron-containing glass composition has a melting temperature between 900.degree.-1100.degree. C. and contains boron oxide (B.sub.2 O.sub.3); silicon dioxide (SiO.sub.2); at least one alkali oxide such as sodium oxide (Na.sub.2 O); or potassium oxide (K.sub.2 O); at least one alkaline earth oxide such as calcium oxide (CaO) or barium oxide (BaO); and a stabilizer such as aluminum oxide (Al.sub.2 O.sub.3); within specified amounts by weight of the boron-containing glass composition. The amounts, by weight, of the various components of the glass composition that is usable are: B.sub.2 O.sub.3 : 20-30 percent PA1 SiO.sub.2 : 30-60 percent PA1 Na.sub.2 O: 5-15 percent PA1 BaO: 5-15 percent PA1 CaO: 5-15 percent PA1 Al.sub.2 O.sub.3 : 5-15 percent PA1 B.sub.2 O.sub.3 : 20 PA1 SiO.sub.2 : 40 PA1 Na.sub.2 O: 10 PA1 BaO: 10 PA1 CaO: 10 PA1 Al.sub.2 O.sub.3 : 10 PA1 SiO.sub.2 -40 gr PA1 B.sub.2 O.sub.3 -20 gr PA1 Na.sub.2 CO.sub.3 -17 gr (10 g Na.sub.2 O) PA1 BaCO.sub.3 -13 gr (10 g BaO) PA1 CaCO.sub.3 -18 gr (10 g CaO) PA1 Al.sub.2 O.sub.3 -10 gr The amount of boron oxide present must be between 20-30 percent by weight. If less than about 20 percent by weight of the boron oxide is present, insufficient encapsulation and entrapment of the boron-containing burnable absorber results, while use of more than about 30 percent by weight in unacceptable due to reaction with water and, hence, moisture adsorption from the atmosphere which must be avoided. Since borosilicate glasses usually have very low thermal expansion coefficients (.alpha.), the alkali oxide having a high .alpha., in excess of that of uranium dioxide, is added in order to obtain an adequate .alpha. of the coating to match or exceed that of the uranium dioxide fuel pellet (.alpha.=10.times.10.sup.-6 /.degree.C.). Since B.sub.4 C, which is added to the glass, has a low .alpha.(4.times.10.sup.-6 /.degree.C.), the boron-containing glass component should have a higher .alpha. such that the resulting mixture has an expansion commensurate with the amount of B.sub.4 C present. Amounts of alkali metal oxide between 5-15 percent by wieght will give the desired expansion. The alkaline earth oxides are used to adjust the melting temperature of the glass composition, with a melting temperature of the glass composition, with a melting temperature of about 1000.degree. C. being preferred. The aluminum oxide is added as a stabilizer for the glass composition. A preferred glass composition has the composition, in percent by weight: This composition, when melted in a silica crucible at about 1100.degree. C. and quenched, gives a clear glass. The glass, after being immersed in water for 24 hours and dried, showed no weight change indicating that the glass does not react with water. In application of the present coating, the boron-containing burnable absorber and boron-containing glass are ground or otherwise provided in a finely divided particulate state, and first mixed together. Both these components should be provided in a particle size finer than 325 mesh, U.S. Standard Sieve. It is preferred, however, that the particle size of the boron carbide be smaller, with at least 90 percent of the particles being of a diameter less than about 10 microns. It is also preferred that the particle size of the boron-containing glass be smaller, with those particles being of a diameter of about 5 microns or less. These smaller particle sizes provide more intimate mixing of the particles and the ability to incorporate a higher amount of boron carbide in the coating, with the resultant coating still exhibiting exceptional bond strength and resistance to peeling and to hydrogen adsorption. In mixing of the two components, the boron carbide content of the mixture must be within a range of 20 to 80 percent by weight, while the boron-containing glass is in an amount of 80 to 20 percent by weight of the mixture. The use of less than about 20 percent by weight of boron carbide would not provide the desired absorption capabilities within a tolerable thickness of the resultant coating, while use of in excess of about 80 percent of boron carbide results in incomplete incorporation of the boron carbide in the resultant coating and possible peeling of the same from the pellets. Amounts of up to 80 percent boron carbide in the coating are achievable when the particle sizes of both components of the mixture are of a size in the above-mentioned preferred ranges. In instances where less than about 40 percent of the composition is boron carbide, particle sizes which are somewhat larger but still below 325 mesh are usable, with formation of a coating that incorporates the boron carbide sufficiently to prevent peeling or hydrogen adsorption. The mixture of boron-containing burnable absorber and boron-containing glass may be applied to the surface of the nuclear fuel pellets by various techniques, such as dipping the pellets in a slurry of the mixture, wet spraying a slurry of the mixture on the pellets, rolling the pellets in a slurry of the mixture, or dry spraying the mixture as a powder on the surface of the pellets using electrostatic charge spraying techniques. In the dipping, wet spraying and rolling applications, the finely ground mixture of boron-containing burnable absorber and boron-containing glass is formed into a slurry with a liquid such as acetone, an alcohol, water, or a liquid hydrocarbon medium such as toluene, to the consistency desired, with a dispersant or surface active agent added to provide the desired dispersion of the particles in the liquid as a slurry. The thickness of the boron carbide-containing coating should be kept at or below a thickness of about 1 mil. Because of the close tolerance required upon loading of fuel pellets in a metallic cladding, the application should also provide a controlled, uniform, thin coating of 1 mil or less. Also, since any coating thickness will remove some of the gap between the pellet and cladding, the coating thickness should be kept to a minimum to avoid a reduction in fuel inventory, and also to provide sufficient space for the liberation of helium, during irradiation, from the B.sup.10 such that the desired fuel rod pressure is not exceeded. The minimum thickness of the coating will be that thickness which contains the desired amount of B.sup.10 to provide sufficient neutron absorption during reactor operation. In general, an amount of about 1 to 2 mg, preferably 1.5 mg, of B.sup.10 per inch of length of pellet, having a constant diameter of about 0.3 inch, has been determined to be a preferred amount. The thickness of the coating should thus be that which will provide an amount of boron, including the boron in the boron-containing burnable absorber and the boron in the boron-containing glass, that results in a B.sup.10 quantity of about 1 to 2 mg per inch of pellet. The coating is applied to the circumferential surface of the pellets and the ends of the pellets are uncoated. In dipping, or otherwise applying the coating where the whole pellet may be coated, the coating is removed from the ends of the pellet to leave the coating only on the circumferential surface. After coating the nuclear fuel pellets with the coating composition of the present invention, the coated pellets are dried and then heated to an elevated temperature to melt the boron-containing glass and incorporate the boron carbide particles therein. The coated pellets are heated to a temperature of between 900.degree.-1100.degree. C., preferably 1000.degree.-1050.degree. C. for a short period of time, under an atmosphere that is inert relative to the uranium dioxide of the fuel pellets and to the boron carbide powder. The temperature range of 900.degree.-1100.degree. C., is important in that the temperature must be high enough to melt the glass and effect encapsulation of the boron carbide, while temperatures in excess of about 1100.degree. C. are avoided to prevent reaction between the boron of the boron-containing burnable absorber with the components of the boron-containing glass, which would, in effect, cause a loss of boron-containing absorber that is needed in the finished pellets. The melting of the glass and encapsulation of the boron-containing absorber in the glass at the above temperatures is effected by heating the coated pellets for only about 5 to 15 minutes, preferably about 10 minutes. The heating is effected in an atmosphere that is inert relative to the uranium dioxide, such as an atmosphere of hydrogen, argon, or mixtures thereof, or a vacuum, with oxygen being excluded from the atmosphere. A short holding time at the required temperature is believed to be a key factor for obtaining an ideal coated pellet. The coated pellets, after the heating step, are cooled and the result is a nuclear fuel pellet coated with a strong, adherent coating of a boron-containing burnable absorber that is encapsulated in a boron-containing glass. The invention is further illustrated by reference to the following example, wherein parts or percentages are by weight unless otherwise indicated. EXAMPLE I As an example of the coating composition and process of the present invention, a series of coated pellets were made using the following composition and procedure. A boron-containing glass composition was prepared by combining the following for 100 g of glass: The above powders were mixed in a plastic bottle with Al.sub.2 O.sub.3 balls on a roller overnight. The mixture was then melted in a pot furnace using a silica crucible at 1200.degree. C. After the melt was clear, containing no bubbles, the melt was quenched into a cold stainless steel crucible which was surrounded with an ice water bath. The glass was then vibra-milled in a plastic bottle with Al.sub.2 O.sub.3 balls and screened to -325 mesh. Thirty-five (35) grams of the above glass composition, milled to a particle size, such that about 95 percent of the particles were less than 10 microns, were mixed with 65 grams of boron carbide (Tetrabor, about 96 percent of particles less than 10 microns). This mixture was formed into a slurry by combining the mixture with 67.71 grams toluene and 11.90 grams of a binder (A-20, acryloid resin sold by Rohm & Haas Co.). The coating composition resulting was sprayed onto uranium dioxide pellets, dried and the coated pellets fired in a hydrogen furnace at 1000.degree. C. for 5 minutes. The resultant coated pellets were subjected to a peel test wherein a piece of Scotch tape was wrapped around the circumference of the pellet, pressed firmly onto the coating, and then removed. The coated pellets passed the peel test, with no coating removed, showing good adhesion of the coating. The coated pellets had a hydrogen content of less than 1 ppm (part per million by weight) indicating resistance to moisture adsorption. The pellets showed the coating weight in thicknesses listed in Table I: TABLE I ______________________________________ Original Weight of Pellet Weight of Coated, Fired Weight of Thickness of No. Pellet (gr) Pellet (gr) Coating (gr) Coating (mil) ______________________________________ 1 7.4909 7.4992 0.0083 0.9-1.00 2 7.3812 7.3894 0.0082 0.85-0.95 3 7.4943 7.5024 0.0081 0.75-1.00 4 7.4808 7.4888 0.0080 0.90-1.00 5 7.3750 7.3829 0.0079 0.85-1.00 ______________________________________ As is evident from the results listed in Table I, the thickness of the coating was one mil or less and the resulting coated pellets contained a desired amount of B.sup.10. A theoretical amount of about 8.04 mg B.sup.10 is desired, with the actual amounts listed being between about 7.9 mg to 8.3 mg. The actual amount of B.sup.10 is calculated by combining the amount of B.sup.10 in the glass and the amount of B.sup.10 in the boron carbide (about 18.9 percent of boron being the B.sup.10 isotope in natural boron). EXAMPLE II A further series of pellets were coated as follows. Powdered boron-containing glass was prepared having the following composition, by weight: SiO.sub.2 -40; B.sub.2 O.sub.3 -20; Al.sub.2 O-10; BaO-10; CaO-10; and Na.sub.2 O-10. The glass was then vibra-milled into a powder (<325 mesh) for mixing with B.sub.4 C to prepare the coating slurry. Several slurries were made by mixing the powdered boron-containing glass and B.sub.4 C powders (Norton Company B.sub.4 C powder, about 90 percent of particles less than 15 microns) in different proportions (20, 30, 40 and 50 percent by weight B.sub.4 C) using acetone as the liquid medium and a dispersing agent (a solution containing 13 volume percent of Tamol and 1 volume percent of Triton from Rohm & Haas Co.). Uranium dioxide pellets were coated with these slurries either by dipping or spraying methods. A uniform layer of coating was obtained and dried quickly. The coated uranium dioxide pellets were fired in a hydrogen furnace at 950.degree. C. for 10-15 minutes. The glass melted and the B.sub.4 C particles became immersed in the melt, but did not react with the glass. The coating containing 30 percent by weight B.sub.4 C or less showed a shiny, adherent, glassy surface which passed the peel test (aforedescribed) without any evidence of coating removal. The coating containing 40 percent by weight B.sub.4 C showed a dull but still adherent coating and also passed the peel test. However, the coating containing 50 percent by weight B.sub.4 C failed to peel test. This is believed to be a result of the glass particles not being in a sufficiently finely divided state to encapsulate all of the B.sub.4 C particles. The moisture content of the coated pellets was measured and showed hydrogen contents in the range of 0.3-0.7 ppm. This low hydrogen content is considered to be due to the smooth, non-porous nature of the surface resulting in less surface area of the coating and the passive nature of the boron-containing glass to moisture. Metallographic sections, at two magnifications, of a pellet so produced are illustrated in FIGS. 1 and 2. It is clear that the coating is adherent, uniform and continuous. There are no cracks in the coating or at the pellet/coating interface. The encapsulated boron carbide particles show as white spots in the glass matrix. EXAMPLE III A series of pellets were coated according to the procedure of Example II, wherein the coating contained 40 percent by weight B.sub.4 C. Before firing of the pellets, a second coating containing only the boron-containing glass, without any added B.sub.4 C was applied to the initially coated pellets, as an overcoat. The dual-coated pellets, after drying, containing a major thickness of boron carbide containing glass and a minor thickness of glass overlay, were then fired as described in Example II. The resultant dual-coated pellets had a shiny and glassy coating and passed the peel test. The moisture content of the dual-coated pellets also showed hydrogen contents in the range of 0.3-0.6 ppm. Metallographic sections of a dual-coated pellet so produced are illustrated at two magnifications, in FIGS. 3 and 4. Again, an adherent, uniform and continuous coating with no cracks either in the coating or at the pellet/coating interface are indicated. The extremely smooth surface of the top, glass layer (without any B.sub.4 C particles) is also visible in FIGS. 3 and 4. It should be noted that the two coating layers merged at their interface such that no bond line is apparent between the two layers, although the bottom layer containing the boron carbide is seen as being covered by a thin glass layer free of boron carbide particles. Again, the boron carbide particles show as white spots in the glass matrix. EXAMPLE IV A series of coated pellets were made according to the procedure of Example I, except that the coating composition comprised 80 grams of boron carbide (Tetrabor, about 96 percent of particles less than 10 microns) and 20 grams of the glass composition, that had been ground to a particle size of less than about 5 microns in diameter. Coated pellets, after drying, were fired at about 1000.degree. C. for 5 to 15 minutes. The thickness of the final coating was between about 0.5 to 0.7 mil. The fired pellets passed the peel test, indicating that up to 80 percent boron carbide can be present in the glazed coating when the boron carbide particles are finely divided and the glass particles are also finely divided. The coatings prepared according to the present invention, wherein a burnable absorber is encapsulated in a boron-containing glass exhibit very low hydrogen (moisture) adsorption (<1 ppm) and have a strong bond with the pellet without any cracks in either the glass, the coating, or at the interface. The coating also provides a smooth surface which could act as a lubricant, and is provided by a process tht is relatively simple, quick, and requires less capital expediture than other processes. Both the thickness of the coating and the B.sup.10 content in the coating can be varied and controlled to fit the exact needs of the user.
	claims	1. A method of irradiating comprising: moving items through a charged particle beam; determining a kinetic energy of the charged particle beam entering the item; and, measuring a kinetic energy of the charged particle beam exiting the item. 2. The method as set forth in claim 1 , further including: claim 1 determining a difference between the energy of the charged particle beam entering and exiting the item; and, determining an absorbed dosage of the charged particle beam from the difference. 3. The method as set forth in claim 2 , further including: claim 2 controlling at least one of a speed with which the items move through the charged particle beam and the energy of the charged particle beam in accordance with the determined absorbed dose. 4. The method as set forth in claim 1 , wherein: claim 1 the items are conveyed through the charged particle beam in a first direction; and, the charged particle beam is swept back and forth in a plane perpendicular to the first direction. 5. The method as set forth in claim 1 , wherein the charged particle beam is an electron beam. claim 1 6. The method as set forth in claim 1 , further including: claim 1 determining a beam current absorbed by the irradiated product. 7. The method as set forth in claim 1 , further including: claim 1 scanning the charged particle beam; and, measuring beam current pulses as the beam current scans past a measurement point. 8. A method of irradiating comprising: irradiating items with a charged particle beam; determining an energy of the charged particle beam entering the item including measuring changes in a charged particle beam current; and determining an energy of the charged particle beam exiting the item including measuring changes in a charged particle beam current. 9. The method as set forth in claim 8 , further including: claim 8 measuring the charged particle beam current at a plurality of locations along the item. 10. The method as set forth in claim 9 , further including: claim 9 determining reductions in the charged particle beam current at the various points along the item and determining an absorbed dose for a plurality of regions of the item from the reduced current. 11. The method as set forth in claim 8 , wherein the measuring of the charged particle beam current includes: claim 8 concentrating magnetic flux changes attributable to the changing current; and with concentrated magnetic flux changes, inducing electrical currents in windings of a coil. 12. A method of detecting energy of an electron beam, the method comprising: collimating an electron beam to a preselected cross-section; inducing a first electromotive force with the collimated electron beam; attenuating the collimated electron beam; inducing a second electromotive force with the attenuated electron beam; and, comparing the first and second electromotive forces. 13. The method as set forth in claim 12 , wherein: claim 12 inducing the first electromotive force includes pulsing the collimated electron beam through a first annular winding; attenuating the collimated electron beam includes passing the electron beam through a metal layer of preselected thickness; and, inducing the second electromotive force includes pulsing the collimated electron beam through a second annular winding, the second annular winding being disposed closely adjacent the metal layer. 14. An irradiation apparatus comprising: a charged particle beam generator for generating and aiming a charged particle beam of a first kinetic energy along a preselected path; a conveyor which conveys items to be irradiated through the beam; and, a beam kinetic energy monitor for monitoring a second kinetic energy of the beam after it has passed through the item. 15. The apparatus as set forth in claim 14 , further including: claim 14 a processor for comparing the first and second beam energies and determining a dose of the charged particle beam absorbed by the item. 16. The apparatus as set forth in claim 15 , wherein the processor is disposed remote from the monitors and further including: claim 15 a transducer for converting an output of the monitors into optical signals, the transducer being disposed adjacent the monitor such that the output from the monitor is conveyed from the irradiation region in an optical format. 17. The apparatus as set forth in claim 15 , wherein the beam generator includes a beam strength control circuit for controlling at least one of charged particle beam voltage and current and wherein the conveyor includes a speed control circuit for controlling a speed with which the items are moved through the charged particle beam, and further including: claim 15 a parameter adjustment processor which compares the determined absorbed doses with target absorbed doses and selectively adjusts at least one of the beam strength control circuit and the conveyor speed control circuit. 18. The apparatus as set forth in claim 17 , wherein the charged particle beam generator further includes a sweep control circuit for sweeping the charged particle beam back and forth across at least one of a planar region and a volumetric region and wherein the beam strength monitor includes: claim 17 first and second current transformers in which a current is induced by the electron beam; a metal absorbing foil disposed between the first and second current transformers whereby the current induced the second current transformer is less than the current induced the first current transformer; and, a vacuum chamber in which the first and second current transformers and the absorbing foil are disposed. 19. The apparatus as set forth in claim 14 , wherein the charged particle beam generator includes an electron accelerator. claim 14 20. An energy detector comprising: first and second inductive coils in which currents are induced by an electron beam; a metal layer of preselected thickness disposed between the first and second inductive coils; a beam collimator upstream of the inductive coils which collimates the electron beam to a preselected cross-section. 21. The energy detector as set forth in claim 20 , further including: claim 20 a vacuum chamber in which the inductive coils and the metal foil are disposed. 22. A method of irradiating comprising: moving items through a charged particle beam; determining a kinetic energy of the charged particle beam entering the item; measuring a kinetic energy of the charged particle beam exiting the item; determining an absorbed kinetic energy by subtracting the kinetic energy of the charged particle beam exciting the item from the kinetic energy of the beam before entering the item; dividing the determined absorbed kinetic energy by a mass of the item irradiated by the charged particle beam. 23. The method as set forth in claim 22 , further including: claim 22 determining a charge deposited in the irradiated item by the absorbed charged particle beam. 24. The method as set forth in claim 23 , further including: claim 23 multiplying the absorbed kinetic energy by the deposited charge. 25. The method as set forth in claim 24 , wherein determining the deposited charge includes: claim 24 measuring a beam current of the charged particle beam after irradiating the product. 26. An irradiating method including: collimating a charged particle beam to a preselected cross-section; passing the charged particle beam through an item; determining the energy of the beam entering the item by inducing a first electromotive force with the collimated beam; attenuating the collimated beam with the item; determining the energy of the beam exiting the item by inducing a second electromotive force with the attenuated electron beam; and, comparing the first and second electromotive forces. 27. A method of determining an absorbed dose deposited by an electron beam in an irradiated product comprising: determining an absorbed kinetic energy by subtracting a final kinetic energy of the electron beam exciting the product from an initial kinetic energy of the beam before entering the product; dividing the determined absorbed kinetic energy by a mass of the product irradiated by the electron beam. 28. An irradiation apparatus comprising: a charged particle beam generator for generating and aiming a charged particle beam of a first energy along a preselected path; a conveyor which conveys items to be irradiated through the beam; and, a beam strength monitor for monitoring a second energy of the beam after it has passed through the item, the monitor including: a vacuum chamber; first and second current transformers; a foil having known absorption characteristics disposed between of the first current transformer and the second current transformer. 29. The apparatus as set forth in claim 28 , further including: claim 28 a collimator disposed upstream of the current transformers for collimating the charged particle beam before it passes through the first current transformer, foil, and the second current transformer. 30. The apparatus as set forth in claim 28 , further including: claim 28 a comparitor which compares the currents induced in the first and second current transformers and determines therefrom the energy of the charged particle beam. 31. An apparatus for detecting energy of an electron beam, the apparatus comprising: a means for collimating an electron beam to a preselected cross-section; a first means in which the collimated electron beam induces a first electromotive force before being attenuated; a second means in which the electron beam induces a second electromotive force after the collimated electron beam has been attenuated; and, a means for comparing the first and second electromotive forces. 32. An apparatus for determining an absorbed dose deposited by an electron beam in an irradiated product comprising: a means for subtracting a final kinetic energy of the electron beam exciting the product from an initial kinetic energy of the beam before entering the product; a means for dividing the difference between the initial and final kinetic energy by a mass of the product irradiated by the electron beam.
	summary
	description	The invention relates generally to collimators for use in diagnostic imaging and, more particularly, to a two dimensional reflector and collimator assembly and method of manufacturing thereof. Typically, in computed tomography (CT) imaging systems, an x-ray source emits a fan-shaped beam toward a subject or object, such as a patient or a piece of luggage. Hereinafter, the terms “subject” and “object” shall include anything capable of being imaged. The beam, after being attenuated by the subject, impinges upon an array of radiation detectors. The intensity of the attenuated beam radiation received at the detector array is typically dependent upon the attenuation of the x-ray beam by the subject. Each detector element of the detector array produces a separate electrical signal indicative of the attenuated beam received by each detector element. The electrical signals are transmitted to a data processing system for analysis which ultimately produces an image. Generally, the x-ray source and the detector array are rotated about the gantry within an imaging plane and around the subject. X-ray sources typically include x-ray tubes, which emit the x-ray beam at a focal point. X-ray detectors typically include a collimator for collimating x-ray beams received at the detector, a scintillator for converting x-rays to light energy adjacent the collimator, and photodiodes for receiving the light energy from the adjacent scintillator and producing electrical signals therefrom. The outputs of the photodiodes are then transmitted to the data processing system for image reconstruction. As stated above, typical x-ray detectors include a collimator for collimating x-ray beams such that collection of scattered x-rays is minimized. As such, the collimators operate to attenuate off-angle scattered x-rays from being detected by a scintillator cell. Reducing this scattering reduces noise in the signal and improves the final reconstructed image. Therefore, it is necessary that the scintillator array and the collimator, typically plates extending along one dimension above the scintillator array, are uniformly aligned. That is, exact mechanical alignment is required between the collimator plates and the cast reflector lines in the array of scintillators. Known manufacturing processes attempt this exact alignment by constructing a continuous collimator that is sized to dimensionally match the width and length of the entire detector array. That is, the collimator plates are arranged or arrayed in a continuous consistent pattern or pitch that spans the entire detector length and is placed and attached to the detector rail structure. As such, individual scintillator arrays or packs must then be exactly aligned to the continuous collimator to ensure that all scintillator cells and collimator cells are aligned exactly; otherwise the collimator must be discarded or repaired, or the scintillator packs must be discarded. This process requires excessively tight tolerancing and requires great operator skill and patience to assemble. Accordingly, these known processes are susceptible to waste of parts, material, and labor. A known CT detector 1 fabricated according to known manufacturing processes is shown in FIG. 1. The CT detector 1 includes a series of tungsten collimator plates 2 configured and position to collimate, in one dimension, x-rays projected toward scintillator cells 3 of a scintillator array 4. As shown, each of the collimator plates 2 is generally aligned with a reflector line 5 disposed between adjacent scintillators 3. The reflector lines 5 prevent light from being emitted between adjacent scintillators. The scintillator array is coupled to a photodiode array 6 that detects light emissions from the scintillator array and transmits corresponding electrical signals to a data acquisition system for signal processing. As readily shown, the collimator plates are not integrated with the individual scintillator elements 3. That is, an air gap 7 exists between the collimator plates and the scintillator cells 3. The air gap 7 typically results in a separation between the collimator plates and the scintillator array of approximately two to four thousandths of an inch. This air gap occurs as a result of the manufacturing process whereupon the collimator plates are formed as a single collimator assembly that accepts and aligns an array of scintillators. The air gap, however, makes the CT detector susceptible to x-rays received between two collimator plates impinging upon an adjacent scintillator thereby resulting in undesirable anomalies in the final reconstructed CT image. Additionally, and as shown in FIG. 1, the collimator plates 2 serve to collimate x-rays projected toward scintillator cells 3 in only one dimension, which places limitations on the effectiveness of the collimator assembly. Therefore, it would be desirable to design a reflector and collimator assembly and method of manufacturing thereof that provides for easy alignment between the scintillator array and the collimator assembly and that effectively prevents cross-talk between adjacent scintillators. It would further be desirable to provide a reflector and collimator assembly and method of manufacturing thereof that provides for two-dimensional collimation of x-rays. Embodiments of the invention are directed to a two dimensional reflector and collimator assembly and a method of manufacturing thereof. In accordance with one aspect of the invention, a collimator assembly for a CT imaging system positioned between an object to be scanned and a CT detector includes a wall structure constructed to form a two dimensional array of channels to collimate x-rays. The wall structure further includes a first portion positioned proximate the object to be scanned and configured to absorb scattered x-rays and a second portion formed integrally with the first portion and extending out from the first portion away from the object to be scanned, with a height of the first portion being greater than a height of the second portion. The second portion of the wall structure includes a reflective material coated on the wall structure in each of the channels forming the two dimensional array of channels. In accordance with another aspect of the invention, a method of fabricating a collimator assembly for a CT medical imaging system includes providing a powder material having a density and atomic number that is sufficient to substantially absorb x-rays, providing a binding agent, and mixing the powder material and the binding agent to form a collimator material. The method also includes the step of extruding the collimator material through a collimator extrusion die to form a honeycomb collimator assembly, with the honeycomb collimator assembly comprising a two dimensional array of channels formed therethrough. In accordance with yet another aspect of the invention, a CT imaging system includes a rotatable gantry having an opening to receive an object to be scanned, a high frequency electromagnetic energy projection source configured to project a high frequency electromagnetic energy beam toward the object, and a scintillator array positioned on the gantry opposite the high frequency electromagnetic energy projection source, the scintillator array including a plurality of scintillator cells configured to detect high frequency electromagnetic energy passing through the object. The CT imaging system also includes a collimator assembly positioned between the object and the scintillator array, with the collimator assembly comprising a honeycomb wall structure configured to form a two dimensional array of channels to collimate x-rays. A portion of the collimator assembly is formed about the scintillator array such that each of the plurality of scintillator cells is housed within a respective channel in the two dimensional array of channels. Various other features and advantages will be made apparent from the following detailed description and the drawings. The operating environment of the invention is described with respect to a sixty-four-slice computed tomography (CT) system. However, it will be appreciated by those skilled in the art that the invention is equally applicable for use with other multi-slice configurations. Moreover, the invention will be described with respect to the detection and conversion of x-rays. However, one skilled in the art will further appreciate that the invention is equally applicable for the detection and conversion of other high frequency electromagnetic energy. The invention will be described with respect to a “third generation” CT scanner, but is equally applicable with other CT systems. Referring to FIG. 2, a computed tomography (CT) imaging system 10 is shown as including a gantry 12 representative of a “third generation” CT scanner. Gantry 12 has an x-ray source 14 that projects a beam of x-rays toward a detector assembly or collimator 18 on the opposite side of the gantry 12. Referring now to FIG. 3, detector assembly 18 is formed by a plurality of detectors 20 and data acquisition systems (DAS) 32. The plurality of detectors 20 sense the projected x-rays 16 that pass through a medical patient 22, and DAS 32 converts the data to digital signals for subsequent processing. Each detector 20 produces an analog electrical signal that represents the intensity of an impinging x-ray beam and hence the attenuated beam as it passes through the patient 22. During a scan to acquire x-ray projection data, gantry 12 and the components mounted thereon rotate about a center of rotation 24. Rotation of gantry 12 and the operation of x-ray source 14 are governed by a control mechanism 26 of CT system 10. Control mechanism 26 includes an x-ray controller 28 that provides power and timing signals to an x-ray source 14 and a gantry motor controller 30 that controls the rotational speed and position of gantry 12. An image reconstructor 34 receives sampled and digitized x-ray data from DAS 32 and performs high speed reconstruction. The reconstructed image is applied as an input to a computer 36 which stores the image in a mass storage device 38. Computer 36 also receives commands and scanning parameters from an operator via console 40 that has some form of operator interface, such as a keyboard, mouse, voice activated controller, or any other suitable input apparatus. An associated display 42 allows the operator to observe the reconstructed image and other data from computer 36. The operator supplied commands and parameters are used by computer 36 to provide control signals and information to DAS 32, x-ray controller 28 and gantry motor controller 30. In addition, computer 36 operates a table motor controller 44 which controls a motorized table 46 to position patient 22 and gantry 12. Particularly, table 46 moves patients 22 through a gantry opening 48 of FIG. 2 in whole or in part. As shown in FIG. 4, detector assembly 18 includes rails 17 having a plurality of reflector-collimator assemblies 19, hereinafter generally referred to as “collimator assemblies,” placed thereon and having detectors 20 secured thereto. Collimator assemblies 19 are positioned on rail to collimate x-rays 16 before such beams impinge upon, for instance, detector elements 50 of FIG. 5 positioned within the collimator assembly. In one embodiment, detector assembly 18 includes 57 detectors 20, each detector 20 having an array size of 64×16 of pixel elements 50. As a result, detector assembly 18 has 64 rows and 912 columns (16×57 detectors) which allows 64 simultaneous slices of data to be collected with each rotation of gantry 12. A detector 20 is shown in FIG. 5 for use with embodiments of the invention. Each detector 20 includes a number of detector elements 50 (i.e., scintillator pixels) forming an array 51 (i.e., scintillator array). Scintillator array 51 is optically coupled to a backlit diode array 53 having a plurality of diodes 59, with backlit diode array 53 in turn being positioned on, and electrically coupled to, multi-layer substrate 54. While scintillator array 51 is described as forming part of detector 20, scintillator pixels 50 are in fact positioned within a portion of collimator assembly 19, which is then positioned relative to diode array 53 and the remainder of detector 20, as is explained in greater detail below. As further shown in FIG. 5, detectors 20 also include pins 52 positioned relative to scintillator array 51 and spacers 55 positioned on multi-layer substrate 54. Flex circuits 56 are attached to face 57 of multi-layer substrate 54 and to DAS 32. Detectors 20 are positioned within detector assembly 18 by use of pins 52. In the operation of one embodiment, x-rays impinging within detector elements 50 generate photons which traverse scintillator array 51, thereby generating an analog signal which is detected on a diode within backlit diode array 53. The analog signal generated is carried through multi-layer substrate 54, through flex circuits 56, to DAS 32 wherein the analog signal is converted to a digital signal. Referring now to FIG. 6, collimator assembly 19 is shown according to an embodiment of the present invention. Collimator assembly 19 is configured as a “two dimensional collimator” in that a wall structure 60 forming the collimator assembly 19 has a honeycomb structure. A plurality of walls 62 forming wall structure 60 are arranged to define a two dimensional array of channels 64 that collimate x-rays attenuated by subject 22, for example, prior to the x-rays impinging upon detector 20 (FIG. 5). The wall structure 60 of collimator assembly 19 is formed and arranged such that a pitch of channels 64 is identical to a pitch of detector elements 50 (FIG. 5), which according to one embodiment are formed as scintillator pixels. According to an exemplary embodiment, walls 62 of wall structure 60 are thus formed to have a thickness of 0.10 to 0.20 mm and walls 62 are spaced apart to have a pitch of 1.0 to 1.2 mm, for example. According to an exemplary embodiment of the invention, wall structure 60 of collimator assembly 19 is composed of a mixed metal and binder material having a density and atomic number that is sufficient to substantially absorb x-rays. According to an exemplary embodiment, a powder composed of a heavy metal, heavy metal alloy powder, or heavy metal oxide is mixed with an organic polymer or thermoplastic material to provide a mixed collimator forming material, hereinafter referred to generally as a “mixed metal-binder material.” Thus, wall structure 60 may be formed of Pb, Ta, W, Au, or Pt powder, for example, that is bonded with an organic polymer or thermoplastic material. The mixed metal-binder material is extruded through a collimator extrusion die (not shown) to form the wall structure 60 and the channels 64 therein. A cross-sectional view of a portion of collimator assembly 19 is shown in FIG. 7. While collimator assembly 19 is shown as having a wall structure 60 defining only four channels 64, it is noted that FIG. 7 is for illustrative purposes only and that collimator assembly 19 would be formed to include a wall structure 60 that defines a greater number of channels arranged in a two-dimensional array, such as shown in FIG. 6. As shown in FIG. 7, wall structure 60 is generally defined as including a first portion 66 and a second portion 68 stacked in a vertical arrangement, according to an exemplary embodiment of the invention. While wall structure 60 of collimator assembly 19 is formed as an integral structure, and thus first and second portions 66, 68 are in fact formed as a single unitary structure, the first portion 66 of the collimator assembly 19 is identified as functioning as a collimator to collimate x-rays, while the second portion 68 is identified as functioning as a reflective grid that separates individual detector cells 50 (i.e., scintillator pixels) from each other to prevent cross-talk therebetween. As shown in FIG. 7, scintillator pixels 50 having a reflective material 71 coated on a top surface thereof are positioned within second portion 68 of wall structure 60, such that each scintillator pixel is housed within a respective channel 64 of the array of channels in collimator assembly 19. The first portion 66 of collimator assembly 19 is positioned proximate subject 22 (FIG. 1) so as to receive x-rays 16 attenuated therefrom. As set forth above, wall structure 60 is formed of a mixed metal-binder material having a density and atomic number that is sufficient to substantially absorb x-rays. Thus, as shown in FIG. 7, x-rays entering collimator assembly 19 at an undesired scatter angle are absorbed by first portion 66 of wall structure 60. The second portion 68 of wall structure 60 extends out from the first portion 66 away from the subject (i.e., downstream of x-rays) so as to receive x-rays 16 that pass through first portion 66. The second portion 68 of wall structure 60 includes a reflective material 70 that is coated on walls 62 such that each of the channels 64 forming the two dimensional array of channels is coated with the reflective material 70. The reflective material 70 and 71 may be composed of Al, Ag, Au, TiO2, BaSO4, and MgO, or some other similar material that acts to reflect light thereoff. That is, as collimated x-rays 16 pass through first portion 66 of wall structure 60 and impinge on the scintillator material of detector cells 50 housed in second portion 68 of wall structure 60, photons are generated. The reflective material 70 coated on walls 62 and reflective material 71 coated on the top of scintillator pixels 50 act to reflect these photons, such that they are trapped within a particular detector cell 50, allowing for readout thereof by diode array 53 (FIG. 5) without cross-talk interference from adjacent detector cells. As shown in FIG. 7, first portion 66 of wall structure 60 is formed to have a height 72 that is greater than a height 74 of second portion 68 of wall structure 60. According to an exemplary embodiment, a height of first portion 66 is at least twice a height of second portion 68. Thus, a height of first portion 66 may be approximately 8 mm and a height of second portion 68 may be approximately 1.5-3 mm, for example. A height ratio between first and second portions 66, 68 such as the one set forth above provides for first portion 66 of wall structure 60 to properly collimate x-rays 16 passing therethrough, while still allowing for a desired dose of x-rays to reach detector cells 50. Referring now to FIG. 8, a technique 76 for manufacturing collimator assembly 19 is set forth according to an embodiment of the invention. The technique 76 begins with the providing of materials for forming the collimator assembly at block 77. The materials include a metal or ceramic material having a density and atomic number that is sufficient to substantially absorb x-rays, as well as a binder material that is mixed with the metal/ceramic material in order to form a collimator assembly having sufficient rigidity and structural strength. According to an exemplary embodiment, the metal/ceramic material is in the form of a powder composed of a heavy metal, heavy metal alloy, heavy metal oxide, or ceramic, examples of which include Pb, Ta, W, Au, Pt, WO3, BiO3, Ta2O5, PbO, and heavy rare earth metal oxides such as Gd2O3, Lu2O3, etc. The metal/ceramic powder is then mixed with the binder material at block 78, which according to the embodiment of FIG. 8, is in the form of an organic polymer such as silicone, epoxy, or polyimide, for example. A mixed metal-binder material is formed upon combination of the metal/ceramic powder and the binding material. The mixed metal-binder material is extruded through a collimator extrusion die at block 79 to form the honeycomb wall structure of the collimator assembly having the two-dimensional array of channels therein. In a next step of the manufacturing technique 76, the extruded wall structure is sintered at block 80 so as to increase the mechanical strength of the wall structure to a desired level. In order to reduce surface roughness of the wall structure resulting from the sintering process, the wall structure is chemically polished at block 81. Upon chemical polishing of the wall structure, a reflective material is coated on the wall structure within each of the channels at block 82. According to an exemplary embodiment, the reflective material is coated on only a bottom or “second” portion of each channel (i.e., a portion adjacent to detector 20). The reflective material may be composed of Al, Ag, Au, TiO2, BaSO4, and MgO, or some other similar material that acts to reflect photons (i.e., light) thereoff. The manufacturing technique 76 continues with positioning of detector elements relative to the collimator assembly at block 83. Detector elements, in the form of scintillator pixels or crystals having a reflective material coated on a top surface thereof, are positioned relative to the collimator assembly such that an individual detector element is positioned within each of the channels in the collimator assembly. That is, a scintillator pixel/crystal is positioned within each of the channels in the collimator assembly in the bottom or “second” portion of the channel, such that the scintillator pixel/crystal is within that portion of the channel that has been coated with the reflective material. Accordingly, as x-rays pass through upper or “first” portion of the wall structure to impinge on the scintillator material housed in the bottom/second portion of the channel, photons generated by the scintillator material will be contained in each pixel by the reflection provided by the reflective material coated within the channels of the wall structure and on the top of the scintillator pixels. Referring now to FIG. 9, a technique 90 for manufacturing collimator assembly 19 is set forth according to another embodiment of the invention. The technique 90 begins with the providing of materials for forming the collimator assembly at block 91. The materials include a metal or ceramic material having a density and atomic number that is sufficient to substantially absorb x-rays, as well as a binder material that is mixed with the metal/ceramic material in order to form a collimator assembly having sufficient rigidity and structural strength. According to an exemplary embodiment, the metal/ceramic material is in the form of a powder composed of a heavy metal, heavy metal alloy, heavy metal oxide, or ceramic. The metal/ceramic powder is then mixed with the binder material at block 92, which according to the embodiment of FIG. 9 is in the form of a thermoplastic material. A mixed metal-binder material is formed upon combination of the metal/ceramic powder and the thermoplastic. The mixed metal-binder material is extruded through a collimator extrusion die at block 93 to form the honeycomb wall structure of the collimator assembly having the two-dimensional array of channels therein. Based on the structural rigidity and strength provided by the thermoplastic binding material, no sintering or further strengthening process need be applied to the extruded wall structure. Thus, the manufacturing technique continues with the application of a reflective material on the wall structure within each of the channels at block 94. According to an exemplary embodiment, the reflective material is coated on only a bottom or “second” portion of each channel (i.e., a portion adjacent to detector 20). The reflective material may be composed of Al, Ag, Au, TiO2, BaSO4, and MgO, or some other similar material that acts to reflect photons (i.e., light) thereoff. The manufacturing technique continues with positioning of detector elements relative to the collimator assembly at block 95. Detector elements, in the form of scintillator pixels or crystals having a reflective material coated on a top surface thereof, are positioned relative to the collimator assembly such that an individual detector element is positioned within each of the channels in the collimator assembly. That is, a scintillator pixel/crystal is positioned within each of the channels in the collimator assembly in the bottom or “second” portion of the channel, such that the scintillator pixel/crystal is within that portion of the channel that has been coated with the reflective material. Accordingly, as x-rays pass through upper or “first” portion of the wall structure to impinge on the scintillator material housed in the bottom/second portion of the channel, photons generated by the scintillator material will be contained in each pixel by the reflection provided by the reflective material coated within the channels of the wall structure and on the top of the scintillator pixels. Beneficially, the manufacturing techniques shown and described in each of FIGS. 8 and 9 allow for fine-tuning of the properties of the collimator assembly. That is, the properties of the collimator assembly can be tuned by the die design, the ratio of metal/ceramic to binder in the collimator formation mixture, and the thickness and height of the wall of the honeycomb collimator assembly. Additionally, the manufacturing techniques shown and described in each of FIGS. 8 and 9 eliminate an air gap that typically exists between collimator plates and scintillator cells by positioning the scintillator cells/pixels into the two-dimensional array of channels in the collimator assembly. Furthermore, the manufacturing techniques shown and described in each of FIGS. 8 and 9 provide for a collimator assembly that allows for higher spatial resolution in generated CT images. Referring now to FIG. 10, a package/baggage inspection system 100 is shown that can incorporate a collimator assembly 19 (FIGS. 6 and 7) and that includes a rotatable gantry 102 having an opening 104 therein through which packages or pieces of baggage may pass. The rotatable gantry 102 houses a high frequency electromagnetic energy source 106 as well as a detector assembly 108 having scintillator arrays comprised of scintillator cells similar to that shown in FIG. 6 or 7. A conveyor system 110 is also provided and includes a conveyor belt 112 supported by structure 114 to automatically and continuously pass packages or baggage pieces 116 through opening 104 to be scanned. Objects 116 are fed through opening 104 by conveyor belt 112, imaging data is then acquired, and the conveyor belt 112 removes the packages 116 from opening 104 in a controlled and continuous manner. As a result, postal inspectors, baggage handlers, and other security personnel may non-invasively inspect the contents of packages 116 for explosives, knives, guns, contraband, etc. Therefore, according to one embodiment of the invention, a collimator assembly for a CT imaging system positioned between an object to be scanned and a CT detector includes a wall structure constructed to form a two dimensional array of channels to collimate x-rays. The wall structure further includes a first portion positioned proximate the object to be scanned and configured to absorb scattered x-rays and a second portion formed integrally with the first portion and extending out from the first portion away from the object to be scanned, with a height of the first portion being greater than a height of the second portion. The second portion of the wall structure includes a reflective material coated on the wall structure in each of the channels forming the two dimensional array of channels. According to another embodiment of the invention, a method of fabricating a collimator assembly for a CT medical imaging system includes providing a powder material having a density and atomic number that is sufficient to substantially absorb x-rays, providing a binding agent, and mixing the powder material and the binding agent to form a collimator material. The method also includes the step of extruding the collimator material through a collimator extrusion die to form a honeycomb collimator assembly, with the honeycomb collimator assembly comprising a two dimensional array of channels formed therethrough. According to yet another embodiment of the invention, a CT imaging system includes a rotatable gantry having an opening to receive an object to be scanned, a high frequency electromagnetic energy projection source configured to project a high frequency electromagnetic energy beam toward the object, and a scintillator array positioned on the gantry opposite the high frequency electromagnetic energy projection source, the scintillator array including a plurality of scintillator cells configured to detect high frequency electromagnetic energy passing through the object. The CT imaging system also includes a collimator assembly positioned between the object and the scintillator array, with the collimator assembly comprising a honeycomb wall structure configured to form a two dimensional array of channels to collimate x-rays. A portion of the collimator assembly is formed about the scintillator array such that each of the plurality of scintillator cells is housed within a respective channel in the two dimensional array of channels. This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.
	summary
	claims	1. A method of manufacturing an integrated circuit (IC) device, the method comprising:forming a photoresist layer on a substrate; andexposing the photoresist layer to light by using a photolithographic apparatus including a light generator,wherein the light generator includes:a chamber having a plasma generation space,an optical collector in the chamber, the optical collector having an aperture, anda debris shielding assembly between the optical collector and the plasma generation space in the chamber,wherein the debris shielding assembly includes:a protective film facing the optical collector and being spaced apart from the optical collector with a protected space therebetween, the protected space including an optical path, the protective film having a through hole in a center region of the protective film, and the through hole being spaced apart from the aperture with the protected space therebetween, anda protective frame attaching the protective film to the optical collector, the protective frame to support the protective film and to shield the protected space from the plasma generation space. 2. The method as claimed in claim 1, wherein the protective film includes a material that is transparent with respect to a laser beam having a wavelength of about 1064 nm, a laser beam having a wavelength of about 10.6 μm, and extreme ultraviolet (EUV) light having a wavelength of about 13.5 nm. 3. The method as claimed in claim 1, wherein the protective film includes carbon nanotube, diamond, graphite, graphene, fullerene, or a combination thereof. 4. The method as claimed in claim 1, wherein the protective film includes a carbon nanotube film having single-wall carbon nanotubes (SWCNT), multiwall carbon nanotubes (MWCNT), or a combination thereof. 5. The method as claimed in claim 1, wherein the protective frame includes a metal. 6. The method as claimed in claim 1, wherein the protective frame includes:a support portion in contact with an edge portion of the optical collector; anda shield portion integrally connected with the support portion, the shield portion extending between the support portion and the protected film to shield the protective space from the plasma generation space. 7. The method as claimed in claim 1, wherein the protective frame includes:a support portion in contact to an edge portion of the optical collector;a shield portion extending between the support portion and the protective film to shield the protected space from the plasma generation space; andan outer fixing portion facing the shield portion with the protective film therebetween and supporting the protective film in cooperation with the shield portion. 8. The method as claimed in claim 7, wherein the protective frame further includes at least one of a first buffer film that is between the shield portion and the protective film, and a second buffer film that is between the protective film and the outer fixing portion. 9. The method as claimed in claim 7, wherein the shield portion includes an elliptic surface facing the protected space. 10. The method as claimed in claim 7, wherein the shield portion includes a reflective surface facing the protected space, and the reflective surface is an elliptic surface. 11. A method of manufacturing an integrated circuit (IC) device, the method comprising:forming a photoresist layer on a substrate; andexposing the photoresist layer to light by using a photolithographic apparatus including a light generator,wherein the light generator includes:a chamber having a plasma generation space,an optical collector in the chamber, the optical collector having an aperture and a reflective surface, anda debris shielding assembly between the optical collector and the plasma generation space in the chamber,wherein the debris shielding assembly includes:a protective film spaced apart from the reflective surface with a protected space therebetween and facing the reflective surface, the protected space including an optical path, the protective film having a through hole at a position corresponding to the optical path in the protective film, and the through hole being spaced apart from the aperture with the protected space therebetween, anda protective frame that is in contact with an edge portion of the optical collector and supports the protective film. 12. The method as claimed in claim 11, wherein the protective frame includes:a support portion in contact with the edge portion of the optical collector;a shield portion integrally connected with the support portion and having an inner surface between the support portion and the protective film, the inner surface facing the protected space; andan outer fixing portion facing the shield portion with the protective film therebetween and supporting the protective film in cooperation with the shield portion. 13. The method as claimed in claim 12, wherein the support portion includes a ring member extending from the shield portion, the ring member having a straight cross-sectional shape or an L-like cross-sectional shape. 14. The method as claimed in claim 12, wherein the shield portion includes a shield frame and a reflective layer on the shield frame, the reflective layer being exposed to the protected space, and the reflective layer defining an elliptic surface together with the reflective surface of the optical collector. 15. The method as claimed in claim 11, wherein the protective frame has widths varying in a circumferential direction with respect to a central axis of the debris shielding assembly. 16. The method as claimed in claim 11, wherein the debris shielding assembly further includes a fixing member that couples the protective film and the protective frame. 17. A method of manufacturing an integrated circuit (IC) device, the method comprising:forming a photoresist layer on a substrate; andexposing the photoresist layer to light by using a photolithographic apparatus including a light generator,wherein the light generator includes:a chamber having a plasma generation space;an optical collector in the chamber, the optical collector having an aperture and a reflective surface; anda debris shielding assembly between the optical collector and the plasma generation space in the chamber,wherein the debris shielding assembly includes:a protective film facing the reflective surface with a protected space therebetween, the protected space including an optical path, the protective film having a through hole at a position corresponding to the optical path in the protective film, and the through hole being spaced apart from the aperture with the protected space therebetween, anda protective frame attaching the protective film to an edge of the optical collector, the protective frame extending along an entire perimeter of the edge of the optical collector. 18. The method as claimed in claim 17, wherein exposing the photoresist layer includes using EUV light generated in the light generator.
	abstract	A multi-layered cladding material including a ceramic matrix composite and a metallic material, and a tube formed from the cladding material. The metallic material forms an inner liner of the tube and enables hermetic sealing of thereof. The metallic material at ends of the tube may be exposed and have an increased thickness enabling end cap welding. The metallic material may, optionally, be formed to infiltrate voids in the ceramic matrix composite, the ceramic matrix composite encapsulated by the metallic material. The ceramic matrix composite includes a fiber reinforcement and provides increased mechanical strength, stiffness, thermal shock resistance and high temperature load capacity to the metallic material of the inner liner. The tube may be used as a containment vessel for nuclear fuel used in a nuclear power plant or other reactor. Methods for forming the tube comprising the ceramic matrix composite and the metallic material are also disclosed.
	claims	1. An optical apparatus for radiation having a wavelength xe2x89xa6160 nm, comprising: a mirror with a mirror surface; and a device for producing elastic oscillations on said mirror surface, wherein said elastic oscillations cause radiation impinging on said mirror surface to be diffracted. 2. The optical apparatus of claim 1 , wherein said device generates surface acoustical waves on said mirror surface produce said elastic oscillations. claim 1 3. The optical apparatus of claim 2 , wherein said surface acoustical waves produce a diffraction grid on said mirror surface. claim 2 4. The optical apparatus of claim 2 , wherein said surface acoustical waves have a wavelength in the range of about 1 xcexcm to 50 xcexcm. claim 2 5. The optical apparatus of claim 2 , wherein said surface acoustical waves have an amplitude in the range of about 1 nm to 100 nm. claim 2 6. The optical apparatus of claim 2 , wherein said surface acoustical waves have a frequency that is varied. claim 2 7. The optical apparatus of claim 2 , claim 2 wherein said device is a first device and said surface acoustical waves are first surface acoustical waves, and wherein said optical apparatus further comprises: a second device for generating second acoustical waves on said mirror surface, wherein said second surface acoustical waves are parallel to said first surface acoustical waves. 8. The optical apparatus of claim 7 , wherein said mirror surface comprises a plurality of individual mirror surfaces. claim 7 9. The optical apparatus of claim 2 , claim 2 wherein said device is a first device and said surface acoustical waves are first surface acoustical waves, and wherein said optical apparatus further comprises: a second device for generating second acoustical waves on said mirror surface, wherein said second surface acoustical waves are not parallel to said first surface acoustical waves. 10. The optical apparatus of claim 9 , wherein said mirror surface comprises a plurality of individual mirror surfaces. claim 9 11. A method, using the optical apparatus of claim 2 , for illuminating a predetermined range of angles (xcex1) with said radiation, said method comprising: claim 2 generating said surface acoustical waves; and varying a frequency of said surface acoustical waves, wherein said surface acoustical waves produce a plurality of grid lines on said mirror surface, wherein said radiation impinges two or more of said plurality of grid lines, and wherein said radiation is diffracted in said predetermined range of angles (xcex1) and, when averaged over time, homogeneously illuminates said predetermined range of angles (xcex1). 12. The method of claim 11 , wherein said predetermined range of angles (xcex1) is about xe2x88x9212.0 mrad xe2x89xa6xcex1xe2x89xa612.0 mrad. claim 11 13. The optical apparatus of claim 1 , wherein said device comprises a piezoelectric foil. claim 1 14. The optical apparatus of claim 13 , wherein said piezoelectric foil is a PZT film. claim 13 15. The optical apparatus of claim 1 , wherein said device comprises a piezoeleetne crystal. claim 1 16. The optical apparatus of claim 1 , wherein said device comprises a point-like or linear-form electrode. claim 1 17. The optical apparatus of claim 1 , wherein the optical apparatus is a component in an exposure device for lithography. claim 1 18. The optical apparatus of claim 17 , wherein said exposure device comprises a source of said raditation, and wherein the optical apparatus broadens a beam of said source. claim 17 19. The optical apparatus of claim 17 , wherein said exposure device comprises an illumination system, and wherein the optical apparatus varies an illumination setting of said illumination system. claim 17 20. The optical apparatus of claim 17 , wherein the optical apparatus homogenizes an illumination of a pupil of said exposure device. claim 17 21. A method for producing the optical apparatus of claim 1 , comprising: claim 1 superpolishing a side of a substrate to yield a surface roughness of less than about 0.5 nm; and attaching an electrode to said substrate, wherein said mirror surface comprises said side of said substrate, and wherein said device comprises said electrode. 22. The method of claim 21 , wherein said electrode is attached to said superpolished side of said substrate. claim 21 23. The optical apparatus of claim 1 , wherein said device comprises a piezoelectric foil. claim 1 24. The optical apparatus of claim 1 , wherein said elastic oscillations generate a plurality of diffraction grids on said mirror surface. claim 1 25. The optical apparatus of claim 24 , wherein said plurality of diffraction grids are provided by varying a frequency of said elastic oscillations. claim 24 26. The optical apparatus of claim 1 , wherein said device is a first device, and wherein said optical apparatus further comprises a second device for producing elastic oscillations on said mirror surface. claim 1 27. The optical apparatus of claim 26 , wherein said first and second devices are arranged on said mirror surface so that a beam of said radiation impinging on said mirror surface is modified in two dimensions. claim 26 28. The optical apparatus of claim 1 , wherein said device comprises an interdigital transformer. claim 1 29. An illumination system for microlithography having a radiation source for emitting radiation having a wavelength xe2x89xa6160 nm, comprising the optical apparatus of claim 1 . claim 1 30. A projection exposure apparatus for microlithography, comprising: the illumination system of claim 29 , for illuminating an object; and claim 29 a projection objective for imaging said object onto a light sensitive substrate. 31. An optical apparatus for radiation having a wavelength xe2x89xa6160 nm, comprising: a mirror with a mirror surface; and a device for producing elastic oscillations on said mirror surface, wherein said elastic oscillations cause radiation impinging on said mirror surface to be diffracted in a predetermined range of angles (xcex1), and wherein said predetermined range of angles (xcex1) is about xe2x88x9212 mrad=xcex1=mrad.
	abstract	A scintillator panel includes a substrate having a substrate main surface, a substrate rear surface, and a substrate side surface; and a scintillator layer having a scintillator rear surface formed of a plurality of columnar crystals, a scintillator main surface, and a scintillator side surface. The substrate side surface and the scintillator side surface are substantially flush with each other. In the substrate, an angle between the substrate rear surface and the substrate side surface is smaller than 90 degrees.
	abstract	A hazardous material storage repository includes a drillhole extending into the Earth and including an entry at least proximate a terranean surface, the drillhole including a substantially vertical drillhole portion, a transition drillhole portion coupled to the substantially vertical drillhole portion, and a hazardous material storage drillhole portion, at least one of the transition drillhole portion or the hazardous material storage drillhole portion including an isolation drillhole portion; a storage canister positioned in the hazardous material storage drillhole portion, the storage canister sized to fit from the drillhole entry through the substantially vertical drillhole portion, the transition drillhole portion, and into the hazardous material storage drillhole portion of the drillhole, the storage canister including an inner cavity sized enclose hazardous material; and a seal positioned in the drillhole, the seal isolating the hazardous material storage drillhole portion of the drillhole from the entry of the drillhole.
	claims	1. A radiological barrier material comprising a matrix and a particulate having a cross sectional dimension of about 500 micrometers or less contained within the matrix, the particulate comprising a radiation absorber that absorbs either one or both of alpha and beta radiation, the particulate comprising a defined nanostructure, the defined nanostructure comprising an aluminosilicate nanotube, the radiation absorber comprising a metal oxide, the radiation absorber further comprising an energy absorbing chromophore on the surface of the particulate. 2. The radiological barrier material of claim 1, wherein the radiation absorber further comprises a semiconductor. 3. The radiological barrier material of claim 1, wherein the matrix comprises an organic matrix. 4. The radiological barrier material of claim 1, wherein the matrix comprises an inorganic matrix. 5. The radiological barrier material of claim 4, wherein the inorganic matrix comprises a glass or a ceramic. 6. The radiological barrier material of claim 1, wherein the radiological barrier material is in the form of a fiber or a sheet. 7. A container for radiation emitting material, the container comprising the radiological barrier material of claim 1. 8. The container of claim 7, wherein the container comprises a flexible bag. 9. The container of claim 8, wherein the container is a single-layer flexible bag. 10. Personal protective equipment comprising the radiological barrier material of claim 1. 11. The personal protective equipment of claim 10, wherein the personal protective equipment comprises a glove. 12. The personal protective equipment of claim 10, wherein the personal protective equipment comprises a face shield or a body suit. 13. The radiological barrier material of claim 1, wherein the metal oxide comprises TiO2, FeO2, AlO2, CeO2, WO4, Cr2O3, SiO2, MgO2, CaO2, BaO2, CoO, VO2, NiO2, CuO2, ZnO, YO2, Na2WO2, ZrO2 or a combination of one or more metal oxides. 14. The radiological barrier material of claim 1, wherein the particulate is formed of the metal oxide.
045432317	summary	BACKGROUND OF THE INVENTION This invention relates generally to plasma devices and particularly to the confinement and stabilization of plasmas in fusion devices by means of average magnetic well. More particularly, the present invention relates to the combination of multipole fields and the plasma pinch effect for the production of average magnetic well, most particularly in a toroidal system. Toroidal plasma devices are devices in which plasma is created in a topologically toroidal space, usually axisymmetric, and is confined therein by appropriate confining magnetic fields. Toroidal plasma devices are useful in the generation, confinement, heating, study and analysis of plasmas. In particular, such devices are useful for the reaction of deuterium and tritium, deuterium and deuterium or other nuclear fusible mixtures, with the production of high energy neutrons and energetic charged particles as products of the nuclear fusion reactions. The problems in nuclear fusion devices are largely to heat the plasma to a high enough temperature to enable the desired reactions to occur and to confine the heated plasma for a time long enough to release energy in excess of that required to heat the plasma to reaction temperature. The present invention is directed to the magnetic confinement of such plasma and finds particular utility in such devices and their applications, including experimental devices and the use thereof in experimentation and investigation with respect to toroidal plasma devices. A number of toroidal plasma devices have been suggested and built. The ones most closely related to the present invention are: tokamak devices, including doublet devices; multipole devices; and z-pinch devices, including reversed field pinch (RFP) devices. In such devices, gas is confined in a toroidal confinement vessel and is heated to form a plasma which is generally held away from the walls of the confinement vessel by appropriate magnetic fields. Such devices are all topologically toroidal and are usually axisymmetric. A topological torus is any geometric solid figure that can be produced by an imagined elastic deformation of an initial circular torus. An axisymmetric torus is obtained by rotating any plane geometric figure about the major toroidal axis. An axisymmetric toroidal device is one in which all quantities are invariant to rotation about the major toroidal axis. A necessary condition for the toroidal magnetic confinement of plasmas is that the complete set of magnetic field components results in a set of nested, toroidally closed magnetic surfaces. A magnetic surface is defined as a mathematical surface on which the magnetic field has no component normal thereto. The magnetic surface enclosing zero volume in the center of the nest is called an elliptic magnetic axis. Most devices have only a single elliptic magnetic axis and a single set of nested surfaces. However, doublet devices have two elliptic magnetic axes, and multipole devices have two or more sets of nested surfaces. In some toroidal devices, such as tokamak and pinch devices, the confining magnetic field includes magnetic field components produced by currents flowing through the confined plasma itself. When nested magnetic surfaces are present, this current is significantly concentrated into those magnetic surfaces closer to elliptic magnetic axes. Such regions of greater current density relative to the remainder of the plasma are called current channels. In those toroidal devices where it is required, a toroidal plasma current is usually produced by a transformer with the toroidal confined plasma acting as the secondary and with the primary being a central solenoid. Upon change of the current in the solenoid, a toroidal electric field is produced to ionize the gas and drive plasma current around the torus. A pinch effect takes place when electric current flowing through the plasma is acted upon by its own magnetic field to exert a confining pressure on the plasma. The large current simultaneously heats the plasma ohmically. However, this simplest configuration by itself, called the Bennett pinch, is unstable, and most of the plasma soon strikes the confinement vessel, hence cooling the plasma and impeding any reaction. For this reason, additional measures are taken to improve the stability of the system. The magnetohydrodynamic (MHD) stability of a magnetically confined plasma is dependent on the pitch of the magnetic field lines encircling the magnetic axis or axes. This pitch P is defined by ##EQU1## where .DELTA..zeta. is the distance traversed along the direction of the magnetic axis and k the number of times the axis is encircled, both while following a field line. This limit is the same for all possible field lines on a given magnetic surface. In toroidal plasma devices it is customary to use instead the safety factor q where EQU q=P/<R>. (2) Here <R> is the average major radius of the magnetic surface in question. For a general topological torus <R>=<C>/2.pi., where <C> is the average major circumference of the nonaxisymmetric magnetic surface in question. There is a corresponding relationship between P and safety factor q for still more general systems. In order to be magnetohydrodynamically stable, toroidal plasma devices must satisfy certain necessary conditions on q. If r is the mean minor radius, then these conditions are: (a) .vertline.q.vertline..noteq.1; and PA1 (b) ##EQU2## must be large enough to satisfy relevant criteria, including the Mercier and the Robinson criteria; in particular, dq/dr must not change sign within the plasma, and it may be zero only at a magnetic axis. Conditions (a) and (b) taken together require that in plasmas with current channels, such as tokamaks and z-pinches, either .vertline.q.vertline..gtoreq.1 on axis and increases monotonically everywhere else in the plasma; or else .vertline.q.vertline.<1 everywhere, decreases monotonically with increasing distance from the magnetic axis, passes smoothly through zero, and then increases monotonically with increasing distance from the magnetic axis in the outside regions of the plasma. The .vertline.q.vertline..gtoreq.1 case is realized in tokamaks, and the .vertline.q.vertline.<1 case in reversed field pinches. Condition (a) above is necessary to avoid a serious kink instability that arises when q.apprxeq.1. In the case of substantially circular flux surfaces in axisymmetric tori, Eq. (2) can be written in the easily applied form ##EQU3## where B.sub.T is the toroidal and B.sub.p the poloidal magnetic field intensity. The quantity s appearing in condition (b) above is the magnetic shear, which exerts a stabilizing effect on many classes of instabilities, particularly on ideal MHD interchange instabilities and on many microinstabilities. Another important property, which enhances stability by suppressing those MHD instabilities that are excited specifically by plasma pressure, is average magnetic well or minimum average B, where B is the magnetic field intensity. A review of the advantages of average magnetic well and of many configurations that have this property is given by H. P. Furth in Advances in Plasma Physics, Simon and Thompson, eds., 1 (Interscience Publishers, New York, 1968), pp. 67-100. The average square of the magnetic field intensity <B.sup.2 > on a flux surface is calculated by ##EQU4## where the integration is taken by following a magnetic field line for a sufficient distance to sample all of the magnetic surface. The simplest definition of average magnetic well in the limit where the plasma pressure is small is a minimum of <B.sup.2 > within the plasma. More generally, it has been shown by J. L. Johnson and J. M. Greene, Plasma Phys. 9 (1967), pp. 611-629, that magnetic well exists if V<0, where ##EQU5## In the above equations, the integrations are over the volume enclosed by the flux surface, d.tau. is a differential volume, and V is the volume so enclosed. L, U, V and plasma pressure p are functions of flux, and the primes indicate differentiation with respect to flux. When p'=0, V<0 is the same as having a minimum of <B.sup.2 > within the plasma. A magnetic well implies that the average of the magnitude of the magnetic field increases outwardly from the center of the device. Therefore, if the plasma is driven outward by an incipient instability, it encounters a stronger magnetic field which opposes its outward motion. The most commonly used toroidal magnetic confinement configuration at present is the tokamak, whose principal defining characteristic is to satisfy the q stability requirements by operating with .vertline.q.vertline.>1 and s.gtoreq.0 by supplying a sufficiently large toroidal magnetic field intensity B.sub.T, in accordance with Eq. (3). Because the aspect ratio A.ident.R/r is generally .gtoreq.3, the toroidal field, which must be provided by a large toroidal field coil system disposed around the confinement vessel, must be large. Typically, B.sub.T =5 B.sub.P to 10 B.sub.P. Therefore, the maximum toroidal current I.sub.p flowing in the plasma, which is related to poloidal magnetic field intensity B.sub.P by the formula B.sub.P =.mu..sub.o I.sub.p /2.pi.r, and with it the ohmic heating of the plasma, are limited by the maximum possible toroidal field intensity B.sub.T that can be withstood in a practical magnet system. A small magnetic well, which is also important for tokamak stability, is obtained by toroidal effects. The theoretically predicted maximum plasma pressure that can be confined is limited to .beta..ltorsim.0.10 and may well be less, where .beta..ident.<p>/(B.sup.2 /2.mu..sub.o) is the ratio of the volume averaged plasma pressure to the magnetic pressure of the confining field. (Here and throughout the remainder of this disclosure the SI mks system of units is used.) Because of the small .beta. of the tokamak, fusion reactor concepts based on it either must be large or must employ extraordinarily high toroidal magnetic field strength. Z-pinches are most readily distinguished form tokamaks, which they superficially resemble, by having .vertline.q.vertline.<1 everywhere throughout the plasma, and usually they have .vertline.q.vertline.>>1. The only toroidal z-pinch previously known to satisfy the necessary conditions on q is the reversed field pinch (RFP). A recent review of the RFP art has been given by H. A. B. Bodin and A. A. Newton, Nucl. Fusion 20 (1980), pp. 1255-1324. The RFP is a diffuse z-pinch in which the magnetic field component sensibly parallel to the magnetic axis has a direction in the outside region of the plasma opposite to that in the inner region, and as a result, q(r) passes through zero and changes sign within the plasma. In fact, greatly reduced instability is observed in z-pinch experiments when the reversed q(r) profile is established. The field and q reversal is achieved by trapping a toroidal field in a pinched plasma and providing external boundary conditions such that a toroidal field of the opposite sign can exist between the plasma and the wall. A conducting shell is also required for stability. The combination of toroidal current and reversed toroidal magnetic field achieved in RFPs produces an equilibrium state of very low free energy, which is stable at low .beta.. This stability is independent of toroidal effects. Therefore, RFP aspect ratios can be chosen at will to optimize engineering and reactor parameters. In the RFP the externally acting toroidal field is smaller than B.sub.P. Therefore, unlike in the tokamak, I.sub.p is limited only by the maximum intensity of B.sub.P that can be withstood in the device, and large ohmic heating of the plasma is possible. Furthermore, the maximum .beta. achievable in RFP devices will probably be greater than in tokamaks. Therefore, fusion reactor concepts based on the RFP can either be smaller or use lower magnetic fields than with tokamaks. Unfortunately, the RFP does not possess a magnetic well, and it has been predicted theoretically and observed in computer plasma simulations that an m=0 resistive interchange instability grows into a large convective cell near the q=0 surface and limits plasma confinement. Here m is the poloidal mode number of the instability in question. There are data suggesting that this instability is present in contemporary RFP experiments. Resistive interchange instabilities are among those that can be stabilized by magnetic well. Multipole plasma confinement devices take a different approach to toroidal plasma confinement. In multipole devices, the toroidal plasma current is replaced by two or more solid conducting rings located internal to the plasma, which produce a set of nested closed magnetic surfaces around each ring. By convention the number of poles is equal to twice of the number of conductors. Thus, for example a device with two internal conductors is termed a quadrupole; four an octopole, etc. Since the current flows through rigid conductors, the current flow is stable. There is no necessity for a strong toroidal magnetic field. The current rings are placed so as to generate a multipolar magnetic field and at least one hyperbolic magnetic axis within the space roughly enclosed poloidally by the rings. Furthermore, these rings and the hyperbolic axis or axes are surrounded by an outer set of nested closed magnetic surfaces. The magnetic surface or surfaces passing through the hyperbolic axis and separating the outer magnetic surfaces from those magnetic surfaces that enclose only a single ring are called separatrix magnetic surfaces. Excellent confinement has been demonstrated in experimental multipole devices. Shear can be added by means of only a small toroidal field. Multipole devices have a number of serious difficulties for high temperature plasma and fusion applications associated with the placement of conducting rings internal to the plasma. The rings require support structure, which intercepts charged particles, destroys the symmetry of the device, and leads to reduced confinement of plasma. Alternatively, the support structure can be eliminated by use of superconducting rings which are levitated by use of magnetic fields, but requirements to shield the superconductor from the high energy fusion neutrons are formidable. SUMMARY OF THE INVENTION The present invention involves a fundamentally different confinement principle, obtaining the best advantages of internal ring multipole and RFP devices in a multipole pinch device. The basic invention can be considered as a multipole device in which the solid internal rings have been replaced by high current z-pinch plasma current channels. Just as in the solid ring multipole devices, approximately equal currents flowing in parallel through the plasma current channels generate a hyperbolic magnetic axis and separatrix magnetic surfaces internal to the plasma. This produces an average magnetic well, provided the component of magnetic field in the direction of the hyperbolic axis is not too large in the vicinity of the hyperbolic axis, which can always be achieved by operating the plasma current channels like reversed field pinches so that q=0 occurs in the vicinity of said hyperbolic axis. Because z-pinch plasmas have a strong tendency to keep a nearly circular poloidal cross section, means are provided to prevent the multiple current channels from coalescing into a single, circular cross section RFP. Furthermore, the precise shape of the plasma can be adjusted and optimized, if necessary, by means of small currents in toroidal coils exterior to the conducting shell. Stability in the multipole pinch invention is obtained by a q profile and conducting shell as in the RFP, plus the average magnetic well. In particular, when the q=0 surface coincides with the hyperbolic magnetic axis in the plasma, q varies monotonically outwardly from the elliptic axes. The magnetic well is then centered on the q=0 surface. This is the optimal theoretical location for the suppression of the m=0 resistive interchange instability that threatens to limit RFP .beta.. In general terms, the average magnetic well increases the maximum .beta. that can be accommodated. The well in multipole pinch devices is independent of toroidal effects, and so the toroidal aspect ratio of such devices can be chosen at will. Like the RFP, the multipole pinch needs only small toroidal fields; thus, plasma current and ohmic heating are limited only by the maximum poloidal fields that can be withstood in the device. The device of the present invention is distinctly different from prior art multipole devices in that the magnetic well is achieved without the use of solid rings immersed in the plasma and the problems that such rings entail. It is distinctly different from prior art RFP devices by provision of means to make plasmas with an average magnetic well by an internal hyperbolic magnetic axis. Furthermore, it is distinctly different from prior art helical pinches as in T. Ohkawa U.S. Pat. No. 4,302,284, sometimes referred to as OHTE, whose multiple hyperbolic axes are at the plasma surface rather than internal. The device of the present invention is also distinctly different from the prior art doublet device, as in T. Ohkawa U.S. Pat. No. 3,692,626, which it superficially resembles. The doublet device is essentially a quadrupole in which the two solid internal conductors have been replaced by two tokamak current channels. The present invention, in its quadrupole form, replaces the two solid conductors by z-pinch current channels. The magnetic fields and currents within the two devices are very different. The most critical difference, from the viewpoint of the efficiency and construction of the device, is that the tokamak current channels of the doublet device require toroidal magnetic fields many times greater than the field produced by the plasma current, whereas in the z-pinch current channels, the fields are comparable. Furthermore, with a given toroidal field it is possible to drive a much larger current through the present device than through the doublet device, and the heating associated with this current drastically reduces the auxiliary heating requirements relative to the doublet device. The multipole pinch also differs from the doublet device in how the magnetic well is generated. Because of the large toroidal magnetic field, the average magnetic well in doublet devices arises from toroidal effects, as in the tokamak, and not because of a hyperbolic magnetic axis. In the low toroidal field environment of the multipole pinch device, average magnetic well is produced by its hyperbolic axis. The multipole pinch device is further differentiated from the doublet device by their different q profiles. The doublet q profile is everywhere greater than unity and passes through infinity at its internal separatrix magnetic surface; wheras in the multipole pinch device, q is much less than unity, is monotonically varying and passes through zero at its separatrix magnetic surface. Finally, the toroidal field in doublet devices varies only slightly throughout the plasma volume, whereas in multipole pinch devices it reverses direction between the elliptic magnetic axes and the boundary of the plasma. Therefore, a doublet device is built with a small aspect ratio A and with very strong toroidal field coils supplied with large currents; whereas a multipole pinch device is built with any convenient aspect ratio, usually A.gtoreq.5, and with toroidal field coils designed for lesser magnetic fields and currents. Furthermore, a preferred multipole pinch device has an induction coil and associated power system designed to induce a toroidal electric field of at least 100 V/m during the plasma pinch formation phase of the discharge cycle; whereas a doublet device is usually designed to induce a weaker toridal electric field, such as less than 25 V/m in the Doublet III device at the General Atomic Company. Thus, it is a primary object of the present invention to provide for magnetic pinch confinement of plasma with an average magnetic well obtained using at least one hyperbolic magnetic axis generated by multipolar magnetic fields produced by multiple z-pinch current channels. Other objects and advantages of the present invention will become evident from the consideration of the following detailed description, particularly when taken in conjunction with the accompanying drawings.
	claims	1. A device for characterizing surfaces, the device comprising:means for generating a beam of neutral atoms or molecules, the means being arranged to direct said beam towards a surface for characterizing; anddetector means that are sensitive to position for detecting the neutral atoms or molecules of said beam that have been diffused forwards by said surface for characterizing;wherein:said means for generating a beam of neutral atoms or molecules produces a beam having energy lying in the range 50 eV to 5 keV with divergence no greater than 0.05°; andsaid means for generating a beam of neutral atoms or molecules directs said beam towards said surface for characterizing at an angle of incidence no greater than 10° relative to the plane of said surface;in such a manner that a diffraction pattern of said neutral atoms or molecules diffused forwards by said surface for characterizing is detectable by said position-sensitive detector means. 2. A device according to claim 1, wherein said means for generating a beam of neutral atoms or molecules produces a beam having energy lying in the range 100 eV to 2 keV. 3. A device according to claim 1, wherein said means for generating a beam of neutral atoms or molecules produces a beam having energy lying in the range 100 eV to 1 keV. 4. A device according to claim 1, wherein said means for generating a beam of neutral atoms or molecules produces a beam having energy dispersion no greater than 5%. 5. A device according to claim 1, wherein said means for generating a beam of neutral atoms or molecules directs said beam towards said surface for characterizing with an angle of incidence lying in the range 0.5° to 3°. 6. A device according to claim 1, wherein the angle of incidence θinc and the energy E0 of said beam of atoms or molecules are selected such that E0 sin2 θinc≦1 eV. 7. A device according to claim 1, wherein said means for generating a beam of neutral atoms or molecules generates a beam constituted by particles having atomic mass lying in the range 1 au to 20 au. 8. A device according to claim 7, wherein said means for generating beam of neutral atoms or molecules generates a beam constituted by a chemical species selected from H, H2, and 3He, and isotopes thereof. 9. A device according to claim 1, wherein said means for generating a beam of neutral atoms or molecules comprise:means for generating a beam of atomic or molecular ions;means for neutralizing said beam of atomic or molecular ions; andmeans for collimating the beam of neutral atoms or molecules obtained by neutralizing said beam of atomic or molecular ions. 10. A device according to claim 9, wherein said means for generating a beam of neutral atoms or molecules also comprise means for filtering said atomic or molecular ions by mass. 11. A device according to claim 9, wherein said means for generating a beam of neutral atoms or molecules comprise chopper means for generating a pulsed beam. 12. A device according to claim 11, wherein said position-sensitive detector means also present time sensitivity, with resolution of not more than 50 ns, so as to determine the energy loss of the neutral atoms or molecules of said beam as a result of being diffused by said surface, by measuring flight time. 13. A device according to claim 12, wherein said position-sensitive detector means present time sensitivity, with resolution of not more than 10 ns. 14. A device according to claim 1, also comprising secondary detector means for detecting neutral or ionized atoms or molecules, said secondary detector means having time resolution no greater than 1 μs, and being arranged in such a manner as to detect neutral or ionized atoms or molecules that leave the surface for characterizing on a trajectory that forms relative to said surface an angle that is greater than the specular reflection angle of said beam of neutral atoms or molecules. 15. A machine for molecular jet epitaxy, the machine including a surface characterizing device according to claim 1, arranged to characterize the surface of a crystal that is being grown. 16. A method of characterizing surfaces, the method comprising the steps of:directing a beam of neutral atoms or molecules on the surface to be characterized; anddetecting in position-sensitive manner the neutral atoms or molecules of said beam that have been diffused forwards by said surface for characterizing;wherein:said beam of neutral atoms or molecules has energy lying in the range 50 eV to 5 keV, and divergence no greater than 0.05°; andthe angle of incidence of said beam on said surface for characterizing is no greater than 10° relative to the plane of said surface;in such a manner that at least some of said forwardly-diffused neutral atoms or molecules are diffracted by said surface for characterizing. 17. A method of characterizing surfaces according to claim 16, wherein said beam of neutral atoms or molecules presents energy lying in the range 100 eV to 2 keV. 18. A method of characterizing surfaces according to claim 17, wherein said beam of neutral atoms or molecules presents energy lying in the range 100 eV to 1 keV. 19. A method of characterizing surfaces according to claim 16, wherein said beam of neutral atoms or molecules presents energy dispersion no greater than 5%. 20. A method of characterizing surfaces according to claim 16, wherein the angle of incidence of said beam on said surface for characterizing lies in the range 0.5° to 3°. 21. A method of characterizing surfaces according claim 16, wherein the angle of incidence θinc and the energy E0 of said beam of atoms or molecules are selected such that E0 sin2 θinc<1 eV. 22. A method of characterizing surfaces according to claim 16, wherein said beam is constituted by particles presenting atomic mass lying in the range 1 au to 20 au. 23. A method of characterizing surfaces according to claim 22, wherein said beam is constituted by a chemical species selected from H, H2, and 3He, and isotopes thereof. 24. A method according to claim 16, also including a step for determining at least one crystallographic parameter of said surface for characterizing from a detected diffraction pattern of said neutral atoms or molecules diffused forwards by said surface for characterizing. 25. A method according to claim 24, implemented during fabrication of a crystal by molecular beam epitaxy, the method also including:a step of observing oscillatory behavior over time of said diffraction pattern; anda step of extracting information relating to the epitaxial growth of successive layers of atoms forming said crystal on the basis of said observation of oscillatory behavior over time of said diffraction pattern.
	abstract	It is possible to improve the workability and the stress corrosion resistance by easily performing a repairing operation in a nozzle repairing method and a nuclear reactor vessel. The repairing method includes: removing a first connection portion ((trepanned portion) 208) with respect to an in-core instrument tube (204) in a groove-welding portion (206); removing the in-core instrument tube (204) from a lower mirror (66); leaving and grooving a second connection portion ((existing welding portion) 211) with respect to the lower mirror (66) in the groove-welding portion (206); inserting a new in-core instrument tube (204A) into an attachment hole (203); and groove-welding (so as to form a new groove-welding portion (213)) the inner side of the lower mirror (66) so as to fix the new in-core instrument tube (204A).
	description	In the various drawings, like parts are indicated by like references. FIG. 1 schematically depicts a lithographic projection apparatus according to a particular embodiment of the invention. The apparatus comprises: a radiation system Ex, IL, for supplying a projection beam PB of radiation (e.g. EUV radiation), which in this particular case also comprises a radiation source LA; a first object table (mask table) MT provided with a mask holder for holding a mask MA (e.g. a reticle), and connected to first positioning means PM for accurately positioning the mask with respect to item PL; a second object table (substrate table) WT provided with a substrate holder for holding a substrate W (e.g. a resist-coated silicon wafer), and connected to second positioning means PW for accurately positioning the substrate with respect to item PL; a projection system (xe2x80x9clensxe2x80x9d) PL (e.g. a mirror group) for imaging an irradiated portion of the mask MA onto a target portion C (e.g. comprising one or more dies) of the substrate W. As here depicted, the apparatus is of a reflective type (i.e. has a reflective mask). However, in general, it may also be of a transmissive type, for example (with a transmissive mask). Alternatively, the apparatus may employ another kind of patterning structure, such as a programmable mirror array of a type as referred to above. The source LA (e.g. a discharge or laser-produced plasma source) produces a beam of radiation. This beam is fed into an illumination system (illuminator) IL, either directly or after having traversed conditioning means, such as a beam expander Ex, for example. The illuminator IL may comprise adjusting means AM for setting the outer and/or inner radial extent (commonly referred to as "sgr"-outer and "sgr"-inner, respectively) of the intensity distribution in the beam. In addition, it will generally comprise various other components, such as an integrator IN and a condenser CO. In this way, the beam PB impinging on the mask MA has a desired uniformity and intensity distribution in its cross-section. It should be noted with regard to FIG. 1 that the source LA may be within the housing of the lithographic projection apparatus (as is often the case when the source LA is a mercury lamp, for example), but that it may also be remote from the lithographic projection apparatus, the radiation beam which it produces being led into the apparatus (e.g. with the aid of suitable directing mirrors); this latter scenario is often the case when the source LA is an excimer laser. The current invention and Claims encompass both of these scenarios. The beam PB subsequently intercepts the mask MA, which is held on a mask table MT. Having been selectively reflected by the mask MA, the beam PB passes through the lens PL, which focuses the beam PB onto a target portion C of the substrate W. With the aid of the second positioning means PW (and interferometric measuring means IF), the substrate table WT can be moved accurately, e.g. so as to position different target portions C in the path of the beam PB. Similarly, the first positioning means PM can be used to accurately position the mask MA with respect to the path of the beam PB, e.g. after mechanical retrieval of the mask MA from a mask library, or during a scan. In general, movement of the object tables MT, will be realized with the aid of a long-stroke module (course positioning) and a short-stroke module (fine positioning), which are not explicitly depicted in FIG. 1. However, in the case of a wafer stepper (as opposed to a step-and-scan apparatus) the mask table MT may just be connected to a short stroke actuator, or may be fixed. The depicted apparatus can be used in two different modes: 1. In step mode, the mask table MT is kept essentially stationary, and an entire mask image is projected at once (i.e. a single xe2x80x9cflashxe2x80x9d) onto a target portion C. The substrate table WT is then shifted in the x and/or y directions so that a different target portion C can be irradiated by the beam PB; 2. In scan mode, essentially the same scenario applies, except that a given target portion C is not exposed in a single xe2x80x9cflashxe2x80x9d. Instead, the mask table MT is movable in a given direction (the so-called xe2x80x9cscan directionxe2x80x9d, e.g. the y direction) with a speed v, so that the projection beam PB is caused to scan over a mask image; concurrently, the substrate table WT is simultaneously moved in the same or opposite direction at a speed V=Mv, in which M is the magnification of the lens PL (typically, M={fraction (1/4)} or {fraction (1/5)}). In this manner, a relatively large target portion C can be exposed, without having to compromise on resolution. Mirror System Classification According to the present invention, a mirror system of n mirrors is classified by reference to the direction of the reflected beam compared to the incident beam at each mirror surface. Having defined the object height to be positive along a Y-axis and a suitable reference plane, e.g. the plane containing the optical axis Z of the projection system and the Y-axis (as shown in FIG. 1), the chief ray CR at a mirror is defined as having a positive angle of incidence xcex1, if the angle between the normal of the surface and the incident ray is counterclockwise (as shown in FIG. 2) and a negative angle of incidence if the angle between the normal and the incident ray is clockwise. Further, one should view this reference plane along a positive X direction, the X, Y, Z directions making up a right-handed orthogonal coordinate system, as shown in FIG. 1. The chief ray is defined as that ray emerging from the object point, which goes through the center of the stop and therefore also through the center of the entrance and exit pupils, i.e. at a height equal to zero from the optical axis. (NB this assignment is arbitrary, the scheme can be implemented with either relative direction of reflection regarded as positive, provided that the assignment is consistent.) By assigning the binary digit xe2x80x9c1xe2x80x9d to a negative angle of incidence and xe2x80x9c0xe2x80x9d to a positive angle of incidence of the chief ray, a mirror system is assigned a binary number defined by the sequence of binary digits assigned to each mirror in the system in sequence along the optical path of the beam from object to source. For convenience, this binary number is expressed in decimal notation. The various classes of the incidence angle classification system are further characterized by indicating the sign of the magnification of the system. Herein, this is indicated by the appropriate sign in parentheses after the class number, e.g. 6(xe2x88x92). The sign is obtained by dividing the magnification M by its absolute value \|M\|. A system has a positive magnification if the object and image are the same side of the optical axis and a negative magnification if they are opposite sides. The decimal incidence angle classification, C, can thus be expressed as: C = ∑ i = 1 n ⁢ a i · 2 ( n - i ) ⁢ ( M "LeftBracketingBar" M "RightBracketingBar" ) ( 1 ) where: ai=1 if the angle of incidence of the chief ray at mirror i is negative, ai=0 if the angle of incidence of the chief ray at mirror i is positive, M is the magnification of the projection system, and index i numbers the mirrors of the system in series from object to source. FIG. 2 shows the four possible arrangements of incident chief rays CR and mirrors M. In A the incident chief ray is travelling left to right and has an angle of incidence xcex1 greater than 0, so ai=0. In B the incident chief ray is travelling right to left and has an angle of incidence xcex1 less than 0, so ai=1. In C the incident chief ray is travelling right to left and has an angle of incidence xcex1 greater than 0, so ai=0. In D the incident chief ray is travelling left to right with an angle of incidence xcex1 less than 0, so ai=1. Note that although convex mirrors are shown, the same assignments apply with concave or plane mirrors. While the incidence angle classification C does not wholly define a mirror system, the basic layout of a system is inherent in its incidence angle classification. By reference to whether the reflection at a given mirror is positive or negative, the orientation of that mirror and the position of the succeeding mirror, above or below the beam, can be determined. Thus a given classification number can be used by the designer of a mirror system to set out the system prior to optimization of that system, e.g. using commercially available ray tracing software such as CODE V(TM) by Optical Research Associates, Pasadena, Calif., USA. It should be noted that previous classifications of mirror systems based on whether the curvature, and hence power, of each mirror in the system is positive or negative, do not give any information as to the layout of a mirror system. It will also be noted that the incidence angle classification of a given mirror system can readily be determined from simple inspection of the beam path. Using the above classification system and numerical simulations, the present inventors have determined that only certain classes contain mirror systems usable as the projection system in a lithographic projection system. For four-mirror systems, feasible projection systems exist in classes 2(xe2x88x92), 6(xe2x88x92), 9(+), 9(xe2x88x92) and 10(xe2x88x92). For six-mirror systems, feasible projection systems exist in classes 5(+), 6(xe2x88x92), 9(+), 13(+), 18(xe2x88x92), 21(+), 22(xe2x88x92), 25(+), 26(xe2x88x92), 29(+), 34(xe2x88x92), 37(+), 38(xe2x88x92), 41(+), 42(xe2x88x92), 45(+) and 54(xe2x88x92). For eight-mirror systems, feasible projection systems exist in class 2(+), 5(+), 9(+), 12(+), 13(+), 18(+), 18(xe2x88x92), 19(+), 20(+), 21(+), 22(+), 23(+), 25(+), 26(+), 34(xe2x88x92), 36(+), 37(+), 38(xe2x88x92), 45(+), 46(+), 49(+), 52(+), 53(+), 54(+), 54(xe2x88x92), 55(xe2x88x92), 58(xe2x88x92), 68(+), 69(+), 73(+), 74(+), 77(+), 82(+), 82(xe2x88x92), 85(+), 88(+), 89(+), 90(xe2x88x92), 92(+), 93(+), 97(+), 100(xe2x88x92), 101(+), 102(xe2x88x92), 104(+), 105(+), 106(+), 106(xe2x88x92), 107(+), 108(+), 109(+), 109(xe2x88x92), 110(+), 110(xe2x88x92), 111(+), 113(+), 116(+), 117(+), 118(+), 118(xe2x88x92), 120(+), 121(+), 122(xe2x88x92), 123(xe2x88x92), 132(+), 133(+), 134(xe2x88x92), 137(+), 138(+), 141(+), 145(+), 145(xe2x88x92), 146(+), 146(xe2x88x92), 147(+), 148(+), 148(xe2x88x92), 149(+), 150(+), 150(xe2x88x92), 151(+), 151(xe2x88x92), 152(xe2x88x92), 153(+), 154(+), 154(xe2x88x92), 155(+), 155(xe2x88x92), 156(+), 157(+), 159(+), 161(+), 162(xe2x88x92), 163(xe2x88x92), 164(+), 165(+), 166(+), 166(xe2x88x92), 167(+), 168(+), 169(+), 170(+), 170(xe2x88x92), 171(+), 172(+), 173(+), 174(+), 175(+), 176(+), 177(+), 178(xe2x88x92), 179(+), 180(+), 180(xe2x88x92), 181(+), 181(xe2x88x92), 182(+), 182(xe2x88x92), 183(+), 183(xe2x88x92), 184(+), 185(+), 185(xe2x88x92), 186(xe2x88x92), 187(+), 187(xe2x88x92), 188(xe2x88x92), 189(+), 196(+), 197(+), 201(+), 203(+), 205(+), 209(+), 214(xe2x88x92), 216(+), 217(+), 218(+), 218(xe2x88x92), 225(+), 228(+), 229(+), 230(+), 232(+), 233(+), 235(+), 236(+), 237(+), 238(xe2x88x92), 243(+), 246(+), 247(+), 248(+), 250(xe2x88x92). Design Methodology As mentioned above, a given class defines an outline layout for a mirror system for which a functional projection system can be designed. A methodology according to the present invention for such a design process is described below. In the design process according to the invention, the mirrors in a system are defined by xe2x80x9cthicknessesxe2x80x9d and curvatures, defined as shown in FIG. 3. (NB the term xe2x80x9cthicknessxe2x80x9d is used by analogy to refractive systems which are conventionally defined in terms of surface curvatures, thicknesses between surfaces and the refractive indices of the media between surfaces.) Thus, thickness d1 is the distance between the object, the mask MA in the present case of a projection system in a lithographic apparatus, and the intersection of the (imaging extended) first mirror M1 with the optical axis OA. The distance between the intersections of the (imaging extended) first mirror M1 and the (imaging extended) second mirror M2 with the optical axis OA is d1. Note that since the second mirror is situated between the first mirror M1 and the object (mask MA), thickness d1 is negative. In general, thickness di is the distance between the intersections of mirror Mi and mirror Mi+1 with the optical axis OA. For an n-mirror system, the thickness dn is the distance between the last mirror Mn and the image plane, where the substrate W is positioned in a lithographic projection apparatus. In specific embodiments described below, an additional thickness dn+1 is given, this represents the distance between the position of the image calculated using a first order approximation and using a real ray tracing algorithm. In a first step the design method identifies conceivable systems under a number of constraints by using a paraxial approach described below. Those systems should not present obscuration, as is also described further below. The paraxial approach and the constraints yield a limited number of variables that are sampled to identify solutions. In a further step those solutions are checked using a real ray tracing method, referred to above, in which the paraxial assumptions are not present and in which also multilayer coatings of the reflectors may be modelled. Paraxial Approach The present inventors have developed an approach to designing mirror systems which starts with a paraxial approximation of a mirror system using matrix formalism. In a paraxial approximation the sine of an angle is approximated as the angle, i.e. sin xcex1=xcex1, and are the mirrors considered as being flat, while the actual curvature of a mirror is considered only to affect the angle of an incident ray, not its point of intersection with the supposedly xe2x80x98flatxe2x80x99 surface. In a matrix formalism, such as described in xe2x80x9cIntroduction to Opticsxe2x80x9d by Frank and Leno Pedrotti, Prentice Hall 1993; ISBN: 0135015456, incorporated herein by reference, the description of an optical system consist of an accumulation of translation and reflection (and/or refraction in a catadioptric or refractive system) matrices Mtrans,Mrefl which are defined as follows: M trans = [ 1 d i 0 1 ] ( 2 ) M refl = [ 1 0 - 2 · c i - 1 ] ( 3 ) where di is the distance to the next surface and ci the curvature of the surface, which is positive if the center of the sphere is on the right side of the surface. The path of a ray is given by a vector made of a height (distance from the optical axis) and an angle: [height, angle]. The multiplication of the vector with one or more matrices gives the ray after the corresponding translations or reflections. The system matrix is the multiplication of all the matrices in the system. The first matrix is the reflection matrix of the first surface, the penultimate matrix is the translation matrix of the thickness preceding the last reflective surface and the last matrix is the reflection matrix of the last reflective surface. The effective focal length, the back focal length, the front focal length and the paraxial image distance can be derived from the system matrix as follows. If the system matrix is defined as: M system = [ a b c d ] ( 4 ) then the effective focal length is given by: efl = - 1 c ( 5 ) the back focal length is given by: bfl = - a c ( 6 ) the front focal length is given by: ffl = d c ( 7 ) and the paraxial image distance, i.e. the distance between the last reflective surface and the image plane, is given by: d n = a · d 0 + b c · d 0 + d ( 8 ) where d 0 = ad - cb - magn · d magn · c and magn is the magnification of the system. The system matrix for the first part of the system, from the object plane to the stop (pupil) can be represented as: M 1 ⁢ st = [ a 1 ⁢ st b 1 ⁢ st c 1 ⁢ st d 1 ⁢ st ] ( 9 ) so that the distance, Lenpup, to the entrance pupil is given by: [ a 1 ⁢ st b 1 ⁢ st c 1 ⁢ st d 1 ⁢ st ] · [ 1 L enpup 0 1 ] · [ 0 A enpup ] = "AutoLeftMatch" xe2x80x83 ⁢ [ "AutoLeftMatch" ( a 1 ⁢ st · L enpup + b 1 ⁢ st ) · A enpup ( c 1 ⁢ st · L enpup + d 1 ⁢ st ) · A enpup ] = [ 0 A stop ] ( 10 ) The second part of the system, from stop to image surface can be represented as: M 2 ⁢ nd = [ a 2 ⁢ nd b 2 ⁢ nd c 2 ⁢ nd d 2 ⁢ nd ] ( 11 ) so that the distance, Lexpup, to the exit pupil is given by: [ 1 L exp ⁢ xe2x80x83 ⁢ up 0 1 ] · [ a 2 ⁢ nd b 2 ⁢ nd c 2 ⁢ nd d 2 ⁢ nd ] · [ 0 A stop ] = "AutoLeftMatch" [ ( b 2 ⁢ nd + L exp ⁢ xe2x80x83 ⁢ up · d 2 ⁢ nd ) · A stop D 2 ⁢ nd · A stop ] = [ 0 A exp ⁢ xe2x80x83 ⁢ up ] ( 12 ) The distances to the entrance and exit pupils, if xcex9enpupxe2x89xa00, are then given by: L enpup = - b 1 ⁢ st a 1 ⁢ st ⁢ xe2x80x83 ⁢ and ⁢ xe2x80x83 ⁢ xe2x80x83 ⁢ L exp ⁢ xe2x80x83 ⁢ up = - b 2 ⁢ nd d 2 ⁢ nd ( 13 ) Constraints Given the above, various constraints that must be applied to the system can be used to determine equations for the curvatures and thicknesses of certain surfaces of the system as functions of the constraints and other curvatures and thicknesses. Some example constraints G1 to G4 are shown in FIG. 5. A first constraint G1 is minimum deviation from telecentricity on the object side that still enables obscuration-free illumination of the object, which may determine the curvature of the first surface or the thickness between mirrors 1 and 2. Another constraint G3, is perfect telecentricity on the image side, which may determine the curvature of the last surface or the thickness between the final and penultimate mirrors. This telecentricity requirement is equivalent to the requirement that the exit pupil is at infinity. The requirement that the object and the image are conjugated and have a prescribed value of the transverse magnification fixes the values of the object (G2) and image (G4) distances. The object distance G2, the first thickness, can be solved as a function of the desired magnification of the system: the paraxial image distance is inserted in the thickness of the surface immediately preceding the image plane and the object distance is modified to satisfy: M = Image ⁢ xe2x80x83 ⁢ Height Object ⁢ xe2x80x83 ⁢ Height ( 14 ) In current lithography apparatus, M is usually set as xc2x10.20 or xc2x10.25, i.e. reduction by a factor of 5 or 4 respectively. A minimum deviation from telecentricity at the object side is an important requirement in lithography. The reflective object (mask MA) is illuminated with a beam coming from the radiation system. The chief ray angle at the object must be such that the incident illuminating beam does not interfere with the beam reflected from the object and going into the projection system. The angle of the chief ray together with the numerical aperture on the object side should be almost zero and the angles of all rays must be smaller or larger than zero, to fulfill these two requirements. For telecentricity on the image side, the angle of the chief ray relative to the optical axis has to be zero. The size of the last mirror increases quickly as a function of the distance between the image and the last mirror, due to the relatively large numerical aperture. A system with zero or an even number of intermediate images has a negative magnification. To have an overall system with a positive magnification the number of intermediate images has to be odd. The working distance at the object side is the minimum distance between the object plane and the surface closest to the object, most of the time the second mirror. On the image side the working distance is the minimum distance between the image plane and the plane closest to the image, most often the penultimate mirror. The working distances provide room for mirror supports and for mechanical movements of the object and the image and must not be too small. An example of applying the above constraints in a six-mirror system is described below. This may be carried out in practice using software such as Maple(TM) produced by Waterloo Maple Inc. 57 Erb Street W. Waterloo, Ontario Canada N2L 6C2. First is a derivation of the formulas used for a six-mirror system, but the formulas are also valid for other numbers of mirrors, using the paraxial approach. In the matrix notation a ray is defined by the vector: [height, angle in radians]. After a distance di the ray [y,a] will be: [ y + d i ⁢ a a ] ( 15 ) using the matrix given in equation (2). After a mirror with curvature ci the ray [y,a] will have the same height but a different angle: [ v - 2 c i ⁢ v - a ] ( 16 ) using the matrix given in equation (3). To derive formulas used later on, firstly the distance between mirror 5 and 6 is solved by requiring telecentricity in the image of the ray going through the optical axis in the stop surface. The following matrix A is from the stop surface to after the 5th mirror, as we don""t now where we will locate the stop surface we take an unknown 2 by 2 matrix: A := [ a b c d ] ( 17 ) From the 5th mirror we travel a distance la to the 6th mirror, la is the variable to solve now. L6 := [ 1 la 0 1 ] ( 18 ) Matrix MC is of the 6th mirror surface: MC := [ 1 0 - 2 ⁢ c6 - 1 ] ( 19 ) The ray going through the center of the stop with an arbitrary angle ap is: Y := [ 0 ap ] ( 20 ) That ray after the 6th mirror will be: Y_image := [ ( b + la ⁢ xe2x80x83 ⁢ d ) ⁢ ap ( - 2 ⁢ c6 + ( - 2 ⁢ c6 ⁢ xe2x80x83 ⁢ la - 1 ) ⁢ d ) ⁢ ap ] ( 21 ) in which the angle is equal to zero since telecentricity is required and the solution opl for the distance la between mirror five and six is now opl := - 1 2 ⁢ 2 ⁢ c6 ⁢ xe2x80x83 ⁢ b + d c6 ⁢ xe2x80x83 ⁢ d ( 22 ) The matrix from the stop surface to after the 6th mirror is now: B := [ 1 2 ⁢ 2 ⁢ c6 ⁢ xe2x80x83 ⁢ ad - 2 ⁢ c6 ⁢ xe2x80x83 ⁢ bc - cd c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ d c6 - 2 ⁢ xe2x80x83 ⁢ c6 ⁡ ( da - bc ) d 0 ] ( 23 ) The next solve is the distance d between the object and the first mirror and the solve ya for the angle of the chief ray (going through the center of the stop) between the object and the first mirror. The ray Ya in the object point yob with the desired angle ya is given by the vector: Ya := [ yob ya ] ( 24 ) and the distance l between the object and the first mirror surface by the matrix: L := [ 1 l 0 1 ] ( 25 ) The first mirror surface is given by: MC := [ 1 0 - 2 ⁢ cl - 1 ] ( 26 ) The distance m between the first mirror and the second mirror is given by: M := [ 1 m 0 1 ] ( 27 ) The unknown matrix from the second mirror surface to the stop position is defined as A := [ e f g h ] ( 28 ) The chief ray in the stop surface is now: Y_stop := xe2x80x83 ⁢ ⁢ xe2x80x83 ⁢ [ xe2x80x83 ⁢ ( e - 2 ⁢ xe2x80x83 ⁢ ( e ⁢ xe2x80x83 ⁢ m + f ) ⁢ xe2x80x83 ⁢ c1 ) ⁢ yob + ( ( e - 2 ⁢ ( e ⁢ xe2x80x83 ⁢ m + f ) ⁢ xe2x80x83 ⁢ c1 ) ⁢ l - em - f ) ⁢ ya ( g - 2 ⁢ ( g ⁢ xe2x80x83 ⁢ m + h ) ⁢ xe2x80x83 ⁢ c1 ) ⁢ yob + ( ( g - 2 ⁢ ( g ⁢ xe2x80x83 ⁢ m + h ) ⁢ c1 ) ⁢ l - g ⁢ xe2x80x83 ⁢ m - h ) ⁢ ya ⁢ xe2x80x83 ] ( 29 ) and in the image the chief ray is: Y_image := xe2x80x83 ⁢ [ ( 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ e c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g c6 - xe2x80x83 ⁢ 2 ⁢ ( ( 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ e c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g c6 ) ⁢ m + xe2x80x83 ⁢ 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ f c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h c6 ) c1 ) ⁢ yob + xe2x80x83 ⁢ ( ( 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ e c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g c6 - xe2x80x83 ⁢ 2 ⁢ ( ( 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ e c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g c6 ) ⁢ m + xe2x80x83 ⁢ 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ f c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h c6 ) c1 ) l - xe2x80x83 ⁢ ( 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ e c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g c6 ) ⁢ m - xe2x80x83 ⁢ 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ f c6 ⁢ xe2x80x83 ⁢ d + 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h c6 ) ⁢ yz ] xe2x80x83 ⁢ [ ( - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ e d - 2 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c6 ⁡ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ e ⁢ xe2x80x83 ⁢ m d - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ f d ) c1 ) yob + ( ( - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ e d - xe2x80x83 ⁢ 2 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ m d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ f d ) ⁢ c1 ) ⁢ l + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ m d + 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ f d ) ⁢ yz ] ( 30 ) The height of the chief ray in the image is by definition magnheight in the object surface (yob), we solve l from equation (30) to impose this reduction to the system giving: Y_image ⁢ _l := xe2x80x83 ⁢ - ( 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d - xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ g - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d + 4 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d + 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ g - 4 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c + 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d + 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ h - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d + 2 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c + ya ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d + xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ g - 2 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d + 2 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c + ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d + xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ h - 2 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d ) / xe2x80x83 ⁢ ( ( 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d - d 2 ⁢ g - 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c + 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d + 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ g - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d + 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c + 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d + 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ d 2 ⁢ h ) ⁢ ya ) ( 31 ) and we force the height of the chief ray to be zero in the stop surface in equation (29), as it should be by definition to solve the distance m Y_stop ⁢ _m := - xe2x80x83 ⁢ - yob ⁢ xe2x80x83 ⁢ e + 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c1 - ya ⁢ xe2x80x83 ⁢ l ⁢ xe2x80x83 ⁢ e + 2 ⁢ ya ⁢ xe2x80x83 ⁢ l ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c1 + ya ⁢ xe2x80x83 ⁢ f e ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 + 2 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ l + ya ) ( 32 ) The solution for the distance m between the first and the second mirror now becomes: Y_stop ⁢ _m := 1 4 ⁢ xe2x80x83 ⁢ xe2x80x83 ⁢ - 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - e ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h + ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g e ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ( 33 ) The solution for the distance m between the object and the first mirror now is: Y_image ⁢ _l := - 1 2 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g + 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g - e ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h - 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ h + 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ya ⁢ xe2x80x83 ⁢ ( f ⁢ xe2x80x83 ⁢ g - e ⁢ xe2x80x83 ⁢ h ) ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ d ( 34 ) We substitute the just derived expressions in the matrices L and M of equations (25) and (27). M := [ 1 1 4 ⁢ xe2x80x83 ⁢ xe2x80x83 ⁢ - 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - e ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h + ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g e ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 0 1 ] ( 35 ) L := [ 1 - 1 2 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g + 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g - e ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h - 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ h + 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ya ⁢ xe2x80x83 ⁢ ( f ⁢ xe2x80x83 ⁢ g - e ⁢ xe2x80x83 ⁢ h ) ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ d 0 1 ] ( 36 ) And as a check we calculate the chief ray after the 6th surface with the new expressions. We see that the angle is always zero and that the height is the object height multiplied with magnification. Y_image := [ magn ⁢ xe2x80x83 ⁢ yob 0 ] ( 37 ) The final solve is the distance n between the last mirror surface and the image surface. In the image surface all rays from the same object point come together in a point with a height=magnificationobject height. First we define a ray Yb from the object point yob and an arbitrary angle yb. Yb := [ yob yb ] ( 38 ) N := [ 1 n 0 1 ] ( 39 ) In the image this ray Yb will become: Y_image := xe2x80x83 ⁢ [ - 1 4 ⁢ ( - f ⁢ xe2x80x83 ⁢ g 2 ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ ya 2 + g ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ ya 2 ⁢ xe2x80x83 ⁢ h - g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h - 4 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ e - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + 4 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya 2 ⁢ xe2x80x83 ⁢ h - 4 ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya 2 ⁢ xe2x80x83 ⁢ h + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ ya 2 ⁢ xe2x80x83 ⁢ h + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya 2 ⁢ xe2x80x83 ⁢ h - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya 2 ⁢ xe2x80x83 ⁢ h - 2 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ h + 4 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ h ⁢ xe2x80x83 - xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + f ⁢ xe2x80x83 ⁢ g 2 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ ya + f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ d ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ ya 2 + 2 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya 2 - 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya 2 + 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya 2 - f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya 2 + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ ya - 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ) / ( ya ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 2 ) ] xe2x80x83 ⁢ [ - xe2x80x83 ⁢ ( - ya + yb ) ⁢ ( f ⁢ xe2x80x83 ⁢ g - e ⁢ xe2x80x83 ⁢ h ) ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) magn ] ( 40 ) The expression for the image distance n is, given that the image height is equal to magn. yob: Y_image ⁢ _n := xe2x80x83 ⁢ - 1 4 ⁢ ( - d 2 ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + 2 ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ e + 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - 2 ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 + 4 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob - e 2 ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ g 2 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ f - 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ) / xe2x80x83 ⁢ ( ( - e ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ h + e ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ h + f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ a - f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ ya ) ( 41 ) 6-mirror system, stop on mirror 2 Now we use these derivations in the first part: solving the variables of a six-mirror system with the stop position on mirror two, defining thicknesses as d:=[d0,d1,d2,d3,d4,d5,d6] and the curvatures as c=[c1,c2,c3,c4,c5,c6]. The stop (pupil) position is on the second surface. A limitation on the Petzval sum (i.e. the sum of curvatures in the system, curvatures of odd surfaces being subtracted from curvatures of even surfaces, or vice versa), e.g. to be zero, can be introduced and used to solve the curvature of the stop surface. However, a zero Petzval sum is not essential and an non-zero value can be accommodated. Now we define all the matrices in the system, the reflectance (even subscripts) and translation (odd subscripts) matrices, from the object to the image. M 1 := [ 1 d0 0 1 ] M 2 := [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c1 - 1 ] M 3 := [ 1 d1 0 1 ] M 4 := [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c2 - 1 ] M 5 := [ 1 d2 0 1 ] M 6 := [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c3 - 1 ] M 7 := [ 1 d3 0 1 ] M 8 := [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c4 - 1 ] M 9 := [ 1 d4 0 1 ] M 10 := [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c5 - 1 ] M 11 := [ 1 d5 0 1 ] M 12 := [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c6 - 1 ] M 13 := [ 1 d6 0 1 ] xe2x80x83 ( 42 ) The first solve is the exit pupil in infinity or telecentricity in the image. The angle of the ray going through the optical axis in the stop surface should be zero in the image. The matrix from the stop surface to the fifth mirror generated by multiplication of the appropriate M matrices derived just above, is given by: \| 1 - 2 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ) + 2 ⁢ xe2x80x83 ⁢ c3 ) , d2 + d3 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + d4 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) \| ⁢ [ - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ) + 2 ⁢ xe2x80x83 ⁢ c3 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ( 1 - 2 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 - 2 ⁢ c3 . - 2 ⁢ xe2x80x83 ⁢ c5 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 \| ( 43 ) The matrix from the second mirror surface to the stop surface is given by: [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c2 - 1 ] ( 44 ) So as we derived the distance between mirror 5 and 6, we solve this new found value in the appropriate matrix and the vector of distances. d5 := xe2x80x83 ⁢ - 1 2 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d2 - 4 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d3 - 4 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 + xe2x80x83 ⁢ 8 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d3 + 4 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d4 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d3 + 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 - xe2x80x83 ⁢ 8 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) / ( c6 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d2 - 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d3 - 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 + 8 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 + 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 + 4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) ( 45 ) The distance between mirror one and two is derived as: d1 := - 1 4 ⁢ - 2 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ( 46 ) and the distance between the object and the first mirror is: d0 := xe2x80x83 ⁢ 1 2 ⁢ ( - angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) - 2 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) / ( angle ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - xe2x80x83 ⁢ 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) ( 47 ) The distance between mirror six and the image surface is: d6 := xe2x80x83 ⁢ - 1 4 ⁢ ( 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d3c3 + d4 ( - "AutoLeftMatch" 2 ⁢ c4 ⁡ ( 1 - "AutoLeftMatch" xe2x80x83 ⁢ 2 ⁢ d3c3 ) + xe2x80x83 ⁢ 2 ⁢ c3 ) ) ⁢ xe2x80x83 ⁢ c6 ( xe2x80x83 ⁢ - 2 ⁢ c5 ( d2 + "AutoLeftMatch" xe2x80x83 ⁢ "AutoLeftMatch" d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + d4 ( - 2 ⁢ c4 ( d2 + xe2x80x83 ⁢ d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) + 2 ⁢ c4 ( d2 + xe2x80x83 ⁢ d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) - 2 ⁢ c3d2 - 1 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d3c3 + d4 ⁡ ( - 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d3c3 ) + 2 ⁢ c3 ) ) + xe2x80x83 ⁢ 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d3c3 ) - 2 ⁢ c3 ) ⁢ c6 ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) - xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d3c3 + d4 ⁡ ( - 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d3c3 ) + 2 ⁢ c3 ) ) + xe2x80x83 ⁢ 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d3c3 ) - 2 ⁢ c3 ) ⁢ ( - 2 ⁢ c5 ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) + xe2x80x83 ⁢ 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) - 2 ⁢ c3d2 - 1 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) + xe2x80x83 ⁢ "AutoLeftMatch" 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) - 2 ⁢ c3d2 - 1 ) "AutoRightMatch" 2 ⁢ c2 + xe2x80x83 ⁢ 4 ⁢ c1 ( - 2 ⁢ c5 ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) + xe2x80x83 ⁢ 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) - 2 ⁢ c3d2 - 1 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ magn 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 2 ) / ( ( ( - 2 ⁢ c5 ( 1 - 2 ⁢ d3c3 + d4 ( - 2 ⁢ c4 ( 1 - xe2x80x83 ⁢ 2 ⁢ d3c3 ) + 2 ⁢ c3 ) ) + 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d3c3 ) - 2 ⁢ c3 ) ⁢ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) - xe2x80x83 ⁢ ( - 2 ⁢ c5 ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + d4 ( - 2 ⁢ c4 ( d2 + xe2x80x83 ⁢ d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) + 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) - xe2x80x83 ⁢ 2 ⁢ c3d2 - 1 ) ⁢ ( 1 - 2 ⁢ d3c3 + d4 ⁡ ( - 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d3c3 ) + 2 ⁢ c3 ) ) ) ⁢ c6 2 ⁢ xe2x80x83 ⁢ angle ) ( 48 ) The variable angle is identical to ya introduced in equation (24) above. 6-Mirror System, Stop on Mirror 3 The original derivations can similarly be used to solve the variables of a six-mirror system with the stop position on mirror three, as will now be shown. The first solve is pupil in infinity or telecentricity in the image. The angle of the ray going through the optical axis in the stop surface should be zero in the image. The matrix from the stop surface to the fifth mirror generated by multiplication of the appropriate M matrices derived just above, is given by: [ 1 - 2 ⁢ d4c4 d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d4c4 ) + 2 ⁢ c4 - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ] ( 50 ) The matrix from the second mirror surface to the stop surface is given by: [ 1 - 2 ⁢ d2c2 - d2 - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 2 ⁢ c3d2 + 1 ] ( 51 ) So, as derived above, the distance between mirror 5 and 6 is, solved this new found value in the appropriate matrix and the vector of distances: d5 := - 1 2 ⁢ xe2x80x83 ⁢ 2 ⁢ c6d3 - 4 ⁢ c6d4c4d3 - 2 ⁢ c6d4 - 2 ⁢ c5d3 + 4 ⁢ c5d4c4d3 + 2 ⁢ c5d4 + 2 ⁢ c4d3 + 1 c6 ⁡ ( - 2 ⁢ c5d3 + 4 ⁢ c5d4c4d3 + 2 ⁢ c5d4 + 2 ⁢ c4d3 + 1 ) ( 51 ) The distance between mirror one and two was: d1 := xe2x80x83 ⁢ - 1 4 ⁢ ( - 4 ⁢ d2c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - 2 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ c4d3 + 1 ) ⁢ ( 2 ⁢ c3d2 + 1 ) + angle ⁢ xe2x80x83 ⁢ d2 ( - 2 ⁢ c5 ( d3 + d4 ( - 2 ⁢ c4d3 - xe2x80x83 ⁢ 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) / ( ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 ) ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) ( 52 ) And the distance between the object and the first mirror: d0 := xe2x80x83 ⁢ - 1 2 ⁢ ( ( 1 - 2 ⁢ d2c2 ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ c4d3 + 1 ) ⁢ ( 2 ⁢ c3d2 + 1 ) + angle ⁢ xe2x80x83 ⁢ d2 ( - 2 ⁢ c5 ( d3 + d4 ( - 2 ⁢ c4d3 - xe2x80x83 ⁢ 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ d2 ( - 2 ⁢ c5 ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( - 2 ⁢ c3 ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 ) + 2 ⁢ c2 ) + 2 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ ( - 2 ⁢ c5 ( d3 + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( 2 ⁢ c3d2 + 1 ) - xe2x80x83 ⁢ 2 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) / ( angle ⁢ xe2x80x83 ⁢ ( ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) ⁢ d2 + ( 2 ⁢ c3d2 + 1 ) ⁢ ( 1 - 2 ⁢ d2c2 ) ) ⁢ c1 ( - 2 ⁢ c5 ( d3 + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ) ( 53 ) And the distance between mirror six and the image surface: d6 := xe2x80x83 ⁢ - xe2x80x83 ⁢ 1 4 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) 2 ⁢ ( 1 - 2 ⁢ d4c4 ) ⁢ c6 ( - 2 ⁢ c5 ( d3 + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( 2 ⁢ c3d2 + xe2x80x83 ⁢ 1 ) - 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ ( 1 - 2 ⁢ d4c4 ) ⁢ c6 ( - 2 ⁢ c5 ( d3 + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ d2 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) 2 ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d4c4 ) + xe2x80x83 ⁢ 2 ⁢ c4 ) ⁢ c6 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) ⁢ ( 2 ⁢ c3d2 + 1 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d4c4 ) + 2 ⁢ c4 ) ⁢ c6 ( d3 + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) ⁢ d2 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) + xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) 2 ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d4c4 ) + xe2x80x83 ⁢ 2 ⁢ c4 ) ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( 2 ⁢ c3d2 + 1 + xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d4c4 ) + 2 ⁢ c4 ) ⁢ ( - 2 ⁢ c5 ( d3 + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ d2 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) + angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + xe2x80x83 ⁢ 1 ) 2 ⁢ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ ( 2 ⁢ c3d2 + 1 ) + xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) 2 ⁢ ( - 2 ⁢ c3 ( 1 - "AutoLeftMatch" xe2x80x83 ⁢ 2 ⁢ d2c2 ) + 2 ⁢ c2 ) "AutoRightMatch" 2 ⁢ d2 - 4 ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ c4d3 + 1 ) ⁢ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ⁢ d2c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - xe2x80x83 ⁢ 4 ⁢ c1 ⁡ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( 2 ⁢ c3d2 + xe2x80x83 ⁢ 1 ) ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + 4 ⁢ xe2x80x83 ⁢ magn 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 2 ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 ) ) / ( ( ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + xe2x80x83 ⁢ 1 ) ⁢ ( 1 - 2 ⁢ d4c4 ) ⁢ d2 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) - ( - 2 ⁢ c5 ( 1 - xe2x80x83 ⁢ 2 ⁢ d4c4 ) + 2 ⁢ c4 ) ⁢ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) ⁢ d2 ( - 2 ⁢ c3 ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 ) + 2 ⁢ c2 ) - ( 2 ⁢ c3d2 + 1 ) ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d4c4 ) + xe2x80x83 ⁢ 2 ⁢ c4 ) ⁢ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + ( 2 ⁢ c3d2 + 1 ) ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 ) ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + xe2x80x83 ⁢ 1 ) ⁢ ( 1 - 2 ⁢ d4c4 ) ) ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ c6 2 ⁢ xe2x80x83 ⁢ angle ) ( 54 ) 6-Mirror System, Stop on Mirror 4 Similarly, the original derivations can be used to solve the variables of a six-mirror system with the stop position on mirror four. Again, the first solve is pupil in infinity or telecentricity in the image. The angle of the ray going through the optical axis in the stop surface should be zero in the image. The matrix from the stop surface to the fifth mirror generated by multiplication of the appropriate M matrices derived above is given by: [ 1 d4 - 2 ⁢ c5 - 2 ⁢ c5d4 - 1 ] ( 55 ) The matrix from the second mirror surface to the stop surface is given by: [ 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) - d2 + d3 ⁡ ( 2 ⁢ c3d2 + 1 ) - 2 ⁢ c4 ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) + 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) - 2 ⁢ c2 - 2 ⁢ c4 ( - d2 + d3 ( 2 ⁢ c3d2 + 1 ) ) - 2 ⁢ c3d2 - 1 ] ( 56 ) So, as derived above, the distance between mirror 5 and 6, solved in the appropriate matrix and the vector of distances, is: d5 := - xe2x80x83 ⁢ 1 2 ⁢ xe2x80x83 ⁢ - 2 ⁢ c6d4 + 2 ⁢ c5d4 + 1 c6 ⁡ ( 2 ⁢ c5d4 + 1 ) ( 57 ) The distance between mirror one and two is: d1 := xe2x80x83 ⁢ - xe2x80x83 ⁢ 1 4 ⁢ ( 4 ⁢ ( - d2 + d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - 2 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 + d3 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5d4 - 1 ) ⁢ ( - 2 ⁢ c4 ( - d2 + d3 ( 2 ⁢ c3d2 + xe2x80x83 ⁢ 1 ) ) - 2 ⁢ c3d2 - 1 ) - angle ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) ⁢ ( - 2 ⁢ c5d4 - xe2x80x83 ⁢ 1 ) ⁢ ( - 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) - 2 ⁢ c2 ) ) / ( ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) ( 58 ) And the distance between the object and the first mirror: d0 := xe2x80x83 ⁢ - 1 2 ⁢ ( ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5d4 - 1 ) ⁢ ( - 2 ⁢ c4 ( - d2 + xe2x80x83 ⁢ d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) - 2 ⁢ c3d2 - 1 ) - angle ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) ⁢ ( - 2 ⁢ c5d4 - 1 ) ⁢ ( - 2 ⁢ c4 ( 1 - 2 ⁢ d2c2 + xe2x80x83 ⁢ d3 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) + 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) - xe2x80x83 ⁢ 2 ⁢ c2 ) - 2 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) ⁢ ( - 2 ⁢ c5d4 - xe2x80x83 ⁢ 1 ) ⁢ ( - 2 ⁢ c4 ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) ) + 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) - 2 ⁢ c2 ) + 2 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 + d3 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) ⁢ ( - 2 ⁢ c5d4 - xe2x80x83 ⁢ 1 ) ⁢ ( - 2 ⁢ c4 ⁡ ( - d2 + d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) - 2 ⁢ c3d2 - 1 ) - xe2x80x83 ⁢ 2 ⁢ ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) / ( angle ⁢ xe2x80x83 ⁢ ( - ( - 2 ⁢ c4 ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 + d3 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) - 2 ⁢ c2 ) ⁢ ( - d2 + d3 ( 2 ⁢ c3d2 + xe2x80x83 ⁢ 1 ) ) + ( - 2 ⁢ c4 ⁡ ( - d2 + d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) - 2 ⁢ c3d2 - 1 ) ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 + d3 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) ) ⁢ c1 ⁡ ( - 2 ⁢ c5d4 - 1 ) ) ( 59 ) And the distance between mirror six and the image surface: d6 := xe2x80x83 ⁢ - xe2x80x83 ⁢ 1 4 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) 2 xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) - 4 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d4 xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 ⁢ xe2x80x83 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + 4 ⁢ xe2x80x83 ⁢ angle xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + ⁢ xe2x80x83 xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) 2 xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) xe2x80x83 ⁢ c5 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) + angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) 2 xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 - 1 ) - xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) 2 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + ( xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) 2 xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 + 1 ) ) ⁢ xe2x80x83 xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( - d2 + d3 ⁡ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + 4 ⁢ xe2x80x83 ⁢ magn 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 2 ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) ) / ( ( - ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ⁢ xe2x80x83 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 + ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) ) xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ angle ) ( 60 ) 6-Mirror System, Stop on Mirror 5 Again, we use the original derivations to solve the variables of a six-mirror system with the stop position on mirror five. As before, the first solve is pupil in infinity or telecentricity in the image. The angle of the ray going through the optical axis in the stop surface should be zero in the image. The matrix from the stop surface to the fifth mirror generated by multiplication of the appropriate M matrices derived above is given by: [ 1 0 0 1 ] ( 61 ) The matrix from the second mirror surface to the stop surface is given by: [ 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) , - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + "AutoLeftMatch" d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + "AutoLeftMatch" 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - xe2x80x83 ⁢ "AutoLeftMatch" 1 ) ] [ xe2x80x83 ⁢ - "AutoLeftMatch" 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) + "AutoLeftMatch" d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + "AutoLeftMatch" d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 , - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ "AutoLeftMatch" "AutoRightMatch" ⁢ "AutoLeftMatch" 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ] ( 62 ) So, as derived above, the distance between mirror 5 and 6, solved in the appropriate matrix and the vector of distances: is: d5 := - xe2x80x83 ⁢ 1 2 ⁢ 1 c6 ( 63 ) The distance between mirror one and two was: d1 := xe2x80x83 ⁢ - 1 4 ⁢ ( 4 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) - angle ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) / ( ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) ( 64 ) And the distance between the object and the first mirror: d0 := xe2x80x83 ⁢ - 1 2 ⁢ ( ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ angle xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) - xe2x80x83 ⁢ angle ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ⁢ xe2x80x83 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ⁢ xe2x80x83 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 + 1 ) - xe2x80x83 ⁢ 2 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) / xe2x80x83 ⁢ ( angle ⁢ xe2x80x83 ⁢ ( - ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) xe2x80x83 ⁢ ( - d2 ⁢ xe2x80x83 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ) ⁢ c1 ) ( 65 ) And the distance between mirror six and the image surface: d6 := xe2x80x83 ⁢ - 1 4 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + xe2x80x83 ⁢ 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) - angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) 2 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + 4 ⁢ xe2x80x83 ⁢ magn 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) ) / ( ( - ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ angle ) ( 66 ) 4-Mirror System, Stop on mirror 2 Yet again, we can use these derivations to solve the variables of a four-mirror system with the stop position on mirror two. As usual, the first solve is pupil in infinity or telecentricity in the image. The angle of the ray going through the optical axis in the stop surface should be zero in the image. The matrix from the stop surface to the third mirror generated by multiplication of the appropriate M matrices derived above, is given by: [ 1 d2 - 2 ⁢ xe2x80x83 ⁢ c3 - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ] ( 67 ) The matrix from the second mirror surface to the stop surface is given by: [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c2 - 1 ] ( 68 ) So as derived above, the distance between mirror 3 and 4, solved in the appropriate matrix and the vector of distances is: d3 := - 1 2 - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 c4 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ( 69 ) The distance between mirror one and two was: d1 := - 1 4 - 2 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 - angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 ( 70 ) And the distance between the object and the first mirror: d0 := 1 2 ⁢ - angle ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 - 1 ) - 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 - 1 ) - 2 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 angle ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 - 1 ) ( 71 ) And the distance between mirror four and the image surface: d4 := xe2x80x83 ⁢ - 1 4 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + 4 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) 2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 + 4 ⁢ xe2x80x83 ⁢ magn 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 2 ) / xe2x80x83 ⁢ ( c4 2 ⁢ xe2x80x83 ⁢ angle ) ( 72 ) 4-Mirror System, Stop on Mirror 3 Again, we use the original derivations to solve the variables of a four-mirror system with the stop position on mirror three. The first solve is pupil in infinity or telecentricity in the image. The angle of the ray going through the optical axis in the stop surface should be zero in the image. The matrix from the stop surface to the third mirror generated by multiplication of the appropriate M matrices derived above is given by: "AutoLeftMatch" [ 1 0 0 1 ] ( 73 ) The matrix from the second mirror surface to the stop surface is given by: "AutoLeftMatch" [ 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 - d2 - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ] ( 74 ) So as we derived the distance between mirror 3 and 4 is: d3 := - 1 2 ⁢ 1 c4 ( 75 ) And we solve this new found value in the appropriate matrix and the vector of distances. The distance between mirror one and two was: d1 := - 1 4 ⁢ - 4 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 - 2 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 + ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + angle ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 ( 76 ) And the distance between the object and the first mirror: d0 := xe2x80x83 ⁢ - 1 2 ⁢ ( ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) - 2 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 ) / xe2x80x83 ⁢ ( angle ⁢ xe2x80x83 ⁢ ( ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ d2 + xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ c1 ) ( 77 ) And the distance between mirror four and the image surface: d4 := xe2x80x83 ⁢ - 1 4 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) 2 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) 2 ⁢ d2 - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ magn 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 2 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ) / xe2x80x83 ⁢ ( ( ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ d2 + ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ) xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ c4 2 ⁢ xe2x80x83 ⁢ angle ) ( 78 ) Obscuration A particular problem in designing mirror systems, not encountered in refractive lens systems, is ensuring that the beam is not obscured in its zigzag course by other mirrors. Because of the necessary zigzag path, as the projection beam proceeds between successive mirrors I and I+1 on the optical path in many cases it will pass by at least one other mirror J. Thus, for an optical system not to be obscured it is necessary to ensure that the position and extent of the intervening mirror J is such that it does not intersect any part of the beam between mirrors I and I+1. This is shown in FIG. 4 in which it can be seen that mirror lies wholly below the beam between I and I+1 whereas mirror Jxe2x80x2 partially intersects the beam. The arrangement of mirror is not permitted. In a model of a potential projection system, obscuration can be detected by the following procedure: 1. For each pair of successive mirrors I, I+1 on the optical path, check if there exists a 20 mirror J (with J not equal to I, I+1) having a position on the optical axis (Z axis) between I and I+1 2. If J exists, calculate the distance from the optical axis (Y position) of the extreme rays from I to I+1 at the position of mirror j on the optical axis. 3. Check that the top and bottom of mirror J are both above (i.e. have greater Y position) or both below (i.e. have smaller Y position) both the extreme rays from I to I+1. If the check in (3) fails, then mirror at least partially obscures the beam from I to I+1 and the mirror system must be modified or rejected. Preferred Four-mirror Systems FIG. 6 shows a mirror system in class 9(+) which can be used in the lithography apparatus of FIG. 1. In this class, the stop can be positioned on mirror 2 or 3; in the system of FIG. 6, the stop position is on surface 2. The ring field of this system is defined on the object side, between 114 and 118 arbitrary units, with a numerical aperture of 0.25 (0.05 on the object side). The magnification is 0.2 and an intermediate image is formed between mirrors 3 and 4. The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 1 below. The values found for the curvatures and thicknesses can be re-scaled using a scaling factor. If the thicknesses are multiplied by that factor, the curvatures should be divided by it, and vice versa. FIG. 7 also shows a mirror system in class 9(+). In this case the stop is on mirror 3 and the intermediate image is between mirrors 1 and 2. The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 2 below. FIG. 8 shows an example of a class 2(xe2x88x92) system having the stop located on the third mirror. From the object (mask MA, surface 0) all the rays go, with a negative angle (a zero angle is parallel to the optical axis), to the first convex mirror M1. The convex mirror M1 reflects the beam upward to a large concave mirror M2. The position of the second mirror M2 has to be above the beam between the object (mask MA) and mirror M1. The beam then goes under mirror M1 to the stop surface mirror M3. From the stop surface the beam is reflected to concave mirror M4. Mirror M4 takes care of a telecentric illumination of the image (surface 5). The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 3 below. A class 6(xe2x88x92) system, shown in FIG. 9, consists of two mirror pairs, in a symmetrical design. From the object (mask MA, surface 0) all the rays go, with a negative angle (a zero angle is parallel to the optical axis), to the first convex mirror M1. The object is illuminated as telecentric as possible, this being a requirement for lithography. The convex mirror M1 reflects the beam upward to a large concave mirror M2. The position of this mirror has to be above the beam between the object and mirror M1. So far this design resembles the class 2(xe2x88x92) design (shown in FIG. 8). The beam then goes over mirror M1 to the stop surface on mirror M3, limited by the top of mirror M1. From the stop surface M3 the beam is reflected to concave mirror M4. Mirror M4 takes care of a telecentric illumination of the image (surface 5). The ring field of this system is defined on the image side, between xe2x88x9222.8 and xe2x88x9223.8, resulting in a Strehl ratio of at least 0.972 with a numerical aperture of 0.15. The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 4 below. A class 9(xe2x88x92) system with a stop on the second surface is shown in FIG. 10. The ring field of this system is defined on the object side, between 114 and 118 arbitrary units, with a numerical aperture of 0.2 (0.05 on the object side). The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 5 below. FIG. 11 shows a system in class 10(xe2x88x92). The ring field of this system is defined on the object side, between 114 and 118 arbitrary units, with a numerical aperture of 0.2 (0.05 on the object side). The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 6 below. Preferred Six-mirror Systems All the six-mirror systems found to be feasible have, as they have a positive magnification, an intermediate image. FIG. 12 shows a six-mirror system in class 9(+) in which the stop can be positioned on mirror 2, 3, 4 and 5. The system has the intermediate image located between mirror 2 and five. The ring field of this system is defined on the object side, between 114 and 118 arbitrary units, with a numerical aperture of 0.24 (0.06 on the object side). The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 7 below. A class 37(+) six-mirror system can have the stop positioned on mirror 2, 3, 4 or 5 and has the intermediate image located between mirror 2 and five. The ring field of such a system is defined on the image side, between 27 and 30 arbitrary units, with a numerical aperture of 0.24. The system shown in FIG. 13 has the stop on surface 2. This system consists of a mirror pair near the object and four-mirrors grouped near the image. From the object (mask MA, surface 0) all the rays go, with a negative angle, to the first concave mirror M1. The concave mirror M1 reflects the beam downward to mirror M2 which is almost flat. The top of mirror M2 is restricted to be below the beam between the object and mirror M,. The beam between mirror M2 and M3 limits the bottom of the small mirror M4, while the beam between mirror M4 and M5 limits the top of mirror M4. Finally, the beam between the last mirror M6 and the image limits the top of mirror M5. The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 8 below. For comparison, FIG. 14 shows a class 37(+) six-mirror system with the stop on surface 5. The ring field of this system is defined on the image side, between 27 and 30 arbitrary units, with a numerical aperture of 0.24. The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 9 below. Preferred Eight-mirror System An eight-mirror system in class 165(+) with stop on surface 3 is shown in FIG. 15. The ring field of this system is defined on the object side, between 116 and 124 arbitrary units, with a numerical aperture of 0.24 (0.06 on the object side). The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 10 below. An eight mirror system in class 169(+) is shown in FIG. 16, the curvatures and thicknesses of its elements are shown in Table 11. This system has a ring field in the object side between 114 and 118 arbitrary units, a numerical aperture of 0.4, distortion less than 2.9 nm and an rms wavefront error less than 0.3xcex. An eight mirror system in class 181(+) is shown in FIG. 17, the curvatures and thicknesses of its elements are shown in Table 12. Again, the ring field on the object side is between 114 and 118 units and the numerical aperture is 0.4. However, the distortion is less than 1.9 nm and the rms wavefront error less than 0.5xcex. An eight mirror system in class 150(xe2x88x92) is shown in FIG. 18, the curvatures and thicknesses of its elements are shown in Table 13. This system provides a distortion less than 2.6 nm and an rms wavefront error less than 0.19xcex. An eight mirror system in class 182(xe2x88x92) is shown in FIG. 19, the curvatures and thicknesses of its elements are shown in Table 14. This system likewise has a ring field on the object side between 114 and 118 arbitrary units, a numerical aperture of 0.4, an rms wavefront error of less than 1xcex and a distortion less than 2.18 nm. While we have described above specific embodiments of the invention it will be appreciated that the invention may be practiced otherwise than described. The description is not intended to limit the invention.
	claims	1. An under vessel automated work platform assembly for remotely servicing a lower portion of a vessel, the platform assembly comprising:a horizontal generally circular work platform extending in a first plane;a generally circular rail extending in a second plane substantially parallel to the first plane, the rail supporting an orbital track on which the work platform is rotationally supported to rotate the work platform in the first plane and the orbital track includes a circumferential drive ring having gear teeth and extending in a third plane substantially parallel to the second plane;a pin gear structured to interact with the gear teeth of the circumferential drive;a remotely controlled motor for rotating the work platform on the orbital track by driving the pin gear;a linear track extending across a diameter of the work platform;a remotely controlled carriage moveable on the linear track across the diameter of the work platform;an automated tool programed to perform at least part of a reactor maintenance task, attached to the remotely controlled carriage and moveable therewith, the automated tool having a vertically extending member moveable in a direction perpendicular to the first plane; anda controller for remotely inputting an in-vessel cell coordinate and automatically positioning the automated tool under the in-vessel cell coordinate by controlling the rotation of the work platform on the orbital track and movement of the remotely controlled carriage on the linear track. 2. The under vessel automated work platform assembly of claim 1 including a hand wheel for manually moving the work platform around the orbital track. 3. The under vessel automated work platform assembly of claim 1 wherein the automated tool is a swappable task robot. 4. The under vessel automated work platform assembly of claim 1 wherein the automated work platform assembly is sized to fit under the vessel. 5. The under vessel automated work platform assembly of claim 1 wherein the work platform supports a camera generally focused on the distal end of the vertically extending member. 6. The under vessel automated work platform assembly of claim 5 wherein the camera has a remote controlled panning capability. 7. The under vessel automated work platform assembly of claim 5 wherein the camera has a remote controlled tilt capability. 8. The under vessel automated work platform assembly of claim 1 for servicing a nuclear reactor having a nuclear core and a refueling system command station for refueling the core, and the remotely controlled motor and the remotely controlled carriage are structured to communicate with the controller that is structured to control the rotation of the work platform and the movement of the remotely controlled carriage and provide an output identifying a position of the remotely controlled carriage in a form that can be received and understood by the refueling system command station so the refueling system command station is notified of the position of the remotely controlled carriage so that proper work processes can be adhered to.
045267448	summary	TECHNICAL FIELD The present invention relates to a fuel assembly for a boiling water reactor, the fuel assembly comprising a plurality of vertical fuel rods, which are surrounded by a fuel channel device with a vertical longitudinal axis, the fuel rods constituting four partial bundles or subassemblies, the fuel rods in each partial bundle being positioned by means of a corresponding group of spacers arranged vertically one after the other, each of the partial bundles resting on a corresponding bottom grid. BACKGROUND ART A fuel assembly of this kind is known from U.K. Patent Specification No. 931,676. In the known fuel assembly the fuel rods are distributed among four partial bundles, each of which is provided with a bottom grid and with a top grid. Each fuel rod is provided with slotted end portions and arranged with the slots in engagement with and hard-soldered to the top grid and the bottom grid, respectively. Further, such a fuel assembly is known from U.S. Patent No. 3,389,056. Which discloses a fuel assembly in which the fuel rods are distributed among four partial bundles, which are positioned with respect to each other by means of a plurality of upwardly-directed fixing members, disposed outside the fuel channel device and extending from one partial bundle each, said fixing members being attached to the top grid of the reactor core. With conventional boiling water reactor fuel assemblies of the kind comprising several partial bundles, it is not possible to lift all the partial bundles out of the fuel channel device in one and the same lifting operation. DISCLOSURE OF THE INVENTION The invention aims to provide a four-part fuel assembly which permits simplified and less time-consuming fuel handling than what is possible when using the above-mentioned prior art fuel assemblies. According to the invention, the majority of the fuel rods in each partial bundle is arranged in the bottom grid freedom of movememnt in a direction vertically upwards. At least one fuel rod in each partial bundle is a tie rod which is detachably arranged in a tensile force transmitting connection with the bottom grid of the partial bundle. The partial bundles are positioned in relation to each other by means of a common top tie plate, positioned above the fuel rods and surrounded by an upper portion of said fuel channel device. The top tie plate is detachably arranged in a tensile force transmitting connection with the bottom grids by means of the tie rods and is provided with a lifting loop adapted for lifting all the partial bundles of the fuel assembly in one and the same lifting operation. A simultaneous lifting is time-saving in case of inspection of the fuel and when, at a certain burnup stage, it is desirec to change the positions and/or orientations of the various partial bundles with a view to achieving better fuel economy.
039430375	abstract	In a nuclear reactor which is housed in a round building and which has a reactor pressure vessel in a reactor pool, a fuel element storage pool of arcuate outline, a gate-controlled channel interconnecting the two pools and an operating platform adjacent the pools, there is provided a fuel element exchange system which has a first fuel element exchange gantry supported on a column disposed in the center of the reactor building and on a rail which is held by the building wall and which is situated above the level of the operating platform, and a second fuel element exchange gantry supported under the first gantry in such a manner that the second gantry may freely pass under the first gantry. There is further provided a fuel element box-stripping machine at the storage pool immediately across from the channel within the operational range of both the first and the second gantries.
039473198	summary	The invention relates to a nuclear reactor plant intended for supplying heat to a steam generator, which plant comprises at least two circuits for conveying this heat, these circuits being hydraulically separated but thermally coupled to each other by means of heat exchangers, specifically one water-steam-circuit equipped with a steam generator, a feed water pump which is included in a feed water conduit with a feed controlling valve as well as with a steam turbine, and one reactor-circuit equipped with a primary circulation pump and charged with a non-water, heat-transferring medium, in such a way that the heat exchangers in the operative state exhibit a relatively small pressure drop. The control systems hitherto known for such a reactor system have been marked by a high degree of complexity. Applicant has arrived at the insight that it is also possible to attain very good results with a control system of very simple design. According to the invention, this aim is reached by dimensioning the feed water conduit with the feed water control valve contained therein in such a way that the pressure drop along this feed water conduit at full load is greater than 10 bars. In proportion as the pump characteristic is steeper, this pressure drop can become somewhat smaller without any objection. If a pump is selected having a steep curve indicating the correlation between lift and output, this will furthermore provide the advantage of such a pump being lower in price. In a given design, use may be made, for example, of a feed pump marked by an almost linear correlation between lift and output. This curve may be actually curved or may be a virtually straight line which, at a constant pump speed, indicates the correlation between lift (=pump pressure) and output, and is in this connection called steeper in proportion as, with a given drop in output, the lift of the pump rises. This curve is in the following sometimes designated as "pump characteristic." Since it is sometimes not a simple matter to realize a fairly appreciable pressure drop in a control valve, use may be made, if required, of a hydraulic turbine. In this liquid turbine, at least part of the pressure drop can be realized which is necessary for the stability of the system. An additional advantage of this is that energy is recovered in the liquid turbine. The liquid turbine, which often needs to comprise only one step, can advantageously be accommodated in the housing of the feed water pump, the blade wheel of this turbine being fastened on the rotor of the pump. A bypass valve, arranged in a bypass of the turbine, in such case regulates the amount of feed water flowing through the turbine. In many cases, the aforementioned hydraulically separated but thermally coupled circuits are separated from each other not only by heat exchangers but also by an additional heat-transferring circuit. This measure will be taken specifically in the case of a nuclear reactor plant provided with a sodium-cooled reactor. In such a case, the precaution is taken of providing an additional heat-transferring circuit for hydraulically separating the primary circuit and the steam-water-circuit; said additional or so-called secondary circuit being equipped with a secondary circulating pump and containing a non-water heat-transferring medium. The three hydraulically separated circuits then are thermally coupled by means of an intermediate heat exchanger for conveying heat from the primary or reactor-circuit to the secondary circuit and the steam generator. For a correct understanding of the following, it is pointed out that a sodium-cooled reactor, on account of the secondary cooling circuits with prolonged dead times (time lags) for heat transportation, gives rise to processes which are difficult to control. In this respect, it has been considered that the use of a steam-water-separator in the sodium-heated steam generator presents advantages with respect to the control of temperature in the steam generator. A consequence of using such a water-steam-separator, however, is that this steam generator gives rise to the formation of a positive feedback between live steam pressure and feed water flow. An important element of the present invention is the insight that this undesired feedback can be simply eliminated by taking the required measures for the pressure drop through the feed water conduit and the control valve, to have a value of at least 10 bars. The aforementioned steam separator is necessary, because the evaporator of the steam generator produces somewhat wet steam. The excess water is separated from the mixture in the steam-water-separator, so as to return it to the feed water preheaters. It has been found in practice that several factors are decisive for the stability of the control system of the steam generator. This steam generator system, consisting of a feed water pump, a control valve, an evaporator, a steam-water-separator, a superheater and a turbine-inlet-valve exhibits -- without the control circuits -- a negative feedback effect on account of the thermal behaviour thereof. In certain circumstances, however, the same system exhibits a positive feedback effect on account of the hydraulic behaviour. The presence of a negative thermal feedback (back coupling) can be observed by an increase in the flow of feed water through the evaporator. Since, in this case, more water must be heated to boiling temperature, less steam will be produced, resulting in a drop of the flow of steam through the superheater. Since the conditions of steam admission to the superheater through the steam water separator must be kept constant, the power transmitted from the sodium to the steam is proportional to the quantity of steam flowing per unit of time through the superheater. A reduced steam production gives a higher sodium outlet temperature at the superheater, causing more power to become available for producing steam in the evaporator. As a result, the entire system will rapidly find its new state of equilibrium. The fact, however, that a positive hydraulic feedback can also arise can be understood by realizing that a change occurs in the position of the turbine inlet valve. An increase in the valve passage of the turbine causes an increase in the amount of steam flowing through the steam conduit, as well as a pressure drop in this steam conduit, in the superheater and in the steam-water-separator. Now the mass flow through the evaporator is directly proportional to the square root of the pressure difference that prevails between the steam-water-separator and the feed water pump. This pressure difference increases as a result of the decrease of pressure in the steam-water-separator. The eventual increase of the feed water flow causes a decrease in the steam flow through the superheater, which in turn causes a decrease of the live steam pressure. In this manner, variations can occur in the steam pressure without leading to a new stable state. It is a fortunate circumstance that the increase in the amount of feed water likewise produces a decrease of the feed water pump pressure as a result of the pressure output characteristic of this pump. If this decrease is of the same order of magnitude as the decrease in pressure of the steam-water-separator, a new, stable adjustment can indeed be reached in operation. The output characteristic of the great majority of feed water pumps exhibits a slight inclination at low outputs. Accordingly, the opposing effect is too small for our purpose. Measures must therefore be taken for the increase in feed water flow, resulting from the pressure drop in the steam-water-separator, to be reduced at low loads. This can be done in a simple manner by introducing an extra pressure drop or resistance in the feed water conduit. According to calculations, a pressure drop of 20 bars at a load of 30 percent is sufficient for ensuring a stable behaviour of the steam generator. This pressure drop should be about 10 bars at full load for attaining the same stabilizing effect. According to the invention, the control system is furthermore so designed that a control impulse coming from the measured amount of water separated in the external water separator gives an impulse to the feed water control valve. A steam generator system equipped with such a control circuit exhibits the following behaviour: A drop of the live steam pressure owing for instance to a greater turbine steam flow, causes an increase in the feed water flow. This causes an increase in the draining of condensate collected in the steam-water-separator. The control circuit over this condensate drainage will slightly close the feed water valve, resulting in a decrease of the feed water flow as well as in a decrease of the steam condensate drainage and an increase in pressure, because of an increase both in the flow of steam to the superheater and the supply of heat. This pressure increase brings about a further decrease of the feed water flow, and thus a still further decrease in the drainage from the water separator. This decrease will again induce the control circuit to open the feed water valve still further, until a correct and stable state has fairly rapidly been established. Now if the coupling factor between the live steam pressure changes and the change in the drainage of condensate from the steam water separator is too high, this control circuit can become unstable. This can be remedied by reducing the coupling factor by increasing the pressure drop in the feed water conduit. It has already been explained in the above that other considerations have also led to the finding that a pressure drop of 20 bars will ensure at all loads a stabilizing dynamic behaviour of this control circuit. According to a preferred embodiment of the invention, the set-point controls of the regulators for the tertiary and for the primary circuit are disconnected, whereby the process has become well regulable. This is preferably accomplished by taking such measures that a control impulse coming from the measured steam pressure, or the measured amount of steam per unit of time, or a combination of these measured values, corrects the mass flow of the secondary circuit, by influencing the speed of the secondary circulating pump. This measure can be effectively supplemented by causing a control impulse from the mass flow measured in the secondary circuit to correct the mass flow of the reactor circuit by influencing the speed of the primary circulating pump. Finally, it has been found effective to cause a control impulse from the mass flow measured in the secondary circuit to adjust the set point of the reactor temperature regulator. With the use of the control method described, according to which the reactor outlet temperature changes as a function of load, the temperature of the live steam does not have to be separately regulated. Calculations have shown that this temperature during very fast load changes, such as, for example, 10 percent of load in 5 seconds, changes by only about 6.degree.C, during a very short time, approximately 30 seconds. The control system according to the invention can be load-following as well as load-forcing. According to the latter method, the secondary sodium pump is controlled with a desired power signal, and the live steam pressure is constantly controlled with the turbine valve, so-called prepressure (initial pressure) control. With the aid of the following figures, two embodiments of the invention will be explained in further detail.
	abstract	This invention relates to a system for regulating a liquid in a circuit, with the system comprising: a plug valve comprising at least one inlet and one outlet, the plug comprising an internal passage through which is intended to pass the liquid flowing from the inlet to the outlet of the valve when the valve is open at least partially, an expansion reservoir in communication with the liquid flowing in the circuit and intended to contain liquid and a compensating gas, characterized in that the plug comprises at least partially an expansion channel which has at least one lateral opening located on a lateral face of the plug and which is conformed to provide a permanent communication between said lateral opening and the expansion reservoir, the valve being conformed in such a way that: at least when the valve is closed: the lateral opening is in direct communication with the liquid coming from the inlet or from the outlet of the valve, when the valve is open at least partially, the lateral opening cooperates with an inner wall integral with a body of the valve in such a way as to form a conduit in communication on the one hand with the expansion reservoir and on the other hand with the internal passage. The invention also relates to a circuit integrating this system as well as a use of this system.
	summary
	summary
	abstract	A technique for processing a workpiece is disclosed. In accordance with one exemplary embodiment, the technique is realized as a method for processing a substrate, where the method comprises: providing the workpiece in the chamber; providing a plurality of electrodes between a wall of the chamber and the workpiece; generating a plasma containing ions between the plurality of electrodes and the workpiece, ion density in an inner portion of the plasma being greater than the ion density in an outer portion of the plasma portion, the outer portion being between the inner portion and the wall of the chamber; and providing a bias voltage to the plurality of electrodes and dispersing at least a portion of the ions in the inner portion until the ion density in the inner portion is substantially equal to the ion density in the periphery plasma portion.
	description	The present application claims foreign priority based on Japanese Patent Application No. 2005-150832, filed May 24, 2005, the content of which is incorporated herein by reference. 1. Technical Field The present invention relates to an ion beam irradiation apparatus so constructed as to irradiate a substrate held by a substrate holding surface of a holder with an ion beam that travels in the horizontal direction. Particularly, the invention relates to means for controlling non-uniformity of ion implantation due to a divergent angle of the ion beam applied onto the substrate. This ion beam irradiation apparatus is, for example, an ion implantation apparatus. 2. Related Art FIG. 4 shows a schematic side view of this type of related-art ion beam irradiation apparatus, showing an example of the constitution in which the substrate held by the holder is irradiated with the ion beam. An ion beam irradiation apparatus having the nearly similar structure to this structure has been disclosed in FIG. 13 in JP-A-2003-110012. Three axes that are orthogonal to each other at one point are taken as an X-axis, a Y-axis and a Z-axis. Generally, an ion beam 58 traveling in the direction along the Z-axis is scanned in the direction along the X-axis by an electric filed or a magnetic field, and applied onto a substrate 54 held by a substrate holding surface 6 of a holder 4. The holder 4 is, for example, an electrostatic chuck. In this example, both the X-axis and the Z-axis are imaginary axes in the horizontal direction. Further, as the ion beam 58, in place of the ion beam scanned in the direction along the X-axis, there is also an ion beam which is long in the shape of a strip from its base without scanning in the direction along the X-axis, and travels in the direction along the Z-axis. In this specification, “direction along an axis” means a direction substantially parallel to its axis. Further, “substantially parallel” includes a parallel state. This ion beam irradiation apparatus includes a counter-rotatable type of irradiation angle setting motor 14 which controls an irradiation angle θ of the ion beam 58 to the substrate holding surface 6 of the holder 4 supported by a rotation shaft 46 through a coupling member 48, that is, to a surface 56 of the substrate 54 by rotating the holder 4 around the rotation shaft 46 substantially parallel to the X-axis in the direction of an arrow A in FIG. 4; and an elevator unit 50 which causes the holder 4 supported by this motor 14 to ascend and descend in the direction along the Y-axis thereby to scan the substrate 54 for the ion beam 58. When ion beam 58 irradiation processing for the substrate 54, for example, ion implantation processing is performed, the irradiation angle θ is usually set in a range of 0° to 60°. This irradiation angle θ is an angle made by a perpendicular line 62 to the substrate holding surface 6 and the traveling direction of the ion beam 58. For example, in the ion implantation apparatus, this angle is referred to as an implantation angle. As described above, in the related-art ion beam irradiation apparatus, in case that the irradiation angle θ is set to an angle that is larger than 0°, the substrate 54 supported by the holder 4, in a tilting state in the irradiation direction of the ion beam 58 (that is, direction along the Z-axis), is scanned in the direction along the Y-axis. However, in case that the substrate 54, in the tilting state in the irradiation direction Z of the ion beam 58, is scanned in the direction along the Y-axis, there is a problem that the density of the ion beam 58 applied onto the substrate 54 becomes non-uniform in the surface 56 of the substrate 54. The cause of this problem will be described with reference to FIG. 5. In this figure, for convenience, the irradiation angle setting motor 14, the rotation shaft 46, the coupling member 48 and the elevator unit 50 are omitted. The ion beam 58 that has passed through a beam slit 52 is applied toward the substrate holding surface 6 of the holder 4 arranged in a vacuum chamber (not shown), that is, the surface 56 of the substrate 54. The substrate 54, by the reciprocating movement of a center O1 on the surface 56 of the substrate 54 together with the holder 4 between a position α and a position γ, is scanned for the ion beam 58. In a position β, the center O1 on the surface 56 of the substrate 54 coincides with the path of the ion beam 58 traveling in the direction along the Z-axis. On the other hand, the ion beam 58 is applied in a state where it diverges to some extent in the direction along the Y-axis due to the space-charge effect. Here, the angle at which the ion beam 58 diverges in the direction along the Y-axis is referred to as a divergent angle ξ. In case that the ion beam 58 is thus applied onto the surface 56 of the substrate 54 in the state where it diverges to some extent in the direction along the Y-axis, according to the distance L from an arbitrary point on the path of the ion beam 58 (for example, an exit point of the beam slit 52) to the surface 56 of the substrate 56, the size of the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 is different. Namely, as the distance becomes longer, the size of the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 becomes larger. Specifically, the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 when the center O1 on the surface 56 of the substrate 54 is in the position α is taken as G1, the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 when the center O1 on the surface 56 of the substrate 54 is in the position β is taken as G2, and the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 when the center O1 on the surface 56 of the substrate 54 is in the position γ is taken as G3. In this case, among the area of the region G1, the area of the region G2 and the area of the region G3, the relation of G1<G2<G3 holds. Regarding the density of the ion beam 58 applied onto the surface 56 of the substrate 54, as the area of the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 becomes larger, the density becomes lower; and as the area of the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 becomes smaller, the density becomes higher. Therefore, in case that the substrate 54 is scanned in the direction along the Y-axis in the titling state in the irradiation direction of the ion beam 58, the distance L changes during irradiation processing of the ion beam 58 onto the surface 56 of the substrate 54. Therefore, a phenomenon is produced in which the density of the ion beam 58 applied onto the substrate 54 becomes non-uniform in the surface 56 of the substrate 54. In result, uniformity of ion implantation in the surface 56 of the substrate 54 worsens. Therefore, it is an object of the invention to prevent, even in case that the substrate is scanned in the tiling state in the irradiation direction of the ion beam, the density of the ion beam applied onto the substrate from becoming non-uniform in the surface of the substrate. However, the present invention need not achieve the above objects, and other objects not described herein may also be achieved. Further, the invention may achieve no disclosed objects without affecting the scope of the invention. An ion beam irradiation apparatus according to a first aspect of this invention is so constructed as to scan, when three axes that are orthogonal to each other at one point are taken as an X-axis, a Y-axis and a Z-axis, in the direction along the X-axis, an ion beam traveling in the direction along the Z-axis, and applies the ion beam onto a substrate held by a substrate holding surface of a holder. This ion beam irradiation apparatus includes: an irradiation angle setting motor which holds the holder, and can set an irradiation angle of the ion beam with respect to the substrate holding surface by rotating the holder around a center axis that is substantially parallel to the X-axis; a Y-axis linear motor which supports the irradiation angle setting motor, and causes the holder and the irradiation angle setting motor to ascend and descend in the direction along the Y-axis; a Z-axis linear motor which supports the Y-axis linear motor, and moves the holder, the irradiation angle setting motor and the Y-axis linear motor in the direction along the Z-axis; and a control unit which operation-controls synchronously the Y-axis linear motor and the Z-axis linear motor so that the substrate holding surface of the holder reciprocates and scans linearly along an S-axis that is substantially parallel to the substrate holding surface and substantially orthogonal to the X-axis. An ion beam irradiation apparatus according to a second aspect of the invention is so constructed as to scan, when three axes that are orthogonal to each other at one point are taken as an X-axis, a Y-axis and a Z-axis, in the direction along the X-axis, an ion beam traveling in the direction along the Z-axis, and applies the ion beam onto a substrate held by a substrate holding surface of a holder. This ion beam irradiation apparatus includes: an irradiation angle setting motor which holds the holder, and can set an irradiation angle of the ion beam with respect the substrate holding surface by rotating the holder around a center axis that is substantially parallel to the X-axis; a Z-axis linear motor which supports the irradiation angle setting motor, and moves the holder and the irradiation angle setting motor in the direction along the Z-axis; a Y-axis linear motor which supports the Z-axis linear motor, and causes the holder, the irradiation angle setting motor and the Z-axis linear motor to ascend and descend in the direction along the Y-axis; and a control unit which operation-controls synchronously the Z-axis linear motor and the Y-axis linear motor so that the substrate holding surface of the holder reciprocates and scans linearly along an S-axis that is substantially parallel to the substrate holding surface and substantially orthogonal to the X-axis. An ion beam irradiation apparatus according to a third aspect of the invention is so constructed as to apply, when three axes that are orthogonal to each other at one point are taken as an X-axis, a Y-axis and a Z-axis, an ion beam that is long in the shape of a strip in the direction along the X-axis direction and travels in the direction along the Z-axis, onto a substrate held by a substrate holding surface of a holder. This ion beam irradiation apparatus includes: an irradiation angle setting motor which holds the holder, and can set an irradiation angle of the ion beam with respect to the substrate holding surface by rotating the holder around a center axis that is substantially parallel to the X-axis; a Y-axis linear motor which supports the irradiation angle setting motor, and causes the holder and the irradiation angle setting motor to ascend and descend in the direction along the Y-axis; a Z-axis linear motor which supports the Y-axis linear motor, and moves the holder, the irradiation angle setting motor and the Y-axis linear motor in the direction along the Z-axis; and a control unit which operation-controls synchronously the Y-axis linear motor and the Z-axis linear motor so that the substrate holding surface of the holder reciprocates and scans linearly along an S-axis that is substantially parallel to the substrate holding surface and substantially orthogonal to the X-axis. An ion beam irradiation apparatus according to a fourth aspect of the invention is so constructed as to apply, when three axes that are orthogonal to each other at one point are taken as an X-axis, a Y-axis and a Z-axis, an ion beam that is linearly long in the shape of a strip in the direction along the X-axis direction and travels in the direction along the Z-axis, onto a substrate held by a substrate holding surface of a holder. This ion beam irradiation apparatus includes: an irradiation angle setting motor which holds the holder, and can set an irradiation angle of the ion beam with respect to the substrate holding surface by rotating the holder around a center axis that is substantially parallel to the X-axis; a Z-axis linear motor which supports the irradiation angle setting motor, and moves the holder and the irradiation angle setting motor in the direction along the Z-axis; a Y-axis linear motor which supports the Z-axis linear motor, and causes the holder, the irradiation angle setting motor and the Z-axis linear motor to ascend and descend in the direction along the Y-axis; and a control unit which operation-controls synchronously the Z-axis linear motor and the Y-axis linear motor so that the substrate holding surface of the holder reciprocates and scans linearly along an S-axis that is substantially parallel to the substrate holding surface and substantially orthogonal to the X-axis. According to these ion beam irradiation apparatuses, the holder is linearly reciprocated and scanned so that the substrate holding surface of the holder is along the S-axis. Therefore, during irradiation processing of the ion beam onto the substrate held by the holder, while the distance from an arbitrary point on the path of the ion beam to the substrate holding surface of the holder, that is, to the surface of the substrate is kept substantially constant, the substrate held by the holder can be scanned in a tiling state in the irradiation direction of the ion beam. It is preferable that the control unit operation-controls synchronously the Y-axis linear motor and the Z-axis linear motor so that: when the control unit causes the Y-axis linear motor to ascend along the Y-axis by the distance Δy, the relation of Δz=Δy tan θ is satisfied or the relation mathematically equivalent to this relation is satisfied; and when the control unit causes the Y-axis linear motor to descend along the Y-axis by the distance Δy, the relation of −Δz=Δy tan θ is satisfied or the relation mathematically equivalent to this relation is satisfied, in which θ represents an irradiation angle of the ion beam applied to the substrate, and Δz represents distance by which the linear motor is moved along the Z-axis (The direction in which the ion beam travels is taken as a positive direction.). According to the invention, while the distance from the arbitrary point on the path of the ion beam to the surface of the substrate is kept substantially constant, the substrate held by the holder can be scanned in the tiling state in the irradiation direction of the ion beam. Therefore, the area of the irradiation region of the ion beam applied onto the substrate becomes always substantially constant. Thus, it is possible to prevent the density of the ion beam applied onto the substrate from becoming non-uniform in the surface of the substrate. In result, uniformity of ion implantation in the surface of the substrate improves. FIG. 1 is a schematically plan view showing one exemplary, non-limiting example of an ion beam irradiation apparatus according to this invention, and FIG. 2 is a schematically side view of the ion beam irradiation apparatus shown in FIG. 1. The same or corresponding parts as or to those in the related art shown in FIGS. 4 and 5 are denoted by the same reference numerals, and the different points from the related art will be mainly described below. In this ion beam irradiation apparatus, an arm 8 for supporting a holder 4 is supported by a disc-shaped turn table 12. At this time, a center O2 of the turn table 12 is on an imaginary center axis 60 that passes through a center O1 of a substrate holding surface 6 of the holder 4 and is substantially parallel to an X-axis (refer to FIG. 1). The shown substrate 54, though it has the same thickness as thickness of the holder 4 for convenience, is very thin actually. Therefore, it can be said that the center axis 60 substantially passes through a surface 56 of the substrate 54. This turn table 12 turns around the center axis 60. Further, in this ion beam irradiation apparatus, an orientation flat angle control motor 10, which is not an essential component, is incorporated in the arm 8. Hereby, step implantation in which an orientation flat angle is changed every time the holder 4, that is, the substrate 54 is scanned once with respect to an irradiation direction Z of the ion beam 58 thereby to perform ion implantation can be executed. Here, the “orientation flat angle” indicates an angle with respect to the predetermined direction, which is made by an orientation flat (that is, a notch (not shown)) formed in the substrate 54. Further, this ion beam irradiation apparatus includes, in place of the related-art counter-rotatable type of irradiation angle setting motor 14 and the elevator unit 50 (refer to FIG. 4), includes a counter-movable type of irradiation angle setting motor 14a and a counter-movable type of Y-axis linear motor 20. The irradiation angle setting motor 14a includes an irradiation angle setting mover 16 which is coupled to the turntable 12, and an irradiation angle setting stator 18 which is opposed to this irradiation angle setting mover 16 and fixed to a Y-axis mover 28. The irradiation angle setting mover 16 is provided for a part of the peripheral portion of the turn table 12, and formed in the shape of a fan along the peripheral surface of the turn table 12, viewed in the direction of the X-axis (refer to FIG. 2). When the irradiation angle setting motor 14a rotates the turn table 12 around the center axis 60, the holder 4 supported through the arm 8 by the turn table 12 is rotated around the center axis 60. Thus, the irradiation angle θ (refer to FIG. 2) of the ion beam 58 with respect to the substrate holding surface 6 of the holder 4, that is, the surface 56 of the substrate 54 can be set. The irradiation angle θ shown in FIG. 2 is an angle with respect to the surface 56 of the substrate 54 which is shown by a chain double-dashed line. The Y-axis linear motor 20 includes a Y-axis stator 22 and a Y-axis mover 28 opposed to this Y-axis stator 22. The Y-axis stator 22 includes a fixing plate 24 that is long in the direction along the Y-axis, and a guide rail 26 that is fixed to this fixing plate 24 and long in the direction along the Y-axis. The Y-axis mover 28 supports the irradiation angle setting motor 14a, and ascends and descends linearly along the guide rail 26. Therefore, when the Y-axis mover 28 ascends and descends in the direction along the Y-axis, the holder 4 and the irradiation angle setting motor 14a ascend and descend linearly with the movement of the mover 28 in the direction along the Y-axis. Further, this ion beam irradiation apparatus includes a counter-movable type of Z-axis linear motor 30. This Z-axis linear motor 30 includes a Z-axis stator 32, and a Z-axis mover 38 (refer to FIG. 1) opposed to this Z-axis stator 32. However, the Y-axis stator 22 and the Z-axis mover 38, and more particularly the fixing plate 24 and the Z-axis mover 38 may be formed as one member to hold these functions simultaneously. The Z-axis stator 32 includes a fixing plate 34 that is long in the direction along the Z-axis, and a guide rail 36 that is fixed to this fixing plate 34 and long in the direction along the Z-axis. In this embodiment, though the fixing plate 34 is fixed to a vacuum chamber 2 and supported as shown in FIG. 1, for example, a table for fixing the fixing plate 34 may be set in the vacuum chamber 2. The Z-axis mover 38 (refer to FIG. 1) supports the Y-axis linear motor 20, and more particularly the fixing plate 24, and moves linearly along the guide rail 36 in the direction along the Z-axis. Therefore, when the Z-axis mover 38 (refer to FIG. 1) moves in the direction along the Z-axis, the holder 4, the irradiation angle setting motor 14a and the Y-axis linear motor 20 move linearly with this movement in the direction along the Z-axis. The irradiation angle setting motor 14a, the Y-axis linear motor 20 and the Z-axis linear motor 30 are arranged in the vacuum chamber 2 that is kept in a vacuum state. As shown in FIG. 2, on the outside of the vacuum chamber 2, a control unit 40 is provided. This control unit 40 controls the irradiation angle setting motor 14a through a field through 64 penetrating a wall surface of the vacuum chamber 2, and is electrically connected to the Y-axis linear motor 20 and the Z-axis linear motor 30 through field throughs 64so as to operation-control synchronously these motors. The control unit 40, when the irradiation angle θ is set or input, causes the irradiation angle setting motor 14a to turn the turn table 12 so that the irradiation angle of the ion beam 58 with respect to the substrate holding surface 6 of the holder 4 becomes θ. Thereafter, the ion beam 58 is applied to the substrate 54 held by the holder 4. Hereby, the substrate 54 receives the ion implantation processing. Next, the operations of the Y-axis linear motor 20 and the Z-axis linear motor 30 controlled by the control unit 40 will be described with reference to FIG. 3. When the distance by which the Y-axis liner motor 20 is caused to ascend in the direction along the Y-axis is taken as Δy, and the distance by which the Z-axis linear motor 30 is moved in the direction along the Z-axis is taken as Δz, the control unit 40 (refer to FIG. 2) operation-controls synchronously the Y-axis linear motor 20 and the Z-axis linear motor 30 so that the relation expression of Expression 1 is satisfied or the relation mathematically equivalent to this relation expression is satisfied.Δz=Δy tan θ [Expression 1] On the other hand, when the distance by which the Y-axis liner motor 20 is caused to descend in the direction along the Y-axis is taken as Δy, and the distance by which the Z-axis linear motor 30 is moved in the direction along the Z-axis is taken as Δz, the control unit 40 (refer to FIG. 2) operation-controls synchronously the Y-axis linear motor 20 and the Z-axis linear motor 30 so that the relation expression of Expression 2 is satisfied or the relation mathematically equivalent to this relation expression is satisfied.−Δz=Δy tan θ [Expression 2] The direction in which the ion beam 58 travels is taken as a positive direction of the Z-axis, and the opposite direction to that direction is taken as a negative direction of the Z-axis. Further, the “distance by which the Y-axis linear motor 20 is caused to ascend in the direction along the Y-axis”, and the “distance by which the Z-axis linear motor 30 is moved in the direction along the Z-axis” are specifically “distance by which the Y-axis mover 28 is caused to ascend in relation to the Y-axis stator 22 in the direction along the Y-axis”, and “distance by which the Z-axis mover 38 (refer to FIG. 1) is moved in relation to the Z-axis stator 32 in the direction along the Z-axis”, respectively. When the control unit 40 (refer to FIG. 2) operation-controls synchronously the Y-axis linear motor 20 and the Z-axis linear motor 30 (namely, when the control unit 40 operates the both motors 20 and 30 substantially simultaneously, the holder 4 reciprocates and scans linearly so that the substrate holding surface 6 of the holder 4is along an S-axis. The “S-axis” is a direction that is substantially parallel to the substrate holding surface 6 of the holder 4 and substantially orthogonal to the X-axis. Further, “substantially orthogonal” includes an orthogonal state. Therefore, even if the holder 4, that is, the substrate 54 is scanned in a tiling state in the irradiation direction Z of the ion beam 58, the distance L from an arbitrary point (for example, an exit point of the beam slit 52) on the path of the ion beam 58 to the surface 56 of the substrate 54 becomes substantially constant. In result, the area of the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 becomes always substantially constant. Therefore, it is possible to prevent the density of the ion beam 58 applied onto the surface 56 of the substrate 54 from becoming non-uniform. Thus, uniformity of the ion implantation in the surface 56 of the substrate 54 improves. Further, since the holder 4 can be moved in the direction along the Y-axis and in the direction along the Z-axis, and can be turned around the center axis 60, the degree of freedom in transport of the substrate 54 improves. Namely, the substrate 54 can be moved to the position where the substrate 54 is easy to be transported. Further, it is also thought that using a ball screw, the holder 4 and the substrate 54 are scanned in the tilting state in the irradiation direction Z of the ion beam 58. However, as the case in this embodiment, the use of the Y-axis linear motor 20 and the Z-axis linear motor 30 can simplify the structure more while keeping the accuracy. Further, this case can prevent occurrence of particles (contaminants) from the screw portion. Further, since both the center O1 of the substrate holding surface 6 of the holder 4 and the center O2 of the turn table 12 are on the center axis 60, by only turning the turn table 12 around the center axis 60, the irradiation angle θ can be set. Namely, it is not necessary to operate the Y-axis linear motor 20 or the Z-axis linear motor 30. Therefore, the control becomes easy, the structure can be simplified and the cost can be reduced. However, even in case that the center O2 of the turn table 12 is shifted from the center axis 60, the object of the invention can be achieved. Namely, in case that the center O2 of the turn table 12 is shifted from the center axis 60, when the turn table 12 is turned, though the position of the holder 4 in the directions along the Y-axis and the Z-axis changes, this position change can be corrected by the Y-axis linear motor 20 and the Z-axis linear motor 30. In the embodiment, the irradiation angle setting motor 14a is supported by the Y-axis linear motor, and this Y-axis linear motor is supported by the Z-axis linear motor. However, the invention is not limited to this. For example, the Y-axis linear motor 20 and the Z-axis linear motor 30 may be replaced. Namely, the irradiation angle setting motor 14a may be supported by the Z-axis linear motor 30, and this Z-axis linear motor 30 may be supported by the Y-axis linear motor 20. In this case, the Z-axis linear motor 30 moves the holder 4 and the irradiation angle setting motor 14a in the direction along the Z-axis. The Y-axis linear motor 20 is fixed to the vacuum chamber 2, and causes the holder 4, the irradiation angle setting motor 14a and the Z-axis linear motor 30 to ascend and descend in the direction along the Z-axis. It will be apparent to those skilled in the art that various modifications and variations can be made to the described preferred embodiments of the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention cover all modifications and variations of this invention consistent with the scope of the appended claims and their equivalents.
042785006	claims	1. A pressurized water reactor comprising: a primary fluid circuit, at least one circulating pump for circulating primary fluid within at least one primary loop of said primary circuit, said primary circuit including a steam generator, a pressure vessel which contains a reactor core, and a bundle of tubes in said steam generator, a secondary fluid circuit containing fluid which enters the steam generator in a liquid state and is discharged therefrom in the form of steam which is returned into the generator after expansion within main turbines and recovery in a condenser, said primary circuit including a driving turbine supplied with steam taken from the steam generator, and fluid circulating pumps each driven by said driving turbine, a feed tank of a water supply unit, an auxiliary turbine, a storage tank and a pump drivingly connected to said auxiliary turbine, each main turbine having an outlet connected to said feed tank by means of conduit means provided with isolating valves and by means of bypass conduit means, for permitting a flow of steam for driving said auxiliary turbine in the event of closure of said isolating valves, and means for injecting high-pressure emergency water into said primary circuit from said storage tank by means of said pump. 2. A pressurized water reactor according to claim 1, comprising at least two injectors, means for passing water under pressure in said feed tank in the event of failure of the primary circuit into said injectors to perform the function of a driving fluid within said injectors, driven fluid within one injector being water derived from a storage tank of a low-pressure safety injection circuit, and driven fluid within the second injector being secondary water derived from a storage tank and fed into an emergency feed circuit of one of the steam generators. 3. A pressurized water reactor according to claim 1, comprising at least two injectors, means for passing water under pressure in said feed tank in the event of failure of the primary circuit into said injectors to perform the function of a driving fluid within said injectors, driven fluid within one injector being primary water in a sump to be recycled to the reactor core, and driven fluid within the second injector being secondary water derived from a storage tank and fed into an emergency feed circuit of one of the steam generators. 4. A pressurized water reactor according to claim 1, wherein the turbine for driving the primary fluid circulating pump is of the back-pressure type and comprises a regulating valve having at least two positions such that a first of said positions permits a minimum flow of steam while a second position permits a normal flow, means being provided for automatically returning the regulating valve to the first position when in the second position in the event of overstepping of a predetermined threshold.
	description	Embodiment 1 As described above, the void coefficient is influenced mainly by the water rod area, and by number and length and further by positions of the short length fuel rods. However, in the conventional example described above, effect of the void coefficient on the core stability depending on number and length of the short length fuel rods has not be quantitatively evaluated. From the viewpoint of backfitting a newly designed fuel assembly to an existing nuclear core, it is necessary to keep the core stability in nearly the same level compared to the case of using conventional fuel assemblies. Therefore, when the void coefficient described above is insufficiently evaluated, it can not be said that evaluation of the core stability (area of water rods, number and length of the short length fuel rods) attainable high burn-up is sufficient. Further, the effect on the pressure loss of assembly important for backfitting, that is, the effect of area of water rods and the effects of number and length of short length fuel rods on the pressure loss are not considered. A preferred embodiment of a fuel assembly in accordance with the present invention will be described below, referring to FIG. 1 and FIG. 2. The fuel assembly 1 is loaded in a reactor core of a boiling water reactor. In the fuel assembly 1, fuel rods 2 are arranged in a square array of 10 rows by 10 columns. The fuel rods 2 include fuel rods 2A having a long axial length and short length fuel rods 2B having an axial length shorter than that of the fuel rod 2A. In the center of the horizontal section of the fuel assembly 1, two water rods 3 are arranged. Each of the water rods 3 has a circular horizontal cross section the area of which occupies a region capable of arranging the four fuel rods. The two water rods 3 are arranged so that a center axis of each of the water rods is positioned on one diagonal line of the fuel assembly 1. These water rods 3 are arranged in a region of the fourth tier from the outer side of the fuel rod array, and arranged in the symmetrical positions with respect to the other diagonal line (the diagonal line which passes through a corner portion 8 facing a control rod when the fuel assembly 1 is loaded into the core of the boiling water reactor). The upper end portions of the fuel rods 2A and the water rods 3 are held by an upper tie plate 4 and the lower end portions are held by a lower tie plate 5. The lower end portions of the short length fuel rods 2B are held by the lower tie plate 5. The fuel rods 2A, 2B and the water rods 3 are held with a spacing one another by fuel spacers 6. These fuel rods are contained in a channel box 7 attached to the upper tie plate 4. Twelve rods among the sixteen short length fuel rods 2B are arranged in the second tier from the outer side of the fuel rod array. In the second tier of the fuel rod array, the twelve short length fuel rods 2B are arranged at positions in each of the corners and in two rods away from each of the corners. The remainder of the four short length fuel rods 2B are arranged adjacent to the water rods 3. In the present embodiment, the inner width Dcb of the channel box 7 is approximately 134 mm, the outer diameter Df of the fuel rods 2A and 2B is 10.26 mm, the fuel rod pitch Pf is 12.95 mm, and the effective fuel length Lf of the fuel rod 2A is approximately 3.7 m. In the present embodiment, the short length fuel rods 2B are not arranged in the outermost tier of the fuel rod array. The present embodiment of the fuel assembly 1 is constructed so that the effective fuel length Lp of the short length fuel rod 1B and the total horizontal sectional area Awr of the water rods 2 satisfy the conditions of Equation 1 to Equation 6. The conditions of Equation 1 to Equation 6 are found from a study performed by the inventors of the present invention. The results of the study will be described in detail below. Firstly, Equation 6 determined from the pressure loss of the fuel assembly will be described. The inventors of the present invention calculated a total horizontal sectional area of water rods 3 in the 10-by-10 fuel assembly having a pressure loss equal to that of a conventional 9-by-9 fuel assembly disclosed in Japanese Patent Application Laid-Open No.7-234293 (hereinafter, simply referred to as the conventional fuel assembly) by varying number of the short length fuel rods and effective fuel length of the short length fuel rod as parameters, and found the relationships between the number of the short length fuel rods, the effective fuel length Lp of the short length fuel rod and the total horizontal sectional area of all the water rods. The relationships are shown in FIG. 3. In FIG. 3, the abscissa indicates a ratio (Lp/Lf) of the effective fuel length Lp of the short length fuel rod 2B to the effective fuel length Lf of the fuel rod 2A, and the ordinate indicates a ratio (Awr/Ach) of the total horizontal sectional area Awr of all the water rods in the fuel assembly to the area Ach of the coolant flow passage of the fuel assembly in the lower portion of the fuel assembly. Therein, the coolant channel area Ach can be roughly expressed by the following equation. The coolant flow passage of the fuel assembly is a region inside the channel box 7 and outside the fuel rods 2 and the water rods 3. Ach=Dcb2xe2x88x92xcfx80/4xc3x97Df2xc3x97(100xe2x88x928)xe2x88x92Awrxe2x80x83xe2x80x83(Equation 20) By substituting the numerical values corresponding to the present embodiment described above into Equation 20, the following equation can be obtained. Ach=10350xe2x88x92Awr(mm2)xe2x80x83xe2x80x83(Equation 21) The diagram means that when a value of the abscissa is 0.5, the effective fuel length of the short length fuel rod 2B is approximately 1.85 m (3.7 mxc3x970.5). Referring to FIG. 3, the reference characters L1, L2, L3 are boundary lines depending on number of the short length fuel rods 2B. The boundary line L1 indicates a case where number of the short length fuel rods 2B is 12, the boundary line L2 indicates a case where number of the short length fuel rods 2B is 16, and the boundary line L3 indicates a case where number of the short length fuel rods 2B is 20. In the case where number of the short length fuel rods 2B is 16, the boundary line L2 in the diagram is a boundary satisfying the condition that the pressure loss is equal to the pressure loss of the conventional fuel assembly. In the case where number of the short length fuel rods 2B is 16, on the boundary line L2 and the zone below the boundary line L2 are a zone where the pressure loss is not larger than the pressure loss of the conventional fuel assembly. Therefore, by constructing the fuel assembly so that the total horizontal sectional area of all the water rods falls in the zone below the boundary line L2 including on the boundary line L2, The pressure loss of the present embodiment of the fuel assembly can be equal to and smaller than that of the conventional fuel assembly. That is, the value Awr/Ach should satisfy Equation 6. Each of the boundary lines depending on number of the short length fuel rods 2B in the fuel assembly is expressed by Equation 6 including number n of the short length fuel rods as the parameter. In addition, the dotted line K in FIG. 3 indicates the maximum value of the total horizontal sectional area of all the water rods occupying a region for 8 rods of the fuel rods, and can be expressed by the following equation. xe2x80x83Awr=Pf2xc3x978xe2x80x83xe2x80x83(Equation 22) Therefore, the value Awr/Ach to the upper limit value of the total horizontal sectional area of all the water rods becomes as follows. Awr/Ach=1342/(10350xe2x88x921342)=0.149xe2x80x83xe2x80x83(Equation 23) Therefore, the value Awr/Ach must be smaller than 0.149, that is, Equation 3. Further, the value corresponding to the abscissa of the dotted line J corresponds to a length that the effective fuel length of the short length fuel rod 2B becomes 11/24 (=0.458) of the effective fuel length of the fuel rod 2A. In this length, the upper end portion of the short length fuel rods including a length of the gas plenum (formed in the fuel rod) are supported by one of the fuel spacers placed in the nearly middle portion in the axial direction of the fuel assembly. However, if the effective fuel length of the short length fuel rod 2B is further shortened, it is necessary from the viewpoint of flow-induced vibration of the short length fuel rod that the effective fuel length of the short length fuel rod is formed about 8/24 of the effective fuel length of the fuel rod 2A. When the effective fuel length of the short length fuel rod 2B is made shorter than 11/24 as described above, the uranium inventory becomes too small to deteriorate the fuel cycle cost. Therefore, the value Lp/Lf must be larger than 11/24 (Equation 4). Next, Equation 5 determined from the core stability will be described below. The core stability is a characteristic relating to fluctuation of the core flow rate and the reactor output power of the whole core after a disturbance is added to the reactor core. Here, it is assumed that a disturbance of sinusoidal core flow rate is added to the reactor core. Further, it is also assumed that the fluctuation of the core flow rate in the reactor core after adding the disturbance is as shown in FIG. 4. In the fluctuation of FIG. 4, the amplitude of the fluctuation is decreased with time and the core flow rate returns to a stable state in a short time. Therein, letting an amplitude of the disturbance added to the reactor core be y0, and an amplitude one cycle after that time be y1, the amplitude damping ratio is defined as the value y1/y0. In the case of FIG. 4, the amplitude damping ratio is smaller than 1, and the reactor core is returned to a stable state (a normal state). In such a case, it is said that the reactor core is stable. On the other hand, in the case of FIG. 5, the amplitude damping ratio is larger than 1, and the fluctuation of the core flow rate in the reactor core is increased as the time elapses. This is not preferable state from the viewpoint of reactor operation. Therefore, the core stability can be evaluated as stable when the amplitude damping ratio is smaller than 1, and as unstable when the amplitude damping ratio is larger than 1. Therefore, although the core stability can be evaluated as stable when the amplitude damping ratio is smaller than 1, design is practically performed by setting the amplitude damping ratio to 0.8 for taking a margin. The inventors of the present invention calculated a horizontal sectional area of water rods in the 10-by-10 fuel assembly satisfying the amplitude damping ratio of 0.8 by varying number of the short length fuel rods and effective fuel length of the short length fuel rod as parameters, and found the relationships between the number of the short length fuel rods, the effective fuel length of the short length fuel rod and the horizontal sectional area of the water rods. Further, in order attain a high burn-up higher than the average unloading burn-up 45 Gwd/t of the conventional 9-by-9 fuel assembly, the average unloading burn-up was set to 60 GWd/t. FIG. 6 shows the analysis results. The ordinate and the abscissa of FIG. 6 are the same as those of FIG. 3. Similarly to the analysis results of the pressure loss, the boundary line is drawn for each number of the short length fuel rods. The boundary line M1 is the result for the case where number of the short length fuel rods is 12, the boundary line M2 is the result for the case where number of the short length fuel rods is 16, and the boundary line M3 is the result for the case where number of the short length fuel rods is 20. In the case of 16 rods of the short length fuel rods, the boundary line M2 is the boundary satisfying the amplitude damping ratio of 0.8, and the zone on the boundary line M2 and above the boundary line M2 is the zone where the amplitude damping ratio is below 0.8. Therefore, when the fuel assembly is constructed so that the total horizontal sectional area of all the water rods falls in the zone above the solid line M2 including on the solid line M2, the average unloading burn-up of 60 GWd/t can be attained, and the allowable core stability can be maintained. That is, Awr/Ach should satisfy Equation 5. Each of the boundary lines depending on number of the short length fuel rods 2B in the fuel assembly is expressed by Equation 5 including number n of the short length fuel rods as the parameter. The boundary lines for the pressure loss shown in FIG. 3, the boundary lines for the core stability shown in FIG. 6 and the boundary lines J and K are shown in FIG. 7. In the case of 12 rods of the short length fuel rods, the boundary line M1 expressing the minimum required total horizontal sectional area of all the water rods determined from the core stability is positioned above the dotted line K. Accordingly, the case of 12 rods of the short length fuel rods requires a total horizontal sectional area of all the water rods larger than the maximum total horizontal sectional area of all the water rods in the region occupied by eight fuel rods in the present embodiment. Therefore, in the case of 12 rods of the short length fuel rods, the core stability can not be satisfied under the condition of average unloading burn-up of 60 GWd/t. As described above, in the case where the water rods are arranged in the region capable of being occupied by 8 fuel rods and the short length fuel rods are arranged in the fuel rod array except the outermost tier, required number of the short length fuel rods is larger than 15 rods. On the other hand, when number of the short length fuel rods is increased above 21, the void coefficient is improved, but the uranium inventory is excessively reduced. In addition, it is not preferable from the viewpoint of the mechanical strength of the fuel spacers for holding the fuel rods with a spacing between one another which are positioned above the upper end of the short length fuel rod. Therefore, number of the short length fuel rods should be smaller than 20. Thus, the number n of the short length fuel rods should satisfy the condition of 15xe2x89xa6nxe2x89xa620, that is, Equation 2. In FIG. 7, the hatched zone is a zone where Equation 1, Equation 3 to Equation 6 are satisfied to the 10-by-10 fuel assembly of the present embodiment having 16 rods of the short length fuel rods. The ratio Lp/Lf and the horizontal sectional area of the water rods 3 are set so as to fall into this zone. However, even in a case of 15xe2x89xa6nxe2x89xa620, there is a zone where Equation 1, Equation 3 to Equation 6 are satisfied. According to the present embodiment, the average unloading burn-up of 60 GWd/t can be attained, and the allowable core stability can be attained without increasing the pressure loss compared to that of the conventional fuel assembly. Further, the fuel assemblies of the present embodiment can be applied to the existing boiling water reactor. In Japanese Patent Application Laid-Open No.5-232273 there is no description that the burn-up above 60 GWd/t is attained using the fuel assembly having a fuel rod array of 10 rows by 10 columns. The fuel assembly of the present embodiment can attain the burn-up above 60 GWd/t by 10 columns by satisfying the conditions of Equation 1 to Equation 6, and in the fuel assembly having the fuel rod array of 10 rows, the allowable core stability can be attained without increasing the pressure loss larger than that of the conventional fuel assembly. In the present embodiment, the same effects can be obtained even in a case where the short length fuel rods are arranged in different positions from those of FIG. 1 unless the short length fuel rods are arranged in the outermost tier. Further, the same effects can be obtained the water rod is changed to a rectangular water rod 3A as shown in FIG. 8 or to a water rod having another shape if the total horizontal sectional area is the same. Since Equation 20 includes the channel box inner width Dcb and the fuel rod outer diameter Df, the present embodiment can also cope with small changes in the channel box inner width and the fuel rod outer diameter. Embodiment 2 A second embodiment of a fuel assembly in accordance with the present invention will be described below, referring to FIG. 9. The present embodiment of the fuel assembly 1C is loaded in a reactor core of a boiling water reactor. In the fuel assembly 1C, the two water rods 3 of the fuel assembly 1 shown in FIG. 1 are replaced with one water rod 3C. The other structure of the present embodiment is the same as that of the fuel assembly shown in FIG. 1. The water rod 3C has a circular horizontal section, and occupies a region capable of arranging 9 fuel rods. The center axis of the water rod 3C is arranged at a position dislocated from a center axis of the fuel assembly toward a side opposite to a corner portion 8 facing a control rod under a condition that the fuel assembly 1C is loaded in the core of the boiling water reactor. Consequently, there exist four tiers of the fuel rod array in the side of the corner portion 8 between the water rod 3C and the channel box 7. On the other hand, there exist three tiers of the fuel rod array in the opposite side of the corner portion 8 between the water rod 3C and the channel box 7. In the second tier from the outer side of the fuel rod array, the twelve short length fuel rods 2B are arranged at positions in each of the corners and in two rods away from each of the corners. The dimensions of the inner width Dcb of the channel box 7, the outer diameter Df of the fuel rod 2, the fuel rod pitch Pf and the effective fuel length Lf of the fuel rod 2A are the same as those of the fuel assembly 1. In the present embodiment, the short length fuel rods 2B are not arranged in the outermost tier of the fuel rod array either. The present embodiment of the fuel assembly 1C is constructed so that the effective fuel length Lp of the short length fuel rod 1B and the total horizontal sectional area Awr of the water rod 3C satisfy the conditions of Equation 1, Equation 4, and Equation 7 to Equation 10. The conditions of Equation 7 to Equation 10 are found from a study performed by the inventors of the present invention. An example of a boundary line derived from individual analyses of the pressure loss and the core stability in the present embodiment of the fuel assembly 1C similarly to Embodiment 1 is shown in FIG. 10. The boundary line L4 shown in FIG. 10 is a boundary line for the pressure loss when 12 rods of the short length fuel rods 2B are arranged in the fuel rod array of the fuel assembly 1C except the outermost tier. Similarly, the boundary line M4 is a boundary line for the core stability when 12 rods of the short length fuel rods 2B are arranged. Therein, the coolant channel area Ach in the fuel assembly 1C can be roughly expressed by the following equation. Ach=Dcb2xe2x88x92xcfx80/4xc3x97Df2xc3x97(100xe2x88x929)xe2x88x92Awrxe2x80x83xe2x80x83(Equation 24) By substituting the numerical values corresponding to the present embodiment described above into Equation 24, the following equation can be obtained. xe2x80x83Ach=10432xe2x88x92Awr(mm2)xe2x80x83xe2x80x83(Equation 25) In addition, the dotted line K1 in FIG. 10 indicates the maximum value of the total horizontal sectional area of all the water rods occupying a region for 9 rods of the fuel rods, and can be expressed by the following equation. Awr=Pf2xc3x979xe2x80x83xe2x80x83(Equation 26) Therefore, the value Awr/Ach to the upper limit value of the total horizontal sectional area of all the water rods becomes as follows. Awr/Ach=1509/(10432xe2x88x921509)=0.169xe2x80x83xe2x80x83(Equation 27) Therefore, the value Awr/Ach must be smaller than 0.169, that is, Equation 8. Further, in this embodiment, the required number of the short length fuel rods 2B is within a range of 10 to 20 which is obtained from a study similar to that of Embodiment 1. In FIG. 10, Equation 8 corresponds to the zone lower than the dotted line K1 including the dotted line K1, and Equation 4 corresponds to the zone in right hand side from the dotted line J including the dotted line J. In FIG. 10, the hatched zone is a zone where Equation 1, Equation 4, and Equation 8 to Equation 10 are satisfied to the fuel assembly having 12 rods of the short length fuel rods 2B arranged as shown in FIG. 9. The ratio Lp/Lf and the horizontal sectional area of the water rod 3 are set so as to fall into this zone. However, even in a case of satisfying Equation 7, that is, 10xe2x89xa6nxe2x89xa620, there is a zone where Equation 1, Equation 4, and Equation 8 to Equation 10 are satisfied. According to the present embodiment, the same effects similar to those of Embodiment 1 can be obtained. The short length fuel rods may be arranged in different positions from those of FIG. 9 unless the short length fuel rods are arranged in the outermost tier, and further, the fuel assembly 1D shown in FIG. 11 may be used. The fuel assembly 1D is a fuel assembly that in the fuel assembly 1C, the water rod 3C is replaced with a water rod 3D having a rectangular horizontal cross section. Embodiment 3 A third embodiment of a fuel assembly in accordance with the present invention will be described below, referring to FIG. 12. The present embodiment of the fuel assembly 1E is loaded in a reactor core of a boiling water reactor. In the fuel assembly 1E, the two water rods 3 of the fuel assembly 1 (FIG. 1) are replaced with three water rods 3E. The three water rods 3E are positioned on one diagonal line intersecting at right angle with the other diagonal line passing through the corner portion 8 of the fuel assembly 1E facing a control rod, and are adjacent to each other. One middle rod among the water rods 3E is also placed on the diagonal line passing through the corner position 8. That is, this one middle rod among the water rods 3E is placed at the axis of the fuel assembly 1E. The three water rods 3E occupy a region capable of arranging 10 rods of the fuel rods 2. The outer diameter of the water rods 3E is smaller than the outer diameter of the water rod 3 (FIG. 1). 10 rods of the short length fuel rods 2B are arranged. 8 rods among the 10 short length fuel rods 2B are arranged in the second tier in the fuel rod array. Each of the remaining 2 short length fuel rods 2B is placed at the corner in the fourth tier of the fuel rod array. In the second tier of the fuel rod array, the short length fuel rod 2B is placed at each of the corners. The dimensions of the inner width Dcb of the channel box 7, the outer diameter Df of the fuel rod 2, the fuel rod pitch Pf and the effective fuel length Lf of the fuel rod 2A in the present embodiment are the same as those of the fuel assembly 1. In the present embodiment, the short length fuel rods 2B are not arranged in the outermost tier of the fuel rod array either. The fuel assembly 1E is constructed so that the effective fuel length Lp of the short length fuel rod 2B and the total horizontal sectional area Awr of the water rod 3E satisfy the conditions of Equation 1, Equation 4, and Equation 11 to Equation 14. The conditions of Equation 11 to Equation 14 are found from a study performed by the inventors of the present invention. An example of a boundary line derived from individual analyses of the pressure loss and the core stability in the present embodiment of the fuel assembly 1E similarly to Embodiment 1 is shown in FIG. 13. The boundary line L5 shown in FIG. 13 is a boundary line for the pressure loss when 10 rods of the short length fuel rods 2B are arranged in the fuel rod array of the fuel assembly 1E except the outermost tier. Similarly, the boundary line M5 is a boundary line for the core stability when 10 rods of the short length fuel rods 2B are arranged. Therein, the coolant channel area Ach in the fuel assembly 1E can be roughly expressed by the following equation. Ach=Dcb2xe2x88x92xcfx80/4xc3x97Df2xc3x97(100xe2x88x9210)xe2x88x92Awrxe2x80x83xe2x80x83(Equation 28) By substituting the numerical values corresponding to the present embodiment described above into Equation 27, the following equation can be obtained. Ach=10515xe2x88x92Awr(mm2)xe2x80x83xe2x80x83(Equation 29) In addition, the dotted line K2 in FIG. 13 indicates the maximum value of the total horizontal sectional area of all the water rods occupying a region for 10 rods of the fuel rods, and can be expressed by the following equation. Awr=Pf2xc3x9710xe2x80x83xe2x80x83(Equation 30) Therefore, the value Awr/Ach to the upper limit value of the total horizontal sectional area of all the water rods becomes as follows. Awr/Ach=1677/(10515xe2x88x921677)=0.190xe2x80x83xe2x80x83(Equation 31) Therefore, the value Awr/Ach must be smaller than 0.190, that is, Equation 12. Further, in this embodiment, the required number of the short length fuel rods 2B is within a range of 9 to 20 which is obtained from a study similar to that of Embodiment 1. In FIG. 13, Equation 12 corresponds to the zone lower than the dotted line K2 including the dotted line K1, and Equation 4 corresponds to the zone in right hand side from the dotted line J including the dotted line J. In FIG. 13, the hatched zone is a zone where Equation 1, Equation 4, and Equation 12 to Equation 14 are satisfied to the fuel assembly having 10 rods of the short length fuel rods 2B arranged as shown in FIG. 12. The ratio Lp/Lf and the horizontal sectional area of the water rods 3 are set so as to fall into this zone. However, even in a case of satisfying Equation 11, that is, 10xe2x89xa6nxe2x89xa620, there is a zone where Equation 1, Equation 4, and Equation 12 to Equation 14 are satisfied. According to the present embodiment, the same effects similar to those of Embodiment 1 can be obtained. The short length fuel rods may be arranged in different positions from those of FIG. 12 unless the short length fuel rods are arranged in the outermost tier, and further, the fuel assembly 1F shown in FIG. 14 may be used. The fuel assembly 1F is a fuel assembly that in the fuel assembly 1E, the water rods 3E are integrated into a single rod of water rod 3F. The water rod 3F is placed at the same position of the three water rods 3C. Embodiment 4 A fourth embodiment of a fuel assembly 1G in accordance with the present invention will be described below, referring to FIG. 15. The present embodiment of the fuel assembly 1G is loaded in a reactor core of a boiling water reactor. The fuel assembly 1G has a construction that in the fuel assembly 1 shown in FIG. 1, the arrangement of the short length fuel rods 2B is changed. That is, the short length fuel rods 2B are not arranged in the second tier of the fuel rod array from the outer side, but arranged in the outermost tier of the fuel rod array. In the outermost tier, two rods of the short length fuel rods 2B are arranged in the middle portion of each side adjacent to each other. The other structure of the fuel assembly 1G is the same as that of Embodiment 1. The dimensions of the inner width Dcb of the channel box 7, the outer diameter Df of the fuel rod 2, the fuel rod pitch Pf and the effective fuel length Lf of the fuel rod 2A are the same as those of the fuel assembly 1. The fuel assembly 1G is constructed so that the effective fuel length Lp of the short length fuel rod 2B and the total horizontal sectional area Awr of the water rod 3E satisfy the conditions of Equation 1, Equation 3, Equation 4, Equation 6, Equation 11 and Equation 15. The conditions expressed by these equations are found from a study performed by the inventors of the present invention. An example of a boundary line derived from individual analyses of the pressure loss and the core stability in the present embodiment of the fuel assembly 1G similarly to Embodiment 1 is shown in FIG. 16. The boundary line L6 shown in FIG. 16 is a boundary line for the pressure loss when 12 rods of the short length fuel rods 2B are arranged in the fuel rod array of the fuel assembly 1G including the outermost tier. Similarly, the boundary line M6 is a boundary line for the core stability when 12 rods of the short length fuel rods 2B are arranged. In the present embodiment, because all the short length fuel rods 2B are arranged at the positions where the effect of improving the void coefficient is large, that is, at the positions in the outermost tier of the fuel rod array and adjacent to the water rods, the condition for the core stability, that is, Equation 15 is different from the condition for the core stability in Embodiment 1, that is, Equation 5. The total horizontal sectional area of the water rods in the present embodiment is smaller than that of Embodiment 1 when the core stability is the same. On the other hand, the condition determined from the pressure loss in the present embodiment, that is, Equation 6 is not influenced by the arrangement of the short length fuel rods, and is the same as that of Embodiment 1. Further, the upper limit value for Awr/Ach is a value shown by Equation 23 similarly to Embodiment 1. In the present embodiment, the required number of the short length fuel rods 2B is within a range of 9 to 20 which is obtained from a study similar to that of Embodiment 1. In FIG. 16, the hatched zone is a zone where Equation 1, Equation 3, Equation 4, Equation 6 and Equation 15 are satisfied to the fuel assembly having 12 rods of the short length fuel rods 2B arranged as shown in FIG. 15. The ratio Lp/Lf and the horizontal sectional area of the water rods 3 are set so as to fall into this zone. However, even in a case of satisfying Equation 11, that is, 10xe2x89xa6nxe2x89xa620, there is a zone where Equation 1, Equation 3, Equation 4, Equation 6 and Equation 15 are satisfied. By arranging the short length fuel rods 2B in the outermost tier, the void coefficient is reduced to more than one half as small as that in the case where the short length fuel rods 2B are arranged in the second tier of the fuel rod array from the outer side. When the short length fuel rods 2B are arranged at the corners of the outermost tier, the reducing rate of the void coefficient becomes maximum. However, in the case where the short length fuel rods 2B are arranged at the corners of the outermost tier, both of the reactivity loss and the local power peaking factor of the short length fuel rods arranged at the corners become large. Therefore, arranging of the short length fuel rods 2B at the corners should be avoided. The reactivity loss can be reduced by arranging the short length fuel rods 2B at positions other than the corner in the outermost tier. Further, by arranging the short length fuel rods at the positions in the outermost tier of the fuel rod array intersecting with a row or a column of the fuel rod array on which each of the water rod 3 is arranged (in concrete, at the four fuel rod positions at middle portions in the individual sides of the outermost tier), the reactivity loss and the local power peaking can be reduced. According to the present embodiment, the same effects as those of the first embodiment can be obtained, and further the void coefficient can be reduced. In addition, the reactivity loss and the local power peaking can be also reduced. The short length fuel rods may be arranged differently from the arrangement of FIG. 15 if the short length fuel rods are arranged both in the positions in the outermost tier and in the positions adjacent to the water rods, or arranged only in the outermost tier, and further the fuel assembly 1H shown in FIG. 17 may be acceptable. The fuel assembly 1H is that in the fuel assembly 1G, the water rods 3 are replaced with the water rods 3A having a rectangular horizontal section. The two water rods 3A are arranged at the same positions as those of the two water rods 3. Embodiment 5 A fifth embodiment of a fuel assembly 1I in accordance with the present invention will be described below, referring to FIG. 18. The present embodiment of the fuel assembly 1I is loaded in a reactor core of a boiling water reactor. The fuel assembly 1I has a construction that in the fuel assembly 1C shown in FIG. 9, the arrangement of the short length fuel rods 2B is changed. The other construction of the fuel assembly 1I is the same as that of the fuel assembly 1C. The arrangement of the water rod 3C of the fuel assembly 1I is also the same as that of the fuel assembly 1C. The present embodiment has 12 rods of the short length fuel rods 2B. These short length fuel rods 2B are not arranged in the second tier from the outer side of the fuel rod array. Eight rods of the short length fuel rods 2B are arranged in the outermost tier of the fuel rod array, and two rods are arranged in the middle portion on each side of the fuel rod array adjacent to each other. The remainder of four rods of the short length fuel rods 2B are arranged in the fourth tier from the outer side of the fuel rod array in the side of the corner portion 8 side facing a control rod under the state when the fuel assembly 1I is loaded in the reactor core of the boiling water and in the third tier from the outer side of the fuel rod array in the opposite side of the corner portion 8 side. Each of these four short length fuel rods 2B is adjacent to the water rod 3C. The dimensions of the inner width Dcb of the channel box 7, the outer diameter Df of the fuel rod 2, the fuel rod pitch Pf and the effective fuel length Lf of the fuel rod 2A are the same as those of the fuel assembly 1. The fuel assembly 1I is constructed so that the effective fuel length Lp of the short length fuel rod 2B and the total horizontal sectional area Awr of the water rod 3 satisfy the conditions of Equation 1, Equation 4, Equation 8, Equation 10, Equation 16 and Equation 17. The conditions expressed by these equations are found from a study performed by the inventors of the present invention. An example of a boundary line derived from individual analyses of the pressure loss and the core stability in the present embodiment of the fuel assembly 1I similarly to Embodiment 1 is shown in FIG. 19. The boundary line L7 shown in FIG. 19 is a boundary line for the pressure loss when 12 rods of the short length fuel rods 2B are arranged in the fuel rod array of the fuel assembly 1I including the outermost tier. Similarly, the boundary line M7 is a boundary line for the core stability when 12 rods of the short length fuel rods 2B are arranged. In the present embodiment, because all the short length fuel rods 2B are arranged at the positions where the effect of improving the void coefficient is large, that is, at the positions in the outermost tier of the fuel rod array and adjacent to the water rods, the condition for the core stability, that is, Equation 17 is different from the condition for the core stability in Embodiment 2, that is, Equation 9. The total horizontal sectional area of the water rods in the present embodiment is smaller than that of Embodiment 2 when the core stability is the same. On the other hand, the condition determined from the pressure loss in the present embodiment, that is, Equation 10 is not influenced by the arrangement of the short length fuel rods, and is the same as that of Embodiment 2. Further, the upper limit value for Awr/Ach is a value shown by Equation 27 similarly to Embodiment 2. In the present embodiment, the required number of the short length fuel rods 2B is within a range of 8 to 20 which is obtained from a study similar to that of Embodiment 1. In FIG. 19, the hatched zone is a zone where Equation 1, Equation 4, Equation 8, Equation 10 and Equation 17 are satisfied to the fuel assembly having 12 rods of the short length fuel rods 2B arranged as shown in FIG. 18. The ratio Lp/Lf and the horizontal sectional area of the water rods 3 are set so as to fall into this zone. However, even in a case of satisfying Equation 16, that is, 8xe2x89xa6nxe2x89xa620, there is a zone where Equation 1, Equation 4, Equation 8, Equation 10 and Equation 17 are satisfied. According to the present embodiment, the effects similar to those of Embodiment 4 can be obtained. Further, the short length fuel rods may be arranged differently from the arrangement of FIG. 18 if the short length fuel rods are arranged both in the positions in the outermost tier and in the positions adjacent to the water rods, or arranged only in the outermost tier, and further the fuel assembly 1J shown in FIG. 20 may be acceptable. The fuel assembly 1J is that in the fuel assembly 1I, the water rod 3C is replaced with the water rod 3D having a rectangular horizontal section. The water rod 3D is arranged at the same positions as those of the two water rod 3C. Embodiment 6 A sixth embodiment of a fuel assembly 1K in accordance with the present invention will be described below, referring to FIG. 21. The present embodiment of the fuel assembly 1K is loaded in a reactor core of a boiling water reactor. The fuel assembly 1K has a construction that in the fuel assembly 1E shown in FIG. 12, the arrangement of the short length fuel rods 2B is changed. The other construction of the fuel assembly 1K is the same as that of the fuel assembly 1E. The arrangement of the water rod 3E of the fuel assembly 1K is also the same as that of the fuel assembly 1E. The present embodiment has 10 rods of the short length fuel rods 2B. These short length fuel rods 2B are not arranged in the second tier from the outer side of the fuel rod array. Eight rods of the short length fuel rods 2B are arranged in the outermost tier of the fuel rod array similarly to the fourth embodiment, and two rods are arranged in the middle portion on each side of the fuel rod array adjacent to each other. The remainder of 2 rods of the short length fuel rods 2B are arranged in the fourth tier from the outer side of the fuel rod array, and each of these 2 short length fuel rods 2B is adjacent to the water rods 3E. The dimensions of the inner width Dcb of the channel box 7, the outer diameter Df of the fuel rod 2, the fuel rod pitch Pf and the effective fuel length Lf of the fuel rod 2A are the same as those of the fuel assembly 1. The fuel assembly 1K is constructed so that the effective fuel length Lp of the short length fuel rod 2B and the total horizontal sectional area Awr of the water rods 3 satisfy the conditions of Equation 1, Equation 4, Equation 12, Equation 14, Equation 18 and Equation 19. The conditions expressed by these equations are found from a study performed by the inventors of the present invention. An example of a boundary line derived from individual analyses of the pressure loss and the core stability in the present embodiment of the fuel assembly 1K similarly to Embodiment 1 is shown in FIG. 22. The boundary line L8 shown in FIG. 22 is a boundary line for the pressure loss when 10 rods of the short length fuel rods 2B are arranged in the fuel rod array of the fuel assembly 1K including the outermost tier. Similarly, the boundary line M8 is a boundary line for the core stability when 12 rods of the short length fuel rods 2B are arranged. In the present embodiment, because all the short length fuel rods 2B are arranged at the positions where the effect of improving the void coefficient is large, that is, at the positions in the outermost tier of the fuel rod array and adjacent to the water rods, the condition for the core stability, that is, Equation 19 is different from the condition for the core stability in Embodiment 3, that is, Equation 13. The total horizontal sectional area of the water rods 3C in the present embodiment is smaller than that of Embodiment 2 when the core stability is the same. On the other hand, the condition determined from the pressure loss in the present embodiment, that is, Equation 14 is not influenced by the arrangement of the short length fuel rods, and is the same as that of Embodiment 3. Further, the upper limit value for Awr/Ach is a value shown by Equation 31 similarly to Embodiment 3. In the present embodiment, the required number of the short length fuel rods 2B is within a range of 7 to 20 which is obtained from a study similar to that of Embodiment 1. In FIG. 22, the hatched zone is a zone where Equation 1, Equation 4, Equation 12, Equation 14 and Equation 19 are satisfied to the fuel assembly having 10 rods of the short length fuel rods 2B arranged as shown in FIG. 21. The ratio Lp/Lf and the horizontal sectional area of the water rods 3E are set so as to fall into this zone. However, even in a case of satisfying Equation 18, that is, 7xe2x89xa6nxe2x89xa620, there is a zone where Equation 1, Equation 4, Equation 12, Equation 14 and Equation 19 are satisfied. According to the present embodiment, the effects similar to those of Embodiment 4 can be obtained. Further, the short length fuel rods may be arranged differently from the arrangement of FIG. 21 if the short length fuel rods are arranged both in the positions in the outermost tier and in the positions adjacent to the water rods, or arranged only in the outermost tier, and further the fuel assembly 1L shown in FIG. 22 may be acceptable. The fuel assembly 1L is that in the fuel assembly 1K, the water rods 3E are replaced with a water rod 3F having a rectangular horizontal section. The water rod 3F is arranged at the same positions as those of the water rods 3E. The fuel assembly in accordance with the present invention is suitable for loading into a core of a boiling water reactor.
056132395	description	DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS In the drawing, an electrical conduction tank 1 contains a solution composed of a chelating solution and/or an organic acid containing radioactive metal ions. Suitable chelating agents for preparation of a chelating solution include ethylenediamine tetraacetic acid, ethylenenitrilodiamine triacetic acid, hydroxyethylethylenediamine tetraacetic acid and the like. Suitable organic acids include citric acid, oxalic acid, acetic acid and the like. The chelating solution and organic acid may be used singly or in combination and contain radioactivity-laden metal ions such as Fe ions, Mn ions, Co ions and other metal ions. Denoted by numeral 9 is an alkaline agent-feeding device from which a NaOH or KOH solution is supplied. An alkaline agent used here is a hydroxide of an alkali metal or of an alkaline earth metal. Numeral 10 is a stirrer, numeral 11 is a pump, and numeral 12 is a filtration device, which is, as an example, a cartridge filter in this embodiment. A filtrate tank is denoted by numeral 13. An electrolytic device 3 is composed of an electrolyzer 14 and a plurality of electrodes 15 designed to flow direct current. An air pump 16 of an electromagnetic type is provided to feed air which removes or blows off various gases. A tank 17 is provided to store a solution electrolyzed in the electrolyzation device 3. A filtration device 4 communicates with the electrolyzer 14 and filters metal hydroxides which are little soluble in water coming out of the electrolyzer 14, to discharge the metal hydroxides as a filter cake and to convey the resultant filtrate to the tank 17. An ultraviolet irradiation device 6 has an elongate tank 18 to which an ultraviolet lamp 19 is secured. The filtrate comes into the device 6 from an inlet 20 and comes out from an inlet 21. A pump 22 is arranged to feed air and provided with an air inlet 23 and an air outlet 24. The air thus fed generates ozone upon irradiation with ultraviolet rays, to promote oxidation of the filtrate. Numeral 25 is a tank. A separation device 5, which is as an example of a reverse osmosis type, is provided to separate organic matter and water resulting from decomposition in the ultraviolet irradiation device 6. The organic matter so decomposed is near mineral, and the water so separated may be recycled as clean water or discharged. The separation device 5 may also be of an ion-exchange resin type. The operation of the apparatus which is constructed as described above will be described hereunder. Firstly, an organic solution composed of a chelating solution and/or an organic acid is applied to radioactive metals laden with radioactivity, to form an organic metal solution. In this embodiment, a mixture of a chelating solution and an organic acid is used. For example, a mixture of ethylenediamine tetraacetic acid and citric acid, each being a 1% aqueous solution, is used. Contained in the metal solution are metal ions such as Fe ions, Mn ions and the like, and here explanation will be made as to Fe ions as an example. The metal solution contained in the electrical conduction tank 1 is applied with a NaOH solution as an example from the alkaline agent-feeding device 9, and stirred by the stirrer 10. For example, the ratio of NaOH to a metal solution is 4 g/liter. Then iron hydroxides are formed in the metal solution and precipitated in colloid. The same kind of action occurs as to metals other than iron, too. Being a typical coprecipitant, iron helps precipitation of other radioactive metal ions. The metal solution is thereafter filtered in the filtration device 2 so that the iron hydroxides are separated and removed, while the resulting filtrate is fed into the electrolytic device 3 where the filtrate is electrolyzed. Efficient electrolyzation is made because the filtrate treated with an alkaline agent has markedly high electrical conductivity. With respect to electrical conductivity of the metal solution treated with an alkaline agent, as an example, the following are the current densities as measured. before addition of an alkaline agent: 0. 8 A/dm2 PA1 after addition of an alkaline agent: 10 A/dm2 Most of Fe ions are lost, and the chelating effect of the chelating solution is lost, presumably due to hydrolysis. For instance, using disodium ethylenediamine tetraacetic acid, C.sub.10 H.sub.14 N.sub.2 O.sub.8 Na.sub.2 +16H.sub.2 O.fwdarw.10CO.sub.2 +2NO+2NaOH+22H.sub.2. CO.sub.2 and NaOH are formed by anode oxidation and H.sub.2 is formed at a cathode side. The organic acid is also decomposed by electrolysis to form CO.sub.2, H.sub.2 and the like. Prior to electrolysis, most of the metal ions are removed in the treatment in the electrical conduction tank 1 and the filtration device 12 so that radioactive metals left to be deposited on the electrodes 15 of the electrolytic device 3 can be reduced greatly. Much deposition on the electrodes 15 is responsible for poor electrolysis efficiency. Moreover, radioactivity of the electrodes 15 is kept low because just a small extent of radioactive metal ions are still remaining. Thus troublesome post-treatment can be minimized. According to the invention, although a chelating solution and/or an organic acid containing radioactive ions are generally little conductive and difficult to be electrolyzed, they can be easily electrolyzed by increasing electrical conductivity by addition of an alkaline agent. This ensures easy collection of radioactive metal ions contained in such solutions. In the above electrolytic treatment, in addition to the decomposition through the anode oxidation, a material convertible by electrolysis into highly oxidative matter, such as NaOH for example, may also be used to take advantage of its high oxidative action. As a result of electrolysis, radioactive metal ions are converted into little-water-soluble hydroxides in the electrolyzer 14. The filtrate in the electrolyzer 14 is filtered in the filtration device 4 where the hydroxides are separated and removed. The separated filtrate is allowed to enter the ultraviolet irradiation device 6 from the lower inlet 20 and to be discharged out of the upper outlet 21 while being supplied with air bubbles. Oxygen in the bubbles generates ozone upon exposure to ultraviolet rays, and ozone acts to decompose any remaining organic matter, promoting decomposition of such organic matter by ultraviolet rays. The organic matter decomposed by ultraviolet irradiation is near mineral and sent to the separation device 5 that is of a reverse osmosis type for example. In the device 5, the irradiated filtrate put inside a translucent membrane (not shown) is brought in pressurized condition so that water alone iscaused to pass through the membrane outside in clean water and thus separated from the decomposed organic matter. The separation device 5 may be an ion-exchange resin type. The solution containing the matter decomposed in the ultraviolet irradiation device 6 is sent to the ion-exchange resin device, where the decomposed matter is absorbed by the ion-exchange resin, while water free from the decomposed matter is separated as cleanwater. The water may be discharged or recycled to the first stage of the apparatus. Being constructed as described above, the present invention enables the following available: It is available to electrolyze a solution composed of a chelating solution and/or an organic acid containing a radioactive metal ions, which is little soluble in water and difficult to be electrolyzed, by increasing electrical conductivity thereof by adding an alkaline agent, and to collect without difficulty radioactive metals contained in the solution. It is also available in collecting radioactive metals by way of dissolution to decrease mass volume of the radioactive matter required to be stored in safety quite significantly because there is no need to store radioactive chelating solutions and/or organic acids. Therefore, it is available to realize a quite high extent of reduction of storage space for radioactive matter. It is also available to make cementing treatment of the chelating solution and the organic solution after electrolysis because carboxyl groups therein have been decomposed. It is available to collect radioactive metal ions dissolved in the chelating solution and/or the organic acid, as hydroxides easily, because inherent activities of such solutions are lost by decomposition by electrolysis. Prior to electrolysis, the radioactive metal ions in the chelating solution and/or the organic acid have already been considerably reduced, through convertion into little-water-soluble matter by addition of an alkaline agent and filtration thereafter. Therefore loading on the electrodes can be minimized, metals to deposit on the electrodes can be minimized, lowering of electrolytic efficiency can be prevented, and further, necessity to remove radioactive metals, which is dangerous to handle, from the electrodes can be minimized. The alkaline agent which is added prior to electrolysis in order to decrease radioactive metal ions through conversion into matter poorly soluble in water and filtration thereafter serves to increase electrical conductivity of the electrolytic solution, and therefore realizes quite effective electrolysis. This may be well understood from the fact that electrical conductivity of the chelating solution and/or the organic acid is low before the treatment. Furthermore, it is available in the invention to collect most of radioactive metal ions through formation of matter poorly soluble in water by alkaline treatment combined with the electrolytic treatment. Further, it is available in the invention to collect almost all of radioactive metal ions by additional ultraviolet irradiation treatment and separation step. Furthermore, it is available in the invention to collect radioactive metal ions almost completely because an additional separation device is that by use of reverse osmosis or ion-exchange resin.
	summary
	claims	1. A charged beam exposure apparatus comprising: a charged beam generating source; a first flat board which has a plurality of first aperture sections having rectangular apertures arranged close to one another and electrodes for deflecting the beam passing through the first aperture sections at the respective apertures; and a second flat board which is arranged parallel with said first flat board and has second aperture sections having basic figure apertures for shaping the beam, which passes or passed through the first aperture sections, wherein a ratio of a width of the first aperture sections to an interval between the first aperture sections is larger than a ratio of a width of the second aperture sections to an interval between the second aperture sections. 2. The charged beam exposure apparatus as in claim 1 , further comprising: claim 1 a first deflector to emit the beam passed through the first aperture sections to the second aperture section; a second deflector to emit the beam passed through the second aperture section to an arbitrary position of a sample; and a lens to image the beam passed through the second aperture section onto the sample. 3. The charged beam exposure apparatus as in claim 1 , wherein the first aperture sections are arranged cyclically. claim 1 4. The charged beam exposure apparatus as in claim 1 , wherein said first flat board has the aperture sections and the electrodes according to LSI wiring pitches. claim 1 5. The charged beam exposure apparatus as in claim 1 , wherein said second flat board has the basic figures according to LSI wiring pitches. claim 1 6. The charged beam exposure apparatus as in claim 1 , wherein a form of the apertures of the second aperture sections has linear wiring patterns in vertical and horizontal directions. claim 1 7. The charged beam exposure apparatus as in claim 6 , wherein a form of the apertures of the second aperture sections further has a connection pattern which connects vertical and horizontal wirings. claim 6 8. The charged beam exposure apparatus as in claim 1 , wherein a form of the apertures of the second aperture sections has a linear wiring pattern in a direction where a vertical direction and a horizontal direction do not form a right angle. claim 1 9. The charged beam exposure apparatus as in claim 1 , wherein a form of the apertures of the second aperture sections has a standard cell pattern. claim 1 10. The charged beam exposure apparatus as in claim 1 , wherein the second aperture sections comprises: claim 1 first slits which are arranged parallel with vertical sides of the rectangles and opposed to one another with equal intervals; and second slits which are arranged parallel with horizontal sides of the rectangles and opposed to one another with equal intervals. 11. The charged beam exposure apparatus as in claim 10 , wherein lengths of the first slits are equal, and both end portions are arranged on a line, and their number is the same as a number of lines of the first aperture sections, the first aperture sections being arranged cyclically. claim 10 12. The charged beam exposure apparatus as in claim 10 , wherein lengths of the second slits are equal, and both end portions are arranged on a line, and their number is the same as a number of rows of the first aperture sections, the first aperture sections being arranged cyclically. claim 10
	description	This application is a national phase application of International Application No. PCT/EP2011/058926, filed May 31, 2011, designating the United States and claiming priority to European Patent Application No. 10164664.4, filed Jun. 1, 2010, which is incorporated by reference herein. The present invention relates to an apparatus for producing a radioisotope by irradiating a target fluid comprising a precursor of said radioisotope with a particle beam produced by a particle accelerator. More particularly, the present invention relates to an apparatus comprising means for an improved maintenance, and a method of maintenance of said apparatus. Radioisotopes used for medicine are generally produced by irradiation of a precursor of radioisotope by a particle beam. The particle beam is produced by a particle accelerator, generally a linear accelerator or a cyclotron able to produce a beam in an energy range of 10 to 50 MeV. When the precursor is under liquid or gaseous state, the precursor is comprised into a housing forming a target cavity, the housing having an opening which is closed by a metal foil. The metal foil is generally made of Havar, Molybdenum or Niobium and has a thickness from about ten to about hundred micrometers for supporting the thermal and mechanical stress and allowing the passage of the particle beam to reach the inside of the cavity with sufficient energy for initiating nuclear reactions with the precursor. The metal foil is advantageously comprised between the said target cavity and a cooling cavity in which is able to flow a cooling fluid directed towards the said metal foil. The cooling cavity is closed by a second foil made of any metal separating the cooling cavity from the vacuum of the particle accelerator. Document WO2000019787 describes a target body having parts fitting with the exit of a particle accelerator, the target body comprising three target body portions: a first target body portion having a target cavity comprising the precursor of the radioisotope; a second target body portion comprising a cooling cavity closed by two metallic foils, said second target body portion in which flows a cooling fluid directed towards the said metallic foils, a first foil separating the said cooling cavity from the said target cavity, and a second foil in contact with a third target body portion; a third target body portion having a cavity under vacuum, said third target body portion fitting with the particle accelerator, the cavity of the third target body portion being separated from the cooling cavity by the said second foil.The said first, second and third target body portions are screwed together by means of bolts. In case of any leakage, for example after the breaking of a metallic foil, the user has to dismantle a lot of parts of the target body for changing the broken window while an important loss of precursor gas and radioisotope occurs. During the exchange of the said foil, the user is exposed to radiations coming from the produced radioisotope and from activated parts of the target body such as the metallic foils. Such operation is time consuming and usually need long cooling down time of the target for decay of the by-product. An apparatus named Kipros 120, for producing iodine-123 by irradiating 124-Xe with an accelerated proton beam, is manufactured and provided by ZAG Zyklotron AG, Hermann-von-Helmoltz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany. Said apparatus comprises a target housing having an opening for allowing the passage of the particle beam and comprising gaseous 124-Xe as radioisotope precursor, a dual foil flange for closing the opening of the said target housing, and a rotatable robot arm for positioning the said dual foil flange in an in-line position in front of the opening of the target housing. A dual foil flange is an appellation for a device comprising two irradiation foils able to allow the passage of a particle beam, a first and a second foil being located respectively on a first and a second side of a hollowed standoff, said first and second foil covering the hole of the standoff and forming a cooling cavity. The said first and second foils are maintained on the said standoff respectively by a first and a second flange. The dual foil flange further comprises an inlet channel for bringing a cooling fluid into said cooling cavity and an outlet channel for the evacuation of the said cooling fluid outside of the said cooling cavity. In the said apparatus named Kipros 120, the inlet and outlet channels are located on the said standoff. Flexible cooling gas pipelines, for flowing a cooling gas through the said cooling cavity, are fixed on the branches of said robot arm. The branches of said robot arm are actuated by means of an air-compressed system for clutching the standoff of said dual foil flange or for releasing the dual foil flange. The said robot arm is rotatable around an axis parallel to the axis of the particle beam for bringing the said dual foil flange from a first loading position to a in-line position in front of the target cavity and from said in-line position to a third position wherein the branches of the robot arm release the said dual foil flange into a shielded box. After the releasing of the dual foil flange, the robot arm returns to its initial loading position. In case of a production run of a radioisotope, if a window foil gets broken, a cryogenic system traps the target fluid and the dual foil flange is evacuated to said shielded box. Then a user has to enter into the room comprising the apparatus for replacing a new dual foil flange into the branches of the robot arm of said apparatus. The replacement of an irradiation foil is faster with such an apparatus since no part has to be dismantled manually. Nevertheless, a first drawback is that the user has to enter in an unsafe high radiation area enclosing the said apparatus, comprising an amount of produced radioisotope in the target or trap. A second drawback is that the time during which the user replaces a dual foil flange is still time consuming. A third drawback is that the said robot arm of the apparatus is a complicated and encumbered device comprising: an air-compressed system comprising two flexible gas ducts adapted to maintain a pressure on the said branches for maintaining the dual foil flange and; the said flexible cooling pipelines.Flexible ducts and pipelines are subject to move and are submitted to some mechanicals constraints. Therefore some leaks could occur in those pieces during the use of the apparatus. These flexible ducts and pipeline are not easily accessible and the detection and reparation of a leak in the apparatus is also time-consuming. It is an object of our invention to provide an apparatus for producing a radioisotope wherein the maintenance of a dual foil flange is safer. It is a further object of our invention to provide an apparatus wherein the maintenance of a dual foil flange is faster than in the apparatuses of the prior art. It is a further object of our invention to provide an apparatus for producing a radioisotope having simplified means for changing a dual foil flange avoiding down time in production. According to a first aspect, the invention relates to an apparatus for producing a radioisotope by irradiating a target fluid comprising a precursor of said radioisotope with a particle beam produced by a particle accelerator, the apparatus comprising: a housing comprising a target cavity for receiving said target fluid, said housing having an opening for allowing the passage of the said particle beam into the said cavity; a dual foil flange for closing said opening of the target cavity, said dual foil flange comprising: a standoff comprising a central hole; a first and a second foil able to allow the passage of the said particle beam and located respectively on a first side and a second side of the said standoff, covering the said central hole and forming a cooling cavity; a first flange and a second flange for sealing respectively the said first and second foil on said standoff; at least an inlet channel and at least an outlet channel, for flowing a cooling fluid through the cavity of the dual foil flange; guiding means for positioning said dual foil flange in an in-line position in which a said foil is facing said opening of said housing;the apparatus being characterized in that the said guiding means are adapted to transfer said dual foil flange through a translation movement, from a stand-by position to the said in-line position. In a preferred embodiment of the invention, said guiding means are adapted to evacuate a defective or dated dual foil flange through translation movements towards a discard position. Preferably, said guiding means comprise parallel elongated parts in which a dual foil flange is able to slide. Advantageously, the apparatus comprises means for moving the said housing following a direction parallel to the axis of the particle beam, said means for moving the said housing being able to position the said housing in two positions: a first position wherein the said opening of the housing is at a distance from the beam exit of the particle accelerator larger than the longitudinal length of the said dual foil flange, in order to have a space for inserting said dual foil flange in the said in-line position or for evacuating said dual foil flange from said in-line position; a second position wherein the said housing presses the said dual foil flange against the said beam exit of the particle accelerator. Preferably, said means for moving the said housing comprise a lever being maintained at rest by a spring and being actionable by a piston able to exert a force opposite to the force exerted by the spring, in order to induce a movement on the said housing for retracting the said housing from the beam exit of the particle accelerator or from the said dual foil flange. Preferably, said guiding means comprise means for moving the said parallel elongated parts following a direction parallel to the axis of the particle beam for providing a first space between said dual foil flange and the said beam exit of the particle accelerator and a second space between said dual foil flange and the opening of the said housing, when said housing is positioned at said first location. Preferably, said inlet and outlet of the said dual foil flange have their first extremity located on a flange and their second extremity located on the standoff, said second extremities being directed towards the inside of the said cooling cavity. Advantageously, the apparatus comprises a first fixed gas pipeline having a fixed extremity connectable with the extremity of the said inlet channel of said dual foil flange and a second fixed gas pipeline connectable with the extremity of the said outlet channel of the said dual foil flange for flowing the said cooling fluid inside the said cooling cavity when said dual foil flange is compressed between said beam exit of the particle accelerator and the said opening of the housing. Advantageously, the apparatus comprises a charger having the capacity for containing at least one dual foil flange and able to position the said dual foil flange into the said parallel elongated parts. Advantageously, the apparatus comprises monitoring means able to detect any leakage. More advantageously, the apparatus comprises means for trapping the said target fluid in case of any detection of a leakage by the said monitoring means. Preferably, the apparatus comprises a program able to start in case of any leakage detected by the said monitoring means, said program being adapted for performing the steps of: actuating the said means for trapping the said target fluid; when the said target fluid is trapped, transferring the said dual foil flange to the said discard position; transferring a new dual foil flange from the said stand-by position to the said in-line position. A second aspect of the present invention relates to a dual foil flange for closing the opening of a housing destined to contain a fluid comprising a precursor of radioisotope, said dual foil flange comprising: a standoff comprising a central hole; a first and a second foil able to allow the passage of a particle beam, located respectively on a first and a second side of the said standoff, covering the said central hole and forming a cooling cavity; a first flange and a second flange for sealing respectively the said first and second foil on said standoff; an inlet channel and an outlet channel for flowing a cooling fluid through the said cooling cavity;characterized in that the said inlet and outlet channels have their first extremity located on a flange and their second extremity located on the said standoff, said second extremities being directed towards the inside of the cooling cavity. The invention also relates to a method for replacing a dual foil flange closing the opening of a housing comprising a target material, comprising the steps of: Trapping the said target fluid; Evacuating the said dual foil flange from its position closing the said opening of the housing to a storage position; Transferring another dual foil flange from another storage position to the said position closing the said opening of the housing;characterized in that the said method is fully automated. Advantageously, said dual foil flanges are evacuated or transferred using a gravity effect. Preferably, the method according to the invention uses a dual foil flange an apparatus as detailed hereabove. FIG. 1 shows a three-dimensional view of an apparatus 100 for producing a radioisotope by irradiating a target fluid comprising a precursor of said radioisotope with a particle beam 102 produced by a particle accelerator. FIG. 2 shows a cross sectional view along the axis of the particle beam 102 of some parts of the apparatus of our invention. The apparatus of our invention comprises: a housing 104 enclosing a target cavity 105 for receiving said target fluid, said housing 104 having an opening 106 for allowing the passage of the said particle beam 102 into the said cavity 105; a dual foil flange 107 for closing said opening 106 of the cavity, guiding means for positioning said dual foil flange 107 in an in-line position 117 between said opening 106 of said housing 104 and the beam exit 118 of the particle accelerator. FIG. 3 shows a cross sectional view of a dual foil flange 107 for use in the apparatus of our invention. Said dual foil flange comprises: a standoff 108 comprising a central hole; a first and a second foil 109, 110 able to allow the passage of a particle beam 102, located respectively on a first and a second side of the said standoff 108, covering the said central hole and forming a cooling cavity 103; a first flange 111 and a second flange 111′ for sealing respectively the said first and second foil 109, 110 on said standoff; an inlet channel 112 and an outlet channel 113, for flowing a cooling fluid through the said cooling cavity 103.The said dual foil flange 107 is characterized in that the said inlet channel 112 and outlet channels 113 have a first extremity respectively 130, 131 located on a flange 111 and/or 111′ and at least another extremity respectively 132, 133 located on the standoff 108 and directed through the inside of the cooling cavity 103. FIG. 4 shows a view in the direction of arrow A of FIG. 2 of a first dual foil flange 107 and a second dual foil flange 107′ into the said guiding means. Said guiding means are adapted for transferring said dual foil flanges 107, 107′ through translation movements from a stand-by position 116 to an in-line position 117 and from said in-line position 117 to a discard position 128. Said guiding means comprises parallel elongated parts 114 in which a dual foil flange 107 is able to slide. Said guiding means further comprises actionable blocking means 134′, for blocking a dual foil flange 107′ in said stand-by position 116 and blocking means 134 for blocking a dual foil flange 107 into said in-line position 117. In an embodiment of our invention, the said dual foil flange comprises notches 135 for allowing the said blocking means 134, 134′ to maintain the said dual foil flange 107, 107′. Various means for blocking said dual foil flange 107, 107′ may be easily realized by a man skilled in the art. Said guiding means are adapted to evacuate a defective or dated dual foil flange through translation movements towards a discard position 128, advantageously into a shielded enclosure. The apparatus of our invention further comprises a means for moving the said housing 104 following a direction parallel to the axis of the said particle beam 102. Said means for moving the said housing 104 is able to position the said housing 104 in two positions: a first position (actuated position) as shown on FIG. 6, wherein the said opening 106 of the housing 104 is at a distance from the beam exit 118 of the particle accelerator, said distance being longer than the longitudinal length 144 of the dual foil flange 107, in order to have sufficient space to insert said dual foil flange 107 in the said in-line position 117 or to evacuate said dual foil flange from said in-line position 117 to said discard position 128; a second position (rest position) as shown on FIG. 5, wherein the said housing 104 presses the said dual foil flange 107 against the said beam exit 118 of the particle accelerator. Said means for moving the said housing may comprise for example a piston located backwards the said housing, following the arrow A of FIG. 2. FIG. 5 shows an embodiment of our invention wherein said means for moving the said housing comprises a lever 121 being maintained at rest by a spring 122 and being actionable by a piston 123. Said piston 123 is able to exert a force opposite to the force exerted by the spring 122, in order to induce a movement on the said housing 104 for retracting the said housing 104 from the said dual foil flange 107. Both said spring 122 and said piston 123 are fixed near the extremity of the said lever 121. Said lever 121 has a main elongated part 141 having a longitudinal axis 138 inclined respect to the longitudinal axis 140 of the housing 104, and a shorter part 142 comprising a pivot 120 and having a longitudinal axis 139 perpendicular to the longitudinal axis 140 of the housing 104. The housing 104 comprises a member 119 able to slide between two abutments 136. Said member 119 comprises a notch 137 in which is inserted the said smaller part 142 of the lever 121. FIG. 6 shows an enlarged view of the said smaller part 142 of the lever 121 and the said member 119 in a configuration in which the lever 121 is actuated by the said piston 123. The said longitudinal axis 139 of the said smaller part 142 of the lever 121 makes an angle of less than 90° with the axis of the said housing, retracting the said housing 104 from the said dual foil flange 107. Said guiding means comprises means for moving the said parallel elongated parts 114 in the direction of the axis of the particle beam. When the said housing is in the said first position (actuated position), said parallel elongated parts 114 are located in a manner that a first side of the said dual foil flange is separated from the said beam exit 118 of the particle accelerator and the second side of the said dual foil flange is separated from the opening of the housing, in order that the insertion in the said in-line position or the evacuation from said in-line position of a dual foil flange is facilitated. When the housing 104 is in the second position (rest position), pressing the said dual foil flange, the said parallel elongated members 114 are moved towards the said beam exit 118 of the particle accelerator, in a manner that the said dual foil flange 107 is tightly compressed between the said housing 104 and the said beam exit 118 of the particle accelerator. For example, said means for moving the said elongated parts 114 may comprise a motor moving the said parallel elongated parts 114 following both direction along the axis of the particle beam 102, or may comprise a spring 115 having a first extremity fixed on said parallel elongated parts 114 and a second extremity fixed in a plan parallel to the said beam exit 118 of the particle accelerator. Referring to FIGS. 2, 3 and 4, the apparatus of our invention further comprises a first fixed gas pipeline 124 having a fixed extremity 143 connectable with the extremity 130 of the inlet channel 112 of the said dual foil flange, and a second fixed gas pipeline 124′ having a fixed extremity 143′ connectable with the extremity 131 of the outlet channel 113 of the said dual foil flange 107. Said fixed gas pipelines 124, 124′ provide a flow of cooling fluid inside said cooling cavity 103 when said dual foil flange is compressed between said beam exit 118 of the particle accelerator and said opening 106 of the housing 104. Advantageously, said fixed connections 143 are located on a surface in the plan of said beam exit 118 of the particle accelerator, in a manner that the compression of the dual foil flange 107 between the said housing 104 and the said beam exit 118, provides a tight sealing between the extremities 143, 143′ of the fixed gas pipelines 124, 124′ with the extremities 130, 131 of the inlet and outlet channels of the dual foil flange 107. The apparatus of our invention further comprises a charger 125 having the capacity for containing at least one dual foil flange 107′ in a stand-by position 116. Said charger 125 is able to position the said dual foil flange 107 into the said parallel elongated parts 114. Advantageously, said charger comprises the said elongated parts 114 and the said actionable blocking means 134′, for blocking a dual foil flange 107′ into said stand-by position 116. Referring to FIGS. 2 and 3, the apparatus of our invention further comprises monitoring means 126 able to detect any leakage. Said monitoring means 126 may be a pressure controller or a radiation monitor connected to the cooling cavity 103 of the dual foil flange and/or to the target cavity 105 of the housing 104. Advantageously, both a pressure controller and a radiation monitor are used as monitoring means. The apparatus of our invention further comprises means for trapping 127 the target fluid comprised into the target cavity 105 of the housing 104. Said means for trapping 127 is actionable in case of any leakage detected by the said monitoring means 126, in order to avoid the dispersion of precursor and radioisotope in the apparatus and the atmosphere. The apparatus of our invention further comprises a program able to start in case of any leakage detected by the said monitoring means 126. Said program is adapted for performing the steps of: actuating the said means for trapping 127 the said target fluid; when the when the said target fluid is trapped, transferring the said dual foil flange 107 to the said discard position 128; transferring a new dual foil flange 107 from the said stand-by position to the said in-line position. A first dual foil flange 107 is located in the said stand-by position 116 in a charger 125. In a first step, the means for moving the said housing 104 is actuated in order to retract the said housing 104 from the said beam exit 118 of the particle accelerator. Said parallel elongated parts 114 are maintained separated from the said beam exit 118 of the particle accelerator by a spring 115. In a second step, the said blocking means 134′ blocking said dual foil flange 107′ into said stand-by position 116 are deactivated while the said blocking means 134 for blocking said dual foil flange 107 into the said in-line position 117 are actuated. Said dual foil flange 107 slides into the said parallel elongated members 114 and falls down in the said in-line position by gravity. In a third step, said means for moving the said housing 104 is deactivated in order to press the said housing 104 against the said dual foil flange 107, pressing in the same time the said dual foil flange 107 against the beam exit 118 of the particle accelerator. In this configuration, both extremities 130, 131 of respectively the inlet channel 112 and the outlet channel 113, located on the flange 111 are connected to the said fixed gas connections 143, 143′. Then, said apparatus is ready for flowing a cooling fluid through the cooling cavity 103 of the dual foil flange and for the introduction of a target fluid into the target cavity 105 of the housing 104. Advantageously, a second dual foil flange 107′ is positioned into said charger 125. Advantageously, the said target fluid is in gaseous state and comprises a precursor of a radioisotope. For example, said target fluid may be 124-Xe for the production of 123-I by proton irradiation or 18-O for the production of 18-F by proton irradiation. A cooling fluid, for example helium, is able to flow through the cooling cavity of said dual foil flange 107, cooling the irradiation foils 109, 110 when they are submitted to the irradiation by the particle beam 102. During a production run of radioisotope, if a monitoring means 126 detects a leakage coming from the dual foil flange 107, the means for trapping 127 the target fluid are actuated. Said means for trapping 127 the target fluid comprises for example a cryopump or storage vessel. Then, the means for moving the housing 104 are actuated in order to retract the said housing 104 from the said dual foil flange 107. Said spring 115 moves away the said parallel elongated members 114 from the beam exit 118 of the particle accelerator in order that the said dual foil flange 107 is separated from the said beam exit 118 and from the opening 106 of the housing 104. The said blocking means 134 maintaining the dual foil flange 107 into the said in-line position 117 are deactivated and the damaged dual foil flange falls down into a discard position 128, advantageously into a shielded enclosure. The said second dual foil flange 107′ already located into the said charger 125 is ready to be positioned in the in-line position in the same manner as the used first dual foil flange 107. When the said second dual foil flange 107′ is in a ready position for restarting the production run of radioisotope, the trapping means reintroduces the trapped target fluid from the cryopump or storage vessel to the target cavity 105 of the housing 104. Then, the production run can restart. The user can also choose a program for changing a dual foil flange periodically in order to avoid that a leakage in the dual foil flange occurs. The apparatus of our invention provides some advantages respect to the prior art. Firstly the maintenance of the apparatus is improved since the method for replacing a dual foil flange is fully automated and does not require any manual intervention of the user. For that reason, said apparatus is safer for the user since he does not need to enter anymore in the high radiation area room enclosing the apparatus. The user is thus less susceptible to be submitted to radiations. A second advantage is that the method provided by the apparatus for replacing a dual foil flange is fast due to the simplification of the guiding means for positioning the dual foil flange in the said in-line position. The time for changing a dual foil flange is also reduced due to the fully automation of the method. Finally, the guiding means and cooling means for a dual foil flange are simplified and does not comprises any flexible gas pipelines. The dual foil flange is safely maintained into the said in-line position with the inlet and outlet channels tightly connected to fixed gas connections for flowing a cooling fluid though said dual foil flange.
	abstract	A method to determine a global core reactivity bias and the corresponding estimated critical conditions of a nuclear reactor core prior to achieving reactor criticality. The method first requires collection and evaluation of the inverse count rate ratio (ICRR) data; specifically, fitting measured ICRR vs. predicted ICRR data. The global core reactivity bias is then determined as the amount of uniform reactivity adjustment to the prediction that produces an ideal comparison between the measurement and the prediction.
	claims	1. A nuclear reactor including: a nuclear reactor vessel containing a body of coolant liquid defining a coolant liquid surface therein, a guard vessel spaced from said nuclear reactor vessel to form an annulus space therebetween, and a thermal load reducing system for controlling thermal stresses in said nuclear reactor vessel comprising: partition members disposed in said annulus space at a position above the surface of the coolant liquid body in said reactor vessel, means for circulating a low temperature gas via the annulus space and above the partition members to cool down the adjacent reactor vessel wall disposed above said coolant liquid surface, and means for circulating a higher temperature gas via the annulus space from a level lower than the surface of the coolant liquid body to the partition members for raising the temperature of the reactor vessel wall disposed below the surface of the coolant liquid body within the reactor vessel. 2. The thermal load reducing system in a nuclear reactor vessel according to claim 1 , wherein said low-temperature gas is circulated at a constant flow velocity during normal operation of said nuclear reactor, and said high-temperature gas is circulated only during starting operation of said nuclear reactor. claim 1
	abstract	Method of optimizing output of sensor for indicating location of metallic object. Sensor having primary electromagnetic coil to generate time varying magnetic field; secondary electromagnetic coil to detect time varying magnetic field as affected, by object to output, on basis of detected time varying magnetic field, signal indicative of location of object. Method includes steps of: supplying primary coil with alternating-current to result generated time varying magnetic field; locating object in first-position and recording signal output by secondary electromagnetic coil for range of frequencies of supplied alternating-current; locating object in second-position and recording signal output by secondary electromagnetic coil for range of frequencies of supplied alternating-current; calculating, for each of frequencies, a value for span to offset ratio of measured signals on basis of respective signals measured for object in first and second positions; determining frequency of supplied alternating-current which provides maximum span to offset ratio on basis of calculations.
	abstract	A collimator is provided with an adjustable focal length, particularly in X-ray testing systems, comprising an outer part with a conical inner surface and with a inner part having an conical outer surface, which are connected to one another at a fixed distance, as well as with at least one cone sliding part situated between the inner part and outer part in a manner that enables it to move.
	abstract	Methods of producing and isolating 68Ga, 89Zr, 64Cu, 63Zn, 86Y, 61Cu, 99mTc, 45Ti, 13N, 52Mn, or 44Sc and solution targets for use in the methods are disclosed. The methods of producing 68Ga, 89Zr, 64Cu, 63Zn, 86Y, 61Cu, 99mTc, 45Ti, 13N, 52Mn, or 44Sc include irradiating a closed target system with a proton beam. The closed target system can include a solution target. The methods of producing isolated 68Ga, 89Zr, 64Cu, 63Zn, 86Y, 61CU, 99mTC, 45-Ti, 52Mn, or 44Sc by ion exchange chromatography. An example solution target includes a target body including a target cavity for receiving the target material; a housing defining a passageway for directing a particle beam at the target cavity; a target window for covering an opening of the target cavity; and a coolant gas flow path disposed in the passageway upstream of the target window.
046718982	summary	TECHNICAL AREA The present invention relates to a process for the treatment of a spent, radioactive, organic ion exchange resin to reduce the volume thereof and to obtain a stable final product. In the context ion exchange resin primarily means a cationic exchange resin but also an anionic exchange resin and an exchange resin of the mixed bed type, containing cation exchanger as well as anion exchanger, can be advantageously treated in accordance with the invention. The invention primarily relates to the treatment of such ion exchange resins which have been utilized to purify cooling water in a nuclear reactor, and the water in a pool for the storage of spent nuclear fuel. TECHNICAL BACKGROUND It is previously known to solidify a spent ion exchange resin in cement or bitumen. However, by such a measure the volume is heavily increased. Furthermore, in the case of solidification in cement, the stability against leaching is not very good. In the case of solidification in bitumen the fire hazards thereof is a problem. Moreover, it is previously known, for instance from Swedish patent specification No. 8101801-2, that the volume of a spent ion exchange resin can be reduced by an incineration thereof. According to said Swedish patent specification the incineration residue is then heated to sintering or melting, a stable product being obtained thereby. The measure of cementing the incineration residue has been considered improper due to the bad stability against leaching which has been observed when solidifying a non-incinerated ion exchange resin in cement.
050770004	summary	CROSS REFERENCE TO RELATED APPLICATIONS Reference is hereby made to the following copending applications dealing with related subject matter and assigned to the assignee of the present invention: 1. "Sealing Devices For The Drive Shaft Of A High Pressure Fluid Pump" by N. Bonhomme, assigned U.S. Ser. No. 379,196 and filed May 17, 1982, now U.S. Pat. No. 4,587,076, issued May 6, 1986. 2. "Nuclear Reactor Coolant Pump Impeller/Shaft Assembly" by L. S. Jenkins, assigned U.S. Ser. No. 761,447 and filed Aug. 1, 1985, now U.S. Pat. No. 4,690,612, issued Sept. 1, 1987. 3. "Improved Shaft Seal" by K. P. Quinn, assigned U.S. Ser. No. 739,745 and filed May 31, 1985, now U.S. Pat. No. 4,693,481, issued Sept. 15, 1987. 4. "Reactor Coolant Pump Hydrostatic Sealing Assembly With Improved Hydraulic Balance" by R. F. Guardiani et al, assigned U.S. Ser. No. 063,331 and filed June 17, 1987, now U.S. Pat. No. 4,838,559, issued June 13, 1989. 5. "Reactor Coolant Pump Sealing Surface With Titanium Nitride Coating" by G. Zottola, assigned U.S. Ser. No. 035,832 and filed Apr. 8, 1987, now U.S. Pat. No. 4,871,297, issued Oct. 3, 1989. 6. "Reactor Coolant Pump Hydrostatic Sealing Assembly With Externally Pressurized Hydraulic Balance Chamber" by R. F. Guardiani, assigned U. S. Ser. No. 091,224 and filed Aug. 31, 1987, now U.S. Pat. No. 4,848,774, issued July 18, 1989. 7. "Reactor Coolant Pump Shaft Seal Utilizing Shape Memory Metal" by D. J. Janacko assigned U.S. Ser. No. 197,174 and filed May 23, 1988. 8. "Reactor Coolant Pump Auxiliary Seal For Reactor Coolant System Vacuum Degasification" by J. D. Fornof, assigned U.S. Ser. No. 222,649 and filed July 21, 1988. BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates generally to shaft seals and, more particularly, is concerned with a reactor coolant pump auxiliary flexible vacuum seal for reactor coolant system vacuum degasification. 2. Description of the Prior Art In pressurized water nuclear power plants, a reactor coolant system is used to transport heat from the reactor core to steam generators for the production of steam. The steam is then used to drive a turbine generator. The reactor coolant system includes a plurality of separate cooling loops, each connected to the reactor core and containing a steam generator and a reactor coolant pump. The reactor coolant pump typically is a vertical, single stage, centrifugal pump designed to move large volumes of reactor coolant at high temperatures and pressures, for example 550 degrees F. and 2500 psi. The pump basically includes three general sections from bottom to top--hydraulic, shaft seal and motor sections. The lower hydraulic section includes an impeller mounted on the lower end of a pump shaft which is operable within the pump casing to pump reactor coolant about the respective loop. The upper motor section includes a motor which is coupled to drive the pump shaft. The middle shaft seal section includes three tandem sealing assemblies--lower primary, middle secondary and upper tertiary sealing assemblies. The sealing assemblies are located concentric to, and near the top end of, the pump shaft. Their combined purpose is to mechanically contain the high positive pressure coolant of the reactor coolant system from leakage along the pump shaft to the containment atmosphere during normal operating condition. Representative examples of pump shaft sealing assemblies known in the prior art are the ones disclosed in U.S. Pat. Nos. to MacCrum (3,522,948), Singleton (3,529,838), Villasor (3,632,117), Andrews et al (3,720,222) and Boes (4,275,891) and in the first three patent applications cross-referenced above, all of which are assigned to the same assignee as the present invention. Thus, the sealing assemblies in the reactor coolant pumps are designed to hold high positive coolant pressures. This fact has raised some concerns about possibility of damage being done to the reactor coolant pumps during reactor coolant system vacuum degasification. Procedures for vacuum degasification of the reactor coolant system are described in U.S. Pat. No. 4,647,425 to Battaglia et al, which is assigned to the same assignee as the present invention and is hereby incorporated by reference. Basically, in vacuum degasification of the reactor coolant system a vacuum or negative pressure is imposed on the system and thus on the reactor coolant pumps. This, in effect, pressurizes the pumps in reverse. One major concern is that reverse pressurization might draw the water used to cool the pump sealing assemblies back into the pump sealing assemblies by a reverse flow of the water through filters which might bring contamination in the form of dirt and foreign matter along with the water from the filters into the sealing assemblies. Then, when the pumps are restarted after conclusion of vacuum degasification, the sealing assemblies may become damaged by the presence of the contamination therein. Consequently, a need exists for an effective way to prevent reverse pressurization of the reactor coolant pumps so as to eliminate these concerns about possible damage to the pump sealing assemblies. SUMMARY OF THE INVENTION The present invention provides a reactor coolant pump auxiliary flexible vacuum seal designed to satisfy the aforementioned needs. The auxiliary flexible vacuum seal of the present invention provides a simple and effective way to prepare the reactor coolant pumps so that the reactor coolant system can be vacuum degasified without applying a reverse pressure to the pump sealing assemblies. The auxiliary flexible vacuum seal is an external, temporary seal that would be installed prior to the start of vacuum degasification between the pump sealing housing and shaft, and then removed after degasification is completed. The auxiliary seal accepts the entire reverse pressure, thus preventing any possible damage to the primary, secondary and tertiary pump sealing assemblies of the pump. The auxiliary flexible vacuum seal of the present invention is an alternative to the invention illustrated and described in the eighth patent application cross-referenced above. The flexible vacuum seal offers several advantages over the rigid segmented seal of the cross-referenced application. First, the flexible seal is embodied primarily in the form of a single flexible split boot member with a pair of axially-spaced integral sealing portions, preferably in the form of ring elements, resulting in fewer parts to handle and less sealing length to be concerned with. Second, all parts of the flexible seal are disposable, thus minimizing decontamination and storage requirements. Third, the flexible seal is easier to manipulate within the limited space of the motor stand. Fourth, deviations in concentricity between the shaft and seal housing would be of no concern with the flexible seal. Fifth, the flexible seal fits with the shaft in either its axially-displaced coupled or uncoupled positions. Sixth, the flexible seal can be installed without the need to remove any of the parts of the pump other than some piping and associated coonections. Accordingly, the present invention is directed to an auxiliary flexible vacuum seal useful in a reactor coolant pump ,for preparing the pump for vacuum degasification of the reactor coolant system. The flexible vacuum seal comprises: (a) a flexible boot member having a pair of longitudinally-displaced opposite open end portions and a pair of side-by-side longitudinally-extending side portions defining a split in the boot member along a side thereof and extending between the open end portions for allowing flexing of the boot member between open and closed side configurations to permit its installation and removal on and from the pump; (b) means for releasably and sealably clamping together the side portions of the at the split to retain the boot member in its closed configuration; and (c) a pair of circumferentially-extending sealably portions on the interior of the boot member at the opposite open end portions thereof for sealably engaging the pump when the boot member is installed and flexed to its closed configuration to thereby permit generation of a vacuum seal condition between the boot member and the pump. Further, the flexible seal includes a boot support member disposable within the boot member between the boot member and the pump for supporting the boot member when in its closed configuration. More particularly, the boot support member is annular in shape and composed of a pair of semi-annular parts. The support member also has an upper surface conformed in shape to that of an intermediate portion of the boot member located between its opposite end portions for engagably supporting the boot member at its intermediate portion. Further, the boot support member has a lower surface conformed in shape to that of the pump for mounting the support member thereon. The boot member of the flexible seal includes a bowl-shaped body having the opposite end portions and defining a hollow cavity. The cavity is open at the opposite end portions and openable at the split defined in the body by the side portions of the boot member. The sealably engaging portions on the boot member at the opposite open end portions thereof are preferably rings projecting radially inwardly and formed integrally on the body of the boot member. In the alternative, these sealably engaging portions may be the interior surface of the boot member itself at its opposite open end portions. The side portions of the boot member are in the form of a pair of radially outward-projecting and longitudinally-extending flanges on the body along opposite sides of the split and disposed in side-by-side contacting relation when the boot member is in its closed configuration. The clamping means of the flexible seal includes a pair of brackets mountable along outer sides of said flanges on the boot member body, and a plurality of fasteners extendible through the brackets and flanges therebetween and being operable for drawing the brackets toward one another and withdrawing the brackets away from one another for clamping and releasing the flanges. The present invention is also directed to a method of preparing a reactor coolant pump for vacuum degasification of a reactor coolant system. The preparing method comprises the steps of: (a) sealing a seal housing of the reactor coolant pump by installing a longitudinally split boot member about a portion of the seal housing and about a shaft extending through the housing; (b) reversing the pressure of the reactor coolant system at start of vacuum degasification of the reactor coolant system, the sealing of the pump seal housing preventing damage to sealing assemblies therein by the reversing of reactor coolant system pressure; (c) terminating reversing of the reactor coolant system pressure at completion of vacuum degasification of the reactor coolant system; and (d) unsealing the pump seal housing of the reactor coolant pump by removing the split boot member. Further, the sealing includes stretching the split boot member. These and other features and advantages of the present invention will become apparent to those skilled in the art upon a reading of the following detailed description when taken in conjunction with the drawings wherein there is shown and described an illustrative embodiment of the invention.
	abstract	An apparatus for use in the field of dentistry consisting of a rotatable c-arm assembly having a housing with an emitter on one end and a fluoroscopic image receptor at another end, a control panel, three mechanical arms connecting the housing and the control panel to each other, an intraoral image receptor and a plastic holder device for the intraoral image receptor. The apparatus has the improved feature of having two modes of operation, a fluoroscopic mode or a conventional radiographic mode. The mode of operation is selected by the operator by a foot pedal for use in fluoroscopic mode, or a hand activator control for use in conventional mode. A beam of x-rays or gamma rays is emitted from the housing corresponding to the selected mode. The beam is incident on the fluoroscopic image receptor or on the intraoral image receptor and the image is converted to visible light, amplified and transmitted to a computer monitor and/or television set and VCR, thus allowing the observation of dental procedures in real time.
	description	This application: is a continuation-in-part of U.S. patent application Ser. No. 12/425,683 filed Apr. 17, 2009, now U.S. Pat. No. 7,939,809 which claims the benefit of: U.S. provisional patent application No. 61/055,395 filed May 22, 2008; U.S. provisional patent application No. 61/137,574 filed Aug. 1, 2008; U.S. provisional patent application No. 61/192,245 filed Sep. 17, 2008; U.S. provisional patent application No. 61/055,409 filed May 22, 2008; U.S. provisional patent application No. 61/203,308 filed Dec. 22, 2008; U.S. provisional patent application No. 61/188,407 filed Aug. 11, 2008; U.S. provisional patent application No. 61/188,406 filed Aug. 11, 2008; U.S. provisional patent application No. 61/189,815 filed Aug. 25, 2008; U.S. provisional patent application No. 61/201,731 filed Dec. 15, 2008; U.S. provisional patent application No. 61/205,362 filed Jan. 21, 2009; U.S. provisional patent application No. 61/134,717 filed Jul. 14, 2008; U.S. provisional patent application No. 61/134,707 filed Jul. 14, 2008; U.S. provisional patent application No. 61/201,732 filed Dec. 15, 2008; U.S. provisional patent application No. 61/198,509 filed Nov. 7, 2008; U.S. provisional patent application No. 61/134,718 filed Jul. 14, 2008; U.S. provisional patent application No. 61/190,613 filed Sep. 2, 2008; U.S. provisional patent application No. 61/191,043 filed Sep. 8, 2008; U.S. provisional patent application No. 61/192,237 filed Sep. 17, 2008; U.S. provisional patent application No. 61/201,728 filed Dec. 15, 2008; U.S. provisional patent application No. 61/190,546 filed Sep. 2, 2008; U.S. provisional patent application No. 61/189,017 filed Aug. 15, 2008; U.S. provisional patent application No. 61/198,248 filed Nov. 5, 2008; U.S. provisional patent application No. 61/198,508 filed Nov. 7, 2008; U.S. provisional patent application No. 61/197,971 filed Nov. 3, 2008; U.S. provisional patent application No. 61/199,405 filed Nov. 17, 2008; U.S. provisional patent application No. 61/199,403 filed Nov. 17, 2008; and U.S. provisional patent application No. 61/199,404 filed Nov. 17, 2008; claims the benefit of U.S. provisional patent application No. 61/209,529 filed Mar. 9, 2009; claims the benefit of U.S. provisional patent application No. 61/208,182 filed Feb. 23, 2009; claims the benefit of U.S. provisional patent application No. 61/208,971 filed Mar. 3, 2009; claims the benefit of U.S. provisional patent application No. 61/270,298, filed Jul. 7, 2009; and claims priority to PCT patent application serial No.: PCT/RU2009/00015, filed Mar. 4, 2009, all of which are incorporated herein in their entirety by this reference thereto. 1. Field of the Invention This invention relates generally to treatment of solid cancers. More particularly, the invention relates to an X-ray system synchronized to patient respiration, where the synchronized system is used in conjunction with charged particle cancer therapy beam injection, acceleration, extraction, and/or targeting methods and apparatus. 2. Discussion of the Prior Art Cancer Treatment Proton therapy systems typically include: a beam generator, an accelerator, and a beam transport system to move the resulting accelerated protons to a plurality of treatment rooms where the protons are delivered to a tumor in a patient's body. Proton therapy works by aiming energetic ionizing particles, such as protons accelerated with a particle accelerator, onto a target tumor. These particles damage the DNA of cells, ultimately causing their death. Cancerous cells, because of their high rate of division and their reduced ability to repair damaged DNA, are particularly vulnerable to attack on their DNA. Due to their relatively enormous size, protons scatter less easily than X-rays or gamma rays in the tissue and there is very little lateral dispersion. Hence, the proton beam stays focused on the tumor shape without much lateral damage to surrounding tissue. All protons of a given energy have a certain range, defined by the Bragg peak, and the dosage delivery to tissue ratio is maximum over just the last few millimeters of the particle's range. The penetration depth depends on the energy of the particles, which is directly related to the speed to which the particles were accelerated by the proton accelerator. The speed of the proton is adjustable to the maximum rating of the accelerator. It is therefore possible to focus the cell damage due to the proton beam at the very depth in the tissues where the tumor is situated. Tissues situated before the Bragg peak receive some reduced dose and tissues situated after the peak receive none. Patents related to the current invention are summarized here. Proton Beam Therapy System F. Cole, et. al. of Loma Linda University Medical Center “Multi-Station Proton Beam Therapy System”, U.S. Pat. No. 4,870,287 (Sep. 26, 1989) describe a proton beam therapy system for selectively generating and transporting proton beams from a single proton source and accelerator to a selected treatment room of a plurality of patient treatment rooms. Respiration K. Matsuda “Radioactive Beam Irradiation Method and Apparatus Taking Movement of the Irradiation Area Into Consideration”, U.S. Pat. No. 5,538,494 (Jul. 23, 1996) describes a method and apparatus that enables irradiation even in the case of a diseased part changing position due to physical activity, such as breathing and heart beat. Initially, a position change of a diseased body part and physical activity of the patient are measured concurrently and a relationship therebetween is defined as a function. Radiation therapy is performed in accordance to the function. Patient Positioning Y. Nagamine, et. al. “Patient Positioning Device and Patient Positioning Method”, U.S. Pat. No. 7,212,609 (May 1, 2007) and Y. Nagamine, et. al. “Patient Positioning Device and Patient Positioning Method”, U.S. Pat. No. 7,212,608 (May 1, 2007) describe a patient positioning system that compares a comparison area of a reference X-ray image and a current X-ray image of a current patient location using pattern matching. D. Miller, et. al. “Modular Patient Support System”, U.S. Pat. No. 7,173,265 (Feb. 6, 2007) describe a radiation treatment system having a patient support system that includes a modularly expandable patient pod and at least one immobilization device, such as a moldable foam cradle. K. Kato, et. al. “Multi-Leaf Collimator and Medical System Including Accelerator”, U.S. Pat. No. 6,931,100 (Aug. 16, 2005); K. Kato, et. al. “Multi-Leaf Collimator and Medical System Including Accelerator”, U.S. Pat. No. 6,823,045 (Nov. 23, 2004); K. Kato, et. al. “Multi-Leaf Collimator and Medical System Including Accelerator”, U.S. Pat. No. 6,819,743 (Nov. 16, 2004); and K. Kato, et. al. “Multi-Leaf Collimator and Medical System Including Accelerator”, U.S. Pat. No. 6,792,078 (Sep. 14, 2004) all describe a system of leaf plates used to shorten positioning time of a patient for irradiation therapy. Motor driving force is transmitted to a plurality of leaf plates at the same time through a pinion gear. The system also uses upper and lower air cylinders and upper and lower guides to position a patient. Computer Control A. Beloussov et. al. “Configuration Management and Retrieval System for Proton Beam Therapy System”, U.S. Pat. No. 7,368,740 (May 6, 2008); A. Beloussov et. al. “Configuration Management and Retrieval System for Proton Beam Therapy System”, U.S. Pat. No. 7,084,410 (Aug. 1, 2006); and A. Beloussov et. al. “Configuration Management and Retrieval System for Proton Beam Therapy System”, U.S. Pat. No. 6,822,244 (Nov. 23, 2004) all describe a multi-processor software controlled proton beam system having treatment configurable parameters that are easily modified by an authorized user to prepare the software controlled system for various modes of operation to insure that data and configuration parameters are accessible if single point failures occur in the database. J. Hirota et. al. “Automatically Operated Accelerator Using Obtained Operating Patterns”, U.S. Pat. No. 5,698,954 (Dec. 16, 1997) describes a main controller for determining the quantity of control and the control timing of every component of an accelerator body with the controls coming from an operating pattern. Problem There exists in the art of particle beam therapy of cancerous tumors a need for an X-ray system that is synchronized with patient respiration. Preferably, the synchronized system is used in conjunction with a negative ion beam source, synchrotron, and/or targeting method apparatus to provide an X-ray timed with patient respiration and performed immediately prior to and/or concurrently with particle beam therapy irradiation to ensure targeted and controlled delivery of energy relative to a patient position. Further, there exists a need in the art to control the charged particle cancer therapy system in terms of specified energy, intensity, and/or timing of charged particle delivery relative to a patient position. Still further, there exists a need for efficient, precise, and/or accurate noninvasive, in-vivo treatment of a solid cancerous tumor with minimization of damage to surrounding healthy tissue in a patient using the proton beam position verification system. The invention comprises an X-ray method and apparatus operating in conjunction with patient respiration monitoring. The invention relates generally to treatment of solid cancers. More particularly, the invention relates to an X-ray system capable of collecting X-rays of a patient (1) during a period of a respiration cycle and (2) in a positioning system for cancer therapy. Novel design features of a charged particle beam cancer therapy system are described. Particularly, a negative ion beam source with novel features in the negative ion source, ion source vacuum system, ion beam focusing lens, and tandem accelerator is described. Additionally, turning magnets, edge focusing magnets, magnetic field concentration magnets, winding and correction coils, flat magnetic field incident surfaces, and extraction elements are described that minimize the overall size of the synchrotron, provide a tightly controlled proton beam, directly reduce the size of required magnetic fields, directly reduce required operating power, and allow continual acceleration of protons in a synchrotron even during a process of extracting protons from the synchrotron. The ion beam source system and synchrotron are preferably computer integrated with a patient imaging system and a patient interface including respiration monitoring sensors and patient positioning elements. Further, intensity control of a charged particle beam acceleration, extraction, and/or targeting method and apparatus used in conjunction with charged particle beam radiation therapy of cancerous tumors are described. More particularly, intensity, energy, and timing control of a charged particle stream of a synchrotron is described. The synchrotron control elements allow tight control of the charged particle beam, which compliments the tight control of patient positioning to yield efficient treatment of a solid tumor with reduced tissue damage to surrounding healthy tissue. In addition, the system reduces the overall size of the synchrotron, provides a tightly controlled proton beam, directly reduces the size of required magnetic fields, directly reduces required operating power, and allows continual acceleration of protons in a synchrotron even during a process of extracting protons from the synchrotron. All of these systems are preferably used in conjunction with an X-ray system capable of collecting X-rays of a patient in (1) a positioning system for proton treatment and (2) at a specified moment of the patient's respiration cycle. In one embodiment, a treatment delivery control system (TDCS) or main controller is used to control multiple aspects of the cancer therapy system, including one or more of: an imaging system, such as a CT or PET; a positioner, such as a couch or patient interface module; an injector or injection system; a ring accelerator or synchrotron; an extraction system; an irradiation plan; and a display system. The TDCS is preferably a control system for automated cancer therapy once the patient is positioned. The TDCS integrates output of one or more of the above described cancer therapy system elements with inputs of one or more of the above described cancer therapy system elements. More generally, the TDCS controls or manages input and/or output of imaging, an irradiation plan, and charged particle delivery. Charged Particle Beam Therapy Throughout this document, a charged particle beam therapy system, such as a proton beam, hydrogen ion beam, or carbon ion beam, is described. Herein, the charged particle beam therapy system is described using a proton beam. However, the aspects taught and described in terms of a proton beam are not intended to be limiting to that of a proton beam and are illustrative of a charged particle beam system. Any of the techniques described herein are equally applicable to any charged particle system. Referring now to FIG. 1, a charged particle beam system 100 is illustrated. The charged particle beam preferably comprises a number of subsystems including any of: a main controller 110; an injection system 120; a synchrotron 130 that typically includes: (1) an accelerator system 132 and (2) an extraction system 134; a scanning/targeting/delivery system 140; a patient interface module 150; a display system 160; and/or an imaging system 170. An exemplary method of use of the charged particle beam system 100 is provided. The main controller 110 controls one or more of the subsystems to accurately and precisely deliver protons to a tumor of a patient. For example, the main controller 110 obtains an image, such as a portion of a body and/or of a tumor, from the imaging system 170. The main controller 110 also obtains position and/or timing information from the patient interface module 150. The main controller 110 then optionally controls the injection system 120 to inject a proton into a synchrotron 130. The synchrotron typically contains at least an accelerator system 132 and an extraction system 134. The main controller preferably controls the proton beam within the accelerator system, such as by controlling speed, trajectory, and timing of the proton beam. The main controller then controls extraction of a proton beam from the accelerator through the extraction system 134. For example, the controller controls timing, energy, and/or intensity of the extracted beam. The controller 110 also preferably controls targeting of the proton beam through the scanning/targeting/delivery system 140 to the patient interface module 150. One or more components of the patient interface module 150 are preferably controlled by the main controller 110. Further, display elements of the display system 160 are preferably controlled via the main controller 110. Displays, such as display screens, are typically provided to one or more operators and/or to one or more patients. In one embodiment, the main controller 110 times the delivery of the proton beam from all systems, such that protons are delivered in an optimal therapeutic manner to the patient. Herein, the main controller 110 refers to a single system controlling the charged particle beam system 100, to a single controller controlling a plurality of subsystems controlling the charged particle beam system 100, or to a plurality of individual controllers controlling one or more sub-systems of the charged particle beam system 100. Synchrotron Herein, the term synchrotron is used to refer to a system maintaining the charged particle beam in a circulating path. Further, the charged particle beam is referred to herein as circulating along a circulating path about a central point of the synchrotron. The circulating path is alternatively referred to as an orbiting path; however, the orbiting path does not refer to a perfect circle or ellipse, rather it refers to cycling of the protons around a central point or region. Referring now to FIG. 2, an illustrative exemplary embodiment of one version of the charged particle beam system 100 is provided. The number, position, and described type of components is illustrative and non-limiting in nature. In the illustrated embodiment, an injector system 210 or ion source or charged particle beam source generates protons. The protons are delivered into a vacuum tube that runs into, through, and out of the synchrotron. The generated protons are delivered along an initial path 262. Focusing magnets 230, such as quadrupole magnets or injection quadrupole magnets, are used to focus the proton beam path. A quadrupole magnet is a focusing magnet. An injector bending magnet 232 bends the proton beam toward the plane of the synchrotron 130. The focused protons having an initial energy are introduced into an injector magnet 240, which is preferably an injection Lamberson magnet. Typically, the initial beam path 262 is along an axis off of, such as above, a circulating plane of the synchrotron 130. The injector bending magnet 232 and injector magnet 240 combine to move the protons into the synchrotron 130. Main bending magnets 250 or dipole magnets or circulating magnets are used to turn the protons along a circulating beam path 264. A dipole magnet is a bending magnet. The main bending magnets 250 bend the initial beam path 262 into a circulating beam path 264. In this example, the main bending magnets 250 or circulating magnets are represented as four sets of four magnets to maintain the circulating beam path 264 into a stable circulating beam path. However, any number of magnets or sets of magnets are optionally used to move the protons around a single orbit in the circulation process. The protons pass through an accelerator 270. The accelerator accelerates the protons in the circulating beam path 264. As the protons are accelerated, the fields applied by the magnets are increased. Particularly, the speed of the protons achieved by the accelerator 270 are synchronized with magnetic fields of the main bending magnets 250 or circulating magnets to maintain stable circulation of the protons about a central point or region 280 of the synchrotron. At separate points in time the accelerator 270/main bending magnet 250 combination is used to accelerate and/or decelerate the circulating protons while maintaining the protons in the circulating path or orbit. An extraction element of the inflector/deflector system 290 is used in combination with a Lamberson extraction magnet 292 to remove protons from their circulating beam path 264 within the synchrotron 130. One example of a deflector component is a Lamberson magnet. Typically the deflector moves the protons from the circulating plane to an axis off of the circulating plane, such as above the circulating plane. Extracted protons are preferably directed and/or focused using an extraction bending magnet 237 and extraction focusing magnets 235, such as quadrupole magnets along a transport path 268 into the scanning/targeting/delivery system 140. Two components of a scanning system 140 or targeting system typically include a first axis control 142, such as a vertical control, and a second axis control 144, such as a horizontal control. In one embodiment, the first axis control 142 allows for about 100 mm of vertical scanning of the proton beam 268 and the second axis control 144 allows for about 700 mm of horizontal scanning of the proton beam 268. A nozzle system 146 is used for imaging the proton beam and/or as a vacuum barrier between the low pressure beam path of the synchrotron and the atmosphere. Protons are delivered with control to the patient interface module 150 and to a tumor of a patient. All of the above listed elements are optional and may be used in various permutations and combinations. Ion Beam Generation System An ion beam generation system generates a negative ion beam, such as a hydrogen anion or H− beam; preferably focuses the negative ion beam; converts the negative ion beam to a positive ion beam, such as a proton or H+ beam; and injects the positive ion beam into the synchrotron 130. Portions of the ion beam path are preferably under partial vacuum. Each of these systems are further described, infra. Referring now to FIG. 3, an exemplary ion beam generation system 300 is illustrated. As illustrated, the ion beam generation system 300 has four major elements: a negative ion source 310, a first partial vacuum system 330, an optional ion beam focusing system 350, and a tandem accelerator 390. Still referring to FIG. 3, the negative ion source 310 preferably includes an inlet port 312 for injection of hydrogen gas into a high temperature plasma chamber 314. In one embodiment, the plasma chamber includes a magnetic material 316, which provides a magnetic field barrier 317 between the high temperature plasma chamber 314 and a low temperature plasma region on the opposite side of the magnetic field barrier. An extraction pulse is applied to a negative ion extraction electrode 318 to pull the negative ion beam into a negative ion beam path 319, which proceeds through the first partial vacuum system 330, through the ion beam focusing system 350, and into the tandem accelerator 390. Still referring to FIG. 3, the first partial vacuum system 330 is an enclosed system running from the hydrogen gas inlet port 312 to the tandem accelerator 390 foil 395. The foil 395 is sealed directly or indirectly to the edges of the vacuum tube 320 providing for a higher pressure, such as about 10−5 torr, to be maintained on the first partial vacuum system 330 side of the foil 395 and a lower pressure, such as about 10−7 torr, to be maintained on the synchrotron side of the foil 390. By only pumping first partial vacuum system 330 and by only semi-continuously operating the ion beam source vacuum based on sensor readings, the lifetime of the semi-continuously operating pump is extended. The sensor readings are further described, infra. Still referring to FIG. 3, the first partial vacuum system 330 preferably includes: a first pump 332, such as a continuously operating pump and/or a turbo molecular pump; a large holding volume 334; and a semi-continuously operating pump 336. Preferably, a pump controller 340 receives a signal from a pressure sensor 342 monitoring pressure in the large holding volume 334. Upon a signal representative of a sufficient pressure in the large holding volume 334, the pump controller 340 instructs an actuator 345 to open a valve 346 between the large holding volume and the semi-continuously operating pump 336 and instructs the semi-continuously operating pump to turn on and pump to atmosphere residual gases out of the vacuum line 320 about the charged particle stream. In this fashion, the lifetime of the semi-continuously operating pump is extended by only operating semi-continuously and as needed. In one example, the semi-continuously operating pump 336 operates for a few minutes every few hours, such as 5 minutes every 4 hours, thereby extending a pump with a lifetime of about 2,000 hours to about 96,000 hours. Further, by isolating the inlet gas from the synchrotron vacuum system, the synchrotron vacuum pumps, such as turbo molecular pumps can operate over a longer lifetime as the synchrotron vacuum pumps have fewer gas molecules to deal with. For example, the inlet gas is primarily hydrogen gas but may contain impurities, such as nitrogen and carbon dioxide. By isolating the inlet gases in the negative ion source system 310, first partial vacuum system 330, ion beam focusing system 350 and negative ion beam side of the tandem accelerator 390, the synchrotron vacuum pumps can operate at lower pressures with longer lifetimes, which increases the efficiency of the synchrotron 130. Still referring to FIG. 3, the ion beam focusing system 350 includes two or more electrodes where one electrode of each electrode pair partially obstructs the ion beam path with conductive paths 372, such as a conductive mesh. In the illustrated example, two ion beam focusing system sections are illustrated, a two electrode ion focusing section 360 and a three electrode ion focusing section 370. In a given electrode pair, electric field lines, running between the conductive mesh of a first electrode and a second electrode, provide inward forces focusing the negative ion beam. Multiple such electrode pairs provide multiple negative ion beam focusing regions. Preferably the two electrode ion focusing section 360, first three electrode ion focusing section 370, and a second three electrode ion focusing section are placed after the negative ion source and before the tandem accelerator and/or cover a space of about 0.5, 1, or 2 meters along the ion beam path 319. Ion beam focusing systems are further described, infra. Still referring to FIG. 3, the tandem accelerator 390 preferably includes a foil 395, such as a carbon foil. The negative ions in the negative ion beam path 319 are converted to positive ions, such as protons, and the initial ion beam path 262 results. The foil 395 is preferably sealed directly or indirectly to the edges of the vacuum tube 320 providing for a higher pressure, such as about 10−5 torr, to be maintained on the side of the foil 395 having the negative ion beam path 319 and a lower pressure, such as about 10−7 torr, to be maintained on the side of the foil 390 having the proton ion beam path 262. Having the foil 395 physically separating the vacuum chamber 320 into two pressure regions allows for a system having fewer and/or smaller pumps to maintain the lower pressure system in the synchrotron 130 as the inlet hydrogen and its residuals are extracted in a separate contained and isolated space by the first partial vacuum system 330. Negative Ion Source An example of the negative ion source 310 is further described herein. Referring now to FIG. 4, a cross-section of an exemplary negative ion source system 400 is provided. The negative ion beam 319 is created in multiple stages. During a first stage, hydrogen gas is injected into a chamber. During a second stage, a negative ion is created by application of a first high voltage pulse, which creates a plasma about the hydrogen gas to create negative ions. During a third stage, a magnetic field filter is applied to components of the plasma. During a fourth stage, the negative ions are extracted from a low temperature plasma region, on the opposite side of the magnetic field barrier, by application of a second high voltage pulse. Each of the four stages are further described, infra. While the chamber is illustrated as a cross-section of a cylinder, the cylinder is exemplary only and any geometry applies to the magnetic loop containment walls, described infra. In the first stage, hydrogen gas is injected through the inlet port 312 into a high temperature plasma region 490. The injection port 442 is open for a short period of time, such as less than about 1, 5, or 10 microseconds to minimize vacuum pump requirements to maintain vacuum chamber 320 requirements. The high temperature plasma region is maintained at reduced pressure by the partial vacuum system 330. The injection of the hydrogen gas is optionally controlled by the main controller 110, which is responsive to imaging system 170 information and patient interface module 150 information, such as patient positioning and period in a respiration cycle. In the second stage, a high temperature plasma region is created by applying a first high voltage pulse across a first electrode 422 and a second electrode 424. For example a 5 kV pulse is applied for about 20 microseconds with 5 kV at the second electrode 424 and about 0 kV applied at the first electrode 422. Hydrogen in the chamber is broken, in the high temperature plasma region 490, into component parts, such as any of: atomic hydrogen, H0, a proton, H+, an electron, e−, a hydrogen anion, and H−. In the third stage, the high temperature plasma region 490 is at least partially separated from a low temperature plasma region 492 by a magnetic field or magnetic field barrier 430. High energy electrons are restricted from passing through the magnetic field barrier 430. In this manner, the magnetic field barrier 430 acts as a filter between, zone A and zone B, in the negative ion source. Preferably, a central magnetic material 410 is placed within the high temperature plasma region 490, such as along a central axis of the high temperature plasma region 490. Preferably, the first electrode 422 and second electrode 424 are composed of magnetic materials, such as iron. Preferably, the outer walls 450 of the high temperature plasma region, such as cylinder walls, are composed of a magnetic material, such as a permanent magnet, ferric, or iron based material, or a ferrite dielectric ring magnet. In this manner a magnetic field loop is created by: the central magnetic material 410, first electrode 422, the outer walls 450, the second electrode 424, and the magnetic field barrier 430. Again, the magnetic field barrier 430 restricts high energy electrons from passing through the magnetic field barrier 430. Low energy electrons interact with atomic hydrogen, H0, to create a hydrogen anion, H−, in the low temperature plasma region 492. In the fourth stage, a second high voltage pulse or extraction pulse is applied at a third electrode 426. The second high voltage pulse is preferentially applied during the later period of application of the first high voltage pulse. For example, an extraction pulse of about 25 kV is applied for about the last 5 microseconds of the first creation pulse of about 20 microseconds. The potential difference, of about 20 kV, between the third electrode 426 and second electrode 424 extracts the negative ion, H−, from the low temperature plasma region 492 and initiates the negative ion beam 390, from zone B to zone C. The magnetic field barrier 430 is optionally created in number of ways. An example of creation of the magnetic field barrier 430 using coils is provided. In this example, the elements described, supra, in relation to FIG. 4 are maintained with several differences. First, the magnetic field is created using coils. An isolating material is preferably provided between the first electrode 422 and the cylinder walls 450 as well as between the second electrode 424 and the cylinder walls 450. The central material 410 and/or cylinder walls 450 are optionally metallic. In this manner, the coils create a magnetic field loop through the first electrode 422, isolating material, outer walls 450, second electrode 424, magnetic field barrier 430, and the central material 410. Essentially, the coils generate a magnetic field in place of production of the magnetic field by the magnetic material 410. The magnetic field barrier 430 operates as described, supra. Generally, any manner that creates the magnetic field barrier 430 between the high temperature plasma region 490 and low temperature plasma region 492 is functionally applicable to the ion beam extraction system 400. Ion Beam Focusing System Referring now to FIG. 5, the ion beam focusing system 350 is further described. In this example, three electrodes are used. In this example, the first electrode 510 and third electrode 530 are both negatively charged and each is a ring electrode circumferentially enclosing or at least partially enclosing the negative ion beam path 319. The second electrode 520 is positively charged and is also a ring electrode circumferentially enclosing the negative ion beam path. In addition, the second electrode includes one or more conducting paths 372 running through the negative ion beam path 319. For example, the conducting paths are a wire mesh, a conducting grid, or a series of substantially parallel conducting lines running across the second electrode. In use, electric field lines run from the conducting paths of the positively charged electrode to the negatively charged electrodes. For example, in use the electric field lines 540 run from the conducting paths 372 in the negative ion beam path 319 to the negatively charged electrodes 510, 530. Two ray trace lines 550, 560 of the negative ion beam path are used to illustrate focusing forces. In the first ray trace line 550, the negative ion beam encounters a first electric field line at point M. Negatively charged ions in the negative ion beam 550 encounter forces running up the electric field line 571, illustrated with an x-axis component vector 572. The x-axis component force vectors 572 alters the trajectory of the first ray trace line to a inward focused vector 552, which encounters a second electric field line at point N. Again, the negative ion beam 552 encounters forces running up the electric field line 573, illustrated as having an inward force vector with an x-axis component 574, which alters the inward focused vector 552 to a more inward focused vector 554. Similarly, in the second ray trace line 560, the negative ion beam encounters a first electric field line at point O. Negatively charged ions in the negative ion beam encounter forces running up the electric field line 575, illustrated as having a force vector with an x-axis force 576. The inward force vectors 576 alters the trajectory of the second ray trace line 560 to an inward focused vector 562, which encounters a second electric field line at point P. Again, the negative ion beam encounters forces running up the electric field line 577, illustrated as having force vector with an x-axis component 578, which alters the inward focused vector 562 to a more inward focused vector 564. The net result is a focusing effect on the negative ion beam. Each of the force vectors 572, 574, 576, 578 optionally has x and/or y force vector components resulting in a 3-dimensional focusing of the negative ion beam path. Naturally, the force vectors are illustrative in nature, many electric field lines are encountered, and the focusing effect is observed at each encounter resulting in integral focusing. The example is used to illustrate the focusing effect. Still referring to FIG. 5, optionally any number of electrodes are used, such as 2, 3, 4, 5, 6, 7, 8, or 9 electrodes, to focus the negative ion beam path where every other electrode, in a given focusing section, is either positively or negatively charged. For example, three focusing sections are optionally used. In the first ion focusing section 360, a pair of electrodes are used where the first electrode encountered along the negative ion beam path is negatively charged and the second electrode is positively charged, resulting in focusing of the negative ion beam path. In the second ion focusing section 370, two pairs of electrodes are used, where a common positively charged electrode with a conductive mesh running through the negatively ion beam path 319 is used. Thus, in the second ion focusing section 370, the first electrode encountered along the negative ion beam path is negatively charged and the second electrode is positively charged, resulting in focusing of the negative ion beam path. Further, in the second ion focusing section, moving along the negative ion beam path, a second focusing effect is observed between the second positively charged electrode and a third negatively charged electrode. In this example, a third ion focusing section is used that again has three electrodes, which acts in the fashion of the second ion focusing section, describe supra. Referring now to FIG. 6, the central regions of the electrodes in the ion beam focusing system 350 are further described. Referring now to FIG. 6A, the central region of the negatively charged ring electrode 510 is preferably void of conductive material. Referring now to FIGS. 6B-D, the central region of positively charged electrode ring 520 preferably contains conductive paths 372. Preferably, the conductive paths 372 or conductive material within the positively charged electrode ring 520 blocks about 1, 2, 5, or 10 percent of the area and more preferably blocks about 5 percent of the cross-sectional area of the negative ion beam path 319. Referring now to FIG. 6B, one option is a conductive mesh 610. Referring now to FIG. 6C, a second option is a series of conductive lines 620 running substantially in parallel across the positively charged electrode ring 520 that surrounds a portion of the negative ion beam path 319. Referring now to FIG. 6D, a third option is to have a foil 630 or metallic layer cover all of the cross-sectional area of the negative ion beam path with holes punched through the material, where the holes take up about 90-99 percent and more preferably about 95 percent of the area of the foil. More generally, the pair of electrodes are configure to provide electric field lines that provide focusing force vectors to the negative ion beam when the ions in the negative ion beam translate through the electric field lines, as described supra. In an example of a two electrode negative beam ion focusing system having a first cross-sectional diameter, d1, the negative ions are focused using the two electrode system to a second cross-sectional diameter, d2, where d1>d2. Similarly, in an example of a three electrode negative beam ion focusing system is provided having a first cross-sectional diameter, d1, the negative ions are focused using the three electrode system to a third cross-sectional diameter, d3, where d1>d3. For like potentials on the electrodes, the three electrode system provides tighter or stronger focusing compared to the two-electrode system, d3<d2. In the examples provided, supra, of a multi-electrode ion beam focusing system, the electrodes are rings. More generally, the electrodes are of any geometry sufficient to provide electric field lines that provide focusing force vectors to the negative ion beam when the ions in the negative ion beam translate through the electric field lines, as described supra. For example, one negative ring electrode is optionally replaced by a number of negatively charged electrodes, such as about 2, 3, 4, 6, 8, 10, or more electrodes placed about the outer region of a cross-sectional area of the negative ion beam probe. Generally, more electrodes are required to converge or diverge a faster or higher energy beam. In another embodiment, by reversing the polarity of electrodes in the above example, the negative ion beam is made to diverge. Thus, the negative ion beam path is optionally focused and expanded using combinations of electrode pairs. For example, if the electrode having the mesh across the negative ion beam path is made negative, then the negative ion beam path is made to defocus. Hence, combinations of electrode pairs are used for focusing and defocusing a negative ion beam path, such as where a first pair includes a positively charged mesh for focusing and a where a second pair includes a negatively charged mesh for defocusing. Tandem Accelerator Referring now to FIG. 7A, the tandem accelerator 390 is further described. The tandem accelerator accelerates ions using a series of electrodes 710, 711, 712, 713, 714, 715. For example, negative ions, such as H−, in the negative ion beam path are accelerated using a series of electrodes having progressively higher voltages relative to the voltage of the extraction electrode 426, or third electrode 426, of the negative ion beam source 310. For instance, the tandem accelerator 390 optionally has electrodes ranging from the 25 kV of the extraction electrode 426 to about 525 kV near the foil 395 in the tandem accelerator 390. Upon passing through the foil, the negative ion, H−, loses two electrons to yield a proton, H+, according to equation 1.H−→H++2e− (eq. 1) The proton is further accelerated in the tandem accelerator using appropriate voltages at a multitude of further electrodes 713, 714, 715. The protons are then injected into the synchrotron 130 as described, supra. Still referring to FIG. 7, the foil 395 in the tandem accelerator 390 is further described. The foil 395 is preferably a very thin carbon film of about 30 to 200 angstroms in thickness. The foil thickness is designed to both: (1) not block the ion beam and (2) allow the transfer of electrons yielding protons to form the proton beam path 262. The foil 395 is preferably substantially in contact with a support layer 720, such as a support grid. The support layer 720 provides mechanical strength to the foil 395 to combine to form a vacuum blocking element 725. The foil 395 blocks nitrogen, carbon dioxide, hydrogen, and other gases from passing and thus acts as a vacuum barrier. In one embodiment, the foil 395 is preferably sealed directly or indirectly to the edges of the vacuum tube 320 providing for a higher pressure, such as about 10−5 torr, to be maintained on the side of the foil 395 having the negative ion beam path 319 and a lower pressure, such as about 10−7 torr, to be maintained on the side of the foil 395 having the proton ion beam path 262. Having the foil 395 physically separating the vacuum chamber 320 into two pressure regions allows for a vacuum system having fewer and/or smaller pumps to maintain the lower pressure system in the synchrotron 130 as the inlet hydrogen and its residuals are extracted in a separate contained and isolated space by the first partial vacuum system 330. The foil 395 and support layer 720 are preferably attached to the structure 750 of the tandem accelerator 390 or vacuum tube 320 to form a pressure barrier using any mechanical means, such as a metal, plastic, or ceramic ring 730 compressed to the walls with an attachment screw 740. Any mechanical means for separating and sealing the two vacuum chamber sides with the foil 395 are equally applicable to this system. Referring now to FIG. 7B, the support structure 720 and foil 395 are individually viewed in the x-, y-plane. Referring now to FIG. 8, another exemplary method of use of the charged particle beam system 100 is provided. The main controller 110, or one or more sub-controllers, controls one or more of the subsystems to accurately and precisely deliver protons to a tumor of a patient. For example, the main controller sends a message to the patient indicating when or how to breath. The main controller 110 obtains a sensor reading from the patient interface module, such as a temperature breath sensor or a force reading indicative of where in a respiration cycle the subject is. The main controller collects an image, such as a portion of a body and/or of a tumor, from the imaging system 170. The main controller 110 also obtains position and/or timing information from the patient interface module 150. The main controller 110 then optionally controls the injection system 120 to inject hydrogen gas into a negative ion beam source 310 and controls timing of extraction of the negative ion from the negative ion beam source 310. Optionally, the main controller controls ion beam focusing the ion beam focusing lens system 350; acceleration of the proton beam with the tandem accelerator 390; and/or injection of the proton into the synchrotron 130. The synchrotron typically contains at least an accelerator system 132 and an extraction system 134. The synchrotron preferably contains one or more of: turning magnets, edge focusing magnets, magnetic field concentration magnets, winding and correction coils, and flat magnetic field incident surfaces, some of which contain elements under control by the main controller 110. The main controller preferably controls the proton beam within the accelerator system, such as by controlling speed, trajectory, and/or timing of the proton beam. The main controller then controls extraction of a proton beam from the accelerator through the extraction system 134. For example, the controller controls timing, energy, and/or intensity of the extracted beam. The controller 110 also preferably controls targeting of the proton beam through the targeting/delivery system 140 to the patient interface module 150. One or more components of the patient interface module 150 are preferably controlled by the main controller 110, such as vertical position of the patient, rotational position of the patient, and patient chair positioning/stabilization/control elements. Further, display elements of the display system 160 are preferably controlled via the main controller 110. Displays, such as display screens, are typically provided to one or more operators and/or to one or more patients. In one embodiment, the main controller 110 times the delivery of the proton beam from all systems, such that protons are delivered in an optimal therapeutic manner to the patient. Circulating System A synchrotron 130 preferably comprises a combination of straight sections 910 and ion beam turning sections 920. Hence, the circulating path of the protons is not circular in a synchrotron, but is rather a polygon with rounded corners. In one illustrative embodiment, the synchrotron 130, which as also referred to as an accelerator system, has four straight elements and four turning sections. Examples of straight sections 910 include the: inflector 240, accelerator 270, extraction system 290, and deflector 292. Along with the four straight sections are four ion beam turning sections 920, which are also referred to as magnet sections or turning sections. Turning sections are further described, infra. Referring now to FIG. 9, an exemplary synchrotron is illustrated. In this example, protons delivered along the initial proton beam path 262 are inflected into the circulating beam path with the inflector 240 and after acceleration are extracted via a deflector 292 to a beam transport path 268. In this example, the synchrotron 130 comprises four straight sections 910 and four bending or turning sections 920 where each of the four turning sections use one or more magnets to turn the proton beam about ninety degrees. As is further described, infra, the ability to closely space the turning sections and efficiently turn the proton beam results in shorter straight sections. Shorter straight sections allows for a synchrotron design without the use of focusing quadrupoles in the circulating beam path of the synchrotron. The removal of the focusing quadrupoles from the circulating proton beam path results in a more compact design. In this example, the illustrated synchrotron has about a five meter diameter versus eight meter and larger cross-sectional diameters for systems using a quadrupole focusing magnet in the circulating proton beam path. Referring now to FIG. 10, additional description of the first bending or turning section 920 is provided. Each of the turning sections preferably comprises multiple magnets, such as about 2, 4, 6, 8, 10, or 12 magnets. In this example, four turning magnets 1010, 1020, 1030, 1040 in the first turning section 20 are used to illustrate key principles, which are the same regardless of the number of magnets in a turning section 920. A turning magnet 1010 is a particular type of main bending or circulating magnet 250. In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. The Lorentz force is given by equation 2 in terms of magnetic fields with the election field terms not included.F=q(v×B) eq. 2 In equation 2, F is the force in newtons; B is the magnetic field in Teslas; and v is the instantaneous velocity of the particles in meters per second. Referring now to FIG. 11, an example of a single magnet bending or turning section 1010 is expanded. The turning section includes a gap 1110 through which protons circulate. The gap 1110 is preferably a flat gap, allowing for a magnetic field across the gap 1110 that is more uniform, even, and intense. A magnetic field enters the gap 1110 through a magnetic field incident surface and exits the gap 1110 through a magnetic field exiting surface. The gap 1110 runs in a vacuum tube between two magnet halves. The gap 1110 is controlled by at least two parameters: (1) the gap 1110 is kept as large as possible to minimize loss of protons and (2) the gap 1110 is kept as small as possible to minimize magnet sizes and the associated size and power requirements of the magnet power supplies. The flat nature of the gap 1110 allows for a compressed and more uniform magnetic field across the gap 1110. One example of a gap dimension is to accommodate a vertical proton beam size of about 2 cm with a horizontal beam size of about 5 to 6 cm. As described, supra, a larger gap size requires a larger power supply. For instance, if the gap 1110 size doubles in vertical size, then the power supply requirements increase by about a factor of 4. The flatness of the gap 1110 is also important. For example, the flat nature of the gap 1110 allows for an increase in energy of the extracted protons from about 250 to about 330 MeV. More particularly, if the gap 1110 has an extremely flat surface, then the limits of a magnetic field of an iron magnet are reachable. An exemplary precision of the flat surface of the gap 1110 is a polish of less than about five microns and preferably with a polish of about one to three microns. Unevenness in the surface results in imperfections in the applied magnetic field. The polished flat surface spreads unevenness of the applied magnetic field. Still referring to FIG. 11, the charged particle beam moves through the gap 1110 with an instantaneous velocity, v. A first magnetic coil 1120 and a second magnetic coil 1130 run above and below the gap 1110, respectively. Current running through the coils 1120, 1130 results in a magnetic field, B, running through the single magnet turning section 1010. In this example, the magnetic field, B, runs upward, which results in a force, F, pushing the charged particle beam inward toward a central point of the synchrotron, which turns the charged particle beam in an arc. Still referring to FIG. 11, a portion of an optional second magnet bending or turning section 1020 is illustrated. The coils 1120, 1130 typically have return elements 1140, 1150 or turns at the end of one magnet, such as at the end of the first magnet turning section 1010. The turns 1140, 1150 take space. The space reduces the percentage of the path about one orbit of the synchrotron that is covered by the turning magnets. This leads to portions of the circulating path where the protons are not turned and/or focused and allows for portions of the circulating path where the proton path defocuses. Thus, the space results in a larger synchrotron. Therefore, the space between magnet turning sections 1160 is preferably minimized. The second turning magnet is used to illustrate that the coils 1120, 1130 optionally run along a plurality of magnets, such as 2, 3, 4, 5, 6, or more magnets. Coils 1120, 1130 running across multiple turning section magnets allows for two turning section magnets to be spatially positioned closer to each other due to the removal of the steric constraint of the turns, which reduces and/or minimizes the space 1160 between two turning section magnets. Referring now to FIGS. 12 and 13, two illustrative 90 degree rotated cross-sections of single magnet bending or turning sections 1010 are presented. The magnet assembly has a first magnet 1210 and a second magnet 1220. A magnetic field induced by coils, described infra, runs between the first magnet 1210 to the second magnet 1220 across the gap 1110. Return magnetic fields run through a first yoke 1212 and second yoke 1222. The combined cross-section area of the return yokes roughly approximates the cross-sectional area of the first magnet 1210 or second magnet 1220. The charged particles run through the vacuum tube in the gap 1110. As illustrated, protons run into FIG. 12 through the gap 1110 and the magnetic field, illustrated as vector B, applies a force F to the protons pushing the protons towards the center of the synchrotron, which is off page to the right in FIG. 12. The magnetic field is created using windings. A first wire is used to construct a first winding coil 1250 and a second wire is used to construct a second winding coil 1260. Isolating or concentrating gaps 1230, 1240, such as air gaps, isolate the iron based yokes from the gap 1110. The gap 1110 is approximately flat to yield a uniform magnetic field across the gap 1110, as described supra. Still referring to FIG. 13, the ends of a single bending or turning magnet are preferably beveled. Nearly perpendicular or right angle edges of a turning magnet 1010 are represented by dashed lines 1374, 1384. The dashed lines 1374, 1384 intersect at a point 1390 beyond the center of the synchrotron 280. Preferably, the edge of the turning magnet is beveled at angles alpha, α, and beta, β, which are angles formed by a first line 1372, 1382 going from an edge of the turning magnet 1010 and the center 280 and a second line 1374, 1384 going from the same edge of the turning magnet and the intersecting point 1390. The angle alpha is used to describe the effect and the description of angle alpha applies to angle beta, but angle alpha is optionally different from angle beta. The angle alpha provides an edge focusing effect. Beveling the edge of the turning magnet 1010 at angle alpha focuses the proton beam. Multiple turning magnets provide multiple magnet edges that each have edge focusing effects in the synchrotron 130. If only one turning magnet is used, then the beam is only focused once for angle alpha or twice for angle alpha and angle beta. However, by using smaller turning magnets, more turning magnets fit into the turning sections 920 of the synchrotron 130. For example, if four magnets are used in a turning section 920 of the synchrotron, then for a single turning section there are eight possible edge focusing effect surfaces, two edges per magnet. The eight focusing surfaces yield a smaller cross-sectional beam size. This allows the use of a smaller gap 1110. The use of multiple edge focusing effects in the turning magnets results in not only a smaller gap 1110, but also the use of smaller magnets and smaller power supplies. For a synchrotron 130 having four turning sections 920 where each turning sections has four turning magnets and each turning magnet has two focusing edges, a total of thirty-two focusing edges exist for each orbit of the protons in the circulating path of the synchrotron 130. Similarly, if 2, 6, or 8 magnets are used in a given turning section, or if 2, 3, 5, or 6 turning sections are used, then the number of edge focusing surfaces expands or contracts according to equation 3. TFE = NTS * M NTS * FE M eq . ⁢ 3 where TFE is the number of total focusing edges, NTS is the number of turning sections, M is the number of magnets, and FE is the number of focusing edges. Naturally, not all magnets are necessarily beveled and some magnets are optionally beveled on only one edge. The inventors have determined that multiple smaller magnets have benefits over fewer larger magnets. For example, the use of 16 small magnets yields 32 focusing edges whereas the use of 4 larger magnets yields only 8 focusing edges. The use of a synchrotron having more focusing edges results in a circulating path of the synchrotron built without the use of focusing quadrupoles magnets. All prior art synchrotrons use quadrupoles in the circulating path of the synchrotron. Further, the use of quadrupoles in the circulating path necessitates additional straight sections in the circulating path of the synchrotron. Thus, the use of quadrupoles in the circulating path of a synchrotron results in synchrotrons having larger diameters, circulating beam pathlengths, and/or larger circumferences. In various embodiments of the system described herein, the synchrotron has any combination of: at least 4 and preferably 6, 8, 10, or more edge focusing edges per 90 degrees of turn of the charged particle beam in a synchrotron having four turning sections; at least about 16 and preferably about 24, 32, or more edge focusing edges per orbit of the charged particle beam in the synchrotron; only 4 turning sections where each of the turning sections includes at least 4 and preferably 8 edge focusing edges; an equal number of straight sections and turning sections; exactly 4 turning sections; at least 4 edge focusing edges per turning section; no quadrupoles in the circulating path of the synchrotron; a rounded corner rectangular polygon configuration; a circumference of less than 60 meters; a circumference of less than 60 meters and 32 edge focusing surfaces; and/or any of about 8, 16, 24, or 32 non-quadrupole magnets per circulating path of the synchrotron, where the non-quadrupole magnets include edge focusing edges. Referring now to FIG. 12, the incident magnetic field surface 1270 of the first magnet 1210 is further described. FIG. 12 is not to scale and is illustrative in nature. Local imperfections or unevenness in quality of the finish of the incident surface 1270 results in inhomogeneities or imperfections in the magnetic field applied to the gap 1110. Preferably, the incident surface 1270 is flat, such as to within about a zero to three micron finish polish, or less preferably to about a ten micron finish polish. Referring now to FIG. 14, additional optional magnet elements, of the magnet cross-section illustratively represented in FIG. 12, are described. The first magnet 1210 preferably contains an initial cross-sectional distance 1410 of the iron based core. The contours of the magnetic field are shaped by the magnets 1210, 1220 and the yokes 1212, 1222. The iron based core tapers to a second cross-sectional distance 1420. The magnetic field in the magnet preferentially stays in the iron based core as opposed to the gaps 1230, 1240. As the cross-sectional distance decreases from the initial cross-sectional distance 1410 to the final cross-sectional distance 1420, the magnetic field concentrates. The change in shape of the magnet from the longer distance 1410 to the smaller distance 1420 acts as an amplifier. The concentration of the magnetic field is illustrated by representing an initial density of magnetic field vectors 1430 in the initial cross-section 1410 to a concentrated density of magnetic field vectors 1440 in the final cross-section 1420. The concentration of the magnetic field due to the geometry of the turning magnets results in fewer winding coils 1250, 1260 being required and also a smaller power supply to the coils being required. In one example, the initial cross-section distance 1410 is about fifteen centimeters and the final cross-section distance 1420 is about ten centimeters. Using the provided numbers, the concentration of the magnetic field is about 15/10 or 1.5 times at the incident surface 1270 of the gap 1110, though the relationship is not linear. The taper 1460 has a slope, such as about 20, 40, or 60 degrees. The concentration of the magnetic field, such as by 1.5 times, leads to a corresponding decrease in power consumption requirements to the magnets. Referring now to FIG. 15, an additional example of geometry of the magnet used to concentrate the magnetic field is illustrated. As illustrated in FIG. 14, the first magnet 1210 preferably contains an initial cross-sectional distance 1410 of the iron based core. The contours of the magnetic field are shaped by the magnets 1210, 1220 and the yokes 1212, 1222. In this example, the core tapers to a second cross-sectional distance 1420 with a smaller angle theta, θ. As described, supra, the magnetic field in the magnet preferentially stays in the iron based core as opposed to the gaps 1230, 1240. As the cross-sectional distance decreases from the initial cross-sectional distance 1410 to the final cross-sectional distance 1420, the magnetic field concentrates. The smaller angle, theta, results in a greater amplification of the magnetic field in going from the longer distance 1410 to the smaller distance 1420. The concentration of the magnetic field is illustrated by representing an initial density of magnetic field vectors 1430 in the initial cross-section 1410 to a concentrated density of magnetic field vectors 1440 in the final cross-section 1420. The concentration of the magnetic field due to the geometry of the turning magnets results in fewer winding coils 1250, 1260 being required and also a smaller power supply to the winding coils 1250, 1260 being required. Still referring to FIG. 15, optional correction coils 1510, 1520 are illustrated that are used to correct the strength of one or more turning magnets. The correction coils 1520, 1530 supplement the winding coils 1250, 1260. The correction coils 1510, 1520 have correction coil power supplies that are separate from winding coil power supplies used with the winding coils 1250, 1260. The correction coil power supplies typically operate at a fraction of the power required compared to the winding coil power supplies, such as about 1, 2, 3, 5, 7, or 10 percent of the power and more preferably about 1 or 2 percent of the power used with the winding coils 1250, 1260. The smaller operating power applied to the correction coils 1510, 1520 allows for more accurate and/or precise control of the correction coils. The correction coils are used to adjust for imperfection in the turning magnets. Optionally, separate correction coils are used for each turning magnet allowing individual tuning of the magnetic field for each turning magnet, which eases quality requirements in the manufacture of each turning magnet. Referring now to FIG. 16, an example of winding coils and correction coils about a plurality of turning magnets 1610, 1620 in an ion beam turning section 920 is illustrated. One or more high precision magnetic field sensors are placed into the synchrotron and are used to measure the magnetic field at or near the proton beam path. For example, the magnetic sensors are optionally placed between turning magnets and/or within a turning magnet, such as at or near the gap 1110 or at or near the magnet core or yoke. The sensors are part of a feedback system to the correction coils. Thus, the system preferably stabilizes the magnetic field in the synchrotron elements rather than stabilizing the current applied to the magnets. Stabilization of the magnetic field allows the synchrotron to come to a new energy level quickly. This allows the system to be controlled to an operator or algorithm selected energy level with each pulse of the synchrotron and/or with each breath of the patient. The winding and/or correction coils correct 1, 2, 3, or 4 turning magnets, and preferably correct a magnetic field generated by two turning magnets. In the illustrated example, in one case a first correction coil 1610 wraps around a single magnet and in a second case a separately used second correction coil wraps around two or more magnets. A winding or correction coil covering multiple magnets reduces space between magnets as fewer winding or correction coil ends are required, which occupy space. Referring now to FIG. 17A and FIG. 17B, the accelerator system 270, such as a radio-frequency (RF) accelerator system, is further described. The accelerator includes a series of coils 1710-1719, such as iron or ferrite coils, each circumferentially enclosing the vacuum system 320 through which the proton beam 264 passes in the synchrotron 130. Referring now to FIG. 17B, the first coil 1710 is further described. A loop of standard wire 1730 completes at least one turn about the first coil 1710. The loop attaches to a microcircuit 1720. Referring again to FIG. 17A, an RF synthesizer 1740, which is preferably connected to the main controller 110, provides a low voltage RF signal that is synchronized to the period of circulation of protons in the proton beam path 264. The RF synthesizer 1740, microcircuit 1720, loop 1730, and coil 1710 combine to provide an accelerating voltage to the protons in the proton beam path 264. For example, the RF synthesizer 1740 sends a signal to the microcircuit 1720, which amplifies the low voltage RF signal and yields an acceleration voltage, such as about 10 volts. The actual acceleration voltage for a single microcircuit/loop/coil combination is about 5, 10, 15, or 20 volts, but is preferably about 10 volts. Preferably, the RF-amplifier microcircuit and accelerating coil are integrated. Still referring to FIG. 17A, the integrated RF-amplifier microcircuit and accelerating coil presented in FIG. 17B is repeated, as illustrated as the set of coils 1711-1719 surrounding the vacuum tube 320. For example, the RF-synthesizer 1740 under main controller 130 direction, sends an RF-signal to the microcircuits 1720-1729 connected to coils 1710-1719, respectively. Each of the microcircuit/loop/coil combinations generate a proton accelerating voltage, such as about 10 volts each. Hence, a set of five microcircuit/loop/coil combinations generate about 50 volts for proton acceleration. Preferably about 5 to 20 microcircuit/loop/coil combinations are used and more preferably about 9 or 10 microcircuit/loop/coil combinations are used in the accelerator system 270. As a further clarifying example, the RF synthesizer 1740 sends an RF-signal, with a period equal to a period of circulation of a proton about the synchrotron 130, to a set of ten microcircuit/loop/coil combinations, which results in about 100 volts for acceleration of the protons in the proton beam path 264. The 100 volts is generated at a range of frequencies, such as at about 1 MHz for a low energy proton beam to about 15 MHz for a high energy proton beam. The RF-signal is optionally set at an integer multiple of a period of circulation of the proton about the synchrotron circulating path. Each of the microcircuit/loop/coil combinations are optionally independently controlled in terms of acceleration voltage and frequency. Integration of the RF-amplifier microcircuit and accelerating coil, in each microcircuit/loop/coil combination, results in three considerable advantages. First, for synchrotrons, the prior art does not use microcircuits integrated with the accelerating coils but rather uses a set of long cables to provide power to a corresponding set of coils. The long cables have an impedance/resistance, which is problematic for high frequency RF control. As a result, the prior art system is not operable at high frequencies, such as above about 10 MHz. The integrated RF-amplifier microcircuit/accelerating coil system is operable at above about 10 MHz and even 15 MHz where the impedance and/or resistance of the long cables in the prior art systems results in poor control or failure in proton acceleration. Second, the long cable system, operating at lower frequencies, costs about $50,000 and the integrated microcircuit system costs about $1000, which is 50 times less expensive. Third, the microcircuit/loop/coil combinations in conjunction with the RF-amplifier system results in a compact low power consumption design allowing production and use of a proton cancer therapy system is a small space, as described supra, and in a cost effective manner. Referring now to FIG. 18, an example is used to clarify the magnetic field control using a feedback loop 1800 to change delivery times and/or periods of proton pulse delivery. In one case, a respiratory sensor 1810 senses the respiration cycle of the subject. The respiratory sensor sends the information to an algorithm in a magnetic field controller 1820, typically via the patient interface module 150 and/or via the main controller 110 or a subcomponent thereof. The algorithm predicts and/or measures when the subject is at a particular point in the respiration cycle, such as at the bottom of a breath. Magnetic field sensors 1830 are used as input to the magnetic field controller, which controls a magnet power supply 1840 for a given magnetic field 1850, such as within a first turning magnet 1010 of a synchrotron 130. The control feedback loop is thus used to dial the synchrotron to a selected energy level and deliver protons with the desired energy at a selected point in time, such as at the bottom of the breath. More particularly, the main controller injects protons into the synchrotron and accelerates the protons in a manner that combined with extraction delivers the protons to the tumor at a selected point in the respiration cycle. Intensity of the proton beam is also selectable and controllable by the main controller at this stage. The feedback control to the correction coils allows rapid selection of energy levels of the synchrotron that are tied to the patient's respiration cycle. This system is in stark contrast to a system where the current is stabilized and the synchrotron deliver pulses with a period, such as 10 or 20 cycles per second with a fixed period. The feedback or the magnetic field design coupled with the correction coils allows for the extraction cycle to match the varying respiratory rate of the patient. Traditional extraction systems do not allow this control as magnets have memories in terms of both magnitude and amplitude of a sine wave. Hence, in a traditional system, in order to change frequency, slow changes in current must be used. However, with the use of the feedback loop using the magnetic field sensors, the frequency and energy level of the synchrotron are rapidly adjustable. Further aiding this process is the use of a novel extraction system that allows for acceleration of the protons during the extraction process, described infra. Referring again to FIG. 16, an example of a winding coil 1630 that covers two turning magnets 1010, 1020 is provided. Optionally, a first winding coil 1640 covers two magnets and a second winding coil covers another two magnets. As described, supra, this system reduces space between turning section allowing more magnetic field to be applied per radian of turn. A first correction coil 1610 is illustrated that is used to correct the magnetic field for the first turning magnet 1010. A second correction coil 1620 is illustrated that is used to correct the magnetic field for a winding coil 1630 about two turning magnets. Individual correction coils for each turning magnet are preferred and individual correction coils yield the most precise and/or accurate magnetic field in each turning section. Particularly, the individual correction coil 1610 is used to compensate for imperfections in the individual magnet of a given turning section. Hence, with a series of magnetic field sensors, corresponding magnetic fields are individually adjustable in a series of feedback loops, via a magnetic field monitoring system, as an independent coil is used for each turning section. Alternatively, a multiple magnet correction coil is used to correct the magnetic field for a plurality of turning section magnets. Flat Gap Surface While the gap surface is described in terms of the first turning magnet 1010, the discussion applies to each of the turning magnets in the synchrotron. Similarly, while the gap 1110 surface is described in terms of the magnetic field incident surface 1270, the discussion additionally optionally applies to the magnetic field exiting surface 1280. The magnetic field incident surface 1270 of the first magnet 1210 is preferably about flat, such as to within about a zero to three micron finish polish or less preferably to about a ten micron finish polish. By being very flat, the polished surface spreads the unevenness of the applied magnetic field across the gap 1110. The very flat surface, such as about 0, 1, 2, 4, 6, 8, 10, 15, or 20 micron finish, allows for a smaller gap size, a smaller applied magnetic field, smaller power supplies, and tighter control of the proton beam cross-sectional area. Proton Beam Extraction Referring now to FIG. 19, an exemplary proton extraction process from the synchrotron 130 is illustrated. For clarity, FIG. 19 removes elements represented in FIG. 2, such as the turning magnets, which allows for greater clarity of presentation of the proton beam path as a function of time. Generally, protons are extracted from the synchrotron 130 by slowing the protons. As described, supra, the protons were initially accelerated in a circulating path 264, which is maintained with a plurality of main bending magnets 250. The circulating path is referred to herein as an original central beamline 264. The protons repeatedly cycle around a central point in the synchrotron 280. The proton path traverses through a radio frequency (RF) cavity system 1910. To initiate extraction, an RF field is applied across a first blade 1912 and a second blade 1914, in the RF cavity system 1910. The first blade 1912 and second blade 1914 are referred to herein as a first pair of blades. In the proton extraction process, an RF voltage is applied across the first pair of blades, where the first blade 1912 of the first pair of blades is on one side of the circulating proton beam path 264 and the second blade 1914 of the first pair of blades is on an opposite side of the circulating proton beam path 264. The applied RF field applies energy to the circulating charged-particle beam. The applied RF field alters the orbiting or circulating beam path slightly of the protons from the original central beamline 264 to an altered circulating beam path 265. Upon a second pass of the protons through the RF cavity system, the RF field further moves the protons off of the original proton beamline 264. For example, if the original beamline is considered as a circular path, then the altered beamline is slightly elliptical. The applied RF field is timed to apply outward or inward movement to a given band of protons circulating in the synchrotron accelerator. Each orbit of the protons is slightly more off axis compared to the original circulating beam path 264. Successive passes of the protons through the RF cavity system are forced further and further from the original central beamline 264 by altering the direction and/or intensity of the RF field with each successive pass of the proton beam through the RF field. The RF voltage is frequency modulated at a frequency about equal to the period of one proton cycling around the synchrotron for one revolution or at a frequency than is an integral multiplier of the period of one proton cycling about the synchrotron. The applied RF frequency modulated voltage excites a betatron oscillation. For example, the oscillation is a sine wave motion of the protons. The process of timing the RF field to a given proton beam within the RF cavity system is repeated thousands of times with each successive pass of the protons being moved approximately one micrometer further off of the original central beamline 264. For clarity, the approximately 1000 changing beam paths with each successive path of a given band of protons through the RF field are illustrated as the altered beam path 265. With a sufficient sine wave betatron amplitude, the altered circulating beam path 265 touches or traverses a material 1930, such as a foil or a sheet of foil. The foil is preferably a lightweight material, such as beryllium, a lithium hydride, a carbon sheet, or a material of low nuclear charge. A material of low nuclear charge is a material composed of atoms consisting essentially of atoms having six or fewer protons. The foil is preferably about 10 to 150 microns thick, is more preferably 30 to 100 microns thick, and is still more preferably about 40 to 60 microns thick. In one example, the foil is beryllium with a thickness of about 50 microns. When the protons traverse through the foil, energy of the protons is lost and the speed of the protons is reduced. Typically, a current is also generated, described infra. Protons moving at a slower speed travel in the synchrotron with a reduced radius of curvature 266 compared to either the original central beamline 264 or the altered circulating path 265. The reduced radius of curvature 266 path is also referred to herein as a path having a smaller diameter of trajectory or a path having protons with reduced energy. The reduced radius of curvature 266 is typically about two millimeters less than a radius of curvature of the last pass of the protons along the altered proton beam path 265. The thickness of the material 1930 is optionally adjusted to created a change in the radius of curvature, such as about ½, 1, 2, 3, or 4 mm less than the last pass of the protons 265 or original radius of curvature 264. Protons moving with the smaller radius of curvature travel between a second pair of blades. In one case, the second pair of blades is physically distinct and/or are separated from the first pair of blades. In a second case, one of the first pair of blades is also a member of the second pair of blades. For example, the second pair of blades is the second blade 1914 and a third blade 1916 in the RF cavity system 1910. A high voltage DC signal, such as about 1 to 5 kV, is then applied across the second pair of blades, which directs the protons out of the synchrotron through an extraction magnet 292, such as a Lamberson extraction magnet, into a transport path 268. Control of acceleration of the charged particle beam path in the synchrotron with the accelerator and/or applied fields of the turning magnets in combination with the above described extraction system allows for control of the intensity of the extracted proton beam, where intensity is a proton flux per unit time or the number of protons extracted as a function of time. For example, when a current is measured beyond a threshold, the RF field modulation in the RF cavity system is terminated or reinitiated to establish a subsequent cycle of proton beam extraction. This process is repeated to yield many cycles of proton beam extraction from the synchrotron accelerator. Because the extraction system does not depend on any change in magnetic field properties, it allows the synchrotron to continue to operate in acceleration or deceleration mode during the extraction process. Stated differently, the extraction process does not interfere with synchrotron acceleration. In stark contrast, traditional extraction systems introduce a new magnetic field, such as via a hexapole, during the extraction process. More particularly, traditional synchrotrons have a magnet, such as a hexapole magnet, that is off during an acceleration stage. During the extraction phase, the hexapole magnetic field is introduced to the circulating path of the synchrotron. The introduction of the magnetic field necessitates two distinct modes, an acceleration mode and an extraction mode, which are mutually exclusive in time. Charged Particle Beam Intensity Control Control of applied field, such as a radio-frequency (RF) field, frequency and magnitude in the RF cavity system 1910 allows for intensity control of the extracted proton beam, where intensity is extracted proton flux per unit time or the number of protons extracted as a function of time. Referring still to FIG. 19, when protons in the proton beam hit the material 1930 electrons are given off resulting in a current. The resulting current is converted to a voltage and is used as part of a ion beam intensity monitoring system or as part of an ion beam feedback loop for controlling beam intensity. The voltage is optionally measured and sent to the main controller 110 or to a controller subsystem 1940. More particularly, when protons in the charged particle beam path pass through the material 1930, some of the protons lose a small fraction of their energy, such as about one-tenth of a percent, which results in a secondary electron. That is, protons in the charged particle beam push some electrons when passing through material 1930 giving the electrons enough energy to cause secondary emission. The resulting electron flow results in a current or signal that is proportional to the number of protons going through the target material 1930. The resulting current is preferably converted to voltage and amplified. The resulting signal is referred to as a measured intensity signal. The amplified signal or measured intensity signal resulting from the protons passing through the material 1930 is preferably used in controlling the intensity of the extracted protons. For example, the measured intensity signal is compared to a goal signal, which is predetermined in an irradiation of the tumor plan. The difference between the measured intensity signal and the planned for goal signal is calculated. The difference is used as a control to the RF generator. Hence, the measured flow of current resulting from the protons passing through the material 1930 is used as a control in the RF generator to increase or decrease the number of protons undergoing betatron oscillation and striking the material 1930. Hence, the voltage determined off of the material 1930 is used as a measure of the orbital path and is used as a feedback control to control the RF cavity system. Alternatively, the measured intensity signal is not used in the feedback control and is just used as a monitor of the intensity of the extracted protons. As described, supra, the photons striking the material 1930 is a step in the extraction of the protons from the synchrotron 130. Hence, the measured intensity signal is used to change the number of protons per unit time being extracted, which is referred to as intensity of the proton beam. The intensity of the proton beam is thus under algorithm control. Further, the intensity of the proton beam is controlled separately from the velocity of the protons in the synchrotron 130. Hence, intensity of the protons extracted and the energy of the protons extracted are independently variable. For example, protons initially move at an equilibrium trajectory in the synchrotron 130. An RF field is used to excite the protons into a betatron oscillation. In one case, the frequency of the protons orbit is about 10 MHz. In one example, in about one millisecond or after about 10,000 orbits, the first protons hit an outer edge of the target material 130. The specific frequency is dependent upon the period of the orbit. Upon hitting the material 130, the protons push electrons through the foil to produce a current. The current is converted to voltage and amplified to yield a measured intensity signal. The measured intensity signal is used as a feedback input to control the applied RF magnitude, RF frequency, or RF field. Preferably, the measured intensity signal is compared to a target signal and a measure of the difference between the measured intensity signal and target signal is used to adjust the applied RF field in the RF cavity system 1910 in the extraction system to control the intensity of the protons in the extraction step. Stated again, the signal resulting from the protons striking and/or passing through the material 130 is used as an input in RF field modulation. An increase in the magnitude of the RF modulation results in protons hitting the foil or material 130 sooner. By increasing the RF, more protons are pushed into the foil, which results in an increased intensity, or more protons per unit time, of protons extracted from the synchrotron 130. In another example, a detector external to the synchrotron 130 is used to determine the flux of protons extracted from the synchrotron and a signal from the external detector is used to alter the RF field or RF modulation in the RF cavity system 1910. Here the external detector generates an external signal, which is used in a manner similar to the measured intensity signal, described in the preceding paragraphs. In yet another example, when a current from material 130 resulting from protons passing through or hitting material is measured beyond a threshold, the RF field modulation in the RF cavity system is terminated or reinitiated to establish a subsequent cycle of proton beam extraction. This process is repeated to yield many cycles of proton beam extraction from the synchrotron accelerator. In still yet another embodiment, intensity modulation of the extracted proton beam is controlled by the main controller 110. The main controller 110 optionally and/or additionally controls timing of extraction of the charged particle beam and energy of the extracted proton beam. The benefits of the system include a multi-dimensional scanning system. Particularly, the system allows independence in: (1) energy of the protons extracted and (2) intensity of the protons extracted. That is, energy of the protons extracted is controlled by an energy control system and an intensity control system controls the intensity of the extracted protons. The energy control system and intensity control system are optionally independently controlled. Preferably, the main controller 110 controls the energy control system and the main controller simultaneously controls the intensity control system to yield an extracted proton beam with controlled energy and controlled intensity where the controlled energy and controlled intensity are independently variable. Thus the irradiation spot hitting the tumor is under independent control of: time; energy; intensity; x-axis position, where the x-axis represents horizontal movement of the proton beam relative to the patient, and y-axis position, where the y-axis represents vertical movement of the proton beam relative to the patient. In addition, the patient is optionally independently rotated relative to a translational axis of the proton beam at the same time. Referring now to FIG. 20, a proton beam position verification system 2000 is described. A nozzle 2010 provides an outlet for the second reduced pressure vacuum system initiating at the foil 395 of the tandem accelerator 390 and running through the synchrotron 130 to a nozzle foil 2020 covering the end of the nozzle 2010. The nozzle expands in cross-sectional area along the z-axis of the proton beam path 268 to allow the proton beam 268 to be scanned along the x- and y-axes by the vertical control element 142 and horizontal control element 144, respectively. The nozzle foil 2020 is preferably mechanically supported by the outer edges of an exit port of the nozzle 2010. An example of a nozzle foil 2020 is a sheet of about 0.1 inch thick aluminum foil. Generally, the nozzle foil separates atmosphere pressures on the patient side of the nozzle foil 2020 from the low pressure region, such as about 10−5 to 10−7 torr region, on the synchrotron 130 side of the nozzle foil 2020. The low pressure region is maintained to reduce scattering of the proton beam 264, 268. Still referring to FIG. 20, the proton beam verification system 2000 is a system that allows for monitoring of the actual proton beam position 268, 269 in real-time without destruction of the proton beam. The proton beam verification system 2000 preferably includes a proton beam position verification layer 2030, which is also referred to herein as a coating, luminescent, fluorescent, phosphorescent, radiance, or viewing layer. The verification layer or coating layer 2030 is preferably a coating or thin layer substantially in contact with an inside surface of the nozzle foil 2020, where the inside surface is on the synchrotron side of the nozzle foil 2020. Less preferably, the verification layer or coating layer 2030 is substantially in contact with an outer surface of the nozzle foil 2020, where the outer surface is on the patient treatment side of the nozzle foil 2020. Preferably, the nozzle foil 2020 provides a substrate surface for coating by the coating layer, but optionally a separate coating layer support element, on which the coating 2030 is mounted, is placed anywhere in the proton beam path 268. Still referring to FIG. 20, the coating 2030 yields a measurable spectroscopic response, spatially viewable by the detector 2040, as a result of transmission by the proton beam 268. The coating 2030 is preferably a phosphor, but is optionally any material that is viewable or imaged by a detector where the material changes spectroscopically as a result of the proton beam path 268 hitting or transmitting through the coating 2030. A detector or camera 2040 views the coating layer 2030 and determines the current position of the proton beam 268 by the spectroscopic differences resulting from protons passing through the coating layer. For example, the camera 2040 views the coating surface 2030 as the proton beam 268 is being scanned by the horizontal 144 and vertical 142 beam position control elements during treatment of the tumor 2120. The camera 2040 views the current position of the proton beam 268 as measured by spectroscopic response. The coating layer 2030 is preferably a phosphor or luminescent material that glows or emits photons for a short period of time, such as less than 5 seconds for a 50% intensity, as a result of excitation by the proton beam 268. Optionally, a plurality of cameras or detectors 2040 are used, where each detector views all or a portion of the coating layer 2030. For example, two detectors 2040 are used where a first detector views a first half of the coating layer and the second detector views a second half of the coating layer. Preferably, the detector 2040 is mounted into the nozzle 2010 to view the proton beam position after passing through the first axis and second axis controllers 142, 144. Preferably, the coating layer 2030 is positioned in the proton beam path 268 in a position prior to the protons striking the patient 2130. Still referring to FIG. 20, the main controller 130, connected to the camera or detector 2040 output, compares the actual proton beam position 268 with the planned proton beam position and/or a calibration reference to determine if the actual proton beam position 268 is within tolerance. The proton beam verification system 2000 preferably is used in at least two phases, a calibration phase and a proton beam treatment phase. The calibration phase is used to correlate, as a function of x-, y-position of the glowing response the actual x-, y-position of the proton beam at the patient interface. During the proton beam treatment phase, the proton beam position is monitored and compared to the calibration and/or treatment plan to verify accurate proton delivery to the tumor 2120 and/or as a proton beam shutoff safety indicator. Patient Positioning Referring now to FIG. 21, the patient is preferably positioned on or within a patient positioning system 2110 of the patient interface module 150. The patient positioning system 2110 is used to translate the patient and/or rotate the patient into a zone where the proton beam can scan the tumor using a scanning system 140 or proton targeting system, described infra. Essentially, the patient positioning system 2110 performs large movements of the patient to place the tumor near the center of a proton beam path 268 and the proton scanning or targeting system 140 performs fine movements of the momentary beam position 269 in targeting the tumor 2120. To illustrate, FIG. 21 shows the momentary proton beam position 269 and a range of scannable positions 2140 using the proton scanning or targeting system 140, where the scannable positions 2140 are about the tumor 2120 of the patient 2130. This illustratively shows that the y-axis movement of the patient occurs on a scale of the body, such as adjustment of about 1, 2, 3, or 4 feet, while the scannable region of the proton beam 268 covers a portion of the body, such as a region of about 1, 2, 4, 6, 8, 10, or 12 inches. The patient positioning system and its rotation and/or translation of the patient combines with the proton targeting system to yield precise and/or accurate delivery of the protons to the tumor. Referring still to FIG. 21, the patient positioning system 2110 optionally includes a bottom unit 2112 and a top unit 2114, such as discs or a platform. Referring now to FIG. 21A, the patient positioning unit 2110 is preferably y-axis adjustable 2116 to allow vertical shifting of the patient relative to the proton therapy beam 268. Preferably, the vertical motion of the patient positioning unit 2110 is about 10, 20, 30, or 50 centimeters per minute. Referring now to FIG. 21B, the patient positioning unit 2110 is also preferably rotatable 2117 about a rotation axis, such as about the y-axis, to allow rotational control and positioning of the patient relative to the proton beam path 268. Preferably the rotational motion of the patient positioning unit 2110 is about 360 degrees per minute. Optionally, the patient positioning unit rotates about 45, 90, or 180 degrees. Optionally, the patient positioning unit 2110 rotates at a rate of about 45, 90, 180, 360, 720, or 1080 degrees per minute. The rotation of the positioning unit 2117 is illustrated about the rotation axis at two distinct times, t1 and t2. Protons are optionally delivered to the tumor 2120 at n times where each of the n times represent different directions of the incident proton beam 269 hitting the patient 2130 due to rotation of the patient 2117 about the rotation axis. Any of the semi-vertical, sitting, or laying patient positioning embodiments described, infra, are optionally vertically translatable along the y-axis or rotatable about the rotation or y-axis. Preferably, the top and bottom units 2112, 2114 move together, such that they rotate at the same rates and translate in position at the same rates. Optionally, the top and bottom units 2112, 2114 are independently adjustable along the y-axis to allow a difference in distance between the top and bottom units 2112, 2114. Motors, power supplies, and mechanical assemblies for moving the top and bottom units 2112, 2114 are preferably located out of the proton beam path 269, such as below the bottom unit 2112 and/or above the top unit 2114. This is preferable as the patient positioning unit 2110 is preferably rotatable about 360 degrees and the motors, power supplies, and mechanical assemblies interfere with the protons if positioned in the proton beam path 269 Proton Beam Position Control Referring now to FIG. 22, a beam delivery and tissue volume scanning system is illustrated. Presently, the worldwide radiotherapy community uses a method of dose field forming using a pencil beam scanning system. In stark contrast, FIG. 22 illustrates a spot scanning system or tissue volume scanning system. In the tissue volume scanning system, the proton beam is controlled, in terms of transportation and distribution, using an inexpensive and precise scanning system. The scanning system is an active system, where the beam is focused into a spot focal point of about one-half, one, two, or three millimeters in diameter. The focal point is translated along two axes while simultaneously altering the applied energy of the proton beam, which effectively changes the third dimension of the focal point. The system is applicable in combination with the above described rotation of the body, which preferably occurs in-between individual moments or cycles of proton delivery to the tumor. Optionally, the rotation of the body by the above described system occurs continuously and simultaneously with proton delivery to the tumor. For example, in the illustrated system in FIG. 22A, the spot is translated horizontally, is moved down a vertical, and is then back along the horizontal axis. In this example, current is used to control a vertical scanning system having at least one magnet. The applied current alters the magnetic field of the vertical scanning system to control the vertical deflection of the proton beam. Similarly, a horizontal scanning magnet system controls the horizontal deflection of the proton beam. The degree of transport along each axes is controlled to conform to the tumor cross-section at the given depth. The depth is controlled by changing the energy of the proton beam. For example, the proton beam energy is decreased, so as to define a new penetration depth, and the scanning process is repeated along the horizontal and vertical axes covering a new cross-sectional area of the tumor. Combined, the three axes of control allow scanning or movement of the proton beam focal point over the entire volume of the cancerous tumor. The time at each spot and the direction into the body for each spot is controlled to yield the desired radiation does at each sub-volume of the cancerous volume while distributing energy hitting outside of the tumor. The focused beam spot volume dimension is preferably tightly controlled to a diameter of about 0.5, 1, or 2 millimeters, but is alternatively several centimeters in diameter. Preferred design controls allow scanning in two directions with: (1) a vertical amplitude of about 100 mm amplitude and frequency up to 200 Hz; and (2) a horizontal amplitude of about 700 mm amplitude and frequency up to 1 Hz. More or less amplitude in each axis is possible by altering the scanning magnet systems. In FIG. 22A, the proton beam is illustrated along a z-axis controlled by the beam energy, the horizontal movement is along an x-axis, and the vertical direction is along a y-axis. The distance the protons move along the z-axis into the tissue, in this example, is controlled by the kinetic energy of the proton. This coordinate system is arbitrary and exemplary. The actual control of the proton beam is controlled in 3-dimensional space using two scanning magnet systems and by controlling the kinetic energy of the proton beam. The use of the extraction system, described supra, allows for different scanning patterns. Particularly, the system allows simultaneous adjustment of the x-, y-, and z-axes in the irradiation of the solid tumor. Stated again, instead of scanning along an x,y-plane and then adjusting energy of the protons, such as with a range modulation wheel, the system allows for moving along the z-axes while simultaneously adjusting the x- and or y-axes. Hence, rather than irradiating slices of the tumor, the tumor is optionally irradiated in three simultaneous dimensions. For example, the tumor is irradiated around an outer edge of the tumor in three dimensions. Then the tumor is irradiated around an outer edge of an internal section of the tumor. This process is repeated until the entire tumor is irradiated. The outer edge irradiation is preferably coupled with simultaneous rotation of the subject, such as about a vertical y-axis. This system allows for maximum efficiency of deposition of protons to the tumor, as defined using the Bragg peak, to the tumor itself with minimal delivery of proton energy to surrounding healthy tissue. Combined, the system allows for multi-axes control of the charged particle beam system in a small space with a small power supply. For example, the system uses multiple magnets where each magnet has at least one edge focusing effect in each turning section of the synchrotron and/or multiple magnets having concentrating magnetic field geometry, as described supra. The multiple edge focusing effects in the circulating beam path of the synchrotron combined with the concentration geometry of the magnets and described extraction system yields a synchrotron having: a small circumference system, such as less than about 50 meters; a vertical proton beam size gap of about 2 cm; corresponding reduced power supply requirements associated with the reduced gap size; an extraction system not requiring a newly introduced magnetic field; acceleration or deceleration of the protons during extraction; and control of z-axis energy during extraction. The result is a 3-dimensional scanning system, x-, y-, and z-axes control, where the z-axes control resides in the synchrotron and where the z-axes energy is variably controlled during the extraction process inside the synchrotron. Referring now to FIG. 22B, an example of a proton scanning or targeting system 140 used to direct the protons to the tumor with 4-dimensional scanning control is provided, where the 4-dimensional scanning control is along the x-, y-, and z-axes along with intensity control, as described supra. A fifth axis is time. Typically, charged particles traveling along the transport path 268 are directed through a first axis control element 142, such as a vertical control, and a second axis control element 144, such as a horizontal control and into a tumor 2120. As described, supra, the extraction system also allows for simultaneous variation in the z-axis. Further, as describe, supra, the intensity or dose of the extracted beam is optionally simultaneously and independently controlled and varied. Thus instead of irradiating a slice of the tumor, as in FIG. 22A, all four dimensions defining the targeting spot of the proton delivery in the tumor are simultaneously variable. The simultaneous variation of the proton delivery spot is illustrated in FIG. 22B by the spot delivery path 269. In the illustrated case, the protons are initially directed around an outer edge of the tumor and are then directed around an inner radius of the tumor. Combined with rotation of the subject about a vertical axis, a multi-field irradiation process is used where a not yet irradiated portion of the tumor is preferably irradiated at the further distance of the tumor from the proton entry point into the body. This yields the greatest percentage of the proton delivery, as defined by the Bragg peak, into the tumor and minimizes damage to peripheral healthy tissue. Imaging/X-Ray System Herein, an X-ray system is used to illustrate an imaging system. Timing An X-ray is preferably collected either (1) just before or (2) concurrently with treating a subject with proton therapy for a couple of reasons. First, movement of the body, described supra, changes the local position of the tumor in the body relative to other body constituents. If the subject has an X-ray taken and is then bodily moved to a proton treatment room, accurate alignment of the proton beam to the tumor is problematic. Alignment of the proton beam to the tumor using one or more X-rays is best performed at the time of proton delivery or in the seconds or minutes immediately prior to proton delivery and after the patient is placed into a therapeutic body position, which is typically a fixed position or partially immobilized position. Second, the X-ray taken after positioning the patient is used for verification of proton beam alignment to a targeted position, such as a tumor and/or internal organ position. Positioning An X-ray is preferably taken just before treating the subject to aid in patient positioning. For positioning purposes, an X-ray of a large body area is not needed. In one embodiment, an X-ray of only a local area is collected. When collecting an X-ray, the X-ray has an X-ray path. The proton beam has a proton beam path. Overlaying the X-ray path with the proton beam path is one method of aligning the proton beam to the tumor. However, this method involves putting the X-ray equipment into the proton beam path, taking the X-ray, and then moving the X-ray equipment out of the beam path. This process takes time. The elapsed time while the X-ray equipment moves has a couple of detrimental effects. First, during the time required to move the X-ray equipment, the body moves. The resulting movement decreases precision and/or accuracy of subsequent proton beam alignment to the tumor. Second, the time required to move the X-ray equipment is time that the proton beam therapy system is not in use, which decreases the total efficiency of the proton beam therapy system. X-Ray Source Lifetime It is desirable to have components in the particle beam therapy system that require minimal or no maintenance over the lifetime of the particle beam therapy system. For example, it is desirable to equip the proton beam therapy system with an X-ray system having a long lifetime source, such as a lifetime of about 20 years. In one system, described infra, electrons are used to create X-rays. The electrons are generated at a cathode where the lifetime of the cathode is temperature dependent. Analogous to a light bulb, where the filament is kept in equilibrium, the cathode temperature is held in equilibrium at temperatures at about 200, 500, or 1000 degrees Celsius. Reduction of the cathode temperature results in increased lifetime of the cathode. Hence, the cathode used in generating the electrons is preferably held at as low of a temperature as possible. However, if the temperature of the cathode is reduced, then electron emissions also decrease. To overcome the need for more electrons at lower temperatures, a large cathode is used and the generated electrons are concentrated. The process is analogous to compressing electrons in an electron gun; however, here the compression techniques are adapted to apply to enhancing an X-ray tube lifetime. Referring now to FIG. 23, an example of an X-ray generation device 2300 having an enhanced lifetime is provided. Electrons 2320 are generated at a cathode 2310, focused with a control electrode 2312, and accelerated with a series of accelerating electrodes 2340. The accelerated electrons 2350 impact an X-ray generation source 2348 resulting in generated X-rays that are then directed along an X-ray path 2470 to the subject 2130. The concentrating of the electrons from a first diameter 2315 to a second diameter 2316 allows the cathode to operate at a reduced temperature and still yield the necessary amplified level of electrons at the X-ray generation source 2348. In one example, the X-ray generation source is the anode coupled with the cathode 2310 and/or the X-ray generation source is substantially composed of tungsten. Still referring to FIG. 23, a more detailed description of an exemplary X-ray generation device 2300 is described. An anode 2314/cathode 2310 pair is used to generated electrons. The electrons 2320 are generated at the cathode 2310 having a first diameter 2315, which is denoted d1. The control electrodes 2312 attract the generated electrons 2320. For example, if the cathode is held at about −150 kV and the control electrode is held at about −149 kV, then the generated electrons 2320 are attracted toward the control electrodes 2312 and focused. A series of accelerating electrodes 2340 are then used to accelerate the electrons into a substantially parallel path 2350 with a smaller diameter 2316, which is denoted d2. For example, with the cathode held at −150 kV, a first, second, third, and fourth accelerating electrodes 2342, 2344, 2346, 2348 are held at about −120, −90, −60, and −30 kV, respectively. If a thinner body part is to be analyzed, then the cathode 2310 is held at a smaller level, such as about −90 kV and the control electrode, first, second, third, and fourth electrode are each adjusted to lower levels. Generally, the voltage difference from the cathode to fourth electrode is less for a smaller negative voltage at the cathode and vise-versa. The accelerated electrons 2350 are optionally passed through a magnetic lens 2360 for adjustment of beam size, such as a cylindrical magnetic lens. The electrons are also optionally focused using quadrupole magnets 2370, which focus in one direction and defocus in another direction. The accelerated electrons 2350, which are now adjusted in beam size and focused strike an X-ray generation source 2348, such as tungsten, resulting in generated X-rays that pass through an optional blocker 2462 and proceed along an X-ray path 2370 to the subject. The X-ray generation source 2348 is optionally cooled with a cooling element 2349, such as water touching or thermally connected to a backside of the X-ray generation source 2348. The concentrating of the electrons from a first diameter 2315 to a second diameter 2316 allows the cathode to operate at a reduced temperature and still yield the necessary amplified level of electrons at the X-ray generation source 2348. More generally, the X-ray generation device 2300 produces electrons having initial vectors. One or more of the control electrode 2312, accelerating electrodes 2340, magnetic lens 2360, and quadrupole magnets 2370 combine to alter the initial electron vectors into parallel vectors with a decreased cross-sectional area having a substantially parallel path, referred to as the accelerated electrons 2350. The process allows the X-ray generation device 2300 to operate at a lower temperature. Particularly, instead of using a cathode that is the size of the electron beam needed, a larger electrode is used and the resulting electrons 2320 are focused and/or concentrated into the required electron beam needed. As lifetime is roughly an inverse of current density, the concentration of the current density results in a larger lifetime of the X-ray generation device. A specific example is provided for clarity. If the cathode has a 15 mm radius or d1 is about 30 mm, then the area (π r2) is about 225 mm2 times pi. If the concentration of the electrons achieves a radius of 5 mm or d2 is about 10 mm, then the area (π r2) is about 25 mm2 times pi. The ratio of the two areas is about 9 (225π/257π). Thus, there is about 9 times less density of current at the larger cathode compared to the traditional cathode having an area of the desired electron beam. Hence, the lifetime of the larger cathode approximates 9 times the lifetime of the traditional cathode, though the actual current through the larger cathode and traditional cathode is about the same. Preferably, the area of the cathode 2310 is about 2, 4, 6, 8, 10, 15, 20, or 25 times that of the cross-sectional area of the substantially parallel electron beam 2350. In another embodiment of the invention, the quadrupole magnets 2370 result in an oblong cross-sectional shape of the electron beam 2350. A projection of the oblong cross-sectional shape of the electron beam 2350 onto the X-ray generation source 2348 results in an X-ray beam that has a small spot in cross-sectional view, which is preferably substantially circular in cross-sectional shape, that is then passed through the patient 2330. The small spot is used to yield an X-ray having enhanced resolution at the patient. Referring now to FIG. 24, in one embodiment, an X-ray is generated close to, but not in, the proton beam path. A proton beam therapy system and an X-ray system combination 2400 is illustrated in FIG. 24. The proton beam therapy system has a proton beam 268 in a transport system after the Lamberson extraction magnet 292 of the synchrotron 130. The proton beam is directed by the scanning/targeting/delivery system 140 to a tumor 2120 of a patient 2130. The X-ray system 2405 includes an electron beam source 2305 generating an electron beam 2350. The electron beam is directed to an X-ray generation source 2348, such as a piece of tungsten. Preferably, the tungsten X-ray source is located about 1, 2, 3, 5, 10, 15, or 20 millimeters from the proton beam path 268. When the electron beam 2350 hits the tungsten, X-rays are generated in all directions. X-rays are blocked with a port 2462 and are selected for an X-ray beam path 2470. The X-ray beam path 2470 and proton beam path 268 run substantially in parallel as they progress to the tumor 2120. The distance between the X-ray beam path 2470 and proton beam path 269 preferably diminishes to near zero and/or the X-ray beam path 2470 and proton beam path 269 overlap by the time they reach the tumor 2120. Simple geometry shows this to be the case given the long distance, of at least a meter, between the tungsten and the tumor 2120. The distance is illustrated as a gap 2480 in FIG. 24. The X-rays are detected at an X-ray detector 2490, which is used to form an image of the tumor 2120 and/or position of the patient 2130. As a whole, the system generates an X-ray beam that lies in substantially the same path as the proton therapy beam. The X-ray beam is generated by striking a tungsten or equivalent material with an electron beam. The X-ray generation source is located proximate to the proton beam path. Geometry of the incident electrons, geometry of the X-ray generation material, and/or geometry of the X-ray beam blocker 262 yield an X-ray beam that runs either in substantially in parallel with the proton beam or results in an X-ray beam path that starts proximate the proton beam path an expands to cover and transmit through a tumor cross-sectional area to strike an X-ray detector array or film allowing imaging of the tumor from a direction and alignment of the proton therapy beam. The X-ray image is then used to control the charged particle beam path to accurately and precisely target the tumor, and/or is used in system verification and validation. Referring now to FIG. 25, additional geometry of the electron beam path 2350 and X-ray beam path 2470 is illustrated. Particularly, the electron beam 2350 is shown as an expanded electron beam path 2352, 2354. Also, the X-ray beam path 2470 is shown as an expanded X-ray beam path 2472, 2474. Referring now to FIG. 26, a 3-dimensional (3-D) X-ray tomography system 2600 is presented. In a typical X-ray tomography system, the X-ray source and detector rotationally translate about a stationary subject. In the X-ray tomography system described herein, the X-ray source and detector are stationary and the patient 2130 rotates. The stationary X-ray source allows a system where the X-ray source 2348 is proximate the proton therapy beam path 268, as described supra. In addition, the rotation of the patient 2130 allows the proton dosage to be distributed around the body, rather than being concentrated on one static entrance side of the body. Further, the 3-D X-ray tomography system allows for simultaneous updates of the tumor position relative to body constituents in real-time during proton therapy treatment of the tumor 2120 in the patient 2130. The X-ray tomography system is further described, infra. In a first step of the X-ray tomography system 2600, the patient 2130 is positioned relative to the X-ray beam path 2470 and proton beam path 268 using a patient semi-immobilization/placement system 2800, described infra. After patient 2130 positioning, a series of reference 2-D X-ray images are collected, on a detector array 2490 or film, of the patient 2130 and tumor 2120 as the subject is rotated about a y-axis 2117. For example, a series of about 50, 100, 200, or 400 X-ray images of the patient are collected as the patient is rotated. In a second example, an X-ray image is collected with each n degrees of rotation of the patient 2130, where n is about ½, 1, 2, 3, or 5 degrees of rotation. Preferably, about 200 images are collected during one full rotation of the patient through 360 degrees. Subsequently, using the reference 2-D X-ray images, an algorithm produces a reference 3-D picture of the tumor 2120 relative to the patient's constituent body parts. A tumor 2120 irradiation plan is made using the 3-D picture of the tumor 2120 and the patient's constituent body parts. Creation of the proton irradiation plan is optionally performed after the patient has moved from the X-ray imaging area. In a second step, the patient 2130 is repositioned relative to the X-ray beam path 2470 and proton beam path 268 using the patient semi-immobilization/placement system 2800. Just prior to implementation of the proton irradiation plan, a few comparative X-ray images of the patient 2130 and tumor 2120 are collected at a limited number of positions using the X-ray tomography system 2600 setup. For example, a single X-ray image is collected with the patient positioned straight on, at angles of plus/minus forty-five degrees, and/or at angles of plus/minus ninety degrees relative to the proton beam path 268. The actual orientation of the patient 2130 relative to the proton beam path 268 is optionally any orientation. The actual number of comparative X-ray images is also optionally any number of images, though the preferable number of comparative X-ray images is about 2 to 5 comparative images. The comparative X-ray images are compared to the reference X-ray images and differences are detected. A medical expert or an algorithm determines if the difference between the reference images and the comparative images is significant. Based upon the differences, the medical expert or algorithm determines if: proton treatment should commence, be halted, or adapted in real-time. For example, if significant differences in the X-ray images are observed, then the treatment is preferably halted and the process of collecting a reference 3-D picture of the patient's tumor is reinitiated. In a second example, if the differences in the X-ray images are observed to be small, then the proton irradiation plan commences. In a third example, the algorithm or medical expert can adapt the proton irradiation plan in real-time to adjust for differences in tumor location resulting from changes in position of the tumor 2120 in the patient 2130 or from differences in the patient 2130 placement. In the third example, the adaptive proton therapy increases patient throughput and enhances precision and accuracy of proton irradiation of the tumor 2120 relative to the healthy tissue of the patient 2130. Patient Immobilization Accurate and precise delivery of a proton beam to a tumor of a patient requires: (1) positioning control of the proton beam and (2) positioning control of the patient. As described, supra, the proton beam is controlled using algorithms and magnetic fields to a diameter of about 0.5, 1, or 2 millimeters. This section addresses partial immobilization, restraint, and/or alignment of the patient to insure the tightly controlled proton beam efficiently hits a target tumor and not surrounding healthy tissue as a result of patient movement. In this section an x-, y-, and z-axes coordinate system and rotation axis is used to describe the orientation of the patient relative to the proton beam. The z-axis represent travel of the proton beam, such as the depth of the proton beam into the patient. When looking at the patient down the z-axis of travel of the proton beam, the x-axis refers to moving left or right across the patient and the y-axis refers to movement up or down the patient. A first rotation axis is rotation of the patient about the y-axis and is referred to herein as a rotation axis, bottom unit 2112 rotation axis, or y-axis of rotation. In addition, tilt is rotation about the x-axis, yaw is rotation about the y-axis, and roll is rotation about the z-axis. In this coordinate system, the proton beam path 269 optionally runs in any direction. As an illustrative matter, the proton beam path running through a treatment room is described as running horizontally through the treatment room. In this section, three examples of positioning systems are provided: (1) a semi-vertical partial immobilization system 2700; (2) a sitting partial immobilization system 2800; and (3) a laying position 2900. Elements described for one immobilization system apply to other immobilization systems with small changes. For example, a head rest will adjust along one axis for a reclined position, along a second axis for a seated position, and along a third axis for a laying position. However, the headrest itself is similar for each immobilization position. Vertical Patient Positioning/Immobilization The semi-vertical patient positioning system 2700 is preferably used in conjunction with proton therapy of tumors in the torso. The patient positioning and/or immobilization system controls and/or restricts movement of the patient during proton beam therapy. In a first partial immobilization embodiment, the patient is positioned in a semi-vertical position in a proton beam therapy system. As illustrated, the patient is reclining at an angle alpha, α, about 45 degrees off of the y-axis as defined by an axis running from head to foot of the patient. More generally, the patient is optionally completely standing in a vertical position of zero degrees off the of y-axis or is in a semi-vertical position alpha that is reclined about 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, or 65 degrees off of the y-axis toward the z-axis. Patient positioning constraints 2715 are used to maintain the patient in a treatment position, including one or more of: a seat support 2720, a back support 2730, a head support 2740, an arm support 2750, a knee support 2760, and a foot support 2770. The constraints are optionally and independently rigid or semi-rigid. Examples of a semi-rigid material include a high or low density foam or a visco-elastic foam. For example the foot support is preferably rigid and the back support is preferably semi-rigid, such as a high density foam material. One or more of the positioning constraints 2715 are movable and/or under computer control for rapid positioning and/or immobilization of the patient. For example, the seat support 2720 is adjustable along a seat adjustment axis 2722, which is preferably the y-axis; the back support 2730 is adjustable along a back support axis 2732, which is preferably dominated by z-axis movement with a y-axis element; the head support 2740 is adjustable along a head support axis 2742, which is preferably dominated by z-axis movement with a y-axis element; the arm support 2750 is adjustable along an arm support axis 2752, which is preferably dominated by z-axis movement with a y-axis element; the knee support 2760 is adjustable along a knee support axis 2762, which is preferably dominated by y-axis movement with a z-axis element; and the foot support 2770 is adjustable along a foot support axis 2772, which is preferably dominated by y-axis movement with a z-axis element. If the patient is not facing the incoming proton beam, then the description of movements of support elements along the axes change, but the immobilization elements are the same. An optional camera 2780 is used with the patient immobilization system. The camera views the patient/subject creating an video image. The image is provided to one or more operators of the charged particle beam system and allows the operators a safety mechanism for determining if the subject has moved or desires to terminate the proton therapy treatment procedure. Based on the video image, the operators optionally suspend or terminate the proton therapy procedure. For example, if the operator observes via the video image that the subject is moving, then the operator has the option to terminate or suspend the proton therapy procedure. An optional video display 490 is provided to the patient. The video display optionally presents to the patient any of: operator instructions, system instructions, status of treatment, or entertainment. Motors for positioning the constraints 2715, the camera 2780, and video display 2790 are preferably mounted above or below the proton path. Respiration control is optionally performed by using the video display. As the patient breathes, internal and external structures of the body move in both absolute terms and in relative terms. For example, the outside of the chest cavity and internal organs both have absolute moves with a breath. In addition, the relative position of an internal organ relative to another body component, such as an outer region of the body, a bone, support structure, or another organ, moves with each breath. Hence, for more accurate and precise tumor targeting, the proton beam is preferably delivered at point a in time where the position of the internal structure or tumor is well defined, such as at the bottom of each breath. The video display is used to help coordinate the proton beam delivery with the patient's respiration cycle. For example, the video display optionally displays to the patient a command, such as a hold breath statement, a breath statement, a countdown indicating when a breath will next need to be held, or a countdown until breathing may resume. Sitting Patient Positioning/Immobilization In a second partial immobilization embodiment, the patient is partially restrained in a seated position 2800. The sitting restraint system has support structures that are similar to the support structures used in the semi-vertical positioning system, described supra with the exception that the seat support is replaced by a chair and the knee support is not required. The seated restraint system generally retains the adjustable support, rotation about the y-axis, camera, video, and breath control parameters described in the semi-vertical embodiment, described supra. Referring now to FIG. 28, a particular example of a sitting patient semi-immobilization system 2800 is provided. The sitting system is preferably used for treatment of head and neck tumors. As illustrated, the patient is positioned in a seated position on a chair 2810 for particle therapy. The patient is further immobilized using any of the: the head support 2740, the back support 2730, a hand support 2750, the knee support 2760, and the foot support 2770. The supports 2720, 2730, 2740, 2750, 2760, 2770 preferably have respective axes of adjustment 2722, 2732, 2742, 2752, 2762, 2772 as illustrated. The chair 2810 is either readily removed to allow for use of a different patient constraint system or adapts to a new patient position, such as the semi-vertical system. Laying Patient Positioning/Immobilization In a third partial immobilization embodiment, the patient is partially restrained in a laying position. The laying restraint system 2900 has support structures that are similar to the support structures used in the sitting positioning system and semi-vertical positioning system, described supra. In the laying position, optional restraint, support, or partial immobilization elements include one or more of: the head support 2740 and the back support, hip, and shoulder 2730 support. The supports preferably have respective axes of adjustment that are rotated as appropriate for a laying position of the patient. The laying position restraint system generally retains the adjustable supports, rotation about the y-axis, camera, video, and breath control parameters described in the semi-vertical embodiment, described supra. If the patient is very sick, such as the patient has trouble standing for a period of about one to three minutes required for treatment, then being in a partially supported system can result in some movement of the patient due to muscle strain. In this and similar situations, treatment of a patient in a laying position on a support table 2920 is preferentially used. The support table has a horizontal platform to support the bulk of the weight of the patient. Preferably, the horizontal platform is detachable from a treatment platform. In a laying positioning system 2900, the patient is positioned on a platform 2910, which has a substantially horizontal portion for supporting the weight of the body in a horizontal position. Optional hand grips are used, described infra. In one embodiment, the platform 2910 affixes relative to the table 2920 using a mechanical stop or lock element 2930 and matching key element 2935 and/or the patient 2130 is aligned or positioned relative to a placement element 2960. Additionally, upper leg support 2944, lower leg support 2940, and/or arm support 2950 elements are optionally added to raise, respectively, an arm or leg out of the proton beam path 269 for treatment of a tumor in the torso or to move an arm or leg into the proton beam path 269 for treatment of a tumor in the arm or leg. This increases proton delivery efficiency, as described infra. The leg supports 2940, 2944 and arm support 2950 are each optionally adjustable along support axes 2942, 2946, 2952. One or more leg support elements are optionally adjustable along an arc to position the leg into the proton beam path 269 or to remove the leg from the proton beam path 269, as described infra. An arm support element is preferably adjustable along at least one arm adjustment axis or along an arc to position the arm into the proton beam path 269 or to remove the arm from the proton beam path 269, as described infra. Preferably, the patient is positioned on the platform 2910 in an area or room outside of the proton beam path 269 and is wheeled or slid into the treatment room or proton beam path area. For example, the patient is wheeled into the treatment room on a gurney where the top of the gurney, which is the platform, detaches and is positioned onto a table. The platform is preferably lifted onto the table or slid onto the table so that the gurney or bed need not be lifted onto the table. The semi-vertical patient positioning system 2700 and sitting patient positioning system 2800 are preferentially used to treatment of tumors in the head or torso due to efficiency. The semi-vertical patient positioning system 2700, sitting patient positioning system 2800, and laying patient positioning system 2900 are all usable for treatment of tumors in the patient's limbs. Support System Elements Positioning constraints 2715 include all elements used to position the patient, such as those described in the semi-vertical positioning system 2700, sitting positioning system 2800, and laying positioning system 2900. Preferably, positioning constraints or support system elements are aligned in positions that do not impede or overlap the proton beam path 269. However, in some instances the positioning constraints are in the proton beam path 269 during at least part of the time of treatment of the patient. For instance, a positioning constraint element may reside in the proton beam path 269 during part of a time period where the patient is rotated about the y-axis during treatment. In cases or time periods that the positioning constraints or support system elements are in the proton beam path, then an upward adjustment of proton beam energy is preferably applied that increases the proton beam energy to offset the positioning constraint element impedance of the proton beam, this time period and energy is a function of rotational orientation of the patient. In one case, the proton beam energy is increased by a separate measure of the positioning constraint element impedance determined during a reference scan of the positioning constraint system element or set of reference scans of the positioning constraint element as a function of rotation about the y-axis. For clarity, the positioning constraints 2715 or support system elements are herein described relative to the semi-vertical positioning system 2700; however, the positioning elements and descriptive x-, y-, and z-axes are adjustable to fit any coordinate system, to the sitting positioning system, or the laying positioning system. An example of a head support system is described to support, align, and/or restrict movement of a human head. The head support system preferably has several head support elements including any of: a back of head support, a right of head alignment element, and a left of head alignment element. The back of head support element is preferably curved to fit the head and is optionally adjustable along a head support axis, such as along the z-axis. Further, the head supports, like the other patient positioning constraints, is preferably made of a semi-rigid material, such as a low or high density foam, and has an optional covering, such as a plastic or leather. The right of head alignment element and left of head alignment elements or head alignment elements, are primarily used to semi-constrain movement of the head. The head alignment elements are preferably padded and flat, but optionally have a radius of curvature to fit the side of the head. The right and left head alignment elements are preferably respectively movable along translation axes to make contact with the sides of the head. Restricted movement of the head during proton therapy is important when targeting and treating tumors in the head or neck. The head alignment elements and the back of head support element combine to restrict tilt, rotation or yaw, roll and/or position of the head in the x-, y-, z-axes coordinate system. Referring now to FIG. 30 another example of a head support system 3000 is described for positioning and/or restricting movement of a human head 2102 during proton therapy of a solid tumor in the head or neck. In this system, the head is restrained using 1, 2, 3, 4, or more straps or belts, which are preferably connected or replaceably connected to a back of head support element 3010. In the example illustrated, a first strap 3020 pulls or positions the forehead to the head support element 3010, such as by running predominantly along the z-axis. Preferably a second strap 3030 works in conjunction with the first strap 3020 to prevent the head from undergoing tilt, yaw, roll or moving in terms of translational movement on the x-, y-, and z-axes coordinate system. The second strap 3030 is preferably attached or replaceable attached to the first strap 3020 at or about: (1) a forehead position 3032; (2) at a position on one or both sides of the head 3034; and/or (3) at or about the support element position 3036. A third strap 3040 preferably orientates the chin of the subject relative to the support element 3010 by running dominantly along the z-axis. A fourth strap 3050 preferably runs along a predominantly y- and z-axes to hold the chin relative to the head support element 3010 and/or proton beam path. The third 3040 strap preferably is attached to or is replaceably attached to the fourth strap 3050 during use at or about the patient's chin position 3042. The second strap 3030 optionally connects to the fourth strap 3050 at or about the support element 3010. The four straps 3020, 3030, 3040, 3050 are illustrative in pathway and interconnection. Any of the straps optionally hold the head along different paths around the head and connect to each other in separate fashion. Naturally, a given strap preferably runs around the head and not just on one side of the head. Any of the straps 3020, 3030, 3040, and 3050 are optionally used independently or in combinations or permutations with the other straps. The straps are optionally indirectly connected to each other via a support element, such as the head support element 3010. The straps are optionally attached to the head support element 3010 using hook and loop technology, a buckle, or fastener. Generally, the straps combine to control position, front-to-back movement of the head, side-to-side movement of the head, tilt, yaw, roll, and/or translational position of the head. The straps are preferably of known impedence to proton transmission allowing a calculation of peak energy release along the z-axis to be calculated, such as an adjustment to the Bragg peak is made based on the slowing tendency of the straps to proton transport. Referring now to FIG. 28, still another example of a head support system 2740 is described. The head support 2740 is preferably curved to fit a standard or child sized head. The head support 2740 is optionally adjustable along a head support axis 2742. Further, the head supports, like the other patient positioning constraints, is preferably made of a semi-rigid material, such as a low or high density foam, and has an optional covering, such as a plastic or leather. Elements of the above described head support, head positioning, and head immobilization systems are optionally used separately or in combination. Still referring to FIG. 31, an example of the arm support 2750 is further described. The arm support preferably has a left hand grip 3110 and a right hand grip 3120 used for aligning the upper body of the patient 2130 through the action of the patient 2130 gripping the left and right hand grips 3110, 3120 with the patient's hands 2134. The left and right hand grips 3110, 3120 are preferably connected to the arm support 2750 that supports the mass of the patient's arms. The left and right hand grips 3110, 3120 are preferably constructed using a semi-rigid material. The left and right hand grips 3110, 3120 are optionally molded to the patient's hands to aid in alignment. The left and right hand grips optionally have electrodes, as described supra. Positioning System Computer Control One or more of the patient positioning unit components and/or one of more of the patient positioning constraints are preferably under computer control, where the computer control positioning devices, such as via a series of motors and drives, to reproducibly position the patient. For example, the patient is initially positioned and constrained by the patient positioning constraints. The position of each of the patient positioning constraints is recorded and saved by the main controller 110, by a sub-controller or the main controller 110, or by a separate computer controller. Then, medical devices are used to locate the tumor 2120 in the patient 2130 while the patient is in the orientation of final treatment. The imaging system 170 includes one or more of: MRI's, X-rays, CT's, proton beam tomography, and the like. Time optionally passes at this point where images from the imaging system 170 are analyzed and a proton therapy treatment plan is devised. The patient may exit the constraint system during this time period, which may be minutes, hours, or days. Upon return of the patient to the patient positioning unit, the computer can return the patient positioning constraints to the recorded positions. This system allows for rapid repositioning of the patient to the position used during imaging and development of the treatment plan, which minimizes setup time of patient positioning and maximizes time that the charged particle beam system 100 is used for cancer treatment. Proton Delivery Efficiency A Bragg peak energy profile shows that protons deliver their energy across the entire length of the body penetrated by the proton up to a maximum penetration depth. As a result, energy is being delivered to healthy tissue, bone, and other body constituents before the proton beam hits the tumor. It follows that the shorter the pathlength in the body prior to the tumor, the higher the efficiency of proton delivery efficiency, where proton delivery efficiency is a measure of how much energy is delivered to the tumor relative to healthy portions of the patient. Examples of proton delivery efficiency include:(1) a ratio proton energy delivered the tumor and proton energy delivered to non-tumor tissue; (2) pathlength of protons in the tumor versus pathlength in the non-tumor tissue; and (3) damage to a tumor compared to damage to healthy body parts. Any of these measures are optionally weighted by damage to sensitive tissue, such as a nervous system element, heart, brain, or other organ. To illustrate, for a patient in a laying position where the patient is rotated about the y-axis during treatment, a tumor near the hear would at times be treated with protons running through the head-to-heart path, leg-to-heart path, or hip-to-heart path, which are all inefficient compared to a patient in a sitting or semi-vertical position where the protons are all delivered through a shorter chest-to-heart; side-of-body-to-heart, or back-to-heart path. Particularly, compared to a laying position, using a sitting or semi-vertical position of the patient, a shorter pathlength through the body to a tumor is provided to a tumor located in the torso or head, which is a higher or better proton delivery efficiency. Herein proton delivery efficiency is separately described from the time efficiency or synchrotron use efficiency, which is a fraction of time that the charged particle beam apparatus is in operation. Patient Placement Preferably, the patient 2130 is aligned in the proton beam path 269 in a precise and accurate manner. Several placement systems are described. The patient placement systems are described using the laying positioning system, but are equally applicable to the semi-vertical and sitting positioning systems. In a first placement system, the patient is positioned in a known location relative to the platform. For example, one or more of the positioning constraints position the patient in a precise and/or accurate location on the platform. Optionally, a placement constraint element connected or replaceably connected to the platform is used to position the patient on the platform. The placement constraint element(s) is used to position any position of the patient, such as a hand, limb, head, or torso element. In a second placement system, one or more positioning constraints or support element, such as the platform, is aligned versus an element in the patient treatment room. Essentially a lock and key system is optionally used, where a lock fits a key. The lock and key elements combine to locate the patient relative to the proton beam path 269 in terms of any of the x-, y-, and z-position, tilt, yaw, and roll. Essentially the lock is a first registration element and the key is a second registration element fitting into, adjacent to, or with the first registration element to fix the patient location and/or a support element location relative to the proton beam path 269. Examples of a registration element include any of a mechanical element, such as a mechanical stop, and an electrical connection indicating relative position or contact. In a third placement system, the imaging system, described supra, is used to determine where the patient is relative to the proton beam path 269 or relative to an imaging marker placed in an support element or structure holding the patient, such as in the platform. When using the imaging system, such as an X-ray imaging system, then the first placement system or positioning constraints minimize patient movement once the imaging system determines location of the subject. Similarly, when using the imaging system, such as an X-ray imaging system, then the first placement system and/or second positioning system provide a crude position of the patient relative to the proton beam path 269 and the imaging system subsequently determines a fine position of the patient relative to the proton beam path 269. X-Ray Synchronization with Patient Respiration In one embodiment, X-ray images are collected in synchronization with patient respiration. The synchronization enhances X-ray image clarity by removing position ambiguity due to the relative movement of body constituents during a patient respiration cycle. In a second embodiment, an X-ray system is orientated to provide X-ray images of a patient in the same orientation as viewed by a proton therapy beam, is synchronized with patient respiration, is operable on a patient positioned for proton therapy, and does not interfere with a proton beam treatment path. Preferably, the synchronized system is used in conjunction with a negative ion beam source, synchrotron, and/or targeting method apparatus to provide an X-ray timed with patient respiration and performed immediately prior to and/or concurrently with particle beam therapy irradiation to ensure targeted and controlled delivery of energy relative to a patient position resulting in efficient, precise, and/or accurate noninvasive, in-vivo treatment of a solid cancerous tumor with minimization of damage to surrounding healthy tissue in a patient using the proton beam position verification system. An X-ray delivery control algorithm is used to synchronize delivery of the X-rays to the patient 2130 within a given period of each breath, such as at the top or bottom of a breath when the subject is holding their breath. For clarity of combined X-ray images, the patient is preferably both accurately positioned and precisely aligned relative to the X-ray beam path 2470. The X-ray delivery control algorithm is preferably integrated with the respiration control module. Thus, the X-ray delivery control algorithm knows when the subject is breathing, where in the respiration cycle the subject is, and/or when the subject is holding their breath. In this manner, the X-ray delivery control algorithm delivers X-rays at a selected period of the respiration cycle. Accuracy and precision of patient alignment allow for (1) more accurate and precise location of the tumor 2120 relative to other body constituents and (2) more accurate and precise combination of X-rays in generation of a 3-dimensional X-ray image of the patient 2130 and tumor 2120. Referring now to FIG. 32, an example of generating an X-ray image 3200 of the patient 2130 and tumor 2120 using the X-ray generation device 2300 or 3-dimensional X-ray generation device 2300 as a known function of time of the patient's respiration cycle is provided. In one embodiment, as a first step the main controller 110 instructs, monitors, and/or is informed of patient positioning 3210. In a first example of patient positioning 3210, an automated patient positioning system, under main controller 110 control, is used to align the patient 2130 relative to the X-ray beam path 2470. In a second example of patient positioning, the main controller 110 is told via sensors or human input that the patient 2130 is aligned. In a second step, patient respiration is then monitored 3220, as described infra. As a first example of respiration monitoring, an X-ray is collected 3240 at a known point in the patient respiration cycle. In a second example of respiration monitoring, the patient's respiration cycle is first controlled in a third step of controlling patient respiration 3220 and then as a fourth step an X-ray is collected 3240 at a controlled point in the patient respiration cycle. Preferably, the cycle of patient positioning 3210, patient respiration monitoring 3220, patient respiration control 3230, and collecting an X-ray 3240 is repeated with different patient positions. For example, the patient 2130 is rotated about an axis 2117 and X-rays are collected as a function of the rotation. In a fifth step, a 3-dimensional X-ray image of the patient 2130, tumor 2120, and body constituents about the tumor is generated using the collected X-ray images, such as with the 3-dimensional X-ray generation device 2300, described supra. The patient respiration monitoring and control steps are further described, infra. Patient Respiration Monitoring Preferably, the patient's respiration pattern is monitored 3220. When a subject, also referred to herein as a patient, is breathing many portions of the body move with each breath. For example, when a subject breathes the lungs move as do relative positions of organs within the body, such as the stomach, kidneys, liver, chest muscles, skin, heart, and lungs. Generally, most or all parts of the torso move with each breath. Indeed, the inventors have recognized that in addition to motion of the torso with each breath, various motion also exists in the head and limbs with each breath. Motion is to be considered in delivery of a proton dose to the body as the protons are preferentially delivered to the tumor and not to surrounding tissue. Motion thus results in an ambiguity in where the tumor resides relative to the beam path. Protons are preferentially delivered at the same point in each of a series of respiration cycles. Initially a rhythmic pattern of breathing of a subject is determined 3220. The cycle is observed or measured. For example, an X-ray beam operator or proton beam operator can observe when a subject is breathing or is between breaths and can time the delivery of the protons to a given period of each breath. Alternatively, the subject is told to inhale, exhale, and/or hold their breath and the protons are delivered during the commanded time period. Preferably, one or more sensors are used to determine the respiration cycle of the individual. Two examples of a respiration monitoring system are provided: (1) a thermal monitoring system and (2) a force monitoring system. Referring again to FIG. 30, a first example of the thermal respiration monitoring system is provided. In the thermal respiration monitoring system, a sensor is placed by the nose and/or mouth of the patient. As the jaw of the patient is optionally constrained, as described supra, the thermal respiration monitoring system is preferably placed by the patient's nose exhalation path. To avoid steric interference of the thermal sensor system components with proton therapy, the thermal respiration monitoring system is preferably used when treating a tumor not located in the head or neck, such as a when treating a tumor in the torso or limbs. In the thermal monitoring system, a first thermal resistor 3070 is used to monitor the patient's respiration cycle and/or location in the patient's respiration cycle. Preferably, the first thermal resistor 3070 is placed by the patient's nose, such that the patient exhaling through their nose onto the first thermal resistor 3070 warms the first thermal resistor 3070 indicating an exhale. Preferably, a second thermal resistor 3060 operates as an environmental temperature sensor. The second thermal resistor 3060 is preferably placed out of the exhalation path of the patient but in the same local room environment as the first thermal resistor 3070. Generated signal, such as current from the thermal resistors 3070, 3060, is preferably converted to voltage and communicated with the main controller 110 or a sub-controller of the main controller. Preferably, the second thermal resistor 3060 is used to adjust for the environmental temperature fluctuation that is part of a signal of the first thermal resistor 3070, such as by calculating a difference between the values of the thermal resistors 3070, 3060 to yield a more accurate reading of the patient's respiration cycle. Referring again to FIG. 28, a second example of the force/pressure respiration monitoring system is provided. In the force respiration monitoring system, a sensor is placed by the torso. To avoid steric interference of the force sensor system components with proton therapy, the force respiration monitoring system is preferably used when treating a tumor located in the head, neck, or limbs. In the force monitoring system, a belt or strap 2850 is placed around an area of the patient's torso that expands and contracts with each respiration cycle of the patient. The belt 2850 is preferably tight about the patient's chest and is flexible. A force meter 2852 is attached to the belt and senses the patients respiration pattern. The forces applied to the force meter 2852 correlate with periods of the respiration cycle. The signals from the force meter 2852 are preferably communicated with the main controller 110 or a sub-controller of the main controller. Respiration Control Once the rhythmic pattern of the subject's breathing is determined, a signal is optionally delivered to the subject to more precisely control the breathing frequency 3230. For example, a display screen 2790 is placed in front of the subject directing the subject when to hold their breath and when to breath. Typically, a respiration control module uses input from one or more of the breathing sensors. For example, the input is used to determine when the next breath exhale is to complete. At the bottom of the breath, the control module displays a hold breath signal to the subject, such as on a monitor, via an oral signal, digitized and automatically generated voice command, or via a visual control signal. Preferably, a display monitor 2790 is positioned in front of the subject and the display monitor displays at least breathing commands to the subject. Typically, the subject is directed to hold their breath for a short period of time, such as about one-half, one, two, or three seconds. The period of time the subject is asked to hold their breath is less than about ten seconds. The period of time the breath is held is preferably synchronized to the delivery time of the proton beam to the tumor, which is about one-half, one, two, or three seconds. While delivery of the protons at the bottom of the breath is preferred, protons are optionally delivered at any point in the respiration cycle, such as upon full inhalation. Delivery at the top of the breath or when the patient is directed to inhale deeply and hold their breath by the respiration control module is optionally performed as at the top of the breath the chest cavity is largest and for some tumors the distance between the tumor and surrounding tissue is maximized or the surrounding tissue is rarefied as a result of the increased volume. Hence, protons hitting surrounding tissue is minimized. Optionally, the display screen tells the subject when they are about to be asked to hold their breath, such as with a 3, 2, 1, second countdown so that the subject is aware of the task they are about to be asked to perform. Proton Beam Therapy Synchronization with Respiration A proton delivery control algorithm is used to synchronize delivery of the protons to the tumor within a given period of each breath, such as at the top or bottom of a breath when the subject is holding their breath. The proton delivery control algorithm is preferably integrated with the respiration control module. Thus, the proton delivery control algorithm knows when the subject is breathing, where in the respiration cycle the subject is, and/or when the subject is holding their breath. The proton delivery control algorithm controls when protons are injected and/or inflected into the synchrotron, when an RF signal is applied to induce an oscillation, as described supra, and when a DC voltage is applied to extract protons from the synchrotron, as described supra. Typically, the proton delivery control algorithm initiates proton inflection and subsequent RF induced oscillation before the subject is directed to hold their breath or before the identified period of the respiration cycle selected for a proton delivery time. In this manner, the proton delivery control algorithm can deliver protons at a selected period of the respiration cycle by simultaneously or nearly simultaneously delivering the high DC voltage to the second pair of plates, described supra, which results in extraction of the protons from the synchrotron and subsequent delivery to the subject at the selected time point. Since the period of acceleration of protons in the synchrotron is constant or known for a desired energy level of the proton beam, the proton delivery control algorithm is used to set an AC RF signal that matches the respiration cycle or directed respiration cycle of the subject. Multi-Field Irradiation The 3-dimensional scanning system of the proton spot focal point, described supra, is preferably combined with a rotation/raster method. The method includes layer wise tumor irradiation from many directions. During a given irradiation slice, the proton beam energy is continuously changed according to the tissue's density in front of the tumor to result in the beam stopping point, defined by the Bragg peak, to always be inside the tumor and inside the irradiated slice. The novel method allows for irradiation from many directions, referred to herein as multi-field irradiation, to achieve the maximal effective dose at the tumor level while simultaneously significantly reducing possible side-effects on the surrounding healthy tissues in comparison with existing methods. Essentially, the multi-field irradiation system distributes dose-distribution at tissue depths not yet reaching the tumor. Although the invention has been described herein with reference to certain preferred embodiments, one skilled in the art will readily appreciate that other applications may be substituted for those set forth herein without departing from the spirit and scope of the present invention. Accordingly, the invention should only be limited by the Claims included below.
	description	1. Field of the Invention The present invention relates to a nuclear reactor building that houses a pressure containment vessel (PCV) of a nuclear power plant and a construction method thereof. 2. Description of the Related Art A conventional nuclear reactor building (or merely reactor building, called hereinafter) of a nuclear power plant has been constructed by a frame made of reinforced concrete in order to meet earthquake resistant design criteria and achieve radiation shielding. The reinforced concrete building is constructed by first arranging a grid of reinforcing bars in a formwork and then pouring concrete into the formwork. After completion of the construction of the building, a pressure containment vessel and other equipment are installed in the building. These works are carried out mainly at the site of the construction of the plant, so that on-site construction work takes long time, and it may sometimes take four or more years to construct the whole of a nuclear power plant. Recently, it is strongly demanded to reduce time and cost for constructing a building of a nuclear power plant, and in order to reduce the construction period, it is contemplated to eliminate the reinforcing bar arranging work and the concrete casting work by adopting a steel plate reinforced concrete structure composed of a combination of a steel plate and concrete (referred to as an SC structure hereinafter) or a steel structure composed mainly of steel members to construct the building, rather than the conventional reinforced concrete structure. However, reducing only the period of construction of the frame of the reactor building is not enough to reduce the total period of construction of the entire nuclear power plant, and it is also required to reduce the period of installation of various equipments into the building. In view of such circumstances, recently, there has been provided a construction method that reduces the construction period by applying the SC structure to the frame of the reactor building, in which a composite module composed of an SC steel plate structure serving as the formwork of the frame and piping and other equipment installed or mounted on the structure is previously manufactured, and then the composite module is placed at the site of installation (see Patent Document 1: Japanese Patent Laid-Open No. 2003-167086, for example). In addition, requirements on the security of the nuclear power plant have become severe in recent years, and there is a demand for including provision not only for design basis accidents but also for unexpected events, such as severe accidents, in the design criteria of plant facilities of nuclear power plants. For example, if a loss of coolant accident (LOCA), which is a design basis accident, occurs, and reactor cooling fails, hydrogen may be generated in the PCV, increasing the pressure in the PCV beyond the design value. In such a case, for a pressure suppression type PCV, a steel PCV is more advantageous than a reinforced concrete PCV in points that thermal deterioration of concrete does not occur and the surface of the PCV can be externally cooled, for example. Thus, it is expected that the superiority of the steel PCV will be appreciated in the future. The reactor building needs a biological shielding wall (which may be called BSW hereinafter) serving as a radiological countermeasure that is made of reinforced concrete and placed outside the steel PCV at a certain distance (1 m or less) so that the wall is not in contact with the PCV. In construction of the reactor building having the steel PCV, the PCV and the surrounding BSW need to be separately independently constructed. Besides, the PCV has outwardly protruding PCV penetration portions, such as pipes for external connection, and in addition, it is also needed to form openings, in the BSW, for the PCV penetration portions so as to pass through the BSW in such a manner that the openings are not in contact with the PCV penetration portions, but the gap between the openings and the PCV penetration portions is made minimal so as to ensure the radiation shielding effect. Thus, when the steel PCV is used, in order to ensure the positional relationship between the PCV and the BSW, the PCV has to be constructed before the construction of the concrete frame of the BSW, and therefore, a downtime waiting for completion of the construction of the PCV may occur. According to another recent method for reducing the construction period based on building modularization, the BSW is constructed as an SC building module by applying the SC structure to the BSW and integrating the BSW with the SC building. In this case, the SC building module is installed vertically from the upper side, which may cause a case that the SC building module inevitably interferes with the PCV penetration ports extending from the PCV. In this regard, the reinforced concrete PCV and the steel plate concrete PCV are advantageous over the steel PCV. These PCVs combine the pressure resistant and confinement capabilities of the steel PCV and the shielding capability of the BSW and do not have the above-described defects or problems with the PCV penetration portion of the steel PCV because the PCV penetration portion and the BSW are previously integrated. A structure of a reactor building of a nuclear power plant and a construction method thereof according to the prior art will be described hereunder with reference to the accompanying drawings. FIG. 7 is a cross-sectional view of a reactor building under construction according to the prior art. This drawing illustrates modularization at the time of the reactor building being constructed. FIG. 8 is a diagram for illustrating mounting of SC building modules of the reactor building. In FIG. 7 a reactor building 2 is constructed of steel PCV blocks 60 and steel plate concrete (SC) building modules 80 and houses a steel pressure containment vessel (PCV) 1. PCV penetration portions 3 protrude to the outside of the PCV and penetrate a biological shielding wall (BSW) 4 made of reinforced concrete disposed outside the PCV. The steel PCV 1 is divided into steel PCV blocks 60 (A to F) by horizontal dividing planes 50, and the reactor building 2 is divided into SC building modules 80 ((i) to (iv)) by horizontal dividing planes 70. FIG. 8 shows interference of an SC building module 80 with the PCV penetration portion 3 of a steel PCV block 60. As described above, in the construction of the reactor building and the steel PCV according to the conventional SC building modularization, the modules are mounted vertically from the upper side. Therefore, the SC building module inevitably interferes with the PCV penetration port protruding form the PCV. This poses an obstacle to reduction in the construction period, and a solution thereto has been required. In view of the above circumstances encountered in the prior art mentioned above, an object of the present invention is to provide a nuclear rector building and a construction method thereof intended to prevent interference between a PCV penetration portion of a steel PCV and an SC building module and reduce the construction period. The above object can be achieved according to the present invention by providing, in one aspect, a reactor building having a steel plate concrete structure that houses a pressure containment vessel formed with a plurality of pressure containment vessel penetration ports in the periphery thereof and includes a biological shielding wall disposed outside the pressure containment vessel, wherein the pressure containment vessel is vertically divided into a plurality of blocks, each of the blocks has one or more pressure containment vessel penetration ports arranged on a same horizontal plane, and the reactor building including the biological shielding wall is divided into a plurality of modules by the horizontal plane. The above object can be also achieved according to the present invention by providing, in another aspect, a nuclear reactor building having a steel plate concrete structure that houses a pressure containment vessel formed of a plurality of pressure containment vessel penetration ports in the periphery thereof and includes a biological shielding wall disposed outside the pressure containment vessel, wherein the pressure containment vessel is vertically divided into a plurality of blocks, each of the blocks has one or more pressure containment vessel penetration ports arranged on a same horizontal plane, and the biological shielding wall is divided into a plurality of modules by the horizontal plane. In the above aspects, the modules may be further divided by a vertical plane. The above object can be also achieved according to the present invention by providing, in a further aspect, a construction method of a nuclear reactor building having a steel plate concrete structure that houses a pressure containment vessel formed with a plurality of pressure containment vessel penetration ports in the periphery thereof and includes a biological shielding wall disposed outside the pressure containment vessel, the construction method comprising the steps of: vertically dividing the pressure containment vessel into a plurality of blocks so that each block has one or more pressure containment vessel penetration ports arranged on a same horizontal plane; dividing the reactor building including the biological shielding wall into a plurality of modules by the horizontal plane; and alternately stacking the blocks of the pressure containment vessel and the modules of the reactor building. 6. The above object can be also achieved according to the present invention by providing, in a still further aspect, a construction method of a nuclear reactor building having a steel plate concrete structure that houses a pressure containment vessel formed with a plurality of pressure containment vessel penetration ports in the periphery thereof and includes a biological shielding wall disposed outside the pressure containment vessel, the construction method comprising the steps of: vertically dividing the pressure containment vessel into a plurality of blocks so that each block has one or more pressure containment vessel penetration ports arranged on a same horizontal plane; dividing the biological shielding wall into a plurality of modules by the horizontal plane; and alternately stacking the blocks of the pressure containment vessel and the modules of the biological shielding wall. According to the present invention having the characteristics described above, when assembling workings of the steel PCV blocks and the SC building modules including the BSW are carried out at the same time, interference between the PCV penetration ports and the SC building modules can be prevented from occurring. Thus, the waiting for completion of the construction of the PCV can be reduced, and the construction period of the reactor building having the steel PCV can be reduced. Structures of and construction methods of a reactor building of a nuclear power plant according to embodiments of the present invention will be described. In the following description, terms indicating directions, such as “upper”, “lower”, “left” and “right”, are used herein with reference to the illustration on the accompanying drawings or in the actual installation state. In the following, a first embodiment of the present invention will be described with reference to FIGS. 1 to 4. FIG. 1 is a cross-sectional view of a reactor building according to the first embodiment of the present invention. This drawing illustrates modularization of a nuclear reactor pressure containment vessel into mounting blocks and of an SC reactor building into SC building blocks during construction. The same parts as those in the prior art described in FIGS. 7 and 8 are denoted by the same reference numerals. A reactor building 2 of the SC structure houses a steel PCV 1, which is formed with a plurality of penetration ports 3 penetrating a wall portion of the PCV (called PCV penetration ports herein) on the periphery of the PCV, and includes a BSW 4 disposed outside the PCV. The steel PCV 1 is vertically divided into a plurality of steel PCV block 61 (A to H) by horizontal steel PCV dividing planes 51, and each block has one or more PCV penetration ports 3 arranged on the same horizontal plane. The reactor building 2 is vertically divided into SC building modules 81 ((i) to (vii)) by horizontal SC building dividing planes 71 passing through the PCV penetration ports 3. The BSW 4 disposed outside the PCV has the SC structure and is divided into modules by the same horizontal planes that pass through the PCV penetration ports 3 and divide the reactor building 2 into the SC building modules 81. FIG. 2 is a diagram showing PCV penetration ports of the steel PCV in the reactor building and building modules of the reactor building viewed from the direction of an arrow A in FIG. 1. The reactor building 2 is divided into modules by the horizontal planes passing through the PCV penetration ports 3. The steel PCV blocks 61 and the SC building modules 81 are alternately stacked. More specifically, the steel PCV blocks 61 and the SC building modules 81 are mounted in the order: A→(i)→B→(ii)→C→(iii)→D→(iv)→E→(v)→F→(vi)→G→(vii)→H. Thus, the steel PCV blocks 61 and the SC building modules 81 can be assembled without interference between the PCV penetration ports 3 and the SC building modules 81. FIG. 3 is a diagram illustrating mounting of the SC building modules of the reactor building. As can be seen from this drawing, interference between the PCV penetration ports 3 and the SC building modules 81 is avoided. FIG. 4 is a diagram illustrating horizontal division of the SC building module. The SC building module 81 is horizontally divided into four parts by vertical SC building module dividing planes 9 that pass through the center of the steel PCV 1, for example. The number of the divisional parts can be arbitrarily selected depending on the capacity of the crane used on the construction site. Furthermore, different horizontally divided parts of the nuclear rector building may be vertically divided into different number of SC building modules. The vertical position of the boundary between the SC building modules 81 passing through the PCV penetration ports 3 (the position of the horizontal SC building dividing plane 71) may not be the center of the penetration ports as far as it is ensured that interference between the PCV penetration ports 3 and the SC building modules 81 does not occur. In the following, a second embodiment of the present invention will be described with reference to FIGS. 5 and 6. FIG. 5 is a cross-sectional view of a reactor building according to the second embodiment of the present invention. This drawing illustrates modularization of a nuclear reactor pressure containment vessel into mounting blocks and of an SC reactor building into SC building blocks during construction. The same parts as those in the prior art shown in FIGS. 7 and 8 are denoted by the same reference numerals. FIG. 6 is a diagram showing a part of a steel PCV in which the PCV penetration ports are concentrated and the SC building modules of the reactor building viewed from the direction of the arrow B in FIG. 5. As in the first embodiment, a reactor building 2 of the SC structure houses a steel PCV 1, which is formed with a plurality of the penetration ports 3 in the periphery the PCV, and includes a BSW 4 disposed outside the PCV. The steel PCV 1 is vertically divided into a plurality of steel PCV block 62 (A to H) by a plurality of horizontal steel PCV dividing planes 51, and each block has one or more PCV penetration ports 3 arranged on the same horizontal plane. The reactor building 2 is vertically divided into SC building modules 82 ((i) to (iv)) by horizontal SC building dividing planes 72 in the same manner as the prior art shown in FIG. 7. Furthermore, with the SC building module 82, a part of the BSW 4 is cut off, and the SC building module 82 is divided into BSW modules 10 ((v) to (vi)) by horizontal planes passing through the PCV penetration ports 3. In this embodiment, the BSW 4 in which PCV penetration ports 3 are concentrated is divided into the same number of parts as the number of different levels of the PCV penetration ports 3 by horizontal planes passing through the PCV penetration ports 3, thereby preventing interference between the PCV penetration ports 3 and the steel PCV 1. Thus, the number of SC building modules can be reduced. The steel PCV blocks 62 and the BSW modules 10 are alternately stacked. More specifically, in the portion in which the PCV penetration ports 3 are concentrated, the steel PCV blocks 62 and the SC building modules 82 including the BSW modules 10 are mounted in the order: D→(iii)→E→(v)→F→(vi)→G→(iv)→H. As a result, the number of mountings of the SC building modules 82, which are heavy and take much time to be mounted in precise alignment, can be reduced, thus reducing the construction period. It is to be noted that the present invention is not limited to the embodiments described above, and many other changes and modifications may be made without departing form the scope of the appended claims. For example, although a portion of the BSW 4 in which PCV penetration ports 3 are concentrated is divided, the whole of the BSW 4 may be divided. Furthermore, the vertical position of the boundary between the BSW modules 10 passing through the PCV penetration ports 3 (the position of the horizontal plane) may not be the center of the penetration ports as far as it is ensured that the PCV penetration ports 3 and the BSW modules 10 have dimensions which do not cause any interference therebetween. Furthermore, as in the first embodiment, the BSW module 10 may be further divided into divisional modules by vertical planes as shown in FIG. 4.
	abstract	The present disclosure relates to a process for recycling a sodium salt by decomposition of a sodium nitride liquid waste, comprising a neutralization step in which a nitric acid liquid waste or an off-gas having nitric acid dissolved therein which is produced through a wet reprocessing process comprising a dissolution step for dissolving a spent nuclear fuel in nitric acid is neutralized by adding or contacting the nitrate liquid waste or the off-gas to or with at least one sodium salt selected from the group consisting of sodium hydroxide, sodium hydrogencarbonate and sodium carbonate, thereby yielding a sodium nitrate liquid waste; a sodium nitrate-decomposition step in which the sodium nitrate liquid waste is reductively decomposed with a reducing agent, thereby decomposing sodium nitrate into a nitrogen gas and the sodium salt; and a recycle step for recycling the sodium salt into the neutralization step or wet reprocessing process.
	abstract	In one aspect, it is disclosed a detection system comprising: a plurality of detectors, each detector being configured to detect radiation scattered by an associated respective portion of a load to inspect, the radiation being scattered in response to the respective portion being irradiated by radiation transmitted through the portion; and a plurality of collimators associated with the plurality of detectors, each collimator of the plurality of collimators being associated with a respective detector of the plurality of detectors and being configured to, for each detector of the plurality of detectors: enable radiation scattered by the respective portion of the load to reach the associated detector of the plurality of detectors, and inhibit other scattered radiation from reaching the associated detector.
062401556	summary	BACKGROUND OF THE INVENTION The present invention relates to a preventive maintenance apparatus for structural members in a nuclear pressure vessel and, more particularly, to a preventive maintenance apparatus for structural members in a nuclear pressure vessel capable of preventing occurrence of stress corrosion cracks of structural members by adding compressive remaining stress to surfaces of the structural members. The present invention relates to a preventive maintenance apparatus for structural members in a nuclear pressure vessel suitable for adding compressive residual stress to a surface of a welded portion and a heat affected zone in each of core internals of, preferably, a boiling water reactor (BWR) such as a core shroud, a shroud support cylinder, a shroud support leg, a shroud support plate and a jet pump diffuser. Japanese Patent Application Laid-Open No.62-63614 discloses a method of releasing tensile remaining stress in a welded portion which may become a cause of occurrence of stress corrosion cracks. In the method, a high pressure water shot peening apparatus is inserted inside of a heat transfer tube of a heat exchanger to peen an inner surface of the heat transfer tube by axial kinetic pressure energy of a high pressure water jet (kinetic pressure energy of a confined water jet in the axial direction). Tensile remaining stress having existed near the inner surface of the heat transfer tube is converted into compressive remaining stress by the peening. The high pressure water shot peening apparatus comprises a rotating nozzle portion for discharging a high pressure liquid jet. Further, Japanese Patent Application Laid-Open No.5-78738 discloses an improving method of converting tensile remaining stress on a surface of a core shroud in a reactor pressure vessel into compressive remaining stress by water jet peening. The water jet peening is performed by arranging a traveling cart mounting a vertical driving apparatus on a flange in a top end portion of the reactor pressure vessel. An upper mast and a lower mast having a water jet discharging head in the top end are mounted onto the vertical driving apparatus. A high pressure water jet is discharged from a water jet discharging nozzle of the water jet discharging head to generate cavitation. Air bubbles generated by the cavitation are hit on a surface of the shroud. Furthermore, Japanese Patent Application Laid-Open No.7-270591 discloses a method in which preventive maintenance apparatuses comprising a nozzle unit having an upper attachment, a lower attachment and a drive mechanism for a discharging nozzle and a main apparatus body are arranged in a top end portion of a CRD housing and a lower core support plate inside a reactor pressure vessel to generate cavitation bubbles by discharging a high pressure jet from the discharging nozzle. The method also discloses a method of improving remaining stress by water jet peening. The cavitation bubbles are hit onto the surfaces of a lower barrel of the core shroud, a core shroud support cylinder and so on. Tensile remaining stress in the surfaces of the lower barrel of the core shroud, the core shroud support cylinder and so on is converted to compressive remaining stress. The method of the prior art disclosed in Japanese Patent Application Laid-Open No.62-63614 is effective as a method of releasing the remaining stress in a heat exchanger and the like. The axial kinetic pressure of the water jet in this method can be effectively used in the work under atmospheric pressure. However, when the high pressure shot peening apparatus of the prior art is used under water, an effective peening effect cannot be obtained because the axial kinetic pressure of the water jet is substantially decayed under water. In order to obtain an axial kinetic pressure equivalent to that under a condition of air atmosphere under a condition of water using the high pressure shot peening apparatus, a water jet of ultra high pressure discharge is necessary. Accordingly, the pump and the related components used need to have structures capable of withstanding the ultra high pressure. In order to avoid such structures, it is required to discharge the high pressure liquid jet under air atmosphere by lowering a core water level inside the reactor pressure vessel. Since lowering of the core water level causes an increase in the environmental radiation dose, radiation exposure to workers may be increased. On the other hand, the method of improving remaining stress by the water jet peening disclosed in Japanese Patent Application Laid-Open No.5-78738 is effective as a method of improving remaining stress in core internals such as a core shroud. However, since the traveling cart having the mast is placed on the top end portion of the reactor pressure vessel, the mast becomes long in order to apply the method of improving remaining stress by water jet peening to the lower barrel of the core shroud, the core shroud support cylinder and so on. In addition to this, the apparatus is difficult to be handled. It cannot be said that this is preferable from the viewpoint of workability. The method of improving remaining stress by the water jet peening disclosed in Japanese Patent Application Laid-Open No.7-270591 is an effective technology aiming to improve the workability which is the problem in the method of improving remaining stress described in Japanese Patent Application Laid-Open No.5-78738 since the apparatus does not have any long mast. However, application of the method in Japanese Patent Application Laid-Open No.7-270591 is limited within a small field of preventive maintenance work since the preventive maintenance apparatus is attached to the top end portion of the CRD housing and the lower core support plate inside the reactor pressure vessel. Therefore, it is necessary that the preventive maintenance apparatus is detached and moved from one CRD housing after completion of the preventive maintenance work to a portion existing in the inner surface of the core shroud to be set to another CRD housing. SUMMARY OF THE INVENTION An object of the present invention is to provide a preventive maintenance apparatus for structural members in a reactor pressure vessel which is capable of being easily arranged on a core shroud and easily moving a discharging nozzle to a portion to perform preventive maintenance. A first invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel which comprises a ring-shaped guide rail having a plurality of lugs, the guide rail being placed on an upper flange of a core shroud provided inside a reactor pressure vessel, at least one of the plurality of lugs engaging with a plurality of guide rods provided on an inner surface of the reactor pressure vessel; a turntable rotatable on the guide rail; a discharging nozzle moving apparatus for moving a discharging nozzle in a radial direction of the core shroud and in an axial direction of the core shroud, the discharging nozzle moving apparatus being placed on the turntable; and a high pressure water supply apparatus for supplying high pressure water to the discharging nozzle. Since the guide rail has the plurality of lugs engaging with the plurality of guide rods provided in the inner surface of the reactor pressure vessel, the guide rail can be easily moved downward up to the upper portion of the core shroud along the guide rods. Therefore, the guide rail can be easily placed on the upper flange without being interfered with main steam line plugs which are inserted into opening portions of main steam pipes. In addition to this, since the turntable can be rotated, the discharging nozzle can be easily moved to a portion to perform preventive maintenance. Since the turntable is rotated on the guide rail placed on the upper flange, the turntable does not contact the upper flange. Accordingly, the upper flange can be prevented from being damaged by the rotation of the turntable. A second invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel which comprises a first discharging nozzle moving apparatus for moving a discharging nozzle in a radial direction of the core shroud and in an axial direction of the core shroud, the discharging nozzle discharging high pressure water to add compressive remaining stress to an outer surface of the core shroud, the discharging nozzle moving apparatus being placed on the turntable; and a second discharging nozzle moving apparatus for moving a discharging nozzle in a radial direction of the core shroud and in an axial direction of the core shroud, the discharging nozzle discharging high pressure water to add compressive remaining stress to an inner surface of the core shroud, the discharging nozzle moving apparatus being placed on the turntable. Since the first and the second discharging nozzle moving apparatuses are installed in the turntable, compressive remaining stress can be added to both of the outer surface and the inner surface of the core shroud. Therefore, it is possible to shorten the time for performing preventive maintenance to the core shroud. A third invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel in which the second discharging nozzle moving apparatus comprises an arm member movable in a horizontal direction; a pole member movable in an axial direction of the core shroud provided in the arm member; a multi-joint arm attached to the pole member; and the discharging nozzle provided in a top end portion of the multi-joint arm. Since the multi-joint arm is provided, it is possible to insert the discharging nozzle into a narrow portion formed between the core shroud and an upper core grid plate placed on the core shroud. Therefore, compressive remaining stress can be added to the inner surface of the core shroud in the narrow portion. A fourth invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel in which the first discharging nozzle moving apparatus comprises an arm member movable in a horizontal direction; a pole member movable in an axial direction of the core shroud provided in the arm member, the pole member being inserted between the reactor pressure vessel and the core shroud; a vertically moved body attached to the pole member, the vertically moved body being movable in a vertical direction; and the discharging nozzle provided in a top end portion of the vertically moved body. Since the vertically moved body having the discharging nozzle can be vertically moved along the pole member, it is possible to easily add compressive remaining stress to a welded portion of the core shroud and the vicinity. A fifth invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel which comprises a water supply apparatus for cleaning reactor water and supplying the water to a high pressure water supply apparatus. Since the reactor water is cleaned to be supplied to the high pressure supply apparatus, the water discharged from the discharging nozzle becomes the reactor water again. Accordingly, an amount of the reactor water inside the reactor pressure vessel and the reactor well is never increased even when the high pressure water is discharged from the discharging nozzle during preventive maintenance work. Therefore, radioactive disposal liquid cannot be produced even when the high pressure water is discharged from the discharging nozzle. A sixth invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel which comprises a crud sucking apparatus for sucking crud suspending in reactor water. Since it is possible to remove crud suspended in the reactor water during preventive maintenance work, visibility under the reactor water can be improved. Therefore, it is possible to clearly monitor a portion under preventive maintenance work using an image in a monitoring camera. A seventh invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel which comprises a bubble collecting apparatus for collecting bubbles reaching a water surface in a reactor well, the bubble collecting apparatus being placed near the water surface. Since the bubble collecting apparatus is provided, it is possible to prevent radioactive materials floating up in the reactor water accompanied by the bubbles from being dispersed. Therefore, it is possible to suppress radiation exposure to workers. An eighth invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel in which the first discharging nozzle moving apparatus comprises an arm member movable in a horizontal direction; a plurality of pole members provided in the arm member, the pole members being inserted between the reactor pressure vessel and the core shroud; vertically moved bodies respectively attached to the pole members, the vertically moved body being movable in a vertical direction; and the discharging nozzles respectively provided in the vertically moved bodies. Since the vertically moved bodies capable of respectively and vertically moving the plurality of pole members are provided, it is possible to perform preventive maintenance work to different positions on the outer surface of the core shroud at the same time. Therefore, it is possible to further shorten the time required for the preventive maintenance work. A ninth invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel which comprises a rotating apparatus for rotating a metal fitting for bundling a plurality of hoses and a plurality of cables, the plurality of hoses and the plurality of cables being connected to the first discharging nozzle moving apparatus and the second discharging nozzle moving apparatus. Since the rotating apparatus for rotating the metal fitting for bundling the plurality of hoses and the plurality of cables is provided, the rotating apparatus can be rotated when the turntable mounting the first discharging nozzle moving apparatus and the second discharging nozzle moving apparatus is rotated during preventive maintenance work. Therefore, it is possible to prevent the plurality of hoses and the plurality of cables from being intertwined by rotation of the turntable. A tenth invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel in which the first discharging nozzle moving apparatus and the second discharging nozzle moving apparatus respectively comprise a discharging nozzle for discharging high pressure water for adding compressive remaining stress to an outer surface of the core shroud and a discharging nozzle for discharging high pressure water for adding compressive remaining stress to an inner surface of the core shroud, and the preventive maintenance apparatus further comprises an apparatus for moving the discharging nozzles. Since the first discharging nozzle moving apparatus and the second discharging nozzle moving apparatus respectively comprise the discharging nozzle for discharging high pressure water for adding compressive remaining stress to an outer surface of the core shroud and the discharging nozzle for discharging high pressure water for adding compressive remaining stress to an inner surface of the core shroud, it is possible to perform preventive maintenance work to four positions in the inner and outer surfaces of the core shroud at the same time. Therefore, it is possible to substantially shorten the time required for the preventive maintenance work to the core shroud.
	description	This application claims the benefit of U.S. Provisional Patent Application No. 61/195,639, filed Oct. 9, 2008, entitled “Four-dimensional Electron Microscope,” U.S. Provisional Patent Application No. 61/236,745, filed Aug. 25, 2009, entitled “4D Nanoscale Diffraction Observed by Convergent-Beam Ultrafast Electron Microscopy,” and U.S. Provisional Patent Application No. 61/240,946, filed Sep. 9, 2009, entitled “4D Attosecond Imaging with Free Electrons: Diffraction Methods and Potential Applications,” which are commonly assigned, the disclosures of which are hereby incorporated by reference in their entirety. The following two regular U.S. patent applications (including this one) are being filed concurrently, and the entire disclosure of the other application is hereby incorporated by reference into this application for all purposes: application Ser. No. 12/575,285, filed Oct. 7, 2009, entitled “4D Imaging in an Ultrafast Electron Microscope”; and application Ser. No. 12/573,312, filed Oct. 7, 2009, entitled “Characterization of Nanoscale Structures Using an Ultrafast Electron Microscope”. The U.S. Government has certain rights in this invention pursuant to Grant No. GM081520 awarded by the National Institutes of Health, Grant No. FA9550-07-1-0484 awarded by the Air Force (AFOSR) and Grant No(s). CME0549936 & DMR0504854 awarded by the National Science Foundation. Electrons, because of their wave-particle duality, can be accelerated to have picometer wavelength and focused to image in real space. With the impressive advances made in transmission electron microscopy (TEM), STEM, and aberration-corrected TEM, it is now possible to image with high resolution, reaching the sub-Angstrom scale. Together with the progress made in electron crystallography, tomography, and single-particle imaging, today the electron microscope has become a central tool in many fields, from materials science to biology. For many microscopes, the electrons are generated either thermally by heating the cathode or by field emission, and as such the electron beam is made of random electron bursts with no control over the temporal behavior. In these microscopes, time resolution of milliseconds or longer, being limited by the video rate of the detector, can be achieved, while maintaining the high spatial resolution. Despite the advances made in TEM techniques, there is a need in the art for improved methods and novel systems for ultrafast electron microscopy. According to embodiments of the present invention, methods and systems for 4D ultrafast electron microscopy (UEM) are provided—in situ imaging with ultrafast time resolution in TEM. Thus, 4D microscopy provides imaging for the three dimensions of space as well as the dimension of time. In some embodiments, single electron imaging is introduced as a component of the 4D UEM technique. Utilizing one electron packets, resolution issues related to repulsion between electrons (the so-called space-charge problem) are addressed, providing resolution unavailable using conventional techniques. Moreover, other embodiments of the present invention provide methods and systems for convergent beam UEM, focusing the electron beams onto the specimen to measure structural characteristics in three dimensions as a function of time. Additionally, embodiments provide not only 4D imaging of specimens, but characterization of electron energy, performing time resolved electron energy loss spectroscopy (EELS). The potential applications for 4D UEM are demonstrated using examples including gold and graphite, which exhibit very different structural and morphological changes with time. For gold, following thermally induced stress, the atomic structural expansion, the nonthermal lattice temperature, and the ultrafast transients of warping/bulging were determined. In contrast, in graphite, striking coherent transients of the structure were observed in the selected-area image dynamics, and also in diffraction, directly measuring the resonance period of Young's elastic modulus. Measurement of the Young's elastic modulus for the nano-scale dimension, the frequency is found to be as high as 30 gigahertz, hitherto unobserved, with the atomic motions being along the c-axis. Both materials undergo fully reversible dynamical changes, retracing the same evolution after each initiating impulsive stress. Thus, embodiments of the present invention provide methods and systems for performing imaging studies of dynamics using UEM. Other embodiments of the present invention extend four-dimensional (4D) electron imaging to the attosecond time domain. Specifically, embodiments of the present invention are used to generate attosecond electron pulses and in situ probing with electron diffraction. The free electron pulses have a de Broglie wavelength on the order of picometers and a high degree of monochromaticity (ΔE/E0≈10−4); attosecond optical pulses have typically a wavelength of 20 nm and ΔE/E0≈0.5, where E0 is the central energy and ΔE is the energy bandwidth. Diffraction, and tilting of the electron pulses/specimen, permit the direct investigation of electron density changes in molecules and condensed matter. This 4D imaging on the attosecond time scale is a pump-probe approach in free space and with free electrons. As described more fully throughout the present specification, some embodiments of the present invention utilize single electron packets in UEM, referred to as single electron imaging. Conventionally, it was believed that the greater number of electrons per pulse, the better the image produced by the microscope. In other words, as the signal is increased, imaging improves. However, the inventor has determined that by using single electron packets and repeating the imaging process a number of times, images can be achieved without repulsion between electrons. Unlike photons, electrons are charged and repel each other. Thus, as the number of electrons per pulse increases, the divergence of the trajectories increases and resolution decreases. Using single electron imaging techniques, atomic scale resolution of motion is provided once the space-charge problem is addressed. According to an embodiment of the present invention, a four-dimensional electron microscope for imaging a sample is provided. The four-dimensional electron microscope includes a stage assembly configured to support the sample, a first laser source capable of emitting a first optical pulse of less than 1 ps in duration, and a second laser source capable of emitting a second optical pulse of less than 1 ns in duration. The four-dimensional electron microscope also includes a cathode coupled to the first laser source and the second laser source. The cathode is capable of emitting a first electron pulse less than 1 ps in duration in response to the first optical pulse and a second electron pulse of less than 1 ns in response to the second optical pulse. The four-dimensional electron microscope further includes an electron lens assembly configured to focus the electron pulse onto the sample and a detector configured to capture one or more electrons passing through the sample. The detector is configured to provide a data signal associated with the one or more electrons passing through the sample. The four-dimensional electron microscope additionally includes a processor coupled to the detector. The processor is configured to process the data signal associated with the one or more electrons passing through the sample to output information associated with an image of the sample. Moreover, the four-dimensional electron microscope includes an output device coupled to the processor. The output device is configured to output the information associated with the image of the sample. According to another embodiment of the present invention, a convergent beam 4D electron microscope is provided. The convergent beam 4D electron microscope includes a laser system operable to provide a series of optical pulses, a first optical system operable to split the series of optical pulses into a first set of optical pulses and a second set of optical pulses and a first frequency conversion unit operable to frequency double the first set of optical pulses. The convergent beam 4D electron microscope also includes a second optical system operable to direct the frequency doubled first set of optical pulses to impinge on a sample and a second frequency conversion unit operable to frequency triple the second set of optical pulses. The convergent beam 4D electron microscope further includes a third optical system operable to direct the frequency tripled second set of optical pulses to impinge on a cathode, thereby generating a train of electron packets. Moreover, the convergent beam 4D electron microscope includes an accelerator operable to accelerate the train of electron packets, a first electron lens operable to de-magnify the train of electron packets, and a second electron lens operable to focus the train of electron packets onto the sample. According to a specific embodiment of the present invention, a system for generating attosecond electron pulses is provided. The system includes a first laser source operable to provide a laser pulse and a cathode optically coupled to the first laser source and operable to provide an electron pulse at a velocity v0 directed along an electron path. The system also includes a second laser source operable to provide a first optical wave at a first wavelength. The first optical wave propagates in a first direction offset from the electron path by a first angle. The system further includes a third laser source operable to provide a second optical wave at a second wavelength. The second optical wave propagates in a second direction offset from the electron path by a second angle and the interaction between the first optical wave and the second optical wave produce a standing wave copropagating with the electron pulse. According to another specific embodiment of the present invention, a method for generating a series of tilted attosecond pulses is provided. The method includes providing a femtosecond electron packet propagating along an electron path. The femtosecond electron packet has a packet duration and a direction of propagation. The method also includes providing an optical standing wave disposed along the electron path. The optical standing wave is characterized by a peak to peak wavelength measured in a direction tilted at a predetermined angle with respect to the direction of propagation. The method further includes generating the series of tilted attosecond pulses after interaction between the femtosecond electron packet and the optical standing wave. According to a particular embodiment of the present invention, a method of operating an electron energy loss spectroscopy (EELS) system is provided. The method includes providing a train of optical pulses using a pulsed laser source, directing the train of optical pulses along an optical path, frequency doubling a portion of the train of optical pulses to provide a frequency doubled train of optical pulses, and frequency tripling a portion of the frequency doubled train of optical pulses to provide a frequency tripled train of optical pulses. The method also includes optically delaying the frequency doubled train of optical pulses using a variable delay line, impinging the frequency doubled train of optical pulses on a sample, impinging the frequency tripled train of optical pulses on a photocathode, and generating a train of electron pulses along an electron path. The method further includes passing the train of electron pulses through the sample, passing the train of electron pulses through a magnetic lens, and detecting the train of electron pulses at a camera. According to an embodiment of the present invention, a method of imaging a sample is provided. The method includes providing a stage assembly configured to support the sample, generating a train of optical pulses from a laser source, and directing the train of optical pulses along an optical path to impinge on a cathode. The method also includes generating a train of electron pulses in response to the train of optical pulses impinging on the cathode. Each of the electron pulses consists of a single electron. The method further includes directing the train of electron pulses along an imaging path to impinge on the sample, detecting a plurality of the electron pulses after passing through the sample, processing the plurality of electron pulses to form an image of the sample, and outputting the image of the sample to an output device. According to another embodiment of the present invention, a method of capturing a series of time-framed images of a moving nanoscale object is provided. The method includes a) initiating motion of the nanoscale object using an optical clocking pulse, b) directing an optical trigger pulse to impinge on a cathode, and c) generating an electron pulse. The method also includes d) directing the electron pulse to impinge on the sample with a predetermined time delay between the optical clocking pulse and the electron pulse, e) detecting the electron pulse, f) processing the detected electron pulse to form an image, and g) increasing the predetermined time delay between the optical clocking pulse and the electron pulse. The method further includes repeating steps a) through g) to capture the series of time-framed images of the moving nanoscale object. According to a specific embodiment of the present invention, a method of characterizing a sample is provided. The method includes providing a laser wave characterized by an optical wavelength (λ0) and a direction of propagation and directing the laser wave along an optical path to impinge on a test surface of the sample. The test surface of the sample is tilted with respect to the direction of propagation of the laser by a first angle (α). The method also includes providing a train of electron pulses characterized by a propagation velocity (vel), a spacing between pulses ( λ 0 ⁢ v el c ) ,and a direction of propagation tilted with respect to the direction of propagation of the laser by a second angle (β). The method further includes directing the train of electron pulses along an electron path to impinge on the test surface of the sample. The first angle, the second angle, and the propagation velocity are related by sin ⁢ ⁢ ( α ) sin ⁡ ( α - β ) = c v el . According to another specific embodiment of the present invention, a method of imaging chemical bonding dynamics is provided. The method includes positioning a sample in a reduced atmosphere environment, providing a first train of laser pulses, and directing the first train of laser pulses along a first optical path to impinge on a sample. The method also includes providing a second train of laser pulses, directing the second train of laser pulses along a second optical path to impinge on a photocathode, and generating a train of electron pulses. One or more of the electron pulses consist of a single electron. The method further includes accelerating the train of electron pulses and transmitting a portion of the train of electron pulses through the sample. Numerous benefits are achieved by way of the present invention over conventional techniques. For example, the present systems provide temporal resolution over a wide range of time scales. Additionally, unlike spectroscopic methods, embodiments of the present invention can determine a structure in 3-D space. Such capabilities allow for the investigation of phase transformation in matter, determination of elastic and mechanical properties of materials on the nanoscale, and the time evolution of processes involved in materials and biological function. Depending upon the embodiment, one or more of these benefits may be achieved. These and other benefits will be described in more detail throughout the present specification and more particularly below. These and other objects and features of the present invention and the manner of obtaining them will become apparent to those skilled in the art, and the invention itself will be best understood by reference to the following detailed description read in conjunction with the accompanying drawings. DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS Ultrafast imaging, using pulsed photoelectron packets, provides opportunities for studying, in real space, the elementary processes of structural and morphological changes. In electron diffraction, ultrashort time resolution is possible but the data is recorded in reciprocal space. With space-charge-limited nanosecond (sub-micron) image resolutions ultrashort processes are not possible to observe. In order to achieve the ultrafast resolution in microscopy, the concept of single-electron pulse imaging was realized as a key to the elimination of the Coulomb repulsion between electrons while maintaining the high temporal and spatial resolutions. As long as the number of electrons in each pulse is much below the space-charge limit, the packet can have a few or tens of electrons and the temporal resolution is still determined by the femtosecond (fs) optical pulse duration and the energy uncertainty, on the order of 100 fs, and the spatial resolution is atomic-scale. However, the goal of full-scale dynamic imaging can be attained only when in the microscope the problems of in situ high spatiotemporal resolution for selected image areas, together with heat dissipation, are overcome. FIG. 1 is a simplified diagram of a 4D electron microscope system according to an embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims herein. One of ordinary skill in the art would recognize many variations, modifications, and alternatives. As illustrated in FIG. 1, a femtosecond laser 110 or a nanosecond laser 105 is directed through a Pockels cell 112, which acts as a controllable shutter. A Glan polarizer 114 is used in some embodiments, to select the laser power propagating in optical path 115. A beam splitter (not shown) is used to provide several laser beams to various portions of the system. Although the system illustrated in FIG. 1 is described with respect to imaging applications, this is not generally required by the present invention. One of skill in the art will appreciate that embodiments of the present invention provide systems and methods for imaging, diffraction, crystallography, electron spectroscopy, and related fields. Particularly, the experimental results discussed below yield insight into the varied applications available using embodiments of the present invention. The femtosecond laser 110 is generally capable of generating a train of optical pulses with predetermined pulse width. One example of such a laser system is a diode-pumped mode-locked titanium sapphire (Ti:Sapphire) laser oscillator operating at 800 nm and generating 100 fs pulses at a repetition rate of 80 MHz and an average power of 1 Watt, resulting in a period between pulses of 12.5 ns. In an embodiment, the spectral bandwidth of the laser pulses is 2.35 nm FWHM. An example of one such laser is a Mai Tai One Box Femtosecond Ti:Sapphire Laser, available from Spectra-Physics Lasers, of Mountain View, Calif. In alternative embodiments, other laser sources generating optical pulses at different wavelengths, with different pulse widths, and at different repetition rates are utilized. One of ordinary skill in the art would recognize many variations, modifications, and alternatives. The nanosecond laser 105 is also generally capable of generating a train of optical pulses with a predetermined pulse width greater than that provided by the femtosecond laser. The use of these two laser systems enables system miniaturization since the size of the nanosecond laser is typically small in comparison to some other laser systems. By moving one or more mirrors, either laser beam is selected for use in the system. The ability to select either laser enables scanning over a broad time scale—from femtoseconds all the way to milliseconds. For short time scale measurement, the femtosecond laser is used and the delay stage (described below) is scanned at corresponding small time scales. For measurement of phenomena over longer time scales, the nanosecond laser is used and the delay stage is scanned at corresponding longer time scales. A first portion of the output of the femtosecond laser 110 is coupled to a second harmonic generation (SHG) device 116, for example a barium borate (BaB2O4) crystal, typically referred to as a BBO crystal and available from a variety of doubling crystal manufacturers. The SHG device frequency doubles the train of optical pulses to generate a train of 400 nm, 100 fs optical pulses at an 80 MHz repetition rate. SHG devices generally utilize a nonlinear crystal to frequency double the input pulse while preserving the pulse width. In some embodiments, the SHG is a frequency tripling device, thereby generating an optical pulse at UV wavelengths. Of course, the desired output wavelength for the optical pulse will depend on the particular application. The doubled optical pulse produced by the SHG device propagates along electron generating path 118. A cw diode laser 120 is combined with the frequency doubled optical pulse using beam splitter 122. The light produce by the cw diode laser, now collinear with the optical pulse produced by the SHG device, serves as an alignment marker beam and is used to track the position of the optical pulse train in the electron generating path. The collinear laser beams enter chamber 130 through entrance window 132. In the embodiment illustrated in FIG. 1, the entrance window is fabricated from materials with high transparency at 400 nm and sufficient thickness to provide mechanical rigidity. For example, BK-7 glass about 6 mm thick with anti-reflection coatings, e.g. MgF2 or sapphire are used in various embodiments. One of ordinary skill in the art would recognize many variations, modifications, and alternatives. An optical system, partly provided outside chamber 130 and partly provided inside chamber 130 is used to direct the frequency doubled optical pulse train along the electron-generating path 134 inside the chamber 130 so that the optical pulses impinge on cathode 140. As illustrated, the optical system includes mirror 144, which serves as a turning mirror inside chamber 130. In embodiments of the present invention, polished metal mirrors are utilized inside the chamber 130 since electron irradiation may damage mirror coatings used on some optical mirrors. In a specific embodiment, mirror 144 is fabricated from an aluminum substrate that is diamond turned to produce a mirror surface. In some embodiments, the aluminum mirror is not coated. In other embodiments, other metal mirrors, such as a mirror fabricated from platinum is used as mirror 144. In an embodiment, the area of interaction on the cathode was selected to be a flat 300 μm in diameter. Moreover, in the embodiment illustrated, the frequency doubled optical pulse was shaped to provide a beam with a beam waist of a predetermined diameter at the surface of the cathode. In a specific embodiment, the beam waist was about 50 μm. In alternative embodiments, the beam waist ranged from about 30 μm to about 200 μm. Of course, the particular dimensions will depend on the particular applications. The frequency doubled optical pulse train was steered inside the chamber using a computer controlled mirror in a specific embodiment. In a specific embodiment, the optical pulse train is directed toward a front-illuminated photocathode where the irradiation of the cathode by the laser results in the generation of electron pulses via the photoelectric effect. Irradiation of a cathode with light having an energy above the work function of the cathode leads to the ejection of photoelectrons. That is, a pulse of electromagnetic energy above the work function of the cathode ejects a pulse of electrons according to a preferred embodiment. Generally, the cathode is maintained at a temperature of 1000 K, well below the thermal emission threshold temperature of about 1500 K, but this is not required by the present invention. In alternative embodiments, the cathode is maintained at room temperature. In some embodiments, the cathode is adapted to provide an electron pulse of predetermined pulse width. The trajectory of the electrons after emission follows the lens design of the TEM, namely the condenser, the objective, and the projector lenses. Depending upon the embodiment, there may also be other configurations. In the embodiment illustrated, the cathode is a Mini-Vogel mount single crystal lanthanum hexaboride (LaB6) cathode shaped as a truncated cone with a flat of 300 μm at the apex and a cone angle of 90°, available from Applied Physics Technologies, Inc., of McMinnville, Oreg. As is often known, LaB6 cathodes are regularly used in transmission and scanning electron microscopes. The quantum efficiency of LaB6 cathodes is about 10−3 and these cathodes are capable of producing electron pulses with temporal pulse widths on the order of 10−13 seconds. In some embodiments, the brightness of electron pulses produced by the cathode is on the order of 109 A/cm2/rad2 and the energy spread of the electron pulses is on the order of 0.1 eV. In other embodiments, the pulse energy of the laser pulse is reduced to about 500 pJ per pulse, resulting in approximately one electron/pulse Generally, the image quality acquired using a TEM is proportional to the number of electrons passing through the sample. That is, as the number of electrons passing through the sample is increased, the image quality increases. Some pulsed lasers, such as some Q-switched lasers, reduce the pulse count to produce a smaller number of pulses characterized by higher peak power per pulse. Thus, some laser amplifiers operate at a 1 kHz repetition rate, producing pulses with energies ranging from about 1 μJ to about 2 mJ per pulse. However, when such high peak power lasers are used to generate electron pulses using the photoelectric effect, among other issues, both spatial and temporal broadening of the electron pulses adversely impact the pulse width of the electron pulse or packet produced. In some embodiments of the present invention, the laser is operated to produce low power pulses at higher repetition rates, for example, 80 MHz. In this mode of operation, benefits available using lower power per pulse are provided, as described below. Additionally, because of the high repetition rate, sufficient numbers of electrons are available to acquire high quality images. In some embodiments of the present invention, the laser power is maintained at a level of less than 500 pJ per pulse to prevent damage to the photocathode. As a benefit, the robustness of the photoemitter is enhanced. Additionally, laser pulses at these power levels prevent space-charge broadening of the electron pulse width during the flight time from the cathode to the sample, thus preserving the desired femtosecond temporal resolution. Additionally, the low electron count per pulse provided by some embodiments of the present invention reduces the effects of space charge repulsion in the electron pulse, thereby enhancing the focusing properties of the system. As one of skill in the art will appreciated, a low electron count per pulse, coupled with a high repetition rate of up to 80 MHz provided by the femtosecond laser, provides a total dose as high as one electron/Å2 as generally utilized in imaging applications. In alternative embodiments, other suitable cathodes capable of providing a ultrafast pulse of electrons in response to an ultrafast optical pulse of appropriate wavelength are utilized. In embodiments of the present invention, the cathode is selected to provide a work function correlated with the wavelength of the optical pulses provided by the SHG device. The wavelength of radiation is related to the energy of the photon by the familiar relation λ(μm)≈1.24÷v(eV), where λ is the wavelength in microns and v is the energy in eV. For example, a LaB6 cathode with a work function of 2.7 eV is matched to optical pulses with a wavelength of 400 nm (v=3.1 eV) in an embodiment of the present invention. As illustrated, the cathode is enclosed in a vacuum chamber 130, for example, a housing for a transmission electron microscope (TEM). In general, the vacuum in the chamber 130 is maintained at a level of less than 1×10−6 torr. In alternative embodiments, the vacuum level varies from about 1×10−6 torr to about 1×10−10 torr. The particular vacuum level will be a function of the varied applications. In embodiments of the present invention, the short duration of the photon pulse leads to ejection of photoelectrons before an appreciable amount of the deposited energy is transferred to the lattice of the cathode. In general, the characteristic time for thermalization of the deposited energy in metals is below a few picoseconds, thus no heating of the cathode takes place using embodiments of the present invention. Electrons produced by the cathode 140 are accelerated past the anode 142 and are collimated and focused by electron lens assembly 146 and directed along electron imaging path 148 toward the sample 150. The electron lens assembly generally contains a number of electromagnetic lenses, apertures, and other elements as will be appreciated by one of skill in the art. Electron lens assemblies suitable for embodiments of the present invention are often used in TEMs. The electron pulse propagating along electron imaging path 148 is controlled in embodiments of the present invention by a controller (not shown, but described in more detail with reference to certain Figures below) to provide an electron beam of predetermined dimensions, the electron beam comprising a train of ultrafast electron pulses. The relationship between the electron wavelength (λde Broglie) and the accelerating voltage (U) in an electron microscope is given by the relationship λde Broglie=h/(2m0eU)1/2, where h, m0, e are Planck's constant, the electron mass, and an elementary charge. As an example, the de Broglie wavelength of an electron pulse at 120 kV corresponds to 0.0335 Å, and can be varied depending on the particular application. The bandwidth or energy spread of an electron packet is a function of the photoelectric process and bandwidth of the optical pulse used to generate the electron packet or pulse. Electrons passing through the sample or specimen 150 are focused by electron lens assembly 152 onto a detector 154. Although FIG. 1 illustrates two electron lens assemblies 146 and 152, the present invention is not limited to this arrangement and can have other lens assemblies or lens assembly configurations. In alternative embodiments, additional electromagnets, apertures, other elements, and the like are utilized to focus the electron beam either prior to or after interaction with the sample, or both. Detection of electrons passing through the sample, including single-electron detection, is achieved in one particular embodiment through the use of an ultrahigh sensitivity (UHS) phosphor scintillator detector 154 especially suitable for low-dose applications in conjunction with a digital CCD camera. In a specific embodiment, the CCD camera was an UltraScan™ 1000 UHS camera, manufactured by Gatan, Inc., of Pleasanton, Calif. The UltraScan™ 1000 CCD camera is a 4 mega-pixel (2048×2048) camera with a pixel size of 14 μm×14 μm, 16-bit digitization, and a readout speed of 4 Mpixels/sec. In the embodiment illustrated, the digital CCD camera is mounted under the microscope in an on-axis, below the chamber position. In order to reduce the noise and picture artifacts, in some embodiments, the CCD camera chip is thermoelectrically cooled using a Peltier cooler to a temperature of about −25° C. The images from the CCD camera were obtained with DigitalMicrograph™ software embedded in the Tecnai™ user interface, also available from Gatan, Inc. Of course, there can be other variations to the CCD camera, cooler, and computer software, depending upon the embodiment. FIG. 2 is a simplified perspective diagram of a 4D electron microscope system according to an embodiment of the present invention. The system illustrated in FIG. 2 is also referred to as an ultrafast electron microscope (UEM2) and was built at the present assignee. The integration of two laser systems with a modified electron microscope is illustrated, together with a representative image showing a resolution of 3.4 Å obtained in UEM2 without the field-emission-gun (FEG) arrangement of a conventional TEM. In one embodiment of the system illustrated in FIG. 2, the femtosecond laser system (fs laser system) is used to generate the single-electron packets and the nanosecond laser system (ns laser system) was used both for single-shot and stroboscopic recordings. In the single-electron mode of operation, the coherence volume is well defined and appropriate for image formation in repetitive events. The dynamics are fully reversible, retracing the identical evolution after each initiating laser pulse; each image is constructed stroboscopically, in seconds, from typically 106 pulses and all time-frames are processed to make a movie. The time separation between pulses can be varied to allow complete heat dissipation in the specimen. Without limiting embodiments of the present invention, it is believed that the electrons in the single electron packets have a transverse coherence length that is comparable to the size of the object that is being imaged. Since the subsequent electrons have a coherence length on the order of the size of the object, the electrons “see” the whole object at once. To follow the area-specific changes in the hundreds of images collected for each time scan, we obtained selected-area-image dynamics (SAID) and selected-area-diffraction dynamics (SADD); for the former, in real space, from contrast change and for the latter, in Fourier space, from changes of the Bragg peak separations, amplitudes, and widths. It is the advantage of microscopy that allows us to perform this parallel-imaging dynamics with pixel resolution, when compared with diffraction. As shown below, it would not have been possible to observe the selected temporal changes if the total image were to be averaged over all pixels, in this case 4 millions. As illustrated in FIG. 2, a TEM is modified to provide a train of electron pulses used for imaging in addition to the thermionic emission source used for imaging of samples. Merely by way of example, an FEI Tecnai™ G2 12 TWIN, available from FEI Company in Hillsboro, Oreg., may be modified according to embodiments of the present invention. The Tecnai™ G2 12 TWIN is an all-in-one 120 kV (λde Broglie=0.0335 Å) high-resolution TEM optimized for 2D and 3D imaging at both room and liquid-nitrogen temperatures. Embodiments of the present invention leverage capabilities provided by commercial TEMs such as automation software, detectors, data transfer technology, and tomography. In particular, in some embodiments of the present invention, a five-axis, motor-driven, precision goniometer is used with computer software to provide automated specimen tilt combined with automated acquisition of images as part of a computerized tomography (CT) imaging system. In these embodiments, a series of 2D images are captured at various specimen positions and combined using computer software to generate a reconstructed 3D image of the specimen. In some embodiments, the CT software is integrated with other TEM software and in other embodiments, the CT software is provided off-line. One of ordinary skill in the art would recognize many variations, modifications, and alternatives. In certain embodiments in which low-electron content electron pulses are used to image the sample, the radiation damage is limited to the transit of the electrons in the electron pulses through the sample. Typically, samples are on the order of 100 nm thick, although other thicknesses would work as long as certain electrons may traverse through the sample. Thus, the impact of radiation damage on these low-electron content electron pulse images is limited to the damage occurring during this transit time. Radiation induced structural damage occurring on longer time scales than the transit time will not impact the collected image, as these damage events will occur after the structural information is collected. Utilizing the apparatus described thus far, embodiments of the present invention provide systems and methods for imaging material and biological specimens both spatially and temporally with atomic-scale spatial resolution on the order of 1 nm and temporal resolution on the order of 100 fs. At these time scales, energy randomization is limited and the atoms are nearly frozen in place, thus methods according to the present invention open the door to time-resolved studies of structural dynamics at the atomic scale in both space and time. Details of the present computer system according to an embodiment of the present invention may be explained according to the description below. Referring to FIG. 2, a photograph of a UEM2 in accordance with embodiments of the present invention is illustrated, together with a high-resolution image of graphitized carbon. As illustrated, two laser systems (fs and ns) are utilized to provide a wide range of temporal scales used in 4D electron imaging. A 200-kV TEM is provided with at least two ports for optical access to the microscope housing. Using one or more mirrors (e.g., two mirrors), it is possible to switch between the laser systems to cover both the fs and ns experiments. The optical pulses are directed to the photocathode to generate electron packets, as well as to the specimen to initiate (clock) the change in images with a well-defined delay time Δt. The time axis is defined by variable delay between the electron generating and clocking pulses using the delay stage 170 illustrated in FIG. 1. Details of development of ultrafast electron microscopy with atomic-scale real-, energy-, and Fourier-space resolutions is now provided. The second generation UEM2 described in FIG. 2 provides images, diffraction patterns, and electron-energy spectra, and has application for nanostructured materials and organometallic crystals. The separation between atoms in direct images, and the Bragg spots/Debye-Scherrer rings in diffraction, are clearly resolved, and the electronic structure and elemental energies in the electron-energy-loss spectra (EELS) and energy-filtered-transmission-electron microscopy (EFTEM) are obtained. The development of 4D ultrafast electron microscopy and diffraction have made possible the study of structural dynamics with atomic-scale spatial resolution, so far in diffraction, and ultrashort time resolution. The scope of applications is wide-ranging with studies spanning diffraction of isolated structures in reactions (gas phase), nanostructures of surfaces and interfaces (crystallography), and imaging of biological cells and materials undergoing first-order phase transitions. Typically, for microscopy the electron was accelerated to 120 keV and for diffraction to 30 keV, respectively, and issues of group velocity mismatch, in situ clocking (time zero) of the change, and frame referencing were addressed. One powerful concept implemented is that of “tilted pulses,” which allow for the optimum resolution to be reached at the specimen. For ultrafast electron microscopy, the concept of “single-electron” imaging is fundamental to some embodiments. The electron packets, which have a well-defined picometer-scale de Broglie wave length, are generated in the microscope by femtosecond optical pulses (photoelectric effect) and synchronized with other optical pulses to initiate the change in a temperature jump or electronic excitation. Because the number of electrons in each packet is one or a few, the Coulomb repulsion (space charge) between electrons is reduced or eliminated and the temporal resolution can reach the ultimate, that of the optical pulse. The excess energy above the work function determines the electron energy spread and this, in principle, can be minimized by tuning the pulse energy. The spatial resolution is then only dependent on the total number of electrons because for each packet the electron “interferes with itself” and a coherent buildup of the image is achievable. The coherence volume, given by:Vc=λde Broglie2(R/a)2ve(h/ΔE)establishes that the degeneracy factor is much less than one and that each Fermionic electron is independent, without the need of the statistics commonly used for Bosonic photons. The volume is determined by the values of longitudinal and transverse coherences; Vc is on the order of 106 nm3 for typical values of R (distance to the source), a (source dimension), ve (electron velocity), and ΔE (energy spread). Unlike the situation in transmission electron microscopy (TEM), coherence and image resolution in UEM are thus determined by properties of the optical field, the ability to focus electrons on the ultrashort time scale, and the operational current density. For both “single electron” and “single pulse” modes of UEM, these are important considerations for achieving the ultimate spatio-temporal resolutions for studies of materials and biological systems. Atomic-scale resolution in real-space imaging can be achieved utilizing the second generation ultrafast electron microscopy system (UEM2) of FIG. 2. With UEM2, which operates at 200 keV (λde Broglie=2.507 pm), energy-space (electron-energy-loss spectroscopy, EELS) and Fourier-space (diffraction) patterns of nanostructured materials are possible. The apparatus can operate in the scanning transmission electron microscope (STEM) mode, and is designed to explore the vast parameter space bridging the gap between the two ideal operating modes of single-electron and single-pulse imaging. With these features, UEM2 studies provide new limits of resolution, image mapping, and elemental analysis. Here, demonstrated are the potential by studying gold particles and islands, boron nitride crystallites, and organometallic phthalocyanine crystals. FIG. 2A displays the conceptual design of UEM2, which, as with the first generation (UEM1—described generally in FIG. 1), comprises a femtosecond laser system and an electron microscope modified for pulsed operation with femtosecond electron packets. A schematic representation of optical, electric, and magnetic components are shown. The optical pulse train generated from the laser, in this case having a variable pulse width of 200 fs to 10 ps and a variable repetition rate of 200 kHz to 25 MHz, is divided into two parts, after harmonic generation, and guided toward the entries of the design hybrid electron microscope. The frequency-tripled optical pulses are converted to the corresponding probe electron pulses at the photocathode in the hybrid FEG, whereas the other optical pump beam excites (T-jump or electronic excitation) in the specimen with a well-defined time delay with respect to the probe electron beam. The probe electron beam through the specimen can be recorded as an image (normal or filtered, EFTEM), a diffraction pattern, or an EEL spectrum. The STEM bright-field detector is retractable when it is not in use. The laser in an embodiment is a diode-pumped Yb-doped fiber oscillator/amplifier (Clark-MXR; in development), which produces ultrashort pulses of up to 10 μJ at 1030 nm with variable pulse width (200 fs-10 ps) and repetition rate (200 kHz-25 MHz). The output pulses pass through two successive nonlinear crystals to be frequency doubled (515 nm) and tripled (343 nm). The harmonics are separated from the residual infrared radiation (IR) beam by dichroic mirrors, and the frequency-tripled pulses are introduced to the photocathode of the microscope for generating the electron pulse train. The residual IR fundamental and frequency-doubled beams remain available to heat or excite samples and clock the time through a computer-controlled optical delay line for time-resolved applications. The electron microscope column is that of a designed hybrid 200-kV TEM (Tecnai 20, FEI) integrated with two ports for optical access, one leading to the photocathode and the other to the specimen. The field emission gun (FEG) in the electron-generation assembly adapts a lanthanum hexaboride (LaB6) filament as the cathode, terminating in a conical electron source truncated to leave a flat tip area with a diameter of 16 μm. The tip is located in a field environment controlled by suppressor and extractor electrodes. The gun can be operated as either a thermal emission or a photoemission source. The optical pulses are guided to the photocathode as well as to the specimen by a computer-controlled, fine-steering mirror in an externally-mounted and x-ray-shielded periscope assembly. Each laser beam can be focused to a spot size of <30 μm full width at half maximum (FWHM) at its respective target when the beam is expanded to utilize the available acceptance angle of the optical path. Various pulse-energy, pulse-length, and focusing regimes have been used in the measurements reported here. For UEM measurements, the cathode was heated to a level below that needed to produce detectible thermal emission, as detailed below, and images were obtained using both the TEM and the UEM2 mode of operation. For applications involving EELS and energy-filtered-transmission-electron microscopy (EFTEM), the Gatan Imaging Filter (GIF) Tridiem, of the so-called post-column type, was attached below the camera chamber. The GIF accepts electrons passing through an entrance aperture in the center of the projection chamber. The electron beam passes through a 90° sector magnet as shown in FIG. 2A, which bends the primary beam through a 10 cm bending radius and thereby separates the electrons according to their energy into an energy spectrum. An energy resolution of 0.87 eV was measured for the EELS zero-loss peak in thermal mode operation of the TEM. A retractable slit is located after the magnet followed by a series of lenses. The lenses restore the image or diffraction pattern at the entrance aperture and finally it can be recorded on a charge-coupled device (CCD) camera (UltraScan 1000 FT) at the end of the GIF with the Digital Micrograph software. The digital camera uses a 2,048×2,048 pixel CCD chip with 14 μm square pixels. Readout of the CCD is done as four independent quadrants via four separate digitizing signal chains. This 4-port readout camera combines single-electron sensitivity and 16-bit pixel depth with high-speed sensor readout (4 Mpix/s). Additionally, for scanning-transmission-electron microscopy (STEM), the UEM2 is equipped with a bright-field (BF) detector with a diameter of 7 mm and an annular dark-field (ADF) detector with an inner diameter of 7 mm and an outer diameter of 20 mm. Both detectors are located in the near-axis position underneath the projection chamber. The BF detector usually collects the same signal as the TEM BF image, i.e., the transmitted electrons, while the ADF detector collects an annulus at higher angle where only scattered electrons are detected. The STEM images are recorded with the Tecnai Imaging & Analysis (TIA) software. To observe the diffraction pattern, i.e., the back focal plane of the objective lens, we inserted a selected area aperture into the image plane of the objective lens, thus creating a virtual aperture in the plane of the specimen. The result is a selected area diffraction (SAD) pattern of the region of interest only. Adjustment of the intermediate and projector lens determines the camera length. Diffraction patterns are processed and analyzed for crystal structure determination. Several features of the UEM2 system are worthy of note. First, the high repetition rate amplified laser source allows us to illuminate the cathode with 343 nm pulses of energies above 500 nJ, compared with typical values of 3 nJ near 380 nm for UEM1. Thus, a level of average optical power for electron generation comparable to that of UEM1 operating at 80 MHz, but at much lower repetition rates, was able to be delivered. The pulse energy available in the visible and IR beams is also at least two orders of magnitude greater than for UEM1, allowing for exploration of a much greater range in the choice of sample excitation conditions. Second, the hybrid 200-kV FEG, incorporating an extractor/suppressor assembly providing an extractor potential of up to 4 kV, allows higher resolving power and greater flexibility and control of the conditions of electron generation. Third, with simple variation of optical pulse width, the temporal and spatial resolution can be controlled, depending on the requirements of each experiment. Fourth, with variation of spacing between optical pulses without loss of pulse energy, a wide range of samples can be explored allowing them to fully relax their energy after each excitation pulse and rewind the clock precisely; with enough electrons, below the space-charge limit, single-pulse recording is possible. Finally, by the integration of the EELS spectrometer, the system is empowered with energy resolution in addition to the ultrafast time resolution and atomic-scale space resolution. The following results demonstrate the capabilities of UEM2 in three areas: real-space imaging, diffraction, and electron energy resolution. Applications of the present invention are not limited to these particular examples. First discussed are the images recorded in the UEM mode, of gold particles and gold islands on carbon films. FIGS. 2Ba-f are UEM2 images obtained with ultrafast electron pulses. Shown are gold particles (a, d) and gold islands (c, f) on carbon films. UEM2 background images (b, e) obtained by blocking the photoelectron-extracting femtosecond laser pulses. For the UEM2 images of gold particles, we used the objective (contrast) aperture of 40 μm to eliminate diffracted beams, while no objective aperture was used for the gold-island images. FIGS. 2Aa and 2Ad show gold particles of uniform size dispersed on a carbon film. From the higher magnification image of FIG. 2Ad, corresponding to the area indicated by the black arrow in FIG. 2Aa, it is found that the gold particles have a size of 15 nm, and the minimum particle separation seen in the image is 3 nm. It should be noted that FIGS. 2Ab and 2Ae were recorded under identical conditions to FIGS. 2Aa and 2Ad, respectively, but without cathode irradiation by the femtosecond laser pulses. No images were observed, demonstrating that non-optically generated electrons from our warm cathode were negligible. Similar background images with the light pulses blocked were routinely recorded and checked for all cathode conditions used in this study. The waffle (cross line) spacing of the cross grating replica (gold islands) seen in FIG. 2Ac is known to be 463 nm. The gold islands are observed in FIG. 2Af, where the bright regions correspond to the amorphous carbon support film and the dark regions to the nanocrystalline gold islands. It is found that the islands may be interconnected or isolated, depending on the volume fraction of the nanocrystalline phases. To test the high-resolution capability of UEM utilizing phase contrast imaging, an organometallic compound, chlorinated copper phthalocyanine (hexadecachlorophthalocyanine, C32Cl16CuN8), was investigated. The major spacings of lattice fringes of copper of this molecule in projection along the c-axis are known to be 0.88, 1.30, and 1.46 nm, with atomic spacings of 1.57 and 1.76 nm. FIGS. 2Ca-b are high-resolution, phase-contrast UEM images. Shown are an image in FIG. 2Ca and digital diffractogram in FIG. 2Cb of an organometallic crystal of chlorinated copper phthalocyanine. The diffractogram was obtained by the Fourier transform of the image in FIG. 2Ca. The high-resolution image was taken near the Scherzer focus for optimum contrast, which was calculated to be 90.36 nm for a spherical aberration coefficient Cs of the objective lens of 2.26 mm. The objective aperture was not used. FIG. 2Da exhibits the lattice fringes observed by UEM, where the black lines correspond to copper layers parallel to the c-axis. The Fourier transform of FIG. 2Da is shown in FIG. 2Db, discussed below, and the clear reciprocity (without satellite peaks in the F.T.) indicates the high degree of order in crystal structure. FIG. 2D shows high-resolution, phase-contrast UEM image and structure of chlorinated copper phthalocyanine The high-resolution image shown in FIG. 2Da is a magnified view of the outlined area in FIG. 2Ca. The representation of the crystal structure shown in FIG. 2Db is shown in projection along the c axis, and the assignment of the copper planes observed in FIG. 2Da is indicated by the gray lines. The spheres are the copper atoms. FIG. 2Da is an enlargement of the area outlined in FIG. 2Ca, clearly showing the lattice fringe spacing of 1.46 nm, corresponding to the copper planes highlighted in gray in FIG. 2Db, in which a unit cell is shown in projection along the c-axis. Regions without lattice fringes are considered to correspond to crystals with unfavorable orientation, or amorphous phases of phthalocyanine, or the carbon substrate. It is known that in high resolution images, the lattice fringes produced by the interference of two waves passing through the back focal plane, i.e., the transmitted and diffracted beams, are observed only in crystals where the lattice spacing is larger than the resolution of the TEM. In the profile inset of FIG. 2Da, it should be noted that the FWHM was measured to be approximately 7 Å, directly indicating that our UEM has the capability of sub-nanometer resolution. The digital diffractogram obtained by the Fourier transform of the observed high-resolution image of FIG. 2Ca is shown in FIG. 2Cb. In the digital diffractogram, the peaks represent the fundamental spatial frequency of the copper layers (0.69 nm−1), and higher harmonics thereof. A more powerful means of obtaining reciprocal-space information such as this is the direct recording of electron diffraction, also available in UEM. FIGS. 2Ea-f show measured and calculated electron diffraction patterns of gold islands and boron nitride (BN) on carbon films, along with the corresponding real-space images of each specimen, all recorded by UEM. Shown are images and measured and calculated electron diffraction patterns of gold islands (a,b,c) and boron nitride (BN) (d,e,f) on carbon films. The incident electron beam is parallel to the [001] direction of the BN. All diffraction patterns were obtained by using the selected-area diffraction (SAD) aperture, which selected an area 6 μm in diameter on the specimen. Representative diffraction spots were indexed as indicated by the arrowheads. In FIG. 2Eb, the electron diffraction patterns exhibit Debye-Scherrer rings formed by numerous diffraction spots from a large number of face-centered gold nanocrystals with random orientations. The rings can be indexed as indicated by the white arrowheads. The diffraction pattern of BN in FIG. 2Ee is indexed by the hexagonal structure projected along the [001] axis as shown in FIG. 2Ef. It can be seen that there are several BN crystals with different crystal orientations, besides that responsible for the main diffraction spots indicated by the white arrowheads. In order to explore the energy resolution of UEM, we investigated the BN specimen in detail by EELS and EFTEM. FIG. 2F shows energy-filtered UEM images and spectrum. FIG. 2F shows a zero-loss filtered image (FIG. 2Fa), boron K-edge mapping image (FIG. 2Fb), thickness mapping image (FIG. 2Fc), and corresponding electron-energy-loss (EEL) spectrum (FIG. 2Fd) of the boron nitride (BN) sample. The 5.0- and 1.0-mm entrance aperture were used for mapping images and EEL spectrum, respectively. The thickness at the point indicated by the asterisk in FIG. 2Fc is estimated to be 41 nm. ZL stands for zero-loss. The boron map was obtained by the so-called three-window method. In the boron map of FIG. 2Fb, image intensity is directly related to areal density of boron. In the thickness map of FIG. 2Fc, the brightness increases with increasing thickness: d (thickness)=λ(β)ln(It/I0), where λ is the mean free path for inelastic scattering under a given collection angle β, I0 is the zero-loss (ZL) peak intensity, and It is the total intensity. The thickness in the region indicated by the asterisk in FIG. 2Fc was estimated to be 41 nm. In the EEL spectrum of FIG. 2Fd, the boron K-edge, carbon K-edge, and nitrogen K-edge are observed at the energy of 188, 284, and 401 eV, respectively. In the boron K-edge spectrum, sharp π* and σ* peaks are visible. The carbon K-edge spectrum is considered to result from the amorphous carbon film due to the existence of small and broad peaks at the position π* and σ, being quite different from spectra of diamond and graphite. With the capabilities of the UEM2 system described herein, structural dynamics can be studied, as with UEM1, but with the new energy and spatial resolution are achieved here. Specimens will be excited in a T-jump or electronic excitation by the femtosecond laser pulses (FIG. 2A) scanned in time with respect to the electron packets which will probe the changes induced in material properties through diffraction, imaging, or electron energy loss in different regions, including that of Compton scattering. Also planned to be explored is the STEM feature in UEM, particularly the annular dark-field imaging, in which compositional changes are evident in the contrast (Z contrast). Such images are known to offer advantages over high-resolution TEM (relative insensitivity to focusing errors and ease of interpretation). Electron fluxes will be optimized either through changes of the impinging pulse fluence or by designing new photocathode materials. In this regard, with higher brightness the sub-angstrom limit should be able to be reached. The potential for applications in materials and biological research is rich. FIG. 3 is a simplified diagram of a computer system 310 that is used to oversee the system of FIGS. 1 and 2 according to an embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims herein. One of ordinary skill in the art would recognize many other modifications, alternatives, and variations. As shown, the computer system 310 includes display device 320, display screen 330, cabinet 340, keyboard 350, and mouse 370. Mouse 370 and keyboard 350 are representative “user input devices.” Mouse 370 includes buttons 380 for selection of buttons on a graphical user interface device. Other examples of user input devices are a touch screen, light pen, track ball, data glove, microphone, and so forth. The system is merely representative of but one type of system for embodying the present invention. It will be readily apparent to one of ordinary skill in the art that many system types and configurations are suitable for use in conjunction with the present invention. In a preferred embodiment, computer system 310 includes a Pentium™ class based computer, running Windows™ NT, XP, or Vista operating system by Microsoft Corporation. However, the system is easily adapted to other operating systems such as any open source system and architectures by those of ordinary skill in the art without departing from the scope of the present invention. As noted, mouse 370 can have one or more buttons such as buttons 380. Cabinet 340 houses familiar computer components such as disk drives, a processor, storage device, etc. Storage devices include, but are not limited to, disk drives, magnetic tape, solid-state memory, bubble memory, etc. Cabinet 340 can include additional hardware such as input/output (I/O) interface cards for connecting computer system 310 to external devices external storage, other computers or additional peripherals, which are further described below. FIG. 4 is a more detailed diagram of hardware elements in the computer system of FIG. 3 according to an embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims herein. One of ordinary skill in the art would recognize many other modifications, alternatives, and variations. As shown, basic subsystems are included in computer system 310. In specific embodiments, the subsystems are interconnected via a system bus 375. Additional subsystems such as a printer 374, keyboard 378, fixed disk 379, monitor 376, which is coupled to display adapter 382, and others are shown. Peripherals and input/output (I/O) devices, which couple to I/O controller 371, can be connected to the computer system by any number of means known in the art, such as serial port 377. For example, serial port 377 can be used to connect the computer system to a modem 381, which in turn connects to a wide area network such as the Internet, a mouse input device, or a scanner. The interconnection via system bus allows central processor 373 to communicate with each subsystem and to control the execution of instructions from system memory 372 or the fixed disk 379, as well as the exchange of information between subsystems. Other arrangements of subsystems and interconnections are readily achievable by those of ordinary skill in the art. System memory, and the fixed disk are examples of tangible media for storage of computer programs, other types of tangible media include floppy disks, removable hard disks, optical storage media such as CD-ROMS and bar codes, and semiconductor memories such as flash memory, read-only-memories (ROM), and battery backed memory. Although the above has been illustrated in terms of specific hardware features, it would be recognized that many variations, alternatives, and modifications can exist. For example, any of the hardware features can be further combined, or even separated. The features can also be implemented, in part, through software or a combination of hardware and software. The hardware and software can be further integrated or less integrated depending upon the application. Further details of the functionality, which may be carried out using a combination of hardware and/or software elements, of the present invention can be outlined below according to the figures. Embodiments of the present invention enable ultrafast imaging with applications in studies of structural and morphological changes in single-crystal gold and graphite films, which exhibit entirely different dynamics, as discussed below. For both, the changes were initiated by in situ femtosecond impulsive heating, while image frames and diffraction patterns were recorded in the microscope at well-defined times following the temperature-jump. The time axis in the microscope is independent of the response time of the detector, and it is established using a variable delay-line arrangement; a 1-μm change in optical path of the initiating (clocking) pulse corresponds to a time step of 3.3 fs. FIG. 5 illustrates both time-resolved images and diffraction. In this example, the images in FIGS. 5A and 5B were obtained stroboscopically at several time delays after heating with the fs pulse (fluence of 1.7 mJ/cm2). The specimen is a gold single crystal film mounted on a standard 3-mm 400-mesh grid. Shown are the bend contours (dark bands), {111} twins (sharp straight white lines) and holes in the sample (bright white circles). The insets in FIG. 5B are image-difference frames Im(tref; t) with respect to the image taken at −84 ps. The gold thickness was determined to be 8 nm by electron energy loss spectroscopy (EELS). FIG. 5C illustrates the time dependence of image cross-correlations of the full image from four independent scans taken with different time steps. A fit to biexponential rise of the 1 ps step scan is drawn, yielding time constants of 90 ps and 1 ns. FIG. 5D illustrates the time dependence of image cross-correlations at 1 ps time steps for the full image and for selected regions of interest SAI #1, #2, and #3, as shown in FIG. 5A. FIGS. 5E and 5F are diffraction patterns obtained using a single pulse of 6×106 electrons at high peak fluence (40 mJ/cm2) and selected-area aperture of 25 μm diameter. Two frames are given to indicate the change. Diffraction spots were indexed and representative indices are shown as discussed below. FIGS. 5A and 5B illustrate representative time-framed images of the gold nanocrystal using the fs excitation pulses at a repetition rate of 200 kHz and peak excitation fluence of ˜1.7 mJ/cm2. In FIG. 5A, taken at −84 ps, before the clocking pulse (t=0), typical characteristic features of the single crystal gold in the image are observed: twins and bend contours. Bend contours, which appear as broad fuzzy dark lines in the image, are diffraction contrast effects occurring in warped or buckled samples of constant thickness. In the dark regions, the zone axis (the crystal [100]) is well aligned with the incident electron beam and electrons are scattered efficiently, whereas in the lighter regions the alignment of the zone axis deviates more and the scattering efficiency is lower. Because bend contours generally move when deformation causes tilting of the local crystal lattice, they provide in images a sensitive visual indicator of the occurrence of such deformations. At positive times, following t=0, visual dynamical changes are observed in the bend contours with time steps from 0.5 ps to 50 ps. A series of such image frames with equal time steps provide a movie of the morphological dynamics. To more clearly display the temporal evolution, image-difference frames were constructed. Depicted as insets in the images of FIG. 5B, are those obtained when referencing to the −84 ps frame; for t=+66 ps and +151 ps. In the difference images, the regions of white or black directly indicate locations of surface morphology change (bend contour movement), while gray regions are areas where the contrast is unchanged from that of the reference frame. It is noted that the white and black features in the difference images are nm-scale dynamical change, indicating the size of the induced deformations. Care was taken to insure the absence of long-term specimen drifts as they can cause apparent contrast change. To quantify the changes in the image the following method of cross-correlation was used. The normalized cross correlation of an image at time t with respect to that at time t′ is expressed as: γ ⁡ ( t ) = ∑ x , y ⁢ C x , y ⁡ ( t ) ⁢ C x , y ⁡ ( t ′ ) ∑ x , y ⁢ C x , y ⁡ ( t ) 2 ⁢ ∑ x , y ⁢ C x , y ⁡ ( t ′ ) 2 where the contrast Cx,y(t)=[Ix,y(t)−Ī(t)]/Ī(t); Ix,y(t) and Ix,y(t′) are the intensities of pixels at the position of (x,y) at times t and t′, and Ī(t) and Ī(t′) are the means of Ix,y(t) and Ix,y(t′), respectively. This correlation coefficient γ(t) is a measure of the temporal change in “relief pattern” between the two images being compared, which can be used as a guide to image dynamics as a function of time. Two types of cross-correlation plots were made, those referenced to a fixed image frame before t=0 and others that show correlation between adjacent time points. (Another quantity that shows time dependence qualitatively similar to that of the image cross-correlation is the standard deviation of pixel intensity in difference images). FIGS. 5C and 5D show the cross-correlation values between the image at each measured time point and a reference image recorded before the arrival of the clocking pulse. The experiments were repeated, for different time-delay steps (500 fs, 1 ps, 5 ps, and 50 ps), and similar results were obtained, showing that morphology changes are completely reversible and reproducible over each 5 μs inter-pulse interval. The adjacent-time cross-correlations reveal the timescales for intrinsic changes in the images, which disappear for time steps below 5 ps, consistent with full-image rise in time. Over all pixels, the time scale for image change covers the full range of time delay, from ps to ns, indicating the collective averaging over sites of the specimen; as shown in FIG. 5C the overall response can be fit to two time constants of 90 ps and 1 ns. The power of selected area image dynamics (SAID) is illustrated when the dynamics of the bend contours are followed in different selected areas of the image, noted in the micrographs as SAI #1, 2, and 3. The corresponding image cross-correlations (FIG. 5D) have different shape and amplitude from each other and from the full image correlation. The large differences observed here and for other data sets, including onsets delayed in time and sign reversals, indicate the variation in local deformation dynamics. In FIGS. 5G-L, a time-resolved SAI at higher magnification is depicted. A broad and black “penguin-like” contour is observed as the dominant feature of this area. As shown in the frames, a colossal response to the fs heating is noted. The gray region inside the black contour appears and broadens with time. Also, a new black contour above the large central white hole begins to be evident at 1200 ps, and gains substantial intensity over the following 50 ps. All frames taken can be used to construct a movie of SAID. The observed SAID changes correspond to diffraction contrast (bright-field) effects in bend contours, as mentioned above. It is known that the shape of bend contours can be easily altered by sample tilting or heating inside the microscope. However, here in the ultrafast electron microscope (UEM) measurements, the changes in local tilt are transient in nature, reflecting the temporal changes of morphology and structure. Indeed, when the experiments were repeated in the TEM mode of operation, i.e., for the same heating laser pulse and same scanning time but with continuous electron probe beam, no image change was observed. This is further supported by the change in diffraction observed at high fluences and shown in FIGS. 5E and 5F for two frames, at negative time and at +50 ns; in the latter, additional Bragg spots are visible, a direct evidence of the transient structural change due to bulging at longer times. Whereas real-space imaging shows the time-dependent morphology, the selected area diffraction dynamics (SADD) patterns provide structural changes on the ultrashort timescale. Because the surface normal of the film is parallel to the [100] zone axis, the diffraction pattern of the sample was properly indexed by the face-centered-cubic (fcc) structure projected along the [100] zone axis at zero tilt angle (see FIG. 5E). From the positions of the spots in FIG. 5F, which are reflections from the {113} and {133} planes, forbidden in the [100] zone-axis viewing, we measured the interplanar spacings to be 1.248 and 0.951 Å, respectively. With selected area diffraction, Bragg peak separations, amplitudes, and widths were obtained as a function of time. The results indicate different timescales from those of image dynamics. FIG. 6A illustrates structural dynamics and heat dissipation in gold and FIG. 6B illustrates coherent resonance of graphite. Referring to FIG. 6A, SADD for fs excitation at 1.7 mJ/cm2 peak fluence (519 nm) is illustrated. The Bragg separation for all peaks and the amplitude of the {042} peaks are shown in the main panel; the inset gives the 2.2 μs recovery (by cooling) of the structure obtained by stroboscopic ns excitation at 7 mJ/cm2. The peak amplitude has been normalized to the transmitted beam amplitude, and the time dependence of amplitude and separation is fit as an exponential rise, and a delay with rise, respectively. Referring to FIG. 6B, resonance oscillations are observed for the Bragg (1 22) peak in the diffraction pattern of graphite; the amplitudes are similar in magnitude to those in FIG. 6A. The sample was tilted at 21° angle to the microscope axis and the diffraction pattern was obtained by using the SAD aperture of 6 μm diameter on the specimen. The graphite thickness is 69 nm as determined by EELS; the oscillation period (τp) is measured to be 56.3 ps. For a thickness of 45 nm, the period is found to be τp=35.4 ps. FIGS. 6D-G illustrate, for selected areas, time dependence of intensity difference (dark-field) for graphite. The image change displays the oscillatory behavior with the same τp as that of diffraction. The dark-field (DF) images were obtained by selecting the Bragg (1 22) peak. In FIG. 6H, each line corresponds to the difference in image intensities, Im(t−30 ps; t), for selected areas of 1×100-pixel slices parallel to contrast fringes in the DF image. The average amplitude of {042} diffraction peaks drop significantly; the rise time is 12.9 ps, whereas the change in separations of all planes is delayed by 31 ps and rises in 60 ps. The delay in the onset of separation change with respect to amplitude change is similar to the timescale for the amplitude to reach its plateau value of 15% reduction in the case of the {042} amplitude shown. In order to determine the recovery time of the structure, we carried out stroboscopic (and also single-pulse) experiments over the timescale of microseconds. The recovery transient in the inset of FIG. 6A (at 7 mJ/cm2) gives a time constant of 2.2 μs; we made calculations of 2D lateral heat transport with thermal conductivity (λ=3.17 W/(cm K) at 300 K) and reproduced the observed timescale. For this fluence, the maximum lattice spacing change of 0.08% gives the temperature increase ΔT to be 60 K, knowing the thermal expansion coefficient of gold (α=14.2×10−6 K−1). The atomic-scale motions, which lead to structural and morphological changes, can now be elucidated. Because the specimen is nanoscale in thickness, the initial temperature induced is essentially uniform across the atomic layers and heat can only dissipate laterally. It is known that for metals the lattice temperature is acquired following the large increase in electron temperature. The results in FIG. 6A give the temperature rise to be 13 ps; from the known electron and lattice heat-capacity constants [C1=70 J/(m3 K2) and C2=2.5×106 J/(m3 K), respectively] and the electron-phonon coupling [g=2×1016 W/(m3 K)] we obtained the initial heating time to be ˜10 ps for electron temperature T1=2500 K, in good agreement with the observed rise. Reflectivity measurements do not provide structural information, but they give the temperature rise. For bulk material, the timescale for heating (˜1 ps) is shorter than that of the nano-scale specimen (˜10 ps), due to confinement in the latter, which limits the ballistic motion of electrons in the specimen, and this is evident in the UEM studies. Because the plane separation is 0.4078 nm, the change of the average peak separation (0.043%), at the fluence of 1.7 mJ/cm2, gives a lattice constant change of 0.17 pm. Up to 30 ps the lattice is hot but, because of macroscopic lattice constraint, the atomic stress cannot lead to changes in lateral separations, which are the only separations visible for the [100] zone-axis probing. However, the morphology warping change is correlated with atomic (lateral) displacements in the structure as it relieves the structural constraint. Indeed the time scale of the initial image change is similar to that of plane separations in diffraction (60-90 ps). This initial warping, which changes image contrast, is followed by longer time (ns) minimization of surface energy and bulging, as shown in FIG. 5D. Given the picometer-scale structural change (0.17 pm), the stress over the 8-nanometer specimen gives the total expansion to be 3.4 pm over the whole thickness. Considering the influence of lateral expansion, the maximum bulge reaches 1 to 10 nm depending on the lateral scale. Finally, the calculated Debye-Waller factor for structural changes gives a temperature of 420 K (ΔT=125 K), in excellent agreement with lattice temperature derived under similar conditions, noting that for the nanoscale material the temperature is higher than in the bulk. Graphite was another study in the application of the UEM methodology. In contrast to the dynamics of gold, in graphite, because of its unique 2D structure and physical properties, we observed coherent resonance modulations in the image and also in diffraction. The damped resonance of very high frequency, as shown below, has its origin in the nanoscale dimension of the specimen and its elasticity. The initial fs pulse induces an impulsive stress in the film and the ultrafast electron tracks the change of the transient structure, both in SAID and SADD. In FIG. 6B, the results obtained by measuring changes of the diffraction spot (1 22) are displayed and in FIGS. 6D-G those obtained by dark-field (DF) imaging with the same diffraction spot being selected by the objective aperture and the specimen tilted, as discussed below. For both the image and diffraction, a strong oscillatory behavior is evident, with a well defined period and decaying envelope. When the transients were fitted to a damped resonance function [(cos 2πt/τp)exp(−t/τdecay)], we obtained τp=56.3±1 ps for the period. The decay of the envelope for this particular resonance is significantly longer, τdecay=280 ps. This coherent transient decay, when Fourier transformed, indicates that the length distribution of the film is only ±2 nm as discussed in relation to the equation below. The thickness of the film was determined (L=69 nm) using electron energy loss spectra (EELS). In order to test the validity of this resonance behavior we repeated the experiments for another thickness, L=45 nm. The period indeed scaled with L, giving τp=35.4 ps. These, hitherto unobserved, very high frequency resonances (30 gigahertz range) are unique to the nanoscale length of graphite. They also reflect the (harmonic) motions due to strain along the c-axis direction, because they were not observed when we repeated the experiment for the electron to be along the [001] zone axis. The fact that the period in the image is the same as that of the diffraction indicates the direct correlation between local atomic structure and macroscopic elastic behavior. Following a fs pulse of stress on a freely vibrating nanofilm, the observed oscillations, because of their well-defined periods, are related to the velocity (C) of acoustic waves between specimen boundaries, which in turn can be related to Young's modulus (Y) of the elastic stress-strain profile: 1 τ p = nC 2 ⁢ L = n 2 ⁢ L ⁢ ( Y ρ ) 1 / 2 ,where n is a positive integer, with n=1 being the fundamental resonance frequency (higher n are for overtones). Knowing the measured τp and L, we obtained C=2.5×105 cm/s. For graphite with the density ρ=2.26 g/cm3, Y=14.6 gigapascal for the c-axis strain in the natural specimen examined. Pyrolytic graphite has Y values that range from about 10 to 1000 gigapascal depending on the orientation, reaching the lowest value in bulk graphite and the highest one for graphene. The real-time measurements reported here can now be extended to different length scales, specimens of different density of dislocations, and orientations, exploring their influence at the nanoscale on C, Y, and other properties. We note that selected-area imaging was critical as different regions have temporally different amplitudes and phases across the image. Uniting the power of spatial resolution of EM with the ultrafast electron timing in UEM provides an enormous advantage when seeking to unravel the elementary dynamics of structural and morphological changes. With total dissipation of specimen heat between pulses, selected-area dynamics make it possible to study the changes in seconds of recording and for selected pixels of the image. In the applications given here, for both gold and graphite, the difference in timescales for the nonequilibrium temperature (reaching 1013 K/s), the structural (pm scale) and morphological (nm scale) changes, and the ultrafast coherent (resonance) behavior (tens of gigahertz frequency) of materials structure illustrate the potential for other applications, especially when incorporating the different and valuable variants of electron microscopy as we have in our UEM. Embodiments of the present invention extend ultrafast 4D diffraction and microscopy to the attosecond regime. As described herein, embodiments use attosecond electron diffraction to observe attosecond electron motion. Pulses are freely generated, compressed, and tilted. The approach can be implemented to extend previous techniques including, for example phase transformations, chemical reactions, nano-mechanical processes, and surface dynamics, and possibly to other studies of melting processes, coherent phonons, gold particles, and molecular alignment. As described herein, the generation of attosecond resolution pulses and in situ probing through imaging with free electrons. Attosecond diffraction uses near mono-energetic attosecond electron pulses for keV-range of energies in free space and thus space charge effects are considered. Additionally, spatiotemporal synchronization of the electron pulses to the pump pulses is made along the entire sample area and with attosecond precision. Diffraction orders are shown to be sensitive to the effect of electron displacement and conclusive of the four-dimensional dynamics. A component of reaching attosecond resolution with electron diffraction is the generation of attosecond electron pulses in “free space,” so that diffraction from freely chosen samples of interest can take place independent of the mechanisms of pulse generation. Electrons with energies of 30-300 keV are ideal for imaging and diffraction, because of their high scattering cross sections, convenient diffraction angles, and the appropriate de Broglie wavelength (0.02 to 0.07 Å) to resolve atomic-scale changes. Moreover, they have a high degree of monochromaticity. For example, electrons accelerated to E0=30-300 keV with pulse duration of 20 attoseconds (bandwidth of ΔE≈30 eV) have ΔE/E0≈10−3-10−4, making diffraction and imaging possible without a spread in angle and resolution. Optical attosecond pulses have typically ΔE/E0≈0.5 and because of this reach of ΔE to E0, their duration is Fourier-limited to ˜100 attoseconds. Free electron pulses of keV central energy can, in principle, have much shorter duration, down to sub-attoseconds, while still consisting of many wave cycles. Pulses with a large number of electrons suffer from the effect of space charge, which determines both the spatial and the temporal resolutions. This can be avoided by using packets of single, or only a few, electrons in a high repetition rate, as demonstrated in 4D microscopy imaging. FIG. 7A depicts the relation of single electron packets to the effective envelope due to statistics. Each single electron (blue) is a coherent packet consisting of many cycles of the de Broglie wave and has different timing due to the statistics of generation. On average, multiple single electron packets form an effective electron pulse (dotted envelope). It will be appreciated that there is high dispersion for electrons of nonrelativistic energy. The small but unavoidable bandwidth of an attosecond electron pulse causes the pulse to disperse during propagation in free space, even when no space charge forces are present. For example, a 20-attosecond pulse with ΔE/E0≈10−3 would stretch to picoseconds after just a few centimeters of propagation. Embodiments of the present invention provide methods and systems for the suppression of dispersion and the generation of free attosecond electron pulses based on the initial preparation of negatively-chirped electron packets. As described herein, femtosecond electron pulses are generated by photoemission and accelerated to keV energies in a static electric field. Preceding the experimental interaction region, optical fields are used to generate electron packets with a velocity distribution, such that the higher-energy parts are located behind the lower-energy ones. With a proper adjustment of this chirp, the pulse then self-compresses to extremely short durations while propagating towards the point of diffraction. To achieve attosecond pulses, the chirp must be imprinted to the electron pulse on a nanometer length scale. Optical waves provide such fields. However, non-relativistic electrons move significantly slower than the speed of light (e.g. ˜0.3 c for 30 keV). The direct interaction with an optical field will, therefore, cancel out over time and can not be used to accelerate and decelerate electrons for compression. In order to overcome this limitation, we make use of the ponderomotive force, which is proportional to the gradient of the optical intensity to accelerate electrons out of regions with high intensity. By optical wave synthesis, intensity profiles can be made that propagate with less than the speed of light and, therefore, allow for co-propagation with the electrons. FIG. 7B illustrates a schematic of attosecond pulse generation according to an embodiment of the present invention. A synthesized optical field of two counter-propagating waves of different wavelengths results in an effective intensity grating, similar to a standing wave, which moves with a speed slower than the speed of light. Electrons can, therefore, co-propagate with a matched speed and are accelerated or decelerated by the ponderomotive force according to their position within the wave. After the optical fields have faded away, this velocity distribution results in self-compression; the attosecond pulses are formed in free space. Depending on the optical pulse intensity, the electron pulse duration can be made as short as 15 attoseconds, and, in principle, shorter durations are achievable. If the longitudinal spatial width of the initial electron pulse is longer than the wavelength of the intensity grating, multiple attosecond pulses emerge that are located with well-defined spacing at the optical minima. This concept of compression can be rigorously described analytically as a “temporal lens effect.” The temporal version of the Kapitza-Dirac effect has an interesting analogy. Some of our initial work was based on an effective ponderomotive force in a collinear geometry. In order to extend the approach to more complex arrangements, here we generalize the approach and consider the full spatiotemporal (electric and magnetic) fields of two colliding laser waves with an arbitrary angle and polarization. The transversal and longitudinal fields of a Gaussian focus were applied. We simulated electron trajectories by applying the Lorentz force with a fourth-order Runge-Kutta algorithm using steps of 100 attoseconds. Space charge effects were taken into account by calculating the Coulomb interactions between all single electrons for each time step (N-body simulations). FIG. 7B illustrates temporal optical gratings for the generation of free attosecond electron pulses for use in diffraction. (a) A femtosecond electron packet (blue) is made to co-propagate with a moving optical intensity grating (red). (b) The ponderomotive force pushes electron towards the minima and thus creates a temporal lens. (c) The induced electron chirp leads to compression to attosecond duration at later time. (d) The electron pulse duration from 105 trajectories reaches into the domain of few attoseconds. FIG. 7C depicts the compression of single electron packets in the combined field of two counter-propagating laser pulses with durations of 300 fs at wavelengths of 1040 nm and 520 nm. The pulse is shown just before, at, and after the time of best compression; the center along Z is shifted for clarity. The plotted pulse shape is a statistical average over 105 packets of single electrons. The beam diameter of the initial electron packet was 10 μm and the beam diameters of the laser pulses were 60 μm; the resulting compression dynamics is depicted before, just at, and some time after the time of best compression to a duration of 15 attoseconds (see FIG. 7C(b)). These results show that an optical wave with a beam diameter of only several times larger than that of the electron packet is sufficient to result in almost homogeneous compression along the entire electron beam. The characteristic longitudinal spread after the point of best compression, as depicted in FIG. 7C is the result of an “M”-shaped energy spectrum of the electrons after interactions with the sinusoidal intensity grating. Coulomb forces prevent concentration of a large number of electrons in a limited volume, and a compromise between electron flux and laser repetition rate must be found to achieve sufficiently intense diffraction. The laser pulses for compression have energies on the order of 5 μJ and can, therefore, be generated at MHz repetition rates with the resulting flux of 106 electrons/s, which is sufficient for conclusive diffraction. Nevertheless, having more than one electron per attosecond pulse is beneficial for improving the total flux. In order to investigate the influence of space charge on the performance in our attosecond compression scheme, we considered electron packets of increasing electron density and evaluated the resulting pulse durations and effective electron density per attosecond pulse. Two findings are relevant with the results shown in FIG. 8. First, the duration of individual attosecond electron pulses increases relatively insignificantly with the number of electrons contained within. Even for 40 electrons in a single pulse, the duration increases only from 15 to 25 attoseconds (see FIG. 8(a)). The reasons for this are the highly oblate shape of the electron pulses, and the approximate linearity of space charge forces in the longitudinal direction, which are compensated for by somewhat longer interaction in the ponderomotive forces of the optical waves. Secondly, for a train of pulses, there is an effect on synchronization. When the initial femtosecond electron packet covers several optical cycles of the compression wave, a train of attosecond pulses results as shown in FIG. 7B. Perfect synchronization to the optical wave is provided, because all attosecond pulses are located at the same optical phase of the fundamental laser wave. This phase matching relation, which permits attosecond resolution, despite the presence of multiple pulses, is altered under space charge conditions. The attosecond pulses repel each other and a temporal spreading of the comb-like train results. For a train of near 10 attosecond pulses, FIG. 8(b) displays the difference in timing for an adjacent attosecond pulse in relation to the central one, which is always locked to the optical phase because the space charge forces cancel out. The total timing mismatch is the product of the plotted value with the number of attosecond pulses in the entire electron packet (near 10 for this example). In order to keep the total mismatch to the optical wave below 20 attoseconds, 10 electrons per attosecond electron pulse represent an optimum value. The total pulse train then consists of 200 electrons for that group of pulses; of course the total flux of electrons is determined by the repetition rate. Note that mismatch to the compression wave is absent with isolated attosecond electron pulses, which are generated when the initial uncompressed electron packet is shorter than a few femtoseconds, or with optical fields of longer wavelength. Numerous imaging experiments have been successful with single electron packets. In state-of-the-art electron crystallography experiments, typically 500 electrons per pulse were used at a repetition rate of kHz to produce the needed diffraction. This is equivalent to having 5 electrons per attosecond pulse at 100 kHz, which is a convenient repetition rate for optical wave synthesis, and provides enough time for letting the material under investigation to cool back to the initial state. Laser systems with MHz repetition rates will provide even higher fluxes. Applications of attosecond electron pulses for diffraction and microscopy use synchronization of events in the pump-probe arrangement with an accuracy that is equal or better than the individual pulse durations. In contrast to recompression concepts that are based on time-dependent microwave fields, the application of laser waves for attosecond electron pulse generation provides exact temporal synchronization when the pump pulses are derived by phase-locking from the same laser system. Many common optical techniques, such as nonlinear frequency conversion, continuum generation in solids, or high-harmonic generation, all provide a phase lock in the sense that the outcome has the same relative phase and timing in relation to the incoming optical wave for each single pulse of the laser. A second requirement for reaching into the temporal resolution of attoseconds is the realization of spatial delay matching along extended areas of the diffraction. The use of large samples, for example with up to millimeters in size in some electron diffraction experiments, provides enhanced diffraction efficiency and offers the possibility to use electron beams with large diameter, in order to maximize the coherence and flux. In this case, the time resolution is limited by differences in the arrival times of pump and probe pulses at different points within the involved beam diameters (group velocity mismatch). Electron pulses at keV energies travel with significantly less than the speed of light (e.g. vel=0.3 c for 30 keV electrons) and are, therefore, “overtaken” by the laser wave. Embodiments of the present invention provide two arrangements for matching the group velocity of electrons with the phase velocity of optical pulses. Both arrangements are suitable for applications in noncollinear, ultrafast electron microscopy and diffraction. FIG. 9(a) presents a concept for the transmission geometry of diffraction and microscopy in which two angles are introduced, one between the laser beam and the electron beam (β), and another one (α) for the tilt angle of the sample (black) to the phase fronts of the laser wave. Total synchrony is achieved if the relative delay between the optical wave and the attosecond electron pulses is made identical for all points along the entire sample surface. Each small volume of the sample is then subject to an individual pump-probe-type experiment with the same time delay. The above condition is found when we match the coincidence along the entire width of the specimen. The effective surface velocity vsurface of the laser and of the electron pulses must be identical. From FIG. 9A, this requirement is expressed by the following equation: sin ⁡ ( α ) sin ⁡ ( α - β ) = c v el . ( 1 ) It follows that an angle of β=10°, for example, results in an optimum angle for the sample tilt of α=14.8°, which are both easily achievable angles in a real experiment. The effective tilt of the sample with respect to the electron direction is then α−β=4.8°. Naturally, if this value is not coincident with a zone axis direction, a complete rocking curve should be obtained in order to optimize α and β with tilt requirements. Although different portions of the laser wavefront impinge on the surface of the sample at different times, this behavior is matched by the electron pulse, resulting in all portions of the surface of the sample being phase matched. As illustrated in FIG. 9(a), the laser beam, also referred to as a laser wave, is used to activate the sample, for example, to heat the sample, cause motion of the sample, or to effect the chemical bonds present in the sample. The timing of the laser wave and the electron pulses are synchronized using the delay stage discussed in relation to FIG. 1. The train of electron pulses can be generated using the configuration illustrated in FIG. 10(a). Another option for synchronization along extended surfaces is the use of tilted electron pulses, for that the electron density makes an angle with respect to the propagation direction. Tilted optical pulses have been used for reaching femtosecond resolution in reflection geometry, but here tilted electron pulses are introduced for effective spatiotemporal synchronization to the phase velocity of the excitation pulses along the entire sample surface. FIG. 9B depicts the concept. If an angle γ is chosen between the laser (red) and the attosecond electron pulses (blue), the electron pulses need to be tilted likewise. The sample is located parallel to the optical phase fronts and its entire surface is illuminated by the attosecond electron pulse at once and at the same time of incidence relative to the optical pulse wave. Because the incidence is delay-free for all points along the surface, velocity matching is provided for the whole probed area. The generation of tilted attosecond electron pulses is outlined in FIG. 10(a). The introduction of an angle between the intensity grating (red) and the electron beam (blue) leads to formation of electron pulses with a tilt. As described above, a femtosecond electron packet (blue) is first generated by conventional photoelectron generation and accelerated in a static electric field. By intersecting the counter-propagating intensity grating at an angle, tilted electron pulses result with attosecond duration. The ponderomotive force accelerates the electrons towards the planes of destructive interference in the intensity wave and they form attosecond pulses that are compressed along the optical beam axis; but the pulses propagate in the original direction. Only a slight adjustment of the electrons' central energy is required to achieve phase matching to the moving optical grating. Based on this concept, we simulated the tilting effect by using 31-keV electron pulses with an initial duration of ˜15 femtoseconds and a spatial beam diameter of ˜10 μm. FIG. 10(b) illustrates the simulation results for an initial packet of 15-femtosecond duration (left) and an intersection angle of 5°. The tilted attosecond pulses have duration of ˜20 attoseconds when measured perpendicular to the tilt (note the different scale of Z and X). The optical intensity wave is synthesized by two counter-propagating laser pulses of 100-fs duration and wavelengths of 1040 and 520 nm. The angle between the electron beam and the laser wave is 5°. The results of compression are shown in FIG. 10(b): The attosecond electron pulses are formed at the minima of the optical intensity wave and, therefore, are tilted by 5° with respect to the electron propagation direction. For other incidence angles of the laser, the electron pulses are tilted accordingly. Perpendicular to the attosecond pulses, the measured duration is ˜20 attoseconds, given as the full width at half maximum. Based on the methodology for generation and synchronization of attosecond electron pulses described above, the diffraction and manifestation of electron dynamics in the patterns are described. By way of two different examples, embodiments of the present invention are utilized to observe electronic motions in molecules and materials with attosecond electron packets. We consider first the physics of electron scattering and the change in scattering factors which characterize individual atoms and the electron density involved. Diffraction from molecular crystals or other crystalline structures provides two distinct advantages over that obtained for gas phase ensembles. First, the sample density is many orders of magnitudes higher (1021 molecules/cm3 as compared to 1010 to 1016/cm3 in gas jets); diffraction is, therefore, more intense. Second, the crystalline order results in Bragg scatterings and they are concentrated into well-defined “spots” for ordered crystals; the patterns become rods for surfaces and narrow rings for amorphous substances. The diffraction results in intensities which are proportional to the square of the diffraction amplitude. As discussed below, coherence in diffraction is used in observing the changes of interest. The diffraction from molecular crystals, or other crystalline materials of interest, is defined by the summation over the contributions of all scatterers in a unit cell. The intensity I of a Bragg spot with the Miller indices (hkl) is determined by the positions (xyz) of the scatterers j the unit cell: I ⁡ ( hkl ) ∝  ∑ j ⁢ f j ⁢ exp ⁡ [ - 2 ⁢ π ⁢ ⁢ ⅈ ⁡ ( hkl ) · ( xyz ) j ]  2 , ( 2 ) where fj are the atomic scattering factors. Electron diffraction is the result of Coulomb interaction between the incoming electrons and the potential formed by nuclei and electrons. The factors fj account for the effective scattering amplitude of atoms and are derived from quantum calculations that take into account the specific electron density distribution around the nuclei, including core electrons. The scattering we are considering here is the elastic one. In order to estimate the influence of electron dynamics on contributions to time-resolved diffraction patterns, we consider typical densities of electrons in chemical bonds, and the possible change. Static electron density maps show that typical covalent bonds consist of about one electron/Å3 and that this density is delocalized over volumes with diameters in the order of 1 Å. For estimating an effective scattering factor of such electron density, we consider a Gaussian sphere with a diameter of 1 Å, consisting of one electron. The electric potential is derived by Gauss' law and results in a radial dependence that is represented in FIG. 11, dotted line. The total scattering amplitude of free charges diverges at small angles, because of the long-range behavior of the potential. Since in real crystals the potential is localized in unit cells, we use a Gaussian distribution of the same magnitude in order to restrict the range to about ±1.5 Å. For potential of spherical symmetry, an effective scattering factor can be calculated from the radial potential Φ(r) according to f el ⁡ ( s ) = 8 ⁢ π 2 ⁢ m e ⁢ e h 2 ⁢ ∫ 0 ∞ ⁢ r 2 ⁢ Φ ⁡ ( r ) ⁢ sin ⁡ ( 4 ⁢ π ⁢ ⁢ sr ) 4 ⁢ π ⁢ ⁢ sr ⁢ ⅆ r , ( 3 ) where s=sin(υ/2)/λel is the scattering parameter for a diffraction angle υ and λel is the de Broglie wavelength of the incident electrons. The result for our delocalized electron density is shown in FIG. 11(b); for comparison we plot also the tabulated scattering factor of neutral hydrogen. Both have comparable magnitude, which is expected because of their similar sizes. Here, we consider the iodine molecule as a model case and invoke the transition from a bonding to an anti-bonding orbital. The crystal structure of iodine consists of nearly perpendicular iodine pairs with a bond length of ˜2.7 Å. Two electrons contribute to the intramolecular σ bond; the intermolecular bond is weaker. FIG. 12 depicts the system under study and the two cases considered. The effect of antibonding excitation is made by comparing the Bragg intensities for the iodine structure, including the binding electrons, to a hypothetical iodine crystal consisting only of isolated atoms (see FIG. 12(a)). In Table 1, we give the results of the calculations following equation 2 with the values off f tabulated for iodine atoms and from equation (3) for the electronic distribution changes. Despite the large difference in f of the iodine nuclei and the electron (about 50:1), the changes of Bragg spot intensity are significant, being on an order of 10-30%. TABLE 1Effects of Electron Motion on Selected Molecular Bragg SpotsMiller Indices (hkl)(a) ΔITransition(b) ΔIMovement(0.08 Å)100, 010, 001(forbidden)(forbidden)200, 400, 60000002−35%0020 (weak)+100% −17%40000040−18%+13%00400111+15% −2%331−20%+15% In column (a), the mMagnitude of Bragg spot intensity change ΔI of crystalline iodine as a result of bonding to antibonding transition is given. In column (b), the magnitude of Bragg spot intensity change as a result of field interaction with charge density, also in iodine. This large change is for two reasons. First, the bonding electrons are located in-between iodine atoms and contribute, therefore, strongly to the enhancement or suppression of all Bragg spots that project from the inter-atomic distances of the molecular units. Second, the large effect is result of the intrinsic “heterodyne detection” scheme of diffraction; the total intensity of a Bragg spot scales with the square of the coherent sum of individual contributions (see equation (2)). Although the total contribution to the intensity of a Bragg spot from bonding electrons is lower by a factor of several hundreds than the intensity contributions from the iodine atoms, the modulation is on the order of several percents as a result of the coherence of diffraction on a nanometer scale. Symmetry in the crystal is evident in the absence of change in certain Bragg orders. From measurements of the dynamics of multiple spots, it follows that electron density movies could be made. This is best achieved in an electron microscope in diffraction geometry; however conventional diffraction is also suitable to simultaneously monitor many Bragg spots and is advantageous for the study of ordered bulk materials. The example given is not far from an experimental observation made on a metal-to-insulator transition for which a σ-type excitation was induced with a femtosecond pulse. As a second model case we consider the reaction of bonded electron density to external electric fields, such as the ones from laser fields. Depending on the restoring force and the resonance, an electron density will oscillate with the driving field in phase or with a phase delay. This charge oscillation re-radiates and is responsible for the refractive index of a dielectric material. In order to estimate the magnitude of charge displacement, we must take into account the polarizability, α, and the electric field strength, Elaser. In the limit of only one moving charge, the displacement D is approximately given by D ≈ α e ⁢ E laser . The polarizability of molecular iodine along the bond is α≈130 ∈0Å3 (˜70 a.u.) in the static limit and a similar magnitude is expected for the crystal for optical frequencies away from the strong absorption bands; the anisotropy of polarizability indicates the role of the bonding electrons. With femtosecond laser pulses, a field of Elaser=109 V/m is possible for intensities below the damage threshold. With these parameters, one expects a charge displacement of D≈0.08 Å, or about 3% of the bond length. FIG. 12(b) is a schematic for the change in charge distribution by an electric field. We assume an active role of only the bonded electrons, and take the polarization of the laser field to be along the b axis of solid iodine. This axis is chosen because it has the least symmetry; a is perpendicular to the bonds. Table 1 gives the intensity changes of selected Bragg spots; the change is in the range of ±20% for some of the indices. The total energy delivered to the molecular system by the laser field is only on the order of 0.01 eV. Nevertheless the changes of charge displacements on sub-angstrom scales are evident. This marks a central advantage of electron diffraction over spectroscopic approaches, which require large energy changes in order to have projections on dynamics. In contrast, diffraction allows for the direct visualization of a variety of ultrafast electron dynamics with combined spatial and temporal resolutions, and independent of the resolution of internal energy levels. The “temporal lens” concept can be used for the focus and magnification of ultrashort electron packets in the time domain. The temporal lenses are created by appropriately synthesizing optical pulses that interact with electrons through the ponderomotive force. With such an arrangement, a temporal lens equation with a form identical to that of conventional light optics is derived. The analog of ray diagrams, but for electrons, are constructed to help the visualization of the process of compressing electron packets. It is shown that such temporal lenses not only compensate for electron pulse broadening due to velocity dispersion but also allow compression of the packets to durations much shorter than their initial widths. With these capabilities ultrafast electron diffraction and microscopy can be extended to new domains, but, as importantly, electron pulses are delivered directly on the target specimen. With electrons, progress has recently been made in imaging structural dynamics with ultrashort time resolution in both microscopy and diffraction. Earlier, nuclear motions in chemical reactions were shown to be resolvable on the femtosecond (fs) time scale using pulses of laser light, and the recent achievement of attosecond (as) light pulses has opened up this temporal regime for possible mapping of electron dynamics. Electron pulses of femtosecond and attosecond duration, if achievable, are powerful tools in imaging. The “electron recombination” techniques used to generate such attosecond electron pulses require the probing electron to be created from the parent ions (to date no attosecond electron pulses have been delivered on an arbitrary target) and for general applications it is essential that the electron pulse be delivered directly to the specimen. In ultrafast electron microscopy (UEM), the electron packet duration is determined by the initiating laser pulse, the dispersion of the electron packet due to an initial energy spread and electron-electron interactions. Since packets with a single electron can be used to image, and the initiating laser pulse can in principle be made very short (sub-10 fs), the limiting factor for the electron pulse duration is the initial energy spread. In photoelectron sources this spread is primarily due to the excess energy above the work function of the cathode, and is inherent to both traditional photocathode sources and optically-induced field emission sources. Energy-time uncertainty will also cause a measurable broadening of the electron energy spread, when the initiating laser pulse is decreased below ˜10 fs. For ultrafast imaging techniques to be advanced into the attosecond temporal regime, methods for dispersion compensation and new techniques to further compress electron pulses to the attosecond regime need to be developed. As described herein techniques for compressing free electron packets, from durations of hundreds of femtoseconds to tens of attoseconds, using spatially-dependent ponderomotive potentials are provided by embodiments of the present invention. Thus, a train of attosecond pulses can be created and used in ultrafast electron imaging. Because they are generated independent of the target they can be delivered to a specimen for studies of transient structures and electronic excitations on the attosecond time scale. The deflection of electrons (as in the Kapitza-Dirac effect) by the ponderomotive potential of intense lasers and the diffraction of electrons in standing waves of laser light have been observed, and so is the possibility (described through computer modeling) of spatial/temporal focusing with combined time-dependent electric and static magnetic fields. The “temporal lens” description analytically expresses how ponderomotive compression can be used to both compensate for the dispersion and magnify, in this case compress, the temporal duration of electron packets. We obtain simple lens equations which have analogies in optics and the results of “electron ray optics” of temporal lenses allows for analytical expressions and for the design of different schemes using geometrical optics. Here, we consider two types of temporal lenses, thin and thick. For the realization of the temporal thin lens, a laser beam with a Laguerre-Gaussian transverse mode, radial index ρ=0 and azimuthal index l=0 (or, in common nomenclature, a “donut” mode, is utilized. In the center of the donut mode, electrons will experience a spatially-varying ponderomotive potential (intensity) that is approximately parabolic. This potential corresponds to a linear spatial force which, for chirped electron pulses, can lead to compression from hundreds of fs to sub-10 fs. The second type, that of a thick lens, is based on the use of two counter-propagating laser beams in order to produce a spatially-dependent standing wave that co-propagates with the electrons. A train of ponderomotive potential wells are produced at the nodes of the standing wave, leading to compression but now with much “tighter focus” (thick lens). Because the electron co-propagates with the laser fields, velocity is matched. Analytical expressions are derived showing that this lens has the potential to reach foci with attosecond duration. Finally, we discuss methods for creating tunable standing waves for attosecond pulse compression, and techniques for measuring the temporal durations of the compressed pulses. Space-charge dispersed packets of electrons that have a linear spatial velocity chirp may also be compressed with the temporal lenses described here. All electron sources, both cw and pulsed, have an initial energy spread. For pulsed electron sources this is particularly relevant as electron packets created in a short time disperse as they propagate. The initial energy spread leads to an initial spread in velocities. These different velocities cause the initial packet to spread temporally, with the faster electrons traveling a further distance and the slower electrons traveling a shorter distance in a given amount of time. The dispersion leads to a correlation between position (along the propagation direction) and electron velocity as described in relation to FIG. 14. The linear spatial velocity “chirp” can be corrected for with a spatially-dependent linear impulsive force (or a parabolic potential). Thus, if a pulsed, spatially-dependent parabolic potential can be made to coincide appropriately with the dispersed electron packet, the slow trailing electrons can be sped up and the faster leading electrons can be slowed down. The trailing electrons, now traveling faster, can catch the leading electrons and the electron pulse will thus be compressed. FIG. 13 illustrates dispersion of an ultrashort electron packet. At t=to the packet is created from a photocathode and travels with a velocity v0. As it propagates along the x-axis it disperses, with the faster electrons traveling further, and the slower ones trailing for a given propagation time t. At t=0 a parabolic potential is pulsed on, giving an impulsive “kick” to the dispersed electron packet. After the potential is turned off, t>τ, the trailing electrons now have a greater velocity than the leading electrons. After a propagation time t=ti, the pulse is fully compressed. Consider a packet of electrons, propagating at a speed v0 along the x-axis, with a spread in positions of Δxo=v0Δto, at time t=to. At t=0, a potential of the form U(x)=½Kx2 interacts with the electron packet for a duration τ in the lab frame. The waist, or spatial extent of the potential (temporal lens) is chosen to be w, while the duration τ is chosen such that it is short compared to w/v0. When this condition is met the impulse approximation holds, and the change in velocity is Δv=−τ/m(dU(x)/dx)=−τKx/m, for \|x\|<w, where m is the electron mass. After the potential is turned off, t>τ, the electrons will pass through the same position, xf−x=(v0+Δv)tf, at the focal time tf=−x/Δv=m/(Kτ). To include an initial velocity spread around v0 (due to an initial ΔE), consider electrons that all emanate from a source located at a fixed position on the x-axis. An electron traveling exactly at v0 will take a time t0 to reach the center of the potential well at x=0. Electrons leaving the source with other velocities v0+vk will reach a location x=vkto at t=0. The image is formed at a location where electrons traveling with a velocity v0 and a velocity v0+vk intersect, this is, when v0ti=x+(v0+Δv+vk)ti. The image time ti is then ti=−x/(Δv+vk). FIG. 14 illustrates ray diagrams for spatial and temporal lenses. The top figure in FIG. 14 depicts three primary rays for an optical thin spatial lens. The object is located at yo, and the spatial lens has a focal length, f. A real image of the object is created at the image plane, position yi. The bottom figure in FIG. 14 is a ray diagram for a temporal thin lens. The diagram is drawn in a frame moving with the average speed v0 of the electron packet. The slopes of the different rays in the temporal diagram correspond to different initial velocities that are present in the electron packet. As shown in the diagram, a temporal image of the original electron packet is created at the image time ti. The initial packet (object) is created at a time to with Δto=Δxo/v0, where the spatial extend of the pulse is directly related to the temporal duration of the object. The lens is pulsed on at t=0 and the temporal focal length of the lens is tf. The lens represents the ponderomotive potential and in this case is on for the very short time τ. For the object time, to=x/vk, image time ti=−x/(Δv+vk) and the focal time tf=−x/Δv, the temporal lens equation holds, 1 t o + 1 t i ⁢ = 1 t f ⁢ . ( 4 ) Ray tracing for optical lenses is often used to visualize how different ray paths form an image, and is also useful for visualizing how temporal lenses work as shown in FIG. 14. As derived in later sections, the magnification M is defined as the ratio of the electron pulse duration (Δti) at the image position to the electron pulse duration (Δto), and is directly proportional to the ratio of the object and image times (−ti/to) and distances (−xi/xo). In polar coordinates, a Laguerre-Gaussian (LG01) mode has a transverse intensity profile given by, I(r,φ)=I0exp(1)2r2exp(−2(r/w)2)/w2 where w is the waist of the focus and I0 the maximum intensity. This “donut” mode has an intensity maximum located at r=√{square root over (2)} w/2 with a value of I0=2EP(√{square root over (1n 2/π3)}/(w2τ) where EP is the energy of the laser pulse and τ is the full-width-at-half-maximum of the pulse duration, assuming a Gaussian temporal profile given by exp(−4 ln 2(t/τ)2). The ponderomotive energy UP(x) is proportional to intensity, U P ⁡ ( x ) = 1 2 [ ⅇ 2 ⁢ λ 2 ⁢ exp ⁡ ( 1 ) ⁢ I 0 2 ⁢ π 2 ⁢ m ⁢ ⁢ ɛ 0 ⁢ c 3 ⁢ w ⁢ 2 ⁢ ln ⁢ ⁢ 2 π ] ⁢ x 2 ≡ 1 2 ⁢ Kx 2 , ( 5 ) where m is the electron mass, e is the electron charge and λ the central wavelength of the laser radiation and replacing r with x. Near the center of the donut mode focus (or x<<w) the intensity distribution is approximately parabolic, and hence the ponderomotive energy near the donut center is also parabolic. In analogy with a mechanical harmonic oscillator, the quantity in the square brackets of equation (5) can be referred to as the stiffness K; it has units of J/m2=N/m, and at 800 nm has the numerical value of, K≈3.1×10−36EP/(w4τ). For this parabolic approximation to be applicable, the spatial extent of the dispersed electron pulse, at t=0, Δx(0)=v0Δto+Δvoto must be much smaller than the laser waist, where the object velocity spread is Δvo=ΔE/√{square root over (2mE)}. The effect of this parabolic potential on an ensemble of electrons emitted from a source will now be analyzed. The velocity distribution of the ensemble is centered around v0, with an emission time distribution centered on −to, where all electrons are emitted from the same location xo=−v0to. Assuming a single donut-shaped laser pulse is applied at t=0, and centered at x=0, the electron ensemble is then influenced by the potential U(x)=½Kx2. The kth electron in the ensemble has an initial velocity v0+vk and emission time −to+tk. Using a Galilean transformation to a frame moving with velocity v0, the propagation coordinate x (lab frame) is replaced with the moving frame coordinate {tilde over (x)}=x−v0t. At t=0 the potential exists for the ultrashort laser pulse duration τ, giving the electron an impulse (or “kick”) dependent on its instantaneous position in the parabolic potential. In both frames, the position of the electron at t=0 is xk(0)={tilde over (x)}k(0)≡−v0tk+vkto−vktk, where xk(t) and {tilde over (x)}k (t) are in the lab and moving frames, respectively. Using the impulse approximation the electron trajectory immediately after the potential is turned off becomes,{tilde over (x)}k(t)=vkt+{tilde over (x)}k(0)(1−t/tf), (6)where tf=m/(Kτ) is the focal time. The electron trajectories, before and after t=0, can be plotted in both frames to give the equivalent of a ray diagram as illustrated in FIG. 15. Electrons emitted at the same time, i.e. tk=0, but with different velocities, will meet at the image position, {tilde over (x)}k=0 in the moving frame at the image time ti. The image time is found by setting {tilde over (x)}k(ti)=0, from equation (6), with tk=0, {tilde over (x)}k(ti)=vkti+vkto(1−ti/tf)=0 which is equivalent to the lens equation, equation (4): to−1+ti−1=tf−1. An expression for the magnification can be obtained when electrons that are emitted at different times tk and different velocities vk are considered. If the magnification is defined as M=−ti/to then the temporal duration at the image time becomes,Δti=MΔto, (7)where Δto and Δti are the duration of the electron packet at the object and image time, respectively. Durations achievable with a thin temporal lens follow from equation (7). An experimentally realistic temporal lens would use a 50 fs, 800 nm laser pulse with 350 μJ energy, focused to a waist of w=25 μm. These values result in a stiffness of K=5.5×10−8 N/m and a focal time of tf=0.3 ns; tf=m/(Kτ). If the lens is applied 10 cm from the source, electrons emitted at v0=c/10 (3 keV) would have an object time of to=xo/v0=0.1/(c/10)=3.0 ns. Using the temporal lens equation, equation (4), ti is obtained to be 0.33 ns. Hence, a magnification of M=−ti/to=0.1. Consequently, a thin temporal lens can compress an electron packet with an initial temporal duration of Δto≈100 fs, after it has dispersed, to an image duration of Δti≈10 fs. While the example presented here is for 3 keV electrons, the thin lens approximation holds for higher energy electrons as long as τ is chosen to be short compared to w/v0. Experimentally, the thin temporal lens can be utilized in ultrafast diffraction experiments which operate at kHz repetition rates with lasers that typically possess power that exceeds the value needed for the ponderomotive compression. Referring to FIG. 15, thin lens temporal ray diagrams for the lab and co-propagating frames are illustrated. The upper left panel is a ray diagram drawn in the lab frame showing how different initial velocities can be imaged to a single position/time. The gray lines are rays representing electrons with different velocities. The lower left panel is a ray diagram drawn in a frame moving with the average velocity v0 of the electron packet. The rays represent velocities of v0/67, v0/100 and 0. In the co-propagating frame, the relationship between Δto and Δti can be visualized as Δti=−Δtoti/to. One major difference between the lab frame and the moving frame is that in the latter the position of the object and image are moving. The lines representing the object and the image positions are drawn with slopes of −v0. The upper right panel depicts the experimental geometry for the implementation of a thin temporal lens. Note that the laser pulse and electron packet propagate perpendicular to each other, and that the interception point between the electrons and photons is at x=0 and t=0. The lower right panel shows how the parabolic (idealized) potential compares to the experimentally realizable donut potential. The colored dots indicate the position of electrons following the rays indicated in the left bottom diagram. Above, it was analytically shown that free electron packets can be compressed from hundreds to tens of femtoseconds using a temporal thin lens, which would correspond to a magnification of ˜0.1. Co-propagating standing wave can be created by using two different optical frequencies, constructed by having a higher frequency (ω1) optical pulse traveling in the same direction as the electron packet and a lower frequency (ω2) traveling in the opposite direction. When the optical frequencies ω1, ω2, and the electron velocity v0 are chosen according to v0=c(ω1−ω2)/(ω1+w2), a standing wave is produced in the rest frame of the electron as illustrated in FIG. 16. If the electron has a velocity v=c/3, and ω1=2ω2 then the co-propagating standing wave has a ponderomotive potential of the form, U P ⁡ ( x ) = 1 2 ⁢ ( ⅇ 2 ⁢ λ ~ 2 ⁢ E 0 2 8 ⁢ π 2 ⁢ m ⁢ ⁢ c 2 ) ⁢ cos 2 ( k ~ ⁢ x ) , ( 8 ) where E0 is the peak electric field, {tilde over (λ)} the Doppler shifted wavelength. The envelopes of the laser pulses are ignored in this derivation, but they can be engineered so that the standing wave contrast is optimized. The standing waves can be provided outside the microscope housing or inside the microscope housing. The presence of the standing wave copropagating with the electron pulse or packet inside the microscope housing can produce a series of attosecond electron pulses as illustrated in FIG. 7B and FIG. 16. Depending on the geometry with which the laser beams interact, the standing wave and the electron pulse can overlap adjacent to the sample, providing attosecond electron pulse generation at distances close to the sample. The attosecond electron pulses can be single electron pulses. To find an analytic solution in the thick lens geometry, each individual potential well in the standing wave is approximated by a parabolic potential that matches the curvature of the sinusoidal potential, UP(x)=½[e2E02/(2mc2]x2≡½Kx2. Using the exact solution to the harmonic oscillator the focal time is,tf=cot(ωPτ)/ωP+τ, (9)where ωp=√{square root over (Km)} and τ is the duration that the lens is on. For τ→0, tf→m/(K τ), which is identical to the thin lens definition. The image time, ti, has a form,ti=(1/ωP2+totf−tfτ+τ2)/(to−tf+τ), (10)and after the two assumptions, τ→0 and to>>1/(tfωP2) becomes equivalent to equation (4), the lens equation: to−1+ti−1=tf−1. The standard deviation of the compressed electron pulse at arbitrary time ta is, Δ ⁢ ⁢ t a = t f 2 ( λ ~ 2 + 4 ⁢ t a 2 ⁢ Δ ⁢ ⁢ v o 2 ) + t a 2 ⁢ λ ~ 2 - 2 ⁢ t f ⁢ t a ⁢ λ ~ 2 48 ⁢ t f 2 ⁢ v 0 2 , ( 11 ) which is valid for an individual well. The time when the minimum pulse duration occurs is ta=tf{tilde over (λ)}2/({tilde over (λ)}2+4tf2Δvo2)≈tf and for experimentally realistic parameters is equal to tf. This implies that the thick lens does not image the initial temporal pulse; it temporally focuses the electrons that enter each individual well. Since there is no image in the thick lens regime, the minimum temporal duration is not determined by the magnification M as in the thin lens section, but is a given by, Δ ⁢ ⁢ t f = t f 2 ⁢ λ ~ 2 ⁢ Δ ⁢ ⁢ v o 2 12 ⁢ v 0 2 ( λ ~ 2 + 4 ⁢ t f 2 ⁢ Δ ⁢ ⁢ v o 2 ) ≃ t f ⁢ Δ ⁢ ⁢ v o v 0 ⁢ 2 ⁢ 3 . ( 12 ) It should be noted that neither the temporal focal length nor the temporal duration are directly dependent on the Doppler shifted wavelength {tilde over (λ)}, as long as the condition to<v0Δto/Δvo is met. An example illustrates what temporal foci are obtainable. A source emits electrons with an energy distribution of 1 eV and a temporal distribution of 100 fs. Electrons traveling at v0=c/3 and having an energy E=31 keV gives a velocity distribution of Δvo=1670 m/s. If the distance between the source and the temporal lens is 10 cm, to=1.0 ns is less than v0Δto/Δvo≈6.0 ns, satisfying the condition to<v0Δto/Δvo and equation (12) is then valid. If the two colors used for the laser beams are 520 nm and 1040 nm, the Doppler-shifted wavelength is {tilde over (λ)}=740 nm. For a laser intensity of 3×1012 Wcm−2 (available with repetition rates up to megahertz), the oscillation frequency in the potential well is ωp≈2×1012 rad/s, which gives a focal time of tf≈1 ps. With these parameters, equation (12) gives a temporal duration at the focus of Δtf≈5 as. To support this ˜5 as electron pulse, time-energy uncertainty demands an energy spread of ˜50 eV. The ponderomotive compression imparts an energy spread to the electron pulse which can be estimated from ΔE˜mv0{tilde over (λ)}(2tf), giving ˜50 eV similar to the uncertainty limit. This ΔE is very small relative to the accelerating voltage in microscopy (200 keV) and only contributes to a decrease of the temporal coherence. In optical spectroscopy such pulses can still be used as attosecond probes despite the relatively large ΔE when the chirp is well characterized. Combining the anharmonicity broadening of 15 as, we conclude that ultimately temporal pulse durations in the attosecond regime can be reached. In the temporal thick lens case, the use of ω and 2ω to create a co-propagating standing wave requires v0=c/3. However, the velocity of the electrons, v0, can be tuned by changing the angle of the two laser pulses. A co-propagating standing wave can still be obtained by forcing the Doppler-shifted frequencies of both tilted laser pulses to be equal. A laser pulse that propagates at an angle θ with the respect to the electron propagation direction has a Doppler-shifted frequency {tilde over (ω)}=γω(1±(v/c)cos θ), where ω is the angular frequency in the lab frame, {right arrow over (v)}=v{circumflex over (x)} is the electron velocity, and γ=1/√{square root over (1−v2/c2)}. When the two laser pulses are directed as shown in FIG. 16, a co-propagating standing wave occurs for an electron with a velocity v0=c(k1−k2)/(k1 cos θ1+k2 cos θ2), where the laser pulse travelling with the electron packet has a wave vector of magnitude k1 and makes an angle of θ1 with the electron propagation axis; the second laser pulse traveling against has a wave vector magnitude of k2 and angle θ2, in the lab frame. An electron moving at v0 will see a standing wave with an angular frequency, ω ~ = 2 ⁢ ( cos ⁢ ⁢ θ 1 + cos ⁢ ⁢ θ 2 ) 2 ⁢ cos ⁢ ⁢ θ 1 + cos ⁢ ⁢ θ 2 ⁢ γ ⁢ ⁢ ω ⁡ ( 1 - β ) , ( 13 ) where 2k=k1=2k2 for experimental convenience, ω=kc, and the wavelength is {tilde over (λ)}=2πc/{tilde over (ω)}=2π/{tilde over (k)}. The standing wave created with arbitrary angles θ1 and θ2 will be tilted with respect to the electron propagation direction, which will temporally smear the electron pulse. This tilting of the standing wave can be corrected for by constraining the angles θ1 and θ2 to be: θ2=arcsin(2 sin θ1). For θ1=150(forcing θ2≈310), electrons with velocity v0=0.36c (E≈33 keV) see a standing wave. A 1 eV electron energy distribution at the source gives a velocity distribution of Δv0≈1630 m/s, at 33 keV. Using the same laser intensity as in the thick lens case, and the new v0 and Δvo, the condition to<v0Δto/Δvo is still satisfied, allowing equation (13) to be used, resulting in a duration at the focus of Δtf≈4.6 as. Using the tunable thick lens makes the experimental realization more practical, allowing for easy optical access and electron energy tuning, while at the same time keeping Δtf approximately the same. For additional tunability, an optical parametric amplifier can be used so that the laser pulse frequencies are not restricted to ω and 2ω. The ability to create electron pulses with duration from ˜10 fs to ˜10 as raises a challenge regarding the measuring of their duration and shape. Two different schemes are presented here for measuring pulses compressed by thick and thin temporal lenses. For measuring the thin lens compressed electron packet, the focused packet could be intersected by a laser pulse with a Gaussian spatial focus as illustrated in FIG. 17. An optical delay line would control the time delay between the measuring laser pulse and the compressed electron packet. As the time delay, Δt, is varied, so is the average energy of the electrons, as shown in FIG. 17. If the delay time is zero, then the average electron energy will be unaffected, as there is no force. If the delay line is changed so that the Gaussian pulse arrives early (late), then the average energy will decrease (increase). The change in the average energy is dependent on the duration of the electron pulse, and the intensity of the probing laser pulse. If the electron pulse is longer than the duration of the measuring laser pulse, then the change in the average energy will be reduced. The steepness of the average energy as a function of delay time, Ē(Δt), is a direct measure of the electron pulse duration, and using fs-pulsed electron energy loss spectra this scheme can be realized. For the thick lens a similar method is described here. At the focal position and time of the compressed temporal electron packet, a second co-propagating potential is introduced. The positions of the individual wells in the second co-propagating standing wave can be moved by phase shifting one of the two laser beams that create the probing potential (FIG. 17). By varying the phase shift, the potential slope (and hence the force) that the electrons encounter at the focus is changed. If no phase shift is given to the probing standing wave, no average energy shift results. When a phase shift is introduced, the electrons will be accelerated (or decelerated) by the slope of an individual well in the standing wave, and as long as the phase stability between the electrons and the probing standing wave is appropriate, attosecond resolution can be achieved. As the electron pulse duration becomes less than the period of the standing wave, the average electron energy change increases. The electron temporal duration of the compressed electron packet can be determined directly by the steepness of the Ē(φ) curve. Diffraction with focused electron probes is among the most powerful tools for the study of time-averaged nanoscale structures in condensed matter. Embodiments of the present invention provide methods and systems for four-dimensional (4D) nanoscale diffraction, probing specific-site dynamics with ten orders of magnitude improvement in time resolution, in convergent-beam ultrafast electron microscopy (CB-UEM). For applications, we measured the change of diffraction intensities in laser-heated crystalline silicon as a function of time and fluence. The structural dynamics (change in 7.3±3.5 ps), the temperatures (up to 366 K), and the amplitudes of atomic vibrations (up to 0.084 angstroms) are determined for atoms strictly localized within the confined probe area of 50-300 nm; the thickness was varied from 2 to 100 nm. A broad range of applications for CB-UEM and its variants are possible, especially in the studies of single-particles and heterogeneous structures. In fields ranging from cell biology to materials science, structures can be imaged in real-space using electron microscopy. Atomic-scale resolution of structures is usually available from Fourier-space diffraction data, but this approach suffers from the averaging over the selected specimen area which is typically on the micrometer scale. Significant progress in techniques has enabled localization of diffraction to nanometer and even angstrom-sized areas by focusing a condensed electron beam onto the specimen. Parallel illumination with a single electron wavevector is reshaped to a convergent beam with a span of incident wavevectors. T his method of convergent beam electron diffraction (CBED), or electron microdiffraction, and with energy filtering, has made possible determination of structures in 3 dimensions with highly precise localization to areas reaching below one unit cell. The applications have been wide-ranging, from revealing bonding charge distribution and local defects and strains in solids to detecting local atomic vibrations and correlations. Today, aberration-corrected, atomic-sized convergent electron beams enable analytical probing using electron-energy-loss spectroscopy (EELS) and scanning transmission electron microscopy (STEM). In order to resolve structural dynamics with appropriate spatiotemporal resolution, femtosecond (fs) and picosecond (ps) electron pulses are ideal probes because of their picometer wavelength and their large cross section, resulting from the effective Coulomb interaction with atomic nuclei and core/valence electrons of matter. Typically, ultrafast electron diffraction is achieved by initiating the physical or chemical change with a pulse of photons (pump) and observing the ensuing dynamics with electron pulses (probe) at later times. By recording sequentially delayed diffraction frames a “movie” can be produced to reveal the temporal evolution of the transient structures involved in the processes under study. FIG. 18 is a simplified schematic diagram of a CB-UEM set-up (top), and observed low-angle diffraction discs according to an embodiment of the present invention. Femtosecond electron pulses are focused on the specimen to form a nanometer-sized electron beam. Structural dynamics are determined by initiating a change with a laser pulse and then observing the consequences using electron packets delayed in time. Insets (right) show the CB-UEM patterns taken along the Si [011] zone axis at different magnifications. At the high camera length used, only the ZOLZ discs indexed in the figure are visible; the kinematically-forbidden 200 disc appears as a result of dynamic scattering. In the reciprocal space representation of the diffraction process (bottom) the Ewald sphere has an effective thickness of 2α, the convergence angle of the electron beam. The diamond structure of Si forbids any reflections from odd numbered Laue planes when the zone axis is [011]. Embodiments of the present invention provide CB-UEM methods and systems with applications in the study of nanoscale, site-selected structural dynamics initiated by ultrafast laser heating (1014 K/s). Because of the femtosecond pulsed-electron capability, the time resolution is ten orders of magnitude improved from that of conventional TEM, which is milliseconds; and because of beam convergence, high-angle Bragg scatterings are visible with their intensities being very sensitive to both the 3D structural changes and amplitudes of atomic vibrations. The CB-UEM configuration is shown in FIG. 18; our chosen specimen is a crystalline silicon slab, a prototype material for such investigations. From these experiments, it is found that the structural change within the locally probed site occurs with a time constant of 7.3±3.5 ps, which is on the time scale of the rise of lattice temperature known for bulk silicon. For these local sites, the temperatures measured at different laser fluences range from 299° K to 366° K, corresponding to vibrational amplitude changes from 0.077 Å to 0.084 Å, respectively. The reported results would be impossible to obtain with conventional, parallel beam diffraction. The electron microscope is integrated with a fs oscillator/amplifier laser system. The fundamental mode of the laser at 1036 nm was split into two beams: the first was frequency doubled to 518 nm and used to initiate the heating of the specimen, whereas the second, which was frequency tripled, was directed to the microscope for extracting electrons from the cathode. The time delay between pump and probe was adjusted by changing the relative optical path lengths of these two pulses. The pulses were sufficiently separated in time (5 μs) to allow for cooling of the specimen. The electron packets were accelerated to 200 keV (corresponding to a de Broglie wavevector of 39.9 Å−1), de-magnified, and finally focused (with a 6 mrad convergence angle) to an area of 50-300 nm diameter on the wedge-shaped specimen, as shown in FIG. 18. A wide range of thicknesses, starting from ˜2 nm was accessible simply by moving the electron beam laterally. The silicon specimen was prepared by mechanical polishing of a wafer along the (011) planes, followed by Ar ion-milling for final thinning/smoothing; the wedge angle was 2°. In the microscope, Kikuchi lines were observed and used as a guide to orient the specimen with the [011] zone axis either parallel or tilted relative to the incident electron beam direction. FIG. 18 display the typical high-magnification (high-value camera length) CB-UEM patterns of Si obtained when the specimen is unexcited and the zone axis is very close to [011]; the magnification (>10×) cab be seen by comparing the disc length scale in FIG. 18 and ring radius in FIG. 19. Unlike parallel-beam diffraction which yields spots, convergent-beam diffraction produces discs in reciprocal space (back focal plane of the objective lens) with their diameter given by the convergence angle (2α) of the electron pulses. These discs form the Zero Order Laue Zone (ZOLZ) of the pattern; they show white contrast with thin specimens and exhibit the interference patterns displayed in FIG. 18 when the thickness is increased. In the reciprocal space, the effective thickness of the Ewald sphere is 2α (bottom panel of FIG. 18), giving rise to multiple spheres that can intersect with Higher Order Laue Zones (HOLZ) reflections, the focus of this study (see FIG. 19) and the key to 3D structural information; the first and second zones, FOLZ and SOLZ, are examples of such zones or rings. The interference patterns in the disks are the result of dynamical scattering in silicon and are reproduced in our CB-UEM patterns (FIG. 18). The scattering vectors of HOLZ rings (R) are related to the inter-zone spacing in the reciprocal space (hz in Å−1) by the tilt angle from the zone axis (η) and by the magnitude of the incident electron's wavevector (k0). In the plane of the detector and for our tilt geometry, the HOLZ ring scattering vector is given by (equation (14)):R≅(k02 sin2(η)+2k0hz)1/2−k0 sin(η), (14)where, for our case of the [011] zone axis, hz=n/(a√{square root over (2)}) with n=1,2,3 . . . for the different Laue zones. Additionally, for this zone axis, k+l=n, where (hkl) are the Miller indices of the reciprocal space. When k+l=1, for FOLZ, k and l must have different parity, which is forbidden by the symmetry of the diamond Si structure. Therefore, the FOLZ along the [011] zone axis should be absent and the first visible ring should belong to SOLZ; in general, all odd numbered zones will be forbidden. Here, HOLZ indexing is defined according to the fcc unit cell and not to the primitive one [1]. FIG. 19 illustrates temporal frames obtained using CBUED. In FIG. 19(a) high angle SOLZ ring obtained for a tilt angle of 5.15° from the [011] zone axis are shown. Besides SOLZ, Kikuchi lines and periodic bands (due to atomic correlations) are visible. The ZOLZ discs are blocked (top left) to enhance the dynamic range in the area of interest; the disc of the direct beam (the center one in FIG. 18 discs) is indicated by a circle. The intensity scale is logarithmic. In FIG. 19(b,c,d) time frames of the SOLZ ring are shown by color mapping for visualization of dynamics. The intensity of the ring changes within picoseconds, but the surrounding background remains at the same level. FIG. 19(a) presents the HOLZ ring taken with the CB-UEM. In order to reduce the strong on-zone-axis dynamic scattering (and to bring the high scattering angles into the range of the recording camera), the slab was tilted 5.15° away from the [011] zone axis, along the [02 2] direction. The scattering vector of the Bragg points of the ring, from the direct beam position, was measured to be 2.2 Å−1, close to the value of 2.22 Å−1 obtained by using equation (14) for n=2, which identifies the spots shown as part of the SOLZ. From this value, the know lattice separation of 5.4 Å was obtained for silicon. In addition to the SOLZ ring, Kikuchi lines and some oscillatory bands are also visible in the CB-UEM, as seen in FIG. 19(a). Kikuchi lines arise from elastic scatterings of the inelastically scattered electrons, whereas the oscillatory bands in the thermal diffuse scattering (TDS) background result from correlations between the atoms. We also observed deficit HOLZ lines and interference fringes in ZOLZ discs for a two-beam condition. The temporal behavior is displayed in FIG. 19, with three CB-UEM frames taken at time delays of t=−14.8 ps, +5.2 ps, and +38.2 ps, together with a static image; the zero of time is defined by the coincidence of the pump and probe pulses in space and time. The frame at negative time has higher ring intensity than that observed at +38.2 ps, whereas the +5.2 ps frame shows an intermediate intensity value. It is clear from the results that the intensity change is visible within the first 5 ps of the structural dynamics. For quantification, the intensities in each frame were normalized to the area of azimuthally integrated background. The normalization of the HOLZ ring intensities to the TDS background makes the atomic vibration estimations insensitive to the thickness changes of the probed area, which may result from slight beam jittering. FIG. 20 illustrates diffraction intensities at different times and fluences. Normalized, azimuthally-integrated intensity changes of the SOLZ ring are shown with time ranging from −20 ps to +100 ps, for two different laser powers. Whereas the 10 mW response does not show noticeable dynamics, the 107 mW transient has a clear intensity change with a characteristic time of 7.3±3.5 ps. The range of fluences studied was 1.7 to 21 mJ/cm2 (see FIG. 21). The red curve is a mono-exponential fit based on the Debye-Waller effect. The red dashed line through the 10 mW data is an average of the points after +20 ps. The dependence on fluence is given in FIG. 21. FIG. 20 depicts the transient behavior of the SOLZ ring intensity for two different laser power, 10 mW and 107 mW, corresponding to pulse fluence of 1.7 and 19 mJ/cm2, respectively; the heating laser beam diameter on the specimen is 60 μm. The intensities were normalized to the average value obtained at negative times. Whereas the intensity change is essentially absent in the 10 mW data, the results for the 107 mW set shows a transient behavior with a characteristic time of 7.3 ±3.5 ps, obtained from the mono-exponential fit shown in red in the figure. The temporal response of UEM-2 is on the fs time scale, as obtained by EELS, and it is much shorter than the 7 ps illustrated here. The local heating of the lattice is responsible for the SOLZ intensity change with time. A pump laser, in our case at 518 nm (2.4 eV), excites the valance electrons of Si to the conduction band; one-photon absorption occurs through the indirect bandgap at 1.1 eV, and multi-photon absorption excites electron-hole pairs through the direct gap. The excited carriers thermalize within 100 fs, via carrier-carrier scatterings, and then electron cooling takes place in ˜1 ps, by electron-phonon coupling. During this time lattice heating occurs through increased atomic vibration, reducing SOLZ intensity. The effective lattice temperature is ultimately established with a time constant of a few picoseconds depending on density of carriers or fluence. However, in CB-UEM measurements the lattice-temperature rise could be slower than in bulk depending on the dimension of the specimen relative to the mean free path of electrons in the solid. The dynamical change can be quantified by considering a time-dependent Debye-Waller factor with an effective temperature describing the decrease in the Bragg spot intensity with time. If the root-mean-square (rms) displacement of the atoms, 1/2, along one of the three principle axes is denoted by ux for simplicity, and the scattering vector by s, then the HOLZ ring intensity can be expressed as (equation (15)):IRingF(t)=I0(t−)exp[−4π2s2ux2(t)], (15)where IRingF(t) is the measured intensity for a given fluence, F, and the vibrational amplitude is now time dependent. Note that ux is ⅓ of the total, utotal. In the Einstein model of atomic vibrations, which has been used successfully for silicon, the atoms are treated as independent harmonic oscillators, with the three orthogonal components of the vibrations decoupled. As a result, a single frequency (ω) is sufficient to specify the energy eigenstates of the oscillators. The relationship of the vibrational amplitude to temperature can be established by simply considering the Boltzmann average over the populated eigenstates. Consequently, the probability distribution of atomic displacements is derived to be of Gaussian form, with a standard deviation corresponding to the rms (ux) of the vibration involved (equation (16)):ux=[(/2ωm)coth(ω/2kBTeff)]1/2 (16)where is Planck's constant, kB the Boltzmann constant, Teff in our case the effective temperature, and m the mass of the oscillator. In the high temperature limit, i.e. when ω/2kBT<<1, eq. 3 simplifies to mω2ux2=kBT, which is the classical limit for a harmonic oscillator; the zero-point energy, which contributes almost half of the mean vibration amplitude at room temperature, is included in equation (16). The value of ω is 25.3 meV. Despite its simplicity, the Einstein model in equation (16) was remarkably successful in predicting the HOLZ rings and TDS intensities by multi-slice simulations. FIG. 21 illustrates the amplitudes of atomic vibrations (rms) plotted against the observed intensity change at different fluences. The inset shows the mono-exponential temporal behavior, with the asymptotes highlighted (circles) for their values at different fluences. The fluence was varied from 1.7 to 21 mJ/cm2. This comparative study of the effect of the fluence was performed at a slightly different sample tilt (corresponding to s=2.7 Å−1), corresponding to a thickness of ˜80 nm. For each fluence, the temperature represents the effective value for the lattice structural change. The error bars given were obtained from the fits at the asymptotes shown in the inset, and they are determined by the noise level of temporal scans. In FIG. 21, we present the change in the asymptotic intensity with fluence (inset), and the derived vibrational amplitudes for the different temperatures. The amplitudes are directly obtained from equation (15), as s is experimentally measured. The relative temperature change (from t− to t+) is then derived from equation (16), taking the value of ux at room temperature (297° K) to be 0.076 Å. The amplitude of atomic vibrations, and hence the temperature, increases as the fluence of the initiating pulse increases. Although the trend is expected for an increased ux with temperature, the absolute values, from 0.077 to 0.084 Å, correspond to a large 3.2% to 3.6% change in nearest neighbor separation; these values are still well below the 15% criterion for a melting phase transition. The linear thermal expansion coefficient has been accurately determined for silicon, and for a value of 2.6×10−6 K−1 at room temperature the vibrational amplitudes reported here are much higher than the equilibrium thermal values at the same temperature. This is because the effective temperature applies to a lattice arrested in a picosecond time window; at longer times, the vibrations equilibrate to a lower temperature. As such, measuring nanoscale local temperatures on the ultrashort time scale enhances the sensitivity of the probe thermometer by orders of magnitude. Moreover, the excitation per site is significantly enhanced. For a single-photon absorption at the fluence used, we estimate, for a 60 nm-thick specimen, the number of absorbed photons per Si atom (for the fs pulse employed) to be ˜0.01, as opposed to 10−9 photons per atom if the experiments were conducted in the time-averaged mode. The achievement of nanoscale diffraction with convergent-beam ultrafast electron microscopy opens the door to exploration of different structural, morphological, and electronic phenomena. The spatially focused and timed electron packets enable studies of single particles and structures of heterogeneous media. Extending the methodology reported here to other variants, such as EELS, STEM and nanotomography, promises possibilities for mapping individual unit cells and atoms on the ultrashort time scale of structural dynamics. With 4D electron microscopy, in situ imaging of the mechanical drumming of a nanoscale material is measured. The single crystal graphite film is found to exhibit global resonance motion that is fully reversible and follows the same evolution after each initiating stress pulse. At early times, the motion appears “chaotic” showing the different mechanical modes present over the micron scale. At longer time, the motion of the thin film collapses into a well defined fundamental frequency of 0.54 MHz, a behavior reminiscent of mode locking; the mechanical motion damps out after ˜200 μs and the oscillation has a “cavity” quality factor of 150. The resonance time is determined by the stiffness of the material and for the 53-nm thick and 55-μm wide specimen used here we determined Young's modulus to be 0.8 TPa, for the in-plane stress-strain profile. Because of its real-time dimension, this 4D microscopy has applications in the study of these and other types of materials structures. Structural, morphological, and mechanical properties of materials have different length and time scales. The elementary structural dynamics, which involve atomic movements, are typically of picometer length scale and occur on the time scale of femto (fs) to picoseconds (ps). Collective phenomena of such atomic motions, which define morphological changes, are observed on somewhat longer time scale, spanning the ps to nanosecond (ns) time domain, and the length scale encompasses up to sub-micrometers. These microscopic structures are very different in behavior from those involved in the mechanical properties. On the nanoscale, when the membrane-like mechanical properties have high frequencies and complex spatial-mode structures, imaging becomes of great value in displaying the spatiotemporal behavior of the material under stress. Utilizing embodiments of the present invention, we have visualized nanoscale vibrations of mechanical drumming in a single-crystalline graphite film (53-nm thick). To study the transient structures, in both space and time, our method of choice has been 4D ultrafast electron microscopy (UEM). This microscope enables investigation of the atomic structural and morphological changes in graphite on the fs to ns time scale and for nm-scale resolution. Additionally, mechanical properties can be determined in real time, which are evident on the ns and microsecond (μs) time scale. The stress is introduced impulsively using a ns laser pulse while observing the motions in real space (in situ) in the microscope using the stroboscopic electron pulses. Remarkably, at times immediately following the initiating pulse the motion appears “chaotic” in the full image transients, showing the different mechanical modes present in graphite. However, after several μs the motion of the nanofilm collapses into a final global resonance of 0.54 MHz. From this resonance of mechanical drumming of the whole plate, we obtained the in-plane Young's modulus of 0.8 terapascal (Tpa). The reported coherent resonance represents the in-phase build up of a mechanical drumming, which is directly imaged without invasive probes. Graphite was chosen because of its unique material properties; it is made of stacked layers of 2D graphene sheets, in which the atoms of each sheet are covalently bonded in a honeycomb lattice, and the sheets separated by 0.335 nm are weakly held together by van der Waals forces. It displays anisotropic electromechanical properties of high strength, stiffness, and thermal/electric conductivity along the 2D basal planes. More recently, with the rise of graphene, a new type of nano-electromechanical system (NEMS) has been highlighted with a prototypical NEMS being a nanoscale resonator, a beam of material that vibrates in response to an applied external force. With the thicknesses reaching the one atomic layer, graphene remains in a high crystalline order, resulting in a NEMS with extraordinary thinness, large surface area, low mass density, and high Young's modulus. Briefly, the setup for ultrafast (and fast) electron imaging involves the integration of laser optical systems into a modified transmission electron microscope (TEM). Upon the initiation of a structural change by either heating of the specimen or through electronic excitation by the laser pulses, an electron pulse generated by the photoelectric effect is used to probe the specimen with a well-defined time delay. A microscopy image or a diffraction pattern is then taken. A series of time-framed snapshots of the image or the diffraction pattern recorded at a number of delay times provides a movie, which displays the temporal evolution of the structural (morphological) and mechanical motions, using either the fs or ns laser system. Because here the visualization is that of the mechanical modes with resonances on the MHz scale, the ns resolution was sufficient. The electrons are accelerated to 200 kV with a de Broglie wavelength of 2.5079 pm. Two laser pulses were used to generate the clocking, excitation pulse at 532 nm and another at 355 nm for the generation of the electron pulse for imaging. The time delay was controlled by changing the trigger time for electron pulses with respect to that of clocking pulses. The delay can be made arbitrarily long and the repetition rate varies from a single shot to 200 kHz, to allow complete heat dissipation in the specimen. The experiments were carried out with a natural single crystal of graphite flakes on a TEM grid. Graphite flakes were left on the surface, covering some of the grid squares completely. The observed dynamics are fully reversible, retracing the identical evolution after each initiating pulse; each image is constructed stroboscopically, in a half second, from typically 2500 pulses of electrons and completing all time-frames (movies) in twenty minutes. FIG. 22 illustrates images and the diffraction pattern of graphite. (A), an image shows features of fringes in contrast (scale bar: 5 μm). Sample thickness was measured to be 53 nm using electron energy loss spectroscopy (EELS). (B) Magnified view of the indicated square of panel A (scale bar: 1 μm). (C) Diffraction pattern obtained by using a selected area diffraction aperture (SAD), which covered an area of 6 μm in diameter on the specimen. The incident electron beam is parallel to the [001] zone axis. Bragg spots are indexed as indicated for some representative ones. Panels A and B of FIG. 22 show the UEM (bright field) images of graphite, and in panel C, a typical electron diffraction pattern is given. The Bragg spots are indexed according to the hexagonal structure of graphite along the [001] zone axis, with the lattice dimension of a=b=2.46 Å (c=6.71 Å). In FIG. 22A, and at higher magnification in FIG. 22B, contrast fringes are clear, typically consisting of linear fringes having ˜1 μm length and a few hundred-nm spacing. These contrast fringes are the result of physical bucking of the graphene layers by constraints or by nanoscale defects within the film. In the dark regions, the zone axis (the crystal [001]) is well aligned with the incident electron beam and electrons are scattered efficiently, whereas in the lighter regions the alignment of the zone axis deviates more and the scattering efficiency is lower. With these contrast patterns, changes in image provide a sensitive visual indicator of the occurrence of mechanical motions. The black spots are natural graphite particles. FIG. 23 illustrates representative image snapshots and difference frames. (A) Images recorded stroboscopically at different time delays, indicated at the top right corner of each image (t1, t2, t3, t4, and t5), after heating with the initiating pulse (fluence=7 mJ/cm2); t1=200 ns; t2=500 ns; t3=10 μs; t4=30 μs; t5=60 μs; and the negative time frame was taken at −1000 ns. Note the change in position of fringes with time, an effect that can be clearly seen in FIG. 23B. (B) Image difference frames with respect to the image taken at −1 μs, i.e., Im(−1 μs; t), which show the image change with time. The reversal in contrast clearly displays the oscillatory (resonance) behavior. In FIG. 23(A), we display several time-framed images of graphite taken at a repetition rate of 5 kHz and at delay times indicated with respect to the clocking (heating) pulse with the fluence of 7 mJ/cm2. At positive times, following t=0, visual changes are seen in the contrast fringes. With time, the contrast fringes change their location in the images, and with these and other micrographs of equal time steps we made a movie of the mechanical motions of graphite following the ns excitation impulse. To more clearly display the temporal evolution on the nanoscale, image-difference frames were constructed. In FIG. 23(B), depicted are the images obtained when referencing to the −1 μs frame, i.e., Im(−1 μs; t). In the difference images, the regions of white or black indicate locations of surface morphology change (contrast pattern movement), while gray regions are areas where the contrast is unchanged from that of the reference frame. Care was taken to insure the absence of long-term specimen drifts as they can cause apparent contrast change; note that in the difference images, the static features are not present. The image changes, reported in this study, are fully reproducible, retracing the identical evolution after each initiating laser pulse, as mentioned above. The reversal of contrast with time in FIG. 23(B) directly images the oscillatory behavior of the drumming. The image change was quantified by using the method of cross-correlation. The normalized cross correlation of an image at time t with respect to that at time t′ is expressed as γ ⁡ ( t ) = ∑ x , y ⁢ C x , y ⁡ ( t ) ⁢ C x , y ⁡ ( t ′ ) ∑ x , y ⁢ C x , y ⁡ ( t ) 2 ⁢ ∑ x , y ⁢ C x , y ⁡ ( t ′ ) 2 ( 17 ) where the contrast Cx,y(t) is given by [tx,y(t)−Ī(t)]/Ī(t), and Ix,y(t) and Ix,y(t′) are the intensities of pixels at the position of (x,y) at times t and t′; Ī(t) and Ī(t′) are the means of Ix,y(t) and Ix,y(t′), respectively. This correlation coefficient γ(t) is a measure of the temporal change in “relief pattern” between the two images being compared, which can be used as a guide to image dynamics as a function of time. Shown in FIG. 24 are cross-correlation values between the image at each measured time point and a reference image recorded before the arrival of the clocking pulse. FIG. 24 illustrates the time dependence of image cross correlation. The whole scan for 100 μs is made of 2000 images taken at 50-ns steps. Also depicted are the zoomed-in image cross-correlations of three representative time regimes (I, II, and III). In each zoomed-in panel, the selected-area image dynamics of five different regions are included. Note the evolution from the “chaotic” to the global resonance (drumming) behavior at long times. Over all pixels, the time scale for image change covers the full range of time delays, from tens of ns to hundreds of μs, indicating the collective averaging over the sites of the specimen. Upon impulsive heating at t=0, the image cross-correlation changes considerably with an appearance of a “chaotic” behavior, in the ˜5 μs range (regime I in FIG. 24). After 10 μs, e.g., regime II, the cross correlation change begins to exhibit periodicity (regime II), and at longer time, a well-defined resonance oscillation emerges (regime III). This is also evident in the selected-area image dynamics (SAID) in several regions (noted as 1 to 5) where the temporal behavior is of different shapes at early time but converges into a single resonance transient after several tens of μs. The shape of image cross correlation dynamics was robust at different fluences, from 2 to ˜10 mJ/cm2, but the amplitude varies. The overall decay of the transients is on a time scale shorter than the separation between pulses. In fact, we have verified the influence of repetition rate and could establish the full recovery at the time intervals indicated. Heat transfer must occur laterally. With an initial z-independent heat profile by absorption of the heating pulse in graphite, we estimated, using a 2D heat diffusion in a homogeneous medium, the time scale for an in-plane transfer, with thermal conductivity λ=5300 W/(m·K), density ρ=2260 kg/m3, and specific heat cV=707 J/(K·kg). For the radius at half height of the initial pulse heat distribution r0=30 μm, t1/2, the time for the axial temperature to drop to a half of its initial value, is deduced to be ˜720 ns, certainly much shorter than the 200-μs time interval between pulses. It follows that the decay of the oscillation [Q/(π·f0)], as derived below, is determined by the damping of mechanical motions. When the specimen absorbs intense laser light, the lattice energy, converted from carriers (electron energy) by electron-phonon coupling, in a few ps, builds up in the illuminated spot on the surface within the duration of the laser pulse. As a consequence, the irradiated volume will expand rapidly following phonon-phonon interaction on the time scale of tens of ps. The resulting thermal stress can induce mechanical vibration in the material, but a coherent oscillatory behavior, due to the thermoelastic stress, will only emerge in the image if the impulsive stress is on a time scale shorter than the period; probing of images should be over the entire time scale of the process, in this case 100 μs. On the ultrashort time scale we have observed the structural and morphological elastic changes. FIG. 25 illustrates resonance dynamics and FFT of graphite. (Left) Time dependences of image cross correlation of full image (A) and image intensity on the selected area of 4×6 pixels as indicated by the arrowhead (B) in FIG. 24. (Right) Fast Fourier transforms of image cross-correlation (C: 0-100 μs; D: 60-100 μs) and image intensity (E: 0-100 μs; F: 60-100 μs). Asterisks in the panels indicate overtones. Note the emergence of the resonance near 1 MHz in panel F. The resonance modes in graphite are highlighted in FIG. 25 by taking the fast Fourier transform (FFT) of image cross-correlation in the time regime of 0-100 μs. The FFT (FIG. 25C) shows several peaks of different frequencies, among which the strongest one around 2.13 MHz is attributed to the overtone of 1.08 MHz. The overtones, due to the truncated nature of cross-correlation close to the value of 1, are greatly reduced in the FFT of image intensity change (FIGS. 25E and 25F). In a few tens of μs, various local mechanical modes observed at early time damp out and one global mode around 1 MHz survives. The peak when fitted to a Lorentzian yields a resonant frequency of 1.08 MHz, and a “cavity” quality factor Q(=f0/Δf)=150±30. This dominant peak gives the fundamental vibration mode of the plate in graphite. For a period of vibration, the contrast pattern of image would recur twice to its initial feature giving the observed frequency to be twice that of structural vibration; the fundamental frequency is, thus, obtained to be 0.54 MHz. A square mechanical resonator clamped at four edges without tension has a fundamental resonance mode of f0 which is given by f 0 = A ⁢ ⁢ d L 2 ⁡ [ Y ( 1 - v 2 ) ⁢ ρ ] 1 / 2 + f ⁡ ( T ) ( 18 ) where f(T) due to tension T is zero in this case. Y is the Young's modulus; ρis the mass density; v is the Poisson's ratio; L is the dimension of a grid square; d is the thickness of the graphite; and A is a constant, for this case equal to 1.655. We measured d to be 53 nm from EELS. Knowing ρ=2260 kg/m3 (300 K), v=0.16 for graphite, and L=55 μm, we obtained from the observed resonance frequency the Young's modulus to be 0.8 TPa, which is in good agreement with the in-plane value of 0.92 TPa, obtained using stress-strain measurements. This value is different by more than an order of magnitude from the c-axis value we measured using the microscope in the ultrafast mode of operation. Thus, using embodiments of the present invention, we have demonstrated a very sensitive 4D microscopy method for the study of nanoscale mechanical motions in space and time. With selected-area-imaging dynamics, the evolution of multimode oscillations to a coherent resonance (global) mode at long time provides the mapping of local regions in the image and on the nanoscale. The time scale of the resonance is directly related to materials anisotropic elasticity (Young's modulus), density, and tension, and as such the reported real-time observation in imaging can be extended to study mechanical properties of membranes (graphene in the present case) and other nanostructures with noninvasive probing. The emergent properties resolved here are of special interest to us as they represent a well-defined “self-organization” in complex macroscopic systems. The function of many nano and microscale systems is revealed when they are visualized in both space and time. Here, four-dimensional (4D) electron microscopy provided in accordance with an embodiment of the present invention is used to measure nanomechanical motions of cantilevers. From the observed oscillations of nanometer displacements as a function of time, for free-standing beams, we are able to measure the frequency of modes of motion, and determine Young's elastic modulus, the force and energy stored during the optomechanical expansions. The motion of the cantilever is triggered by molecular charge redistribution as the material, single-crystal organic semiconductor, switches from the equilibrium to the expanded structure. For these material structures, the expansion is colossal, typically reaching the micron scale, the modulus is 2 GPa, the force is 600 μN, and the energy is 200 pJ. These values translate to a large optomechanical efficiency (minimum of 1% and up to 10% or more), and a pressure of nearly 1,500 atm. We note that the observables here are real-material changes in time, in contrast to those based on changes of optical/contrast intensity or diffraction. As the physical dimensions of a structure approach the coherence length of carriers, phenomena not observed on the macroscopic scale (e.g., quantization of transport properties) become apparent. The discovery and understanding of these quantization effects requires continued advances in methods of fabrication of atomic-scale structures and, as importantly, in the determination of their structural dynamics in real-time when stimulated into a configuration of a nonequilibrium state. Of particular importance are techniques that are noninvasive and capable of nanoscale visualization in real-time. Examples of the rapid progress in the study of nanoscale structures are numerous in the field of micro and nanoelectromechanical systems (i.e., MEMS and NEMS, respectively). Recent advancements have resulted in structures having single-atom mass detection limits and binding specificities on the molecular level, and especially for biological systems. Beyond mass measurement and analyte detection, changes in the dynamics of these nanoscale structures have been shown to be sensitive to very weak external fields, including electron and nuclear spins, electron charge, and electron and ion magnetization. The response to external stimuli is manifested in deflections of the nanoscale, and a variety of techniques have been used to both actuate and detect the small-amplitude deflections. Optical interference is often used for measurement purposes, wherein the deflections of the structure cause a phase shift in the path-stabilized laser light thus providing detection sensitivities that are much less than the radius of a hydrogen atom. High spatiotemporal resolutions (atomic-scale) can be achieved in 4D ultrafast electron microscopy (UEM). Thus it is possible to image structures, morphologies, as well as nanomechanical motions (e.g., nanogating and nanodrumming) in real-time. Using embodiments of the present invention, we direct visualized nano and microscale cantilevers, and the (resonance) oscillations of their mechanical motions. The static images were constructed from a tomographic tilt series of images, whereas the in situ temporal evolution was determined using the stroboscopic configuration of UEM, which is comprised of an initiating (clocking) laser pulse and a precisely-timed packet of electrons for imaging. The pseudo-one-dimensional molecular material (copper 7,7,8,8-tetracyanoquinodimethane, [Cu(TCNQ)]), which forms single crystals of nanometer and micrometer length scale, is used as a prototype. The optomechanical motions are triggered by charge transfer from the TCNQ radical anion (TCNQ−) to copper (Cu+). More than a thousand frames were recorded to provide a movie of the 3D movements of cantilevers in time. As shown below, the expansions are colossal, reaching the micrometer scale, and the spatial modes are resolved on the nanoscale in the images (and angstrom-scale in diffraction) with resonances of megahertz frequencies for the fixed-free cantilevers. From these results, we obtained the Young's modulus, and force and energy stored in the cantilevers. Here, different crystals were studied and generally are of two types: (1) those “standing”, which are free at one end (cantilevers), and (2) those which are “sleeping” on the substrate bed; the latter will be the subject of another report. For cantilevers, the dimensions of the two crystals studied are 300 nm thick by 4.6 μm long and 2.0 μm thick by 10 μm long (see FIG. 26). As such, they define an Euler-Bernoulli beam, for which we expect the fundamental flexural modes to be prominent, besides the longitudinal one(s) which are parallel to the long axis of the crystal. Our interest in Cu(TCNQ) stems from its highly anisotropic electrical and optical properties, which arise from the nature of molecular stacking in the structure. As illustrated in FIG. 26, Cu(TCNQ) consists of an interpenetrating network of discrete columns of Cu− and TCNQ− running parallel to the crystallographic a-axis. The TCNQ molecules organize so that the π-systems of the benzoid rings are strongly overlapped, and the favorable interaction between stacked TCNQ molecules makes the spacing between the benzoid rings only 3.24 Å, significantly less than that expected from purely van der Waals-type interactions. It is this strong π-stacking that results in the pseudo-one-dimensional macroscale crystal structure and is responsible for the anisotropic properties of the material. With electric field or light, the material becomes mixed in valence with both Cu+(TCNQ) and Cu°(TCNQ°) in the stacks, weakening the interactions and causing the expansion. At high fluences, the reversible structural changes become irreversible due to the reduction of copper from the +1 oxidation state to copper metal and subsequent formation of discrete islands of copper metal driven by Ostwald ripening. The methodology we used here for synthesis resulted in the production of single crystals of phase I. FIG. 26 illustrates atomic to macro-scale structure of phase I Cu(TCNQ). Shown in the upper panel is the crystal structure as viewed along the a-axis (i.e., π-stacking axis) and c-axis. The unit cell is essentially tetragonal (cf. ref 19) with dimensions: a=3.8878 Å, b=c=11.266 Å, α=γ=90°, β=90.00(3)°; gray corresponds to carbon, blue corresponds to nitrogen, and yellow corresponds to copper. The hydrogen atoms on the six-membered rings are not shown for clarity. The lower panel displays a typical selected-area diffraction pattern from Cu(TCNQ) single crystals as viewed down the [011] zone axis along with a micrograph taken in our UEM. The rod-like crystal habit characteristic of phase I Cu(TCNQ) is clearly visible. FIG. 27 illustrates a tomographic tilt series of images. The frames show images (i.e., 2D-projections) of the Cu(TCNQ) single crystals acquired at different tilt angles of the specimen substrate. The highlighted region illustrates a large change in the position of the free-standing microscale crystal relative to another, which is lying flat on the substrate, as we change the tilt angle. The scale bar in the lower left corner measures two micrometers. The tilt angle at which each image was acquired is shown in the lower right corner of each frame in degrees. The tilt angle is defined as zero when the specimen substrate is normal to the direction of electron propagation in the UEM column. The tilt series images shown in FIG. 27 provide the 3D coordinates of the cantilevers. The dimensions and protrusion angles of these free-standing crystals were characterized by taking static frames at different rotational angles of the substrate. By placing the crystal projections into a laboratory frame orthogonal basis and measuring the length of the projections in the x-y (substrate) plane as the crystal is rotated by an angle α about the x-axis, the measured projections were obtained to be Θ of 37.8° and φ of 25.3°, where Θ is the angle the material beam makes with respect to substrate-surface normal and φ is the azimuthal angle with respect to the tilt axis, respectively. Note that the movie of the tilt series clearly shows the anchor point of the crystal to be the substrate. The dimensions and geometries of the crystals are determined from the tilt series images with 5% precision. To visualize real-time and space motions, the microscope was operated at 120 kV and the electron pulses were photoelectrically generated by laser light of 355 nm. The clocking optical pulses (671 nm laser), which are well-suited to induce the charge transfer in Cu(TCNQ), were held constant at 3 μJ, giving a maximum fluence of 160 mJ/cm2. Because the relevant resonance frequencies are on the MHz scale, the ns pulse arrangement of the UEM was more than enough for resolving the temporal changes. The time delay between the initiating laser pulse and probe electron pulse was controlled with precision, and the repetition rate of 100 Hz ensured recovery of the structure between pulses. A typical static image and selected-area diffraction are displayed in FIG. 26. From the selected-area diffraction and macroscopic expansion we could establish the nature of correlation between unit cell and the crystal change. The 4D space-time evolution of cantilevers is shown in FIGS. 28 and 29. The referenced (to negative time, tref=−10 ns; i.e., before the arrival of the clocking pulse) difference images of the microscale (FIG. 28) and nanoscale (FIG. 29) free-standing single crystal clearly display modes of expansion on the MHz scale. Each image illustrates how the spatial location of the crystal has changed relative to the reference image as a function of the time delay, elucidating both the longitudinal and transverse displacements from the at-rest position. In order to accurately measure the positions in space we used a reference particle in the image. These reference particles, which are fixed to the surface of the substrate, do not appear in frame-reference images if drift is absent or corrected for. This is an important indication that the observed crystal dynamics do not arise from motion of the substrate due to thermal drift or photothermal effects. Moreover, there is no significant movement observed in images obtained before the arrival of the excitation pulse, indicating that, during the time of pulse separation, the motion has completely damped out and the crystal has returned to its original spatial configuration. The thermal, charging, and radiation effects of the electron pulses are negligible here and in our previous studies made at higher doses. This is evidenced in the lack of blurring of the images or diffraction patterns; no beam deflection due to sample charging was observed. Lastly, no signs of structural fatigue or plasticity were observed during the course of observation, showing the function of the cantilever to be robust for at least 107 pulse cycles. Shown in FIG. 30 is the displacement of the microscale single crystal as a function of time, in both the longitudinal and transverse directions, along with the fast Fourier transforms (FFT) of the observed spatial oscillations for the time range shown (i.e., 0 to 3.3 μs). The motions in both directions of measurement are characterized by a large initial displacement from the at-rest position. The scale of expansion is enormous. The maximum longitudinal expansion possible (after accounting for the protrusion angle) for the 10 μm crystal would be 720 nm or over 7% of the total length. For comparison, a piezoelectric material such as lead zirconate titanate has typical displacements of less than 1% from the relaxed position, but it is known that molecular materials can show enormous optically-induced elastic structural changes on the order of 10% or more. The large initial motion is transferred into flexural modes in the z and x-y directions, and these modes persist over the microsecond (or longer) scale. The overall relaxation of the crystal to its initial position is not complete until several milliseconds after excitation. From the FFTs of the measured displacements, we obtained the frequency of longitudinal oscillation to be 3.3 MHz, whereas the transverse oscillations are found at 2.5 and 3.3 MHz (FIG. 30). We note that the motion represents coupling of modes with dephasing, so it is not surprising that the FFT gives more than one frequency. In fact, from an analysis consisting of a decomposition of the motion via rotation of a principle axes coordinate system relative to the laboratory frame, we found that the plane of lateral oscillation of the crystal was tilted by 18° relative to the plane of the substrate. The nature of contact with the substrate influences not only the mode structure but also the damping of cantilevers. Because of the boundary conditions of a fixed-free beam, the vibration nodes are not evenly spaced and the overtones are not simple integer multiples of the fundamental flexural frequency (f1), but rather occur at 6.26, 17.5, and 34.4 for f2, f3, and f4, respectively. This is in stark contrast to the integer multiples of the fundamental frequency of a fixed-fixed beam. Taking 3 MHz to be the main fundamental flexural frequency of the microscale crystal, we can deduce Young's elastic modulus of the crystal. The expression for the frequencies of transverse (flexural) vibrations of a fixed-free beam is given by, f n = η ⁢ ⁢ π ⁢ ⁢ κ 8 ⁢ L 2 ⁢ ⁢ c ≡ η ⁢ ⁢ π ⁢ ⁢ κ 8 ⁢ L 2 ⁢ Y ρ ( 19 ) where fn is the frequency of the nth mode in Hz, L is the beam length at rest, Y is Young's modulus, and ρ is the density. The radius of gyration of the beam cross section is κ and is given as t/√{square root over (12)}, where t is the thickness of the beam with rectangular cross section. The value of η for the beam is: 1.1942; 2.9882; 52; 72; . . . ;(2n−1)2, approaching whole numbers for higher η values The overtones are not harmonics of the fundamental, and the numerical terms for f1 and f2, which result from the trigonometric solutions involved in the derivation, must be used without rounding. For the longitudinal modes of fixed-free beam, fn=(2n−1)c/4L. From the above equation, and knowing ρ=1.802 g·cm−3, we obtained Young's modulus to be 2 GPa, with the speed of sound, therefore, being 1,100 m·s−1; we estimate a 12% uncertainty in Y due to errors in t, L, and f. This value of Young's modulus (N·m−2) is very similar to that measured for TTF-TCNQ single crystals using a mm-length vibrating reed under an alternating voltage. Both materials are pseudo-one-dimensional, and the value of the modulus is indicative of the elastic nature along the stacking axis in the direction of weak intercolumn interactions. Young's modulus slowly varies in value in the temperature range of 50 to 300 K but, when extrapolated to higher temperatures, decreases for both TTF-TCNQ and K(TCNQ). From the absorbed laser pulse energy (30 nJ), the amount of material (7.2×10−14 kg), and assuming the heat capacity to be similar to TTF-TCNQ (430 J·K−1·mol−1), the temperature rise in the microscale crystal is expected to be at most 260 K. Finally, we note that for the same modulus reported here, the frequency of longitudinal mode expansion [f=c/4L; n=1] should be nearly 25 MHz, which is not seen in the FFT with the reported resolution, thus suggesting that the observed frequencies in the longitudinal direction are those due to cantilever motion in the z direction; the longitudinal expansion of the crystal is about 1 to 2% of its length, which in this case will be 100 to 200 nm. The potential energy stored in the crystal and the force exerted by the crystal at the moment of full extension along the long axis just after time zero [cf. FIG. 30(A)] can be estimated from the amplitudes and using Hooke's law: V = 1 2 ⁢ ( YA L ) ⁢ Δ ⁢ ⁢ L 2 ( 20 ⁢ a ) F = ( YA L ) ⁢ Δ ⁢ ⁢ L ( 20 ⁢ b ) where V and F are the potential energy and force, respectively, and A is the cross-sectional area of the crystal. The bracketed term in equation (20) is the spring constant (assuming harmonic elasticity, and not the plasticity range), and by simple substitution of the values, we obtained 200 pJ and 600 μN for the potential energy and force, respectively, considering the maximum possible expansion of 720 nm; even when the amplitude is at its half value [see FIG. 30(A)], the force is very large (˜300 μN). For comparison, the average force produced by a single myosin molecule acting on an actin filament, which was anchored by two polystyrene beads, was measured to be a few piconewtons. In other words, because of molecular stacking, the force is huge. Also because of the microscale cross-section, the pressure of expansion translates to 0.1 GPa, only a few orders of magnitude less than pressures exerted by a diamond anvil. Based on the laser fluence, crystal dimensions, and absorptivity of Cu(TCNQ) at 671 nm (3.5×106 m−1), the maximum pulse energy absorbed by the crystal is 30 nJ. This means that, of the initial optical energy, a minimum of ˜1% is converted into mechanical motion of the crystal. But in fact, it could reach 10 or more percent as determined by the projection of the electric field of light on the crystal. In order to verify the trend in frequency shifts, the above studies were extended to another set of crystal beams, namely those of reduced dimensions. Because the resonant frequencies of a fixed-free beam are determined, in part, by the beam dimensions [cf. equation (19)], a Cu(TCNQ) crystal of different length than that shown in FIG. 30 should change the oscillation frequencies by the κ/L2 dependence. With a smaller cantilever beam we measured the oscillation frequencies for a crystal of 300 nm thickness and 4.6 μm length, using the same laser parameters as for the larger crystals, and found them to be at higher values (FIG. 31). This is confirmed by the FFTs of the displacement spanning the range 0 to 3.3 μs [FIGS. 31(C) and (D)]; a strong resonance near 9 MHz with another weaker resonance at 3.6 MHz in the longitudinal direction [FIG. 31(C)] is evident. Within a few microseconds, the only observed frequency in the FFT was near 9 MHz. This oscillation persists up to the time scans of 30 μs, at which point the amplitude was still roughly 40% of the leveling value near 2 μs. By taking this duration (30 μs) to be the decay time (τ) required for the amplitude to fall to 1/e of the original value, the quality factor (Q=πfτ) of the crystal free oscillator becomes near 1,000. However, on longer time scales, and with less step resolution, the crystal recovers to the initial state in a few milliseconds, and if the mechanical motion persists, Q would increase by an order of magnitude. It is clear from the resonance value of the flexural frequency at 9 MHz that as the beam reduces in size, the frequency increases, as expected from equation (19). However, if we use this frequency to predict Young's modulus we will obtain a value of 30 GPa, which is an order of magnitude larger than that for the larger microscale crystal. The discrepancy points to the real differences in modes structure as we reach nanometer-scale cantilevers. One must consider, among other things, the anchor-point(s) of the crystals, the frictional force with substrate and other crystals, and the curvature of the beam (see movie in supporting information). This curvature will cause the crystal to deviate from ideal Euler-Bernoulli beam dynamics, thus shifting resonance frequencies from their expected positions. Interestingly, by using the value of 30 GPa for Young's modulus, the minimum conversion efficiency increases by a factor of 15. These dependencies and the extent of displacement in different directions, together with the physics of modes coupling (dephasing and rephasing), will be the subject of our full account of this work. Thus, with 4D electron microscopy it is possible to visualize in real space and time the functional nanomechanical motions of cantilevers. From tomographic tilt series of images, the crystalline beam stands on the substrate as defined by the polar and azimuthal angles. The resonance oscillations of two beams, micro and nanocantilevers, were observed in situ giving Young's elastic modulus, the force, and the potential energy stored. The systems studied are unique 1D molecular structures, which provide anisotropic and colossal expansions. The cantilever motions are fundamentally of two types, longitudinal and transverse, and have resonance Q factors that make them persist for up to a millisecond. The function is robust, at least for 107 continuous pulse cycles (˜1011 oscillations for the recorded frames), with no damage or plasticity. With these imaging methods in real-time and with other variants, it is now possible to test the various theoretical models involved in MEMS and NEMS. Electron energy loss spectroscopy (EELS) is a powerful tool in the study of valency, bonding and structure of solids. Using our 4D electron microscope, we have performed ultrafast EELS, taking the time resolution in the energy-time space into the femtosecond regime, a 10 order of magnitude increase, and for a table-top apparatus. It is shown that the energy-time-amplitude space of graphite is selective to changes, especially in the electron density of the π+σ plasmon of the collective oscillation of the four electrons of carbon. Embodiments of the present invention related to EELS enable the microscope to be used as an analytical tool. As electrons pass through the specimen, each type of material (e.g., gold, copper, or zinc) will have a different electron energy. Thus, it is possible to “tune” into a particular element and study the dynamic behavior of the material itself. In microscopy, EELS provides rich characteristics of energy bands describing modes of surface atoms, valence- and core-electron excitations, and interferences due to local structural bonding. The scope of applications thus spans surface and bulk elemental analysis, chemical characterization and electronic structure of solids. The static, time-integrated, EEL spectra do not provide direct dynamic information, and with video-rate scanning in the microscope could changes be recorded only with a time resolution of millisecond or longer. Dedicated time-resolved EELS apparatus, without imaging, have obtained millisecond resolution, being determined primarily by detector response and electron counts. However, for studies of dynamics of electronic structure, valency and bonding, the time resolution must increase by at least nine orders of magnitude. We have performed femtosecond resolved EELS (FEELS) using our ultrafast electron microscope (UEM), developed for 4D imaging of structures and morphology. Embodiments of the present invention are conceptually different from time-resolved EELS (termed TREELS) as the time resolution in FEELS is not limited by detector response and sweep rate. Moreover, both real-space images and energy spectra can be recorded in situ in UEM and with energy filtering the temporal resolution can be made optimum. We demonstrate the method in the study of graphite which displays changes on the femtosecond (fs) time scale with the delay steps being 250 fs. Near the photon energy of 2.4 eV (away from the zero energy loss peak), and similarly for the π+σ plasmon band, the change is observed, but it is not as significant for the π plasmon band. Thus it is possible to chart the change from zero to thousands of eV and in 3D plots of time, energy and amplitude; the decrease in EELS intensity at higher energies becomes the limiting factor. This table-top approach using electrons is discussed in relation to recent achievements using soft and hard (optical) X-rays in laboratory and large-scale facilities of synchrotrons and free electron lasers. According to embodiments of the present invention, the probing electrons and the initiating light pulses are generated by a fs laser, and the EEL spectra of the transmitted electrons are recorded in a stroboscopic mode by adjusting the time delay between the pump photons and the probe electron bunches. The concept of single-electron packet used before in imaging is utilized in this approach. When each ultrafast electron packet contains at most one electron, “the single-electron mode,” space-charge broadening of the zero-loss energy peak, which decreases the spectrometer's resolution, is absent. FIG. 32 is a schematic diagram of a microscope used in embodiments of the present invention. A train of 220 fs laser pulses at 1.2 eV was frequency doubled and tripled and then split into two beams. In other embodiments, a range of laser pulse widths could be used, for example from about 10 femtoseconds to about 10 microseconds. The frequency tripled light at 3.6 eV was directed to the microscope photocathode, and the photoelectron probe pulse was accelerated to 200 keV. The 2.4 eV pulses were steered to the specimen, and provided the excitation at a fluence of 5.3 mJ/cm2. In other embodiments, a fluence ranging from about 1 mJ/cm2 to about 20 mJ/cm2 could be utilized. By varying the delay time between the electron and optical pulses, the time dependence of the associated EEL spectrum was followed. The electrons pass through the sample and a set of magnetic lenses to illuminate the CCD camera, forming either a high resolution image of the specimen, a diffraction image, or they can be energy dispersed to provide the EEL spectra. The apparatus is equipped with a Gatan imaging filter (GIF) Tridiem, of the postcolumn type, which is attached below the transmission microscope camera chamber. The energy width of near 1 eV was measured for the EELS zero-loss peak and it is comparable to that obtained in thermal-mode operation of the TEM, but increases significantly in the space-charge limited regime. The experiments were performed at repetition rates of 100 kHz and 1 MHz, and no difference in the EEL spectra or the temporal behavior was observed, signifying a complete recovery of electronic structure changes between subsequent pulses. The reported temporal changes were missed when the scan resolution exceeded 250 fs, and the entire profile of the transient is complete in 2 ps. The electron beam passes through the graphite sample perpendicular to the sample surface while the laser light polarization was parallel to the graphene layers. Finally, the zero of time was determined to the precision of the reported steps, and was observed to track the voltage change in the FEG module of the microscope. The semi-metal graphite is a layered structure, which was prepared as free-standing film. The thickness of the graphite film was estimated from the EEL spectrum to be 106 nm (inelastic mean-free path of ˜150 nm), and the crystallinity of the specimen was verified by observing the diffraction pattern which was indexed as reported. FIG. 33 shows a static EEL spectrum of graphite taken in UEM. The distinct features are observed in the spectrum and indeed are typical of the electronic structure bands of graphite; the in-plane π plasmon is found near 7 eV, while at higher energy, the peak at 27 eV is observed with a shoulder at 15 eV. These latter peaks correspond to the π+σ oscillation of the bulk and surface plasmons, respectively. The results are in agreement with those of literature reports. The bands displayed in different colors (FIG. 33) are the simulations of the profiles with peak positions reproducing the theoretical values near 7, 15 and 27 eV. The 3D FEELS map of the time-energy evolution of the amplitude of the plasmon portion of the spectrum (up to 35 eV) is shown in FIG. 34, together with the EEL spectrum taken at negative time. The spectra were taken at 1 MHz repetition-rate, for a pump fluence of 5.3 mJ/cm2 at room temperature and for ts=250 fs for each difference frame. The map reflects the difference for all energies and as a function of time, made by subtracting a reference EEL spectrum at negative time from subsequent ones. The relatively strong enhancement of the energy loss in the low energy (electron-hole carriers) region is visible and the change is near the energy of the laser excitation. This feature represents the energy loss enhancement due to the creation of carriers by the fs laser excitation in the ππ* band structure, as discussed below. At higher energy, the 7 eV π plasmon peak remains nearly unperturbed by the excitation, and no new features are observed at the corresponding energies. For the 27 eV π+σ bulk plasmon an increased spectral weight at positive time is visible as a peak in the time-resolved spectrum. In order to obtain details of the temporal evolution of the different spectroscopic energy bands, we divided the spectrum into three regions: the low energy region between 2 and 5 eV, the π plasmon region between 6 and 8 eV, and the π+σ plasmon region between 20 and 30 eV. The 3D data are integrated in energy within the specified regions of the spectrum, and the temporal evolution of the different loss features are obtained; see FIG. 35. For regions where changes occur, the time scales involved in the rise and subsequent decay are similar. In FEELS, the shortest decay is 700 fs taken with the steps of 250 fs. The duration of the optical pulse is ˜220 fs, but we generate the UV pulse for electron generation through a non-linear response, and it is possible that the pulses involved are asymmetric in shape and that multiphotons are part of the process; full analysis will be made later. We note that the observed ˜700 fs response indeed reflects the joint response from both the optical and electron pulses and it is an upper limit for the electronic change. It is remarkable that, in FIG. 35, the temporal evolution of the interlayer spacing of graphite obtained by ultrafast electron crystallography (UEC) at a similar fluence, i.e. 3.5 mJ/cm2, the timescale of the ultrafast compression corresponds well to the period in which the bulk plasmon is out of equilibrium; in this plot the zero of time is defined by the change of signal amplitude. In graphite, the characteristic time for the thermalization of photo-excited electrons is known to be near 500 fs at low fluences (a few μJ/cm2). When excited by an intense laser pulse, a strong electrostatic force between graphene layers is induced by the generated electron-hole (carrier) plasma. This causes the structure to be out of equilibrium for nearly 1 ps; a stressful structural rearrangement is imposed on the crystal, which, at very high fluences (above 70 mJ/cm2), has been proposed as a cause of the phase transformation into diamond. Because graphite is a quasi two-dimensional structure, distinct spectral features are visible in EELS. The most prominent and studied peaks are those at 7 eV and the much stronger one at 27 eV. From the solution of the in-plane and out-of-plane components of the dielectric tensor it was shown, for graphite, that the 7 eV band is a π plasmon, resulting from interband ππ* transitions in the energy range of 2-5 eV, whereas the 27 eV band is a π+σ plasmon dominated by σσ* transitions beyond 10 eV (FIG. 5). We note that in this case the plasmon frequencies are not directly given by the ππ* and σσ* transition energies as they constitute tensorial quantities. For example ϖ π + σ 2 = ϖ p 2 + 1 4 ⁢ ( Ω π 2 + 3 ⁢ Ω σ 2 ) ,where ωp=npe2/∈0m)1/2 is the free electron gas plasma frequency; Ωπ and Ωσ are the excitation energies for ππ* and σσ* transitions, respectively. For ωP, the electron density is np, n is the number of valence electrons per atom and p is the density of atoms, and ∈0 is the vacuum dielectric constant. It follows that the density of occupied and empty (π, σ, π, and σ) states is critical, and that the π Plasmon is from the collective excitation of the πelectrons (one electron in the p-orbital, with screening corrections) whereas the π+σ plasmon is the result of all 4 valence electrons collectively excited over the coherent length scale of bulk graphite; there are also surface plasmons but at different energies. Recently it was demonstrated, both theoretically and experimentally, that the π and π+σ plasmons are sensitive to the inter-layer separation, but while the former shows some shift of peaks the latter is dramatically reduced in intensity, and, when reaching the grapheme limit, only a relatively small peak at ˜15 eV survives. This is particularly evident when the momentum transfer is perpendicular to the c-axis, the case at hand and for which the EEL spectrum is very similar to ours. With the above in mind, it is now possible to provide, in a preliminary picture, a connection between the selective fs atomic motions, which are responsible for the structural dynamics, and changes in the dielectric properties of Plasmon resonances, the electronic structure. The temporal behavior, and coherent oscillation (shear modes of ˜1 ps), of c-axis expansion display both contraction and expansion on the picometer length scale per unit cell. The contraction precedes the expansion, as shown in FIG. 35, with velocity that depends on the fluence, i.e., the density of carriers. With fs excitation, the electronic bands are populated anisotropically, and, because of energy and momentum conservation, the carriers transiently excite large-momentum phonons, so called strongly coupled phonons. They are formed on the fs time scale (electron-phonon coupling) but decay in ˜7 ps. The initial compression suggests that the process is a cooperative motion and is guided by the out-of-equilibrium structure change dictated by the potential of excited carriers; in this case ππ* excitation which weakens c-axis bonding. The initial atomic compression, when plotted with transient EELS data (FIG. 35), shows that it is nearly in synchrony with the initial change, suggesting that the spacing between layers (c-axis separation) is the rate determining step, and that in the first 1 ps, the compressed ‘hard graphite’ effect is what causes the increase in the amplitude of the π+σ plasmon peak. In other words, the decrease of the spectral weight due to the change of electronic structure upon increasing the interlayer separation (to form graphene) becomes an increase when the plates are compressed, because of the enhanced collectiveness of all four valence electrons of carbon. The change involves shear motions and it is not surprising that the π+σ peak (dominated by σσ* excitation) is very sensitive to such changes. The π peak is less influenced as only one electron is involved, as discussed above, and the amplitude change is relatively small. The faster recovery of EEL peaks in 700 fs is, accordingly, the consequence of expansion which ‘decouples’ the π and σ system. Lastly, the relatively large increase in EEL near the photon energy is due to carrier excitation (π*) which leads to a loss of electron energy at near 3 eV, possibly by electronic excitation involving the cy system (FIG. 36). The created carriers cause an increase in the Drude band as evidenced in the decrease in optical transmission. The demonstration of ultrafast EELS in electron microscopy opens the door to experiments that can follow the ultrafast dynamics of the electronic structure in materials. The fs resolution demonstrates the ability of UEM to probe transients on the relevant sub-picosecond time scale, while keeping the energy resolution of EELS. Moreover, the selectivity of change in the collective electron density (for graphite) suggests future experiments, including those with changes in polarization, shorter optical pulses, core excitation and oxidation sites. We believe that this table-top UEM-EELS should provide the methodology for studies which have traditionally been made using synchrotrons (and free electron lasers) especially in the UV and soft X-ray regions. Chemical bonding dynamics are important to the understanding of properties and behavior of materials and molecules. Utilizing embodiments of the present invention, we have demonstrated the potential of time-resolved, femtosecond electron energy loss spectroscopy (EELS) for mapping electronic structural changes in the course of nuclear motions. For graphite, it is found that changes of milli-electron volts in the energy range of up to 50 electron volts reveal the compression and expansion of layers on the subpicometer scale (for surface and bulk atoms). These nonequilibrium structural features are correlated with the direction of change from sp2 [two-dimensional (2D) grapheme] to sp3 (3D-diamond) electronic hybridization, and the results are compared with theoretical charge-density calculations. The reported femtosecond time resolution of four-dimensional (4D) electron microscopy represents an advance of 10 orders of magnitude over that of conventional EELS method. Bonding in molecules and materials is determined by the nature of electron density distribution between the atoms. The dynamics involve the evolution of electron density in space and the motion of nuclei that occur on the attosecond and femtosecond time scale, respectively. Such changes of the charge distribution with time are responsible for the outcome of chemical reactivity and for phenomena in the condensed phase, including those of phase transitions and nanoscale quantum effects. With convergent-beam electron diffraction, the static pattern of charge-density difference maps can be visualized, and using x-ray absorption and photoemission spectroscopy substantial progress has been made in the study of electronic-state dynamics in bulks and on surfaces. Electron energy loss spectroscopy (EELS) is a powerful method in the study of electronic structure on the atomic scale, using aberration-corrected microscopy, and in chemical analysis of selected sites; the comparison with synchrotron-based near-edge x-ray absorption spectroscopy is impressive. The time and energy resolutions of ultrafast electron microscopy (UEM) provide the means for the study of (combined) structural and bonding dynamics. Here, time-resolved EELS is demonstrated in the mapping of chemical bonding dynamics, which require nearly 10 orders of magnitude increase in resolution from the detector-limited millisecond response. By following the evolution of the energy spectra (up to 50 eV) with femtosecond (fs) resolution, it was possible to resolve in graphite the dynamical changes on a millielectronvolt (subpicometer motion) scale. In this way, we examined the influence of surface and bulk atoms motion and observed correlations with electronic structural changes: contraction, expansion, and recurrences. Because the EEL spectra of a specimen in this energy range contain information about plasmonic properties of bonding carriers, their observed changes reveal the collective dynamics of valence electrons. Graphite is an ideal test case for investigating the correlation between structural and electronic dynamics. Single-layered grapheme, the first two-dimensional (2D) solid to be isolated and the strongest material known, has the orbitals on carbon as sp2 hybrids, and in graphite the π-electron is perpendicular to the molecular plane. Strongly compressed graphite transforms into diamond, whose charge density pattern is a 3D network of covalent bonds with sp3 hybrid orbitals. Thus, any structural perturbation on the ultra-short time scale of the motion will lead to changes in the chemical bonding and should be observable in UEM. Moreover, surface atoms have unique binding, and they too should be distinguishable in their influence from bulk atom dynamics. The experiments were performed on a nm-thick single crystal of natural hexagonal graphite. The sample was cleaved repeatedly until a transparent film was obtained, and then deposited on a transmission electron microscopy (TEM) grid; the thickness was determined from EELS to be 108 nm. The fs-resolved EELS (or FEELS) data were recorded in our UEM, operating in the single-electron per pulse mode to eliminate Boersch's space charge effect. A train of 220 fs infrared laser pulses (λ=1038 nm) was split into two paths, one was frequency-doubled and used to excite the specimen with a fluence of 1.5 mJ/cm2, and the other was frequency-tripled into the UV and directed to the photoemissive cathode to generate the electron packets. These pulses were accelerated in the TEM column and dispersed after transmission through the sample in order to provide the energy loss spectrum of the material. The experimental, static EEL spectra of graphite in our UEM, with grapheme for comparison, are displayed in FIG. 37A; FIG. 37B shows the results of theoretical calculations. The spectral feature around 7 eV is the π Plasmon, the strong peak centered around 26.9 eV is the π+σ bulk plasmon, and the weaker peak on its low energy tail is due to the surface Plasmon. The agreement between the calculated EEL spectra and the experimental ones is satisfactory both for graphite and grapheme. Of relevance to our studies of dynamics is the simulation of the spectra for different c-axis separations, ranging from twice as large as naturally occurring (2c/a; a and c are lattice constraints) to 5 times as large. This thickness dependence is displayed in FIG. 37B. As displayed in FIG. 37, the surface and bulk Plasmon bands (between 13 and 35 eV) can be analyzed using two Voigt functions, thus defining the central position, intensity, and width. At different delay times, we monitored the changes and found that they occur in the intensity and position; the width and shape of the two spectral components are relatively unchanged. FIGS. 37C and 37D, show the temporal changes of the intensity for both the surface and bulk plasmons. As noted, the behavior of bulk dynamics is “out of phase” with that of the surface dynamics, corresponding to an increase in intensity for the former and a decrease for the latter. Each time point represents a 500-fs change. Within the first 1 ps, the bulk Plasmon gains spectral weight with the increase in intensity. With time, the intensity is found to return to its original (equilibrium) value. At longer times, a reverse in sign occurs, corresponding to a decrease and then an increase in intensity—an apparent recurrence or echo occurring with dispersion. The intensity change of the surface plasmon in FIGS. 37C and 37D, shows a π phase-shifted temporal evolution with respect to that of the bulk plasmon. The time dependence of the energy position of the different spectral bands is displayed in FIG. 38. The least-squares fit converges for a value of the surface plasmon energy at 14.3 eV and of the bulk plasmon at 26.9 eV. The temporal evolution of the surface plasmon gives no sign of energy dispersion, whereas the bulk plasmon is found to undergo first a blueshift and then a redshift at longer times (FIGS. 38A and 38B). The overall energy-time changes in the FEEL spectra are displayed in FIG. 39. To make the changes more apparent, the difference between the spectra after the arrival of the initiating laser pulse (time zero) and a reference spectrum taken at ˜20 ps before time zero is shown. The most pronounced changes are observed in the region near the energy of the laser itself (2.39 eV), representing the energy-loss enhancement due to the creation of carriers by the laser excitation, and in the region dominated by the surface and bulk plasmons (between 13 and 35 eV). Clearly evident in the 3D plot are the energy dependence as a function of time, the echoes, and the shift in phase. A wealth of information has been obtained on the spectroscopy and structural dynamics of graphite. Of particular relevance here are the results concerning contraction and expansion of layers probed by diffraction on the ultra-short time scale. Knowing the amplitude of contraction/expansion, which is 0.6 pm at the fluence of 1.5 mJ/cm2, and from the charge of plasmon energy with interlayer distance (FIG. 37), we obtained the results shown in FIG. 38C. The diffraction data, when now translated into energy change, reproduce the pattern in FIG. 38A, with the amplitude being within a factor of two. When the layers are fully separated, that is, reaching grapheme, the bulk plasmon, as expected, is completely suppressed. The dynamics of chemical bonding can now be pictured. The fs optical excitation of graphite generates carriers in the nonequilibrium state. They thermalize by electron-electron and electron-phonon interactions on a time scale found to be less than 1 ps, less than 500 fs, and −200 fs. From our FEELS, we obtained a rise of bulk plasmons in ˜180 fs (FIG. 39). The carriers generated induce a strong electrostatic force between grapheme layers, and ultrafast interlayer contraction occurs as a consequence. In FIG. 37D, the increase of the bulk plasmon spectral weight on the fs time scale reflects this structural dynamics of bond-length shortening because it originates from a denser and more 3D charge distribution. After the compression, a sequence of dilatations and successive expansions along the c axis follows, but, at longer times lattice thermalization dephases the coherent atomic motions; at a higher fluence, strong interlayer distance variations occur, and grapheme sheets can be detached as a result of these interlayer collisions. Thus, the observations reported here reflect the change in electronic structure: contraction toward diamond and expansion toward grapheme. The energy change with time correlates well with the EELS change calculated for different interlayer distances (FIG. 37). We have calculated the charge density distribution for the three relevant structures. The self-consistent density functional theory calculations were made using the linear muffin-tin orbital approximation, and the results are displayed in FIG. 40. To emphasize the nature of the changes observed in FEELS, and their connection to the dynamics of chemical bonding, we pictorially display the evolution of the charge distribution in a natural graphite crystal, a highly compressed one, and the extreme case of diamond. Once can see the transition from a 2D to a 3D electronic structure. The compressed and expanded graphite can pictorially be visualized to deduce the change in electron density as interlayer separations change. With image, energy, and time resolution in 4D UEM, it is possible to visualize dynamical changes of structure and electronic distribution. Such stroboscopic observations require time and energy resolutions of fs and meV, respectively, as evidenced in the case study (graphite) reported here, and for which the dynamics manifest compression/expansion of atomic planes and electronic sp2/sp3-type hybridization change. The application demonstrates the potential for examining the nature of charge density and chemical bonding in the course of physical/chemical or materials phase change. It would be of interest to extend the scale of energy from ˜1 eV, with 100 meV resolution, to the hundreds of eV for exploring other dynamical processes of bonding. The following articles are hereby incorporated by reference for all purposes: 4D imaging of transient structures and morphologies in ultrafast electron microscopy, Brett Barwick, et al., Science, Vol. 322, Nov. 21, 2008, p. 1227. Temporal lenses for attosecond and femtosecond electron pulses, Shawn A. Hibert, et al., PNAS, Vol. 106, No. 26, Jun. 30, 2009, p. 10558. Nanoscale mechanical drumming visualized by 4D electron microscopy, Oh-Hoon Kwon, et al., Nanoletters, Vol. 8, No. 11, November 2008, p. 3557. Nanomechanical motions of cantilevers: direct imaging in real space and time with 4D electron microscopy, David J. Flannigan, et al., Nanoletters, Vol. 9, No. 2 (2009), p. 875. EELS femtosecond resolved in 4D ultrafast electron microscopy, Fabrizio Carbone, et al., Chemical Physics Letters, 468 (2009), p. 107. Dynamics of chemical bonding mapped by energy-resolved 4D electron microscopy, Fabrizio Carbone, et al., Science, Vol. 325, Jul. 10, 2009, p. 181. Atomic-scale imaging in real and energy space developed in ultrafast electron microscopy, Hyun Soon Park, et al., Nanoletters, Vol. 7, No. 9, September 2007, p. 2545. It is also understood that the examples and embodiments described herein are for illustrative purposes only and that various modifications or changes in light thereof will be suggested to persons skilled in the art and are to be included within the spirit and purview of this application and scope of the appended claims.
059498374	claims	1. A nuclear reactor having a core including a plurality of seed-blanket units, each said seed-blanket unit comprising: a) a central seed region, said seed region containing plutonium seed fuel elements; b) a blanket region surrounding said seed region and containing blanket fuel elements comprising predominantly thorium oxide; c) moderator in said seed region in the volume ratio of moderator to fuel in the range of approximately 2.5 to 3.5; and d) moderator in said blanket region in the volume ratio of moderator to fuel of approximately 1.5 and 2.0. a) a central seed region, said seed region containing plutonium seed fuel elements, each of said seed fuel elements being comprised of plutonium-zirconium alloy; b) a blanket region surrounding said seed region and containing blanket fuel elements comprising predominantly thorium oxide with approximately 1% or less plutonium oxide, and approximately 2-5% by volume uranium tailings; c) moderator in said seed region in the volume ratio of moderator to fuel in the range of approximately 2.5 to 3.5; and d) moderator in said blanket region in the volume ratio of moderator to fuel of between approximately 1.5 and 2.0. 2. The nuclear reactor of claim 1, wherein each of said seed fuel elements is comprised of plutonium-zirconium alloy. 3. The nuclear reactor of claim 1, wherein said seed region comprises between approximately 45 and 55% of the total volume of each said seed-blanket unit. 4. The nuclear reactor of claim 1, wherein said blanket fuel elements further include plutonium oxide in the amount of no more than approximately 1%. 5. The nuclear reactor of claim 1, wherein said blanket fuel elements comprise approximately 2-5% by volume uranium tailings. 6. The nuclear reactor of claim 1, wherein the volume ratio of moderator to fuel in said seed region is in the range of approximately 2.5 to 3.0. 7. The nuclear reactor of claim 1, wherein said central seed region further contains a plurality of burnable poison containing rods. 8. The nuclear reactor of claim 7, wherein said plurality of burnable poison containing rods includes WABA poison rods and gadolinium containing fuel rods. 9. A nuclear reactor having a core including a plurality of seed-blanket units, each said seed-blanket unit comprising: 10. The nuclear reactor of claim 9, wherein said seed region comprises between approximately 45 and 55% of the total volume of each said seed-blanket unit. 11. The nuclear reactor of claim 10, wherein the volume ratio of moderator to fuel in said seed region is in the range of approximately 2.5 to 3.0. 12. The nuclear reactor of claim 11, wherein said central seed region further contains a plurality of burnable poison containing rods. 13. The nuclear reactor of claim 12, wherein said plurality of burnable poison containing rods includes WABA poison rods and gadolinium containing fuel rods.
055770819	summary	BACKGROUND OF THE INVENTION 1. Technical Field of the Invention The present invention relates to a method of forming grids for nuclear fuel assemblies, as well as to the grids formed by the application of the same method. 2. Background Art In the conventional method of manufacturing nuclear fuel assembly grids, straps 1, which are formed, for example, of nickel alloy so as to have slits therein, are, as shown in FIGS. 7A to 7C, assembled into a grid form, and the intersections 2 of the straps 1 are then brazed. In this method, nickel is usually plated on the surfaces of the straps 1 in advance in order to ensure high-quality brazing. More specifically, FIG. 7A depicts a part of the assembled straps 1, showing a brazing filler metal (hereinafter referred to as "filler metal") being adherently placed on top of the intersections 2 of the straps 1. When the straps 1 are heated in a vacuum type brazing furnace (hereinafter referred to as "vacuum furnace"), the filler metal melts and flows down along the intersections 2, so that the intersections 2 are presumed to be brazed uniformly over their entire lengths. FIG. 7B depicts the result of brazing in the case where the brazing is effected on the straps having nickel-plated surfaces, whereas FIGS. 7C and 7D depict the result of brazing in the cases where the brazing is carried out on the non-Ni plated straps. In either of the straps shown in FIGS. 7C and 7D, good brazing results have not been obtained due to insufficient or ununiform flow of the filler metal flowing down from the top of the intersections 2 therealong. In FIG. 7C, unbrazed portions are shown remaining, whereas in FIG. 7D, the width and thickness of the brazed parts have become excessive. Thus, it has hitherto been conventional to carry out nickel plating on the straps 1 in order to ensure excellent brazing quality. However, such a plating process is unavoidably associated with an increased cost and environmental pollution. Therefore, there has been the need for the development of a novel brazing technique which requires no plating treatment but achieves excellent brazing quality. SUMMARY OF THE INVENTION It is therefore the primary object of the present invention to provide a method of forming a nuclear fuel assembly grid which requires no plating treatment but ensures improved brazing quality. Another object of the invention is to provide a nuclear fuel assembly grid which is obtained by the aforesaid method. According to a first aspect of the invention, there is provided a method of forming a nuclear fuel assembly grid, which includes the steps of (a) preparing a plurality of formed alloy straps each having slits, (b) arranging the straps into a grid form by intersecting the straps with each other through the slits, and (c) brazing intersections of the associated straps, the method further comprising the step of: (d) subjecting those portions to be brazed to a pretreatment prior to the arranging step (b), the pretreatment including applying a paste, comprising a mixture of a filler metal and a vehicle, to the portions to be brazed to form a thin film thereon. In the foregoing, the pretreatment step (d) may further include drying the paste film, heating the straps in a vacuum furnace to melt the filler metal in the paste, and cooling the straps; and the brazing step (c) may include placing a filler metal daub on top of the intersections of the straps, and heating the straps in a vacuum furnace to effect the brazing of the straps. Alternatively, the method may further comprise the steps of drying the paste film, heating the straps in a vacuum furnace to melt the filler metal in the paste, and cooling the straps between the arranging step (b) and the brazing step (c); and the brazing step (c) may include placing a filler metal daub on top of the intersections of the straps, and heating the straps in a vacuum furnace to effect the brazing of the straps. Furthermore, the brazing step (c) may include placing a filler metal daub on top of the intersections of the straps, and heating the straps in a vacuum furnace to effect the brazing of the straps; and the method may further comprise the steps of drying the paste film after the pretreatment step (d), subsequently effecting the brazing step (c), and heating the straps in a vacuum furnace to effect the brazing of the straps. In this modification, the step of drying the paste film may be omitted. Moreover, the filler metal may contain Ni powder, whereas the vehicle may contain a synthetic resin and an organic solvent. In addition, the paste may further contain an additional substance selected from the group consisting of water, an organic solvent such as methyl alcohol and a liquid surface active agent such as polyethylene glycol fatty acid ester. According to another aspect of the invention, there is provided a nuclear fuel assembly grid formed using the aforesaid method. In the method of the present invention, since the pretreatment is carried out on the surfaces of the straps, excellent solderability can be ensured even though the plating is omitted. Therefore, the nuclear fuel assembly grids of excellent quality can be obtained at reduced cost without causing any environmental problems.
051679086	summary	BACKGROUND The invention relates to a device for recombination of hydrogen and oxygen. A device of this kind, to be described later in greater detail, is known from U.S. Pat. No. 4,911,879 (Heck et al.). An apparatus of that nature is discussed in German Patent No. DE-A-36 04 416 (corresponding to the Klatt et al U.S. Pat. No. 4,755,359). As set forth in detail in the Klatt et al. patent, the problem of eliminating hydrogen from a gas mixture arises in particular in nuclear reactor accidents, in which hydrogen escapes into the oxygen-containing atmosphere of the containment vessel or a pressure suppression system of the nuclear reactor, thus creating the risk of an explosion. To avoid this explosion danger, known methods are employed to eliminate the hydrogen through catalytically supported recombination with oxygen to form steam. Especially suitable catalyst materials for this purpose and hence also within the scope of the present invention are described in German Patent No. DE-A-37 25 290. Since a catalyst of this kind forms part of the safety equipment, which is only supposed to operate in the event of a malfunction, care must be taken to ensure that the catalyst retains its functional ability over very many years of storage. For this purpose, methods are known in which the catalyst is stored in an airtight sealed housing, within the vessel or space in which the hydrogen is to be eliminated in the event of an accident, said housing opening automatically when the accident occurs as a result of the influence of pressure and/or temperature, thus exposing the catalyst to the atmosphere-containing hydrogen and oxygen. During a core meltdown in a reactor pressure vessel (RPV), a temperature rise in the melt of up to 2400.degree. C. is reached, with large quantities of fission products and structural materials being released into the atmosphere of the containment. This results in a mixture of steam and gases in which aerosol particles with a weight concentration of up to 20 g/m.sup.3 can be suspended. The term "aerosol" is used herein in a broad sense to mean a suspension of liquid or solid particles in a gas. Thus for example in the low-pressure path at the beginning of the interaction between the melt and the concrete, 1 to 3 tons of dispersed material can be suspended in the air inside the containment vessel. By far the largest component, more than 95%, is non-radioactive. However, most of the radioactive substances are bound to the aerosol particles. The release of hydrogen during reactor accidents, mentioned at the outset, coincides in time with the above release of aerosols. Model tests have shown that the release of steam occurs practically simultaneously with the beginning of a core meltdown accident, while the release of hydrogen and simultaneously therewith, the release of aerosols, take place only after a certain delay. In the presence of large quantities of steam and a strong flow, the catalytic reaction to remove hydrogen proceeds more slowly. The reaction rate increases exponentially with temperature. It is only when a sufficiently high temperature has been reached on the surface of the catalyst system that a sufficient convection flow develops which is adequate to prevent the aerosol particles contained in the gas mixture from being deposited on the surface of the catalyst. This prevention is aided by the constant generation of reaction steam at the surface of the catalyst system, which becomes constant at a correspondingly high temperature and conversion rate. However, as long as the temperature of the catalyst system is still not sufficiently high during the initial phase, aerosol particles and grease particles contained in the steam can settle on the surface of the catalyst, thus reducing the effective catalyst surface and having a highly negative effect on catalytic reaction. Heck et al. mentioned at the outset, contains a catalyst system inside a cylindrical tube whose two ends are closed off by seals which open automatically in the event of an accident. The tube is mounted vertically in the area to be protected and has a filter system between its lower end and the catalyst system for chemically neutralizing catalyst poisons. The filter system can be a porous ceramic body or a molded fiber structure containing silver nitrate. When the seals at the two ends of the tube open, the atmosphere containing hydrogen penetrates the tube and passes through the filter into the catalyst system, which heats up because of the exothermic reaction, thus generating a gas flow through the tube. Examples cited in Heck et al. of seals which open automatically as a function of temperature are diaphragms made of a plastic which melt at high temperatures, as well as bimetallic sheet metal. The bimetallic sheet metal has no gas-tight seal. On the other hand, plastic diaphragms do not provide reliable long-term gas-tight seals. In addition, in the event of ignition, they can burn and impose a burden on the environment through the release of gases. The steam released initially in the event of an accident, in accordance with the above statements, passes through the rooms of the installation in which circulating pumps, slide bearings, electric motors, etc. are located, thereby carrying with it certain amounts of lubricating and sealing grease. Grease particles that reach the catalyst system can settle out on the catalyst surface, provided their temperature is below the vaporization point of the grease. It has been found that grease deposits of this kind have a highly disadvantageous effect on the action of the catalyst. Even a small amount of grease, only 0.05 g of grease per liter of steam, can prevent the catalytic reaction. To avoid the problems created by the grease, German Patent application P 40 03 833.5, not published previously, describes a protective device for the catalyst system. This protective device essentially consists of filters which are permeable to gas but have a high separation efficiency for aerosols and grease particles. The filters are so-called HEPA (High Efficiency Particulate Air) filters. These filters are made of glass wool and a binder which are highly temperature-resistant (up to about 900.degree. C.). The filters surround the catalyst system in such a way that aerosols and grease particles are kept away from the catalyst surface, while still permitting hydrogen and oxygen to reach this surface. As a result of inclusion by the filter and a correspondingly low heat loss, the temperature of the catalyst surface quickly rises because of the exothermic recombination reaction. As soon as the temperature has reached a value at which grease particles and aerosols can no longer settle on the catalyst surface, the filters open, thus exposing the catalyst system to unimpeded access by the atmosphere of the room to be protected, so that the catalyst system can then produce its total effect. The filters described in that patent application protect the catalyst system in the initial phase of an accident before aerosols and grease particles are deposited, however they cannot prevent the long-term deterioration of the catalyst as a result of catalyst poisons contained in the ambient atmosphere of the vessel, during the storage period prior to an accidental meltdown. The operating time of a reactor is up to forty years. During this long period of time, the devices for recombination of hydrogen and oxygen must maintain total functional ability in a state of readiness. It is known that palladium and platinum as catalyst materials are sensitive to surface contamination and lose their effectiveness. The alloys described in DE-A-37 25 290 are less sensitive, but no results are available on long-term tests on the effects of impurities such as chlorine, sulfur, and the like. SUMMARY OF THE INVENTION The goal of the invention is to design a device of the type described at the outset such that it does not lose its effectiveness either 1) because of a long-term state of readiness or 2) when an accident occurs, as the result of deposition of aerosols and grease particles on the catalyst surface. The solution to the stated goals provides that the catalyst system is located during the readiness state in a housing which is sealed gas-tight, preventing surface contamination of the catalyst surface. Preferably the housing is filled with an inert gas such as argon, nitrogen, hydrogen, or helium under pressure (on the order of 10.sup.5 Pa). On the basis of the design of the device according to the invention, three operating states can be distinguished, namely the readiness state before an accident occurs, a preliminary operating state following the occurrence of an accident, and the final operating state after a temperature is reached on the surface of the catalyst which guarantees effective recombination and at which a negative effect on the catalyst action produced by aerosol or grease deposits need no longer be feared. The occurrence of an accident is linked to a temperature increase to which the first seals, which open as a function of temperature, respond and expose openings in the housing, sealed gas-tight previously, so that the ambient atmosphere can penetrate the housing. The device thus shifts from its readiness state to the preliminary operating state. The response temperature of these first seals in the preferred application of the device is in the range of about 100.degree. C. The position of the catalyst system, the filter system in the housing, as well as the position and size of the openings, are selected so that sufficient hydrogen and oxygen for recombination reach the catalyst system, but an overly strong flow is not produced and grease and aerosol particles are kept away from the filter system, so that they cannot settle on the catalyst surface. The flow, which is relatively weak in this operating state, results in a rapid temperature rise in the catalyst system due to the exothermic reaction of the hydrogen, so that after a relatively short time a temperature above approximately 160.degree. C. is reached. at which a so-called self-sustaining accelerated catalytic reaction takes place. Upon this temperature rise, the response temperature of a second seal which opens as a function of temperature is reached, which then exposes another opening in the housing, thus bringing the device to its final operating state. In this final operating state, the catalyst system is fully exposed to the surrounding gas mixture from which the hydrogen is to be removed without the interposition of the filter system. The seals which open as a function of temperature are preferably soldered to the housing so that a reliable permanently gas-tight connection is produced. By choosing a solder which melts at a given temperature, preferably 100.degree. C. for the first seals and 160.degree. C. for the second seals, the seals can be welded to the housing such that at the melting point of the solder used, the seals are opened. Two embodiments of the invention will now be described in greater detail with reference to the schematic diagrams.
	abstract	A crystal thin film is adopted as a specimen for measurement. A change in the contrast of crystal lattice fringes is measured under a condition that a diffracted wave and other wave are caused to interfere with each other. Thus, an information transfer limit of a transmission electron microscope can be measured quantitatively. Since the measurement is performed with a condition for interference restricted, the information transfer limit of the transmission electron microscope can be quantitatively assessed.
	claims	1. A method comprising:maintaining a containment region at a below atmospheric pressure prior to a high pressure event, wherein the below atmospheric pressure is less than 300 mmHG absolute;identifying the high pressure event for a reactor vessel;releasing coolant into the containment region located between a containment vessel and the reactor vessel to remove decay heat from the reactor vessel, wherein the reactor vessel is substantially surrounded by the containment region;increasing a pressure within the containment region in response to releasing the coolant until the pressure reaches an upper pressure limit; anddecreasing the pressure through condensation until the pressure reaches a lower pressure limit, wherein the pressure is cyclically increased and decreased by alternatively releasing and prohibiting the release of coolant into the containment region. 2. The method according to claim 1, further comprising:condensing the coolant on an inner wall of the containment vessel during an over-pressurization or over-heating event. 3. The method according to claim 1, wherein the below atmospheric pressure prohibits substantially all convective heat transfer between the reactor vessel and the containment vessel prior to releasing the coolant. 4. The method according to claim 1, wherein the containment region remains substantially evacuated of all non-condensable gases both prior to and after releasing the coolant. 5. The method according to claim 1, wherein the containment region is substantially dry prior to the high pressure event. 6. The method of claim 1, wherein an outer surface of the reactor vessel is substantially surrounded by the below atmospheric pressure prior to releasing the coolant. 7. The method of claim 1, wherein the containment region remains substantially evacuated of air and hydrogen gases during normal operation of the reactor module to substantially eliminate all convective heat transfer between the reactor vessel and the containment vessel. 8. The method of claim 1, wherein a release valve mounted to the reactor vessel releases the coolant into the containment region during an emergency condition, and wherein a mixture of hydrogen and oxygen in the containment region is maintained at below combustible limits during the emergency condition without the use of a hydrogen recombiner. 9. An apparatus, comprising:means for maintaining a containment region at a below atmospheric pressure prior to a high pressure event, wherein the below atmospheric pressure is less than 300 mmHG absolute;means for identifying the high pressure event for a reactor vessel; andmeans for releasing coolant from the reactor vessel into the containment region located between a containment vessel and the reactor vessel to remove decay heat from the reactor vessel, wherein the reactor vessel is substantially surrounded by the containment region, wherein a reactor core is submerged in the coolant, and wherein the means for releasing comprises means for controllably releasing the coolant as steam into the containment region when the reactor core becomes over-heated or over-pressurized. 10. The apparatus according to claim 9, wherein a condensation of the steam on an interior wall of the containment vessel reduces pressure in the containment region at approximately the same rate that the released steam adds pressure to the containment region. 11. The apparatus according to claim 9, wherein the steam is released into the containment region to remove a decay heat of the reactor core primarily through condensation of the steam on an inner surface of the containment vessel. 12. The apparatus according to claim 9, wherein the containment region remains substantially evacuated of all non-condensable gases prior to releasing the coolant into the containment region. 13. The apparatus according to claim 9, wherein any hydrogen that is released together with the steam is released at a level that maintains an oxygen-hydrogen mixture within the containment region at a non-combustible level without using a hydrogen recombiner. 14. The apparatus according to claim 9, wherein an inner surface of the containment vessel substantially surrounds the reactor vessel, and wherein the inner surface of the containment vessel is substantially dry prior to releasing the coolant. 15. The apparatus of claim 9, wherein controllably releasing the coolant comprises increasing a pressure in the containment region, wherein the pressure in the containment region is decreased through condensation of the steam in the containment region, and wherein the pressure in the containment region is cyclically increased to an upper pressure limit and decreased to a lower pressure limit by alternatively releasing and prohibiting the release of the steam into the containment region. 16. A method, comprising:maintaining a containment region at a below atmospheric pressure prior to a high pressure event, wherein the below atmospheric pressure prohibits substantially all convective heat transfer between a reactor vessel and a containment vessel which substantially surrounds the reactor vessel;monitoring a pressure associated with the reactor vessel to identify the high pressure event; andin response to identifying the high pressure event, controllably releasing coolant as steam into the containment region located between the containment vessel and the reactor vessel, wherein a reactor core is submerged in the coolant, and wherein the coolant is controllably released as steam into the containment region when the reactor core becomes over-heated or over-pressurized. 17. The method of claim 16, wherein maintaining the containment region at a below atmospheric pressure comprises maintaining the containment region at a pressure that is less than 300 mmHG absolute. 18. The method of claim 16, wherein the steam is released from the reactor vessel into the containment region to remove a decay heat of the reactor core primarily through condensation of the steam on an inner surface of the containment vessel. 19. The method of claim 16, wherein controllably releasing the coolant comprises increasing a pressure in the containment region, wherein the pressure in the containment region is decreased through condensation of the steam in the containment vessel, and wherein the pressure in the containment region is cyclically increased to an upper pressure limit and decreased to a lower pressure limit by alternatively releasing and prohibiting the release of the steam into the containment region. 20. The method of claim 16, wherein maintaining the containment region at a below atmospheric pressure comprises evacuating substantially all non-condensable gases from the containment region prior to identifying the high pressure event. 21. An apparatus, comprising:means for maintaining a containment region at a below atmospheric pressure prior to a high pressure event, wherein the below atmospheric pressure prohibits substantially all convective heat transfer between a reactor vessel and a containment vessel which substantially surrounds the reactor vessel; andin response to identifying the high pressure event, means for controllably releasing coolant as steam into the containment region located between the containment vessel and the reactor vessel to remove decay heat from the reactor vessel, wherein the means for controllably releasing the coolant comprises means for increasing a pressure within the containment region, wherein the pressure is decreased through condensation of the steam in the containment region, and wherein the pressure in the containment region is cyclically increased to an upper pressure limit and decreased to a lower pressure limit by alternatively releasing and prohibiting the release of the steam into the containment region. 22. The apparatus of claim 21, wherein the means for maintaining comprises means for maintaining the containment region at a pressure that is less than 300 mmHG absolute. 23. The apparatus of claim 21, wherein the means for maintaining comprises means for evacuating substantially all air and hydrogen gases from the containment region prior to releasing the coolant.
053612884	claims	1. In a spacer having a matrix of individual cells, each cell for surrounding a fuel rod in a corresponding matrix of fuel rods, said spacer comprising: a plurality of spacer cells; said cells each including stop means for centering said fuel rods with respect to said cells and spring means for biasing said fuel rods into said stop means of said cells; each said spacer cell including upper and lower octagonal crowns, said octagonal crowns panel heights adjoining adjacent cells including means for adjoining like panels from adjacent panel cells in a single thickness along horizontal edges such that said like panels are in substantially vertical, co-planar alignment. said crowns at opposite ends of each octagonal spacer cell having inverted edge means; wherein respective cells surrounding a central cell are inverted with respect to said central cell whereby said crowns form a single thickness in forming upper and lower crown matrices holding adjoining cells of the spacer together. said stop means includes cell legs extending between the crowns with upper and lower stops immediately adjacent the crowns; and, said spring means includes cell legs extending between the crowns defining the required cell springs with spring contact points centrally of the legs with respect to the crowns. a full panel height adjoining the defined subchannel volume between fuel rods; and, half height walls adjoining adjacent cells. said cell legs extending between four full height sides; two adjacent legs define upper and lower stops; and two adjacent legs define springs and spring contact points. half wall heights at one crown panel are defined towards adjoining spacer cells and half wall heights at the other crown end are defined away from said spacer cell. a plurality of spacer cells; said cells each including stop means for centering said fuel rods with respect to said cells and spring means for biasing said fuel rods into said stop means of said cells; each said spacer cell including upper and lower octagonal crowns, said octagonal crown panel heights adjoining adjacent cells including edge means for adjoining like panels in single thickness from adjacent panel cells including a full panel height adjoining the defined sub-channel volume between fuel rods and vertically aligned substantially co-planar half height walls adjoining adjacent cells; and said crowns at opposite ends of each octagonal spacer cell having inverted edge means; and wherein respective cells surrounding a central cell are inverted with respect to said central cell whereby said crowns form a single thickness in forming upper and lower crown matrices holding adjoining cells of the spacer together. said stop means includes cell legs extending between the crowns with upper and lower stops immediately adjacent the crowns; and, said spring means includes cell legs extending between the crowns defining the required cell springs with spring contact points centrally of the legs with respect to the crowns. outer band means surrounding said spacer for abutting a channel at said band means; and, a defined interior aperture of said matrix of spacer cells for receiving a water rod; and, inner band means lining said interior aperture. a plurality of spacer cells; said cells each including stop means for centering said fuel rods with respect to said cells and spring means for biasing said fuel rods into said stop means of said cells; each said spacer cell including upper and lower octagonal crowns, said octagonal crowns panel heights adjoining adjacent cells including edge means for adjoining like panels in single thickness form adjacent panel cells including a full panel height adjoining the defined sub-channel volume between fuel rods and vertically aligned substantially co-planar half height walls adjoining adjacent cells; said crowns at opposite ends of each octagonal spacer cell having inverted edge means; respective cells surrounding a central cell being inverted with respect to said central cell whereby said crowns form a single thickness in forming upper and lower crown matrices holding adjoining cells of the spacer together; wherein said stop means includes cell legs extending between the crowns with upper and lower stops immediately adjacent the crowns; and further wherein said spring means includes cell legs extending between the crowns defining the required cell springs with spring contact points centrally of the legs with respect to the crowns. 2. In a spacer having a matrix of individual cells according to claim 1 and further including: 3. In a spacer having a matrix of individual cells according to claim 1 and further including: 4. In a spacer having a matrix of individual cells according to claim 1 and further including: 5. In a spacer having a matrix of individual cells according to claim 4 and further including: 6. In a spacer having a matrix of individual cells according to claim 4 and further including: 7. In a spacer having a matrix of individual cells, each cell for surrounding a fuel rod in a corresponding matrix of fuel rods, said spacer comprising: 8. In a spacer having a matrix of individual cells according to claim 7 and further including: 9. In a spacer having a matrix of individual cells according to claim 7 and further including: 10. In a spacer having a matrix of individual cells, each cell for surrounding a fuel rod in a corresponding matrix of fuel rods, said spacer comprising:
	claims	1. A method for inspecting an annulus region of a reactor pressure vessel in a nuclear power plant, comprising:positioning a partial track on an annular rim of a core shroud in the reactor pressure vessel such that the track is horizontally movable along the rim;positioning a frame assembly on the partial track, the frame assembly comprising:a frame movably connected to the partial track such that the frame is horizontally movable along the partial track;connecting at least one mast assembly to the frame assembly;connecting at least one mast positioning assembly to the frame assembly;connecting at least one inspection device to the frame assembly;connecting a braking system to the partial track and the frame assembly; andmoving horizontally at least one of the partial track and the frame assembly along the rim, which comprises:activating the braking system to horizontally move the frame assembly along the partial track with the partial track being stationary; anddeactivating the braking system to horizontally move the partial track along the rim of the annular rim of the core shroud and the frame assembly being stationary; andinspecting a component in a limited access area. 2. The method of claim 1, further comprising assessing the inspection results and determining if modification or repair of the component is needed. 3. The method of claim 1, wherein the at least one mast assembly comprises a mast that is capable of becoming rigidly stable in an extended tube form and a retracted rolled form. 4. The method of claim 1, wherein the connecting at least one mast assembly to the frame assembly comprises positioning a first mast assembly on one side of the frame and a second mast assembly on an opposite side of the frame. 5. The method of claim 1, wherein the connecting at least one mast positioning device to the frame assembly comprises positioning a first mast positioning device on one side of the frame and a second mast positioning device on an opposite side of the frame. 6. The method of claim 1, wherein the connecting at least one mast positioning device to the frame assembly comprises positioning a first pan and tilt assembly on one side of the frame and a second pan and tilt assembly on an opposite side of the frame. 7. The method of claim 1, wherein moving the frame assembly along the partial track comprises connecting to the frame assembly a positioning motor and gear combination. 8. The method of claim 1, wherein the inspection device is a camera. 9. A method for inspecting a component in a nuclear power plant, comprising:positioning a partial track on an annular rim of a core shroud in the reactor pressure vessel such that the track is horizontally movable along the rim;positioning a frame assembly on the partial track, the frame assembly comprising:a frame movably connected to the partial track such that the frame is horizontally movable along the partial track;connecting at least one mast assembly to the frame assembly;connecting at least one mast positioning assembly to the frame assembly;connecting at least one inspection device to the frame assembly;connecting a braking system to the partial track and the frame assembly;moving horizontally at least one of the partial track and the frame assembly along the rim, which comprises:activating the braking system to horizontally move the frame assembly along the partial track with the partial track being stationary; anddeactivating the braking system to horizontally move the partial track along the rim of the annular rim of the core shroud and the frame assembly being stationary; andinspecting a component in a limited access area selected from a core annulus, core spray region and feedwater sparger region. 10. The method of claim 9, further comprising lowering the inspection device into an annulus formed between the reactor pressure vessel and the core shroud; and inspecting the core shroud.
	description	One or more embodiments of the present invention relate to thermal interface materials made from graphite sheets under high vacuum condition having no risk of outgassing under ultrahigh vacuum. The boron neutron capture therapy (BNCT) in which neutrons are used has been attracting attention (Non-Patent Document 1), since it can remove a tumor at a deep part for which there is no cure by a routine surgical operation with regard to encephaloma, hepar, melanoma and the like. Examples of a method for generating neutrons used in this therapy include a method using a nuclear reactor and a method using an accelerator. As a simple and safe neutron-generating method, at present, a method using an accelerator has been attracting attention. In the apparatus, neutrons are generated by a method in which protons are gradually accelerated to be made into a proton beam and thereafter a neutron is made by a method in which the proton beam impinge on a metal-made or graphite-made lump called a target (Non-Patent Document 2). Moreover, such an accelerator-type neutron generator is expected to be utilized as an apparatus for nondestructively inspecting the soundness of steel frames in a bridge, and is expected to be utilized in the automobile industry, aircraft industry and space industry (Non-Patent Document 3). In order to generate neutrons with such an accelerator, it is necessary to make the beam have a high intensity. When this high-intensity beam passes through a target, the target results in high temperature and the target is tend to deform by heat. A heat sink for cooling is assembled behind the target and a cooling water circulates in the heat sink for cooling to protect the target from heat generated by the beam. However, a limited portion of the target is periodically intensely heated by the beam, and it follows that the heating is repeated for a long time. As such, there is a fear that not only a target but also a heat sink for cooling are broken by a heat shock. As a metal usually used for the heat sink is radioactivated and obstructs beam, only specific ones can be used. For example, titanium (22 W/mK), vanadium (31 W/mK), palladium (72 W/mK), niobium (54 W/mK), tantalum (58 W/mK) and the like are usable, but these are low in thermal conductivity. As such the heat from a target does not conduct to the whole heat sink and the cooling efficiency is poor. In reducing the thermal resistance, an thermal interface material (TIM: Thermal Interface Material) plays an important role. However, since the interior of an accelerator is kept in an ultra-high vacuum state (10−6 to 10−7 Pa), in the case where heat release grease or a phase change sheet, which is generally used, is adopted, contamination of the interior of the apparatus is caused by outgassing. Moreover, when a TIM containing a metal and inorganic filler is adopted, there is a fear that filler scatters and contaminates the inside of a beam line. Patent document 1: JP-B-4299261 Patent document 2: JP-B-4684354 Non-Patent Document 1: Association for Nuclear Technology in Medicine “Karada Ni Yasashii Kyuukyoku No Gantiryou (Ultimate Cancer Therapy Gentle To The Body) Boron Neutron Capture Therapy”, May, 2011 Non-patent Document 2: YAMAGATA, Y. et al, The 27th World Conference of the International Nuclear Target Development Society State-of-the-art Technologies for Nuclear Target and Charge Stripper Japan, Tokyo, September, 2014 Non-Patent Document 3: Yutaka Yamagata, “RIKEN Accelerator-driven compact Neutron Source RANS” Non-patent Document 4: Y. Hishiyama, A. Yoshida, Y. Kaburagi, Carbon 254, 176(2012) Non-patent Document 5: P. G. Klemens and D. F. Pedraza, Carbon 32 735(1994) Non-patent Document 6: P. G. Klemens, J. W. Bandgap, Materials, 7(4), 332(2000) One or more embodiments of the present invention have been made in view of the above-mentioned circumstances, and one or more embodiments provide a material which is excellent in a characteristic of thermal conductivity as an thermal interface material and has no risk of outgassing or contaminating the interior of an apparatus even under high-vacuum and high-temperature conditions. As a result of diligent researches, the present inventors have found that a graphite sheet eliminates the risk of outgassing even under ultrahigh vacuum and is a promising material as an thermal interface material (TIM). Moreover, the present inventors have found that, even in the case where a graphite sheet is used in an accelerator-type neutron generator, there is no fear of radioactivation or a beam obstruction, and moreover, the graphite sheet can withstand irradiation conditions in which a high-intensity beam is used at a high temperature for a long period of time and is promising especially in such applications. Incidentally, as a kind of graphite sheet, natural graphite has been known (Patent Document 1), and the use of such a material as the TIM is also conceivable. However, the thermal conductivity in the surface direction of a natural graphite sheet is 200 to 500 W/mK or so, and the natural graphite sheet is characterized as being light in weight but weak in sheet strength because powdery or scale-like natural graphite is used as the raw material, and in the case of being broken, there has been a risk that graphite flakes are scattered inside a housing body. A method of directly thermally treating a special polymer film to be graphitized has been developed (hereinafter, described as a polymer-annealing method). The graphite sheet preparation by this method is simple as compared with a preparation method of a conventional natural graphite sheet, and also, the resulting sheet is characterized as being excellent in mechanical properties, and furthermore, characterized in that extremely excellent thermal conductivity is attained (Patent Document 2). Since a graphite sheet prepared by the polymer-annealing method has a high thermal conductivity in the surface direction of 600 to 1600 W/mK, and furthermore, is resistant to bending, impacts or the like, at present, the sheet has been adopted in many mobile terminals. However, as described above, a graphite sheet exhibiting higher thermal conductivity than that of conventional ones under an ultrahigh-vacuum condition has been desired, and especially, a thermal interface material made from graphite sheet under high vacuum condition capable of withstanding irradiation with a high-intensity proton beam under ultrahigh-vacuum and high-temperature conditions has been eagerly desired. On that account, as a result of further studies, by using an aromatic polymer (especially, an aromatic polyimide) as a polymer, making the thickness of the finally resultant graphite sheet lie within the range of 9.6 μm to 50 nm, making the density of the graphite sheet become not less than 1.8 g/cm3 and performing the graphitization at an ultrahigh temperature of not less than 2900° C., a thermal interface material made from graphite sheet under high vacuum condition with a thermal conductivity of not less than 1000 W/mK is prepared. This sheet is a high thermal conducting material at the highest level as a film with a large area which can be easily practically handled, has no risk of outgassing even under ultrahigh vacuum and high temperature, and is greatly high in chemical stability and heat resistance. Accordingly, it is thought that the range of application thereof is extremely wide. A thermal interface material made from graphite sheet under high vacuum condition is characterized in having a thickness of not more than 9.6 μm and not less than 50 nm and a thermal conductivity in the a-b surface direction at 25° C. of not less than 1000 W/mK. It is preferred that a density be not less than 1.8 g/cm3. The graphite sheet of one or more embodiments of the present invention is preferably obtained by thermally treating a polymer film at a temperature of not less than 2900° C. The polymer film is preferably at least one kind selected from among polyamides, polyimides, polyquinoxalines, polyoxadiazoles, polybenzimidazoles, polybenzoxazoles, polybenzthiazoles, polyquinazolinediones, polybenzoxazinones, polyquinazolones, benzimidazobenzophenanthroline ladder polymers and derivatives thereof. The polymer film is preferably an aromatic polyimide. The aromatic polyimide is preferably a polyimide obtained by using either or both of pyromellitic acid anhydride and 3,3′,4,4′-biphenyltetracarboxylic acid dianhydride as the raw material, or by using either or both of 4,4′-diaminodiphenyl ether and p-phenylenediamine as the raw material. One or more embodiments of the present invention also include a graphite substrate material under high vacuum condition and a target substrate material under high vacuum condition, which are prepared from any one of the above-mentioned thermal interface material made from graphite sheet under high vacuum condition. One or more embodiments of the present invention also include a layered type target material for generating neutrons, comprising a neutron-producing metal member and a proton-absorbing metal substrate which are layered, wherein any one of the above-mentioned thermal interface material made from graphite sheet under high vacuum condition is interposed between the neutron-producing metal member and the proton-absorbing metal substrate. Further, one or more embodiments of the present invention include a target module for generating neutrons, comprising a neutron-producing metal member, a proton-absorbing metal substrate and a heat sink member which are layered in this order, wherein any one of the above-mentioned thermal interface material made from graphite sheet under high vacuum condition is interposed between the neutron-producing metal member and the proton-absorbing metal substrate, and any one of the above-mentioned thermal interface material made from graphite sheet under high vacuum condition is interposed between the proton-absorbing metal substrate and the heat sink member. In the target module, it is preferred that the neutron-producing metal member be a beryllium target, the proton-absorbing metal substrate be formed of at least one kind of material selected from among vanadium, niobium and tantalum, and the heat sink member be formed of at least one kind of material selected from among aluminum and titanium. According to the graphite sheet according to one or more embodiments of the present invention, there is no fear of outgassing even under high vacuum and excellent heat release properties are attained because the sheet has an extremely high thermal conductivity in the a-b surface direction at 25° C. of not less than 1000 W/mK. Moreover, even in the case of being used in an accelerator-type neutron generator, there is no fear of radioactivation or a beam obstruction, and furthermore, the sheet can withstand irradiation conditions in which a high-intensity beam is used at a high temperature for a long period of time. Hereinafter, the details of one or more embodiments of the present invention will be described, but the present invention should not be limited to the details given below. <Graphite Sheet> One or more embodiments of the present invention are characterized firstly in the point that used is a graphite sheet with a higher thermal conductivity (not less than 1000 W/mK, preferably not less than 1800 W/mK) compared with the natural graphite sheet with a thermal conductivity of 200 to 500 W/mK or so or the graphite sheet prepared by a conventional polymer annealing method with a thermal conductivity of 600 to 1600 W/mK or so. Such a graphite sheet with a high thermal conductivity is produced by a method in which a polymer film obtained from an aromatic polymer (especially, an aromatic polyimide) is heated to be carbonized and graphitized, and especially, can be produced by making the thickness of the finally resultant graphite sheet lie within the range of 9.6 μm to 50 nm, making the density of the graphite sheet become not less than 1.8 g/cm3 and performing the graphitization at an ultrahigh temperature of not less than 2900° C. <Polymer Raw Material> First, a polymer film raw material used in the production of the graphite sheet according to one or more embodiments of the present invention will be described. The polymer raw material preferably used in the graphite preparation is an aromatic polymer, and the aromatic polymer is preferably at least one kind selected from among polyamides, polyimides, polyquinoxalines, polyoxadiazoles, polybenzimidazoles, polybenzoxazoles, polybenzthiazoles, polyquinazolinediones, polybenzoxazinones, polyquinazolones, benzimidazobenzophenanthroline ladder polymers and derivatives thereof. A film composed of these polymer raw materials may be produced by a known production method. Especially preferred examples of the polymer raw material can include an aromatic polyimide, polyparaphenylene vinylene, and polyparaphenylene oxadiazole. Of these, an aromatic polyimide prepared through a polyamic acid from an acid dianhydride (especially an aromatic acid dianhydride) and a diamine (especially an aromatic diamine) which are described below is especially preferred as the polymer raw material for the graphite preparation. Examples of the acid dianhydride that can be used for the synthesis of the aromatic polyimide include pyromellitic acid anhydride, 2,3,6,7-naphthalenetetracarboxylic acid dianhydride, 3,3′,4,4′-biphenyltetracarboxylic acid dianhydride, 1,2,5,6-naphthalenetetracarboxylic acid dianhydride, 2,2′,3,3′-biphenyltetracarboxylic acid dianhydride, 3,3′,4,4′-benzophenonetetracarboxylic acid dianhydride, 2,2-bis(3,4-dicarboxyphenyl)propane dianhydride, 3,4,9,10-perylenetetracarboxylic acid dianhydride, bis(3,4-dicarboxyphenyl)propane dianhydride, 1,1-bis(2,3-dicarboxyphenyl)ethane dianhydride, 1,1-bis(3,4-dicarboxyphenyl)ethane dianhydride, bis(2,3-dicarboxyphenyl)methane dianhydride, bis(3,4-dicarboxyphenyl)ethane dianhydride, oxydiphthalic acid dianhydride, bis(3,4-dicarboxyphenyl)sulfone dianhydride, p-phenylenebis(trimellitic acid monoester acid anhydride), ethylenebis(trimellitic acid monoester acid anhydride), bisphenol A bis(trimellitic acid monoester acid anhydride), and analogues thereof, and those can be used alone or in combination of two or more kinds thereof as an arbitrary ratio mixture. In particular, from the viewpoints of a tendency for the orientation property of a polyimide film to be heightened as the film is made to have a more rigid polymer structure and the availability, pyromellitic acid anhydride and 3,3′,4,4′-biphenyltetracarboxylic acid dianhydride are especially preferred. Examples of the diamine that can be used for the synthesis of the aromatic polyimide include 4,4′-diaminodiphenyl ether, p-phenylenediamine, 4,4′-diaminodiphenyl propane, 4,4′-diaminodiphenyl methane, benzidine, 3,3′-dichlorobenzidine, 4,4′-diaminodiphenyl sulfide, 3,3′-diaminodiphenyl sulfone, 4,4′-diaminodiphenyl sulfone, 4,4′-diaminodiphenyl ether, 3,3′-diaminodiphenyl ether, 3,4′-diaminodiphenyl ether, 1,5-diaminonaphthalene, 4,4′-diaminodiphenyl diethylsilane, 4,4′-diaminodiphenyl silane, 4,4′-diaminodiphenyl ethylphosphine oxide, 4,4′-diaminodiphenyl N-methylamine, 4,4′-diaminodiphenyl N-phenylamine, 1,4-diaminobenzene(p-phenylenediamine), 1,3-diaminobenzene, 1,2-diaminobenzene, and analogues thereof, and those can be used alone or in combination of two or more kinds thereof as an arbitrary ratio mixture. Furthermore, from the viewpoints of heightening the orientation property of a polyimide film and the availability, it is especially preferred that 4,4′-diaminodiphenyl ether or p-phenylenediamine be used as the raw material to synthesize the aromatic polyimide. For the preparation of a polyamic acid from an acid dianhydride and a diamine, any known method can be used, and usually, at least one kind of aromatic acid dianhydride and at least one kind of diamine are dissolved in an organic solvent, and the obtained organic solvent solution of a polyamic acid is stirred under a temperature-controlled condition until the polymerization of the acid dianhydride and the diamine is completed to produce the polyamic acid. The solution of the polyamic acid is usually obtained with a concentration of 5 to 35 wt %, preferably 10 to 30 wt %. In the case where the concentration lies within this range, suitable molecular weight and solution viscosity can be attained. It is preferred that substantially equimolar amounts of an acid dianhydride and a diamine be dissolved in the raw material solution, and for example, the mole ratio is 1.5:1 to 1:1.5, preferably 1.2:1 to 1:1.2 and more preferably 1.1:1 to 1:1.1. <Synthesis of Polyimide, Film Formation> As a production method of a polyimide, a heat-curing method in which a polyamic acid as a precursor is imide-converted by heating and a chemically curing method in which a polyamic acid is imide-converted using a dehydrating agent typified by an acid anhydride such as acetic anhydride and a kind of tertiary amine as an imidation accelerator such as picoline, quinoline, isoquinoline and pyridine can be exemplified, and either thereof may be used. The chemically curing method is preferred, in the point that the coefficient of linear thermal expansion of the resulting film is likely to be small, the elastic modulus thereof is likely to be high, the birefringence thereof is likely to be large, the film is not broken even when tension is applied thereto during annealing, and moreover, graphite of good quality can be obtained. Moreover, the chemically curing method is also excellent in an aspect of the enhancement in thermal conductivity of a graphite film. With regard to the high thermal conducting graphite sheet (with a thermal conductivity of not less than 1000 W/mK) used in one or more embodiments of the present invention, the thickness thereof lies within the range of 9.6 μm to 50 nm, and in order to obtain the graphite sheet with a thickness lying within such a range, it is preferred that the thickness of the raw material polymer film lie within the range of 18 μm to 120 nm. This is because there are many cases in which the thickness of the finally resultant graphite sheet generally becomes 60 to 30% or so of the thickness of a starting polymer film with a thickness of not less than 1 μm and becomes 50 to 20% or so of the thickness of a starting polymer film with a thickness of not more than 1 μm. Thus, finally, in order to obtain a graphite sheet with a thickness of 9.6 μm to 50 nm, it follows that the thickness of a starting polymer film preferably lies within the range of not more than 30 μm and not less than 100 nm. On the other hand, with regard to the length direction, there are many cases in which the dimension is reduced to 100 to 70% or so of the dimension of a starting polymer film. The polymer film can be produced from the polymer raw material or the synthetic raw material thereof by any of the known various methods. For example, an organic solvent solution of a polyamic acid as the polyimide precursor is cast on a support such as an endless belt and a stainless steel drum and dried and imidized to produce the polyimide film. Specifically, the method for producing a film by a chemically curing method is as follows. First, to the polyamic acid solution, a stoichiometric amount or more of a dehydrating agent and a catalytic amount of an imidation accelerator are added, the solution is cast or applied on a support plate or a support such as an organic film including PET, a drum or an endless belt to be formed into a film shape, and the organic solvent is made to evaporate to obtain a film having a self-supportability. Then, this film is imidized while further being heated and dried to obtain a polyimide film. It is preferred that the temperature at the time of heating lie within the range of 150° C. to 550° C. Furthermore, it is preferred that a process of fixing or stretching the film to prevent the shrinkage be included in the production process of the polyimide. This is because the conversion to graphite proceeds more easily by using a film in which the molecular structure and the higher order structure thereof are controlled. That is, for making the graphitization reaction proceed smoothly, it is necessary for carbon molecules in the carbon precursor to be rearrayed, and it is presumed that the conversion to graphite easily proceeds even at a low temperature since the number of carbon molecules to be rearrayed can be minimized in a polyimide having an excellent orientation property. <Carbonization and Graphitization> Next, a method for carbonization and graphitization of a polymer film typified by a polyimide will be described. In one or more embodiments of the present invention, a polymer film as a starting material is preheated in an inert gas to be carbonized. As the inert gas, nitrogen, argon or a mixed gas of argon and nitrogen is preferably used. The preheating is usually performed at 100° C. or so. The temperature increasing rate to the preheating temperature is not particularly limited, and for example, the rate can to 5 to 15° C./minute. At a stage of the preliminary treatment, effective is applying a pressure in the surface direction to the degree, which doesn't cause breakage of a film, so as not to make the film lose the orientation property of the starting polymer film. A film carbonized by the above-mentioned method is fitted to the inside of a high-temperature furnace to perform graphitization. It is preferred that a carbonized film be fitted in a state of being sandwiched between CIP materials or glassy carbon substrates. Graphitization is usually performed at a high temperature of not less than 2600° C., and in order to create such a high-temperature atmosphere, a current is usually allowed to flow directly through a graphite heater and the Joule heat is utilized to perform heating. Graphitization is performed in an inert gas, and as the inert gas, argon is the most suitable and the argon may be added with a small amount of helium. The higher the treatment temperature is, the better quality the graphite after being converted can have. There are many cases in which, by pyrolysis and carbonization, the area of the carbonized film is contracted by about 10 to 40% or so compared with its original polyimide film, and conversely, the area thereof is expanded by about 10% or so in the process of graphitization. Due to such contraction or expansion, an internal stress is generated in a graphite sheet to generate a strain inside the graphite sheet. Such a strain and an internal stress are relaxed by being treated at a temperature of not less than 2900° C., layers of graphite are arrayed with regularity, and furthermore, the thermal conductivity is heightened. In order to obtain the graphite according to one or more embodiments of the present invention, the temperature of 2600° C. is still insufficient, the treatment temperature is preferably not less than 2900° C., treatment at a temperature of not less than 3000° C. is more preferable, and treatment at not less than 3100° C. is most preferable. Of course, this treatment temperature may be the highest treatment temperature in the graphitization process, and the resultant graphite sheet may be subjected to a reheating treatment (may be thermally treated again) so as to be annealed. In this connection, for example, even when the treatment temperature is set to a temperature of not more than 3700° C. (especially not more than 3600° C., or not more than 3500° C.), an excellent graphite film is obtained. For example, the temperature increasing rate from the preheating temperature to the heat treatment temperature can be 15 to 25° C./minute. For example, the retention time at the treatment temperature is not less than 20 minutes and preferably not less than 30 minutes, and may be not less than 1 hour. Although the upper limit of the retention time is not particularly limited, the upper limit is usually not more than 5 hours, and especially, may be not more than 3 hours or so. In the case of being thermally treated at a temperature of not less than 3000° C. to be graphitized, it is preferred that the inner atmosphere of a high-temperature furnace be pressurized by the inert gas. When the heat treatment temperature is high, carbon begins to sublime from the sheet surface, and deterioration phenomena such as expansion of a hole or a crack on the graphite sheet surface and film thinning are caused, but such deterioration phenomena can be prevented by pressurizing and an excellent graphite sheet can be obtained. For example, the atmospheric pressure (gauge pressure) of a high-temperature furnace by an inert gas is not less than 0.10 MPa, preferably not less than 0.12 MPa and further preferably not less than 0.14 MPa. Although the upper limit of the atmospheric pressure is not particularly limited, for example, the upper limit is not more than 2 MPa, and especially, may be not more than 1.8 MPa or so. After the heat treatment, for example, the temperature needs only to be dropped at a rate of 30 to 50° C./minute. <Features of Graphite Sheet> From the viewpoint that the thinner the thickness of the graphite sheet used in one or more embodiments of the present invention is, the more the graphite sheet is excellent in high thermal conductivity, the thickness thereof is preferably not more than 9.6 μm. The reason is presumed to be as follows. That is, in the graphite sheet production by a polymer-annealing method, it is considered that, at the time of the graphitization reaction, the graphite structure is formed on the outermost surface layer of the polymeric carbonized sheet and grows toward the inside of the film. When the film thickness of the graphite sheet becomes thick, the graphite structure of the inside of the carbonized sheet is disturbed at the time of graphitization and a cavity or a deficit portion is easily formed. Conversely, when the sheet becomes thin, graphitization of the graphite layer structure in a well-ordered state proceeds from the sheet surface to the inside thereof, and as a result, a well-ordered graphite structure is easily formed in the whole sheet. It is considered that a graphite sheet exhibiting high thermal conductivity is formed because the graphite layer structure is well-ordered as described above. On the other hand, in the preparation method of one or more embodiments of the present invention, when the thickness of a graphite sheet is not more than 50 nm, it is difficult to exhibit high thermal conductivity. The reason for this has not been necessarily elucidated yet, and when the thickness of a graphite sheet prepared by the method disclosed herein is not more than 50 nm, the sheet is made rich in flexibility but made poor in elasticity. Since it has been known that most of the thermal conduction of a graphite sheet is caused by a lattice vibration (phonon), it is presumed that this is because the reduction in elasticity of a film inhibits the expression of high thermal conductivity. It is difficult to prepare a graphite sheet which has a thickness of not more than 50 nm and is rich in elasticity. As described above, the thickness of the graphite sheet ranges from 9.6 μm to 50 nm, and is preferably 7.5 μm to 50 nm, more preferably 6.5 μm to 100 nm, further preferably 5.0 μm to 100 nm and most preferably 3.0 μm to 200 nm. A sheet thinned in thickness sticks to the substrate surface along the irregularity of the substrate, and once the sheet has stuck thereto, the sheet cannot be removed without using a tape or the like. When the thickness of a graphite sheet is more than 9.6 μm, the sheet is not preferred because there are cases where the graphite structure of the inside of the carbonized sheet is disturbed at the time of graphitization and a cavity or a deficit portion is easily formed. Moreover, when the thickness of a graphite sheet is less than 50 nm, the sheet is made rich in flexibility but made poor in elasticity, and is not preferred because there are cases where the expression of high thermal conductivity is inhibited. It is preferred that the density of the graphite sheet not be less than 1.8 g/cm3. In general, a high thermal conducting graphite sheet has a very dense structure in which a deficit portion or a cavity does not exist. When a deficit portion or a cavity exists in a graphite sheet, the density is decreased and there is also a tendency for thermal conductivity to be lowered. From this, it is preferred that the graphite be large in density, and the density is not less than 1.8 g/cm3, more preferably not less than 2.0 g/cm3 and most preferably not less than 2.1 g/cm3. The upper limit of the density is not more than 2.26 g/cm3, and may be not more than 2.20 g/cm3. As compared with highly oriented pyrolytic graphite (HOPG) prepared by further treating pyrolytic graphite (thermal decomposition graphite), which is obtained by supplying an organic gas such as methane onto a heated substrate and making the resultant grow out in a vapor phase therefrom, at a high temperature, a graphite sheet obtained by carbonizing and graphitizing such a polymer film used in one or more embodiments of the present invention also has a feature that no trace of the pyrolytic graphite exists. The pyrolytic graphite has a columnar structure, and even if this is subjected to a high-temperature treatment to prepare HOPG, this columnar grain boundary structure does not disappear completely. The average crystal grain diameter (domain size) of the graphite used in one or more embodiments of the present invention may be not more than 10 μm, may be not more than 7 μm and may be not more than 5 μm. Although it is advantageous for the achievement of high thermal conductivity to make the crystal grain diameter large, the graphite sheet used exhibits excellent thermal conductivity even when the average crystal grain diameter is not more than 10 μm. It is presumed that this is because the graphite sheet used is a high-quality graphite having no columnar grain boundary structure as described above. In the first place, the reason why the thermal conductivity is affected by the crystal grain diameter is because phonons, which contribute to thermal conductivity, are scattered at the crystal grain boundary. However, in the high-quality graphite, scatter of phonons becomes less dependent on a crystal grain diameter of small size. It is interpreted that this is because only a kind of scatter called the umklapp process becomes dominant in the high-quality graphite (Non-Patent Document 4). In this connection, for example, the average crystal grain diameter of a graphite sheet used is not less than 2 μm, preferably not less than 3 μm and more preferably not less than 4 μm. Moreover, for example, the average crystal grain diameter (domain size) is not less than 0.1 times the thickness of the graphite sheet, preferably not less than 1 time the thickness thereof and further preferably not less than 2 times the thickness thereof. Although the graphite sheet used in one or more embodiments of the present invention has a thermal conductivity in the a-b surface direction at a temperature of 25° C. of not less than 1000 W/mK, the thermal conductivity is preferably not less than 1800 W/mK, more preferably not less than 1960 W/mK, further preferably not less than 2000 W/mK, especially preferably not less than 2050 W/mK and most preferably not less than 2100 W/mK. There has been reported a theoretical limit value of the thermal conductivity in the graphite a-b surface direction of 1910 W/mK (Non-Patent Documents 5 and 6), and the thermal conductivity of not less than 1960 W/mK largely exceeds this limit value and is a result which had not been expected before. In this connection, for example, the thermal conductivity may be not more than 2400 W/mK and may be not more than 2300 W/mK. <Graphite Substrate Material Under High Vacuum Condition> The graphite sheet is recommended to be used for a thermal interface material (TIM) under high vacuum (not more than 10−4 Pa, for example, 10−6 to 10−7 Pa or so or not more than 10−7 Pa), and the graphite sheet itself can be used as a graphite substrate, and furthermore, can be used as a substrate prepared by being layered together with another base material. The graphite sheet does not contain impurities other than blacklead and is of high quality because the graphite sheet has already been subjected to graphitization at a temperature of not less than 2900° C. As such, even under high vacuum, and furthermore, even if being locally heated, outgassed components are not generated. In this connection, the graphite sheet is chemically stable, and as necessary, the graphite sheet may be used for applications other than the application under a high vacuum atmosphere. Examples of the atmosphere other than the high vacuum atmosphere include nitrogen, argon, neon, helium, hydrogen and the like. <Target Substrate Material Under High Vacuum Condition> Moreover, examples of the new application of the graphite sheet according to one or more embodiments of the present invention other than the TIM include a target substrate material under high vacuum condition which can be used under a high vacuum and highly reactive atmosphere by taking advantage of the property of being of high purity and being chemically stable. The target substrate material under high vacuum condition means a material prepared by bonding a target and a heat sink together using a graphite sheet by means of heat, pressurization, a laser or the like or a layered material prepared by mounting a target on a graphite sheet by a vapor deposition method, a sputtering method or an electrodeposition method, and the target can be irradiated with various kinds of beams to take out a reaction product between the target and the beam. The graphite sheet can be suitably used for such an application under a high vacuum and highly reactive atmosphere. As the beam, protons, neutrons, ions (heavy atoms, light atoms) and the like can be used. The graphite sheet does not affect the reaction product between any of these beams and the target, and contributes to the heat dissipation from the target. The source material for the target and the peripheral material thereof (heat sink material, casing material and the like) is not particularly limited, examples thereof include lithium, beryllium, boron, carbon, calcium, gold, silver, copper, aluminum, titanium, palladium, vanadium, tantalum, niobium, stainless steel, brass, molybdenum, and technetium, and moreover, examples thereof may include a doped product prepared with one kind thereof and a doped product prepared with combined two or more kinds thereof. Furthermore, an airtight container which is made of one kind of the element or combined two or more kinds thereof and allows the inside thereof to be filled with a gas such as hydrogen, helium, argon and nitrogen may be adopted. <Target Module for Generating Neutrons> The graphite sheet can also be used as a material for a target supporting substrate, an accelerator, an apparatus for generating neutrons, a sensor for a nuclear reactor, a beam sensor or the like, in addition to the graphite substrate material and target substrate material described above. Hereinbelow, as an example of such application technologies, an accelerator-type neutron generator will be given as an example to be explained. FIG. 1 is a schematic perspective view showing an example of the target module for generating neutrons constituting the center of a neutron generator. The target module 70 for generating neutrons is provided with a substrate 1 for fixing a target, and a layered type target material 60 for generating neutrons composed of a neutron-producing metal member (target) 10 and a proton-absorbing metal substrate 30 which is layered at the back side of this neutron-producing metal member 10 and has an outer circumference being a size larger than that of the neutron-producing metal member 10. The substrate 1 and the layered type target material 60 are objects to be irradiated with a beam, and at the back side of this layered type target material 60, a heat sink member 40 for cooling the layered type target material 60 is connected. And then, to the rear side of this heat sink member 10, a moderator 50 for making protons decelerate is fixed. The neutron generator is provided with an accelerator (not illustrated) for generating accelerated protons and a neutron flight unit (not illustrated), in addition to such a target module 70 for generating neutrons, and protons from the accelerator are made to collide with the neutron-producing metal member 10 under high vacuum (not more than 10−4 Pa) to produce neutrons. And then, the protons produced are made to pass through the proton-absorbing metal substrate 30, the heat sink member 40 and the moderator 50, which exist at the back side of the neutron-producing metal member 10, and made to reach the neutron flight unit (not illustrated) to be used for various kinds of applications such as the boron neutron capture therapy and the nondestructive inspection. In such a target module 70 for generating neutrons, the layered type target material 60 for generating neutrons becomes high in temperature by the reaction with high-energy protons. In order to cool the layered type target material 60, the heat sink member 40 is attached thereto, and the heat sink member as the illustrated example is a water-cooled one. Specifically, the heat sink member 40 as the illustrated example is provided with a chamber (jacket) 42 into which cooling water is introduced and two water flow pipes 41 for supplying/draining water to/from this jacket 42, and water in the jacket 42 can be brought into contact with the layered type target material 60 to cool the layered type target material 60. However, in the target module 70, a limited portion of the neutron-producing metal member 10 is periodically intensely heated (subjected to ultraheating) by the proton beam, and it follows that the heating is repeated for a long period of time. As such, just by simply being cooled with water, there is a fear that both of the layered type target material 60 and the heat sink member 40 are broken by a heat shock. On that account, in the module according to one or more embodiments of the present invention, a graphite sheet is used as a thermal interface material (TIM). In the illustrated example, the graphite sheet-made thermal interface materials 20 and 25 are interposed between the neutron-producing metal member (target) 10 and the proton-absorbing metal substrate 30 and between the proton-absorbing metal substrate 30 and the heat sink member 40, respectively. At least one (preferably both) of such graphite-made thermal interface materials 20 and 25 can be incorporated into the target module 70 to heighten the heat-release properties of the layered type target material 60, and the breakage thereof can be prevented. Moreover, since such a graphite-made TIM is a highly heat-resistant material, the material itself is not broken under a high temperature condition. In this connection, in the illustrated example, the graphite-made thermal interface material 20 between the neutron-producing metal member (target) 10 and the proton-absorbing metal substrate 30 has a circular shape equal to that of the neutron-producing metal member 10, and the graphite-made thermal interface material 25 between the proton-absorbing metal substrate 30 and the heat sink member 40 has a hollow disk-type (doughnut-type) shape, but the planar shape of the thermal interface material is not particularly limited as long as respective members between which the thermal interface material is interposed can be thermally bonded together and the thermal interface material may exist so as to overlap with the locus of a proton beam or a neutron beam. The graphite sheet is chemically stable, and even if the graphite sheet overlaps with the locus of a proton beam or a neutron beam, the graphite sheet does not adversely affect these beams, and moreover, the graphite sheet is not radioactivated. In the target module 70, as the source material for the neutron-producing metal member 10, beryllium can be adopted. As the source material for the proton-absorbing metal substrate 30, one kind or two or more kinds of metal such as vanadium, niobium and tantalum can be adopted. As the source material for the heat sink member 40, one kind or two or more kinds of metal such as aluminum and titanium can be adopted. The present application claims the profit of the right of priority to Japanese Patent application No. 2014-246129 filed on Dec. 4, 2014. The entire contents of the specification of the Japanese Patent application No. 2014-246129 filed on Dec. 4, 2014, are incorporated by reference herein. Hereinafter, the embodiment according to one or more embodiments of the present invention will be described in more detail with reference to examples. Of course, the present invention should not be limited to these examples, not to mention that various embodiments are possible with regard to the small details. (Evaluation Methods for Physical Properties) <Film Thickness> Each of the thicknesses of a polymer film as the raw material and a graphite sheet has an error of plus/minus 5 to 10% or so. As such, the ten-point average thickness of the film or sheet obtained was defined as the thickness of the sample in one or more embodiments of the present invention. <Density> With regard to the density of the graphite prepared, a graphite sheet was measured for the volume by means of a helium gas replacement type density meter [AccuPyc II 1340 SHIMADZU CORPORATION] and separately measured for the mass to calculate the density from the equation of Density (g/cm3)=Mass (g)/Volume (cm3). In this connection, the density of a graphite sheet with a thickness of not more than 200 nm failed to be measured by this method because the magnitude of the error was too large. As such, in the case of calculating the thermal conductivity from the thermal diffusivity of a graphite sheet with a thickness of not more than 200 nm, the density thereof was assumed to be 2.1 to calculate the thermal conductivity thereof. <Thermal Conductivity> A graphite sheet was measured for the thermal diffusivity using a thermal diffusivity measuring apparatus (ADVANCE RIKO, Inc., the “LaserPit” apparatus) by a periodic heating method at a frequency of 10 Hz under vacuum (10−2 Pa or so) at 25° C. This was a method of attaching a thermocouple to a point apart by a certain distance from an irradiation point irradiated with a laser beam to be heated and measuring a change in temperature at the point. By this method, the thermal conductivity (W/mK) was calculated by multiplying the thermal diffusivity (m2/s) by the density (kg/m3) by the specific heat (798 kJ/(kg·K)). In this context, in the case of using this apparatus, a graphite sheet with a thickness of not less than 1 μm can be measured for the thermal diffusivity, but the thermal diffusivity of a graphite sheet with a thickness of not more than 1 μm failed to be accurately measured because the magnitude of the measurement error became too large. On that account, using a periodic heating radiant temperature measuring method (the Thermoanalyzer TA3 available from BETHEL Co., Ltd.) as the second measuring method, the measurement was performed. This was an apparatus in which periodic heating is performed by a laser and temperature measurement is performed by a radiation thermometer, and even a sample of a graphite sheet with a thickness of not more than 1 μm can be measured since the radiation thermometer and a graphite sheet are in a completely non-contact state at the time of measurement. In order to confirm the reliability of measured values of the two apparatuses, with regard to some samples, the sample was measured by the respective two apparatuses and it was confirmed that the two numerical values coincide with each other. In the apparatus of BETHEL Co., Ltd., the frequency of periodic heating can be made to vary within a range of at most 800 Hz. That is, this apparatus is characterized in the point that temperature measurement, which is usually performed in a contact manner by a thermocouple, is performed by a radiation thermometer and the measurement frequency can be made to vary. In principle, a constant thermal diffusivity as a measured value should be attained even when the frequency is made to vary, and thus, in the measurement using this apparatus, the frequency was made to vary and the measurement of a thermal diffusivity was performed. In the case where a sample with a thickness of not more than 1 μm was measured, there were many cases in which the measured value fluctuates when measured at a frequency of 10 Hz or 20 Hz, but the measured value became almost constant when measured at each of frequencies ranging from 70 Hz to 800 Hz. On that account, a measured value (a numerical value measured at frequency ranging from 70 Hz to 800 Hz) obtained as a constant value irrespective of the frequency was defined as the thermal diffusivity. A hardener comprising 20 g of acetic anhydride and 10 g of isoquinoline was mixed to 100 g of an 18 wt % DMF solution of a polyamic acid synthesized from pyromellitic acid anhydride and 4,4′-diaminodiphenyl ether in a proportion of 1/1 in terms of the mole ratio to be stirred, and after being centrifuged to be degassed, the liquid was cast and applied on a sheet of aluminum foil. The liquid was stirred and then centrifuged to be degassed while being cooled to 0° C. The layered product of the sheet of aluminum foil and the polyamic acid solution was heated at 120° C. for 150 seconds and at 300° C., 400° C. and 500° C. for 30 seconds respectively, and thereafter the sheet of aluminum foil was removed to prepare a polyimide film (Polymer sample A) with a different thickness. Moreover, as in the case of the sample A, pyromellitic acid anhydride and p-phenylenediamine were used as the raw material to prepare a polyimide film (Polymer sample B), and 3,3′,4,4′-biphenyltetracarboxylic acid dianhydride and p-phenylenediamine were used as the raw material to prepare a polyimide film (Polymer sample C). With regard to the thickness of the polyimide film, by adjusting the casting speed and the like, several kinds of films differing in thickness within the range of 18 μm to 100 nm were prepared. Eight kinds of polyimide films (Polymer sample A) with respective thicknesses ranging from 18 μm to 100 nm, three kinds of polyimide films (Polymer sample B) with respective thicknesses ranging from 9.2 to 1.1 μm and three kinds of polyimide films (Polymer sample C) with respective thicknesses ranging from 7.5 to 1.0 μm were placed in an electric furnace, and the internal temperature thereof was elevated to 1000° C. at a rate of 10° C./minute in a nitrogen gas atmosphere and the temperature was kept at 1000° C. for 1 hour to perform a preliminary treatment. Next, the carbonized sheet obtained was fitted to the inside of a cylindrical graphite heater, and the internal temperature thereof was elevated to a treatment temperature (maximum temperature) of 2900° C., 3000° C., 3100° C. or 3200° C. at a temperature increasing rate of 20° C./minute. The sheet was held in place for 30 minutes or 120 minutes (treatment time) at this temperature, and afterward, the internal temperature was dropped at a rate of 40° C./minute to prepare a graphite sheet. The treatment was performed under a positive pressure of 0.15 MPa in an argon atmosphere. Values of the thickness (μm), density (g/cm3) and thermal conductivity (W/mK) of the graphite sheet obtained were shown in Table 1. It has been found that, when the film has a thickness lying within the range shown in this table, all of the samples exhibit excellent thermal conductivity of not less than 1000 W/mK, preferably not less than 1800 W/mK, after being subjected to a heat treatment at 2900° C. or higher for 30 minutes or more. TABLE 1MaximumThermalProductionPolymerTemperatureTreatmentThicknessDensityConductivityExampleSample(° C.)Time Minute )(μm)(g/cm3)(W/mK)1A3000309.62.0519602A3000304.72.0720103A3000302.12.1120804A3000301.22.2221005A3000300.722.2320806A3000300.312.221207A3000300.14—21208A3000300.06—19909A2900301.22.18180010A29001201.22.21188011A3100302.12.12215012A3200302.02.16223013B3000304.32.15202011B3000302.62.20210015B3000300.62.20198016C3000303.42.20204017C3000302.12.10200018C3000300.52.181980 Although only a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from embodiments disclosed herein. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims. 1: Substrate for fixing a target 10: Neutron-producing metal member 20, 25: Thermal interface material 30: Proton-absorbing metal substrate 40: Heat sink member 60: Layered type target material for generating neutrons 70: Target module for generating neutrons
	description	With reference to the accompanying drawings, embodiments according to the present invention are explained. FIG. 1 is a block diagram showing a first embodiment of a radiation image taking apparatus according to the present invention. The radiation image taking apparatus of the first embodiment generally includes an X-ray source 10 for irradiating X-rays to a sample to be measured; a grid 20 for removing dispersion rays contained in the X-rays passing through the sample to be measured; a flat panel type X-ray sensor 30 for detecting the X-rays passing through the grid 20; an image correcting portion 40 for correcting a detected image outputted from the flat panel type X-ray sensor 30; an operation process portion 50 for carrying out an equalizing process of X-ray detection signals based on the X-ray detection signals outputted from the image correction portion 40; and an image displaying device 60 for outputting an image information outputted from the operation process portion 50 to display. Incidentally, the X-ray source 10 corresponds to the radiation irradiation device; the flat panel type X-ray sensor 30 corresponds to the radiation detecting device; the operation process portion 50 corresponds to the operation process device; and the image displaying device 60 corresponds to the image outputting device, of the present invention, respectively. Hereunder, structures and functions of the respective portions are explained. The X-ray source 10 irradiates cone-shape X-ray beams (hereinafter referred to as xe2x80x9cX-raysxe2x80x9d) to the sample to be measured. As shown in FIG. 2, when X-rays are ejected to detection pixel groups 31 of the flat panel type X-ray sensor 30 through the grid 20, the projection image is enlarged by a magnification determined by a distance L1 from the X-ray source 10 to the grid 20 and a distance L from the X-ray source 10 to the flat panel type X-ray sensor 30. In other words, a relationship between a pitch GP of the grid 20 and a pitch GPxe2x80x2 of the projection image can be expressed by the following equation (1): GPxe2x80x2=GPxc2x7L/L1xe2x80x83xe2x80x83(1) Also, as a characteristic structure of the present invention, the pitch or length GP of the slit of the grid 20 has a relationship such that the length obtained by multiplying odd-number to a half pitch of the projection image on the X-ray sensor 30 through the grid 20 is equal to a pitch SP of detection pixels of the flat panel type X-ray sensor 30. Namely, a relationship between the pitch GPxe2x80x2 of the projection image and the pitch SP of the detection pixel can be expressed by the following equation (2): (GPxe2x80x2/2)(2nxe2x88x921)=SPxe2x80x83xe2x80x83(2), wherein n represents a positive integer. More specifically, the pitch GP of the grid 20 has a relationship of the following equation (3) from the above equations (1) and (2): GP=2xc2x7SPxc2x7L1/Lxc2x7(2nxe2x88x921)xe2x80x83xe2x80x83(3) More specifically, in the first embodiment, the pitch GP of the grid 20 is structured such that when the X-rays are projected to the flat panel type X-ray sensor 30 through the grid 20, a length of a half of the pitch GPxe2x80x2 of the projection image is equal to the pitch SP of the detection pixels 31. Incidentally, the pitch GP of the grid 20 or slits is not limited to the above-mentioned relationship of the present embodiment, and there may be a relationship such that a length obtained by multiplying odd-number to the half pitch GPxe2x80x2 of the projection image, such as three times, five time, seven time . . . , is equal to the pitch SP of the detection pixels 31 of the flat panel type X-ray sensor 30. Also, in the grid 20, there are used flakes, such as Pb (lead), W (tungsten) of a high atomic number, U (uranium), through which X-rays do not relatively pass, and Al (aluminum) for a slit portion, through which X-rays pass. Also, a size of the grid 20 is changed according to a size of the flat panel type X-ray sensor 30. The flat panel type X-ray sensor 30, as shown in FIG. 3, includes X-ray detecting base plates 31; capacitors Cs for storing collection carriers through carrier collection electrodes of the X-ray detecting base plates 31; thin film transistors as switching elements 32, which are normally in an off state, for taking out charges stored in the capacitors Cs; a reading circuit 33 in an X-axis direction; and a reading circuit 34 in a Y-axis direction. Incidentally, although FIG. 3 shows a matrix structure consisting of only nine in total, i.e. 3 in a lengthwise direction and 3 in a widthwise direction for the sake of convenience, if necessary, for example, practically, a matrix has a structure of 1024 in a lengthwise direction and 1024 in a widthwise direction. The image correcting portion 40 carries out an operation process through filtration to remove artifacts and the like generated on a detection image. The operation process portion 50, as shown in FIG. 4, equalizes the irregularities of levels of X-ray detecting signals by carrying out the operation process through addition average or moving average with a two-pixel unit of the detection pixels, i.e. signs on an X-axis in the drawing, continuously lined up in a pitch direction of the grid based on the X-ray detection signals outputted from the image correction portion 40. Incidentally, the addition average and moving average are not limited to those of the two-pixel unit, and they may be carried out with a detection pixel group unit of even number continuously lined up in the pitch direction of the grid. The image displaying device 60 displays image information subjected to the operation process, such as various corrections. Incidentally, the image output device according to the present invention is not limited to the image displaying device 60, and it may be a light sensitive substance, such as a printer and a film. Next, operations of the radiation image taking apparatus of the present embodiment as described above are explained. As shown in FIG. 2, X-rays irradiated from the X-ray source 10 and passing through the sample to be measured pass through slits for the respective pitches GP provided on the grid 20 and are projected to the detection pixel groups 31 on the flat panel type X-ray sensor 30. The projected images detected at the detection pixel groups 31 are carrier-converted by the flat panel type X-ray sensor 30 and stored in the respective capacitors Cs. Then, the stored carriers are properly outputted to the image correction portion 40 for filtering, and the pixel information, artifacts of which are removed, is outputted to the operation process portion 50. The image information inputted into the operation process portion 50, for example, as shown in FIG. 4, is subjected to an addition average process or moving average process with two pixels, as a unit, of the detection image group 31 continuously lined up in the pitch direction of the grid 20 (in the drawing, X-axis plus direction). In other words, assuming that a level of the X-ray detection signal detected from each detection pixel is Sn (n represents a detection pixel number and is positive integer), the two-pixel addition average in an area A becomes an average of levels S1 and S2 of the X-ray detection signals of the first and second detection pixels. An average value obtained through the operation process is assigned to the first and second detection pixels. Also, in an area B, an average value of levels Sixe2x88x921 and Si of the X-ray detection signals from the detection pixels of the ixe2x88x921st and i-th is assigned to the respective detection pixels; and in an area C, an average value of levels Snxe2x88x921 and Sn of the X-ray detection signals from the detection pixels of the nxe2x88x921st and n-th is assigned to the respective pixels. As a result, the irregularities in levels of the X-ray detection signals caused by the grid 20 can be solved. Also, the two-pixel moving average is obtained such that, among levels Sn of the X-ray detection signals detected from the respective detection pixels, in the area A, an equalizing process of the levels S1 and S2 of the X-ray detection signals of the first and second detection pixels is carried out; the obtained average value is assigned to the first detection pixel; then, an equalizing process of the levels S2 and S3 of the X-ray detection signals of the second and third detection pixels is carried out; and the obtained average value is assigned to the second detection pixel. The two-pixel moving average as described above is carried out from area A to area C. As a result, irregularities of the levels of the X-ray detection signals can be solved. Further, by the two-pixel moving average, an output image having a higher resolution than that of the two-pixel addition average can be obtained. Incidentally, in the present embodiment, for the sake of explanatory convenience, although it is assumed that the X-ray detection signal levels are uniform, actually, the values obtained from the equalizing process are superposed on the detected X-ray detection signal levels of the sample to be measured. The image information, in which irregularities in the X-ray detection signal levels have been equalized at the operation process portion 50, is outputted to the image displaying device 60. At this time, as shown in FIG. 5, moires caused by the irregularities in the X-ray detection signal levels have been removed, and a clear image can be displayed. By the way, in the present embodiment, after the image correction is carried out at the image correction portion 40, the operation process is carried out at the operation process portion 50 to remove moires. However, after moires are removed, filtering of the structural images may be made at the image correction portion 40. FIG. 6 is a block diagram of a second embodiment of the radiation image taking apparatus according to the present invention. Characteristics of the present embodiment, as shown in FIG. 6, reside in that a driving portion 70 for swinging or moving the grid 20, and an operation portion 80 for operating the driving portion 70 are included. In case a stationary image is taken, the driving portion 70 horizontally swings the grid 20 while facing the flat panel type X-ray sensor 30 in the pitch direction. Thus, it is possible to prevent a resolution of the output image from being reduced by removing moires through the swinging of the grid 20. In other words, in case moires are removed through the equalizing process of a plurality of pixel units, since levels of the equalized X-ray detection signals are assigned to the respective detection pixels to be operated, the levels are slightly deteriorated when compared with the levels of the original X-ray detection signals detected from the respective detection pixels. In order to prevent such a resolution from being lowered, the grid 20 is swung or moved. In case of the stationary picture, since it is not necessary to swing or move the grid 20 at a high speed as in a moving image, it is not required to enlarge a structure of the device so much. Also, in case the moving image is taken, the grid 20 is not swung, and is fixed as in the first embodiment described above. Thus, since it is not required to forcibly swing the grid 20 at a high speed, a good moving image without moires can be taken. Incidentally, the driving portion 70 corresponds to the swinging device of the present invention. The operation portion 80 makes a switching operation in accordance with the stationary image or moving image taking condition. By the way, the operation portion 80 corresponds to the switching device of the grid 20. Since the other structures are the same as those of the first embodiment, explanations of the same are omitted. While the grid 20 in the present embodiment is used for taking images of both stationary image and moving image, in case the grids are provided separately, it is not necessary to use the grid 20 of the invention for the stationary image, and the pitch on the grid can be suitably set. The present invention is not limited to the above-described embodiments and can be modified as described below. An X-ray source 10 for outputting fan beams, a grid 20 and an X-ray detecting device having a one-dimensional matrix arrangement disposed to face the X-ray source 10 with respect to a sample to be measured therebetween may scan the sample to be measured. By using an X-ray source 10 for outputting cone beams, a grid 20 and an X-ray detecting device having a one-dimensional matrix arrangement may scan an area of a sample to be measured to which the cone beams are irradiated. The radiation detecting device is not limited to the flat panel type X-ray sensor 30. It may be a solid state image-taking element, such as a charge-coupled device (CCD). As apparent from the above description, according to the radiation image taking apparatus of the first aspect of the invention, when radiations are projected to the radiation detecting device through the grid, the radiation image is taken by using the grid having such a relationship that a length obtained by multiplying odd-number to a half pitch of a projection image on the radiation detecting device through the grid is equal to a pitch of detection pixels of the radiation detecting device. Then, the radiation detection signals detected from the detection pixels of the radiation detecting device through the grid are subjected to an equalizing process for every pixel groups, each having an even number of detection pixels, continuously lined up in a pitch direction of the grid to thereby remove moires from the output image outputted from the output image device. Even if the positions of the pitches of the slits on the grid and pitches of the detection pixels are slightly displaced, since the equalizing process is carried out with a combination, as a unit, of a high level radiation detection signal and a low level radiation detection signal from the respective even-number detection pixels lined up in the pitch direction of the grid, irregularities of the radiation detection signals can be reduced to a sufficiently practical level. As a result, it is not necessary to keep the pitches of the grid accurately, so that the radiation image taking apparatus can be made economical. Further, since the grid can be fixedly disposed without swing, the apparatus can be miniaturized. According to the radiation image taking apparatus of the second aspect of the invention, the grid used in the radiation image taking apparatus of the first aspect is set to have such a relationship that when radiations are projected to the radiation detecting device through the grid, a length of a half pitch of a projection image is equal to a pitch of a detection pixel of the radiation detecting device. Then, the radiation detection signals detected by the radiation detecting device through the grid are inputted into the operation device, and the equalizing process is carried out for every two detection pixel groups continuously lined up in the pitch direction of the grid to thereby keep reduction in a resolution of the output image outputted from the image output device to a minimum. According to the radiation image taking apparatus of the third aspect of the invention, when a stationary image is taken, since it is not necessary to swing the swinging device at a high speed as in case of taking a moving image, the grid is swung in its pitch direction with respect to the radiation detecting device. In other words, with use of the swinging device, it is not necessary to make corrections by the operation device to thereby prevent a resolution of the output image from being lowered. Also, when a moving image is taken, since it is not required that the grid is forcibly swung at a high speed by stop swinging of the grid with a switching device, a good moving image can be taken and moires can be removed from the output image outputted from the output device. While the invention has been explained with reference to the specific embodiments of the invention, the explanation is illustrative and the invention is limited only by the appended claims.
	summary
039379710	summary	This invention relates to a shield of the kind employed in connection with radiation therapy machines to limit the area of exposure of a patient to cobalt rays or the like such that the radiation rays only strike at the very exact spot intended on the human body. In order that the rays strike only the intended spots, lead shields are positioned between the source of the cobalt rays and the patient's body such that the shields serve to protect those areas of the body that are not to be treated. Conventionally, focused shields are custom-made for each individual and contain an aperture therein having a configuration corresponding to the area of the body that is to be treated so that any cobalt rays directed to an area laterally of the aperture are blocked by the lead shield. Inasmuch as the patients normally require more than one treatment the shields must be very exact in order that the very same spot is uniformly and consistently exposed to the rays each time the patient is treated. The lead shields, which are approximately 2 inches thick, are disposed to intersect a radiation beam and thus block off all rays except those which are in a position to pass through the aperture in the shield. However, because of the thickness of the shields, as conventionally known, all of the rays entering the aperture do not necessarily exit the same because their angular disposition relative to the shield and the aperture sidewalls is such that they strike a sidewall before they have a chance to exit the aperture. Also, because of this aforementioned angularity of the rays relative to the focused shield, which is normally disposed perpendicular to the central, longitudinal axis of the radiation beam, there is also a "dead" spot below that portion of the aperture where the upper or entry edge of the aperture intersects the radiation rays proximal thereto. It is, therefore, a very important object of this invention to provide a method of fabricating a focused shield for use in connection with a radiation therapy machine or the like which the focused shield has a field of radiation aperture configured to permit precise exposure of a predetermined area of a patient's body and in which all of the radiation rays in alignment with the aperture pass therethrough to expose an area of the patient corresponding to the full area and configuration of the aperture. Another very important object of the invention is to provide a focused shield having an aperture therein through which any rays entering the aperture also exit the aperture in an unimpeded manner. It is another very important object of our invention to provide a method and apparatus for use in connection therewith for making a focused shield having an aperture therein that permits all radiation rays entering the aperture to exit therefrom in an unimpeded manner. Yet another important object of the instant invention is to provide a focused shield, as well as a method and apparatus for making the same, in which the focused shield has an aperture in which the sidewalls thereof are disposed to permit all radiation rays in alignment with the aperture to pass therethrough. A still further object of the instant invention is to provide a focused shield having a bevel-walled field of radiation aperture in which the sidewalls thereof are in substantial parallelism with the radiation rays passing through the aperture and proximal a sidewall thereof. A still further object of our invention is to provide a focused shield blank holding fixture adapted especially for use with a band saw or the like to permit cutting an aperture having the desired radiation field outline in which the sidewalls of the aperture are automatically beveled in order that the sidewalls will be substantially parallel with the radiation rays passing thereby and proximal thereto when the focused shield is inserted in a radiation therapy machine.
	claims	1. A linkage mechanism of a scattered ray inhibition apparatus and a radiation field control apparatus, said linkage mechanism comprising:a first timing belt;a second timing belt; anda transmission mechanism between said first timing belt and said second timing belt, wherein said scattered ray inhibition apparatus is mounted on said first timing belt, said radiation field control apparatus is mounted on said second timing belt, the transmission ratio of said transmission mechanism is equal to the ratio of the moving speed of said scattered ray inhibition apparatus to the moving speed of said radiation field control apparatus. 2. The linkage mechanism according to claim 1, wherein said transmission mechanism comprises at least two gears. 3. The linkage mechanism according to claim 2, wherein said transmission mechanism further comprises:a third timing belt connected to said first timing belt; anda fourth timing belt connected to said second timing belt, wherein said at least two gears are disposed between said third timing belt and said fourth timing belt. 4. The linkage mechanism according to claim 1 further comprising a first linear guideway, said scattered ray inhibition apparatus connected to said first timing belt through said first linear guideway. 5. The linkage mechanism according to claim 4 further comprising a second linear guideway, said radiation field control apparatus connected to said second timing belt through said second linear guideway. 6. The linkage mechanism according to claim 5 further comprising an electrical motor configured to supply power to said transmission mechanism. 7. The linkage mechanism according to claim 1 further comprising a second linear guideway, said radiation field control apparatus connected to said second timing belt through said second linear guideway. 8. The linkage mechanism according to claim 7 further comprising an electrical motor configured to supply power to said transmission mechanism. 9. A collimator comprising a linkage mechanism of a scattered ray inhibition apparatus and a radiation field control apparatus, wherein said linkage mechanism comprises:a first timing belt;a second timing belt; anda transmission mechanism between said first timing belt and said second timing belt, wherein said scattered ray inhibition apparatus is mounted on said first timing belt, said radiation field control apparatus is mounted on said second timing belt, the transmission ratio of said transmission mechanism is equal to the ratio of the moving speed of said scattered ray inhibition apparatus to the moving speed of said radiation field control apparatus. 10. The collimator according to claim 9, wherein said transmission mechanism comprises at least two gears. 11. The collimator according to claim 10, wherein said transmission mechanism further comprises:a third timing belt connected to said first timing belt; anda fourth timing belt connected to said second timing belt, wherein said at least two gears are disposed between said third timing belt and said fourth timing belt. 12. The collimator according to claim 9 further comprising a first linear guideway, said scattered ray inhibition apparatus being connected to said first timing belt through said first linear guideway. 13. The collimator according to claim 12 further comprising a second linear guideway, said radiation field control apparatus being connected to said second timing belt through said second linear guideway. 14. The collimator according to claim 9 further comprising a second linear guideway, said radiation field control apparatus being connected to said second timing belt through said second linear guideway. 15. An X-ray machine comprising a linkage mechanism of a scattered ray inhibition apparatus and a radiation field control apparatus, said linkage mechanism comprising:a first timing belt;a second timing belt; anda transmission mechanism between said first timing belt and said second timing belt, wherein said scattered ray inhibition apparatus is mounted on said first timing belt, said radiation field control apparatus is mounted on said second timing belt, the transmission ratio of said transmission mechanism is equal to the ratio of the moving speed of said scattered ray inhibition apparatus to the moving speed of said radiation field control apparatus. 16. The X-ray machine according to claim 15, wherein said transmission mechanism comprises at least two gears. 17. The X-ray machine according to claim 16, wherein said transmission mechanism further comprises:a third timing belt connected to said first timing belt; anda fourth timing belt connected to said second timing belt, wherein said at least two gears are disposed between said third timing belt and said fourth timing belt. 18. The X-ray machine according to claim 15 further comprising a first linear guideway, said scattered ray inhibition apparatus being connected to said first timing belt through said first linear guideway. 19. The X-ray machine according to claim 18 further comprising a second linear guideway, said radiation field control apparatus being connected to said second timing belt through said second linear guideway. 20. The X-ray machine according to claim 15 further comprising a second linear guideway, said radiation field control apparatus being connected to said second timing belt through said second linear guideway.
	summary
050930729	abstract	Process for the radioactive decontamination of metal surfaces, particularly portions of the primary circuits of water-cooled nuclear reactors, characterized in that it comprises subjecting said surfaces to the successive stages of an oxidizing pretreatment with the aid of a solution of potassium permanganate KMnO.sub.4 and nitric acid, rinsing with demineralized water and then reducing treatment in a basic medium with the aid of a solution of alkali metal gluconate of formula HOH.sub.2 C--CHOH--CHOH--CHOH--CHOH--COOM, in which M is an alkali metal chosen from among Na and K, as well as soda NaOH.
039390390	abstract	A nuclear reactor with a reactor core having a plurality of individual core elements is provided with a clamping device for at least some of the core elements, which clamping device includes a plurality of pawls pivotally mounted to the interior of each wall of the hexagonal outer wrapping tube for movement between a position within the wrapper tube and a position extending through an adjacent hole in the side wall of the wrapper tube, and an operating tube axially slidably mounted within the wrapper tube for moving the pawls between their two positions. When the pawls are extended by the operating tube, they will move outwardly a predetermined distance transversely of the core element to cooperatively engage other core elements and clamp the assembly. A lock mechanism is provided to lock the operating tube and wrapper tube in one position of the pawls, preferably the withdrawn position, to assist in inserting and removing the core element.
051204878	description	DETAILED DESCRIPTION OF THE INVENTION When superthermal electrons are heated briefly in a tokamak plasma, the change in the electron distribution function, particularly at high energy, is manifest in a change, or increment in the synchrotron emission. Since the excitation is brief, the changes incurred in both the electron distribution function and the synchrotron emission are transient. Thus, the incremental synchrotron radiation is a two-dimensional pattern in frequency-time space. The details of this pattern are governed by plasma parameters; for example, the higher the plasma density, the faster the decay of the incremental radiation. As is well known in the prior art, high-velocity, superthermal electrons radiate most copiously, but lose energy slowly, so that there can be independent time points in the radiation pattern R (.omega.,t). Dominated by Coulomb collisions and the dc electric field, these electrons mainly flow along the magnetic field, largely immune to temperature fluctuations and other turbulence in the bulk of the ion or electron distributions. Because relatively few parameters govern this response, given powerful analytic tools and the method of this invention, it is possible to determine the parameters from the radiation response. A relatively modest diagnostic embodiment of the current invention relies upon a brief, probing rf signal that leads to the incremental synchrotron signal, and an array of frequency detectors with submillisecond time resolution. FIGS. 1a and 1b numerically simulate the incremental synchrotron radiation response to a deliberate, brief heating of the plasma (e.g., by lower-hydrid waves) to produce radiation directly attributable to this probe. Both FIGS. 1a and 1b exhibit radiation at several harmonics from electrons initially with about 700 keV parallel energy, or tail electrons in a 20-keV reactor plasma. In FIG. 1a the parallel dc electric field corresponds to 0.02 V/m at density 10.sup.14 /cm.sup.3 ; in FIG. 1b it is -0.0067 V/m. The incremental or transient radiation response is defined as R(.omega.,t;.zeta.).XI.R.sub.tot (.omega.,t;.zeta.)-R.sub.back (.omega.,t;.zeta.), where R.sub.back is the background radiation associated with a relatively constant distribution function and R is the incremental radiation specifically due to the externally imposed impulsive momentum-space flux .GAMMA.(p,t). We can then write the distribution function f as f=.function..sub.m (1+.phi..sub.B +.phi., where .function..sub.m is a Maxwellian distribution, .phi..sub.B describes the relatively constant deviation from Maxwellian of the background distribution, and .phi. describes the time-dependent distribution specifically associated with the source .GAMMA.. For problems of interest, in terms of contributing to the collision integral, both .phi..sub.B and .phi. may be treated as small, so that f obeys the linearized Fokker-Planck equation. The evolution of .phi. is then governed, after the brief excitation, by Coulomb collisions and the dc electric field, EQU .function..sub.M .differential..phi./.differential.t+qE.multidot..gradient..sub.p .differential..sub.M .phi.-C(.phi.)=0 (1) with initial condition .function..sub.M .phi.(p,t=0)=Q(p), which is the result of the impulse .GAMMA.. The incremental or transient radiation response, viewed at angle .zeta. with respect to the magnetic field is then EQU R(.omega.,t;.zeta.)=.intg.d.sup.3 p.function..sub.M .phi.(p,t)I(.omega.,p;.zeta.), (2) where the radiation intensity I can be of ordinary or extraordinary polarization; for the latter, I=I.sup.x, we have ##EQU1## where n is the cyclotron harmonic, J.sub.n is the derivative of the nth Bessel function of the first kind, .omega..sub.c =e.sup.B /mc is the cyclotron frequency of nonrelativistic electrons, .mu.=p/mc, .gamma..sup.2 (u).XI.1+u.sup.2, .mu..XI.p.sub.11 /p, and .lambda.=1-u Sin .zeta./.gamma. is the extent of the Doppler shift through viewing the radiation signal at angle .zeta.. Very fast algorithms have been developed for solving for the radiation response R(.omega.,t). The fast algorithms make feasible a statistical analysis which would otherwise be unthinkable, and exploit several properties of Eqs. (1)-(3). First, note that Eqs. (1)-(3) admit several scale invariant transformations of the radiation response R(.omega.,t). Having solved for R(.omega.,t;.theta.), where .theta. is a set of parametric dependences which includes the magnetic field amplitude B, the electric field E, the density n, the viewing angle I and the perturbation amplitude Q, we also have for any constants .alpha..sub.1, .alpha..sub.2, and .alpha..sub.3, EQU R(.omega.,t;.alpha..sub.1 B,.alpha..sub.2 Q,.alpha..sub.3 n,E)=.alpha..sub.1 .alpha..sub.2 R(.omega./.alpha..sub.1,t/.alpha..sub.3 ;B,Q,n,E/ .alpha..sub.3). (4) The impulsive heating can be arranged to affect only nonrunaway electrons, so that Eq. (4) simplifies further through the linearization R=R.sub.0 +ER.sub.1. Second, since Eq. (1) is linear in .phi., a Green's function, .psi., can be defined for the radiation response. We write the radiation response as an integral over initial condition Q(p), EQU R(.omega.,t;.zeta.)=.intg.d.sup.3 u .psi.(.omega.,p,t;.zeta.)Q(p).(5) The Green's function makes efficient the simultaneous consideration of many perturbations Q(p). Third, choosing to perturb electrons on the tail of the distribution function (i.e. superthermal electrons but not runaways) makes possible an analytic solution for .psi.. For these electrons, energy diffusion by collisions is ignorable compared to energy loss. The Green's function for the radiation response, .psi., solves the relativistic Fokker-Planck adjoint equation, which we write as ##EQU2## written for superthermal excitation in the high-velocity limit and in terms of the normalized variables .tau.=v.sub.c t, v.sub.c =nq.sup.4 ln.LAMBDA./4.pi.m.sup.2 .epsilon..sub.0.sup.2 c.sup.3, and E=q E/mcv.sub.c, and to be solved with the following initial condition .psi.(.omega.,u;.zeta.,.tau.=0)=I(.omega.,u;.zeta.). An analytic solution is available as follows: separate .psi. and the initial conditions into Legendre harmonics [.psi.(u,.mu., .tau.)=.SIGMA..sub.k P.sub.k (.mu.).sub..psi.k (u, .tau.)], expand in the electric field [.psi..sub.k (u, .tau.)=.psi..sub.k.sup.(o) +E.psi..sub.k.sup.(1) +. . . , and then integrate the equation for .psi..sub.k.sup.(0) along characteristics to obtain ##EQU3## where .alpha..sub.k .XI.k(k+1) (Z.sub.eff + 1)/2, and the characteristic function X(.tau., u) can be written as x=g.sup.-1 [g(u)-.tau.], with g(u).XI.u-tan.sup.-1 u; g.sup.-1 is defined such that g.sup.-1 [ g(u)]=1. . The equation governing .psi..sub.k.sup.(1) to be solved with homogeneous initial conditions, is driven by the kth Legendre harmonic of .differential..psi..sup.(0) /.differential..mu..sub.11 ; fortunately, this inhomogeneous term can be simplified enormously so that .psi..sub.k.sup.(1) can be put into an efficient closed form. These fast algorithms enable consideration of essentially all competing parameter sets that might possibly explain obtained data. More than that, the worth of data can be estimated prior to obtaining it. Suppose that experimental measurements are of the following form R.sub.x (.omega.,t)=R(.omega.,t)+R(.omega.,t), where the extraneous signal R(.omega.,t) is Gaussian noise, uncorrelated in both frequency and time, with (R)=0 and (R.sup.2)=.sigma..sup.2. Given this model for data generation, and given a set of plasma parameters {.theta.}, we can express the probability P(R.sub.x .vertline..theta.;.sigma.) of generating a specific data set R.sub.x in the presence of noise characterized by .sigma. Given an a priori distribution P(.theta.) for the parameter set {.theta.}, by Bayes's theorem we can write P(.theta..vertline.R.sub.x ;.sigma.)=P(R.sub.x .vertline..theta.;.sigma.)P(.theta.)/P(R.sub.x). The probability distribution of the plasma parameter set {.theta.}, given that the data were obtained in the presence of noise .sigma. and generated with the specific plasma parameter set {.theta..sub.P }, can now be written as ##EQU4## where, in the first equality, the summation over all possible data sets {R.sub.x } is both unfeasible and, in practice, unnecessary; the second equality obtains, since, by construction, P(.theta..vertline.R.sub.x ;.sigma.) is sampled with probability P(R.sub.x .vertline..theta..sub.p ;.sigma.). Generally N.sub.R .about.80 suffices to approximate P(.theta..vertline..theta..sub.p ;.sigma.). Of course, the fast algorithms for generating R(.omega.,t) are indispensable, since R must be obtained for each competitive data set. Carrying out a program of examining P(.theta..vertline..theta..sub.p ;.sigma.) with various sets of plasma and heating parameters unknown, we find that the a priori probabilities P(.theta.) can be improved upon meaningfully. To take an example of particular interest, consider the simultaneous viewing of radiation from the core periphery of a tokamak, where in a coarse model, the two regimes have, respectively, densities n.sub.c and n.sub.p, and electric fields E.sub.c and E.sub.p. In other relevant respects, such as viewing angle or ion charge state, the two regimes are presumed identical. One detector then sums EQU R(.omega.,t)=Q.sub.c R(.omega.,t;n.sub.c,.epsilon..sub.c)+Q.sub.p R(.omega.,t;n.sub.p .epsilon..sub.p), where Q.sub.c, Q.sub.p, .epsilon..sub.c, and .epsilon..sub.p are assumed unknown, but n.sub.c and n.sub.p are known from other measurements. Of course, where n.sub.c =n.sub.p. there would be no distinguishing the radiation source. However, even a 10% variation in density is exploitable. In FIG. 2, data were simulated on a 40.times.40 grid in frequency-time space, with noise .sigma. of 10% of the maximum signal R(.omega.,t). In practice, purely experimental noise can be kept much lower and a larger differential in density makes this discrimination much easier. As shown in FIG. 2, the marginal probability distribution P(.epsilon..sub.c, .epsilon..sub.p) (the joint probability summed over all {Q.sub.c, Q.sub.p }) reveals the true parameters E.sub.c =0.08, E.sub.p 0, i.e., a loop voltage on axis not yet relaxed via magnetic diffusion. The model employed can be improved upon in several ways, particularly in accounting for cross-field transport due to imperfect magnetic surfaces. Accounting for losses of the fast electrons can probably be done analytically by introducing only a few new parameters; the fast algorithms should remain useful and the inference problem should remain tractable. Of course, in many instances the model as presented may suffice. The foregoing description of a preferred embodiment of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The embodiments described explain the principles of the invention and practical applications and should enable others skilled in the art to utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto.
	description	FIG. 2 shows a preferred embodiment of a canister for the containment of a radioactive item according to the invention. Canister 101 comprises substantially tubular body 124, interior 128, a first, preferably closed, end 125, and second end 140. Interior 128 is adapted by size and geometric configuration to receive a radioactive item such as an nuclear reactor pressure vessel for storage, transportation, and disposal. Preferably interior 128 is large enough for such radioactive item to be disposed within the canister without difficulty, and to allow the addition of a stabilizer, as described herein, yet simultaneously as small as practicable, in order to reduce the size and weight of the completed package and to ease transportation and handling. Thus length width 134 and length 135 of the canister and in particular the canister interior are large enough to accommodate the item to be contained, but not larger than necessary for the purposes described herein. The selection of suitable dimensions and geometry will not trouble the designer of ordinary skill once he or she has been made familiar with disclosure. For most RPVs substantially circular cross sections will serve satisfactorily, and facilitate easy and inexpensive fabrication and employment of the canister. Body 124 of canister 101 further comprises integral sacrificial fenders 126 located adjacent each end of the canister. Sacrificial fenders 126 are comprised of extensions of body 124 of the canister beyond the end caps or closures of the canister, that is, beyond those portions of the canister actually used for containing the radioactive item, and are adapted to absorb or dissipate shocks administered to the completed containment package by deforming under contact loads. The mechanics of such fenders and their role in attenuating or absorbing shocks are well understood and will be plain to those of skill in the art, given the disclosure herein. The canister 101 shown in FIG. 2 further comprises lid or other closure means 108, which is adapted for attachment of a portion of the item to be contained. Lid or closure 108 can comprise a simple end plate, as shown, or might take the form of a cap-type enclosure sized to encompass the entire end of the canister, or any other suitable means for closing the canister. In the embodiment depicted in FIG. 2 closure 108 is adapted for the attachment of a portion of the contained device by means of holes 141, which are sized and positioned to accept attachment fittings present on the item to be contained, for example, the head attachment posts in a PWR pressure vessel. Preferably any portions of items to be attached to the exterior of the canister are not highly radioactive, or are sealable in their own right. Lid or top plate 108 further comprises optional fill and vent ports 160 and 161. Central ports 160 are provided for optional filling of the interior of the RPV body with grout or other sealant; peripheral ports 161 for filling the gap between the canister interior and the RPV exterior. Canister 101 in FIG. 2 further comprises optional secondary circumferential shield 130. Secondary shields are advantageously employed to provide additional containment of relatively highly radioactive portions of any contained items, such as some of the internal structures in a PWR pressure vessel. Preferably circumferential shields are employed in conjunction with cap or lid-type shields such as shields 122 and 142 shown in FIG. 4. A particular advantage of using substantially cylindrical canisters of the type shown in FIG. 2 is that secondary shields are relatively simple to fabricate and install, and provide substantial structural reinforcement as well. In the case of circumferential shields, open-ended cylinders of nearly the same size as the canister body may be employed, and may be disposed around the inner or outer surfaces of the canister, at any axial position along the canister that may be desired. Cap or lid type shields may be fabricated from flat plate material merely by trimming them to size, and may be placed at any axial location within the canister or covering one or both ends of the canister. In either case it is often suitable, as will be understood by those having ordinary familiarity with the art of radiation shielding, that the same materials as those employed in fabricating the canister body may be used in fabricating secondary shield structures, with substantial savings in cost. Cap or lid shields are particularly useful for providing ALARA (As Low As Reasonably Achievable) shields during stacking of internal parts, external fittings, and/or insulation inside an RPV as described herein, as an added shield against radiation for workers. Canisters or containment vessels according to the invention and as shown in FIG. 2 are substantially easier and less expensive to fabricate than prior art containment vessels. This is in large part due to their simplified construction, as described. They are also economical to use, especially during the containment and removal of decommissioned RPV""s, because they may easily be separated into sections, moved into place for containment of the RPV or other item, and reassembled easily. For example, the containment canister shown in FIG. 2 may be cut anywhere along the length of its body into two or more sections merely by cutting the container, as for example by means of any conventional metal cutting methods, along a circumference such as that shown by reference numeral 138 in FIG. 2, the location of which may be varied anywhere along the body of the canister, such that two sections 136 and 137 result. In such cases reassembly is accomplished merely by replacing second section 137 back in place adjacent to first section 136 and reattaching, as for example by welding. The use of secondary radiation shield 130 also facilitates the use of the canister in this fashion, as it can be used as a doubler or structural reinforcement as well as an additional radiation shield. Canister 101 may be fabricated economically and easily by rolling or otherwise forming tubular body 124 by conventional means from sheet or plate metal, and welding or otherwise attaching a bottom plate at closed end 125 and lid or closure plate 108. Integral fenders 126 are easily formed in such processes by placing the end closures at a suitable distance from the ends of the body structure, leaving the fenders protruding or extending from the body. Provision of optional fillet 143, which is also readily formed by rolling or other conventional means, is particularly beneficial, as it permits provision of integral fenders 126 as described, in such fashion that fenders 126 are able to perform their function with full efficiency, while optionally permitting the canister weight and the weight of any of its contents to be transferred directly to the floor or other surface on which canister 101 and any contents are placed, without passing through and possibly harming the fenders or reducing their capacity to absorb or dissipate shocks. Optionally fenders 126 are of sufficient depth to allow them to provide protection not only to the containment package as a whole, and in particular to the packaged radioactive item, but also to any additional items, such as removed reactor vessel pressure head, which may be attached to the exterior of the canister. An early part of the process for containing a radioactive item according to the invention is preparing the radioactive item for packing. Generally this comprises removing at least one external fitting from the item, and optionally portions of the internals of the item as well. A process of preparing the item for packing is shown in FIGS. 3 and 4. FIG. 3 is a cutaway schematic elevation of an intact radioactive item, specifically a PWR pressure vessel, prior to being processed for containment according to the invention. Reactor pressure vessel (RPV) 102 comprises body 114 and head 115, internals 117, and a number of external fittings 103, including water nozzles 144 and control structures 145. Head 115 is joined to body 114 at flange 146 by means of attachments 132, and insulation 116 is in place around exterior 105 of the RPV. Internals 117 comprise upper internals 147 and lower internals 148. In FIG. 4 the RPV of FIG. 3 has been at least partially processed for containment according to the invention. External fittings 103 have been trimmed so that non-removed portions 104 of the fittings are substantially flush with external surface 105 of body 114. In particular, non-removed portions 104 of the external fittings do not protrude past the outer circumference of flange 146. Moreover, internals portions 148 (FIG. 3), including the central portion of the core barrel and the core baffle assembly, have been removed from interior 109 of the RPV, and upper internals 147 have been stacked on top of support plate 142, which preferably serves also as a secondary radiation shield. Portions 149 of core barrel 151 (FIG. 3) are also disposed within the RPV. Additional portions 119 of the upper internals and insulation 116 removed from the exterior of the RPV are also placed in otherwise vacant space within the RPV body. A secondary support structure and ALARA shield 122 is placed atop internals 117, 147, and removed portions of external fittings 103 are placed thereupon. Additional insulation 116 taken from the exterior of the RPV body is placed atop fittings 103. Penetrations 120 of RPV body 114 have been stopped by means of plugs 121. As described herein, it is beneficial during at least the first portions of this process to leave the reactor coolant fluid or other liquid in the RPV, to serve as a radiation shield for those working on the containment process. Preferably this is accomplished by leaving water or other liquid in the RPV body to at least the level of 123 in FIG. 4 until the more highly-radioactive components of the core have been removed and all penetrations 120, for example, have been plugged; at this point it is advantageous to drain the fluid, install secondary supports and shield structures such as 142 and 122, and proceed with packaging. FIG. 5 is a schematic view of a radioactive item being disposed within a canister in accordance with the invention. Presented is one scenario of placing RPV 102 within canister 101. This scenario can be altered to accommodate plant specific and unique conditions. Internal shields 130 are welded to lower section 136 and upper section 137 of the canister during manufacturing. Lower section 136 of canister 101 has been placed atop transfer cart 160 with a removal frame and trunnions 139. Transfer cart 160 with lower section 136 has initially been placed in position 161 near RPV installation point 152. Head 115 of RPV 102 has been removed and lifting device 163 attached to RPV body 114. RPV 102 has been disconnected from the remainder of the plant of which it formed part by disconnecting external fittings 103, including piping 144, and penetrations 120 in RPV body 114 have been sealed. RPV external surfaces 105 are sealed with paint or other suitable substance to immobilize surface contaminants. RPV body 114 has been removed from its prior position 114xe2x80x2 in RPV installation 152 and raised, whereupon transfer cart 160 with lower section 136 has been moved into loading position 169, and RPV body 114 has been disposed within section 136 of the canister. Canister 101 and RPV body 114 are ready for a stabilizer to be introduced in gap 106 between the RPV body 114 and the interior wall of canister 101. After gap 106 has been filled to a level sufficient to allow the stabilizer to support RPV body 114 and the stabilizer allowed time to set sufficiently, or RPV body 114 otherwise sufficiently supported, upper section 137 of canister 101 is placed over the RPV body and reattached to lower section 136 by welding or other suitable means. RPV studs 185 are installed through top plate 108 of upper section 137 into the flange of RPV body 114. Spray metalizing is used to seal openings between RPV studs 185 and attachment penetrations 141 (FIG. 2) through upper section 137. Head 115 is placed atop external surface 127 of the canister, and fixed thereto, preferably by means of head attachments 132 (FIG. 3) threaded onto RPV studs 185. If necessary, the completed containment package will be turned about its upright longitudinal axis by pivoting the package with trunnions 139 on the removable frame on lower section 136. The package may then be removed from the plant housing and made ready for shipment by removing the frame with trunnions 139. It may be seen that division of canister 101 into two or more sections provides a number of benefits, such as a reduction in clearance height requirements to place RPV body 102 within the canister. This is especially beneficial in the limited workspaces of most nuclear plant installations. FIG. 6 is a cutaway schematic view of a radioactive item packaged in accordance with the invention. In addition to elements shown in other Figures, stabilizer 107 is shown substantially filling gap 106 between canister 101 and RPV 102. RPV head 115 is in place atop lid 108 of the canister, and attached by means of RPV head-body attachments 132, which, together with stabilizer 107, further comprise the sole attachment between the RPV body 114 and the containment canister. Optionally the entire interior of the RPV body is filled with stabilizer 107, to further immobilize contaminants and stored components. A containment package for a PWR pressure vessel is described. This example corresponds to plans for disposal of the Connecticut Yankee PWR. A containment canister according to the invention and as shown generally in FIG. 2, including top and bottom plates and fillet, is fabricated from three-inch thick structural carbon steel. Secondary shielding of two-inch thick carbon steel is placed within the canister body so as to shield the most highly radioactive portions of the completed package. The canister is fabricated in two sections, with the weld seam located behind the secondary shielding on rejoining. Rejoining is accomplished by full penetration weld. The canister, including integral fenders, 35xe2x80x2 3xe2x80x3 feet in length, 17xe2x80x2 10xe2x80x3 diameter, and weighs 190 tons empty. The completed package, with stabilizing grout and externally-attached RPV head, weighs 800 tons. The height of the package, with head attached, is 39xe2x80x2 7xe2x80x3. The head and RPV body are attached to each other, and to the canister, by means of the approximately twelve (12) head closure studs present on the reactor in service, which pass through canister lid and into upper flange of the RPV body. The canister provides containment shielding equivalent to DOT Industrial Package type 2, analyzed to withstand a 1 foot horizontal drop and a 1 foot drop with 2 feet of slap-down at either end. Ninety-nine point eight (99.8) percent of the radioactive material present is intrinsically contained within RPV activated metals themselves; remaining 0.2% is affixed to metal surfaces and is immobilized by grout or epoxy. A method for placing and sealing a PWR pressure within a containment vessel is described. The RPV is disconnected from external piping, controls, and the like, and the head is removed, as described and as shown generally in FIGS. 2-6. Highly radioactive portions of the internals are removed for separate containment and storage. Segmented internals, including particularly upper internal components, are placed inside the RPV body as described. Nominal 30 pcf low-density cellular concrete (LDCC) is placed inside the RPV body to seal and immobilize remaining and relocated internals. The RPV body is lifted over and lowered into position within the canister lower section, with a gap between the RPV and the canister interior. Nominal 70 pcf LDCC is poured into the gap to a sufficient depth to support the RPV after curing, and is allowed to cure. The lifting rig used to position the RPV is removed. Removed portions of the RPV nozzles are placed inside the RPV, atop an ALARA plate. RPV head closure guide studs (ref. 132 in FIG. 6) are installed in some of the RPV head attachment stud holes. The canister upper section is lifted and lowered into place over the guide studs, so that it rests upon the RPV head flange. RPV hold down studs are installed using remaining RPV head attachment stud holes. The canister upper and lower sections are welded together. Openings between the canister top plate and the RPV hold down and guide studs are sealed with metalizing spray. Nominal 70 pcf LDCC is pumped into remaining voids between the canister and the RPV body through peripheral fill ports opened in the top of the canister. Nominal 30 pcf LDCC is pumped into remaining voids inside the RPV body through center fill ports opened in the canister top plate. Fill and vent ports in the canister top plate are plugged and sealed. The RPV head is placed on top of the canister and the guide studs already in place. The guide studs are cut flush with the top of the RPV head flange. All LDCC is allowed to complete curing. The package is rigged for removal from the assembly location by the attachment of lugs and/or other structures to the canister exterior. The package is lifted and turned to a substantially horizontal position, secured to transport conveyance, and transported to a disposal site. Preferred embodiments of the various structures disclosed herein are fabricated from any materials having sufficient strength, durability, corrosion resistance, and radioactive shielding qualities to serve the purposes described for such structures. Suitable materials are known, and have been identified herein where appropriate; but any materials having suitable qualities will serve. While the invention has been described and illustrated in connection with preferred embodiments, many variations and modifications as will be evident to those skilled in this art may be made without departing from the spirit and scope of the invention, and the invention is thus not to be limited to the precise details of methodology or construction set forth above as such variations and modification are intended to be included within the scope of the invention.
052672743	claims	1. A method of determining the geological evolution of apatite grains contained within rock samples comprising obtaining a sufficiently pure quantity of representative apatite grains from a rock sample; forming at least one epoxy wafer containing said representative apatite grains for examination and polishing said epoxy wafer containing said representative apatite grains in order to expose internal planar surfaces of the apatite grains; chemically etching naturally occurring fission tracks and other crystallographic imperfections that intersect the polished internal planar surfaces of the said apatite grains with an acidic solution; selecting a first-set of apatite grains from among suitable candidate apatite grains for fission track age measurement; determining the density of naturally occurring fission tracks of said first-set apatite grains; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each first-set apatite grain; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each first-set apatite grain; selecting a second-set of apatite grains from among suitable candidate apatite grains for measurement of perceived track lengths of confined fission tracks; measuring the perceived track lengths of confined naturally occurring fission tracks within the second-set apatite grains; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each second-set apatite grain; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each second-set apatite grain; determining the concentration of .sup.238 U for the first-set apatite grains; determining the fission track ages of the first-set apatite grains; determining the chemical composition of first-set and second-set apatite grains; calculating the pooled fission track age and pooled distribution of perceived track lengths of fluorine-rich first-set and fluorine-rich second-set apatite grains; and calculating the pooled fission track age and pooled distribution of perceived track lengths of relatively non-fluorine-rich first-set and relatively non-fluorine-rich second-set apatite grains. spreading the representative apatite grains on a non-stick surface within an area of approximately one square centimeter defined by a form which is 1.5 millimeters deep and in contact with the non-stick surface; pouring a mix of epoxy resin and epoxy hardener over the sampling of representative apatite grains contained within the form; placing a petrographic microscope slide on top of the epoxy resin and applying a slight downward force to ensure that said slide will be attached to the epoxy resin; allowing the epoxy resin mix to harden for twenty four hours at room temperature thereby forming an epoxy wafer; detaching the resulting epoxy wafer from the non-stick surface while allowing the epoxy wafer to remain attached to the petrographic microscope slide; and polishing the planar surface of the resulting epoxy wafer opposite that attached to the petrographic slide to an extremely smooth finish thereby removing a portion of the epoxy wafer and a similar thickness of the apatite grains aligned with the planar surface being polished thereby exposing internal surfaces of the apatite grains. immersing the epoxy wafer and attached petrographic slide in an acidic solution whereby all naturally occurring fission tracks and other crystallographic imperfections exposed to the acidic solution will be chemically etched; removing the epoxy wafer and attached petrographic slide from the solution; washing the epoxy wafer and attached petrographic slide with distilled water; and drying the epoxy wafer and attached petrographic slide sufficiently to remove all fluid from the resulting etch pits. observing the etched apatite grains contained within the polished and etched surface of the epoxy wafer and identifying suitable candidate apatite grains for fission track age measurement which have their crystallographic c-axes oriented parallel to the polished and etched planar surface of the epoxy wafer; and selecting apatite grains from among the suitable candidate apatite grains possessing a relatively high fraction of etch pits that represent etched naturally occurring fission tracks in combination with a relatively large available etched surface area. viewing the first-set apatite grains through a magnifying device possessing a graticule grid of known dimensions and which is imposed upon viewed images; counting the number of etch figures resulting from the intersection of etch pits that represent etched naturally occurring fission tracks with the etched planar surface within an area of known dimensions defined by the graticule grid; and calculating the spontaneous fission track density according to the formula: EQU P.sub.S =N.sub.S /AREA where N.sub.S, in units of tracks, is the number of etch figures created by the intersection of etch pits that represent etched naturally occurring fission tracks with the etched planar surface of the first-set apatite grain within the area outlined by a portion of the graticule grid; and where AREA, in units of length squared, is the area of the surface of the first-set grain outlined by the graticule grid. viewing the first-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.1,Y.sub.1, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.2,Y.sub.2, of the point; calculating the length of the maximum diameter parallel to the crystallographic c-axis of each etch figure using the formula: EQU DPAR.sub.i =C sqrt ((X.sub.2 -X.sub.1).sup.2 +(Y.sub.2 -Y.sub.1).sup.2) where DPAR.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter parallel to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the first-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters parallel to the crystallographic c-axis for each first-set apatite grain studied by summing all values of DPAR.sub.i measured for each first-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. viewing the first-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.3,Y.sub.3, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.4,Y.sub.4, of the point; calculating the length of the maximum diameter perpendicular to the crystallographic c-axis of each etch figure using the formula: EQU DPER.sub.i =C sqrt ((X.sub.4 -X.sub.3).sup.2 +(Y.sub.4 -Y.sub.3).sup.2) where DPER.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter perpendicular to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the first-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters perpendicular to the crystallographic c-axis for each first-set apatite grain studied by summing all values of DPER.sub.i measured for each first-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. observing the etched apatite grains contained within the polished and etched surface of the epoxy wafer and identifying suitable candidate apatite grains that contain etched confined fission tracks and which have their crystallographic c-axes oriented parallel to the polished and etched planar surface of the epoxy wafer; and identifying as many as 200 confined fission tracks which are etched to their ends and which lie within approximately 10 degrees of parallel to the polished and etched planar surface of the apatite grains. viewing the second-set apatite grains under a binocular optical microscope having multiple illuminating light sources, and a projection tube by which a point source of light from a cursor apparatus attached to a digitizing tablet can be visually observed while looking through the microscope; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of each linear etched confined fission track, wholly contained within a second-set apatite grain, and electronically recording the coordinates, X.sub.5,Y.sub.5, of the point; placing the point source of the light from the cursor apparatus at precisely the opposite extreme of each linear etched confined fission track, wholly contained within a second-set apatite grain, and electronically recording the coordinates, X.sub.6,Y.sub.6, of the point; and calculating the perceived track length of each linear etched confined fission track, wholly contained within the second-set apatite grains, according to the formula: EQU TL=C sqrt((X.sub.6 -X.sub.5).sup.2 +(Y.sub.6 -Y.sub.5).sup.2) where TL, in units of length, is the perceived track length of a confined fission track in a second-set apatite grain; and where C, in units of length, is a scaling factor that converts the units of the digitizing tablet into units of length. viewing the second-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.1,Y.sub.1, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.2,Y.sub.2, of the point; calculating the length of the maximum diameter parallel to the crystallographic c-axis of each etch figure using the formula: EQU DPAR.sub.i =C sqrt ((X.sub.2 -X.sub.1).sup.2 +(Y.sub.2 -Y.sub.1).sup.2) where DPAR.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter parallel to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the second-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters parallel to the crystallographic c-axis for each second-set apatite grain studied by summing all values of DPAR.sub.i measured for each second-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. viewing the second-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.3,Y.sub.3, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.4,Y.sub.4, of the point; calculating the length of the maximum diameter perpendicular to the crystallographic c-axis of each etch figure using the formula: EQU DPER.sub.i =C sqrt ((X.sub.4 -X.sub.3).sup.2 +(Y.sub.4 -Y.sub.3).sup.2) where DPER.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter perpendicular to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the second-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters perpendicular to the crystallographic c-axis for each second-set apatite grain studied by summing all values of DPERi measured for each second-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. placing a muscovite mica detector in intimate contact with the etched planar surface of the epoxy wafer containing the first-set apatite grains; placing the epoxy wafer and muscovite mica detector in close proximity to the core of a nuclear reactor; placing a portion of uranium-doped glass in intimate contact with a muscovite mica detector in close proximity to the core of a nuclear reactor; irradiating the epoxy wafer and the uranium-doped glass and their respective muscovite mica masks with thermal neutrons thereby inducing fission of .sup.235 U in the first-set apatite grains within the epoxy wafer and the uranium-doped glass; removing the epoxy wafer, uranium-doped glass, and muscovite mica detectors from close proximity to the core of a nuclear reactor; chemically etching the induced fission tracks within the muscovite mica detectors; calculating the concentration of .sup.238 U for each first-set apatite grain according to the formula: EQU [.sup.238 U]=137.88 [.sup.235 U.sub.g ] (R.sub.g /R.sub.a) (P.sub.ia /P.sub.ig) where [.sup.238 U], in units of nuclei per length cubed, is the concentration of the uranium isotope .sup.238 U in a first-set apatite grain within the apatite volume of interest; where 137.88, in units of nuclei per nuclei, is a constant for all first-set apatite grains which represents the naturally occurring concentration ratio of the uranium isotopes .sup.238 U to .sup.235 U; where [.sup.235 U.sub.g ],in units of nuclei per length cubed, is the concentration of the uranium isotope .sup.235 U in the uranium-doped glass; where R.sub.g, in units of length, is the average distance travelled by a single fission fragment nucleus in the uranium-doped glass; where R.sub.a, in units of length, is the average distance travelled by a single fission fragment nucleus in the first-set apatite grain; where P.sub.ia, in units of tracks per length squared, is the surface density of induced fission track etch pits that cross the etched planar surface of the detector within the area of the detector outlined by the graticule grid that was in intimate contact with the previously studied area of the first-set apatite grain; and where P.sub.ig, in units of tracks per length squared, is the surface density of induced fission track etch pits that cross the etched planar surface of the detector that was in intimate contact with the uranium-doped glass. calculating the fission track age for each first-set apatite grain using the formula: EQU T=(1/l.sub.D) ln((l.sub.D /l.sub.F)([FT]/[.sup.238 U])+1) where T, in units of millions of years, is the fission track age for the first-set apatite grain; where l.sub.D, in units of nuclei per million years, is the total decay constant for .sup.238 U; where l.sub.F, in units of nuclei per million years, is the fission decay constant for .sup.238 U; where [FT], in units of tracks per length cubed, is the number of naturally occurring fission tracks, resulting from the spontaneous fission decay of .sup.238 U, per unit volume in a volume of interest in the first-set apatite; and where [.sup.238 U], in units of nuclei per length cubed, is the concentration of the uranium isotope .sup.238 U in the first-set apatite grain within the apatite volume of interest. plotting the individual apatite grain ages of the first-set apatite grains as a function of the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis; plotting the individual track lengths of the second-set apatite grains as a function of the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis; grouping each of the first-set apatite grains and second-set apatite grains into either a group which is predominantly composed of fluorine-rich apatite or a group which is predominantly composed of relatively non-fluorine-rich apatite by determining whether the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis on the planar surface of the apatite grain is less than or equal to a length of 2 micrometers, in the case of fluorine-rich apatite, or greater than 2 micrometers, in the case of relatively non-fluorine-rich apatite. calculating the fluorine concentration or [F] for first-set and second-set apatite grains according to the following formula: EQU [F]=4.6748-1.3106 DPAR+0.041759 DPAR.sup.2 where [F], in units of weight percent, is the fluorine concentration in the first-set or second-set apatite grain being studied; and where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied. calculating the chlorine concentration or [Cl] for first-set and second-set apatite grains according to the following formula: EQU [Cl]=-0.31045-0.053515 DPAR+0.26067 DPAR.sup.2 where [Cl], in units of weight percent, is the chlorine concentration in the first-set or second-set apatite grain being studied; and where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied. calculating the water concentration or [H2O] for first-set and second-set apatite grains according to the following formula: EQU [H.sub.2 O]=-0.048074+0.28092 DPAR where [H2O], in units of weight percent, is the water concentration in the first-set or second-set apatite grain being studied; and where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied. obtaining a sufficiently pure quantity of representative apatite grains from a rock sample; forming at least one epoxy wafer containing said representative apatite grains for examination and polishing said epoxy wafer containing said representative apatite grains in order to expose internal planar surfaces of the apatite grains; chemically etching naturally occurring fission tracks and other crystallographic imperfections that intersect the polished internal planar surfaces of the said apatite grains with an acidic solution; selecting a first-set of apatite grains from among suitable candidate apatite grains; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each first-set apatite grain; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each first-set apatite grain; selecting a second-set of apatite grains from among suitable candidate apatite grains; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each second-set apatite grain; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each second-set apatite grain; and determining the chemical composition of first-set and second-set apatite grains. spreading the representative apatite grains on a non-stick surface within an area of approximately one square centimeter defined by a form which is 1.5 millimeters deep and in contact with the non-stick surface; pouring a mix of epoxy resin and epoxy hardener over the sampling of representative apatite grains contained within the form; placing a petrographic microscope slide on top of the epoxy resin and applying a slight downward force to ensure that said slide will be attached to the epoxy resin; allowing the epoxy resin mix to harden for twenty four hours at room temperature thereby forming an epoxy wafer; detaching the resulting epoxy wafer from the non-stick surface while allowing the epoxy wafer to remain attached to the petrographic microscope slide; and polishing the planar surface of the resulting epoxy wafer opposite that attached to the petrographic slide to an extremely smooth finish thereby removing a portion of the epoxy wafer and a similar thickness of the apatite grains aligned with the planar surface being polished thereby exposing internal surfaces of the apatite grains. immersing the epoxy wafer and attached petrographic slide in an acidic solution whereby all naturally occurring fission tracks and other crystallographic imperfections exposed to the acidic solution will be chemically etched; removing the epoxy wafer and attached petrographic slide from the solution; washing the epoxy wafer and attached petrographic slide with distilled water; and drying the epoxy wafer and attached petrographic slide sufficiently to remove all fluid from the resulting etch pits. observing the etched apatite grains contained within the polished and etched surface of the epoxy wafer and identifying suitable candidate apatite grains which have their crystallographic c-axes oriented parallel to the polished and etched planar surface of the epoxy wafer; and selecting apatite grains from among the suitable candidate apatite grains possessing etch figures on their polished and etched planar surfaces. viewing the first-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.1,Y.sub.1, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.2,Y.sub.2, of the point; calculating the length of the maximum diameter parallel to the crystallographic c-axis of each etch figure using the formula: EQU DPAR.sub.i =C sqrt ((X.sub.2 -X.sub.1).sup.2 +(Y.sub.2 -Y.sub.1).sup.2) where DPAR.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter parallel to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the first-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters parallel to the crystallographic c-axis for each first-set apatite grain studied by summing all values of DPAR.sub.i measured for each first-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. viewing the first-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.3,Y.sub.3, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.4,Y.sub.4, of the point; calculating the length of the maximum diameter perpendicular to the crystallographic c-axis of each etch figure using the formula: EQU DPER.sub.i =C sqrt ((X.sub.4 -X.sub.3).sup.2 +(Y.sub.4 -Y.sub.3).sup.2) where DPER.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter perpendicular to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the first-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters perpendicular to the crystallographic c-axis for each first-set apatite grain studied by summing all values of DPER.sub.i measured for each first-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. observing the etched apatite grains contained within the polished and etched surface of the epoxy wafer and identifying suitable candidate apatite grains which have their crystallographic c-axes oriented parallel to the polished and etched planar surface of the epoxy wafer; and identifying suitable candidate apatite grains that contain confined fission tracks which are etched to their ends and which lie within approximately 10 degrees of parallel to the polished and etched planar surface of the apatite grains. viewing the second-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.1,Y.sub.1, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.2,Y.sub.2, of the point; calculating the length of the maximum diameter parallel to the crystallographic c-axis of each etch figure using the formula: EQU DPAR.sub.i =C sqrt ((X.sub.2 -X.sub.1).sup.2 +(Y.sub.2 -Y.sub.1).sup.2) where DPAR.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter parallel to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the second-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters parallel to the crystallographic c-axis for each second-set apatite grain studied by summing all values of DPAR.sub.i measured for each second-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. viewing the second-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.3,Y.sub.3, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.4,Y.sub.4, of the point; calculating the length of the maximum diameter perpendicular to the crystallographic c-axis of each etch figure using the formula: EQU DPER.sub.i =C sqrt ((X.sub.4 -X.sub.3).sup.2 +(Y.sub.4 -Y.sub.3).sup.2) where DPER.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter perpendicular to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the second-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters perpendicular to the crystallographic c-axis for each second-set apatite grain studied by summing all values of DPER.sub.i measured for each second-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. grouping each of the first-set apatite grains and second-set apatite grains into either a group which is predominantly composed of fluorine-rich apatite or a group which is predominantly composed of relatively non-fluorine-rich apatite by determining whether the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis on the planar surface of the apatite grain is less than or equal to a length of 2 micrometers, in the case of fluorine-rich apatite, or greater than 2 micrometers, in the case of relatively non-fluorine-rich apatite. calculating the fluorine concentration or [F] for first-set and second-set apatite grains according to the following formula EQU [F]=4.6748-1.3106 DPAR+0.041759 DPAR.sup.2 where [F], in units of Weight percent, is the fluorine concentration in the first-set or second-set apatite grain being studied; and where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied. calculating the chlorine concentration or [Cl] for first-set and second-set apatite grains according to the following formula EQU [Cl]=-0.31045-0.053515 DPAR+0.26067 DPAR.sup.2 where [Cl], in units of weight percent, is the chlorine concentration in the first-set or second-set apatite grain being studied; and where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied. calculating the water concentration or [H2O] for first-set and second-set apatite grains according to the following formula EQU [H.sub.2 O]=-0.048074+0.28092 DPAR where [H2O], in units of weight percent, is the water concentration in the first-set or second-set apatite grain being studied; and where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied. 2. A method according to claim 1 including forming at least one epoxy wafer containing said representative apatite grains for examination and polishing said epoxy wafer containing said representative apatite grains in order to expose internal planar surfaces of the apatite grains comprises 3. A method according to claim 1 including chemically etching naturally occurring fission tracks and other crystallographic imperfections that intersect the polished internal planar surfaces of the said apatite grains with an acidic solution comprises 4. A method according to claim 3 including said epoxy wafer and attached petrographic slide are immersed in a nitric acid solution of 5.5 Molar strength at 21 degrees Celsius for 20 seconds while being swirled vigorously within the solution. 5. A method according to claim 1 including selecting a first-set of apatite grains from among suitable candidate apatite grains for fission track age measurement comprises 6. A method according to claim 1 including determining the density of naturally occurring fission tracks of said first-set apatite grains comprises 7. A method according to claim 1 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each first-set apatite grain comprises 8. A method according to claim 1 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each first-set apatite grain comprises 9. A method according to claim 1 including selecting a second-set of apatite grains from among suitable candidate apatite grains for measurement of perceived track lengths of confined fission tracks comprises 10. A method according to claim 1 including measuring the perceived track lengths of confined naturally occurring fission tracks within the second-set apatite grains comprises 11. A method according to claim 1 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each second-set apatite grain comprises 12. A method according to claim 1 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each second-set apatite grain comprises 13. A method according to claim 1 including the determination of the concentration of .sup.238 U for first-set apatite grains comprises 14. A method according to claim 1 including determining the fission track age of said first-set apatite grains comprises 15. A method according to claim 1 including determining the chemical composition of the first-set and second-set apatite grains comprises 16. A method according to claim 1 including determining the chemical composition of the first-set and second-set apatite grains comprises 17. A method according to claim 1 including determining the chemical composition of the first-set and second-set apatite grains comprises 18. A method according to claim 1 including determining the chemical composition of the first-set and second-set apatite grains comprises 19. A method of determining the chemical composition of apatite grains contained within rock samples comprising 20. A method according to claim 19 including forming at least one epoxy wafer containing said representative apatite grains for examination and polishing said epoxy wafer containing said representative apatite grains in order to expose internal planar surfaces of the apatite grains comprises 21. A method according to claim 19 including chemically etching naturally occurring fission tracks and other crystallographic imperfections that intersect the polished internal planar surfaces of the said apatite grains with an acidic solution comprises 22. A method according to claim 21 including said epoxy wafer and attached petrographic slide are immersed in a nitric acid solution of 5.5 Molar strength at 21 degrees Celsius for 20 seconds while being swirled vigorously within the solution. 23. A method according to claim 19 including selecting a first-set of apatite grains from among suitable candidate apatite grains comprises 24. A method according to claim 19 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each first-set apatite grain comprises 25. A method according to claim 19 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each first-set apatite grain comprises 26. A method according to claim 19 including selecting a second-set of apatite grains from among suitable candidate apatite grains comprises 27. A method according to claim 19 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each second-set apatite grain comprises 28. A method according to claim 19 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each second-set apatite grain comprises 29. A method according to claim 19 including determining the chemical composition of the first-set and second-set apatite grains comprises 30. A method according to claim 19 including determining the chemical composition of the first-set and second-set apatite grains comprises 31. A method according to claim 19 including determining the chemical composition of the first-set and second-set apatite grains comprises 32. A method according to claim 19 including determining the chemical composition of the first-set and second-set apatite grains comprises
	abstract	A lens system for a plurality of charged particle beams comprises a lens body with a first pole piece, a second pole piece and a plurality of lens openings for the respective charged particle beams; a common excitation coil arranged around the plurality of lens openings for providing a respective first magnetic flux to the lens openings; and a compensation coil arranged between the lens openings for providing a respective second magnetic flux to at least some of the lens openings so as to compensate for an asymmetry of the first magnetic flux.
040627241	abstract	A nuclear reactor construction comprising a fast reactor core submerged in a pool of liquid sodium in a primary vessel. A collecting tray for core debris is submerged in the pool below the core. The collecting tray comprises a base plate constituting a plane tube sheet while the wall of the tray constitutes an annular tube sheet. Coolant conducting tubes are end received in the tube sheets. An internal skirt of the primary vessel overlaps the wall of the tray.
	summary
	abstract	A charged particle beam irradiation apparatus includes: an irradiation section configured to irradiate an irradiated body with a charged particle beam; a multi-leaf collimator configured to set an irradiation range of the charged particle beam which is irradiated from the irradiation section; an imaging section that is provided so as to be able to advance and retreat with respect to an irradiation axis of the charged particle beam which is irradiated from the irradiation section, between the irradiation section and the multi-leaf collimator, and directly images an opening portion of the multi-leaf collimator; and a drive section configured to move the imaging section between an imaging position corresponding to an irradiation area which includes the irradiation axis of the charged particle beam and a retreated position away from the irradiation area.
	abstract	The kind of a particle is determined by pressing a hard atomic force microscope stylus having a spring constant equal to or larger than 300 N/m onto a particle to be removed and detecting bending quantity relative to a press force and a kind of a stylus used for removing the particle is changed in accordance with the kind of the particle.
	claims	1. A method of controlling the criticality of a nuclear fuel cycle facility, comprising:producing a reactor fuel by adding from 305 to 915 ppm of gadolinia to a uranium dioxide powder with a uranium enrichment of greater than 5% and 10% or less by weight;controlling an effective neutron multiplication factor of a uranium dioxide system containing the uranium dioxide powder to which gadolina is added to be less than or equal to a maximum of an effective neutron multiplication factor of a uranium dioxide system with a uranium enrichment of 5% by weight;ensuring a control of a mass subcriticality by:not handling any fuel having a mass exceeding a predetermined value relating to criticality safety design;not handling any fuel having a size exceeding a size of a predetermined value relating to criticality safety design; andmaintaining the fuel under complete submergence conditions such that spaces between particles of the uranium dioxide powder with a uranium enrichment are filled with water and the particles are surrounded by water;whereinthe control of the effective neutron multiplication factor is obtained by adding an amount of gadolinia to the enriched uranium dioxide powder such that the maximum of the effective neutron multiplication factor of the enriched uranium dioxide powder is less than or equal to an effective neutron multiplication factor of uranium dioxide powder with a uranium enrichment of 5% by weight, andthe amount of gadolinia added to the uranium dioxide powder with a uranium enrichment of greater than 5% by weight is proportional to the uranium enrichment thereof that exceeds 5% and a constant of the proportion is determined by dividing the amount of gadolinia added to a uranium dioxide powder with a uranium enrichment of 10% by weight by five.
	abstract	There are provided a control rod holding unit 16 for releasably holding a control rod 7 which is loaded in a reactor vessel 1, and fuel support/control rod guide tube holding unit 17 for releasably holding a fuel support 8 which supports a bottom end of a fuel assembly 10 and a control rod guide tube 6 on which the fuel support 8 is placed at top end. The control rod holding unit 16 and the fuel support/control rod guide tube holding unit 17 are fitted to a main body frame 26 which can be hoisted down inside the reactor vessel 1. Accordingly, there can be provided a reactor-internal equipment handling apparatus and method which are capable of reducing a term of work which is required for operations to load/unload the control rods, the fuel supports, and the control rod guide tubes.
	abstract	Examples of a system for generating and compressing magnetized plasma are disclosed. The system comprises a plasma generator with a first closed end and an outlet, and a flux conserving chamber that is in tight fluid communication with the outlet of the plasma generator such that the generated plasma is injected into an inner cavity of the flux conserving chamber. An elongated central axial shaft is also provided such that the central shaft extends through the outlet of the plasma generator into the flux conserver. The end of the central shaft in connected to the flux conserver. A power source that comprises a formation power circuit and a shaft power circuit is provided to provide a formation power pulse to the plasma generator to generate magnetized plasma, and a shaft power pulse to the central axial shaft to generate a toroidal magnetic field into the plasma generator and the flux conserving chamber. The duration of the shaft power pulse is longer than the duration of the formation power pulse to maintain plasma q-profile at a pre-determined range. During plasma compression the shaft power pulse is increased to match the raise of the plasma poloidal field due to the compression and thus maintain the q-profile of the plasma.
051820510	description	DESCRIPTION OF THE PREFERRED EMBODIMENTS The particles which can be made radioactive of the present invention are particles which contain a target element which is embedded in a sintered ceramic matrix. The radioactive isotope particles of the present invention are ceramic particles that emit gamma rays to allow their detection by instruments. The particles are made of sintered ceramic components and an element which has been bombarded with neutrons to become a gamma ray-emitting isotope. The ceramic components are common oxides, normally silica or alumina, but other oxides used in the ceramic art may be used. In the mixtures comprising predominantly silica and alumina, a range of mixtures from pure alumina to predominantly silica can be used. Mixed crystalline materials of silica and alumina such as mullite may be used. The ceramic components are first finely divided or powdered and mixed with the target element. By this technique, the target element can be uniformly distributed through the particle. The structure of the powdered starting materials may still be present in the finished particles, but the particles will have an effective amount of strength resulting from bonding of the original powder of ceramic components which has occurred during the sintering process. Other components may be added to aid sintering and to substantially lower the sintering temperature, such components being well known in the ceramics art. The sintered matrix of the particles should have sufficient strength to resist breaking when the particles are pumped in a stream of fluid. The amount of strength needed will depend upon their application. If the particles are to be pumped at high flow rates in a slurry, such as in hydraulic fracturing treatments in wells, the particles should be strong enough to prevent breaking at high stress, substantially like the ceramic particles now provided as proppant for this application. For added strength, particles having an alumina content above 30 percent by weight are preferred. Also, sintered particles made from very finely divided powder are higher in strength. Powder less than 25 microns in size is preferred. If the radioactive particles are to be incorporated into a flow stream moving at a low speed and without abrasive conditions, much lower strength ceramic particles are acceptable, although high strength will not be a disadvantage. In addition to strength, density and size may be important properties of the ceramic particles to be considered in each application. The target element added to emit gamma rays is embedded in the matrix of the ceramic materials before sintering. The element is selected based upon several variables. One of the important characteristics is the half-life of the radioactive isotope produced by neutron bombardment. This property is selected based on the measurements to be made and does not limit this invention. Half-lives of from about two days to about 250 days are commonly used. The energies of the gamma rays emitted by the isotope are also an important factor in selecting the element. This is especially true when two or more radioactive isotopes are to be used in the same flow stream, when it is desirable that the energy spectra of the different isotopes not excessively overlap. It is preferred that the energy spectrum of the gamma rays of the different isotopes not overlap such that the intensity of the gamma rays from each element can be more accurately measured. Thereby, the concentration of each individual isotope can be measured by spectral analysis of the gamma rays. The cost and availability of the target element embedded in the ceramic particles is one consideration in the selection of which element to use in a particle. Target elements suitable for use in the particles of this invention include gold, iodine, iridium, scandium, antimony, silver, hafnium, zirconium, rubidium, chromium, iron, strontium, cobalt, and zinc. Preferred target elements are antimony, iridium, scandium, silver, and hafnium. Most preferred are iridium and scandium. The target element may be present in its elemental form or as a compound. Compounds of elements useful in this invention are commonly salts or oxides. Iridium oxide is available as a black powder known as "iridium black." Hafnium oxide is available in pure form. Antimony bromide is available is very pure form as crystals. Other compounds of the element may be used, but oxides and salts are readily available. The compound should be stable at the high temperature of processing of the ceramic particle, such that sublimation does not deplete the particles of the compound. The temperature of sintering the particles will normally be above the melting point of the compound of the element. The concentration of the element in the ceramic particle will depend on the application of the particles, but an effective amount will be less than 5 per cent of the weight of the particle, preferably less than 1 per cent and most preferably less than 0.5 per cent by weight. Sizes of the particles will normally range from about 8 mesh to about 400 mesh. Particles of a wide range of sizes can be separated into desired sizes by sieving or other particle size separation techniques. Specific gravity of the particles will range from about 0.5 gm/cc to about 3.9 gm/cc. Particles of different densities can be made and separated by density using well known particle separation techniques. Radioactive ceramic particles may be manufactured by methods known in the ceramic industry for manufacturing proppants for use in hydraulic fracturing of wells or for manufacturing synthetic gravel for use in gravel packing of wells. Such ceramic particles for proppants are manufactured and used for their strength, their density and their sphericity. U.S. Pat. 4,668,645 discloses a particle for use as a proppant and a method of manufacturing such particles. U.S. Pat. No. 4,068,718 discloses the use of high strength and high density bauxite-containing particles for use as a proppant in wells and describes the methods of manufacture of such particles. The two aforesaid U.S. patents are incorporated herein for all purposes. Other methods for manufacturing sintered ceramic particles from powder, employing a variety of grinding, mixing, pelletizing and sintering techniques can be used. Ceramic particles of various densities and strengths can be made by mixtures of the oxides of aluminum, silicon, iron, magnesium and other minerals. Ceramic particles made for use as proppants or in gravel packing are manufactured by grinding the ceramic components to fine particle sizes, preferably less than 25 micron particle size, forming a paste of the finely ground material, forming the paste into rounded particles with pelletizing equipment and then sintering the particles. Such particles are sold by Norton Alcoa Proppants of Dallas, TX and by Carbo Ceramics Company of Dallas, TX. We have discovered that the ceramic components of such particles can be mixed with an element which, when bombarded with neutrons, forms a gamma ray emitting isotope, to produce a radioactive particle which has essentially the properties of the ceramic particle not containing the element. Such particles have high strength and resistance to crushing, and can be pumped into a variety of fluid streams without loss of radioactive material to the fluid stream and the conduits for the stream. MACROLITE.RTM. ceramic spheres sold by 3M Company of St. Paul, MN are made from a ceramic powder to have void spaces and specific gravities as low as about 0.58 gm/cc. The particles of this invention can be manufactured by incorporating a target element into the ceramic materials of MACROLITE.RTM. ceramic spheres before they are formed. It is advantageous to use elements which are not radioactive during formation of the particles, so that health hazards from radioactive materials are avoided during manufacture of the particles. This is an important feature of our invention. After the particles to be made radioactive, i.e. the precursor radioactive particles, are formed and sintered, the particles may be injected into a flow system or the particles may be transported to a nuclear reactor and radiated with neutrons such that the element present forms a radioactive isotope of that element. The equation given below describes the level of activity resulting from neutron radiation: EQU A=N.sub.f * (g/M)* X.sub.sect * h * N.sub.L * (1-e.sup.-(0.693/t1/2)) * t/3.7.times.10.sup.7 where: A.times.Activity in millicuries PA1 N.sub.L .times.6.022.times.10.sup.23 PA1 h=Isotopio Abundanoe PA1 X.sub.sect =Neutron Capture Cross Section PA1 g=Target element mass in grams PA1 t.sub.1/2 =Half life of produced nuclide in seconds PA1 N.sub.f =Neutron flux (neutron cm sec PA1 M=Target nuclide atomic weight in grams PA1 t=Neutron bombardment time in seconds. Activity produced is directly proportional to neutron bombardment time, neutron flux and target element mass. Once an element has been selected for its half-life of radioactivity and its desirable gamma ray spectrum, the concentration of the element needed to seed the particles and the neutron bombardment time can be calculated for a certain location in a certain nuclear reactor having a known neutron flux rate at different locations. The costs of the element and the neutron irradiation are selected to minimize the total cost of producing particles having an effective level of radioactivity. The selected amount of the target element is added to a suitable amount of ceramic powder which is to be formed into particles, such that the amount of powder to be irradiated, stored and injected into a stream is convenient for the irradiation facility, storage facilities and pumping equipment available for injecting the radioactive powder. Twenty millicuries of radioactivity is a common amount of radioactivity to transport in one batch. Therefore, this amount of radioactivity will be used as an example. Other amounts, for example 40 millicuries, are often used and the same principles are applicable. The equation above shows, for example, that if 20 millicuries of radioactivity from iridium-192 is to be produced, and the nuclear reactor produces a flux in the cans to be used in the reactor of 5=10.sup.12 neutrons cm.sup.-2 sec.sup.-1, 11.5 milligrams of iridium is needed for a bombardment time of 96 hours. This amount of iridium in the form of iridium black is added to a measured amount of ceramic powder, thoroughly mixed and blended, and formed into particles which are then sintered in accord with known techniques for producing sintered particles. The equation shows that if the amount of target element is doubled the amount of bombardment time can be halved. Therefore, the cost of producing particles having differing amounts of target elements can readily be determined, depending on the cost of the element and the cost of irradiation time. For many elements to be made radioactive, the lowest cost of radioactivity will be obtained with the largest amount of the target element in the ceramic particles. Then the highest limiting concentration of the element is determined by that concentration which changes the physical properties of strength or specific gravity of the ceramic particles into an unacceptable range of the property. Tests should be performed to determine the maximum acceptable concentration of target element by mixing various concentrations of element and ceramic components, sintering the particles and measuring the desired property. Specific gravity of particles may be measured by well known methods. Strength may be measured by crush tests of packed beds of particles or by individual particles strength tests which are well known for testing proppant particles. For some applications, only a small amount of particles is needed to contain 20 millicuries of radioactivity. But, it is possible to vary the concentration of target element in the ceramic over a wide range of concentrations. The lowest practical level of concentration will normally be determined by the volume available in the reactor used for irradiation or by the pump used to meter the particles into the stream where they will be used. For particles to be used in hydraulic fracturing, 20 millicuries of activity will preferably be contained in a volume of particles in the range from about 5 milliliters to about 100 milliliters of particles. Much larger amounts of particles could be used to contain the radioactivity, but the minimum concentration of target element in the ceramic will usually be determined by the pumping apparatus used to add the particles to a stream and the volume limitations of the reactor used for irradiation of the particles. Small volumes of particles can be used when accurate means are available for metering small amounts of particles into a stream. Radioactivity levels in the range from about 0.02 to about 20.0 millicuries per milliliter of particles are suitable. Preferably, the radioactivity level is in the range from about 0.2 to about 4.0 millicuries per milliliter of particles. After the particles are radiated with neutrons, their manufacture is complete. The particles must then be handled as radioactive sources. Well known techniques are used for protecting personnel from exposure to gamma rays emitted from the particles. Radioactive particles are added to a fluid which is being pumped into a well or are added to a fluid passing through surface piping or equipment for other applications by first mixing the radioactive particles with fluid to form a concentrated slurry. The liquid of the slurry may be viscosified by polymers. The slurry of radioactive particles is stored in a small closed radioactive materials reservoir. The reservoir may contain an agitator to keep the radioactive particles in suspension. The slurry is pumped from the reservoir into the low-pressure section of the flow stream to be traced With a low pressure pump such as a peristaltic pump. A high-pressure positive displacement pump can be used when the particles are injected into a high-pressure stream. The concentration of radioactive particles in the concentrated slurry or radioactive particles is usually in the range of about 10 grams to about 1000 grams per gallon of slurry. For most applications in wells, the slurry of radioactive particles is pumped out of the reservoir and into the stream at a rate such that 20 millicuries is used to trace from about 10,000 to about 100,000 pounds of solid particles or about 10,000 to about 100,000 gallons of fluid The activity level may vary in the range from about 0.1 to about 10 millicuries per thousand gallons of fluid or thousand pounds of solids. This amount of radioactivity is preferably contained in a volume of particles from about 5 cc to about 100 cc, but much larger volumes of particles may be used with a suitable pump for pumping the slurry of radioactive particles. If this amount of radioactivity is contained in a larger volume of particles, the radioactive particles will either contain a proportionately lower concentration of target element or the particles will be irradiated with neutrons for a proportionately smaller time. Preferably, the radioactive particles have about the same size and specific gravity as the non-radioactive particles in the flow stream when applied to tracing the particles in hydraulic fracturing and gravel packing operations. The particles should be small enough to produce low settling rates when used in cement slurries. For other types of fluids, the size and specific gravity will be selected to accomplish the purpose of the tracing application. For example, particles less than a certain size may be sieved from a mixture of sizes and added to a flow stream to determine the size of constrictions in the flow stream. Other applications dependent on size and specific gravity will be obvious to users of the particles. Specific gravity of the particles can be varied to be compatible with the application. The ceramic particles produced for hydraulic fracturing of wells vary in specific gravity from about 2.6 gm/cc to about 3.8 gm/cc. The density of these particles will not be significantly changed when the element to be made radioactive is embedded into the particles. Preferably, radioactive particles will be made to have approximately the same density as the non-radioactive particles with which they are used. Particles sold by 3M Company under the trademark MACROLITE.RTM. may have a specific gravity as low as 0.58 gm/cc. Again, preferably the radioactive particles will be made to approximately match the density of the non-radioactive particles. Strength of the particles will also vary with specific gravity, but even the relatively low strength of these low specific gravity particles will be adequate for gravel packing applications. Other applications not requiring high-strength can also use the low specific gravity particles. To avoid breaking and abrasion of particles, which can lead to loss of radioactivity from the particles, strength is preferably as high as consistent with other properties of the particles. After the radioactive particles are pumped into a well and out of the casing of the well so that they are no longer in the wellbore, a logging instrument is lowered into the well which is capable of detecting the gamma rays emitted by the isotope of the element. The gamma rays are capable of penetrating at least several inches of the earth surrounding the well and of penetrating the casing in the well. The gamma rays specific to the isotope of the element may be detected by performing an analysis of the energy of the gamma rays detected by the logging tool. A spectrum of energy of gamma rays characteristic of each radioactive element present is obtained. Techniques are used for determining, based on differing attenuation by Compton scattering of gamma rays having differing energy levels, the amount of gamma radiation coming from inside the wellbore, which would result from radioactive material lost from the particles during flow down the wellbore. Ceramic particles containing different target elements may be used at the same time or at different times in the pumping operation, may have different specific gravity or may have different size. The locations of the particles having different target elements are then determined with the gamma ray detector. In gravel packing operations, the radioactive particles may be inside the casing and outside a screen or other type filter in the wellbore. In this application, also, the logging tool is surrounded by the radioactive particles. In a flow stream or other surface apparatus, the gamma ray detection instrument is located in the vicinity of the radioactive particles to detect the gamma rays. Particle location of particles containing different target elements, which may also have different sizes and specific gravities, can be determined by spectral analysis of the gamma rays. The applications described above assumed that the particles had been irradiated by neutrons before injection into the well or flow stream. It should be understood that the precursor particles, obtained after sintering and before irradiation with neutrons, can be used in all applications if a neutron source is applied to the particles after they are in the flow stream or well. The particles of this invention will be stable to their environment of use, and can be irradiated or re-irradiated long after the time they are injected into a flow stream or well. EXAMPLE Ceramic particles containing iridium were manufactured. The procedures normally used for manufacturing a ceramic proppant particle containing primarily alumina and silica and smaller amounts of other oxide minerals were used. The ceramic materials were finely ground. About 20 grams of iridium black, available from Aldrich Chemical Company, was thoroughly mixed with 30,418 grams of the ceramic powder. The powdered mixture was then formed into a paste containing chemical binders. The paste was formed into approximately spherical particles. The ceramic materials are said to be "green" at this stage. The green ceramic particles were then sintered by firing in an oven at a temperature in the range of about 1400.degree. to 1500.degree. C. The particles containing the iridium were essentially the same density and crush resistance as the particles of high strength ceramic material without the iridium. The size range of the particles was from about 20 mesh to about 40 mesh. A portion of the particles containing iridium was then placed in a nuclear reactor for a period of 42 hours. A volume of 15 milliliters of particles was irradiated at a neutron flus of 9=10.sup.12 neutrons cm.sup.-2 sec.sup.-1. At the end of irradiation, the activity of the particles was measured to be about 20 millicuries. The activity calculated form the above equation was 20.7 millicuries. The radioactive particles was transported to a well where hydraulic fracturing operations was performed. Fracturing fluid is pumped down the casing of the well and through perforations. Sand in the size range 20-40 mesh is used as proppant. Radioactive ceramic particles manufactured according to the methods described herein are added to the fluid along with the sand at an appropriate time. The ceramic radioactive particles have about the density of sand and are 20-40 mesh size. After these fracturing operations are complete, the well is logged with the TRACERSCAN system. Results of the log show that gamma ray radiation from iridium is present only near the perforations. The very low level of radioactivity in the wellbore above the perforations shows that loss of radioactive iridium material from the particles during the operations is negligible. The invention has been described with reference to its preferred embodiments. Those of ordinary skill in the art may, upon reading this disclosure, appreciate changes or modifications which do not depart from the scope and spirity of the invention as described above or claimed hereafter.
	description	This application is a continuation of U.S. patent application Ser. No. 10/620,101, filed Jul. 14, 2003, now abandoned which is a continuation of application Ser. No. 10/012,193, filed Dec. 5, 2001, now abandoned which is a continuation-in-part of prior U.S. patent application Ser. No. 09/921,363, filed Aug. 2, 2001 (now U.S. Pat. No. 6,546,066), priority from the filing date of which is hereby claimed under 35 U.S.C. § 120. This application also claims the benefit of U.S. Provisional Patent Application No. 60/311,328 filed Aug. 9, 2001, under 35 U.S.C. § 119. This invention relates to reactor vessel closure head assemblies and, in particular, to an integrated head assembly for a pressurized light water reactor. In a typical pressurized water reactor (PWR) power plant, various mechanical components and systems are installed on the reactor vessel closure head. These mechanical components and systems include, for example, a control rod drive mechanism (CRDM) cooling system, a reactor vessel closure head lift rig, CRDM seismic restraints, and a CRDM missile shield. Each of these components is typically designed and installed as a permanent fixture to perform designated functions during plant operation. However, during refueling of the reactor these components have to be disassembled in order to remove the reactor vessel closure head from the reactor vessel. These components are stored in designated storage areas, generally inside the reactor containment. Typically, in a PWR plant, a series of steps are followed before the reactor vessel closure head is removed from the reactor vessel. The operational steps that are performed prior to detensioning the reactor vessel closure head studs include some or all of the following: Remove and store heavy concrete missile shields. Remove and store the CRDM cooling ducts. Remove the seismic restraints. Disconnect and store the CRDM power and rod position indicator cables. Install the reactor head lifting rig tripod. Remove cable trays and cables running from the reactor head to the operating deck or walls. Disconnect heated junction thermocouples, nuclear steam supply system instrumentation, monitoring system cables, and reactor head vent lines. Install temporary lead shield blankets around the vessel closure head area. The procedure also requires that the nuts and washers be removed from the reactor vessel closure head and placed in storage racks during preparation for refueling. The storage racks are then removed from the refueling cavity and stored at convenient locations inside containment prior to reactor vessel closure head removal and refueling cavity flooding. The above steps are then reversed while reinstalling the reactor vessel closure head and the related reactor systems. Each of these steps contributes significantly to the total cost associated with refueling the reactor. The total costs include costs associated with personnel man-hours required to perform the refueling, power plant down time and consequent loss of electricity production, radiation exposure to personnel, and potential human errors. In addition, the various components that must be removed for refueling activities require a large amount of the limited storage space available inside containment and raise the risk of inadvertent contamination of work and storage areas. Concepts and designs for integrating some of the reactor vessel closure head systems into a modular integrated head design have been proposed. For example, in U.S. Pat. No. 4,678,623 to Malandra et al., a modular head assembly is disclosed wherein vertical lift rods are attached to the reactor vessel lifting lugs, and a missile shield, seismic support platform, CRDM cooling system, and lift rig are supported by the lift rods above the reactor vessel closure head. Because most or all of the modular head assembly taught by Malandra et al. is supported by the lift rods, however, very large loads are concentrated at the clevis connection at the reactor vessel closure head lifting lugs, which may cause damage to the lifting lugs and/or the body of the reactor vessel closure head. In addition, very heavy components such as the missile shield and the fans are supported at the distal ends of three relatively long lift rods, resulting in an unstable structure that may subject the lift rods to undesirable compressive, bending and torsional stresses. Malandra et al. also does not provide a structure for putting a shroud around the CRDMs. In U.S. Pat. No. 4,830,814, Altman discloses an integrated head package having a missile shield that is slidably mounted near the distal end of three lift rods connecting to the reactor vessel closure head lifting lugs. A shroud is shown disposed about the CRDMs. Similar to the apparatus disclosed by Malandra et al., however, the heavy missile shield and lifting rig are installed at the distal end of three elongate lift rods that are connected at their proximal end to the reactor vessel closure head lifting lugs. The Altman apparatus, therefore, will also produce relatively high local loads in the reactor vessel lifting lugs and head. Altman also does not disclose any system for cooling the CRDMs. Some commercial light water reactors—for example, pressurized water reactors produced by Babcock & Wilcox (B&W)—have a reactor vessel closure head having inverted L-shaped flanges that extend upwardly from the reactor vessel closure head. Many B&W reactors also employ a control rod design wherein the lead screw from each control rod must be decoupled from the control rod and parked before the reactor vessel closure head is removed from the reactor vessel. In order to decouple and park the control rod lead screw, a 15-foot tool is typically inserted from above into the CRDM housing. For these types of commercial reactors, therefore, significant overhead space, or headroom, is required above the reactor vessel to accommodate the control rod tool, prior to removing the reactor vessel closure head. To provide the necessary head room, various components disposed above the reactor may need to be disassembled, removed, and stored before the control rod lead screws can be decoupled and parked and the closure head removed. There is a need, therefore, for an integrated head assembly for a pressurized water reactor that can be removed from the reactor vessel integrally with the reactor vessel closure head, and that does not introduce undue local stresses at the reactor vessel closure head and lifting lugs. The present invention is directed to an apparatus and method that satisfies this need. The apparatus includes an integrated head assembly for a pressurized light water nuclear reactor having a lift assembly that engages the lifting lugs on the reactor vessel closure head. A support structure is provided above the reactor vessel closure head with a shroud assembly and a baffle structure attached thereto. At least one upwardly extending duct for a CRDM cooling system is also provided. The apparatus includes a seismic support system and a missile shield attached to the support structure and disposed generally above the control rod drive mechanisms. At least one cooling air fan is fluidly connected to the duct. In an embodiment of the invention, the duct is cooperatively formed by the baffle and the shroud assemblies. In an embodiment of the invention, the support structure includes a ring beam with a number of saddle members that are disposed atop the reactor vessel closure head. The ring beam may be formed from three annular segments that are joined end to end. The support structure may also include a cylindrical support grid that extends upwardly from the ring beam. The shroud assembly may also comprise multiple axial segments and provide air inlet port(s) for the air cooling system. In a disclosed embodiment, the air cooling system includes an upper plenum interconnecting three cooling fans and two vertical ducts. An embodiment of a method for retrofitting a pressurized water nuclear reactor according to the present invention includes shutting down the nuclear reactor and removing the reactor vessel closure head from the reactor vessel and placing it on a reactor head stand. Lift rods are then attached to the lifting lugs on the reactor vessel closure head. An integrated head assembly module is then installed, the module including a ring beam that rests atop the reactor vessel closure head, a shroud assembly that sets atop the ring beam, and a baffle assembly attached to the shroud assembly. A seismic support system is then connected to the control rod drive mechanisms and a missile shield is installed above the CRDMs. A lifting assembly is then operatively attached to the lift rods above the missile shield, and the reactor vessel closure head is reinstalled on the reactor vessel. In yet another embodiment of the present invention, an integrated head assembly includes a lower ring beam that is disposed atop the reactor vessel closure head, lift rods that attach to the vessel head lifting lugs, a shroud assembly with cooling air ducts that is supported by the ring beam, a seismic support assembly and missile shield assembly installed above the reactor vessel closure head, and fans connected to the cooling air ducts. An upper ring beam and lifting tripod may be provided at the upper end of the lift rods, wherein the upper ring beam acts as a spreader for the lifting tripod. The upper ring beam is annular, providing access to the upper portion of the integrated head assembly. In a disclosed embodiment, the missile shield assembly includes an array of shield plates, each shield plate positioned above a control rod drive mechanism, the shield plates being removable such that individual control rod drive mechanisms can be accessed from above. The shield plates are slidably retained between grooved beams and a center shield plate in each row is removable, allowing adjacent shield plates to be slid to access the desired control rod drive mechanism. Referring now to the figures, an integrated head assembly 100 according to the present invention is shown atop a reactor vessel closure head 90 in FIG. 1. The reactor vessel closure head 90 is attachable to the top of a reactor vessel (not shown) and seals the reactor vessel, which contains the nuclear fuel (not shown). As seen more clearly in FIG. 2, the reactor vessel closure head 90 is a circular structure that typically includes a dome-shaped central portion 92 and an outer ring portion 94 having a plurality of stud mounting holes 95. The dome portion 92 supports a number of control rod drive mechanisms (CRDMs) 96 that extend vertically above the reactor vessel closure head 90 and pass through the head into the reactor vessel. The CRDMs 96 are electrically operated devices that control the vertical position of the control rods (not shown) inside the reactor vessel. CRDMs 96 are well known in the art and are therefore depicted in the figures in functional form, without showing the structural detail. For example, CRDMs generally include upwardly extending guide tubes that, for clarity, are not shown in FIG. 2. The reactor vessel closure head 90 includes three integral lifting lugs 98 that are used to facilitate lifting the head for removal and replacement. The preferred embodiment of the integrated head assembly 100 includes a lift assembly 150 that provides support structure for lifting the reactor vessel closure head 90, a cylindrical shroud assembly 200 that rests atop the reactor vessel closure head 90, a seismic support system 300 (see FIG. 12) that protects the CRDMs 96 and integrated head assembly 100 from seismically-induced loads, a missile shield 400 (see FIGS. 11A and 11B) that provides protection in certain accident scenarios wherein the CRDMs 96 and/or control rods are ejected, a baffle assembly 500 (see FIG. 8) for directing the flow of cooling air to the CRDMs 96, and a CRDM cooling system including cooling air ducts 600 connected through an upper air plenum 680 to cooling fans 190. The primary components of the lift assembly 150 are shown in FIG. 2. The lift assembly 150 includes a bottom ring beam 151 that sets atop the reactor vessel closure head 90. The ring beam 151 of the preferred embodiment has a short, cylindrical lower portion 152 and a flange portion 153 that extends outwardly from the top edge of the cylindrical portion 152. A plurality of saddle members 155 is disposed peripherally around the ring beam 151, the saddle members 155 having a lower surface that generally conforms with the shape of the reactor vessel closure head 90, thereby distributing the weight of the integrated head assembly 100 over a larger portion of the reactor vessel closure head 90. In the preferred embodiment, the ring beam 151 comprises three generally identical segments that are connected through the lift rod connecting members 162, as described below. Three lift rods 160 extend vertically upwardly from the ring beam 151. Each lift rod 160 includes a connecting member 162 at one end having a clevis-type connector 163 that slidably engages one of the head lifting lugs 98. The connecting member 162 is attached to the head-lifting lug 98 with a clevis pin 166. A detail of the connecting member 162 of the preferred embodiment is shown in FIG. 3. The connecting member 162 is positioned between ring beam 151 segments, and includes oppositely disposed horizontal flanges 164 that connect to the ring beam 151 with bolts 165, thereby interconnecting the ring beam segments and removably attaching the ring beam 151 to the reactor vessel closure head 90. Although the preferred embodiment utilizes three ring beam segments, it will be appreciated that other configurations are possible and contemplated by the present invention, including, for example, a unitary ring beam having cut out portions to accommodate connecting members. The upper end of the lift rods 160 are threaded and extend through orifices 182 in a circular fan support plate 180 (see FIG. 10), where they are attached to the fan support plate 180 with the tripod base brackets 172 and/or other suitable connecting hardware. A lift tripod 170 is disposed above the fan support plate 180 and includes three rods 171, each rod 171 pivotally connected at one end to a tripod base bracket 172, and pivotally connected at the opposite end to a lift shackle 174. It will be appreciated that the lift assembly 150 permits the integrated head assembly 100 and the reactor vessel closure head 90 to be lifted as a single unit by an appropriate lifting mechanism, such as a hoist (not shown), acting on the lift shackle 174. It will be appreciated that the fan support plate 180 also functions as a spreader for the lift tripod 170. The three large apertures 184 through the fan support plate 180 are the outlet air ports for the upper air plenum 680 fluidly connected to the cooling fans 190 as described below. As seen most clearly in FIG. 4, a generally cylindrical support column assembly 202 is provided on top of the ring beam 151. The support column assembly 202 includes six support columns 204 that extend upwardly from the ring beam 151, each support column 204 preferably being positioned above one of the saddle members 155. The support columns 204 are attached to the ring beam 151 with a clip angle bolted connection 206. Curved transverse members 208 interconnect the support columns 204 at three vertically spaced locations. The support column assembly 202 provides a cylindrical grid support structure over the reactor vessel closure head 90 that supports the integrated head assembly components, and transfers the weight and dynamic loads from the integrated head assembly 100 to the ring beam 151. Although the preferred support structure has been described, it will be apparent to one of skill in the art that many variations in the support structure may be made without departing from the present invention. For example, and not by way of limitation, more or fewer support columns 204 and/or transverse members 208 may be utilized, or the transverse members 208 may be replaced with hoop beams that encircle the support columns. The shroud assembly 200 of the preferred embodiment includes bottom shroud 220, a middle shroud 240 and an upper shroud 260 (see FIG. 1). The bottom shroud 220, shown in FIG. 5, is a cylindrical assembly that is installed at the lower end of the support column assembly 202, extending upwardly from the ring beam 151. The bottom shroud 220 includes an outer wall panel 222 that is preferably formed in multiple sections. The outer wall 222 includes access openings 224 that provide access to the interior of the shroud assembly 200—for example, to monitor and/or service the CRDMs 96. A plurality of doors 226 are attached at the access openings 224, whereby the access openings 224 can be closed, for example, during operation of the reactor and when access to the interior of the shroud assembly 200 is not otherwise required. It will be appreciated that although hinged attachments are shown, any other suitable closure system could be used—for example, removable panels, sliding panels, and the like. The bottom shroud outer wall 222 and doors 226 may be made from any suitable material such as, for example, ASTM-A36 carbon steel. The thickness of the panel 222 and doors 226 are selected depending on the required level of radiation shielding that is desired. For example, in the preferred embodiment, the panel 222 and doors 226 are ¼ inch thick if radiation shielding is not an issue, and 1½ inches thick if radiation shielding is desired. A lower baffle portion 520 extends through the bottom shroud 220, comprising a left panel 521, a right panel 522, a forward panel 523, and a rearward panel 524. The baffle panels 521, 522, 523, and 524 are oriented approximately parallel to and generally surround the CRDMs 96. The lower baffle portion 520 defines a central airflow path for cooling airflow. The left and right panels 521, 522, cooperatively with a portion of the outer wall panel 222, form a pair of longitudinal channels 620 near the periphery of the integrated head assembly 100. Referring now to FIG. 6, a middle shroud 240 is aligned with the bottom shroud 220 and extends upwardly from the bottom shroud 220. Similar to the bottom shroud, the middle shroud 240 includes a multisection outer wall panel 242 that attaches to the support column assembly 202. Air inlet ports 244 are provided on opposite sides of the middle shroud 240 that permit ambient air to enter the shroud assembly 200 for cooling the CRDMs 96. A middle baffle portion 540 of the baffle assembly 500 extends vertically through the middle shroud 240. The baffle middle portion 540 includes a left panel 541 and a right panel 542 that each attach to the shroud outer wall 242, forming a pair of peripheral longitudinal channels 640, aligned with and vertically continuing the channels 620 formed in the bottom shroud 220. The baffle assembly middle portion 540 is preferably open at the oppositely disposed forward and rearward regions between the baffle left and right panels 541, 542, which openings are generally aligned with the shroud air inlet ports 244. Horizontal plates 248 extend inwardly from the bottom of the middle shroud 240 from the air inlet ports 244, such that air entering the air inlet ports 244 is directed to the interior of the baffle assembly 500 towards the CRDMs 96. An upper shroud 260 is shown in FIG. 7. The upper shroud 260 extends upwardly from the middle shroud 240 and includes an outer wall 262 that attaches to the support column assembly 202. A baffle upper portion 560 of the baffle assembly 500 extends vertically through the upper shroud 260, including a left panel 561 and a right panel 562, aligned with the middle baffle portion 540. The baffle upper portion 560 and upper shroud outer wall 262 cooperatively form a pair of longitudinal channels 660 aligned with and continuing the middle section channels 640. The forward and rearward portions of the upper shroud 260 have apertures 264 to provide electric power and control access to the CRDMs 96 through a CRDM cable disconnect panel 120 (see FIG. 13). It will be appreciated that the shroud channels 620, 640, and 660 cooperatively form longitudinal cooling ducts 600 that extend from near the reactor vessel closure head 96 upwardly substantially through the length of the shroud assembly 200. A view of the baffle assembly 500 disposed within the support column assembly 202 is shown in FIG. 8, with the shroud outer walls 222, 242, 262 removed for clarity. The baffle structure 500 extends upwardly from near the reactor vessel closure head 90 and provides a flow path for cooling air to the CRDMs 96. A gap is provided between the reactor vessel closure head 90 and the baffle assembly 500 that functions as an air outlet port such that the cooling air flowing downwardly along the CRDMs 96 exits the baffle and flows outwardly toward the periphery of the integrated head assembly. An upper air plenum 680, shown in FIG. 9, is provided at the top of the integrated head assembly 100. The upper air plenum 680 is a generally circular plenum that includes the fan support plate 180 having outlet ports 184 to the cooling air fans 190. The fan support plate 180, with three cooling air fans 190 installed, is shown in FIG. 10. The plenum lower panel comprising the missile shield 400 discussed in more detail below and a vertical peripheral wall 682 are provided between the fan support plate 180 and the missile shield 400. The missile shield 400 includes left and right cutout portions 420 that are disposed over the cooling air ducts 600 and provide the inlet ports to the upper air plenum 680. In the preferred embodiment, the cooling air fans 190 draw air upwardly through the upper air plenum 680. In operation, therefore, the fans 190 draw air into the middle shroud inlet ports 244, downwardly along the CRDMs 96 in the baffle assembly 500, upwardly through the ducts 600 into the upper air plenum 680, and out of the integrated head assembly 100. Referring now to FIGS. 11A and 11B, the missile shield 400 is provided above the CRDMs 96 near the top of the baffle assembly 500. The primary purpose of the missile shield 400 is to protect against the possible ejection of the CRDMs 96 or fuel rods in certain accident scenarios. The missile shield 400 may be made from any suitably strong material and is preferably a steel panel having circular forward and rearward portions 410 and cutout left and right portions 420 that are shaped to accommodate the cooling air ducts 600 as discussed above. The missile shield 400 is supported by the support columns 204 and includes outwardly extending tab portions 430 to facilitate attachment to the support columns 204. FIG. 11B shows a plan view of the missile shield 400 installed in the integrated head assembly 100 (with some structural detail removed for clarity). A seismic support system 300 for the integrated head assembly 100 is shown in FIG. 12. The seismic support system 300 is designed to support the CRDMs 96 in a seismic event to ensure that the control rods are able to drop down into the reactor if it is necessary to shut the reactor down. The seismic support system 300 includes an array of seismic cap plates 310 of various shapes (310a, 310b, 310c, and 310d), each seismic cap plate attached to the upper end of a CRDM 96. The seismic cap plates 310 include a generally flat portion 311 with a notched-out section 312 to accommodate electrical power and control cables. A hat-shaped recess or cavity 313 is formed at an intermediate portion of the seismic cap plate 310, and sized to accommodate the end of a CRDM 96. The CRDM 96 extends into the cavity 313 and is attached to the respective seismic cap plate 310. As shown in FIG. 12, the flat portions 311 of the cap plates 310 are approximately adjacent neighboring cap plates 310, such that the cap plates 310 cooperatively form a lateral support panel across the CRDMs 96. A baffle stiffener ring beam 320 surrounds the seismic cap plate 310 array, and preferably a plurality of adjustable engagement mechanisms (not shown) are provided between the cap plate 310 array and the baffle stiffener ring beam 320, whereby only a slight gap is provided therebetween. A seismic ring beam 340, comprising a generally circular beam, surrounds the baffle stiffener ring beam 320 and is connected to the ring beam 320 with forward and rearward seismic stiffener plates 330 and left and right seismic stiffener beams 335. In the preferred embodiment, a bolt tensioner rail 350 is provided on the outer perimeter of the seismic ring beam 340 to accommodate a bolt tensioning/detensioning apparatus (not shown). A plurality of seismic restraints 360 connects the seismic ring beam 340 to a relatively stable anchor such as the reactor containment walls (not shown). FIG. 13 shows the CRDM cable disconnect panel 120 discussed above, which is preferably installed in the upper shroud 260. The cable disconnect panel 120 provides an array of electrical connectors 122 providing a central location to disconnect the CRDMs 96 from their electric power and control systems prior to removal of the reactor vessel closure head 90. More than one cable disconnect panel 120 may be provided. The integrated head assembly 100 of the present invention simplifies the removal and replacement of the reactor vessel closure head 90 for standard maintenance procedures, as well as for unscheduled outages, by integrating the lifting support, CRDM cooling system, missile shield, and seismic support into a single assembly that may be removed as a unit from the reactor vessel. In practice, to remove the integrated head assembly a polar crane hook or other appropriate lifting and moving mechanism is attached to the tripod assembly lift shackle 174, the CRDM cables are disconnected at the cable disconnect panel 120, the seismic restraints 360 are disconnected, and the reactor vessel closure head studs are loosened and removed. Additional site-specific steps well known in the art and not important to understanding of the present invention may also be required, such as moving one or more cable bridges away from the lift path of the head. The reactor vessel closure head can then be removed from the reactor vessel to permit the necessary maintenance procedures to be performed. Although the preferred embodiment has been described in some detail, it will be readily apparent to one of skill in the art that many variations in the present invention may be made without departing from the present invention. It will be appreciated that the present invention is amenable to retrofitting of existing nuclear power plants. No modifications to the reactor vessel closure head 90 would be required. In a preferred method of retrofitting an existing plant, it is contemplated that the design, fabrication, and installation effort for the integrated head assembly 100 of the present invention would be performed over a period of approximately 24 calendar months. The integrated head assembly 100 installation would preferably be performed during a refueling outage of the plant, such as are typically scheduled every 18 months. Accordingly, the design/fabrication/installation process needs to be scheduled based on the plant refueling schedule. The integrated head assembly shroud assembly 200 and associated components may be fabricated and shipped in three modules. The first module comprises the bottom ring beam 151, the bottom shroud 220, the baffle lower portion 520, and other appurtenances associated with the bottom shroud 220. The second module would comprise the middle shroud 240, the baffle middle portion 540, including the cooling air inlets, and other associated appurtenances. The third module would include the upper shroud 260, baffle upper portion 560, partial air inlet, partial assembly of the CRDM 96 seismic support system 300, and related head area cable support systems and wires in pre-routed condition, the cable disconnect panel(s) 120, the missile shield 400, the cooling fans 190, and other associated appurtenances. It is contemplated, although clearly not critical to the present invention, that the three lift rods 160 and the lift tripod 170 would be shipped as separate items. The assembly of these components would preferably be accomplished while the reactor vessel closure head 90 is resting on a reactor head stand inside the containment. In a typical installation, the existing rig assembly would first be disassembled from the reactor vessel closure head 90. The three lift rods 160 are then attached to the three lift lugs 98 on the reactor vessel closure head 90. Temporary supports are preferably provided at the top of the lift rods 160 to hold them in place. Assembly of integrated head assembly components is accomplished starting from the bottom of the integrated head assembly (i.e., near the reactor vessel closure head 90) and continuing on in upward direction. The first module is inserted through three lift rods 160 and the bottom ring beam 151 is attached to the connecting members 162 of the lift rods 160. Once the lower shroud 220 is in place, the second module is lowered through the lift rods 160 and bolted to the bottom shroud 220 at the transverse members (i.e., ring angles) 208 and at the support columns 204. For accessibility for bolted connections, some or all of the outer wall panel 242 of the middle shroud 240 may be removed from the shroud. It is possible that the elevation of the top of the second module is very close to the elevation of the CRDM seismic cap plates 310. In such cases, install all CRDM seismic cap plates 310 on all CRDMs 96 prior to lowering the third module over the lift rods 160. In the next step of this preferred method, lower the third module through three lift rods 160 and attach it to the top of the middle shroud 240 by bolts at the transverse members 208 as well as at the support columns 204. Again for accessibility for bolted connections, some or all of the outer wall panel 262 of the upper shroud 260 may be removed from the shroud. The installation of the CRDM seismic support system 300 may be completed at this time, excepting attachment of the seismic restraints 360. The seismic restraints 360 are preferably installed when the integrated head assembly is in place atop the reactor vessel. After the third module is assembled and installed, the missile shield 400 may be installed along with the cooling fan support plate 180 including the rest of the upper air plenum 680, the cooling fans 190, and the lift tripod 170. After the cooling fan base is installed, the refueling disconnect panels may be installed near the bottom surface of the cooling fan support plate 180. The retrofit is completed with the assembly of miscellaneous non-structural elements. After the assembly is complete, the whole integrated head assembly 100 with the reactor vessel closure head 90 is lifted and held in a lifted position for some time by the containment polar crane and then put back on the head stand. At this time all component connections are checked once again for their effectiveness. When it is ready to install the reactor vessel closure head 90 back on the reactor vessel, the entire integrated head assembly 100, with the reactor vessel closure head 90, is lifted from the head stand and moved over the reactor vessel and lowered slowly until the head is properly aligned and resting on the reactor vessel, and the assembly is attached to the reactor vessel. After the reactor vessel closure head studs are properly torqued, the seismic restraints 360 are attached to the integrated head assembly 100 on one side and to the refueling walls on the other side. After the integrated head assembly is installed it is contemplated that airflow test would be performed to ensure proper operation of the cooling fans 190 and the entire CRDM cooling system. It will be apparent to one of skill in the art that other assembly methods are possible although less preferred, including, for example, installing or partially installing the integrated head assembly to the reactor vessel closure head while it is attached to the reactor vessel, or installing the integrated head assembly to the reactor vessel closure head utilizing more smaller modules, or fewer larger modules. In particular, it is contemplated that the integrated head assembly 100 could be substantially completely assembled prior to installing it on the reactor vessel closure head. As discussed above, some commercial nuclear reactors require that the lead screw from each control rod be decoupled from the control rod and parked prior to removal of the reactor vessel closure head. Such reactors typically require significant headroom over the reactor vessel in order to decouple and park the control rod lead screws. A second embodiment of the present invention that provides substantial reactor vessel headroom, is shown in FIGS. 14 to 20. Referring now to FIG. 14, a perspective view of a second embodiment of an integrated head assembly 1100 according to the present invention is shown. The integrated head assembly 1100 includes three lift rods 160 that attach to lifting lugs 1098 on a reactor vessel closure head 1090—for example, in a manner similar to that shown in FIG. 3. Although it is not essential to the present invention, in the disclosed example the reactor vessel closure head 1090 includes an upwardly-extending flange 1093, generally in the shape of an inverted “L,” as seen most clearly in FIG. 15. Such flanges are a common feature of certain existing commercial light water reactor designs. The integrated head assembly 1100 includes a ring beam 1151 having an L-shaped lower portion 1152 that is adapted to rest atop the reactor vessel closure head flange 1093. It will be appreciated that this configuration distributes the weight of the integrated head assembly 1100 over a large portion of the reactor vessel closure head 1090. As on the first embodiment disclosed above, the ring beam 1151 also includes a ring-shaped horizontal flange portion 1153. The ring beam 1151 may further be attached to the reactor vessel closure head flange 1093—for example, with nuts and bolts or other clamps (not shown) as are well known in the art. In the preferred embodiment, the ring beam 1151 is formed in three approximately 120° segments, although more or fewer segments that cooperatively form a ring beam are also contemplated by the present invention. The integrated head assembly 1100 includes a lift assembly having three lift rods 160 (two shown in FIG. 14) that connect at the lower end to the lifting lugs 1098 on the reactor vessel closure head 1090 (for example, with clevis-type connecting members 162) and at the upper end to a lift tripod 170 (for example, with tripod base brackets 172). The lift assembly is generally the same as that shown in FIG. 2, except that an upper ring beam 1180 acts as a spreader for the lift tripod 170 (rather than the fan support plate 180). The upper ring beam 1180 is an annular beam, thereby providing access to the interior of the integrated head assembly 1100 from above. The upper end of the lift rods 160 are threaded and extend through orifices in the upper ring beam 1180, where they are attached to the upper ring beam 1180 with the tripod base brackets 172 and/or other suitable connecting hardware. The lift tripod 170 is disposed above the upper ring beam 1180, and includes three rods 171, each rod 171 pivotally connected at one end to one of the tripod base brackets 172 and pivotally connected at the opposite end to a lift shackle 174. It will be appreciated that the lift assembly 170 permits the integrated head assembly 1100 and the reactor vessel closure head 1090 to be lifted as a single unit by an appropriate lifting mechanism, such as a hoist (not shown), acting on the lift shackle 174. A generally cylindrical shroud assembly 1200 extends upwardly from the ring beam 1151, preferably including a bottom shroud 1220, a middle shroud 1240, and an upper shroud 1260. Access doors 226 are provided in the bottom shroud 1220 over access openings 224. A baffle assembly 1500 extends upwardly from the reactor vessel closure head 1090, the baffle assembly being attached to the shroud assembly 1200, and cooperatively with the shroud assembly 1200 forming a plurality of vertical cooling air ducts 1600 that extend upwardly for a substantial portion of the integrated head assembly height. In the preferred embodiment three cooling air ducts 1600 are provided, circumferentially spaced around the integrated head assembly 1100, as seen most clearly in FIG. 16. Referring again to FIG. 14, three cooling fans 190 are installed in the vertical wall of the upper shroud 1260. The cooling fans 190 are directed outwardly, and each fan 190 is fluidly connected to one of the vertical cooling air ducts 1600, to draw air upwardly through the air duct 1600. Inlet ports 1244 through the middle shroud 1240 and the baffle assembly 1500 provide a flow path for cooling air to enter the integrated head assembly 1100 for cooling the control rod drive mechanisms 96. Horizontal plates 1248 are provided at the inlet ports 1244 between the shroud wall and the baffle assembly 1500. It will now be appreciated that the cooling fans 190 operate to draw ambient air into the integrated head assembly 1100 through the inlet ports 1244. The air flows into the baffle assembly 1500 and downwardly over the CRDMs 96 convectively cooling the CRDMs 96, and into the inlet disposed at the bottom of the cooling air ducts 1600, where the air flows upwardly and out of the assembly 1100 through the cooling fans 190. Although the upper end of the cooling air ducts 1600 of the preferred embodiment are not fluidly interconnected at the top end, it is contemplated that an annular upper air plenum (not shown) could be provided to fluidly connect the cooling air ducts 1600. An upper air plenum would improve airflow over the control rods 96 if one or two of the fans 190 fail or are otherwise not operational. A seismic support system 1300 for the integrated head assembly 1100 is shown in FIG. 17. The seismic support system stabilizes the CRDMs 96 in a seismic event to ensure that the control rods are able to drop down into the reactor if it is necessary to shut the reactor down. In this embodiment, the seismic support system 1300 includes an array of seismic support plates 1310 having an aperture 1313 that is sized to slidably receive the end of a CRDM 96. The seismic support plates 1310 include a second aperture 1312, which may overlap the first aperture, to accommodate electrical power and control cables and piping for the CRDM stator cooling water. A seismic support plate 1310 is provided for each CRDM 96, forming an array of plates as shown in FIG. 17, and the seismic support plate 1310 clamps to the CRDM 96. As shown in FIGS. 17 and 18, the seismic support plates 1310 are approximately adjacent to neighboring seismic support plates 1310, such that the seismic support plates 1310 cooperatively form a lateral support panel across the CRDMs 96. Although the seismic support plates are shown fixedly attached to each CRDM 96, is it also contemplated that the seismic support plates 1310 may alternatively loosely engage the CRDMs 96 and be attached to a rectangular grid frame structure (not shown) that holds the seismic support plates 1310 in proper alignment. A baffle stiffener ring beam 1320 surrounds the seismic cap plate 1310 array. Adjustable engagement mechanisms (not shown) may be provided between the cap plate 1310 array and the baffle stiffener ring beam 1320, to adjustably maintain a slight gap therebetween. A seismic ring beam 1340, comprising a generally circular beam, surrounds the baffle stiffener ring beam 1320, and is connected to the ring beam 1320 with a plurality of seismic stiffener plates 1330. In the preferred embodiment, a bolt tensioner rail 1350 is provided on the outer perimeter of the seismic ring beam 1340 to accommodate a bolt tensioning/detensioning apparatus (not shown). In this embodiment the seismic support system does not include any seismic restrains for connection to the containment wall. The seismic forces are therefore transmitted to the reactor vessel closure head 1090 through the integrated head assembly 1100 structure. A missile shield assembly 1400 is disposed above the seismic support system 1300, as shown in more detail in FIG. 19. The missile shield assembly 1400 includes a support structure 1410 including three work platforms 1412 that are circumferentially spaced around the missile shield assembly. A sliding frame structure comprising a number of parallel slotted beams 1420 is disposed generally between the work platforms 1412. A plurality of missile shield plates 1422 are slidably inserted between adjacent slotted beams 1420, as shown in FIG. 19. The missile shield plates 1422 are arranged in an array between adjacent slotted beams 1420 substantially filling the area between the work platforms 1412 over the CRDMs 96. A central portion of each slotted beam 1420 is provided with a removable frame member 1424 that is secured to the slotted beam 1420, for example, with bolts 1426, such that removal of adjacent frame members 1424 will permit the missile shield plate 1422 disposed therebetween to be lifted out. It will be apparent from FIG. 19 that if a shield plate 1422 in any row of shield plates is removed, adjacent shield plates 1422 in the same row can be slidably moved to provide access therebelow. In the preferred embodiment, the missile shield plates 1422 are each provided with a pair of handles 1428 to facilitate sliding the shield plates 1422 within the slotted tracks. In the embodiment shown in FIG. 19, the shield plates 1422 are sized such that one shield plate 1422 is disposed directly above each one of the CRDMs 96. It is also preferred that the missile shield assembly 1400 be made from a suitable material to provide radiation shielding to workers above the missile shield assembly 1400, and that the assembly be sturdy enough to safely support such workers. It should now be appreciated that the missile shield assembly 1400 disclosed above provides a work platform directly over the CRDMs 96, whereby the 15-foot tool can be inserted into the CRDM casing to decouple and park the lead screw in each CRDM 96 so that the reactor vessel closure head 1090 can be removed. It will also be appreciated that by removing only a single shield plate 1422 at a time and sliding adjacent shield plates 1422 to access the desired CRDM 96, the workers' radiation exposure will be minimal when performing this task. As seen most clearly in FIGS. 14 and 20, in the disclosed embodiment the integrated head assembly 1100 is provided with a retractable cable bridge 1700. The retractable cable bridge 1700 provides a platform for supporting cables that provide electric power and control signals (i.e., rod position indicator cables) to the CRDMs 96. The cables are preferably removably connected to the CRDMs 96 through a CRDM cable disconnect panel 120 such as that described above and shown in FIG. 13. The cable bridge 1700 includes a support platform 1710 that is pivotally connected at an inner end 1720 to a work platform 1412 of the missile shield assembly 1400. A pair of cables 1724 pivotally connects an outer end 1722 of the support platform 1710 to the upper ring beam 1180 through an attachment bracket 1730. A pair of motorized pulleys 1732 is provided to retract and extend the cable bridge 1700, as desired. While the preferred embodiment of the invention has been illustrated and described, it will be appreciated that various changes can be made therein without departing from the spirit and scope of the invention.
054917301	abstract	Pipes are mounted horizontally on an outlet portion of a gas vent pipe in a condenser-type heat removal system, and have-openings which are formed only in a portion below a horizontal plane in which axes of these pipes lie, thereby enlarging a region where uncondensed steam is mixed with water in a suppression pool. With this arrangement, a surface portion of the water of the suppression pool is prevented from becoming hot, and the temperature of this pool water is uniformed. As a result, the temperature of the water surface of the suppression pool is lowered, thereby decreasing the pressure within a primary containment vessel. This enhances the reliability of the primary containment vessel, and reduces a design strength of the primary containment vessel.
	claims	1. An apparatus for measuring film stack characteristics of a sample, the apparatus comprising: a beam generator configurable to direct an electron beam towards the sample such that the electron beam completely penetrates a plurality of desired layers of the film stack, the electron beam causing X-rays to emanate from the sample; at least a first and a second wavelength dispersive X-ray detector positioned above the sample wherein each detector detects X-rays about a different characteristic emission level, wherein the first detector is configured to detect X-rays having characteristic emission levels for a top layer of the film stack and the second detector is configured to detect X-rays having characteristic emission levels for an underlying layer that lies beneath the top layer, whereby material characteristics of the desired layers can be measured simultaneously; and an analysis unit that collects data resulting from the detected X-rays, wherein the data that is collected is raw data, the analysis unit also configured to compare predicted data derived from one or more equations that model the film stack against the raw data. 2. The apparatus as recited in claim 1 wherein the first X-ray detector is configured to detect X-rays of a specific energy level. claim 1 3. The apparatus as recited in claim 1 wherein the wavelength dispersive system contains a reflective surface and a sensor, the reflective surface configured to direct X-rays of a predetermined energy level to the sensor. claim 1 4. The apparatus as recited in claim 1 further comprising a processor linked to the beam generator and to the first X-ray detector. claim 1 5. The apparatus as recited in claim 4 wherein the processor is configured to control the first X-ray detector so that it detects X-rays of a specific energy level. claim 4 6. The apparatus as recited in claim 4 wherein the processor is configured to control the beam generator so that the electron beam directed to the sample penetrates at least a conductive film layer and a liner film layer of the sample. claim 4 7. An apparatus as recited in claim 1 wherein each of the characteristic emission levels correspond to a different layer of the film stack. claim 1 8. An apparatus as recited in claim 1 wherein the electron beam completely penetrates the top and the underlying layers of the film stack so that the thickness of the top and the underlying layers can be determined. claim 1 9. An apparatus as recited in claim 1 wherein the electron beam completely penetrates at least a conductive film layer and a liner film layer of the sample. claim 1 10. An apparatus as recited in claim 1 wherein the electron beam is set at a substantially constant voltage level. claim 1 11. The method of determining film stack characteristic values as recited in claim 10 further comprising recording the set of estimated film stack characteristic values when a difference between the predicted data and the raw data is equal to or smaller than the predetermined margin of error, wherein the estimated film stack characteristic values are an acceptable estimate of the film stack""s characteristic. claim 10 12. A method for measuring at least one characteristic of a film stack on a sample, the method comprising: directing a charged particle beam towards the sample such that the charged particle beam completely penetrates at least two layers of the film stack, the charged particle beam causing X-rays to emanate from the sample; detecting X-rays at a first characteristic emission level that represents an emission level for a top layer of the film stack using at least a first wavelength dispersive X-ray detector that is positioned above the sample; detecting X-rays at a second characteristic emission level that represents an emission level for an underlying layer of the film stack using at least a second wavlength dispersive X-ray detector that is positioned above the sample, the underlying layer being a layer of material underneath the top layer; collecting data resulting from the detected X-rays, wherein the data that is collected is raw data; and comparing predicted data derived from one or more equations that model the film stack against the raw data. 13. The method for measuring as recited in claim 12 , further comprising configuring the first X-ray detector to detect X-rays of a specific energy level. claim 12 14. The method for measuring as recited in claim 12 further comprising positioning a reflective surface contained within the wavelength dispersive system in an orientation to direct X-rays of a predetermined energy level to a sensor contained within the wavelength dispersive system. claim 12 15. The method for measuring as recited in claim 12 , the method further comprising selecting a charged particle beam energy and a charged particle beam current at which the charged particle beam will be produced. claim 12 16. The method for measuring as recited in claim 12 wherein a conductive film layer and a liner film layer are two of the at least two layers that are penetrated by the charged particle beam. claim 12 17. The method of determining film stack characteristic values as recited in claim 12 wherein the raw and predicted data represent a count value of X-rays having a specific energy level, the count value being the total number of X-rays received by each of the wavelength dispersive systems over a period of time. claim 12 18. A method as recited in claim 12 wherein each of the characteristic emission levels correspond to a different layer of the film stack. claim 12 19. A method as recited in claim 12 wherein the charged particle beam completely penetrates the thickness of the top and the underlying layers of the film stack so that the thickness of the top and the underlying layers are determined. claim 12 20. An apparatus for measuring the thickness of two or more layers within a film stack sample, the apparatus comprising: a beam generator configurable to direct an electron beam towards the sample such that the electron beam completely penetrates at least two layers of the film stack, the electron beam causing X-rays to emanate from the sample; at least a first and a second wavelength dispersive X-ray detector positioned above the sample wherein each detector is configured to detect a respective portion of the X-rays emanating from the sample, whereby material characteristics of the at least two layers can be measured simultaneously; and an analysis unit that collects data resulting from the detected X-rays, wherein the data that is collected is raw data, the analysis unit also configured to compare predicted data derived from one or more equations that model the film stack against the raw data. 21. An apparatus as recited in claim 20 wherein the first X-ray detector is configured to detect X-rays of a specific energy level. claim 20 22. An apparatus as recited in claim 20 wherein the first X-ray detector is a wavelength dispersive system. claim 20 23. An apparatus as recited in claim 22 wherein the wavelength dispersive system contains a reflective surface and a sensor, the reflective surface configured to direct X-rays of a predetermined energy level to the sensor. claim 22 24. An apparatus as recited in claim 20 further comprising a second X-ray detector, wherein the first and second X-ray detectors are wavelength dispersive systems. claim 20 25. A method for measuring as recited in claim 12 , further comprising: claim 12 selecting a set of estimated film stack characteristic values; and obtaining the predicted data by solving the one or more equations that model the film stack using the set of estimated film stack characteristic values. 26. A method for measuring as recited in claim 25 , further comprising: claim 25 selecting a new set of estimated film stack characteristic values when a difference between the predicted data and the raw data is larger than a predetermined margin of error; and obtaining a new set of predicted data by solving equations which model the film stack using the new set of estimated film stack characteristic values when the difference between the predicted data and the raw data is larger than the predetermined margin of error. 27. An apparatus as recited in claim 20 wherein the electron beam can be scanned over the film stack sample in a scan pattern. claim 20 28. An apparatus as recited in claim 27 further comprising: claim 27 an octupole for aligning the electron beam generated by the beam generator; and a lower quadrupole for further adjusting the alignment of the electron beam.
056595905	summary	TECHNICAL FIELD This invention relates to boiling water nuclear reactors and specifically, to a dew core shroud and pump deck design which allows for easy removal and/or replacement of these reactor structural components when damaged or otherwise in need of repair or replacement. BACKGROUND Typical boiling water nuclear reactors include a reactor assembly which consists of the reactor vessel and its internal components including the core, core shroud, top guide assembly, core plate assembly, steam separator and dryer assemblies, and jet pumps. Also included in the reactor assembly are the control rods, control rod drive housings and the control rod drives. The reactor vessel is a generally cylindrical pressure vessel (RPV) with a single full diameter removable head. The shroud is a cylindrical stainless steel structure located within the RPV and which surrounds the core, providing a barrier to separate the upward flow through the core from the downward flow in the annulus between the RPV wall and the core shroud. The conventional core shroud is welded to the bottom of the RPV and supports the weight of the top guide, core plate and shroud head along with attached steam separators. Recent discoveries of unexpected circumferential cracks propagating through the thickness of the shrouds in relatively young operating BWR's has prompted a re-design of the core shrouds for future BWR's. The primary cause of the observed cracking has been intergranular stress corrosion in the heat affected zones near many of the horizontal welds of the shroud and shroud supports. There have also been some cracks observed in the mid-belt regions of BWR shrouds, and these have been thought to be caused by irradiation assisted stress corrosion. The current advanced boiling water reactor (ABWR) shroud, like the conventional BWR shroud, is permanently welded to the bottom of the vessel and is not intended to be removed or replaced. The shroud in the ABWR has various horizontal welds similar to the BWR shrouds in current operating plants, and therefore may also be at risk of similar stress corrosion cracking problems. The conventional pump deck section is permanently welded in place between the shroud and the reactor pressure vessel, and it too is not intended to be removed or replaced. As with the shroud welds, the pump deck welds are also susceptible to stress corrosion cracking. SUMMARY OF THE INVENTION This invention relates to a new and improved shroud and pump deck design which allows for the relatively easy removal of both components. In accordance with the invention, both the shroud and pump deck are bolted to the top of the shroud support leg extending upwardly from the bottom of the RPV. Specifically, the shroud has a radially inwardly extending flange at its bottom end for bolting into the upper cylindrical section of the shroud support leg. The bolts restrain vertical loading on the shroud while horizontal loading is restrained by wedges mounted between the shroud and a plurality of wedge support blocks on the pump deck. Thus, the inner diameter portion of the pump deck is vertically sandwiched between the shroud flange and the upper edge of the cylindrical section of the shroud support leg. At the same time, the outer diameter of the pump deck is held in place within a radially inwardly facing groove on the inside wall of the reactor pressure vessel. The pump deck is formed in ten separate segments with a reactor internal pump diffuser adapted to extend vertically through an opening in the middle of each segment. In a further feature of the invention, a keyed pump deck segment locks the remaining nine deck segments of the pump deck in place. It is the last portion of the pump deck to be installed and the first portion of the pump deck to be removed. This keyed segment is very similar in construction to the other nine segments; however, it is bolted into a support ledge on the reactor pressure vessel wall as opposed simply to being held by the groove on the reactor pressure vessel wall as in the case of the other nine pump deck segments. From the above, it will be appreciated that after the shroud bolts have been removed, the shroud may be lifted vertically from the core. The keyed pump deck segment can then be removed, followed by the remaining pump deck segments. Thus, in accordance with one aspect of the subject invention, there is provided in a pressure vessel of a nuclear reactor containing a core assembly enclosed within a core shroud, the core shroud spaced radially inwardly of a side wall of the pressure vessel with an annular pump deck located between the core shroud and the side wall of the pressure vessel, the improvement wherein the shroud is removably secured to an annular support of the pressure vessel. In accordance with another aspect, the subject invention relates to a pressure vessel of a nuclear reactor containing a core assembly enclosed within a core shroud, the core shroud spaced radially inwardly of a side wall of the pressure vessel with an annular pump deck located between the core shroud and the side wall of the pressure vessel, the improvement wherein the annular pump deck is provided in the form of a plurality of removable segments. In accordance with still another aspect, the invention relates to a pressure vessel of a nuclear reactor containing a core assembly enclosed within a core shroud, the core shroud spaced radially inwardly of a side wall of the pressure vessel with an annular pump deck located in an annular radial space between the core shroud and the side wall of the pressure vessel, the improvement wherein the shroud is removably secured to an annular support leg extending upwardly from the bottom of the pressure vessel; and further wherein the annular pump deck is provided in the form of a plurality of removable segments. It will thus be appreciated that the invention provides a shroud and a pump deck capable of being easily removed and reused or replaced. The invention also provides a wedge mechanism to transfer the horizontal loads of a core shroud to the pump deck or other supporting member. The construction in accordance with this invention also results in most horizontal welds being located in otherwise removable elements, facilitating repair and/or replacement of faulty welds. Other objects and advantages of the subject invention will become apparent from the detailed description which follows.
	description	This application is a national stage application of PCT/EP2011/060626, filed on Jun. 24, 2011, which claims priority to German Application 10 2010 025 033.3, filed on Jun. 23, 2010, herein incorporated by reference in its entirety. The present invention relates to the field of analyzing and/or repairing of an EUV mask defect. As a result of the shrinking sizes of integrated circuits, photolithographic masks have to project smaller and smaller structures onto a photosensitive layer i.e. a photoresist dispensed on a wafer. In order to enable the decrease of the critical dimension (CD) of the structure elements forming the integrated circuits (ICs), the exposure wavelength of photolithographic masks has been shifted from the near ultraviolet across the mean ultraviolet into the far ultraviolet region of the electromagnetic spectrum. Presently, a wavelength of 193 nm is typically used for the exposure of the photoresist on wafers. As a consequence, the manufacturing of photolithographic masks with increasing resolution is becoming more and more complex. In the future, photolithographic masks will use even smaller wavelengths in the extreme ultraviolet (EUV) wavelength range of the electromagnetic spectrum. The term EUV mask denotes in the following a photolithographic mask for the EUV wavelength range (preferably 10 nm to 15 nm). The optical elements for the EUV wavelength range will preferably be reflective optical elements. For the fabrication of an EUV optical element a multilayer structure or a multilayer film is deposited on a substrate having an ultralow thermal expansion (ULE). Fused silica is an example of a substrate used for EUV optical elements. The multilayer system typically comprises 80 to 120 alternating layers of molybdenum (Mo) and silicon (Si). A pair of a Mo—Si layer or a Mo—Si bilayer has a depth of approximately 7 nm. At the boundary of the Mo—Si layers a portion of the incident EUV radiation is reflected, so that a Mo—Si multilayer layer system ideally reflects more than 70% of the incident EUV radiation. In addition to the multilayer structure, an EUV mask comprises a pattern or an absorbing pattern structure on top of the multilayer. For example, the EUV radiation absorbing pattern can be formed of titanium nitride, tantalum nitride, or chromium. The interaction of the EUV radiation absorbing portions and EUV radiation reflecting portions of the EUV mask generates in case of an illumination with EUV radiation the pattern to be presented in the photoresist dispensed on a semiconductor wafer. Highest precision is required at the fabrication of EUV optical elements, in particular for EUV masks. Errors in the order of 1 nm can already cause errors in the image of the pattern structure on the wafer. Mask errors or defects which are apparent on the pattern of the wafer generated by the mask are called printing errors. Defects of different types can occur at various positions of the EUV mask leading to various effects. EUV inspection and review systems operating at the illumination wavelength are already known. The U.S. Pat. Nos. 6,954,266, or 5,808,312 describe EUV inspection and review systems or tools operating in combination with a mask repairing system. EUV review systems are also denoted as EUV mask inspection microscopes (EUVM). Further investigation methods for EUV masks are also known. The US 2009/0 286 166 discloses the use of an atomic force microscope (AFM) for the localization of concave defects on EUV masks. The U.S. Pat. No. 6,844,272 describes the determination of the height of the surface of EUV masks by the use of an interferometer. Defects of the absorbing pattern structure may occur if absorbing material is missing at positions which should be opaque, or when absorbing material is existent at positions which should be dear. Further, dirt particles may be attached to the surfaces of EUV optical elements. This type of error results predominantly in amplitude errors. It can be recognized by a surface analysis of the EUV optical element; for example by using a scanning electron microscope (SEM). Using a known mask repairing system, as for example the MeRiT® system of Carl Zeiss SMS excessive material can be removed. An electron beam in combination with a suitable etching gas can be used for this task. Missing absorber material can for example be added by locally depositing chromium with the aid of an electron beam together with a respective precursor gas. EUV optical elements can be washed or polished in order to dean their surfaces from disturbing particles or substances. On the other hand, so-called buried defects can occur in EUV optical elements, i.e. EUV mirrors and/or EUV masks. In the following, the term “buried defect” means a defect or an error which is located on the substrate and/or within the multilayer structure of the EUV optical element. Buried defects lead to both, amplitude and phase errors, i.e. buried defects comprise amplitude and phase error portions. Buried defects are also called topological errors. The U.S. Pat. No. 6,016,357 describes a method for correcting errors of the absorbing pattern structure by the measurement of focus stacks in phase shift masks (PSM) illuminated with deep ultraviolet (DUV) radiation. Further, this document describes a repairing method for removing excessive absorbing materials and for depositing missing absorbing material. This repairing method is denoted as compensational repair. The U.S. Pat. No. 6,235,434 describes the repair of amplitude and phase errors of EUV masks. Independent of the type of error, the repair is done by compensation, i.e. correcting of the absorbing pattern by removing excessive material from the absorbing pattern structure or depositing absorbing material to the absorbing pattern structure, respectively. Further, the US 2005/0 157 384 also discloses the removal of material, whereas the U.S. Pat. No. 6,849,859 describes the adjustment of a thickness of a layer by depositing an additionally layer and by adjusting the thickness of the additional layer. When excessive absorbing material is removed by an ion beam, ions are implanted in a buffer layer arranged between the multilayer film and the absorbing pattern structure. The implanted ions may vary the reflectivity of the corrected EUV mask portion. The JP 2008 085 223 A discloses a method to correct the reflectivity change induced by the implanted ions by respectively correcting the absorbing pattern structure. The article “Study of critical dimensions of printable phase defects using an extreme ultraviolet microscope” by Y. Kamaji et al., Jpn. J. of Appl. Phys. 48 (2009), pp. 06FA07-1-06FA07-4 explains why pits are more often defects in multilayer films of EUV masks than bumps. Further, the article reports on the fabrication of programmed phase defects and their analysis in order to determine the resolution limit of an EUV microscope (EUVM). The thesis of C. H. Clifford: “Simulation and compensation methods for EUV lithography masks with buried defects”, Electrical Engineering and Computer Sciences, University of California at Berkeley, Techn. Report No. UCB/EECS-2010-62 describes simulation methods which allow generating simulation configurations based on aerial images of defects. This document also reports on two methods for defect compensation by adjusting the absorber pattern of EUV masks. The article “Natural EUV mask blank defects: evidence, timely detection, analysis and outlook” by D. van den Heuvel et al., SPIE/BACUS Conf. Proc. 2010, describes a method to combine aerial images, marks and AFM measurement data in order to localise and to measure an EUV defect which cannot be recognized in a scanning electron microscope (SEM). Moreover, this paper describes that both, pits as shallow as 3 nm and bumps just 3 nm high at the surface can results in critical printing defects buried in the multilayer. The above mentioned documents do often not clearly distinguish between amplitude errors and phase errors of buried defects, i.e. of defects on substrates and/or multilayer films of EUV masks. The repair methods denoted as “compensational repair” addresses the amplitude error portions of buried defects, but ignores their phase error portions. FIG. 1 schematically illustrates the compensational repair of a multilayer defect by removing a portion of the absorbing pattern elements adjacent to the defect in order to compensate for the reduced reflectivity of the buried multilayer defect. The compensational repair has the drawback that it results in a diminution of the process window at the wafer illumination, since an EUV mask compensated with this approach has a focus dependency which deviates significantly from the ideal focus characteristics. Moreover, the compensational repair method cannot be applied to correct defects in EUV mirrors not having an absorbing pattern structure. It is therefore one object of the present invention to provide a method and an apparatus for analysing and/or repairing of a defect of an EUV mask, which at least partially overcome the above mentioned drawbacks of the prior art. According to a first aspect of the invention, a method according to claim 1 is provided. In an embodiment, a method for analyzing a defect of a photolithographic mask for an extreme ultraviolet (EUV) wavelength range (EUV mask) comprises (a) generating at least one focus stack relating to the defect using an EUV mask inspection tool, (b) determining a surface configuration of the EUV mask at the position of the defect, (c) providing model structures having the determined surface configuration which have different phase errors and generating the respective focus stacks, and (d) determining a three dimensional error structure of the EUV mask defect by comparing the at least one generated focus stack of the defect and the generated focus stacks of the model structures. The described method exploits that amplitude errors and phase errors become manifest in different focus characteristics. Therefore, the measured focus stack enables discriminating between amplitude errors and phase errors. Amplitude errors basically correspond to surface defects and phase errors basically corresponds to buried defects. Amplitude errors are corrected using a method known in the state of the art. The surface configuration of an identified buried defect which demonstrates in a phase error is analyzed. From the measured surface configuration model structures are calculated from which a three dimensional (3D) error structure of the defect is determined. Thus, the described methods define a procedure to reliably detect and discriminate defects of an EUV mask and to determine an individual 3D error structure of identified buried defects. The 3D error structure of the buried defect can be used to develop a repairing or a compensation policy individually designed for the analyzed buried defect. An EUV mask is preferably a reflective optical element. However, it is also possible to apply the method defined in the first paragraph of this section to transmissive optical elements. Furthermore, the described method is not restricted for analyzing defects of EUV masks. In fact, it can also be applied to analyze defects of photolithographic masks or more general of optical elements designed for a longer wavelength range as well as for a shorter wavelength range. In a further aspect determining the surface configuration comprises scanning the defect with an atomic force microscope, and/or with a scanning tunnelling microscope, and/or with a stylus profilometer, and/or with an interferometer. After a phase error has been identified and localised by analysing a focus stack measured with a mask inspection tool, the surface of the EUV mask above the buried defect causing the phase error is scanned in detail in order to determine the surface configuration. The surface configuration corresponds to the surface topology at the defective position of the EUV optical element. The exemplary combination of both measurement data allows the determination of a 3D error structure for the analyzed defect. Another aspect comprises the step of applying different repairing methods to the three dimensional error structure and simulating associated focus stacks in order to determine an optimal repairing method. After having determined a 3D error structure, the effect of various repairing methods on the resulting focus stack can be evaluated by simulation prior to the application of the respective repairing method. A repairing method is identified by simulation which is optimally adapted to the analyzed defect prior to the correction of the defect. In particular, the described repairing method is not restricted to a modification of the pattern structure arranged on the multilayer film of an EUV mask. Rather, the defined repairing method explicitly includes a modification of the substrate and/or of the multilayer film of the EUV mask in order to correct analyzed defects not only of EUV mask but also of EUV mirrors. Therefore, the defined method corrects buried defects instead of just compensating their amplitude error portion by a compensational repair. In a further aspect determining the optimal repairing method comprises selecting one of the different repairing methods as the optimal repairing method which generates a focus stack which maximizes a process window for the EUV optical element at the illumination of a wafer. The process window is maximized for the repairing method whose aerial images of the focus stack fulfill a predetermined critical dimension (CD) variation for the largest defocus range of the different repairing methods. The application of this optimization criterion maximizes the process window at the illumination of the corrected EUV optical element or which maximizes the depth of focus (DOF), which is of utmost interest for the application of the EUV optical element in a lithography system. Another aspect comprises applying the optimal repairing method to the defective position. The specific treatment of the defective position minimizes the influence of the defect on the image of the EUV pattern in the photoresist arranged on a wafer, so that the EUV optical element can again be utilized in the production process after the respective error handling. In still a further aspect, the model structures comprise an absorbing pattern structure on a surface of the EUV mask. The existence of an absorbing pattern structure facilitates the determination of model structures for a defective position, as the absorbing pattern structure can be used for the identification of the defect position on the surface of the EUV mask. Further, a modification of the pattern elements can also be part of the error correction process. On the other hand, it is not mandatory that the model structures of a buried defect comprise a pattern structure. Rather, the described method can also be applied to EUV mirrors which do not have an absorbing pattern. Another aspect comprises providing the absorbing pattern structure from EUV mask design data and/or from of a recording of at least one image. When the pattern data is available, it is used as input for the simulation process of the effects of the various repairing methods. On the other hand, if this information is not available, it can alternatively be obtained from the recording of an image of the pattern structure. A scanning electron microscope (SEM) can be used for recording an image of the pattern. It is also possible to use a combination of both methods in order to determine the pattern data of an EUV mask. A further aspect comprises using a repairing method correcting the three dimensional error structure so that a resulting multilayer structure is at least approximately corrected to an ideal multilayer structure. In contrast to a compensational repair which just modifies pattern elements when trying to compensate a buried defect, i.e. a multilayer and/or a substrate defect, the described method modifies the substrate and/or the multilayer in order to correct a buried error. Thus, the defined method allows correcting analyzed buried defects to a much higher amount than by a compensational repair, which just addresses the amplitude error portion of a buried defect. Consequently, the described method maximizes the process window of an EUV optical element at its use in a lithography system. Another aspect comprises applying the repairing method directly onto the defective position of the EUV mask. As already mentioned above, the described method analyzes the 3D error structure of a buried defect and corrects the defect by acting on the substrate and/or on the multilayer film instead of only partially compensating the defect by locally modifying pattern elements close to the buried defect. According to another aspect, the repairing method comprises at least partially removing the multilayer structure, in particular drilling at least one hole into the multilayer structure. By removing the portion of the multilayer structure which comprises the buried defect, the defect is also removed. Then a defect-free multilayer film can be newly deposited. Although, this procedure requires some efforts, it does not compensate the defect; rather it is removed by the repairing process. In still another aspect, the repairing method comprises locally compacting and/or expanding the multilayer structure and/or of a substrate of the EUV mask or generally of an EUV optical element by locally focusing femtosecond laser pulses into the EUV mask. The defined repairing method is an example of a repairing which directly corrects a buried defect by acting upon the substrate and/or the multi-layer film of the EUV optical element. In this context, a variation of the substrate is preferred, because the impact of the repair of the defect on the multilayer can be minimized. In another aspect, the femtosecond laser pulses are incident through the substrate of the EUV mask. When the femtosecond laser pulses are directed through the substrate to the defective position, the multilayer or at least the most important upper Mo—Si layers of the multilayer film are not or at least not significantly influenced by the correction of the buried defect. According to a further aspect, an inspection microscope for photolithographic masks in the extreme ultraviolet wavelength range performs a method of any of the aspects described above. According to a further aspect of the invention, a method according to patent claim 11 is provided. In an embodiment, a method for repairing a buried defect in an extreme ultraviolet (EUV) optical element comprises directing an ion beam onto the buried defect so that an ion dose is implanted in the EUV optical element suitable to locally change a volume of the EUV optical element. The EUV optical element comprises an EUV mirror having a substrate and a multilayer structure and/or an EUV mask having a substrate, a multilayer structure and an absorbing pattern structure. The inventive method corrects buried defects of EUV optical elements by directly modifying the substrate and/or the multilayer instead of just compensating the amplitude error portions of these defects by applying a compensational repair. Thus, the inventive method can not only be applied to EUV masks, but it can also be used to correct buried defects of EUV mirrors. EUV optical elements will probably be reflective optical elements. However, the inventive method is not restricted to reflective optical elements, but can also be applied to transmissive optical elements. Moreover, the defined method is also not limited for the correction of buried errors of EUV optical elements. Rather, it can be applied to compensate buried defects of optical elements designed for longer as well as for shorter wavelengths. In still a further aspect, the ion beam comprises inert gas ions, preferably noble gas ions, and most preferably helium ions. Inert gas ions have the advantage that they do not react with the material into which they are implanted. This means, the mechanical and/or the optical properties of the substrate and/or the multilayer film are not significantly modified as a consequence of implanting ions. Further, the noble gas characteristics of the inert gas ions also prevents that the EUV photons of the lithography system induce a reaction of the implanted inert gas with the surrounding material during the operation of the EUV optical element which could change its optical properties in the course of time. A further aspect comprises adapting an ion beam energy to a depth of the buried defect below a surface of the EUV optical element. In yet another aspect, the ion beam energy comprises a range of 1 keV to 200 keV, preferably 5 keV to 100 keV, and most preferably of 10 keV to 50 keV. Ions are implanted in the EUV optical element with a specific spatial distribution. The spatial distribution as well as the maximum of the distribution depend on the energy with which the ions hit on the EUV optical element. The distribution of the implanted ions in beam direction is in the following called depth distribution. The energy with which the ions impinge of the EUV optical element can be selected so that the maximum of the depth distribution of the implanted ions fits to the depth of the buried defect. In still another aspect, the EUV optical element comprises a multilayer structure and the energy of the ion beam is selected such that the ions are essentially implanted below layers of the multilayer structure of the EUV optical element which determine its reflective properties. The term “essentially” means here as well as at further positions within this specification that the maximum and/or the width of the depth distribution are adjusted to the respective Mo—Si layers so that these layers comprise the majority of the implanted ions. As already mentioned in the second section, ions implanted in the multi-layer structure may locally change the reflectivity of EUV photons and may such form an amplitude error. It is well known that a multilayer film shows an asymptotic reflectance characteristic. This means that the Mo—Si layers close to the surface of the EUV element account for the major portion of the reflected EUV radiation, whereas layers close to the substrate only insignificantly contribute to the reflectivity of the EUV optical element. Consequently, ions implanted in the lower Mo—Si layers (the Mo—Si layers dose to the substrate) can efficiently correct a buried defect without essentially influencing the reflective properties of the EUV optical element. In a further aspect, the EUV optical element comprises at least one capture layer arranged between the substrate and the multilayer structure, and wherein ion beam energy is adjusted so that the ions are essentially implanted in the at least one capture layer. By implanting the majority of the ions in the capture layer the reflective properties of the multilayer structure is not or at least not significantly changed. A defect located on the substrate surface in the Mo—Si layers close to the substrate may propagate through at multilayer and thus affecting its reflective characteristic. Therefore, by implanting the majority of the ions in a capture layer, a buried defect can efficiently be removed, so that the defect correction process does not significantly influence the reflective properties of the multilayer structure. Still a further aspect comprises arranging a local protection layer on a surface of the EUV optical element through which the ion beam is directed when repairing the defect prior to directing the ion beam onto the defect and removing the local protection layer at the end of the repairing. Ions impinging on an EUV optical element have a sputter effect on the surface of the EUV optical element, i.e. they have an energy to remove atoms from the surface of the EUV optical element. Hence, the impinging ions may damage the surface of the EUV optical element. This effect can be avoided by locally arranging of a protection layer on the multi-layer prior to the ion bombardment and by removing the protection layer at the end of the defect repairing process. In accordance with a further aspect, the ion beam is not perpendicularly directed through a surface of the EUV optical element onto the buried defect. As already mentioned, beside the sputter effect, ions may induce damages in the multilayer along their paths from the multilayer surface to their implanted position. By using an inclined incidence for the ion beam, a portion of the EUV optical element can be selected for the paths of the ions which has less impact on the imaging of the mask pattern on the wafer. In particular, an incidence angle can be chosen so that the ion beam incidents on an absorbing element. By this approach the multi-layer structure above a buried defect is not damaged during the repairing of the defect. In yet another aspect, the buried defect is a concave defect, in particular a pit and/or a scratch and the local volume change comprises a local volume increase, in particular a local height increase. According to another aspect, the buried defect is a convex defect, in particular a bump and the local volume change comprises a local volume decrease, in particular a local height decrease. Moreover, still a further aspect comprises the step of analyzing the buried defect with a method of any of the aspects described above. Finally, according to another aspect, a focused ion beam apparatus performs a method of any of the aspects described above. In the following, the present invention will be more fully described with reference to the accompanying figures, in which exemplary embodiments of the invention are illustrated. However, the present invention may be embodied in different forms and should not be construed as limited to the examples set forth herein. Rather, these examples are provided so that the disclosure will be thorough and will convey the scope of the invention to persons skilled in the art. FIG. 1 shows a top view of a cut-out of an EUV mask 100. The left diagram no comprises a multilayer structure 120 which has a multilayer defect 130 buried in the multilayer structure 120, which is called a buried defect. On the multilayer 120 two pattern elements 140 are arranged having a form of absorbing stripes. The right diagram 150 illustrates the absorber structure 160 of the left diagram no of the EUV mask 100 after the multilayer defect 130 of has been partially compensated by removing a portion of the absorbing material of the pattern elements 160 around the buried defect 130 in order to compensate the reduced reflectance of the area covered by the buried defect 130. As already mentioned in the third section, this approach of buried defect repairing is called “compensational repair”. FIG. 2 shows a schematic cross-sectional view of a photolithographic mask 200 for an exposure wavelength of 13.5 nm. Different from presently applied photolithographic masks, the EUV mask 200 is a reflective optical element based on a multilayer structure 205. The multilayer structure 205 acts as a mirror which selectively reflects incident EUV photons. The multilayer structure 205 of the EUV mask 200 is deposited on a front substrate surface 215 of a suitable substrate 210, such as a fused silica substrate. Other transparent dielectrics, glass materials or semiconducting materials may also be applied as substrates for photolithographic masks as for example ZERODUR®, ULE® or CLEARCERAM®. It is preferred that the material of the substrate 210 has a very low thermal expansion coefficient. The multilayer film or multilayer structure 205 comprises 40 to 60 pairs of alternating molybdenum (Mo) 220 and silicon (Si) layers 225 (referred to in the following as Mo—Si layers). The thickness of each Mo layer 220 is 4.15 nm and that of the Si layer 225 amounts to 2.80 nm. In order to protect the multilayer structure 205, a capping layer 230 of silicon with a native oxide of 7 nm depth is arranged on top of the multilayer structure 205. Other materials can also be used for forming a capping layer 230 as for example ruthenium. In the multilayer 205, the Mo layers 220 act as scattering layers, whereas the silicon layers 225 function as separation layers. For the scattering layers instead of Mo other elements with a high Z number may be utilized, such as cobalt (Co), nickel (Ni), tungsten (W), rhenium (Re) and iridium (Ir). As already mentioned, the multilayer structure 205 on the substrate 210 of the EUV mask 200 acts as a mirror for EUV electromagnetic radiation. In order to become an EUV mask 200, a buffer structure 235 and an absorbing pattern structure 240 are additionally deposited on the capping layer 230. The buffer layer 235 may be deposited to protect the multilayer structure 205 during processing, for example during etching and/or repairing of the absorbing pattern structure 240. Possible buffer structure materials are for example of fused silica (SiO2), silicon-oxygen-nitride (SiON), ruthenium (Ru), chromium (Cr), and/or chromium nitride (CrN). The absorbing structure 240 comprises a material having a large absorption constant for photons in the EUV wavelength range. Examples of these materials are chromium (Cr), titanium nitride (TiN) and/or tantalum nitride (TaN). An anti-reflective (AR) layer 245 can additionally be arranged on the absorbing pattern structure 240 in order to secure that no photons are reflected by the surface of the absorber pattern 240. A material for an AR layer is for example tantalum oxynitride (TaON). A thickness of about 50 nm is sufficient to absorb basically all EUV photons 250 incident on the absorbing structure 240. In contrast, the majority of the photons 250 incident on the capping layer 230 is reflected as photons 255. In this context as well as on further positions of this description the term “basically” means a numeric value of a quantity within its measurement limit. The substrate 210 of the EUV mask 200 has typical lateral dimensions of 152 mm×152 mm and a thickness or height of essentially 6.35 mm. The rear surface 270 of the substrate 210 or the rear substrate surface 270 has a thin metallic coating 275. Typically this coating 275 comprises chromium. The metallic coating 275 is used to fix the EUV mask 200 at the EUV scanner by the application of electrostatic forces. FIG. 3 represents the EUV mask 300 of FIG. 2 having various defects. In order to keep the following consideration simple, the capping layer 230, the buffer layer 235 as well as the AR layer 245 is omitted in FIG. 3. On the multilayer structure 305 an absorbing pattern 340 is deposited. The pattern element 350 of the absorbing pattern 340 has a portion which partially misses the absorbing material. Furthermore, a dirt particle 360 is attached on the surface 370 of the multilayer 305. The dirt particle 360 can be removed by a cleaning process, i.e. by washing and/or polishing the EUV mask 300. Both types of defect, absorber defects 350 and particle defects 360 on the surface 370 of the EUV mask 300 are in the following called surface defects 380. The surface defects 380 can be detected by a surface analysis of the EUV mask 300. An electron beam of a scanning electron microscope (SEM) can for example be applied for the surface analysis of the EUV mask 300. Furthermore, the surface defects 380 are accessible to a repair by a modification of the absorbing pattern 340. As already mentioned in the second section, this can be performed by using a mask inspection and repairing system, as for example the MeRiT® system of Carl Zeiss SMS. Such a tool allows adding absorber material to the defective pattern element 350 by using an electron beam in combination with a suitable precursor gas or a combination of precursor gases. Examples of precursor gases are metal carbonyls, in particular dicobalt octacarbonyl (Co2(CO)8). When the dirt particle 360 can not be removed by a cleaning process, the absorbing pattern 340 can be modified in order to compensate for the reduced reflectance in the area of multilayer 305 of the EUV mask 300 which comprises the dirt particle 360. This can be done by removing a portion the absorbing pattern 340 around the particle defect 360 as it is schematically indicated in FIG. 1 for the compensational repair of a buried defect 130. An electron beam together with an etching gas or a combination of etching gases can be applied in order to selectively remove a portion of the absorbing pattern 340. For example, xenon difluroride (XeF2) can be used as an etching gas. Further, the EUV mask 300 of FIG. 3 also shows a defect 320 in the substrate 310. In the example of FIG. 3, the substrate defect 320 is a pit or a scratch on the surface of the substrate 310. The substrate defect 320 propagates as defect 330 in the multilayer structure 305 of EUV mask 300. During its propagation through the multilayer structure 305, the multilayer defect 330 increases its lateral dimension, i.e. the distortion of the Mo—Si layers towards the multilayer surface extends on a larger area. At the same time, the variation of the height of the individual Mo—Si layers reduces during the propagation of the multilayer defect 330 through the multilayer structure 305. As indicated in FIG. 3, the substrate defect 320 of the substrate 310 is reflected in a shallow depression of the surface 370 of the multilayer 305 above the buried defect 320. The height variation of the depression at the surface 370 of the multilayer 305 may be as small as a few nanometers. As discussed above, FIG. 3 represents a buried defect 320 caused by a pit or a scratch on the substrate 310. It is also possible that there is for example a dust particle on the surface of the substrate 310 at the beginning of the deposition of the multilayer 305. Furthermore, the substrate 310 may have a small local raise of its surface 370. FIG. 4 schematically depicts a cross section of a cut-out of an EUV mask 400 wherein a substrate 410 has a bump defect 420. Similar to the pit defect 320 of FIG. 3, the bump defect 420 propagates as multilayer defect 430 through the multilayer 405. In addition to the substrate defects 320, 420, buried defects can also be localized in the multilayer 305, 405. For example, individual Mo and/or Si layers may have defective positions at which the width of one or several layers may deviate from its target value (not indicated in FIGS. 3 or 4). Moreover, it is conceivable that a dust particle on a specific Mo and/or Si layer may disturb the periodicity of successively deposited Mo—Si layers of the multilayer structure 305, 405. Similar to the substrate defects 320, 420, these local distortions of the periodicity of the multilayer structure 305, 405 can propagate towards the surface 370, 470 of the multilayer 305, 405. In the following, defects of a substrate 310, 410 and defects within a multilayer structure 305, 405 are summarized as buried defects 480. In contrast to surface defects 380 which lead to amplitude errors on a wafer, buried defects 480 primarily result in phase errors at wafer illumination. Although the substrate defects 320, 420 as well as the defects within the multilayer 305, 405 often become manifest only in a small local depression or a small local increase of the multilayer surface 370, these defects may cause printable errors on a wafer at its illumination. The detection of the substrate defects 320, 420 or generally of buried defects 480 is involved. An electron beam of a SEM can neither detect the substrate defects 320, 420 nor the shallow depression or increase at the surface 370, 470 of the multilayer 305, 405 induced by the defects 320, 420. For example, an atomic force microscope (AFM) can detect the shallow variation of the surface 370, 470 of the multilayer system 305, 405. However, the substrate defects 320, 420 or generally the buried defect 480 causing a small local increase or depression have already been identified and localized by another metrology tool. Time constraints prevent to scan the overall EUV mask 300, 400 which an AFM. Recording not only a single aerial image of the defective position of an EUV mask 300, 400 with a mask inspection tool, but recording of a set of aerial images through focus can reveal the buried defects 320, 420. For this purpose, an aerial image of the defective position is recorded in the best focus plane. Additionally, aerial images are recorded with a distance above and below to the focal plane, as for example ±15 nm, ±30 nm, ±45 nm, ±60 nm, and ±75 nm. In this example, the focus stack comprises 11 images. The number of images as well as the defocus distance can be adjusted to the analyzed defect. FIG. 5 shows a diagram 500 of a simulation of the critical dimension (CD) variation as a function of the offset which is the distance between the center 650 of an absorbing pattern element 640 and the location 660 of the center of the defect 630. FIG. 6 illustrates the configuration simulated in FIG. 5. FIG. 6 depicts a multilayer structure 605 having a buried defect 620 similar to the bump defect 420 of FIG. 4. The bump defect 620 propagates as defect 630 towards the multilayer surface 680. The multilayer surface 670 has an absorbing pattern element 640. The center 650 of the absorbing pattern element 640 is the reference point 650 of the offset of or the distance to the center 660 of the defect 630. A shift of the buried defect 620 in the left direction in FIG. 6 results in FIG. 5 in a positive offset and vice versa. In FIG. 5 the CD amounts to 22 nm as indicated by the vertical dashed line 510 at this CD numerical value. An upper dashed line 520 and the lower dashed line 530 represent boundary lines of a CD variation of ±10%. The curve 540 represents a simulation of the CD variation in focus as a function of the distance of the defect 620 from the center 650 of the pattern element 640. For an offset in the range between 60 nm and 80 nm the simulated CD variation is larger than 2.2 nm, i.e. the CD variation is larger than 10%. The curve 550 shows the simulated CD variation as a function of the offset for a defocus of +75 nm. For this defocus, the CD variation is within the ±10% CD variation bandwidth across the overall simulated offset. On the other hand, the curve 560 simulated with a defocus of −75 nm is for the larger portion of the simulated offset range beyond the tolerable CD variation of ±10%. The simulated curves 540, 550, 560 indicate a strong dependence of the CD variation of the focus position. Such a behaviour is expected for a phase error as is indicated by the buried defect 620 in FIG. 6. FIG. 5 demonstrates that the measurement of aerial images of a focus stack or through focus can be used to discriminate between amplitude errors of surface defects 380 and phase errors of buried defects 480 of EUV masks 300, 400, 600. The curves 540, 550 and 560 of FIG. 5 can be used for a compensational repair. An improvement of the in focus curve 540 can be obtained by modifying the pattern element 640 as schematically indicated in FIG. 1, so that the in focus curve 540 fulfils the ±10% variation criterion across the overall offset range. However, the CD variation of the defocus curves 550 and/or 560 may still be beyond the ±10% variation criterion. Thus, such a repairing diminishes the process window at the illumination of a wafer with the EUV mask 600. This situation is unsatisfactory; therefore a defect recognition method is necessary which analyzes a buried defect in detail. Further, a defect repairing method is required which repairs buried defects in such a way that the process window is as large as possible at the end of the repairing process. The surface configuration of the EUV mask 300, 400, 600 is measured around the identified buried defect 320, 420, 620 for example with an atomic force microscope (AFM). Further tools which can be applied to scan the defective position are for example a scanning tunnelling microscope, a stylus profilometer, and/or an interferometer. The measured surface configuration allows the determination of the deviation of the measured surface configuration from an ideal surface configuration for the EUV masks 300, 400, 600. In the next step, model structures are generated for various buried defects of an EUV mask. For the generation of the model structures, the data of the absorber pattern of the EUV mask at the defective position is required. This data is obtained from the design data of the mask, or it is obtained from the image recorded with an SEM. Although the defect analysis is in the following explained for an EUV mask, it is appreciated that the described method can also be applied for the defect analysis of EUV mirrors. Moreover, the defined method is not restricted to the EUV wavelength range, but can also be utilized for the defect analysis of transmissive optical elements. For each of the generated model structures aerial images for each focus position of a focus stack are simulated. In this simulation process, a plurality of the above discussed defects is considered for each surface configuration. Then the measured surface configuration and the measured aerial images of the focus stack at the defective position are compared with the simulated aerial images of the focus stacks of the generated model structures. The model structure whose aerial images provide the best agreement with the measured aerial images across the focus stack is taken as the three dimensional (3D) error structure of the identified defect. Finally, based on the determined 3D error structure, a repairing or compensation policy is developed which minimizes the impact of the 3D error structure of the EUV mask at the wafer illumination by a specific treatment of the defective position. The objective of the treatment is to again utilize the EUV mask in a production process for the wafer illumination at the end or the repairing process. Two alternative approaches for the determination of a 3D error structure are conceivable: (a) if the measured aerial images of the focus stack indicate that the identified error is an amplitude error, the surface defect 380 causing the amplitude error can directly be corrected by varying the pattern structure 340, 640. This alternative does not analyze the surface configuration of the EUV mask around the detected surface defect 380 by scanning with an AFM. (b) Irrespective of the identified error type, the surface configuration of the detected defect in scanned for example with an AFM in order to determine a surface configuration for a subsequent determination of a 3D error structure for each identified defect. For the correction of the determined 3D error structure various repairing methods can be applied. As already mentioned above, a portion of an absorbing pattern structure can be removed by using an electron beam and/or an ion beam and as appropriate in combination with an etching gas or a combination of etching gases. Absorbing material can be removed in the vertical as well as in the horizontal direction. Alternatively, absorber material, as for example chromium, may be added in both vertical and horizontal directions. The deposition can also be performed with an electron beam and/or with an ion beam and as appropriate together with a respective precursor gas or a combination of precursor gases. Both methods can be applied to correct surface defects 380 and may be employed for a compensational repair of buried defects 480 as schematically illustrated in FIG. 1. A further repairing method comprises at least partially removing of the multilayer structure 305, 405, 605, as for example by drilling a hole into the multilayer structure 305, 405, 605 having a suitable dimension. If the portion of the multilayer structure 305, 405, 605 which comprises the buried defect 480 is removed, the defect 480 is also removed. Then a defect-free multilayer structure 305, 405, 605 can newly be deposited on the removed multilayer portion. The effect of the repairing method described in the preceding paragraph is investigated by simulation prior to performing the replacement of a portion of the multilayer structure 305, 405, 605. This means, the intended correction is initially applied to the determined 3D error structure and a simulation of the resulting aerial images of the focus stack is performed. Only when the result confirms that the resulting aerial images of the corrected position have a sufficiently wide process window, the repairing method is really executed. If this is not the case, further simulations are performed with varied repairing methods or repairing parameters, respectively. The parameters of a repairing method can be optimized by an iterative method. For example, if a buried defect 480 in a multilayer structure 305, 405, 605 is to be repaired by drilling of a hole into the multilayer 305, 405, 605, simulations are performed for holes having various depths, different diameters and/or having various distances from the buried defect. For performing the above mentioned repairing methods an EUV mask inspection microscope is provided having an integrated repairing system. It is also possible to apply the defect analyzing and the defect repairing in separate systems. A further repairing method comprises a local compaction and/or a local expansion of the substrate 310, 410 and/or of the multilayer structure 305, 405, 605 by the impact of electromagnetic radiation. The substrate 310, 410 and/or the multilayer structure 305, 405, 605 can for example be compacted or expanded by the usage of femtosencond laser pulses. A compaction as well as an expansion of the various layers of an EUV optical element can also be achieved by implanting ions at a suitable position of an EUV optical element. In the example described in the following, the method is discussed in the context of a volume expansion. However, it is appreciated that the discussion of a volume expansion does not restrict the described method to volume expansion. Rather, it is also applicable to perform a respective volume compaction. FIG. 7 presents a curve which shows an induced change of the height of a photolithographic mask as a function of the implanted ion dose. In the example of FIG. 7, the mask was irradiated with a helium ion beam having a beam energy of 30 keV. As already mentioned, the helium beam or generally an ion beam has basically two effects: (a) a sputtering effect, i.e. (helium) ions collide with atoms of the sample and release atoms from the sample, (b) implantation, (helium) ions stay in the sample material. In the example of FIG. 7, the implantation of helium atoms does basically not lead to a volume change below a built in ion dose of approximately 2·1016 cm2. Above this value the implantation of helium ions results in a volume expansion of the mask material which goes steeply up with an increase of the implanted helium dose. FIG. 7 illustrates the interrelationship between a volume expansion of a photolithographic mask and the implanted ion dose for the example of helium ions. It is appreciated that similar curves also exist of other inert gas atoms, in particular for noble gas atoms. The focussed ion beam of an ion beam (FIB) apparatus can be used in order to implant an ion dose in an EUV mask with a defined depth distribution as well as with a defined lateral distribution of the implanted ions. Alternatively, the FIB source can be integrated in the mask inspection tool which is applied for the defect analysis as discussed above. Furthermore, an AFM can for example be utilized to determine the volume change induced by the implanted ions. It is also possible to use one of the scanning tools or a combination of them mentioned in the context of the determination of the surface configuration in order to detect the local height change caused by the implantation of ions into an EUV mask. FIG. 8 shows a simulation of the depth distribution of a helium ion beam into an EUV mask as a function of the ion energy. The helium beam hits the EUV mask at a position without an absorbing pattern element. The ordinate indicates the cumulated normalized sum of implanted ions. As can be seen from FIG. 2, the EUV mask has a thin capping layer 230 which is denoted with the reference numeral 830 in FIG. 8. The multilayer structure 805 has a width of approximately 280 nm. It is deposited on a substrate 810 having a width in the millimetre range of which only the upper relevant portion is indicated in FIG. 8. FIG. 9 presents a simulation of the depth distribution of a helium ion beam into an EUV mask as a function of the ion energy. The helium beam hits the EUV mask at a position of an absorbing pattern element. Similar to FIG. 8, the ordinate indicates again the cumulated normalized sum of implanted ions. As indicated in FIG. 2, the absorbing pattern 940 has a thin AR layer 945 of a few nanometers arranged on the absorbing pattern elements 940. The absorbing pattern structure 940 has a width of approximately 70 nm. As already mentioned in the context of the discussion of FIG. 2, depending of the absorber material, a thickness of approximately 50 nm is sufficient to basically absorb all incident EUV photons. The multilayer structure 905 and the substrate 910 of FIG. 9 are identical the multilayer 805 and the substrate 810 of FIG. 8. As can be seen from FIGS. 8 and 9, the depth at which the ions are implanted in the EUV mask depends on the energy with which the ions hit on the surface of the EUV mask. This means that the depth distribution of the implanted ions can be set by selected by the ion beam energy. Further, FIGS. 8 and 9 also reveal that the width of the depth distribution also varies with the energy of the helium beam. Even for ion beam energies of 90 keV the ions are implanted in a way so that more than 50% of the implanted ions are integrated in a depth range of 200 nm. For ion beam energies of 50 keV of less the majority of the build in ions is implanted in a depth range of 100 nm or less. A comparison of FIG. 8 and FIG. 9 shows that an absorbing pattern element does not significantly change the depth distribution of the implanted helium ions. The simulations of FIGS. 8 and 9 have been performed with the software program SRIM, which is described in the article “The Stopping and Range of Ions in Solids” by J. F. Ziegler, J. P. Biersack, and U. Littmark, Pergamon Press, New York, 1985. The implanted dose distribution within an EUV mask can for example be determined by preparing cross-section samples of an EUV mask and investigating the samples with transmission electron microscopy (TEM). The relationship between an exposition of the EUV mask for a predetermined time with predetermined ion beam parameters and the resulting implanted dose distribution within the EUV mask can also be obtained for example from TEM measurements of a series of prepared test samples. This means that the spatial distribution of the implanted ions can be controlled by the selection of the ion beam parameters. FIG. 10 schematically shows in the left partial image a pit defect 1020 in a substrate 1020 of an EUV mask 1000. Similar to the FIGS. 3, 4 and 6 the pit defect propagates as defect 1030 through the multilayer structure 1005. The right partial image schematically shows the multilayer structure 1005 after the implantation of ions as for example helium ions. The helium ions are preferably integrated in Si layers 1040 which causes a local increase of the volume of the Si layers 1040. It has been observed that the induced volume change varies as function of the ion species and ion absorbing material. Built-in helium ions in Mo—Si layers predominantly result in a volume expansion of the Si layers 1040. As a result, the local volume expansion of the Si layers 1040 corrects the effect of the pit defect 1020 at the surface 1070 of the multilayer structure 1005. In the example of FIG. 10, the correction of the pit defect 1020 is performed by a local volume increase of individual Mo layers 1040 of the multilayer structure 1005. This repairing method results in a local breach of the Bragg reflection condition. This problem can be avoided or at least reduced if the ions are preferably implanted in the lowest Mo—Si layers of the multilayer structure 1005 which are close to the substrate 1010. As already explained above, the multilayer structure 1005 shows an asymptotic reflective behaviour. The upper Mo—Si layers close to the surface 1070 of the EUV mask moo contribute the major portion to the reflected EUV radiation, whereas the contribution of the lowest Mo—Si layers is insignificant. Therefore, by correcting the pit defect 1020 of the EUV mask moo by implanting ions in the lowest Mo—Si layers of the multilayer structure 1005 the local breach of the Bragg reflection condition due to the repairing process has a minor effect on the reflectivity of the multilayer structure 1005. FIG. 11 schematically illustrates a further approach with allows the repairing of a defect buried in a multilayer without basically distort the reflectivity of the multilayer structure. In the EUV mask 1100 a so-called capture layer 1115 is inserted between the substrate 1210 and the multilayer structure 1105. The capture layer 1115 has a width of approximately several hundred nanometers. Suitable materials for a capture layer are for example silicon (Si) and/or molybdenum disilicide (MoSi2). It is the purpose of the capture layer 1115 to efficiently capture ions and to provide a large local volume change. The diagram of the right partial image of FIG. 11 schematically presents the depth distribution of the implanted ions. In the thin capture layer 1115 the majority of the ions impinging on the multilayer 1105 is captured and integrated. FIG. 7 depicts that there is a threshold for the ion dose below which a material does not show a volume expansion. Therefore, the depth distribution of the implanted ions (right partial image) indicates that the capture layer 1115 can provide a large local volume expansion which can be adjusted by controlling the beam parameters of the incident ion beam. On the other hand, the doses implanted in the substrate 1110 and in the multilayer structure 1105 are not high enough in order to induce a volume change in these layers. As already mentioned, the bombardment of a surface with an ion beam leads to a local removal of atoms from the material surface. This effect may be detrimental to a multilayer as the upper Mo—Si layers provide an important contribution to the overall reflectivity of the multilayer structure. FIG. 12 shows an EUV optical element 1200 which can comprise an EUV mask and/or an EUV mirror. The EUV optical element 1200 has as substrate 1210 which has a pit defect 1220 and a multilayer structure 1205. For simplicity reasons the propagation of the buried defect through the multilayer structure 1205 is suppressed. Before starting the defect repairing process by implanting of ions with an incident ion beam, a local protection layer 1230 is deposited on the multilayer structure 1205. As can be seen from a comparison of FIGS. 8 and 9, the use of a thin protection layer does not significantly distort the spatial distribution or depth distribution of the implanted ions. The protection layer 1230 has a width of at least the lateral dimension of the buried defect and a height of about 100 nm. Preferred materials for a protection layer 1230 are for example carbon (C) and/or tetraethyl orthosilicate (TEOS). The protection layer 1230 is locally deposited on the multilayer structure 1205 by using an electron bean and/or an ion beam in combination with a precursor gas. After the local deposition of the protection layer 1230, the buried defect 1220 is corrected by implanting an appropriate ion dose in the multilayer structure 1205 as discussed above. The correction of the buried defect 1320 is schematically depicted in the middle part of FIG. 12. The incident ions sputter a portion 1240 of the upper part of the protection layer 1230. Therefore, the protection layer 1230 efficiently protects the surface of the multilayer structure 1205 from the sputter action of the incident ions. At the end of the ion implantation process, the protection layer 1230 is again removed. This can for example be done by an etching process using an electron beam and/or an ion beam together with one etching gas or a combination of etching gases. Beside the sputter action at the surface, the interaction of the ions with the material along their path through the material may induce damages in the material along the ion path. Therefore, it can be beneficial to guide the incident ions through portions of a multilayer structure of an EUV optical element whose integrity is of less importance for the reflectivity of the multilayer film. FIG. 13 schematically illustrates an example how such an improvement can be realized for EUV mask 1300. Similar to the left partial image of FIG. 12, the left partial image of FIG. 13 presents again a substrate 1310 having a pit defect 1320. The propagation of the buried defect through the multilayer structure 1305 is again ignored. An absorbing pattern 1340 is deposited on the multilayer film 1305. The buried defect 1320 is not localised below an absorbing pattern element 1340, but below the surface 1370 of the multilayer structure 1305. If an ion beam perpendicularly incidents on the buried defect 1320, it has to pass through the surface 1370 of the multilayer 1305 and may damage the surface 1370 by sputtering atoms from the Mo—Si layers closest to the surface 1370. Furthermore, the ion beam might damage the multilayer structure 1305 along its path to the buried defect 1320 as explained in the preceding paragraph. FIG. 13 illustrates a configuration with which a possible damage of reflectivity critical portions of the multilayer can at least partially be avoided. The left partial image of FIG. 13 schematically shows the configuration at the beginning of the ion beam irradiation. The ion beam 1380 obliquely impacts on the pattern element 1340 and obliquely crosses the multilayer structure 1305 on its path to the buried defect 1320. The right partial image of FIG. 13 schematically shows the situation at the end of the repairing process. The local volume expansion caused by the implanted ions corrected the buried defect 1320. The surface 1360 of the pattern element 1340 is damaged by the sputter action of the ion beam 1380 during the repairing process. If necessary, the surface damage 1360 of the pattern element 1340 can be corrected by locally depositing absorber material on the damaged surface 1360 by using a method described above. The white area 1330 below the absorbing pattern element 1340 indicates the area with might be damaged by the interaction of the ions of the ion beam 1380 with the Mo and Si atoms of the multilayer structure 1305. It has a drop shaped form. The major portion of the potentially damaged area is located below the pattern element 1340. In particular, ions do not cross the Mo—Si layers closest to the surface 1370 of the multilayer structure 1305. Thus, by the selected path of the ion beam 1380, the impact of the ion beam 1380 on the reflectivity of the multilayer structure 1305 is minimized. An EUV mirror which does not have an absorber pattern can also be corrected with the discussed procedure if a protection layer 1230 of FIG. 12 in arranged on the EUV mirror instead of the pattern element 1340. Finally, the discussed repairing methods can also be applied on defects of a mask blank prior to the deposition of a multilayer structure. By correcting defects existent on the substrate already on the mask blank possible damages of the multilayer structure can be avoided. The defined method for defect analysis reliably discriminates between surface defects and buried defects of EUV optical elements. Instead of incompletely compensating the impact of buried defects of EUV masks by modifying of the absorbing pattern, the discussed repairing method corrects buried defects by a modification of the substrate and/or of the multilayer structure of EUV optical elements.
	summary
	summary
	claims	1. Goggles for receiving at least one radiation protection material which protects the eyes of a patient from radiation being harmful to the eyes, wherein the goggles comprise:two goggle frames each comprising a continuously circumferential side wall structure completely enclosing an area around the respective eye of the patient,a length-adjustable connection element between the two goggle frames in the area of the nose of the patient for changing the distance between the two goggle frames relative to one another, andat least one length-adjustable holding element for fixing the two goggle frames to the head of the patient,wherein the side wall structures are configured for receiving at least one radiation protection material substantially completely around its circumference,wherein each side wall structure comprises an inner and an outer side wall which are connected by means of a base wall at an end of the side wall structure, wherein the inner and the outer side wall have a predetermined distance in the cross direction to the viewing direction of the patient in order to form a space, the space being configured for receiving the at least one radiation protection material. 2. The goggles according to claim 1, wherein the at least one radiation protection material is configured so as to fill the space completely in the longitudinal direction. 3. The goggles according to claim 2, comprising a light transmissive element which is preferably arranged in the area of the distal end of each goggle frame, wherein preferably the inner side wall has a smaller height in the distal direction than the outer side wall, wherein the transmissive element is substantially flush with the outer side wall and/or rests against the distal end of the inner side wall. 4. The goggles according to claim 3, wherein the light transmissive element comprises a radiation protection material. 5. The goggles according to claim 4, wherein said radiation protection material is a low-Z material. 6. The goggles according to claim 5, wherein said low-Z material is acrylic glass or plastic materials loaded with high-Z materials. 7. The goggles according to claim 6, wherein said high-Z materials are bismuth or lead acrylic. 8. The goggles according to claim 3, wherein the shape and size of the light transmissive element are substantially adapted to the shape and size of the inner circumference of the outer side wall. 9. The goggles according to claim 1, wherein the at least one radiation protection material comprises a first material layer formed of a material having a low atomic number Z, and/or a second material layer formed of a material having a high atomic number Z, wherein the first material layer and the second material layer are provided as a compound layer, as a thin film or as a powder dispersed in a matrix material or as a liquid for casting or injection molding. 10. The goggles according to claim 9, wherein the first material layer is arranged in the space neighboring the outer side wall and the second material layer is arranged in the space neighboring the inner side wall. 11. The goggles according to claim 9, wherein said first material layer is Aluminum and said second material layer is lead or lead replacement materials such as bismuth, tungsten, tantalum or compounds of these metals. 12. The goggles according to claim 1, further comprising a first eye provided at the part of the respective side wall structure of a goggle frame facing the nose for attaching the connection element and/or further comprising a second eye provided at the part of the respective side wall structure of a goggle frame opposite the part facing the nose for attaching the holding element. 13. The goggles according to claim 1, wherein the proximal end of the side wall structure, has a shape and/or size being ergonomically adapted to the shape of the patient's head in the area around the eyes. 14. The goggles according to claim 1, wherein said goggles protects the eyes of a patient from β-radiation, x-ray radiation and/or gamma radiation.
047864605	description	DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The right-hand part of FIG. 1 shows a portion of the main vessel 10 of a fast neutron nuclear reactor. In known manner the vessel 10 is filled with sodium 12 and contains the reactor core 14, only a small portion of which is shown in FIG. 1. The core is formed by a large number of fissile, fertile assemblies, one 16 of which is shown. In reactors of integrated type the main vessel 10 also contains all the components of the primary circuit, more particularly the pumps and heat exchangers. In loop-type reactors at least a proportion of these components is situated outside the vessel 10. The main reactor vessel 10 is received in a vessel well formed by a concrete structure a portion 18 of which is shown in FIG. 1. A metal skin 20 lining the vessel well 18 forms a safety vessel. The main vessel 10 is suspended by its top end from a horizontal floor 22 covering the peripheral edge of the vessel well. At its top end the main vesssel 10 is closed by a caisson-type closure slab 24 bearing at its centre, generally via a system of two over-lapping rotary plugs (not shown), an assembly-handling apparatus 16, such as a stirring rod 26. The rod 26 enables an assembly 16 to be introduced into a handling or transporting pot 28 forming one of the elements of the handling installation according to the invention. To this end the assembly 16 can be taken either from the reactor core 14, or from a storage zone (not shown) provided inside the main reactor vessel 10. Of course, the rod 26 permits the converse handling operation consisting in taking a new assembly from the pot 28 to introduce it into the reactor core 14. In addition to the pot 28, the handling installation according to the invention comprises a primary ramp 30, a secondary ramp 34 and a transfer hood 32. The ramps 30 and 34 are inclined in opposite directions by an angle of about 20.degree. to the vertical. More precisely, their axes lie in the same plane, forming an inverted V. The primary ramp 30 extends through the slab 24 and opens at its bottom end inside the vessel 10 in a zone close to the core 14 and generally called the loading-unloading station of the reactor, referred to hereinafter as the primary station to simplify matters. The secondary ramp 34 extends through the top end of the vessel well 18 and then the wall 35 of a structure adjacent such well, to enter an adjoining vessel 36 via a tube 36a. The vessels 10 and 36 are situated at approximately the same level one alongside the other. As a variant, the wall 35 and the wall of the vessel well 18 might be formed by one single wall. The diameter of the adjoining vessel 36 differs in dependence on whether the assemblies placed in the vessel have or have not previously been stored inside the reactor vessel itself. In the embodiment illustrated in FIG. 1, it is supposed that the assemblies have been stored in the primary vessel. The diameter of the vessel 36 is therefore small, since the assemblies can be evacuated directly. To this end a handling system (not shown) can be placed in a cell disposed above the vessel 36. Like the main reactor vessel 10, the adjoining vessel 36 is filled with liquid sodium 12, as well as the bottom portion of the secondary ramp 34 disposed in the tube 36a. The zone defined by the bottom end of the vessel 36 into which the secondary ramp 34 opens is generally called the secondary loading-unloading station, but to simplify matters will be hereinafter referred to as the secondary zone. The transfer hood 32 rests on the slab 24 and on the floor 22 and is so mounted as to pivot around a vertical axis (arrow F1) in a manner which will be disclosed in greater detail hereinafter. It should be noted that the axis of rotation of the hood 32 coincides with the axis of symmetry of the ramps 30 and 34. The hood 32 is mainly formed by a thick cylindrical tube 32b whose geometrical axis is inclined by an angle identical with the angle of inclination of the primary ramp 32 and the secondary ramp 34. By rotating the hood 32 through 180.degree., therefore, the open bottom end of the hood can be successively moved into the prolongation of the open top end of the primary ramp 30 and into the prolongation of the open bottom end of the secondary ramp 34. The hood 32 is closed at its top end and its internal diameter is approximately the same as that of the ramps 30 and 34. Due to this configuration the biological screening is situated as close as possible to the assembly during transfer. Although the thickness of the screening is compulsory, in this way its mass and therefore cost are reduced. The simplicity of shape of the biological screening also enables it to be hermeticized. It therefore ensures the containment of the covering gas above the sodium 12 in the period of handling during the power-generating operation of the reactor. The thick tube 32b is lined on the outside by a heat insulation 32c allowing an ascending circulation of air or gas by natural convection in an annular space bounded between the heat insulation 32c and the wall of the tube 32b. To this end inlet and outlet windows, whose opening is controlled by closure members 32d, are formed at the bottom and top of the heat insulation 32c respectively. The circulation of air by the natural convection of the air enables the residual power of the fissile assemblies to be evacuated when they are unloaded. Moreover, the thermal inertia of the thick walls of the tube 32b make a number of hours available to take action in case of an incident. The hood 32 thus forms a "hot" biological screening ensuring by conduction the thermal regulation of the pot which it contains, without the necessity to use forced ventilation. To prevent the solidification of the liquid metal contained in the pot during the handling period, a heating system 32 is disposed around the thick tube 32b and in contact therewith. The handling installation according to the invention comprises a single pot 28 which is moved from the secondary station to the primary station and conversely, passing successively via the secondary ramp 34, the rotary hood 32 and the primary ramp 30 (arrows F2 in FIG. 1). To this end the pot 28 is attached to lifting means which will be disclosed in greater detail hereunder. It will simply be pointed out here that the lifting means comrise two cables 40 whose bottom ends are attached to the pot 28 or, more precisely, to the top end of a rocking rod 28b whose bottom end is articulated at a place 28c to the body 28d of the pot, substantially halfway up such body. To ensure its guidance when it moves inside the ramps 30 and 34 and the hood 32, the pot has two pairs of wheels 28a guided by rails 30a, 32a and 34a disposed in the ramp 30, the hood 32 and the ramp 34 respectively. One of the pairs of wheels 28a is mounted at the top end of the rockig rod 28b, while the other pair of wheels is mounted on the body 28d, below the articulation 28c. As shown in FIG. 1, due to the structure of the pot 28 just described and the attachment of the pot to the cables 40 by the top end of the rocking rod 28b, the pot is inclined to follow the rails disposed inside the ramps and the hood and resumes its vertical position when it arrives at the primary or secondary loading-unloading station (arrow F3). As a result of limiting the number of wheels 28a to two pairs, the pot 28 is guided isostatically inside the ramps and the hood. This eliminates any risk of the pot being blocked during its movement, even if there should be angular offsetting between the hood and one or other of the ramps. Referring to FIG. 2, it can be seen that the isostatic nature of the guiding of the pot is made possible by the fact that there is practically no break between the rails 32a of the hood and the rails 30a or 34a of the ramp with which the hood is aligned. There is therefore no longer any need to give the pot extra pairs of guide wheels, as was the case with the handling installation of the Super Phenix reactor. According to the invention this result is made possible by eliminating the sluice-like operation of the transfer hood during handling. It should be noted that such elimination is perfectly possible, since the sodium 12 contained in the lower portion of the secondary ramp 34 disposed in the tube 36a (FIG. 1) then ensures that the internal atmosphere of the main reactor vessel 10 is contained in relation to the outside. Thus, according to the invention the open top ends of the primary ramp 30 and the secondary ramp 34 are closed only during the power operation of the reactor. Such closure is performed by means of two flaps 46 (FIG. 3b) mounted on a rotary horizontal platform 48 to which the hood 32 is also attached (preferably demountably). The platform 48 takes the form of a disc whose geometrical axis coincides with the vertical axis of rotation of the platform. The flaps 46 are disposed symmetrically in relation to the vertical axis of rotation of the hood 32 and the platform 48, for example at 90.degree. on either side of the hood. Each of the flaps 46 is formed by a solid disc of vertical axis bearing at its periphery two toric sealing joints. The platform 48 is disposed immediately above a fixed base plate 50 which ensures that the platform is supported and rotated. As shown in FIG. 3a, the plate 50 is a horizontal disc-shaped plate which has a diameter slightly larger than that of the platform 48 and whose geometrical axis coincides with the axis of rotation of the platform 48. The top ends of the ramps 30 and 34 open into the plate at diametrically opposite locations. More precisely, the rails 30a ad 34a of the ramps 30 and 34 project upwards beyond the upper face of the plate 50, the rails 32a of the hood 32 projecting downwards beyond the lower face of the platform 48, so that a very small clearance (a few millimetres) is left between the ends of the rails when the hood is placed above one of the ramps (FIG. 2). A larger space is formed between the plate 50 and the platform 48, so that the latter can rotate when a flap closes one of the ramps. Thus, at the end of a handling period and before the reactor power rises, the effect of a rotaton of the plate 48 through 90.degree. is to move the diametrically opposite flaps 46 to face the top ends of the ramps 30 and 34. The control mechanisms of the flaps 46 will be disclosed in greater detail hereinafter with reference to FIG. 5. Here it will merely be stated that during handling, the flaps 46 occupy a raised position in which they are retracted into recesses 48b (FIGS. 2 and 5) formed inside the rotary platform 48, so as not to impede the rotation of the platform. In contrast, when the reactor is operating, the flaps are lowered to hermetically seal the top ends of the ramps. In that position the flaps 46 are completely released from the recesses 48b, so that the platform 48 can similarly be rotated. In addition to the two flaps 46 disposed at diametrically opposite locations on the platform 48, the installation according to the invention advantageously comprises another flap 46' forming a spare flap. The third flap 46' is mounted on the platform 48 at a location diametrically opposite that occupied by the hood 32 (FIG. 3b). When the hood 32 is disposed in the prolongation of one or other of the primary 30 and secondary 34 ramps, therefore, the spare flap 46' is situated opposite the top end of the other ramp. The spare flap 46' is identical with the two other flaps. Similarly, the spare flap control mechanism is identical with the control mechanisms of each of the two other flaps 46. The presence of the spare flap 46' on the rotary platform 48 has the advantage of enabling either of the two other flaps 46 to be very rapidly interchanged, for example, when the sealing joints of the flaps have become damaged. To allow such interchange, the base plate 50 comprises, at a location angularly offset, for example, by 90.degree. in relation to the top ends of the ramps, a recess 60 opening on to the upper face of the plate 50 (FIGS. 3a and 4). The recess 60 forms a withdrawal station for the flaps as a result of which one of the two "active" flaps 46 can be replaced by the spare flap 46'. The replacement can be performed very simply in the following manner. In a first stage, with the spare flap 46' and the hood 32 facing the ramps 30 and 34, the operator actuates the control mechanism of the flap 46 to be replaced, which is disposed above the recess 60, to introduce such plate into the recess and disconnect it from its control mechanism. By a rotation of the platform 48 through half a turn, the second flap 46 is in turn moved above the recess 60. The spare flap 46' is then opposite the top end of one of the ramps 30 or 34. The operator lowers such flap inside the base plate 50 and disconnects the flap from its control mechanism, to close the end of the corresponding ramp. By rotating the platform 48 through a quarter of a turn in the opposite direction, the second flap 46 is moved above the other ramp, then introduced into the base plate by the actuation of its control mechanism. The installation is then in a position to operate, the worn flap 46 having been replaced by the spare flap 46'. These operations for replacing the flap 46 are so performed that the hood 32 is never opposite a ramp closed by a flap. In this way the cutting of the rails 30a, 32a and 34a is reduced to the minimum compatible with the mechanical constructional tolerances. In practice it is a few millimetres. Moreover, these operations are performed without infringing the hermeticity of the assembly. To enable the worn flap 46 to be evacuated and a fresh, spare flap 46' to be introduced in its place, the control mechanism of the spare flap 46' is mounted in the rotary platform 48 via a demountable plug 62, as shown more particulary in FIG. 5. The plug 62 is mounted and demounted, for example, by unscrewing three shoes 64 screwed on to the top horizontal surface of the rotating platform 48 and bearing against the upper surface of the plug 62. To maintain the containment of the space formed between the rotary platform 48 and the base plate 50, two sealing joints are mounted on the periphery of the plug 62 and an argon-circulating system is provided between the joints. It should be noted that a similar system is used for all the joints ensuring containment. Referring to FIGS. 3a, 3b and 4, it can be seen that a hood closure member 140 can also be received in the recess 60 formed in the base plate 50. In that case the upper surface of the closure member 140 is formed with a circular recess 140a whose dimensions enable it to receive the spare flap 46' or one of the flaps 46. The closure member 140 also comprises two diametrically opposite lugs which are formed with tapped holes 142b. When the bottom end of the hood 32 is to be closed, the flaps 46 and 46' are retracted into the rotary platform 48 by actuating the control means associated with them. By rotating the rotary platform 48 the operator moves the bottom end of the hood 32 above the recess 60 receiving the hood closure member 140. Screws 142 permanently received in the wall of the hood 32 are then screwed into the tapped holes 140b. The hood closure member is then attached to the hood 32 to hermetically close its open bottom end. The hood 32 thus closed can then be demounted from the rotary platform to which it is attached, for example, by screws or pins (not shown). This feature can be used more particularly to take action on the transporting pot 28, which is then moved back into the hood 32. The feature also enables fuel to be handled on a number of reactors situated on the same site, using a single hood 32. A description will now be given, with reference to FIG. 2, of the means for supporting and rotatably entraining the rotary platform 48 from the base plate 50. These functions are moved upwards, due to coaxial tubes 48a and 50a prolonging the peripheral edges of the platform 48 and the plate 50 respectively upwards, so as to prevent the heat at the level of the plate 50 from breaking down the hermeticity of the rotary joints. The platform 48 is supported by a rolling bearing 52 with three sets of rollers which is disposed between the top end of the flanges 48a and 50a. The entrained rotation of the platform 48 is performed by a step-down motor 54 supported by the top end of the tube 48a. The output shaft of the step-down motor 52 bears a pinion 56 meshing with a toothed rim 58 with which the top end of the external surface of the tube 50a is formed. Preferably the step-down motor 54 provides a fast rotary speed and a slow speed, the latter being used at the end of the movement. To maintain the containment of the space bounded between the rotary platform 48 and the base plate 50, rotary sealing joints (not shown) are associated with the rolling bearing 52. Moreover, an argon circulation is provided between these joints to enable a leakage of one of them to be detected immediately. FIG. 5 shows to an enlarged scale the mechanism 66 controlling the movement of the spare flap 46' between its bottom closure position, shown in solid lines, and its raised retracted position inside a recess 48b formed in the platform 48 below the plug 62 (this position being shown in chain-dot lines). The mechanism also enables the gripping of the flap to be controlled and its presence to be checked. As already mentioned, the control mechanisms associated with each of the flaps 46 are identical with the control mechanism 66 associated with the spare flat 46a. The following description of the mechanism 66 therefore also applies to the mechanisms used for controlling the two flaps 46, the only difference being that the latter mechanisms are placed directly in the platform, and not in a plug 62. The control mechanism 66 comprises a supporting member 68 whose lower portion 68a, taking the form of a sheath, is attached hermetically, for example, by screws 69, in a bore extending through the centre of the plug 62. The member 68 is prolonged upwards beyond the flat upper surface of the platform 48, in the form of a vertical portion 68b having a U-shaped horizontal section. At its top end the portion 68b of the member 68 terminates in a horizontal plate 68c. The member 68 supports a member 70 which can move vertically along the vertical axis shared by the plug 62 and the flap 46'. The lower portion 70a of the member 70 takes the form of a cylindrical sleeve tube slidably received in the lower sheath-shaped portion 68a of the member 68. The member 70 is prolonged above the upper surface of the rotary platform 48 by a vertical portion 70b having a U-shaped section and disposed inside the portion 68b of the member 68. At its top end the portion 70b terminates in a horizontal plate 70c disposed below the plate 68c. A screwthreaded rod 70d projects vertically upwards along the axis of the plug 62 and the flap 46a, passing freely through the plate 68c. The plate 68c supports an endless screw jack 72 which is actuated manually, for example, by means of a flywheel shown diagrammatically at a place 74 in FIG. 4. By taking action of the jack 72 using the wheel 74, the raising or lowering of the member 70 inside the member 68 can be controlled as required. The square flap 46' (or one of the flaps 46) is connected to the bottom end of the member 70 via a hollow vertical rod 76 extending through the lower portion 70a of the member 70. At its bottom end the rod 76 has a screwthreading and projects beyond the bottom end of the portion 70a, so that it can be screwed into a nut 46a borne at the centre of the upper surface of the flap 46. At its top end projecting above the portion 70a of the member 70, the rod 76 has a hexagonal head 76a enabling the rod of the nut 64a to be tightened or unscrewed using a suitable spanner. The portion of the rod 76 adjacent the head 76a is also screwthreaded to receive a counternut 78 adapted to bear against the upper surface of the portion 70a, to immobilize the rod 76 in the member 70 when the rod is screwed into the nut 46a. In that position a nose 70e in the form of a collar formed at the bottom end of the portion 70a of the member 70 is fitted into the flap 46 around the nut 46a. The hollow rod 76 has a central bore in which a central rod 80 forming a finger checking for the presence of the flap 46 moves freely. A compression spring 82 interposed between the top end of the finger 80 and the plate 70c of the member 70 always exerts a downward thrust on the finger 80. Sealing bellows 84 are interposed between the bottom end of the member 68 and the bottom end of the member 70. Similarly, sealing bellows 86 are interposed between the top end of the hollow rod 76 and the top end of the finger 80. Two annular sealing joints are also provided between the portion 68a of the member 68 and the plug 62, an intermediate argon circulation being provided between such joints. Contactors 88 and 90 are mounted on the plug 62 and the portion 68b of the member 68 respectively to detect the bottom and top positions of the member 70. These two positions of the member 70 correspond to the closure of the corresponding ramp by the flap 46 or the retraction of such flap inside the rotary platform 48 respectively. In the embodiment shown in FIG. 5, a visual check is made on the gripping of the flap 48 by the hollow rod 76 and the presence of the flap opposite such rod. For this purpose the top end of the hollow rod 76 is surmounted by a drum 94 bearing a visual reference mark. Similarly, the top end of the rod 80 is surmounted by a drum 94 bearing a visual reference mark. The drums 92 and 94 are disposed inside the portion 70b of the member 70. Corresponding reference marks made on the fixed member 68 enable the gripping of the flap 46 and its presence to be checked. Thus, when the hollow rod 76 is screwed into the nut 46a, the reference mark formed on the drum 92 is normally opposite a first reference mark on the member 68. When the rod 76 is completely unscrewed from the nut 46a, the reference mark on the drum 92 is opposed a second reference mark on the fixed member. By taking action on the wheel 74, the member 70 is then moved upwards to disengage the nose 70e formed at the bottom end of this member 70 from the flap 46'. When this operation is completed, the reference mark on the drum 92 is opposite a third reference mark formed on the fixed member 68. In parallel, when the nose 70e of the member 70 is fitted into the flap 46', the reference marker formed on the drum 94 always remains opposite a corresponding reference mark formed on the fixed member 68, since in that case the bottom end of the finger 80 bears against the flap 46. In contrast, when the rod 76 is unscrewed from the nut 46a and the member 70 moves away from the flap 46', the finger 80 is forced down by the compression spring 82. The reference mark formed on the drum 94 then moves downwards in relation to the corresponding reference marked formed on the fixed member 68. A visual check can therefore be made that the member 70 is properly separated from the flap 46. FIG. 6 shows diagrammatically the principle of the supporting of the base plate 50 by the slab 24 closing the reactor vessel and by the floor 22 disposed on the peripheral wall of the vessel well. A tube 96 encloses the primary ramp 30 in the portion thereof which extends through the slab 24 and is situated thereabove. The tube 96 is welded to the top flange 24a of the slab 24 and comprises at its top end a spherical bearing area 96a received in a cylindrical passage 50a in the plate 50, as illustrated in FIGS. 6 and 7. The base plate 50 rests on the top end of the tube 96 via a shoulder 50b disposed in the passage 50a above the cylindrical portion thereof in which the spherical bearing surface 96a is received. So as not to block the swivel link formed by the cooperation between the surface 96a and the bore 50a, the plate 50 is attached to the end of the tube 96 only in that portion of the shoulder 50b which is furthest away from the vertical axis of the base plate 50. Such attachment is obtained by means of pins 98 or the like, a bearing wedge 100 being interposed between the shoulder 50b and the tube 96. Hermeticity is produced between the base plate 50 and the top end of the tube 96 by a resilient diaphragm 102 (FIG. 7) in the form of washer, whose external and internal peripheries are welded to the upper surface of the plate 50 and the end of the tube 96 respectively. To prevent any differential expansion between the base plate 50, the upper flange 24a of the slab and the floor 22 from affecting the mechanical behaviour of these members, the swivel link just described, between the tube 96 borne by the slab and the base plate 50, is completed by two shoes 104 disposed at about 120.degree. in relation to such swivel link. The shoes 104 are sliding shoes with which the lower surface of the base plate 50 is formed and which rest on the floor 22. To prevent the plate 50 from rotating horizontally around the swivel link 96a-50a, a key-type guide system 106 is provided at a location diametrically opposite from the swivel link. The guide system 106 is oriented radially in relation to the vertical axis of the plate 50 and disposed between the lower surface of the plate 50 and the upper surface of the floor 22. As was already shown, one of the main advantages of the invention is the small clearance between the guide rails 30a and 34a formed inside the ramps and the guide rails 32a formed in the hood 32. To keep such spacing substantially constant at all temperatures, the ramps 30 and 34 are suspended from the base plate 50 in a manner which will now be disclosed in greater detail with reference to FIGS. 7 and 8. As shown by FIG. 7, the primary ramp 30 is supported by a spherical bearing surface 30b bearing swivelably against a conical bearing 96b formed inside the tube 96 adjacent the base plate 50. In a comparable manner (FIG. 8), the secondary ramp 34 has adjacent its top end a spherical bearing surface 34b which bears swivelably against a frustoconical bearing surface 108a formed on a member 108 attached to the lower surface of the base plate 50. Hermeticity between the top end of the ramp 34 and the base plate 50 is provided by a resilient diaphragm 110 in the form of a washer, whose external and internal peripheral edges are welded to the upper surface of the plate 50 and the lower surface of the secondary ramp 34 respectively. Of course, means are provided in association with the swivel links just described with reference to FIGS. 7 and 8, to prevent the ramps from rotating in relation to the members supporting the ramps. As shown in FIG. 8 in the case of ramp 34, the means can more particularly be formed by a finger 112 connected in this case to the member 108 and entering a suitably shaped recess in the ramp 34. To complete the supporting performed by these swivel links without producing mechanical stress in the primary and secondary ramps, their bottom ends are guided by guide members 114 and 116 (FIG. 1) attached to the internal structures of the main vessel 10 and the adjoining vessel 36 respectively. As already stated, the means for lifting the pot 28 comprise two cables 40. FIG. 1 shows how the cables pass over two return pulleys 42 of common horizontal axis disposed above the hood 32, before being wound on two drums 44 also having a common horizontal axis. FIGS. 9 and 9a show the motorization system for simultaneously driving the two drums 44 on which the lifting cables 40 are wound (the system is shown in section in the right-hand half of FIG. 9). FIG. 9 clearly shows that the motorization system is symmetrical in relation to the vertical plane containing the axis of the hood 32. The drums 44 are therefore disposed on either side of such plane of symmetry on two coaxial driving shafts 118 separately supported rotatably by a single casing 120 attached to the outside of the hood 32. The shafts 118 project outside the casing 120, where each of them is rotated by an irreversible step-down motor 126 whose casing is not connected to the casing 120. The input of each of the step-down motors 126 is connected to the output shaft of a single asynchronous motor assembly via an angle gear 122 and two universal joint mechanisms 124. More precisely, the geometrical axis shared by the motor 122 at its output shaft and at the angle gear 122 lies in the plane of symmetry of the motorization system, the mechanism 124 being oriented normally in a direction perpendicular to such plane and lying on either side thereof. The motor assembly 121 preferably enables the movment of the pot to be controlled at high and low speed, the latter being used only at the end of movement of the pot, or on its arrival in the hood, or on its arrival at the primary and secondary loading-unloading stations. To this end the assembly 121 in that case has two asynchronous motors with incorporated brakes, whose common output shaft also comprises a torque limiter. Preferably an optical encoder 128 is disposed at the end of each of the shafts 118, if necessary behind a reducing gear 129, so that the position of the pot in the installation can be detected at any moment. A bolt 150 is mounted on the casing 120 opposite a toothed rim 152 rotated by one of the shafts 111, to block the drum 44 if action must be taken on the corresponding reducing gear 126. Although this is not shown in FIG. 9, a similar arrangement is provided on the other shaft 118. The motorization system just described comprises two kinematic chains which are perfectly symmetrical in relation to the vertical plane of symmetry defined hereinbefore. In this system, due to the floatable mounting of the casings 126 of the step-down units and the presence of universal joint mechanisms 124, any imbalance occurring between the torques exerted on each of the shafts 118 results in the pivoting in the opposite direction of the casings of the step-donwn units around such shafts. By detecting such pivoting, it is therefore possible to immediately detect such an imbalance and therefore the start of rupture of one of the cables 40. To this end the casing 120 also supports the pivot 130 of an imbalance-detecting level or rocker 132. The pivot 130 coincides with the axis of the motor assembly 121 and the lever 132 extends symmetrically on either side of such pivot 130. At each of its ends the lever 132 is attached to the end of a shock-absorber 134 whose axis is oriented in a direction at right angles to both the geometrical axes of the motor 121 and of each of the shafts 128. Each of the shock-absorbers 134 comprises a weighing cell 135 (FIG. 9a) and is articulated by its opposite end to a lever 136 connected to the casing of each of the step-down units 126 and oriented radially in relation to the corresponding shaft 128. When the torques exerted on the shafts 128 are equal, the levers 136 are perfectly symmetrical in relation to the plane of symmetry of the system. In contrast, if an imbalance appears between the torques exerted on each of the shafts 128, for example, because of the start of rupture of one of the cables 40, the casings 126 of the step-down units tend to rotate in the opposite direction around the axis shared by the two shafts 128. The relative rotation is transmitted to the lever 130 via the shock-absorbers 134 and is immediately detected by electric contacts 138 (FIG. 9a) mounted on the casing 120 and sensitive to any offsetting of the level 132 in relation to its equilibrium position. It should be noted that the lever 132 also allows the incorrect winding of one of the cables 40 on to the corresponding drums 44. From this aspect the structure of the drums 44 and the casing 120 is such that the cables can never escape from the drums. Advantageously sight holes can be provided, more particularly in the casing 120, to enable the condition of the cables 40 to be checked visually. Moreover, the casing 120 (which also contains the return pullies 42) and the hood 32 are heated to about 150.degree. C. to avoid hooping on the drums due to cable. Preferably the installation is also designed in such a way that the portion of the cables 40 wetted by the sodium 12 is never wound on to the drums 44. Lastly, a manual control (not shown) enables the movable equipment to be returned to a safe position in all cases. As a result of all these features of the pot-lifting system, safety is such that the pot parachute of the existing installations is no longer needed. The elimination of the parachute enables another possible cause of the jamming of the pot in the ramps to eliminated. It also results in an appreciable reduction in the cost of the installation. Finally, the installation according to the invention leads to considerable progress in comparison with existing installations. In the first place, it practically eliminates any risk of the pot getting jammed, and all the difficulties arising therefrom. Secondly, it reduces the mass, space occupied and more particularly the cost of the installation (more particularly the hood) to a very important extent. Lastly, it allows a global doubling of the rate of handling, despite the simplification of the system (one single pot). Of course, the installation disclosed can be modified in various ways without exceeding the scope of the invention. Thus, merely by way of example, the flaps and the hood can be differently positioned on the rotary platform from the way shown in FIG. 3a. More particularly, if the vertical pivoting axis of the platform is offset in relation to the vertical plane containing the axes of the ramps, the flaps will not be situated at diametrically opposite locations on the platform. The ramps can also be located in two parallel planes, so as to deal with two pots associated with two hoods identical with the hood 32 described, but offset on the platform 48 in relation to the vertical pivoting axis of the platform. This arrangement enables the handling rate to be substantially improved.
	summary
	claims	1. A structure for suppressing flow induced vibration in a nuclear reactor vessel comprising:a guide tube provided inside a hollow upper core support column interposed between an upper core support plate and an upper core plate in a reactor vessel;a head nozzle provided at a lower end of the upper core support column; andan instrumentation tube disposed inside the guide tube, whereina lower hole is provided at a lower portion of a side surface of the guide tube, andthe instrumentation tube is disposed to contact with an inner circumferential surface of the side surface of the guide tube on which the lower hole is provided, such that the instrumentation tube is pressed against the side surface by a differential pressure between coolant inside and outside the lower hole. 2. The structure for suppressing flow induced vibration according to claim 1, whereina pressure adjustment hole is provided at a side surface of the upper core support columnfor allowing coolant flowing into the guide tube from a lower end of the guide tube to flow out to outside from inside the guide tube through a gap between the instrumentation tube and the lower hole, and then to flow out to outside from inside the upper core support column through the pressure adjustment hole. 3. A structure for suppressing flow induced vibration in a nuclear reactor vessel comprising:a guide tube provided inside a hollow upper core support column interposed between an upper core support plate and an upper core plate in a reactor vessel;a head nozzle provided at a lower end of the upper core support column; andan instrumentation tube disposed inside the guide tube, whereinan upper hole and a lower hole are provided at two portions, namely an upper portion and a lower portion, of a side surface of the guide tube, andthe instrumentation tube is disposed to contact with an inner circumferential surface of the side surface of the guide tube on which the upper hole and the lower hole are provided, such that the instrumentation tube is pressed against the side surface by a differential pressure between coolant inside and outside the upper hole and the lower hole. 4. The structure for suppressing flow induced vibration according to claim 3, whereinan upper pressure adjustment hole and a lower pressure adjustment hole are provided at two positions, namely, an upper portion and a lower portion, of a side surface of the upper core support columnfor allowing the coolant flowing into the guide tube from an upper end of the guide tube to flow out to outside from inside the guide tube through a gap between the instrumentation tube and the upper hole, and also to flow out to outside from inside the upper core support column through the upper pressure adjustment hole, andfor allowing coolant flowing into the guide tube from a lower end of the guide tube to flow out to outside from the inside of the guide tube through a gap between the instrumentation tube and the lower hole, and also to flow out to outside from inside the upper core support column through the lower pressure adjustment hole. 5. The structure for suppressing flow induced vibration according to claim 3, whereinthe upper hole and the lower hole are formed in slits extending in an axis direction of the guide tube, and includes expanded portions expanded in oval shapes at middle portions of the slits.
	claims	1. A beam line system of an ion implanter, the beam line system comprising:a hollow tube having an inlet and an outlet, wherein the hollow tube is a collimator tube, an ion beam emitted by the ion implanter is introduced into the hollow tube through the inlet and exited from the hollow tube through the outlet; anda plurality of protruding structures formed on an inner wall of the hollow tube, wherein each of the protruding structures has a reflective surface for reflecting a portion of the ion beam. 2. The beam line system according to claim 1, wherein the hollow tube is made of graphite. 3. The beam line system according to claim 1, wherein the protruding structures are contiguous wedge-shaped structures on the inner wall of the hollow tube. 4. The beam line system according to claim 1, wherein the reflective surface of the protruding structure is substantially vertical to a traveling direction of the ion beam. 5. The beam line system according to claim 1, wherein a ratio of a height of the reflective surface of the protruding structure to a length of the protruding structure along a traveling direction of the ion beam is about 1:5. 6. The beam line system according to claim 1, wherein the portion of the ion beam which is not reflected by the protruding structures is exited from the outlet of the hollow tube. 7. The beam line system according to claim 6, wherein an end analyzer is positioned at a terminal of the beam line system to detect the portion of the ion beam which is exited from the outlet of the hollow tube. 8. The beam line system according to claim 7, wherein the end analyzer is a Faraday cup detector. 9. An ion implantation process, which is implemented by the beam line system according to claim 1. 10. An ion implanter, comprising:an ion source for producing ions;an analyzing magnet for producing an ion beam by selecting desired types of ions; anda beam line system for transmitting the ion beam, wherein the beam line system comprises a hollow tube with an inlet and an outlet and a plurality of protruding structures formed on an inner wall of the hollow tube, wherein the hollow tube is a collimator tube, the ion beam is introduced into the hollow tube through the inlet and exited from the hollow tube through the outlet, wherein each of the protruding structures has a reflective surface for reflecting a portion of the ion beam. 11. The ion implanter according to claim 10, further comprising:an accelerating system for accelerating the ion beam;a focusing system for focusing the accelerated ion beam; anda target chamber for receiving the ion beam from the focusing system. 12. The ion implanter according to claim 10, wherein the hollow tube is made of graphite. 13. The ion implanter according to claim 10, wherein the protruding structures are contiguous wedge-shaped structures on the inner wall of the hollow tube. 14. The ion implanter according to claim 10, wherein the reflective surface of the protruding structure is substantially vertical to a traveling direction of the ion beam. 15. The ion implanter according to claim 10, wherein a ratio of a height of the reflective surface of the protruding structure to a length of the protruding structure along a traveling direction of the ion beam is about 1:5. 16. The ion implanter according to claim 10, wherein the portion of the ion beam which is not reflected by the protruding structures is exited from the outlet of the hollow tube. 17. The ion implanter according to claim 16, wherein an end analyzer is positioned at a terminal of the beam line system to detect the portion of the ion beam which is exited from the outlet of the hollow tube. 18. The ion implanter according to claim 17, wherein the end analyzer is a Faraday cup detector.

claims

1. A system comprising:a laser source adapted to provide a laser beam directed along an optical path, wherein the laser beam is characterized by an output power in the range of 1 petawatt or higher; anda target positioned along the optical path and including:a laser incidence area for receiving the laser beam;an electron generation region adapted to absorb a portion of the laser energy associated with the laser beam and generate a plurality of electrons along an electron path;a compression region disposed along the electron path; anda capsule embedded within the compression region and including deuterium tritium (DT) gas. 2. The system of claim 1 wherein the target further includes a shock absorption region disposed between the electron generation region and the compression region, the shock absorption region configured to absorb a shock wave generated by the laser beam. 3. The system of claim 1 wherein the laser source comprises a Titanium Sapphire laser. 4. The system of claim 1 wherein the compression region includes a high Z material comprising one of gold, lead, tungsten, or silver. 5. The system of claim 1 wherein the electron generation region includes a first material and the compression region includes a second material different from the first material. 6. The system of claim 1 wherein the capsule includes an outer shell comprising a low Z material, wherein the low Z material comprises one of silicon dioxide, aluminum oxide, or carbon. 7. The system of claim 6 wherein the outer shell includes a plurality of layers. 8. The system of claim 6 wherein the outer shell comprises a porous material. 9. The system of claim 8 wherein the porous material includes aerogel. 10. The system of claim 1 wherein the capsule is characterized by a diameter of between 50 μm and 100 μm. 11. The system of claim 1 wherein the target further includes an electron transport region disposed along the electron path between the electron generation region and the capsule. 12. The system of claim 11 wherein the electron transport region comprises at least one of a high Z material or a low Z material, wherein the high Z material comprises one of gold, tungsten, lead or silver and the low Z material comprises one of silicon, beryllium, boron, or carbon. 13. A target comprising:a laser incidence area for receiving a laser beam;an electron generation region adapted to absorb a portion of laser energy associated with the laser beam and generate a plurality of electrons along an electron path;a compression region disposed along the electron path, the compression region configured to interact with the plurality of electrons and heat up to a first temperature of between 100 electron volts and 1000 electron volts; anda capsule embedded within the compression region and including deuterium tritium (DT) gas, wherein the capsule is configured to absorb radiated heat from the compression region and heat up to the first temperature. 14. The target of claim 13 further comprising a shock absorption region disposed between the electron generation region and the compression region, the shock absorption region configured to absorb a shock wave generated by the laser beam. 15. The target of claim 13 wherein the compression region includes a high Z material comprising one of gold, lead, tungsten, or silver. 16. The target of claim 13 wherein the electron generation region includes a first material and the compression region includes a second material different from the first material. 17. The target of claim 13 wherein the capsule includes an outer shell comprising a low Z material and wherein the low Z material includes at least one of silicon dioxide, aluminum oxide, or carbon. 18. The target of claim 17 wherein the outer shell includes a plurality of layers. 19. The target of claim 17 wherein the outer shell comprises a porous material and wherein the porous material includes aerogel. 20. The target of claim 13 further comprising an electron transport region disposed along the electron path between the electron generation region and the capsule, the electron transport region comprising at least one of a high Z material or a low Z material, wherein the high Z material comprises one of gold, tungsten, lead or silver and the low Z material comprises one of silicon, beryllium, boron, or carbon.

abstract

The present invention makes it possible to obtain a multilayer film reflective mirror 61 comprising a first multilayer film 67 which is formed by alternately laminating Mo layers 671 and Si layers 673 on a substrate 63, and a second multilayer film 65 which is formed on top of the first multilayer film 67, and which is formed by alternately laminating Mo layers 651 and Si layers 653, wherein the thickness of the Mo layers in the first multilayer film is substantially equal to or smaller than the thickness of the Mo layers in the second multilayer film, and the ratio of the thickness of the Mo layers to the thickness of the Si layers in the first multilayer film is different from the ratio of these thicknesses in the second multilayer film. As a result, a multilayer film reflective mirror with a low internal stress in which a drop in the reflectivity is suppressed can be obtained.

043409709

claims

1. A nuclear power wheel comprising a stationary side gear having a central substantially horizontal axis and mounted on a frame means, a shaft having first and second ends, said shaft being mounted on said axis, means for rotating said shaft solely in one direction, a satellite gear fixed to said first end of said shaft, a wheel fixedly mounted between the first and second ends of said shaft, said wheel having an outer perimeter, a plurality of expansion valves mounted on said outer perimeter on radial axes, each of said expansion valves including a drive gear for delivering useful work output mounted on the second end of said shaft, 2. The nuclear power wheel of claim 1 wherein the nuclear heat element includes two fixed distinct masses of uranium-235, and a freely moveable cadmium means which is moveable solely by means of gravity which separates said two masses when inserted therebetween at the uppermost vertical point of the wheel and which is completely withdrawn at the lowermost vertical point of the wheel. 3. The nuclear power wheel of claim 1 wherein the frame means is secured to the sea floor and the drive gear is joined to a plural section drill means. 4. The nuclear power wheel of claim 3 including a hose extending from the sea floor to a sea surface means, said sea surface means having an air compressor means which injects air in at least one point in said hose in an upwardly flowing direction to assist in the movement of the contents of said hose.

description

The present application is a divisional of U.S. patent application Ser. No. 11/296,438, filed on Dec. 8, 2005, which claims priority to Japanese patent application JP 2004-357319, filed on Dec. 9, 2004. 1. Field of the Invention The present invention relates to a technology for suppressing corrosion of metal components, such as nuclear power plant's structural components, in contact with high-temperature water, and more particularly, relates to a nuclear power plant having a corrosion-resistant coating, a method of making such a corrosion-resistant coating and a method of operating the nuclear power plant. 2. Related Art Metal components exposed to high temperature environment are found in almost all of the modern industrial and commercial plants. For example, in the course of steam reforming in a hydrogen production chemical plant, the reaction is carried out at high temperatures and pressures. Inside a boiler or a metal pipe connected to the boiler, hot water and steam move or travel while causing corrosion. The conventional preventive measures against corrosion of metal components have involved use of expensive, special corrosion-resistant materials, improvements on the environment to which the metal components are exposed, etc. For example, in a thermal power plant, a pH control reagent, a deoxidizer, or the like is added to control water chemistry and to thereby reduce the corrosion. In a boiling-water nuclear power plant, oxygen, hydrogen peroxide, and the like produced by radiolysis of water in the radiation field exist in a state dissolved in the reactor water. It is a well-known fact that stainless steel and nickel-based alloys, which are used for reactor structural components of the nuclear power plant, generate stress corrosion cracking in the presence of oxygen and hydrogen peroxide in a high-temperature environment such as a nuclear reactor. Hydrogen injection of injecting hydrogen into the reactor water has applied to some BWR plants in the world to reduce oxygen and hydrogen peroxide dissolved in the reactor water (refer to GENSHIRO MIZU-KAGAKU HANDBOOK [Handbook of Water Chemistry of Nuclear Reactor System], edited by Atomic Energy Society of Japan, published by Corona Publishing Co., Ltd., on Dec. 27, 2000, p. 210). The effect of the oxygen and hydrogen peroxide reduction by the hydrogen injection is confirmed as the decrease in corrosion potential of the metal components. The generation of stress corrosion cracking and the crack growth rate depends on the corrosion potential. The lower the corrosion potential, more suppressed the generation of stress corrosion cracking and development of cracks. As a result, the lifetime of the metal components can be extended. Other nuclear power plants in and outside Japan employ noble metal injection technology of conducting hydrogen injection after deposition of a noble metal, such as platinum (Pt) or rhodium (Rh), on surfaces of reactor structural components to accelerate reaction with hydrogen, increase the anode current to thereby decrease the corrosion potential (see the specification of Japanese Patent No. 2624906). The meaning of the corrosion potential of the metal components is as follows. When a metal is immersed in an electrolyte, the metal shows a potential inherent to that metal. This potential is called “spontaneous potential” of that metal. A corroded metal material shows a potential different (polarized) from its spontaneous potential due to the corrosion reaction. This difference in potential is referred to as the “corrosion potential”. A continuous measurement of the potential difference will estimate the progression of the corrosion. In a uniformly corroded metal material, the cathode reaction (reduction reaction) and the anode reaction (oxidization reaction) reach an equilibrium at the intersection of the cathode reaction polarization curve and the anode reaction polarization curve. This intersection corresponds to the corrosion potential. Another approach that has recently drawn much attention for decreasing the corrosion potential is to utilize the photocatalytic reaction. By coating surfaces of the metal components with a photocatalyst and irradiating the photocatalyst with light having wavelength near ultraviolet, electrons activated by the photoexcitation reaction cause the corrosion potential to decrease. The photoexcitation reaction can be accelerated with a noble metal disposed nearby. Accordingly, by depositing a photocatalyst or a high-efficiency photocatalyst containing a noble metal onto surfaces of the reactor structural components and inducing photoexcitation reaction by Cerenkov radiation generated in the reactor core, the corrosion potential during operation can be reduced (for example, refer to Japanese Patent Laid-open Publication Nos. 2001-4789 and 2001-276628). As the method of preventing parts of the metal components from corrosion in the absence of light, a technology for decreasing the potential difference by generating thermostimulated current utilizing thermal energy instead of light energy has been suggested (refer to Japanese Patent Laid-open Publication No. 2003-232886). Another corrosion reduction method proposed is to alternately laminate N-type semiconductor coatings and P-type semiconductor coatings onto surfaces of metal components (refer to Japanese Patent Laid-open Publication No. 9-125283). Yet another corrosion method proposed is to provide a coating consisting of three or more alternately stacked layers of an anion-permselective substance and a cation-permselective substance (refer to Japanese Patent Laid-open Publication No. 11-12719). According to the technology disclosed in Japanese Unexamined Patent Application Publication No. 2001-4789, electrons irradiated with light are activated by the photoexcitation reaction, thereby generating electrical current that decreases the corrosion potential. The corrosion prevention effect is, however, rarely expected in parts not exposed to light. In contrast to the corrosion prevention technology utilizing photoexcitation, a technology of decreasing the corrosion potential by utilizing electrical current produced by thermostimulated electrons is disclosed in Japanese Patent Laid-open Publication No. 2003-232886. According to this technology of producing the thermostimulated current, holes generated by thermostimulation cause anode reaction to occur and thereby increase the current. In an actual cases, however, the electrons stimulated by heat recombine with holes generated by the same thermostimulation, and the electric current does not easily flow. In order to efficiently convert the stimulated electrons and holes into a flow of electrical current, charge separation needs to be reliably carried out. Furthermore, the state that allows charge separation needs to be constantly maintained, and the ambient environmental conditions to which the metal components are exposed must be taken into consideration. In addition, nuclear power plants have inside a substantially large number of narrowed parts and parts with complicated shapes. Thus, the corrosion prevention methods utilizing the semiconductor properties disclosed in Japanese Patent Laid-open Publication Nos. 9-125283 and 11-12719 would face difficulty in application. The present invention was conceived in consideration of the circumstances in the prior art mentioned above and has an object to provide a nuclear power plant having a corrosion-resistant coating that can ensure suppression of corrosion due to stress corrosion cracking in various locations of reactor structural components not exposed to light and that can effectively maintain the effect of corrosion suppression for a long time. Another object of the present invention is to provide a method of forming such a corrosion-resistant coating and a method of operating the nuclear power plant at an improved efficiency. These and other objects can be achieved according to the present invention by providing, in one aspect, a nuclear power plant, wherein a corrosion-resistant oxide film is formed on a surface of a metal component of a reactor structure exposed to high-temperature water, the corrosion-resistant oxide film containing an oxide having a property of a P-type semiconductor, and a catalytic substance having an N-type semiconductor is deposited on the corrosion resistant oxide film so that the oxide film maintains the property of the P-type semiconductor. In another aspect, there is also provided a method of forming a corrosion-resistant coating on a surface of a metal component of a reactor structure exposed to high-temperature water, the method comprising: an oxide film forming step of controlling a water chemistry inside a reactor using a hydrogen injection device to deposit and/or form an oxide having a property of a P-type semiconductor in a reducing atmosphere or converting an existing oxide film; and a catalytic substance deposition step of depositing a catalytic substance on the oxide film, the catalytic substance having a property of an N-type semiconductor while retaining the property of the P-type semiconductor. In a further aspect of the present invention, there is also provided a method of operating a nuclear reactor in which a corrosion-resistant coating is formed on a surface of a metal component of a reactor structure exposed to high-temperature water, the method comprising the steps of: monitoring a corrosion potential at the surface of the metal component to examine a property of the oxide film; and controlling a water chemistry in the reactor to maintain and restore a corrosion-resistant oxide film. According to the above aspects of the present invention, the corrosion-resistant oxide film can be formed so as to achieve the functions and effects of the property or performance of the N-type semiconductor while maintaining or retaining the property of the P-type semiconductor. The suppression of corrosion due to stress corrosion cracking of metal components of a reactor structure can be ensured, and the effect of suppressing corrosion of metal components can be maintained for a long period of time. The nature and further characteristic features of the present invention will be made more clear from the following descriptions made with reference to the accompanying drawings. The preferred embodiments of the nuclear power plant, method of forming a corrosion-resistant coating for the nuclear power plant, and method of operating the nuclear power plant according to the present invention will be described hereunder with reference to the attached drawings. Further, it is to be noted that terms “upper”, “lower”, “right’, “left” and the likes terms are used herein with reference to the illustrations on the drawings or actually installing state of a reactor power plant. FIG. 1 is a schematic diagram showing a boiling water reactor (BWR, hereinafter) 11 and a Reactor Water Clean-up system 12 of a nuclear power plant 10 according to the present invention. The BWR 11 includes a reactor pressure vessel 13 and a cylindrical shroud 14 inside the reactor pressure vessel 13. A reactor core 15 is disposed inside the cylindrical shroud 14. A lower plenum 16 is disposed below the reactor core 15, and the reactor water inside the reactor pressure vessel 13 is introduced into the lower plenum 16 through a plurality of jet pumps 17, for example, ten jet pumps 17. The jet pumps 17 operate by tracking the operation of recirculation pumps 19 of a pair of reactor recirculation systems 18. Each recirculation pump 19 is provided to a recirculation pipe 20 for recirculating the reactor water inside the reactor pressure vessel 13. The ejection (pump-out) side of the recirculation pipe 20 is opposed to the inlet side of the jet pump 17. In each reactor recirculation system 18, the recirculation pump 19 is driven to discharge recirculation water from the ejection side of the recirculation pipe 20, and the flow of the discharged recirculation water merges with the reactor water around the jet pump 17 to thereby guide the reactor water into the lower plenum 16. The flow of the reactor water is reversed in the lower plenum 16 and heated by means of nuclear reaction as it passes over the reactor core 15, thereby forming a steam-liquid two-phase flow. The steam-liquid two-phase flow is separated by a steam separator, not shown, into a steam component and a liquid component above the reactor core 15. The liquid component returns to reactor water and re-enters a downcomer portion 21 of the reactor pressure vessel 13. The steam component is dried in a steam drier (not shown), and the resulting dry steam (main steam) is fed to a main steam system 25. The main steam fed into the main steam system 25 is then introduced into a steam turbine 27 through a main steam pipe 26 to drive a generator 28. The expanded steam that had been used to drive the steam turbine 27 is led to a condenser 29 where the steam is cooled and condensed to give a steam condensate. The condensate passes through a condensate water supply system 30 and flows back into the reactor pressure vessel 13 via a water supply pipe 31 serving as a water supply line so as to combine with the reactor water inside the reactor pressure vessel 13. A water supply pump 32 and a multistage water supply heater (not shown) are provided to the water supply pipe 31. The water fed into the reactor pressure vessel 13 via the condensate water supply system 30 partially circulates in the recirculation pipes 20 of the reactor recirculation systems 18 by the operation of the recirculation pumps 19. Part of the recirculation water in the recirculation pipe 20 is circulated in a residual heat removal (RHR) system 35 with an RHR-system pump 36 or in a reactor water cleanup (CUW or RWCU) system 40 with a CUW-system pump 41. The RHR-system pump 36 has an RHR pipe 37 diverging from the recirculation pipe 20 of the reactor recirculation system 18. The RHR pipe 37 has the RHR-system pump 36 and a heat exchanger 38. The downstream end of the RHR pipe 37 is connected to the reactor pressure vessel 13 so that part of the recirculation water can be circulated and returned to the reactor pressure vessel 13. The pipe configuration of the RHR system 35 is designed to suit the most typical operation mode for removing decay heat after the reactor shutdown. The circulation water cooled in the RHR system 35 is sprayed from the upper portion or the top of the reactor pressure vessel 13 to cool the head unit of the reactor pressure vessel 13. The pipe arrangement of the RHR system 35 is designed to operate in five modes, namely, a reactor shutdown cooling mode, a low-pressure water injection mode, a reactor container cooling mode, a pressure suppression pool water cooling mode, and a fuel pool cooling mode. The reactor water cleanup (CUW) system 40 has a CUW-system pipe 42 diverging from the recirculation pipe 20 of the reactor recirculation system 18. The CUW-system pipe 42 has a heat exchanger 43, the CUW-system pump 41 and a filter demineralizer 44, and is connected to the water supply pipe 31 of the condensate water supply system 30. The CUW system 40, the RHR system 35, a reactor auxiliary cooling system (not shown), a high-pressure reactor core spray system (not shown), and a fuel pool cooling and cleanup system (not shown) constitute the cooling water circulation system 12. The reactor pressure vessel (RPV) 13, the reactor recirculation systems 18, the main steam system 25, and the condensate water supply system 30 constitute a reactor primary cooling system 45. The nuclear power plant 10 has the reactor primary cooling system 45 and the cooling water circulation system 12, in each of which an austenitic stainless steel, such as SUS304 (18Cr-8Ni-0.06C), SUS304L containing 0.03% or less of C, SUS316 (18Cr-12Ni-2.5Mo) having improved corrosion and acid resistance, or SUS316L containing Mo, having excellent corrosion resistance, workability, formability and weldability, is widely used. The nuclear power plant 10 also has injection points P for connecting with a hydrogen injection system 46. The hydrogen injection system 46 is provided to form corrosion-resistant oxide films having properties of a P-type semiconductor onto surfaces of reactor structural metal components, such as pipes, various devices, and structural materials inside the reactor. The hydrogen injection system 46 can be connected to one or more injection points P located in the water supply pipe 31 of the condensate water supply system 30, the recirculation pipe 20 of the reactor recirculation system 18, the RHR pipe 37, of the RHR system 35, the CUW-system pipe 42 of the CUW system 40, and the like. The amount of injection hydrogen can be controlled from these injection points P. The water chemistry in the reactor can be controlled by adjusting the amount of the injection hydrogen. By controlling the water chemistry inside the reactor as mentioned above, oxide films having the properties of a P-type semiconductor can be formed on the surfaces (inner and outer surfaces) of the reactor structural metal components, such as various pipes, devices, and internal structural materials. These oxide films are corrosion resistant. Referring to FIG. 1, the reactor is also provided with a corrosion potential analyzer 47 including a test piece for monitoring the corrosion potential and shut-off valves 48. The corrosion potential analyzer 47 is installed onto the recirculation pipe 20 of the reactor recirculation system 18. Hereunder, preferred embodiments of the present invention will be described more specifically. A first embodiment of the present invention will be described with reference to FIGS. 2 to 4. In the first embodiment, the austenitic stainless steel widely used in the reactor structural materials of the reactor primary cooling system 45 and the cooling water circulation system 12 of the nuclear power plant 10 is provided with corrosion-resistant oxide films. FIG. 2 is a schematic diagram showing a surface of a metal component having a corrosion-resistant coating on the surface of SUS316L stainless steel, which is one example of the austenitic stainless steel. In this embodiment, a corrosion-resistant, corrosion-protective oxide film (film) 51 composed of an oxide, such as Fe3O4, having the properties of a P-type semiconductor is formed on a metal base material 50 composed of SUS316L stainless steel, and titanium oxide serving as a catalytic substance 52 having the properties of a N-type semiconductor is deposited on the oxide film 51. The catalytic substance 52 may be deposited on the oxide film 51 by forming a layer. The form of the catalytic substance 52 is not limited to the layer form. The catalytic substance 52 may be scattered into a matrix form or may be deposited as lines. The metal base material 50 is exposed to high-temperature water of 150° C. or higher, in particular, to reactor water of about 280° C. Although FIG. 2 shows an example that uses the SUS316L stainless steel as the austenitic stainless steel for the metal base material 50, the metal base material 50 may be made of a stainless steel alloy, iron steel, a non-steel material, or a non-ferrous metal. Although the oxide film for the metal base material 50 described above is composed of Fe3O4, the oxide film may instead be formed of an oxide such as FeO, NiO, PdO, UO2, WO2, Cr2O3, NiCr2O4, ZnCr2O4, CoCr2O4, FeCr2O4, MnO, Mn2O3, Mn3O4, Co3O4, CoO, Cu2O, Ag2O, CoAl2O4, MgCr2O4, NiAl2O4, or PbO, or at least one of them. The oxide film 51 having the properties of a P-type semiconductor should be formed on the surface of the metal base material 50 exposed to high-temperature water. In an actual nuclear power plant, the thickness of the oxide film 51 is preferably 0.01 μm to 5 μm, for example. Titanium oxide (TiO2) having the properties of a N-type semiconductor and serving as the catalytic substance 52 is deposited on the oxide film 51 having the properties of a P-type semiconductor. Instead of the titanium oxide (TiO2), BaTiO3, Bi2O3, ZnO, WO3, SrTiO3, Fe2O3, FeTiO3, KTaO3, MnTiO3, SnO2, ZrO2, CeO2, In2O3, Al2O3, MgO, MgFe2O4, NiFe2O4, MnO2, MoO3, Nb2O5, SnO2, SiO2, PbO2, V2O5, ZnFe2O4, ZnAl2O4, ZnCo2O4, or Ta2O5, or at least one of them may be used as the catalytic substance 52 that serves as the N-type semiconductor. A pn-junction is formed at the junction face between the P-type semiconductor and the N-type semiconductor, as shown in FIG. 3, by depositing the oxide film 51 composed on an oxide having the properties of a P-type semiconductor on the surface of the metal base material 50 and by depositing the catalytic substance 52 having the properties of an N-type semiconductor on the oxide film 51. The change in energy level causes a band 55 to contain a bandgap G. Since the band 55 contains a gap, an electron 56 and a hole 57 produced by thermal excitation E respectively migrate to a conduction band 58 of the N-type semiconductor and a valence band 59 of the P-type semiconductor. The migration of the electron 56 and the hole 57 can suppress recombination of the electron 56 and the hole 57 and allows charge separation to proceed. The electron 56 and the hole 57 contribute to the oxidation-reduction reaction in high-temperature water and thereby change the corrosion potential. FIG. 4 is a graph showing dependence of the corrosion potential on the water chemistry of high-temperature water of, for example, 280° C. In the graph, the corrosion potential of a case in which the oxide film 51 composed of Fe3O4, which is a P-type semiconductor, is disposed onto the surface of the austenitic stainless steel, 316L (metal base material 50) and 10 μg/cm2 or more, in particular, about 50 μg/cm2, of the catalytic substance 52, which is titanium oxide (TiO2) and is an N-type semiconductor, is deposited on the oxide film 51 is plotted (solid line A), and the corrosion potential of a case in which no titanium oxide is deposited is plotted (dotted line B). In the case of the BWR 11, due to the presence of titanium oxide, the corrosion potential does not exceed −0.1 V(SHE) and is about −0.5 V when the circulation water in the recirculation pipe 20 of the reactor recirculation system 18 has a feedwater hydrogen concentration of 0.3 ppm. As is described above, the formation of the pn-junction in the oxide film 51 causes charge separation, decreases the corrosion potential and suppresses corrosion of the metal base material 50. The lower the corrosion potential, the greater the corrosion resistance achieved by the oxide film 51. A second embodiment of the present invention will be described hereunder with reference to FIGS. 5 and 6. In this second embodiment, the structures identical to those of the first embodiment are referred to by adding the same reference numerals and explanation thereof is omitted herein, and the effects identical to those of the first embodiment are also attained, which are not described to avoid redundancy. FIG. 5 is a graph showing the influence of the particle diameter of the oxide having the properties of the P-type semiconductor deposited on the surface of the metal base material 50 on the corrosion potential V. The graph shows results of a case in which an Fe3O4 oxide film 51 is formed on the metal component made of austenitic stainless steel, SUS316L, and a case in which an NiO oxide film 51 is formed on the metal base material 50 made of stainless steel alloy, i.e., an Ni-based corrosion-resistant alloy, Alloy 600 (Inconel 600). A solid line C shows the corrosion potential curve of the case in which the Fe3O4 oxide film 51 is formed on the austenitic stainless steel, SUS316L, and a dotted line D shows the corrosion potential curve of the case in which the NiO oxide film 51 is formed on the surface of the Ni—Cr—Fe alloy, i.e., Alloy 600. The catalytic substance 52 deposited on the oxide film 51 is titanium oxide, and the amount of the titanium oxide is 50 μg/cm2 in both the cases. The corrosion potential V is measured under water chemistry conditions of the recirculation water of the reactor recirculation system 18 having a feedwater hydrogen concentration of 0.3 ppm. As is apparent from the results of the test in FIG. 5, the corrosion potential V shows a tendency to decrease as the particle diameter of the oxide having the properties of the P-type semiconductor decreases. As the particle diameter of the oxide (Fe3O4 or NiO) decreases, the area of the pn-junction formed between the oxide and titanium oxide, which is the N-type semiconductor, increases. Presumably, this is advantageous for the charge separation and thus decreases the corrosion potential. The results show that, since the corrosion potential needs to be −0.05 V(SHE) or less for SUS316L and 0.0 V(SHE) or less for Alloy 600, the particle diameter of the oxide needs to be 1 μm or less. FIG. 6 is a graph showing the influence of the thickness of the oxide film 51 having the properties of the P-type semiconductor on the corrosion potential V(SHE). The graph shows the results of a case in which an Fe3O4 oxide film 51 is formed on the metal component made of austenitic stainless steel, SUS316L, and a case in which a NiO oxide film 51 is formed on the metal base material 50 made of stainless steel alloy, i.e., a Ni-based corrosion-resistant alloy, Alloy 600 (Inconel 600). A solid line C1 is a corrosion potential curve of the case in which the Fe3O4 oxide film 51 is formed on the austenitic stainless steel, SUS316L, and a dotted line D1 shows the corrosion potential curve of the case in which the NiO oxide film 51 is formed on the surface of the Ni-based stainless steel alloy of Alloy 600. The corrosion potential curve C1 for SUS316L shows that the corrosion potential does not exceed −0.05 V(SHE) with the oxide film 51 having a thickness of 0.001 to 1 μm. The corrosion potential curve D1 for the Ni-based stainless steel alloy of Alloy 600 shows that the corrosion potential is maintained at 0.0 V or less with an oxide film 51 having a thickness of 0.001 μm to 1 μm. The curves C1 and D1 indicate that the corrosion potential is maintained at a negative value with the oxide film 51 having the properties of a P-type semiconductor and a thickness of 0.001 to 1 μm and that the interaction between the oxide, e.g., titanium oxide, and the P-type semiconductor decreases the corrosion potential. In an actual nuclear power plant 10, deposition of an oxide film in a thickness of 0.01 to 0.05 μm is confirmed. Thus, the corrosion resistance of the oxide film can be expected even in an actual plant. The particles of the Fe3O4 oxide film 51 are small and maintained to about 0.01 μm to about 0.1 μm diameter. The thickness of the oxide film 51 is not likely to decrease to less than 0.01 μm even when the thin film of the oxide particles is formed as a single layer. Thus, the oxide film 51 will have a thickness of at least 0.01 μm. In an actual plant, the substantial application range of the thickness of the oxide film 51 is from about 0.01 μm to about 5 μm. The longevity of the nuclear power plant 10 is determined by the lifetimes of the metal components (metal materials) used in reactor structural components such as various devices and pipes of the reactor primary cooling system 45 and the cooling water circulation system 12. The corrosion potential is set according to the longevity of the nuclear power plant 10 by adjusting the oxide film 51 deposited onto the surface of the metal base material 50. When a nuclear power plant 10 has a typical longevity, the corrosion potential of the metal components such as various devices and pipes of the reactor primary cooling system 45 and the cooling water circulation system 12 is maintained within regions F and H respectively shown in FIGS. 7A and 7B. When a longer lifetime of the nuclear power plant 10 is needed, the corrosion potential of the metal components of the reactor structural materials is set within regions F1 and H1 respectively shown in FIGS. 8A and 8B. FIG. 7A and FIG. 8A respectively show curves L and L1 each indicating the relationship between the thickness of the oxide film 51 having the properties of the P-type semiconductor and the amount of the deposited catalytic substance 52, i.e., titanium oxide (TiO2) when austenitic stainless steel, SUS316L, is used as the metal base material 50. The solid line L in FIG. 7A is a corrosion potential curve that yields a corrosion potential of −0.05 V(SHE), and the solid line L1 in FIG. 8A is a corrosion potential curve that yields a corrosion potential of −0.01 V(SHE). When the metal base material 50 is composed of stainless steel such as SUS316L, the use in a region G for a normal lifetime and a region G1 for extended lifetime is avoided. FIG. 7B and FIG. 8B respectively show curves M and M1 each indicating the relationship between the thickness of the oxide film 51 composed of an oxide having the properties of a P-type semiconductor and the amount of the deposited catalytic substance 52, i.e., titanium oxide (TiO2) when a Ni-based stainless steel alloy, Alloy 600, is used in the metal base material 50. Substantially the same results are yielded by using nickel oxide (NiO) instead of titanium oxide (TiO2). Alloy 600 is a Ni-based corrosion-resistant alloy having 0.05C-16Cr-8Fe as the main component. The solid line M in FIG. 7B is a corrosion potential curve that yields a corrosion potential of 0.0 V(SHE), and the solid line M1 in FIG. 8B is a corrosion potential curve that yields a corrosion potential of −0.05 V(SHE). When the metal base material 50 is composed of a Ni-based stainless steel alloy, Alloy 600 (Inconel 600), the use in a region I for a normal lifetime and in a region I1 for an extended lifetime is avoided. FIG. 9 is a graph related to a third embodiment of the present invention. In the description of the third embodiment, the structures identical to those of the first embodiment are referred to by the same reference numerals to omit repeated explanation, and the effects identical to those of the first embodiment are also attained, but omitted in description to avoid redundancy. The graph in FIG. 9 shows the corrosion potential characteristics observed from a test piece in which the metal base material 50 composed of SUS316L is coated with an Fe3O4 oxide film 51 having the properties of a P-type semiconductor and a thickness of 0.05 μm, and from a test piece in which the metal base material 50 composed of a Ni-based stainless steel alloy, i.e., Alloy 600, is coated with a NiO oxide film 51 having a thickness of 0.05 μm, while varying the amount of titanium oxide serving as the catalytic substance 52 deposited on the oxide film 51. The graph shows that as the amount of titanium oxide deposited on the oxide film 51 increases, the corrosion potential of the metal base material 50 decreases. A solid line N is a characteristic curve showing the relationship between the corrosion potential of the metal base material 50 composed of SUS316L and the amount of titanium oxide deposited. A dotted line O is a characteristic curve showing the relationship between the corrosion potential of the metal base material 50 composed of Alloy 600 and the amount of titanium oxide deposited. The curves N and O show that when 10 μg/cm2 of titanium oxide serving as the catalytic substance 52 is deposited, the corrosion potential of the metal base material 50 composed of SUS316L is lower or less than −0.05 V(SHE) and that of the metal base material 50 composed of Alloy 600 is lower or less than 0.0 V(SHE) due to the interaction with the P-type semiconductor. This result shows that stress corrosion cracking can be sufficiently suppressed by depositing the titanium oxide of the amount of 10 μg/cm2 or more serving as the catalytic substance 52. A fourth embodiment of the present invention will now be described with reference to FIGS. 1, 2, and 10 to 17. The fourth embodiments represents a method of forming a corrosion-resistant coating, including a step of oxide film formation of forming an oxide film 51 having the properties of a P-type semiconductor on the surface of the nuclear power plant 10 shown in FIG. 1 and the metal base material 50, which is a structural component of the nuclear power plant 10, and a step of catalytic substance deposition of depositing the catalytic substance 52 on the oxide film 51. There are provided methods possible to form a corrosion-resistant coating having the properties of a P-type semiconductor on the surface of the metal base material 50, the method including a method of preliminarily forming the coating before the metal base material 50 is processed and shipped as the reactor structural materials, a method of forming the coating during a trial run or operation after the structural materials are installed in the nuclear power plant 10, and a method of forming the coating during the operation of the nuclear power plant 10 by controlling the water chemistry. A method of forming the oxide film on the surface of the metal base material 50 according to any one of the timings may be employed. The oxide film formed on the surface of the metal base material 50 is known to undergo a significant change due to ambient aquatic environment. In this embodiment, a method of forming an oxide film that takes into account the water chemistry controllable in the BWR 11 and a real plant is described from the viewpoint of preventing the corrosion of peripheral structural components such as those inside the BWR 11 and the recirculation pipe 20. [First Method of Forming the Oxide Film] A first method of forming the oxide film includes an oxide film forming step of forming the oxide film 51 having the properties of a P-type semiconductor directly from the metal base material 50. This first method is used when a new metal component is installed in the nuclear power plant 10. The oxide film 51 is deposited by controlling the ambient aquatic conditions. The oxide film forming step for forming the oxide film 51 on the surface of the metal base material 50 in a real plant will be described hereunder. For example, in order to improve the reactor water chemistry of an actual plant in which hydrogen injection operation is already carried out, dissolved hydrogen and dissolved oxygen are controlled at an injection amount of 0.4 ppm, and the surfaces of an austenitic stainless steel, SUS316L are oxidized with high-temperature water of 280° C. The dissolved oxygen concentration is about 10 ppb, and the dissolved hydrogen concentration is 30 ppb or more, i.e., about 80 ppb. The hydrogen injection is carried out by connecting the hydrogen injection system 46 to the injection points P of the reactor primary cooling system 45 and the cooling water circulation system 12 of the nuclear power plant 10. In general, there are a large number of methods for forming an oxide film having the properties of a P-type semiconductor conducted in water having reducing properties, in which the reactor water is maintained at a reducing state by hydrogen injection. As far as the water chemistry of an actual plant is concerned, the hydrogen concentration in the feedwater is preferably 1.0 ppm or less, in particular, about 0.3 ppm during the operation of the nuclear power plant 10 since high-concentration hydrogen injection disadvantageously increases the turbine-system dose rate during the operation. In a reducing atmosphere, the corrosion potential of the metal surface is maintained at a low level. As shown in FIG. 10, the pH morphology of the ferrous oxide greatly changes with the change in corrosion potential brought about by controlling the water chemistry. By controlling the chemistry of the reactor water as mentioned above, an oxide film having the properties of a P-type semiconductor can be formed. With respect to the temperature for forming the oxide film, it is possible to choose one from a method forming an oxide film at room temperature which takes a longer time and a method of forming an oxide film at a temperature of reactor water, e.g., about 280° C., which takes into account the actual operation of the reactor. It is possible to choose the timing by taking into account the status of the actual plant, e.g., whether the plant is under inspection or in operation. FIG. 11 is a graph showing the corrosion potential observed under the water chemistry of the recirculation water in the reactor recirculation system 18 in which the hydrogen concentration in the feedwater is 1.0 ppm or less, in particular, about 0.3 ppm. In the observation, a test piece in which an oxide having properties of a P-type semiconductor was formed on the metal surface of SUS316L according to the first method of forming the oxide film was used. Before the corrosion potential testing, the test piece was exposed to high-temperature of 280° C. under the water chemistry of the reactor water at the reactor bottom (lower plenum), i.e., a feedwater hydrogen concentration of 0.4 ppm, for 500 hours. The surface of the resulting test piece was subjected to Raman analysis. The crystal morphology was confirmed to be Fe3O4. Titanium oxide of an amount of 200 μg/cm2 was deposited on the Fe3O4 oxide film 51 by using a sprayer 60 such as shown in FIG. 12. The sprayer 60 has a spray main unit 61 equipped with a solution tank 62 for storing titanium oxide, i.e., the catalytic substance. Deposition of an adequate amount of titanium oxide on the test piece can be carried out by rotating an adjustor knob 64 to adjust the nozzle opening of a spray nozzle 63 attached to the front end of the spray main unit 61, connecting the spray main unit 61 to a gas supply (gas cylinder) 67 containing nitrogen gas or inert gas via a gas feed pipe 66 equipped with a flow adjustor valve 65, and then pulling a spray switch 68 which functions as a control lever. Titanium oxide, which is the catalytic substance, is sucked out by the flow of the inert or nitrogen gas and is sprayed toward the test piece from the nozzle opening of the spray nozzle 63. Using this sprayer 60, titanium oxide serving as the catalytic substance was deposited onto the SUS316L test piece having the Fe3O4 oxide film 51. The test piece provided with a required amount of titanium oxide was subjected to corrosion potential testing in water having recirculation water chemistry in the reactor recirculation system 18, as shown in FIG. 11. FIG. 11 shows that, in corrosion potential analysis of the test piece, a temperature elevation process (heating process) of recirculation water was conducted up to 200 minutes after initiation of the analysis and that the corrosion potential was measured at a constant recirculation water temperature after the temperature elevation process. The recirculation water had a dissolved oxygen concentration of about 10 ppb, a dissolved hydrogen concentration of 30 ppb or more, in particular 31 ppb, and a hydrogen peroxide concentration of 65 ppb. The operation conditions, such as 280° C. high-temperature water and a pressure of 8.5 MPa, applicable to an actual plant were satisfied. As is apparent from the observed results of the corrosion potential, the corrosion potential of the test piece having titanium oxide deposited on the Fe3O4 oxide film 51 could be decreased to −0.1 V(SHE) or less, i.e., about −0.15 V(SHE), under the water chemistry of the recirculation water having a feedwater hydrogen concentration of 0.3 ppm, thereby improving the corrosion resistance. The test piece having no titanium oxide deposited on the Fe3O4 oxide film exhibited a corrosion potential increasing with time. The corrosion potential in this case is expected to further increase if the test is carried out for a longer time. [Second Method of Forming the Oxide Film] A second method of forming the oxide film includes a step of depositing atoms that constitute a P-type semiconductor onto the surface of the metal base material 50 and allowing an oxide having the properties of the P-type semiconductor to form by controlling the ambient aquatic conditions. Although FIG. 1 shows the cooling water circulation system 12 of the nuclear power plant 10 in which the hydrogen injection system 46 is connected through the injection points P. In this method, a solution injection system 70 (shown in FIG. 13) including atoms which constitute the P-type semiconductor should be connected to the injection points P (Pa and Pb) to replace the hydrogen injection system 46. The solution injection system 70 containing atoms constituting the P-type semiconductor has a structure shown in FIG. 13 and is connected to the injection points P of the cooling water circulation system 12. As shown in FIG. 13, the solution injection system 70 includes a hydrogen tank 71 which is connected to the injection point Pa of the cooling water circulation system 12 via a hydrogen feeding pipe 73 equipped with a flow adjustor valve 72. Hydrogen gas inside the hydrogen tank 71 is injected into the cooling water circulation system 12 from the injection point Pa. A solution 75 containing atoms which constitute the P-type semiconductor is stored in a solution tank 76, and the solution tank 76 is connected to the injection point Pb of the cooling water circulation system 12 via a solution injection pipe 78 having an injection pump 77. In this second method of forming the oxide film, the injection pump 77 shown in FIG. 13 is operated to inject atoms constituting the P-type semiconductor into the cooling water circulation system 12. The atoms circulate inside the cooling water circulation system 12 with cooling water and are deposited onto the surface of the metal base material 50 constituting the reactor structural components. The deposition of the atoms constituting the P-type semiconductor may be conducted during the shutdown or running operation of the reactor. In order to form an oxide having properties of a P-type semiconductor from the deposited atoms, the hydrogen gas controlled with the flow adjustor valve 72 in FIG. 13 is injected to change the chemistry of the reactor water. In this manner, the ambient aquatic environment and potential can be controlled, and the atoms deposited on the metal surface can be grown into an oxide having the properties of the P-type semiconductor. As the deposited atoms form an oxide, an oxide film functioning as a corrosion-resistant coating is formed on the surfaces (including inner surfaces) of the metal base material 50. FIG. 14 is a graph showing the corrosion potential of a test piece observed under the water chemistry of the recirculation water having a feedwater hydrogen concentration of 0.3 ppm. The test piece includes an oxide having the properties of the P-type semiconductor formed on the surface of an austenitic stainless steel, SUS316L by the second method of forming the oxide film. In this corrosion potential test, a Zn solution is injected to form the oxide film 51 on the surface of SUS316L. An oxide of ZnCr2O4 is formed on the surface of SUS316L by injecting the Zn solution. Titanium oxide serving as the catalytic substance is deposited in an amount of 70 μg/cm2 on the oxide film 51 on SUS316L of this test piece by using a plasma spraying equipment (not shown in the drawing) in a catalytic substance deposition step. By depositing a required amount of titanium oxide on the ZnCr2O4 oxide film 51, the corrosion potential can be decreased to −0.1 V(SHE) or less under the water chemistry of the recirculation water having a feedwater hydrogen concentration of 0.3 ppm. [Third Method of Forming an Oxide Film] A third method of forming an oxide film includes a step of changing the properties of the existing oxide film 51 on the metal base material 50 by controlling the ambient aquatic environment and a catalytic substance deposition step of depositing a catalytic substance on the oxide film. In an actual plant, the operation is conducted under various water qualities or chemistries, such as those required for operation of a reactor without hydrogen injection or for ultra-low iron operation, depending the type of the nuclear power plant 10. Thus, the properties of the oxide film 51 formed on the metal base material 50 are also different. By converting the oxide film 51 of the metal base material 50 through the controlling of the chemistry of the reactor water and potential, an oxide having the properties of a P-type semiconductor is produced. Alternatively, the metal base material 50 may be, for example, chemically decontaminated to expose the surface, and then an oxide having the properties of a P-type semiconductor may be deposited thereon by the first or second method of forming the oxide film so that a desired oxide film 51 can be formed on the surface of the metal base material 50. FIG. 15 shows corrosion potential of a test piece observed under the water chemistry of recirculation water having a feedwater hydrogen concentration of 0.3 ppm. The test piece had an oxide having the properties of a P-type semiconductor deposited on the surface of an austenitic stainless steel, SUS304L. In this corrosion potential test, a test piece having an Fe2O3 oxide film was treated in water at 280° C. having a dissolved oxygen concentration of about 10 ppb and a dissolved hydrogen concentration of 30 ppb or more, in particular, about 80 ppb, for 100 hours. Subsequently, the test piece was subjected to surface analysis. The results showed that the oxide film was changed to an oxide film mainly composed of Fe3O4. Subsequently, in the catalytic substance deposition step, a required amount, for example, 120 μg/cm2, of titanium oxide was deposited using a titanium oxide water chemistry deposition device 80 shown in FIG. 16. The water chemistry deposition is a method of injecting a titanium oxide solution of a particular concentration into high-temperature water and controlling the temperature, flow rate, titanium oxide concentration, and duration to deposit titanium oxide on the metal surfaces. This corrosion potential test was conducted at 200° C., a flow rate of 9.6 m/s, and a titanium oxide concentration of 10 ppm for 24 hours. The water chemistry was controlled to that of the core bottom water having a feedwater hydrogen concentration of 0.4 ppm. The water chemistry deposition device 80 is an experimental device having a structure shown in FIG. 16. The water chemistry deposition device 80 has a water chemistry (chemistry) control system 82 for maintaining and controlling the chemistry of water inside a water tank 81 and a catalytic substance deposition controlling system 83 for controlling the amount of the catalytic substance deposited on the test piece. Using a resin 86, such as an ion exchange resin, and a hollow fiber membrane filter 87, the water chemistry control system 82 purifies the water fed from the catalytic substance deposition controlling system 83 to the water tank 81 via a heat exchanger 84 and a cooling tower 85 to thereby produce pure water. The property of the resulting water is analyzed with a dissolved hydrogen meter 88, a dissolved oxygen meter 89, and a conductivity meter 90 to control the properties of the water inside the water tank 81 to the target levels. The water (pure water) having its chemistry controlled through the resin 86 and the hollow fiber membrane filter 87 is temporarily stored in the water tank 81 and fed to the catalytic substance deposition controlling system 83 using a high-pressure pump 91 via the heat exchanger 84. The catalytic substance deposition controlling system 83 is a closed circulation cycle 95. An example of injecting a titanium oxide (TiO2) solution as the catalytic substance into the closed circulation cycle 95 will be described below. The closed circulation cycle 95 includes a test piece deposition section 96 containing the test piece, a circulation pump 97 for controlling the amount and flow rate of water circulated, and a heat exchanger 98. These three devices are provided sequentially in this order. The suction side of the circulation pump 97 can in-take pure water fed from the water chemistry control system 82. The discharge side of the circulation pump 97 can discharge the pumped-out water to the water chemistry control system 82. FIG. 17 is a graph showing the change in amount of deposited titanium oxide over time when titanium oxide serving as the catalytic substance 52 is deposited on the oxide film 51 of the test piece using the water chemistry deposition device 80. The graph shows that the amount of the titanium oxide deposited increases with an increase in flow rate in the closed circulation cycle 95. The time required for depositing a target amount of titanium oxide can be easily estimated by controlling the concentration of the titanium oxide injected and the temperature. By converting the test piece deposition section 96, it becomes possible to deposit the catalytic substance, i.e., titanium oxide, onto surfaces of a reactor structural metal component having a different shape. In a case of installing a new reactor structural component, such as replacement of the recirculation pipe 20, it is possible to deposit an adequate amount of titanium oxide serving as the catalytic substance 52 on an existing oxide film 51 exhibiting the properties of a P-type semiconductor. In an actual plant, the deposition of the catalytic substance 52 can be conducted by connecting a titanium oxide injection device, not shown, to the injection points P shown in FIG. 1. The deposition is possible during the reactor shutdown operation or during the running operation. As is apparent from the graph of FIG. 15, titanium oxide deposited on the oxide film 51 by water chemistry deposition using the water chemistry deposition device 80 can decrease the corrosion potential to −0.1 V(SHE) or less, and sufficient corrosion prevention effects can be efficiently exhibited. A method of driving a reactor according to a fifth embodiment of the present invention will be further described hereunder with reference to FIGS. 18 to 21. In consideration of the fact that measurement of the corrosion potential of the structural component surface of the reactor primary cooling system 45 and the cooling water circulation system 12 is difficult in an actual plant, in this embodiment, as shown in FIG. 1, the corrosion potential analyzer 47 accommodating a corrosion potential monitoring test piece 100 is provided to the nuclear power plant 10 so that the corrosion potential of the structural components in the reactor water can be simulated and that the safety of the structural components can be monitored. The corrosion potential monitoring test piece 100 is exposed to high-temperature water from the BWR 11. As shown in FIG. 18, the corrosion potential analyzer 47 is a unit including a main device 101, the corrosion potential monitoring test piece 100, and a reference electrode 102 that can withstand high pressure. The corrosion potential monitoring test piece 100 and the reference electrode 102 are connected to an electrometer 104 via a cable 103. The corrosion potential of the corrosion potential monitoring test piece 100 measured with the electrometer 104 is input to a computer, i.e., a personal computer 105, either via a data cable 106 or by radio transmission, stored, and processed. By monitoring the processed data, the durability of the structural components and the properties of the oxide film can be monitored. The main device 101 having the corrosion potential monitoring test piece 100 and the reference electrode 102 of the corrosion potential analyzer 47 is detachably attached to the recirculation pipe 20 of the reactor recirculation system 18, as shown in FIG. 1. Alternatively, the main device 101 may be attached to the cooling water circulation system 12 or the reactor primary cooling system 45. FIGS. 19 to 21 are graphs showing the change in corrosion potential of the structural component of the nuclear power plant 10 in time elapsing due to changes in water chemistry. The graph in FIG. 19 shows the corrosion potential of a test piece in which an Fe3O4 oxide film 51 is formed on the surface of SUS316L under the water chemistry corresponding to that of the recirculation water having a feedwater hydrogen concentration of 0.3 ppm and in which 70 μg/cm2 of titanium oxide serving as the catalytic substance 52 is deposited onto the oxide film 51 by spraying. The first 200 minutes from the start of corrosion potential testing was spent for adjusting the water chemistry and measurement conditions under elevating temperature. Under the water chemistry corresponding to that of recirculation water having a feedwater hydrogen concentration of 0.3 ppm, a low corrosion potential was maintained due to the presence of titanium oxide, and the corrosion potential of the test piece was not more than −0.1 V(SHE). On the next day, the water chemistry was controlled to that of the recirculation water having a feedwater hydrogen concentration of 0.1 ppm. The results of the corrosion potential measurement are shown in FIG. 20. Under the water chemistry corresponding to a feedwater hydrogen concentration of 0.1 ppm, the corrosion potential increased to a level 0.0 V(SHE) or higher despite the deposition of titanium oxide. These results show that under an oxidizing atmosphere corresponding to a feedwater hydrogen concentration of 0.1 ppm, the metal surface cannot maintain the properties or performances of the P-type semiconductor, and the pn-junction face cannot be utilized. In other words, the effect of suppressing recombination of an electron and a hole is no longer exhibited, and the thermally excited electron recombines with the hole. Two days after, the water chemistry was changed to that of PLR (Primary Loop Recirculation) with a feedwater hydrogen concentration of 0.7 ppm or more, e.g., 0.7 ppm, to monitor the change in corrosion potential. In FIG. 21, the objective is to restore the P-type semiconductor properties in the oxide film in a reducing atmosphere corresponding to a feedwater hydrogen concentration of 0.7 ppm until up to about 450 minutes. As shown in the graph, the corrosion potential of the test piece with titanium oxide deposited thereon significantly decreased to about −0.55 V(SHE). As shown in FIG. 10, it can be assumed that the oxide film 51 changed from Fe2O3 to Fe3O4 due to the change in corrosion potential. After 500 minutes, the water chemistry was controlled to that corresponding to a feedwater hydrogen concentration of 0.3 ppm, thereby decreasing the reducing atmosphere, and the corrosion potential was measured under a steady state. The results shown in FIG. 21 show that a corrosion potential not exceeding −0.1 V(SHE) is maintained even after 1,000 minutes. This shows that even when the oxide film 51 has experienced the oxidizing atmosphere and changed in properties, the P-type semiconductor properties can be restored in the oxide film 51 by decreasing the corrosion potential to, for example, −0.5 V(SHE) or less in a reducing atmosphere, and that this oxide film 51 can still maintain a low potential in a moderately reducing atmosphere corresponding to a feedwater hydrogen concentration of 0.3 ppm. In an actual plant, it is possible to maintain and restore the corrosion-resistant coating and to thereby suppress corrosion of the metals of the reactor structural components by using the hydrogen injection system 46 (see FIG. 1) to change the reactor water chemistry and by monitoring the corrosion potential to set the corrosion potential of the material to the target level. FIG. 22 is a graph for explaining a sixth embodiment of the present invention. The graph shows the relationship between the corrosion potential of the structural components used in the nuclear power plant 10 and the rate at which cracks are developed. The crack development rate indicated by the longitudinal axis is logarithmically plotted. As the corrosion potential decreases, the crack development rate is largely decreased, showing that the development of the cracks is significantly suppressed. It is a well-known fact that the corrosion potential under normal water chemistry (NWC) of a typical BWR 11 is about +100 mV(SHE). The results of the monitoring of the corrosion potential of the reactor structural component indicate that the crack development rate can be reduced by about one order of magnitude by maintaining the oxide film 51 such that the corrosion potential of the austenitic stainless steel (SUS304SS) is −50 mV(SHE) or less. This also shows that sufficient corrosion suppressing effect is exhibited. The corrosion suppressing potential for the Ni-based stainless steel alloy, such as Alloy 600, is also evaluated based on the same concept. In the graph shown in FIG. 22, “K” represents a stress intensity factor indicating susceptibility of reactor structural components to crack, and “μS/cm” is a value indicating the purity of water, such as reactor water. In a typical reactor 11, a purity of about 1.0 μS/cm is observed during the inspection. FIG. 22 shows that the crack development rate observed with reactor water having a purity as high as 0.1 μS/cm is significantly lower than that with reactor water having a purity of 0.3 μS/cm even when the corrosion potentials of the reactor structural components are the same. Note that although the embodiments above concern application of the reactor recirculation system to boiling water reactors having circulation pumps outside the reactor, application to improved boiling water reactors having reactor recirculation pumps inside the reactor pressure vessels is also possible. The present invention can also be applied to nuclear power plants having pressurized-water reactors and CANDU reactors (Canadian deuterium uranium reactors).

039403122

summary

The invention relates to nuclear fuel comprised of particles of fuel carbide in which vanadium carbide is dissolved. By fuel carbide is meant within the scope of the invention, any carbide which may be used as fuel in a nuclear reactor. Said fuel carbide will thus mostly be uranium carbide or uranium-plutonium carbide. The use of carbide as fuel for nuclear reactors comes up against two main difficulties. There should first be taken into account the problem of joinability of the fuel carbide and of the stainless steel used as case material. When carbon migrates from the carbide to the case material, the mechanical properties of the steel deteriorate, which may cause a breaking of the case. The fuel carbide has moreover the property to swell strongly during the irradiating. Such swelling is caused by gaseous fission products which are insoluble in the carbide and which collect mostly on the boundaries of the grain-like particles, in the shape of gas bubbles. Due to the growing of such gas bubbles there occurs an undesirable volume increase. It is already known to obviate the chemical incompatibility between the fuel carbide and the case material, to add small amounts of metals or metal carbides, for example vanadium carbide. Due to such an addition, the chemical carbon potential is stabilized to a level where carbon migration to the case becomes thermodynamically impossible. To the contrary the problem of swelling of the fuel due to the formation of gaseous fission products during irradiating has not yet been solved. To oppose the fuel swelling, empty space has already been provided both between the case and the carbide and inside the carbide itself, as a porosity. This arrangement is but partly successful and causes further disadvantages. It has also already been proposed to precipitate finely-divided tungsten during the irradiating, because the elementary gas bubbles would be retained on the precipitate, in such a way that they will not coalesce and thus swelling of the aggregate will not take place. This measure also is not completely successful. The invention now provides a successful and economical solution, both to the fuel carbide swelling and to the incompatibility between said fuel and the stainless steel of the case material, without bringing substantial new disadvantages. For this purpose vanadium carbide is present in the particules as supersaturated solid solution and the particles are coated with a thin porous layer of vanadium carbide. It is also very important that the particles be monocrystalline. In an advantageous embodiment, the thin layer of vanadium carbide is comprised of vanadium monocarbide and vanadium hemicarbide. Preferably the density of the thin layer is low. In a particular embodiment of the invention, the thin layer has a density of about 65 percent of the theoretical density. The invention does not only relate to the above-described fuel, but also to a method for preparing a nuclear fuel. According to the invention, the method comprises preparing a supersaturated solid solution of vanadium carbide in fuel carbide, comminuting the material thus obtained down to a maximum size of the resulting grains of about 400 .mu., sieving out the particles with a maximum size lying between 20 and 400 .mu., coating the resulting particles with a thin layer of vanadium carbide having a maximum thickness of 10 .mu., and pressing together the coated particles. The particles pressed in a mold are preferably sintered. In an advantageous embodiment, the particles are coated with a thin layer of vanadium monocarbide and vanadium hemicarbide. In an useful embodiment, the supersaturated solid solution is prepared with approximately 1.5 atoms % vanadium carbide. In a preferred embodiment, to prepare the supersaturated solid solution, the fuel carbide is molten with the vanadium carbide, the resulting product is left to solidify, the product is annealed and it is very rapidly cooled. In a very particular embodiment, the particles are coated with a thin layer of vanadium monocarbide-vanadium hemicarbide with a maximum thickness of 10 .mu. by slightly moistening the particles and then bringing same in a mixer together with powder-like vanadium monocarbide-vanadium hemicarbide.

052001393

summary

FIELD OF THE INVENTION The present invention relates to protecting nuclear reactors, i.e. to controlling such reactors in such a manner as to enable them at all times to deliver the power that is required for satisfying varying needs, while avoiding as much as possible both unnecessary burning of fuel and any risk of an accident. Very strict safety criteria are defined for limiting such risks, in particular with respect to the boilers constituted by such reactors. The present invention relates more particularly to pressurized water nuclear boilers. BACKGROUND OF THE INVENTION In a power station including such a boiler, it is necessary to exercise accurate monitoring on the three-dimensional distribution of power within the core of the reactor. Such monitoring makes it possible both under normal operation and during accidental transients to make sure that safety criteria for the boiler are satisfied. Thus, an authorized operating range for the core is defined by a network of straight line limits plotted in a plane (see FIG. 1) in which the coordinates are nuclear power and axial power difference. The axial power difference parameter, referred to below by the letters DI, is defined as being the difference between the power PH measured at the top of the core and the power PB measured at the bottom of the core. EQU DI=PH-PB This parameter is representative of the axial distribution of power within the core. By keeping the operating point of the core within the domain delimited in this manner, it is possible to ensure, inter alia that safety criteria are satisfied in the event of accidental loss of primary cooling fluid. In addition, in order to avoid excessive variations in the temperature of the primary heat exchange fluid which cools the core, a program is defined for a reference temperature as a function of power level. When there is a difference between the measured temperature and the reference temperature, a regulation system is capable of acting automatically on the core control clusters in such a manner as to correct the difference. When this temperature regulation system is in action, the clusters are said to be in automatic mode. A cooling transient causes clusters to be extracted, and a heating transient causes them to be inserted. A problem arises with respect to this regulation: During certain accidental transients that cause the primary fluid to cool down suddenly, the temperature regulation system will cause the control clusters to be raised quickly if they are in automatic mode. However, such sudden extraction of the absorbent clusters has two consequences which are shown in one particular case by two curve segments C1 (solid line) and C2 (dashed line) in FIG. 1: firstly, core reactivity increases, thereby raising the nuclear power DT as plotted up the Y axis of FIG. 1; and secondly, power distribution rises towards the top of the core, thereby increasing the axial power difference DI which is plotted along the X axis. In FIG. 1, the authorized operating domain is represented by an outer limit FA which is constituted by straight line segments. In the event of a pre-accidental situation of the core represented by a point situated to the right of this operating domain, the nuclear power and axial power difference excursion may give rise to the operating point moving a considerable distance outside the domain. The characteristic evolution of such a cooling transient is shown by segments C1 and C2. A detailed analysis of this type of transient has shown that the core safety limits are approached and even exceeded without intervention of one of the reactor protection systems necessarily being guaranteed. A particular object of the present invention is to limit the risk that may result from an uncontrolled excursion of the reactor operating point outside said operating domain in the event that said excursion is related to a rapid extraction of the temperature regulating group of clusters. The invention is based on creating an inhibit signal for inhibiting instructions to extract the temperature regulation group whenever the reactor operating point leaves the operating domain dangerously. With conventional reactors, leaving the operating domain dangerously is equivalent to leaving it to the right in FIG. 1. SUMMARY OF THE INVENTION In the method of the invention, the reactor temperature regulation system is inhibited whenever a combination of the nuclear power and the axial power difference exceeds a predetermined inhibit threshold.

description

The present invention relates to a fluoride sintered body and a method for producing the same, and more particularly, to a fluoride sintered body for a neutron moderator having a compact structure suitable for a moderator to restrict the radiation velocity of radioactive rays of every kind such as neutrons and a method for producing the same. Among fluorides, a calcium fluoride (CaF2) single crystal body, a magnesium fluoride (MgF2) single crystal body and the like have been relatively widely used in the optical field. There are very few cases where a fluoride is used in other than the optical field. The CaF2 single crystal body, having the advantage of a high plasma resistance, has been rarely used in a semiconductor manufacturing process. An application thereof to a member which is required to have the highest plasma resistance within a plasma etching furnace of silicon wafers, such as a ring boat or a ceiling board, has been considered. However, the CaF2 single crystal body is extremely expensive, and there has been no report that it was used in the actual manufacturing line. The CaF2 single crystal body, and a lithium fluoride (LiF) or an aluminum fluoride (AlF3) single crystal body have been rarely used as a shield to neutrons, one of radioactive rays. Large quantities of radioactive rays exist in the space, but most of them are cut off due to the earth's magnetic field and the influence of the atmosphere, resulting in the presence of just a trace quantity of them on the earth. Artificially, for example, radioactive rays such as neutrons are generated by nuclear reaction within a nuclear reactor. The radioactive rays are classified into alpha (α)-rays, beta (β)-rays, gamma (γ)-rays. X-rays, neutrons and the like. The power passing through a substance (penetrability) gradually increases in this order. The neutrons which are said to have the highest penetrability among the radioactive rays are further classified into small groups according to energy level. One example thereof is shown below. The energy level each type of neutrons has is shown in parentheses, and the larger the value is, the higher the penetrability is. In the order of the lowest penetrability, they are classified into cold neutrons (up to 0.002 eV), thermal neutrons (up to 0.025 eV), epithermal neutrons (up to 1 eV), slow neutrons (0.03-100 eV), immediate neutrons (0.1-500 keV) and fast neutrons (500 keV or more). Here, the energy values in the parentheses are not precise, and there are various views concerning the classification of neutrons. For example, there is a view which mentions 40 KeV or less, which is within the above energy region of intermediate neutrons, as the energy of epithermal neutrons. The typical effective utilization of neutrons is an application to the medical care field. The radiation therapy in which malignant tumor cells are irradiated with neutrons so as to be broken has been rapidly coming into general use in recent years. In order to obtain sufficient medical effects in the present radiation therapy, neutrons of a certain high energy must be used. In irradiation with high-energy neutrons, the influence on a part (a healthy part) other than an affected part of a patient cannot be avoided, leading to side effects. Therefore, in the present situation, the application of the radiation therapy is limited to severe patients. When a normal cell is exposed to high-energy radiation, its DNA is damaged, leading to side effects such as dermatitis, anemia due to radiation and leukopenia. Furthermore, in some cases, a late injury may be caused some time after treatment, and a tumor may be formed and bleed in the rectum or the urinary bladder. In order not to cause such side effects and late injuries, methods of pinpoint irradiation on a tumor have been studied. Examples thereof are: ‘Intensity Modulated Radiation Therapy (IMRT)’ in which only a tumor portion is three-dimensionally irradiated accurately with a high radiation dose; ‘Motion Tracking Radiation Therapy’ in which radiation is emitted to motions in the body of a patient such as breathing or heartbeat; and ‘Particle Beam Radiation Therapy’ in which a baryon beam or a proton beam each having a high remedial value is intensively emitted. The half-life of a neutron which is often used in such radiation therapies is short. 887.0±2.0 sec (about 15 min). The neutron decays in a short period of time, releases electrons and neutrinos, and turns into protons. The neutron has no charge, and therefore, it is easily absorbed when it collides with a nucleus. The absorption of neutrons in such a manner is called neutron capture, and one example of an application of neutrons to the medical care field by use of this feature is ‘Boron Neutron Capture Therapy (hereinafter, referred to as BNCT)’, which is recently gaining attention. In this method, by causing malignant tumor cells of a patient to react with boron, a reaction product (a boron compound) is formed in the tumor portion, and the reaction product is then irradiated with neutrons (comprising mainly epithermal neutrons and thermal neutrons) which have less influences on a healthy portion. And a nuclear reaction is caused only within the very small range where the boron compound has been formed, resulting in making only the tumor cells extinct. This method was proposed about 60 years ago. Because of small influences on a healthy portion of a patient, it has been attracting attention as an excellent radiation therapy since quite long before and has been studied in varied countries. However, there are wide-ranging problems on the development such as a neutron generator, a device for a choice and selection of neutrons to be remedially effective (a moderation system device), and avoidance of influences on a healthy portion of a patient (one of the requirements is to form a boron compound only in a tumor portion). At the present time, many of these problems cannot be said to have been sufficiently solved, and the method has not come into wide use as a general therapy. One of significant factors why it has not come into wide use is that in most of the past cases, a neutron generator was attached to an existing nuclear reactor and that all of the studies, developments and medical practices were conducted at the site, that is, the situation suitable for medical use could not be realized. In order to radically improve such situation, a neutron generator for medical use only must be developed and be put to practical use, and in Japan, a few device manufacturers are promoting the development of a neutron generator of this kind, in order to meet the expectations. In addition to the development of a small-sized high-performance neutron generator, another significant factor why it has not come into wide use is that a moderation system device must be also made high-performance and downsized. This is another major problem in aiming at practical use of the method. In order to effectively utilize neutrons as a particle beam for medical treatment, the selection of neutron types is important, and one example is shown below. From the point of view of medical effects, by removing high-energy neutrons which adversely influence healthy bodily tissues and reducing extremely-low-energy neutrons having little medical effect (such as thermal neutrons and cold neutrons), leading to a higher ratio of neutrons having high medical effects (such as a low-energy part of intermediate neutrons and epithermal neutrons), a desirable particle beam for medical treatment can be formed. The epithermal neutrons and the low-energy part of intermediate neutrons have a high invasive depth to the internal tissues of a patient. Therefore, for example, without craniotomy required in the case of brain tumor, or without an abdominal operation required even if the abdominal operation on another important internal organ cannot be easily performed, it is possible to carry out effective irradiation on an affected part. On the other hand, when the extremely-low-energy neutrons such as thermal neutrons are used, because of their low invasive depth, craniotomy or an abdominal operation is required, resulting in a significant burden on the patient. In order to safely and effectively utilize radiation, it is necessary to suitably select and arrange moderators. In order to effectively use neutrons having the highest penetrability among radioactive rays, it is important to know the moderation performance of materials of every kind to neutrons, leading to effective moderation. Most of neutrons generated by an accelerator such as a cyclotron are high-energy neutrons, and by using a moderator, high-energy neutrons whose energy level adversely influences a body (such as fast neutrons and a high-energy part of intermediate neutrons) should be removed as many as possible. In order to secure a required dose of the above-mentioned neutrons having high medical effects as well as cut off the high-energy neutrons which adversely influence the body to non-existent, highly difficult moderation control is required. Generally, when trying to secure a required dose of neutrons having high medical effects, high-energy neutrons are inevitably included. Therefore, the high-energy neutrons need be removed as many as possible in the next moderation step. There is one system of the above-mentioned Boron Neutron Capture Therapy (BNCT), which a group with Kyoto University as the central figure has been recently promoting (Non-Patent Document 1 and Non-Patent Document 2). In this system, without being attached to an existing nuclear reactor, a cyclotron accelerator as a neutron generator is exclusively installed. The neutron generator for medical use only is adopted. However, the cyclotron accelerator is large due to insufficient downsizing. And as a moderator selected for a radiation shield in order to safely and effectively utilize radiation (mainly neutrons) generated by this cyclotron accelerator, polyethylene containing calcium fluoride (CaF2) and lithium fluoride (LiF) is used, as well as lead (Pb), iron (Fe), aluminum (Al) and polyethylene. It cannot be said that the moderation performance of these moderators is sufficient. Though the details are described below, on condition that a required dose of epithermal neutrons most suitable for treatment by BNCT should be obtained, the neutrons obtained after moderation with the combination of these moderators are mixed with a large quantity of last neutrons having an adverse influence on healthy tissues. In order to conduct required moderation, the moderator becomes quite thick. In other words, the moderation system device becomes large. Therefore, there is a problem that the whole apparatus cannot be sufficiently downsized. In order to allow this BNCT to come into wide use in general hospitals, downsizing of the whole apparatus is a necessary condition. In order to downsize both of the accelerator and the moderation system device, the development of a moderator excellent in moderation performance is an urgent necessity. The selection of a moderator which is important for improving remedial values and downsizing a BNCT apparatus is described below in detail. In the BNCT, it is required to remove high-energy neutrons such as fast neutrons and to irradiate an affected part with neutrons comprising mainly epithermal neutrons and a small quantity of thermal neutrons. Specifically, an estimated dose of epithermal neutrons and thermal neutrons required in cases where the irradiation time is in the order of one hour, is said to be about 1×109 [n/cm2/sec]. In order to secure the dose, it is said that as the energy of an outgoing beam from an accelerator being a source of neutrons, about 5 MeV-10 MeV is required when beryllium (Be) is used as a target for the formation of neutrons. The selection of particle beam types through moderators of every kind in a neutron radiation field for BNCT using an accelerator is described below. A beam emitted from the accelerator collides with a target (Be), and by nuclear reaction, high-energy neutrons, mainly fast neutrons and the like are generated. As a method for moderating the fast neutrons, using Pb and Fe each having a large inelastic scattering cross section, the neutrons are moderated while suppressing the attenuation thereof. They are moderated to some extent (up to the order of 1 MeV) using these two kinds of moderators, and then moderated/optimized according to the neutron energy required in the radiation field. As a moderator to the neutrons moderated to some extent, aluminum oxide (Al2O3), aluminum fluoride (AlF3), CaF2, graphite, heavy water (D2O) or the like is used. By injecting the neutrons moderated nearly to 1 MeV into these moderators, it is required to moderate them to the epithermal neutron energy region (4 keV-40 keV) suitable for BNCT. In the case of the above group with Kyoto University as the central figure, as moderators, Pb, Fe, Al, CaF2, polyethylene and polyethylene containing LiF are used. The polyethylene and polyethylene containing LiF among them are moderators for shielding arranged in a manner that cover the outside portion of the apparatus in order to prevent leakage of high-energy neutrons out of the radiation field. To moderate the high-energy neutrons to some extent using Pb and Fe among these moderators (the first half of a moderation stage) is desirable, but it cannot be said that the second half of the moderation stage using Al and CaF2 after the moderation to some extent is very desirable. In this type of neutrons moderated to some extent, a quite large quantity of high-energy neutrons harmful to healthy cells is left. It is required to remove these high-energy neutrons to non-existent while allowing a required dose of intermediate-energy-level neutrons such as epithermal neutrons having high medical effects to remain, but it cannot be said that this point has been sufficiently achieved. That is, in the case of the moderators (Al and CaF2) used in the second half of the stage, many of the high-energy neutrons left through the moderation in the first half of the stage pass through them without cutoff. If such neutrons are used in a therapy as they are, a bad influence on healthy tissues of a patient cannot be avoided. That is because CaF2 in the moderators used in the second half of the stage does not have sufficient cutoff performance to the high-energy neutrons, and part of them passes without cutoff. The polyethylene containing LiF as well as CaF2 used in the second half of the stage is used in a manner that covers over the entire surface except an outlet of neutrons on the treatment room side. It is arranged so as to prevent whole-body exposure of a patient to the fast neutrons, and is not used as a moderator on the outlet. The polyethylene as a moderator in the first half of the stage is used in a manner that covers over the entire surface of the periphery of the apparatus except the treatment room side, like the polyethylene containing LiF in the second half of the stage, and it is arranged so as to prevent the fast neutrons from leaking to the surroundings of the apparatus. Therefore, instead of CaF2 in the second half of the stage, the development of an excellent moderator which can cut off and moderate high-energy neutrons while suppressing the attenuation of intermediate-energy-level neutrons required for treatment has been desired. From various kinds of researches/studies, the present inventors paid attention to MgF2 system sintered bodies as a moderator for obtaining neutrons having an energy distribution optimal to treatment (4 keV-40 keV), mainly comprising epithermal neutrons in anticipation of the highest remedial value, from the above neutrons moderated to some extent (up to 1 MeV). The MgF2 system sintered bodies include a MgF2 sintered body as well as a MgF2—CaF2 binary system sintered body, a MgF2—LiF binary system sintered body, a MgF2—CaF2—LiF ternary system sintered body, and the like. Until now, there is no report that MgF2 was used as a moderator to neutrons. There is no report of an example in which MgF2 system sintered bodies, including a MgF2 sintered body and a MgF2—CaF2 binary system sintered body, were adopted as neutron moderators. In the present application, an invention concerning a sintered body of MgF2 simple (equivalent to single) (hereinafter, referred to as a MgF2 sintered body) is described below. MgF2 is a colorless crystal, having a melting point of 1248° C., a boiling point of 2260° C. a density of 3.15 g/cm3, a cubic system and a rutile structure according to a science and chemistry dictionary. A single crystal body thereof has a high transparency, and since a high light transmittance is obtained within a wide range of wavelength of about 0.2 μm-7 μm and it has a wide band gap and a high laser resistance, it has been mainly used as a window material for eximer laser. Or MgF2 is deposited on the surface of a lens to be used for protection of the inner parts thereof or prevention of irregular reflection, both of them for optical use. Though in either case, a MgF2 single crystal body is used for optical use, the single crystal body is extremely expensive since the single crystal growth thereof takes long time and control of the crystal growth is highly difficult. Therefore, the use thereof is limited from the point of view of economical efficiency. On the other hand, since the MgF2 sintered body has a poor light transmittance and a low transparency because of its polycrystalline structure, it is not suitable for optical use. There are very few cases where MgF2 in the form of a single crystal body as well as a sintered body was used for other than optical use. There are just a few cases where a sintered body thereof was used for a plasma-resistant member, which are described below. As one example of an application of a sintered body mainly containing MgF2 to a plasma-resistant member, Japanese Patent Application Laid-Open Publication No. 2000-86344 (the below-mentioned Patent Document 1) is cited. In the scope of claims concerned, a sintered body comprises a fluoride of at least one kind of alkaline earth metals selected from the group of Mg, Ca, Sr and Ba, in which the total amount of metallic elements other than the alkaline earth metals is 100 ppm or less on a metal basis, a mean diameter of crystal grains of the fluoride is 30 μm or less, and the relative density is 95% or more. However, the substances in the list of examples of this publication were obtained by firing a metal fluoride of each single kind of the above four alkaline earth metals (i.e. MgF2, CaF2, SrF2 and BaF2) as a raw material, and there is no description that a mixture of those raw materials was fired. In firing of MgF2 and CaF2 as raw materials according to the examples shown in Table 1, the firing temperatures in the cases evaluated as appropriate (shown with ⊚ or ◯ in the Table) are 850° C., 950° C. and 1050° C. with MgF2, and any relative density of the sintered bodies is 95% or more. Likewise, with CaF2, the appropriate firing temperatures are 950° C., 1040° C. and 1130° C., and any relative density of the sintered bodies is 97% or more. On this point, according to the studies/experiments by the present inventors, MgF2 and CaF2 each presented a sublimation phenomenon at temperatures equal to these firing temperatures or lower than these, and a violent foaming phenomenon occurred at the above firing temperatures. Therefore, it was found that it was impossible to obtain a sintered body of MgF2 with a relative density of 95% or more, and a sintered body of CaF2 with a relative density of 97% or more. The present inventors ascertained prior to such firing experiments through differential thermal analysis of raw material powders that the sublimation of MgF2 starts at about 800° C. and becomes brisk at 850° C. or more, and that the sublimation of CaF2 starts at about 850° C. and becomes brisk at 900° C. or more. The results of this differential thermal analysis show that all of the firing temperatures in three cases of MgF2 and CaF2 each indicated as ‘appropriate’ in the examples of the Patent Document 1 are temperature conditions wherein a sublimation phenomenon briskly occurs in the firing process, and that it is actually difficult to make the sintered bodies compact. The inventors of this Patent Document 1 indicate in the description “since AlF3 starts to sublimate at a relatively low temperature, resulting in a necessity of firing while suppressing sublimation, it was difficult to obtain a compact sintered body”. They appear to have known ‘a sublimation phenomenon revealed in firing’, that is, ‘foaming of a sintered body’, that is. ‘it is difficult to obtain a compact sintered body’. However, for reasons unclear, as mentioned above, in either case of MgF2 and CaF2, it is described that the sintered bodies were produced at firing temperatures higher than the above temperatures at which the sublimation phenomenon starts. This means that sintering was conducted under the conditions difficult to obtain a compact sintered body due to the occurrence of brisk foaming within the sintered body in the firing process to promote sintering of a raw material powder. The present inventors grabbed such phenomenon and studied a method for minimizing the influence of the sublimation phenomenon in the sintering process, and developed an excellent sintering method by which compact sintered bodies can be stably obtained. Another example of an application of a sintered body mainly containing MgF2 to a plasma-resistant member is the Japanese Patent Application Laid-Open Publication No. 2012-206913 (the below-mentioned Patent Document 2). This invention discloses a method wherein, since a sintered body of MgF2 simple has a defect of low mechanical strength, by mixing at least one kind of non-alkaline metallic substance having a lower mean linear thermal expansion coefficient than MgF2 such as Al2O3, AlN, SiC or MgO, the defect of low mechanical strength of a MgF2 simple sintered body is compensated for. When a sintered body of such mixture is used as the above moderator to neutrons, the moderation performance thereof is greatly different from that of MgF2 simple because of the influence of the non-alkaline metal mixed with MgF2. Therefore, it was predicted that it was difficult to apply a sintered body of this kind of mixture to use as a moderator. As an invention related to a MgF2 sintered body, the Japanese Patent Application Laid-Open Publication No. 2000-302553 (the below-mentioned Patent Document 3) is cited. The greatest defect of sintered bodies of fluoride ceramics such as MgF2, CaF_, YF3 and LiF is low mechanical strength, and in order to solve this problem, invented was a sintered body made by compounding these fluorides and Al2O3 at a predetermined ratio. However, as the corrosion resistance and mechanical strength of the sintered body produced by this method, in any combination, a sintered body having just an intermediate characteristic between both of the characteristics of those fluorides and Al2O3 was obtained. A sintered body having a characteristic exceeding both of the characteristics was not obtained by compounding. As described above, in order to use a sintered body obtained by firing a mixture of MgF2 sintered by a conventional method with other substances for use other than plasma-resistant members, specifically, for new use such as a moderator to neutrons, one of radiation, there were a lot of problems left to be solved. Patent Document 1: Japanese Patent Application Laid-Open Publication No. 2000-86344 Patent Document 2: Japanese Patent Application Laid-Open Publication No. 2012-206913 Patent Document 3: Japanese Patent Application Laid-Open Publication No. 2000-302553 Non-Patent Document 1: H. Tanaka et al., Applied Radiation and Isotopes 69 (2011) 1642-1645 Non-Patent Document 2: H. Tanaka et al., Applied Radiation and Isotopes 69 (2011) 1646-1648 Non-Patent Document 3: Hiroaki Kumada et al., Health Physics, 42 (2007) 23-37 The present invention was developed in order to solve the above problems, and it is an object of the present invention to provide a fluoride sintered body for a neutron moderator, which is used in order to moderate the energy of neutrons in the good use of the neutrons, a kind of radiation, and is inexpensive unlike a high-purity single crystal body, and with which effective moderation effects can be obtained, resulting in capability of enhancing remedial values while downsizing an apparatus for therapy, and a method for producing the same. The present inventors first gave basic consideration to the selection of substances (metals or compounds) having a sufficient moderation effect on high-energy neutrons. In the BNCT, as described above, it is important to irradiate an affected part with neutrons comprising mainly epithermal neutrons and a trace quantity of thermal neutrons in order to minimize high-energy neutrons which are harmful in therapy while obtaining a large remedial value. Specifically, an estimated dose of epithermal neutrons and thermal neutrons required in the case of the order of one hour of irradiation time is about 1×10° [n/cm2/sec]. It is said that the energy of an outgoing beam from an accelerator being a source of neutrons required for that is about 5 MeV-10 MeV when beryllium (Be) is used as a target for the formation of neutrons. The selection of particle beam types by moderators of every kind in a neutron radiation field for BNCT using an accelerator is described below. A beam emitted from the accelerator collides with a target (Be), and by nuclear reaction, mainly high-energy neutrons (fast neutrons) are generated. As a method for moderating the fast neutrons, using Pb, Fe or the like having a large inelastic scattering cross section, the neutrons are moderated to some extent while suppressing the attenuation thereof. The moderator to the neutrons moderated to some extent (up to 1 MeV) is optimized according to the quantity of neutron energy required in the radiation field. As a moderator to the neutrons moderated to some extent, generally, aluminum oxide (Al2O3), aluminum fluoride (AlF3), CaF2, graphite, heavy water (D2O) or the like is used. By injecting the neutrons moderated nearly to 1 MeV into these moderators, the neutrons are moderated to the range of epithermal neutrons having energy (4 keV-40 keV) suitable for BNCT. However, by the method using the above moderators, the removal of fast neutrons which adversely influence healthy tissues of a patient in therapy tends to be insufficient. Then, if priority is given to this removal of fast neutrons, the neutrons are contrarily moderated too much and further moderated below the range of epithermal neutrons, and the ratio of thermal neutrons having a smaller remedial value than epithermal neutrons becomes large. Therefore, the present inventors selected two kinds of fluorides, MgF2 and CaF2, as candidates of hopeful moderators to the neutrons moderated to some extent from among compounds of every kind, and examined the below-described moderation effects. As a result (FIG. 4), it was ascertained that by injecting the neutrons moderated nearly to 1 MeV into a moderator made of MgF2, fast neutrons harmful in BNCT could be almost perfectly removed, and that epithermal neutrons in the energy range (4 keV-40 keV) optimal to the therapy could be obtained. There were various kinds of problems in producing a moderator made of MgF2, and what should have been thought first of all was a method for producing it. As a method for producing it, a crystal method, a single crystal method, a polycrystal method (i.e. a sintering method) and the like may be exemplified. A crystal produced by a crystal method generally has segregation in crystal orientation and impurities also easily result in segregation. When it is used as a moderator, variation easily arises in moderation performance depending on the part. Therefore, it appears to be unsuitable for a moderator. A single crystal produced by a single crystal method requires a high control accuracy in production, the stability of its quality is poor, and the cost thereof is extremely high. Therefore, it must be said that it is unsuitable for a moderator. Then, this time, the present invention was completed by studying and developing a method for producing a moderator through a polycrystal method (hereinafter, referred to as a sintering method). (1) Securing the purity of products in order to secure the performance as a moderator In order to secure the performance as a MgF2 moderator, first of all, securing the purity of products is important. In order to secure the purity thereof, it was thought that securing the purity on the raw material level, and keeping impurities from getting mixed in the manufacturing process were important, and taking these into consideration, the moderation performance was secured. There are three purity levels of MgF2 raw materials on the market such as 2N (99.0%), 3N (99.9%) and 4N (99.99%), and in a preliminary small-scale test, using these three purity levels of raw materials, the states of sintering characteristics were evaluated. (2) Relaxing sintering conditions by pulverizing the raw materials By pulverizing the raw material grains, reaction interfaces between grains in the sintering process were increased, so as to promote the progress of defoaming and make the progress of sintering reaction of every sintering part uniform. (3) Making the sintering reaction uniform by dividing the sintering step The sintering step was divided into preliminary sintering and main sintering (when the main sintering is further divided, the effects tend to increase). In the preliminary sintering step, the sintering reaction was mainly caused by grain growth by solid phase reaction (hereinafter, referred to as solid-phase sintering), while in the main sintering step, the sintering reaction was caused in the solid solution formation temperature region mainly by sintering body formation through solid solution formation reaction (hereinafter, referred to as solid solution sintering), or by sintering body formation through melt formation reaction (hereinafter, referred to as melting sintering). As a result, combined with the effect of pulverizing the raw materials in the above paragraph (2), the progress of the sintering reaction of every sintering part could be made uniform, and the sintered body could be allowed to have strong cohesion between particles. In addition to the moderation performance, the moderator needs to have a resistance to damage occurrence in handling such as the installation thereof in a moderation system device and a resistance to dust generation caused by neutron irradiation impacts. That is, it is required to have a characteristic excellent in mechanical strength. The mechanical strength of a sintered body is determined by micro strength of bonding parts between particles and the defoaming state such as the size, shape, distribution and number of bubbles, in other words, the shape such as the width and length of the bonding parts and a bound body (parent) of ex-particles (the compactness of the sintered body), and moreover, the brittleness originated from a crystal structure (such as single crystal or polycrystal) of the parent. (4) MgF2, a raw material for forming a high-density sintered body by foaming restriction and reduction of large-sized residual bubbles in the sintering process, easily causes a vaporization (sublimation) phenomenon in the sintering process, generates fluorine gas and easily causes a large number of fine bubbles within the sintered body. This foaming by vaporization and the decrease of voids essentially with the progress of the sintering process are contrary to each other. Therefore, it was decided to minimize the foaming. When a fluoride system raw material is heated at a high temperature, part of the material vaporizes. The temperature of the starting of vaporization depends on the composition. In the case of a composition chiefly comprising MgF2, vaporization starts at about 800° C. and becomes very brisk at about 850° C. Since the vaporization causes fluorine gas, fine bubbles are formed in the sintered body. The shapes of the formed bubbles are almost spherical, and when observing the broken-out section of the sintered body with an electron microscope (SEM), the sections of the bubbles look circular close to a perfect circle. The sizes of the bubbles are in the order between several μm of smaller ones and 20 μm-40 μm of larger ones described in diameter seen in the broken-out section. The shapes of the smaller bubbles of several μm in diameter are almost circular, while the shapes of the larger ones are rarely circular. Most of them are long and narrow, or angular, or irregular. From these shapes, it is considered that the smaller bubbles are freshly formed, and that the larger ones are aggregates of some of the formed bubbles. Therefore, it was decided to avoid the formation of small bubbles (foaming) as much as possible by means of sintering by heating at a low temperature, and also to avoid gathering of small bubbles through the process of heating as much as possible so as to make the sintered body compact. Combining the ideas of the above paragraphs (1)-(3), it was decided to produce a fluoride sintered body for a neutron moderator having a characteristic excellent in mechanical strength which is a required characteristic other than moderation performance as a member of a neutron moderation system device. In order to achieve the above object, a fluoride sintered body for a neutron moderator according to a first aspect of the present invention is characterized by comprising MgF2 of a compact polycrystalline structure, having a bulk density of 2.90 g/cm3 or more. Since the fluoride sintered body for a neutron moderator according to the first aspect of the present invention is a sintered body of MgF2 of a compact polycrystalline structure having a bulk density of 2.90 g/cm3 or more, the organizational structure of the sintered body is uniform, the difference between the internal and external parts is small, and by restricting the generated quantity of solid solution, the crystal growth is suppressed, leading to reducing the formation of brittle portions, resulting in enhancing the strength of the sintered body. Therefore, in the processing steps in producing the sintered body, or in handling between the steps, cracks or chips are not easily caused. A sintered body having a mechanical strength with which no damage such as cracks or chips may be caused when it is set in a BNCT apparatus, or even when neutron irradiation impacts are given thereto during operation of the apparatus, can be obtained. As a result, a fluoride sintered body for a neutron moderator having a good moderation performance and mechanical strength leading to easy handling can be provided. The fluoride sintered body for a neutron moderator according to a second aspect of the present invention is characterized by having a bending strength of 10 MPa or more and a Vickers hardness of 71 or more as regards mechanical strengths in the fluoride sintered body for a neutron moderator according to the first aspect of the present invention. The fluoride sintered body for a neutron moderator according to the second aspect of the present invention has extremely excellent mechanical strengths. Therefore, no crack or the like is caused in mechanical processing for finishing it as a moderator, and it can be a moderator having a sufficient impact resistance to neutron irradiation impacts given during use as a moderator. In order to achieve the above object, a method fir producing a fluoride sintered body for a neutron moderator according to a first aspect of the present invention is characterized by comprising the steps of: pulverizing a high-purity MgF2 raw material to the order of 1 μm-2 μm in median diameter and adding 0.1-1% by weight of a sintering aid thereto to mix; molding said mixed raw material as a starting raw material using a uniaxial press molding device at a molding pressure of 5 MPa or more; molding said uniaxially molded article using a cold isostatic pressing (CIP) device at a molding pressure of 5 MPa or more; conducting preliminary sintering by heating said CIP molded article to 550° C.-600° C. in an air atmosphere; and conducting main sintering by heating the same in the temperature range just below the starting temperature of foaming for 4-16 hours in an inert gas atmosphere to allow the sintering to make progress more uniformly, and then heating the same in the vicinity of the temperature limits in which a solid solution starts to be formed for 0.5-3 hours so as to form a MgF2 sintered body having a compact structure. Here, the CIP is a method for pressure molding wherein a uniaxially molded article is put into a bag sealed with a vinyl bag or the like in order not to directly touch clean water. The bag after deairing, is put within a pressure vessel, and the vessel is filled with clean water to apply a prescribed hydraulic pressure. Here, the starting temperature of foaming is a temperature at which part of a fluoride compound starts to decompose and fluorine gas is generated so as to start to form fine bubbles. A preliminary sintered body formed by heating a MgF2 raw material at 550° C. for 6 hours in an air atmosphere was grinded, and using the grinded substance as a sample of a differential thermal analyzer, alterations in weight and in endothermic and exothermic amount of the sample were examined while heating. A minute quantity of weight decrease was found at approximately 800° C. but it appeared that this was because, for example, fluorine attached to a parent of the preliminary sintered body or boron fluorine resolving in the parent, with a weak bonding property, dissociated and decomposed first of all. After further heating, a point of inflection of the weight decrease curve appeared at approximately 850° C., and the weight decrease became noticeable. It was anticipated that in the temperature limits above that, part of bonded boron fluorine in MgF2 would start to decompose, which would cause the generation of fluorine gas and the formation of fine bubbles. Therefore, the temperature corresponding to this point of inflection, that is, about 850° C. is referred to as the starting temperature of foaming. Here, the temperature range just below the starting temperature of foaming is specifically a temperature range of 750° C.-840° C. Here, the temperature limits in which a solid solution starts to be formed are temperature limits in the vicinity of 980° C. in which a solid solution starts to be formed in a phase diagram of the MgF2—CaF2 binary system shown in FIG. 1. The sintered body produced by the method for producing a fluoride sintered body for a neutron moderator according to the first aspect of the present invention has a strong bonding power between particles, leading to a high mechanical strength (micro strength) of the bonding parts. The bending strength and impact resistance which were problems to be solved are remarkably improved, and a sintered body which can be used as a neutron moderator without problems for actual use can be obtained. A sintered body to be produced has a higher degree of compactness according to the selection of the purity of MgF2, heating atmosphere, heating temperature pattern and the like. Since the body is sintered, the crystalline structure thereof is polycrystalline, resulting in remarkable improvement of the brittleness compared with a single crystal. Therefore, since the sintered body produced by the method for producing a fluoride sintered body for a neutron moderator according to the first aspect of the present invention has sufficient mechanical strengths in processing such as cutting-off, grinding and polishing as a moderator in a moderation system device for BNCT, and further in handling such as the installation thereof in the moderation system device, it can be installed without problems. Even if it is irradiated with neutrons, it can be used without problems to irradiation impacts thereof: and the moderation performance to neutrons is also extremely excellent. The method for producing a fluoride sintered body for a neutron moderator according to a second aspect of the present invention is characterized by the inert gas atmosphere in the main sintering step comprising one kind of gas or a mixture of plural kinds of gases, selected from among nitrogen, helium, argon and neon, in the method for producing a fluoride sintered body for a neutron moderator according to the first aspect of the present invention. Thus, as the inert gas, nitrogen (N2), helium (He), argon (Ar) or neon (Ne) may be used. The preferred embodiments of the fluoride sintered body for a neutron moderator and the method for producing the same according to the present invention are described below by reference to the Figures. In order to produce a fluoride sintered body suitable for a neutron moderator according to the preferred embodiments, a high-purity (purity of 99.9% by weight or more) MgF2 powder was used, and as a sintering aid, for example, a carboxymethyl cellulose (CMC) solution was added in the proportion of 0.03-0.5% by weight (not included in 100) to 100 of the powder. The mixture was used as a starting raw material. After filling the raw material into a mold form of a prescribed size, it was compressed at a molding pressure of 5 MPa or more using a uniaxial press molding device, and the molded article was further molded at a molding pressure of 5 MPa or more using a cold isostatic pressing (CIP) device. Preliminary sintering was conducted by heating this CIP molded article in the temperature range between 550° C. and 600° C. in an air atmosphere, and the preliminary sintered article was heated in the temperature range just below the starting temperature of foaming (the temperature defined through the measurement using a differential thermal analyzer, about 850° C.) (750° C.-840° C.) for 4-16 hours in an air atmosphere or an inert gas atmosphere. By this heating, sintering was more uniformly promoted, and thereafter, the same was heated in the vicinity of the temperature limits in which a solid solution starts to be formed, that is, in the temperature range of 900° C.-1100° C. for 0.5-3 hours, and then cooled so as to produce a MgF2 sintered body having a compact structure. As described above, in the phase diagram of the MgF2—CaF2 binary system shown in FIG. 1, the temperature at which a solid solution starts to be formed is in the temperature limits in the vicinity of 980° C. However, the present inventors presumed from the observation of the sections of actually sintered bodies, that there was a high possibility that a solid solution would be formed at a temperature dozens lower than 980° C., the temperature indicated in this phase diagram in the case of MgF2 simple. Therefore, they considered that the vicinity of the temperature limits in which a solid solution starts to be formed should be 900° C. or more, and guessed that a solid solution would be formed even in the case of heating at a temperature less than 980° C. Concerning the pulverization of MgF2 being a raw material, balls for ball mill were filled into a pot mill, 3 kg of the raw material was filled therein and mixed for one week so as to be pulverized. The pot mill made of alumina, having an inside diameter of 200 mm and a length of 250 mm was used. As the filled balls made of alumina, ϕ5: 1800 g, ϕ10: 1700 g, ϕ20: 3000 g and ϕ30: 2800 g were used. The particle sizes of the raw material after pulverization were measured using a laser diffraction/scattering particle size distribution analyzer LA-920 made by HORIBA. Ltd. The median diameters were approximately 1.2 μm-1.3 μm. As the sintering aid, two kinds, the CMC and calcium stearate, were selected. With various addition proportions of each of them, the tests for examining the effects thereof were conducted. For comparison, a test with no sintering aid was also conducted. Concerning mixing of the sintering aid, the two kinds of sintering aids were added in the proportion of 0-2% by weight, respectively. As is the case with the pulverization of the raw material, after filling the balls for ball mill into the pot mill, the sintering aid was mixed a whole day and night. This mixed raw material was filled into a mold form of a uniaxial press molding device (mold size 220 mm×220 mm×H150 mm) and compression molding thereof was conducted at a press pressure of 20 MPa. Then, this press molded body was put into a vinyl bag and sealed, and it was put into a molding part of a CIP device (inside size: inside diameter 350 mm×height 120 mm). The space in said molding part was filled with clean water, and cool isostatic pressing (CIP) was conducted with variations of isostatic pressures by hydraulic pressure at room temperature. Preliminary sintering was conducted on this CIP molded body in an air atmosphere with various kinds of heating conditions in the temperature range between 500° C. and 700° C. and in the time range of 3 to 18 hours. After observing the appearance of this preliminary sintered body, in a nitrogen gas atmosphere, the temperature was raised from room temperature to 550° C. at a fixed rate for 6 hours, and held there for 8 hours. Then, it was raised to 950° C. at a fixed rate for 2 hours and held there for 1 hour, and then lowered for 20 hours to 100° C. By observing the appearance of the taken-out sintered body and the compact state of the inside thereof, proper compositions, processing conditions and preliminary sintering conditions were investigated. As a result, there was no big difference between the effects of the two kinds of sintering aids, but in the case of no sintering aid, the shape keeping performance of the uniaxial press molded body was poor, so that loss of shape frequently occurred in handling to the following CIP molding step. When the mix proportion of the sintering aid was 0.03% by weight or more, the loss of shape was not noticed, while coloring which appeared to be a residual of the sintering aid was sometimes noticed on the preliminary sintered body or sintered body when the mix proportion thereof exceeded 0.6% by weight. Accordingly, the proper range of the mix proportion of the sintering aid was decided to be 0.03-0.5% by weight. When the molding pressure of the CIP device was less than 5 MPa, the bulk density of the sintered body in any of optimizing tests of the heating conditions of preliminary sintering and main sintering was lower by 2% or more than the case of the molding pressure of 5 MPa or more. For example, in the case of a molding pressure of 10 MPa, the bulk density of a sintered body sintered with the same sintering conditions was 2.95 g/cm3, while in the case of a molding pressure of 4.8 MPa, the bulk density of a sintered body was 2.86 g/cm3, 3% lower than the former. When the molding pressure was increased gradually from 5 MPa to 20 MPa, it was recognized that the bulk density of a sintered body after sintering tended to increase little by little. The tests were conducted until the molding pressure was gradually increased further to 50 MPa. The increase of the bulk density of a preliminary sintered body or a sintered body in the case of a molding pressure of 20 MPa or more was just slight, and a linear improvement like between 5 MPa and 20 MPa was not recognized. Accordingly, the proper value of the molding pressure was decided to be 5 MPa or more, preferably 20 MPa or more. Concerning the preliminary sintering conditions of a molded body in an air atmosphere, as shown in FIG. 2, at a heating temperature of less than 550° C. shrinkage was small compared with the size of the molded body, while at a heating temperature of 610° C. or more, the shrinkage was large and difficult to control. Accordingly, the proper range of the preliminary sintering temperature was decided to be between 550° C. and 600° C. Concerning the proper value of the heating time, as shown in FIG. 2, at 550° C. 8-9 hours were optimal from the evaluation of the shrinkage rate, and it could be judged that 4-10 hours were proper. At 600° C., 6-8 hours were optimal, and it could be judged that 4-10 hours were proper. From these results, the heating condition of the preliminary sintering was decided to be at 550° C.-600° C. 4-10 hours in an air atmosphere. The main sintering step important in producing a MgF2 sintered body suitable for a neutron moderator and the sintering mechanism thereof are described below. The definition of ‘primary flocculation process’ and ‘secondary flocculation process’ which are the terms expressing the degree of progress of the sintering step, is described below. The ‘primary flocculation process’ is the first half of the stage of sintering, and at the initial stage thereof, the intervals between particles gradually become narrower and the voids among particles also become smaller. Furthermore, the particle-to-particle contact portions become thick and the voids among them become small. Here, the majority of the voids are open pores connecting to the surrounding atmosphere. Such whole stage is called ‘primary flocculation process’. After the end of the primary flocculation process, with further progress of sintering, the open pores gradually decrease and turn into closed pores. Roughly the stage of turning into closed pores and the following stage of defoaming and compacting are called ‘secondary flocculation process’. In the present invention, due to pulverization of raw materials, particle size control, mixing of a sintering aid, uniaxial press molding, CIP molding, preliminary sintering and the like, it was recognized that the voids among particles of the preliminary sintered body were small, and that the voids almost uniformly scattered without gathering (the first half stage of the primary flocculation process). In the heating process of the next main sintering step, the heating temperature is gradually raised. Around the preliminary sintering temperature limits (550° C.-600° C.), particles start to gather, and thereafter, solid phase reaction starts in the temperature limits far lower than 980° C. at which a solid solution starts to be formed. With that, flocculation of particles makes progress, the particle-to-particle distances become short and the voids become small. Here, in the case of heating at a relatively low temperature (in the vicinity of 550° C.) like preliminary sintering for a short period of time, most of the voids remain in the open pore state (the second half stage of the primary flocculation process). It is generally said that the solid phase reaction starts in the temperature limits lower by the order of 10% or further lower than 980° C. From the observation of the sections of the sintered bodies in the preliminary test by the present inventors, it was considered that the solid phase reaction started in further lower temperature limits than generally said, at approximately 500° C. Its grounding is that at 550° C. the lowest limit of the proper preliminary sintering temperature, sintering had already made progress considerably and that the preliminary sintered body considerably shrunk compared with the molded body. In this preliminary test, the bulk volume shrunk in the order of 10-20% by volume. It was considered that the reaction made progress at a slow reaction rate in the temperature limits and that it made progress at a quite high reaction rate in the temperature limits in the vicinity of approximately 700° C. or more up to 980° C. What attention should be paid to is behavior of fine bubbles (foaming gas) generated through vaporization of part of a raw material in the temperature limits of about 8500° C. or more. In the case of heating at about 850° C. or more, it was considered that the heating time should be as short as possible, since this formation of bubbles became noticeable. Micro behavior of raw material particles is described below. Around a temperature exceeding 980° C. at which a solid solution starts to be formed, melting starts in the vicinity of a particle interface where fine particles of MgF2 are present, and a solid solution of MgF2 starts to be formed. As described by reference to FIG. 1, the present inventors presumed from the observation of the sections of the sintered bodies in the preliminary test that in the case of MgF2 simple, a solid solution would start to be formed in the temperature limits in the order of dozens of degrees lower than 980° C. as the true state. It was presumed that this solid solution filled the voids among particles and that in some parts, more fine voids were also filled in through capillary phenomenon. On the other hand, even if the heating temperature is lower than 980° C. by heating at about 700° C. or more for a long period of time as described above, the solid phase reaction makes progress, the voids gradually decrease with the elapse of time so as to be closed pores. Parallel with that, a gas component within the closed pores scatters within the bulk (parent) of the sintered body, leading to the progress of defoaming so as to make the sintered body compact with few bubbles (secondary flocculation process). Here, in order to make it compact by heating in the relatively low temperature limits of the order of 700° C., heating for a quite long period of time is required, resulting in low productivity and being uneconomical. Also here, in heating at about 850° C. or more, attention should be paid to the presence of line bubbles (foaming gas) generated through vaporization of a raw material. It is presumed that the bubbles contain fluorine gas. Fluorine, the atomic number of 9, having an atomic weight of 18.998, is heavier than the air, and a relatively heavy element among light elements. The diffusion velocity thereof within the bulk (equivalent for the parent) of the sintered body is slow (it is difficult to diffuse), and it is considered that once formed bubbles do not easily disappear. As measures for suppressing foaming, to avoid heating in the temperature limits of foaming as much as possible, and to hold heating in the temperature limits thereof to a short period of time are exemplified. The difference in appearance between such foaming gases and bubbles left after pores became closed but could not be defoamed in the sintering step (hereinafter, referred to as residual bubbles) is described below. The sizes of the foaming gases generated by general heating for a relatively short period of time are approximately several μm diameter, and the shapes thereof are almost perfect spheres. On the other hand, the sizes of the residual bubbles are all mixed up, large, medium and small, and the shapes thereof are not perfect spheres but irregular. Therefore, it is possible to distinguish the both according to the difference in shape. Here, in the case of heating at a high temperature far exceeding 980° C., or heating in the temperature limits exceeding 980° C. for a long period of time, a foaming gas and a foaming gas, or a residual bubble and a foaming gas gather and grow to a large irregular bubble, resulting in difficulty in judging its origin. With the progress of the secondary flocculation process, the voids among particles become smaller, all or most of the voids are surrounded by particles or a bridge portion of the sintered body so as to be closed pores (bubbles). Depending on the conditions, gases are released through the voids (open pores), or gas components within the bubbles permeate into the bulk such as the particles or the bridge portion of the sintered body to degas, resulting in extinction of the bubbles (defoaming phenomenon). Whether the voids among particles are left as closed pores (bubbles) or by degassing, they do not remain as bubbles so as to disappear, is a significant element for deciding the degree of achievement of compactness of the sintered body, leading to the characteristics of the sintered body. Particularly in the case of sintering in an inert gas atmosphere (a light element gas such as Hie or Ne), it was considered that the lighter element easily diffused within the pores or bulk of the sintered body, leading to promoting the capillary phenomenon and defoaming phenomenon, and that bubbles were difficult to remain, leading to easy compacting. Thus, in order to make the whole compact, it is important to advance the primary flocculation process and the secondary flocculation process continuously with good balance. In the present invention, the preliminary sintering step chiefly corresponding to the first half stage of the primary flocculation process and the main sintering step chiefly corresponding to the second half stage of the primary flocculation process and the secondary flocculation process are separately conducted, so as to make the two flocculation processes easy to make progress uniformly throughout the sintered body. However, it is meaningless to divide the sintering step into two steps of preliminary sintering and main sintering like this, if the heating conditions are not proper. For example, in the case of heating at a high temperature exceeding the proper limits in the preliminary sintering step, in the case of rapidly heating at the temperature raising stage of the main sintering step, or in cases where the holding temperature in the main sintering step is a high temperature exceeding the proper limits, a remarkable difference in the degree of compactness is caused between the periphery portion of the sintered body and the inside thereof. When such situation is caused, degassing becomes difficult in the process of compacting the inside of the sintered body, resulting in insufficient compactness of the inside thereof. Therefore, it is important to make the heating temperature pattern in the sintering step according to the size proper. As described above, the proper conditions till just before the main sintering step are disclosed. The preliminary sintered body provided to this main sintering step is in a state that the whole body has already advanced to the first half stage of the primary flocculation. What is important here is the whole of the preliminary sintered body has already advanced uniformly to the middle of the primary flocculation. In order to find a method for producing a fluoride sintered body suitable for a neutron moderator, various kinds of main sintering steps were conducted. Preliminary sintered bodies obtained by conducting uniaxial press molding and CIP molding on a compound material made of MgF2 being a pulverized raw material with CMC of 0.2% by weight as a sintering aid added thereto and conducting preliminary sintering thereon at 550° C. for 6 hours were used. In any case, the heating time was set to be 6 hours. In each case of a sintering temperature varying between 600° C. and 1200° C., at an interval of every 50° C., the bulk density of the sintered body was measured. In the case of a range approximately between 900° C. and 1100° C., the bulk densities exceeded 2.90 g/cm3, which were high, but in either case of a sintering temperature of 850° C. or less, and that of 1150° C. or more, the bulk densities were lower than 2.90 g/cm3. When observing the sections of those sintered bodies, in the case of those sintered at 800° C. or less, the bridge widths of the sintering portions were narrow, so that it could be judged as absolutely insufficient progress of sintering. In the case of a body sintered at 850° C. a few open pores were noticed. In the case of a body sintered at 1100° C., some irregular bubbles were found inside, and in the case of those sintered at 1150° C. or more, those had a porous pumiceous structure as if irregular bubbles were innumerably formed inside. Fine bubbles which were almost perfect spheres of several to dozen μm in diameter were observed all over the sintered body and innumerable irregular bubbles of 10 μm or more in diameter were found all over the sections observed. It could be judged that these perfect sphere bubbles were foaming gases from their shapes, and that these irregular bubbles were bubbles in clusters similarly from their shapes. On the other hand, from the examination by the present inventors, it was found out that in the process of heating the MgF2 raw material obtained by pulverizing those as measured by a differential thermal analyzer, the weight clearly started to decrease at about 800° C., and that the weight started to drastically decrease at about 850° C. This means that a sublimation phenomenon in which MgF2 starts to dissolve/vaporize to generate fluorine gas starts at about 800° C., and that this phenomenon becomes brisk at about 850° C. (what is called presenting a foaming phenomenon). Through this sublimation, as described above, fine bubbles are formed all over the sintered body. The behavior of the formed fine bubbles (foaming gases) such as defoaming or remaining as bubbles is decided according to the degree of progress of the sintering step, in which portion of the sintered body they were formed and the like. In the primary flocculation process, for example, since the whole sintered body contains mainly open pores, the majority of bubbles are defoamed through the open pores, leading to few bubbles left. In the secondary flocculation process, since the sintered body contains mainly closed pores, a lot of foaming gases cannot be defoamed, leading to bubbles left. Basically it can be said that to swiftly complete the sintering in the secondary flocculation process is a course to be taken to reduce residual bubbles. Thus, it is preferable that the transition from the primary flocculation process to the secondary flocculation process should be advanced in the whole sintered body with as small a time lag as possible. However, it is not easy to undergo the transition from the primary flocculation process to the secondary flocculation process in the whole sintered body without time lag. Then, the present inventors decided to complete the primary flocculation process and the first half of the secondary flocculation process by heating at a rather low temperature in the temperature limits just below the starting temperature of foaming (about 850° C.) for a relatively long period of time, and then, to complete the second half of the secondary flocculation process by heating at a temperature in the vicinity of the temperature at which a solid solution starts to be formed (980° C.) for a relatively short period of time. They found out that this was an excellent sintering method by which the degree of progress of sintering in the whole sintered body could be made uniform with formation of few foaming gases. The proper range of the sintering conditions is described below. As preliminary sintering, a molded body was held at 600° C. for (hours in an air atmosphere. The preliminary sintered body was about 212 mm×212 mm×t72 mm in size and a cuboid shape with two square surfaces on the top and bottom. The heating atmosphere was set to be a nitrogen gas atmosphere. Preliminary tests concerning each of heating and cooling conditions in the heating pattern were conducted in three cases of the required time of 3, 6 and 9 hours. As a result, in the case of 3 hours, small cracks occurred in the sintered body, while in the other cases, the results were good. Therefore, the required time was set to be 6 hours. The heating atmosphere was continuously set to be the nitrogen gas atmosphere. The heating temperature was varied in the range of 700° C. to 1250° C., and in eleven cases of the holding time of 2, 3, 4, 5, 6, 8, 10, 12, 14, 16 and 18 hours, the tests were conducted. As shown in FIG. 3, in the case of 750° C. or less, the compactness was insufficient, regardless of the holding time. In the case of a holding time of 4 hours or less, the compactness was insufficient in any case other than 1100° C. On the other hand, in the case of a heating temperature exceeding 1150° C., a large number of bubbles were generated due to too fast sintering speed, regardless of the holding time, while in the case of a holding time of 16 hours or more, foaming occurred in part of the periphery of the sintered body, leading to getting out of shape in appearance. Reviewing the results in FIG. 3 in detail, in the case of heating at 850° C., the sintering state was good with a holding time of 8 hours or more, while slightly insufficient with 6 hours or less. In the case of 900° C., the sintering state was good with a holding time of 5 hours or more, while slightly insufficient with 4 hours or less, and beyond decision of quality with 16 hours or more. In the case of 950° C., the sintering state was good with a holding time of 5 to 14 hours, while slightly insufficient with 4 hours or less, and beyond decision of quality with 15 hours or more. In the case of 1000° C. the sintering state was good with a holding time of 5 to 12 hours, while slightly insufficient with 4 hours or less, and much foaming with 14 hours or more. In the case of 1100° C., the sintering state was good with a holding time of 3 to 8 hours, while much foaming with 10 hours or more. In the case of 1150° C., much foaming was seen with any holding time. In the case of 1200° C., the sintering was insufficient with a holding time of 3 hours or less, while beyond decision of quality or poor because of too much melting with 4 hours or more. When the heating temperature was a comparatively low temperature of 800° C. to 850° C., the sintering was slightly insufficient when the holding time was between 4 and 8 hours. However, since the main sintering step was divided into two, the first main sintering step and the following second main sintering step in the present invention, that was regarded as being good as the evaluation in the first main sintering step. In order to examine the relationship among the heating temperature, the bulk density of the sintered body and the mass decrease TG thereof corresponding to a yield, using the same preliminary sintered body as the above, the holding time was set to be 6 hours, and the heating temperature was varied within the range of 600° C. to 1300° C. As a result, in the case of a heating temperature of 900° C., the bulk density was approximately 2.90 g/cm3. Like the results shown in FIG. 3, the sintered body having a bulk density of that or more could be judged to have sufficient compactness without troubles such as losing its shape in the treatment of the second step. On the other hand, in the case of a heating temperature of 1150° C. or more, the mass decrease TG was −0.8% or more, and the decrease of the yield was remarkable. When the heating temperature was more than that, foaming occurred in part of the periphery of the sintered body, resulting in a trouble such as getting out of shape in appearance. From the results shown in FIG. 3, it could be judged that, if the sintering step was one of the heating steps, the heating temperature of 850° C. to 1100° C. and the holding time of 3 to 14 hours (high-temperature short-time heating, or low-temperature relatively-long-time heating within these ranges) were proper conditions. What was clarified here is, when relatively long time heating, such as at 900° C. for 16 hours or more, at 1000° C. for 14 hours or more, or at 1100° C. for 10 hours or more, was conducted, the quantity of bubbles was large and part of those gathered and was growing to a large bubble. It was confirmed that such sintered body involved defects which would cause cracks to occur from a large bubble portion or cause splitting in the next mechanical processing step. From these situations, the present inventors decided as a fundamental plan of the main sintering step that foaming should be suppressed as much as possible, as well as the sintering reaction should be allowed to sufficiently make progress, leading to producing a sintered body having a good processability in the subsequent mechanical processing step. The fundamental plan at the beginning of the main sintering step was that forming should be tried not to occur as much as possible, that the sintering should be allowed to make slow progress, and that the difference between the degree of progress of the inner portion of the sintered body and that of the periphery portion thereof should be kept as small as possible. The heating temperature limits were decided to be within the range of 800° C. to 1100° C. as described above. Since the temperature at which foaming became noticeable was about 850° C., the heating temperature at the beginning of the main sintering step was set to be below 850° C., 840° C. or less, that is, from 750° C. to 840° C., and the holding time was set to be 5 to 12 hours. Heating at the next stage of enhancing the sintering reaction of the sintered body was decided to be conducted in the temperature limits in the vicinity of 980° C. at which a solid solution started to be formed, that is, 900° C. to 1100° C. within the above proper conditions. The holding time was decided to be made as short as possible in order to enhance the sintering reaction and suppress foaming. Judging from the results in FIG. 3 and the below-described examples and comparative examples, the holding time was decided to be 0.5 to 3 hours, since the enhancement of the sintering reaction was poor in the case of less than 0.5 hour, and too many bubbles were formed in the case of 4 hours or more. When the atmospheric gas was changed to helium, the results were not different from those in the case of nitrogen gas. At less than 800° C., the compactness was not sufficient regardless of the holding time, and in the case of a holding time of 4 hours or less, the compactness was insufficient. In the case of 1110° C. or more, the sintering speed was too fast regardless of the holding time as is the case with the nitrogen gas, resulting in occurrence of many bubbles, and in the case of a holding time of 4 hours or more, because of foaming, the appearance got out of shape in some cases. In order to examine the relationship among the heating temperature, the bulk density of the sintered body and the mass decrease TG thereof corresponding to a yield, using the same preliminary sintered body as the above, the holding time was set to be 6 hours, and the heating temperature was varied within the range of 600° C. to 1300° C. As a result, as is the case with the nitrogen gas, the bulk density was approximately 2.90 g/cm3 at a heating temperature of 900° C. It was judged that the sintered body having a bulk density of that or more would not lose its shape in the treatment of the subsequent step, as is the case with the nitrogen gas, resulting in having sufficient compactness. On the other hand, at a heating temperature of 1110° C. or more, the mass decrease TG was −0.8% or more and the yield decrease was remarkable. And foaming occurred in part of the periphery of the sintered body, resulting in a trouble such as getting out of shape in appearance. Therefore, it was judged that the heating temperature of 900° C. to 1100° C. and the holding time of 0.5 to 2.5 hours were proper conditions. Furthermore, since in the case of a heating temperature of 950° C. to 1050° C. and a holding time of 0.5 to 3 hours, defects such as cracks were difficult to occur when providing the sintered body to the mechanical processing, resulting in good mechanical processability, it was judged that the heating temperature of 950° C. to 1050° C. and the holding time of 0.5 to 3 hours were desirable. Therefore, as proper heating conditions of the main sintering step in a helium gas atmosphere, as is the case with the above nitrogen gas atmosphere, the proper condition of the first heating of the main sintering step was at 750° C. to 840° C. for a holding time of 5 to 12 hours, while that of the second heating thereof was at 900° C. to 1100° C. for a holding time of 0.5 to 3 hours. The inert gas is not limited to nitrogen and helium. In the case of argon or neon, the same effects can be obtained. Since neon is expected to have a high resolution degree or a scattering characteristic in the parent of this sintered body, like helium, the defoaming phenomenon can be further promoted and an improvement thereby equal to or more than that by helium can be expected. When the heating conditions of the main sintering step were within the proper range, the state of the completed sintered body was wholly compact in any case, and no clearly defective portion such as a locally large void or a crack seen in a general ceramic sintered body could be found. The present invention is more specifically described below by reference to Examples, but the present invention is not limited to these Examples. First, a typical characteristic evaluation test conducted on sintered bodies in the Examples is described. In order to evaluate the neutron moderation performance, a beam emitted from an accelerator is allowed to collide with Be being a target, and by nuclear reaction, high-energy neutrons (fast neutrons) are mainly generated. Using Pb and Fe each having a large inelastic scattering cross section as a moderator in the first half of moderation, the neutrons are moderated to some extent (approximately up to 1 MeV) while suppressing the attenuation of the number of neutrons. These are irradiated to a moderator to be evaluated (a moderator in the second half of moderation), and by examining the neutrons after moderation, the moderator is evaluated. The measurement of the contents of the neutrons (hereinafter, referred to as a ‘neutron flux’) was conducted according to the method devised by the present inventors (the above Non-Patent Document 3). The total thickness of each moderator in the second half to be evaluated was set to be 320 mm, and two kinds of moderators, MgF2 and CaF2 were selected. Furthermore, the case wherein MgF1 and CaF2 were superposed on each other (the total thickness was set to be 320 mm) was also evaluated. What was evaluated here is how many fast neutrons having high possibilities of adversely influencing a patient remained in the neutrons moderated by the moderator. The results are shown in FIG. 4. Here, as MgF2 and CaF2, compact sintered bodies thereof each having a relative density (100×(actual density)/(true density), unit %) of 95±2% were used. From FIG. 4, as the layer thickness of MgF2 increases as a moderator, (goes in a right direction on the axis of abscissas), the number of fast neutrons having possibilities of adversely influencing a patient decreases. In the case of MgF2 only, compared with the case of CaF2 only, the number thereof could be reduced to about ⅓ to ¼. It can be known that MgF2 is superior as a moderator. Using the above evaluation device, in the same manner, how the relative density (i.e. the compactness) of MgF2 influences the moderation performance was examined. As a moderator, only MgF2 sintered bodies, having a relative density of 90% to 97% were used. The results are shown in Table 1. The higher relative density the sintered body had, the less the quantity of mixed fast neutrons was, leading to obtaining excellent performance as a moderator. The sintered bodies having a relative density of less than 92% were varied in moderation performance. Some unstable cases, wherein the quantity of mixed fast neutrons suddenly increased, or the epithermal neutron dose drastically increased, were noticed. This appears to be because insufficient compactness resulted in insufficient moderation performance, or with the formation of open pores, impurities were mixed in the sintered body in molding thereof, resulting in irregular influence on the moderation performance. In order to allow the sintered body to present stable moderation performance, it was found that the relative density of 92% or more, that is, the bulk density of 2.90 g/cm3 or more was required. As evaluation indexes of mechanical strength, bending strength and Vickers hardness were adopted. The samples for bending strength, having a size of 4 mm×46 mm×t3 mm with the upper and lower surfaces optically polished were prepared according to JIS C2141, and tested according to the three-point bending test JIS R1601. To obtain the Vickers hardness, using ‘Micro Hardness Tester’ made by Shimadzu Corporation, an indenter having a load of 100 g was pressed for 5 seconds of loading time so as to measure the diagonal length of the impression, which was converted into hardness.Hardness=0.18909×P/(d)2 Here, P: load (N) and d: diagonal length of impression (mm) A high-purity MgF2 raw material (mean particle diameter of 20 μm and purity of 99.9% by weight or more) was pulverized using the pot mill and alumina balls described in the ‘Mode for Carrying Out the Invention’, to a high-purity MgF2 powder (mean particle diameter of 1.2 μm and purity of 99.9% by weight or more). To the powder, a carboxymethyl cellulose (CMC) solution was added as a sintering aid in the proportion of 0.2% by weight to 100 of the MgF2 powder, and mixed in the pot mill for 12 hours so as to be a starting raw material. This starting raw material was filled into a mold form (mold size of 220 mm×220 mm×H150 mm) using a uniaxial press device and compressed at a uniaxial press pressure of 10 MPa to be molded. This press molded body (size of about 220 mm×220 mm×t85 mm), which was put into a thick vinyl bag and sealed after deairing, was put into a molding part (inside size: inside diameter 350 mm×H120 mm) of a cold isostatic pressing (CIP) device. Clean water was filled into the space between the vinyl bag with this press molded body therein and the molding part of the CIP device, and isostatic pressing was conducted at a molding pressure of 20 MPa, resulting in a CIP molded body (size of about 215 mm×215 mm×t75 mm). Preliminary sintering at 600° C. for 5 hours in an air atmosphere was conducted on this molded body, resulting in a preliminary sintered body having a size of about 208 mm×208 mm t72 mm. This preliminary sintered body was heated from room temperature to 830° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 6 hours. It was then raised to 1000° C. at a fixed rate for 2 hours and held there for 1 hour. Heating was then stopped, and the temperature was lowered by self-cooling (furnace cooling) for about 20 hours to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The bulk density of the sintered body was calculated at 3.05 g/cm3 (relative density of 96.8%) from the rough size (193 mm×193 mm×t62 mm) and the weight thereof. The sintering state was good. Since the appearance of the sintered body was a square form in a plan view, the ‘bulk density’ here was obtained by a method wherein the bulk volume was calculated from the measured two sides of the square and thickness, and the weight separately measured was divided by the bulk volume. This also applied to the following. Using samples taken from this sintered body, by the method shown in the Non-Patent Document 3, evaluation tests of neutron moderation performance and characteristics of every kind were conducted. The results are shown in Table 1. This also applied to the following Examples and Comparative Examples. Concerning the neutron moderation performance, the decrease of epithermal neutron dose was slightly small compared with CaF2 as a comparative material, but the dose of fast neutrons having high possibilities of adversely influencing a patient was reduced to about ¼, so that it was found that MgF2 had an excellent moderation performance. As shown in Table 2, the other mechanical strengths were also good without problems. Using the same starting raw material as in the above Example 1, preliminary sintering at 550° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 208 mm×208 mm×t73 mm. This preliminary sintered body was heated from room temperature to 750° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 9 hours. It was then raised to 920° C. at a fixed rate for 2 hours and held there for 2 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 195 mm×195 mm×t64 mm, the bulk density thereof was 2.90 g/cm3 (relative density of 92.1%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 600° C. for 8 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 206.5 mm×207 mm×t71 mm. This preliminary sintered body was heated from room temperature to 840° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 12 hours. It was then raised to 1080° C. at a fixed rate for 2 hours and held there for 1 hour. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 192 mm×192 mm×t61 mm, the bulk density thereof was 3.00 g/cm3 (relative density of 95.2%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, this raw material was filled into the mold form of uniaxial press molding and compressed at a uniaxial press pressure of 70 MPa to be molded. Then, molding was conducted using the cold isostatic pressing (CIP) device at a molding pressure of 40 MPa, so as to obtain a molded body (size of about 213 mm×214 mm×t74 mm). Preliminary sintering at 600° for 10 hours in an air atmosphere was conducted on this molded body to obtain a preliminary sintered body of 204.5 mm×205 mm×t70 mm. This preliminary sintered body was heated from room temperature to 830° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 12 hours. It was then raised to 1080° C. at a fixed rate for 2 hours and held there for 1 hour. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 190.5 mm×191 mm×t60 mm, the bulk density thereof was 3.07 g/cm3 (relative density of 97.5%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 580° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 206 mm×206 mm×t70.5 mm. This preliminary sintered body was heated from room temperature to 800° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 12 hours. It was then raised to 920° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 191.0 mm×191.5 mm×t62 mm, the bulk density thereof was 3.02 g/cm3 (relative density of 95.9%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 580° C. for 7 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 207 mm×207 mm×t71.5 mm. This preliminary sintered body was heated from room temperature to 830° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 12 hours. It was then raised to 1000° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 192.5 mm×192.5 mm×t63 mm, the bulk density thereof was 2.99 g/cm3 (relative density of 94.9%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 580° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 206 mm×206 mm×t70.5 mm. This preliminary sintered body was heated from room temperature to 840° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 8 hours. It was then raised to 980° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 193 mm 193.5 mm×t62.5 mm, the bulk density thereof was 2.96 g/cm3 (relative density of 94.0%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 560° C. for 8 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 207 mm×206 mm×t70.5 mm. This preliminary sintered body was heated from room temperature to 8409° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 5 hours. It was then raised to 920° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 194.5 mm×194.5 mm×t64 mm, the bulk density thereof was 2.91 g/cm3 (relative density of 92.4%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 580° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 205 mm×205 mm×170.5 mm. This preliminary sintered body was heated from room temperature to 840 t at a fixed rate for 6 hours in a helium gas atmosphere, and the temperature was held there for 8 hours. It was then raised to 980° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 192.5 mm×192.5 mm×t62 mm, the bulk density thereof was 3.00 g/cm3 (relative density of 95.2%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics oft every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 560° C. for 6 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 207 mm×207 mm×t70.5 mm. This preliminary sintered body was heated from room temperature to 770° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 10 hours. It was then raised to 900° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 194.5 mm×194.5 mm×t64 mm, the bulk density thereof was 2.90 g/cm3 (relative density of 92.1%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 550° C. for 8 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 207 mm×207 mm×t70 mm. This preliminary sintered body was heated from room temperature to 790° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 6 hours. It was then raised to 940° C. at a fixed rate for 2 hours and held there for 1.5 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 194.5 mm×194.5 mm×t64 mm, the bulk density thereof was 2.91 g/cm (relative density of 92.4%), and the sintering state was good. Any of the evaluation results of the neutron moderation performance and characteristics of every kind were good as shown in Table 2. Using the same starting raw material as in the above Example 1, preliminary sintering at 550° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 208 mm×208 mm×t73 mm. This preliminary sintered body was heated from room temperature to 750° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 9 hours. It was then raised to 920° C. at a fixed rate for 2 hours and held there for 2 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 195 mm×195 mm×t64 mm, the bulk density thereof was 2.90 g/cm3 (relative density of 92.1%), and the sintering state was good. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of low mechanical strength. Using the same starting raw material as in the above Example 1, preliminary sintering at 530° C. for 5 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 209 mm×209 mm×t76 mm. This preliminary sintered body was heated from room temperature to 740° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 4 hours. It was then raised to 890° C. at a fixed rate for 2 hours and held there for 2 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 198 mm×198 mm×t68 mm, the bulk density thereof was 2.80 g/cm3 (relative density of 88.9%), and the sintering state was obviously porous and inconvenient, leading to a problem in handling. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of unmeasurably low mechanical strength. Using the same starting raw material as in the above Example 1, preliminary sintering at 550° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 208 mm×208 mm×t73 mm. This preliminary sintered body was heated from room temperature to 750° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 9 hours. It was then raised to 880° C. at a fixed rate for 2 hours and held there for 1.5 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 197 mm×196 mm×t67 mm and the bulk density thereof was 2.88 g/cm3 (relative density of 91.4%). The sintering state was good in appearance, but at the stage of grinding wherein the sintered body was finished using a grinder, a phenomenon that a grinding fluid was absorbed into the sintered body was recognized. Therefore, the microstructure of the inside of the sintered body was examined in detail. As a result, it was clarified that a large number of open pores were formed, resulting in insufficient sintering. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of low mechanical strength. Using the same starting raw material as in the above Example 1, preliminary sintering at 600° C. for 10 hours in an air atmosphere was conducted on a molded body to which uniaxial press molding and cold isostatic pressing (CIP) were applied in the same manner, so as to obtain a preliminary sintered body of 208 mm×208 mm×t73 mm. This preliminary sintered body was heated from room temperature to 840° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 8 hours. It was then raised to 1150° C. at a fixed rate for 2 hours and held there for 3 hours. The temperature was then lowered by furnace cooling to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The rough size of the sintered body was 196.5 mm×197 mm×t68 mm and the bulk density thereof was 2.87 g/cm3 (relative density of 91.1%). The sintering state was porous. When examining the microstructure of the inside of the sintered body, the structure was not compact and a trace of violent foaming resulting in porosity was observed. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of low mechanical strength. Using the same starting raw material as in the above Example 1, this raw material was filled into a mold form (mold size of 220 mm×220 mm×H150 mm) using a uniaxial press device, and compressed at a uniaxial press pressure of 4 MPa to be molded. This press molded body (size of about 220 mm×220 mm×t85 mm) was put into a thick vinyl bag, and sealed after deairing. That was put into a molding part (inside size: inside diameter 350 mm×H120 mm) of a cold isostatic pressing (CIP) device. Clean water was filled into the space between the vinyl bag with this press molded body therein and the molding part of the CIP device and isostatic pressing was conducted at a molding pressure of 4 MPa, resulting in a CIP molded body (size of about 218 mm×218 mm×t75 mm). Preliminary sintering at 550° C. for 5 hours in an air atmosphere was conducted on this molded body, so as to obtain a preliminary sintered body of about 211 mm×211 mm×t73 mm. This preliminary sintered body was heated from room temperature to 740° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 6 hours. It was then raised to 900° C. at a fixed rate for 2 hours and held there for 1 hour. Heating was then stopped, and the temperature was lowered by self-cooling (furnace cooling) for about 20 hours to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The bulk density of the sintered body calculated from the rough size (199 mm×199 mm×t68 mm) and the weight thereof was 2.86 g/cm3 (relative density of 90.8%). The sintering state was slightly porous. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of low mechanical strength. Using the same starting raw material as in the above Example 1, this raw material was filled into a mold form (mold size of 220 mm×220 mm×H150 mm) using a uniaxial press device, and compressed at a uniaxial press pressure of 10 MPa to be molded. This press molded body (size of about 220 mm×220 mm×t851 nm) was put into a thick vinyl bag, and sealed after deairing. That was put into a molding part (inside size: inside diameter 350 mm×H120 mm) of a cold isostatic pressing (CIP) device. Clean water was filled into the space between the vinyl bag with this press molded body therein and the molding part of the CIP device and isostatic pressing was conducted at a molding pressure of 20 MPa, resulting in a CIP molded body (size of about 215 mm×215 mm×t75 mm). Preliminary sintering at 500° C. for 4 hours in an air atmosphere was conducted on this molded body so as to obtain a preliminary sintered body of about 211 mm×211 mm×t72 mm. This preliminary sintered body was heated from room temperature to 730° C. at a fixed rate for 6 hours in a nitrogen gas atmosphere, and the temperature was held there for 5 hours. It was then raised to 900° C. at a fixed rate for 2 hours and held there for 1 hour. Heating was then stopped, and the temperature was lowered by self-cooling (furnace cooling) for about 20 hours to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The bulk density of the sintered body calculated from the rough size (198 mm×198 mm×t68 mm) and the weight thereof was 2.85 g/cm3 (relative density of 90.5%). The sintering state was insufficient and slightly porous. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of low mechanical strength. Using the same starting raw material as in the above Example 1, this raw material was filled into a mold form (mold size of 220 mm×220 mm×H150 mm) using a uniaxial press device, and compressed at a uniaxial press pressure of 4 MPa to be molded. This press molded body (size of about 220 mm×220 mm×t85 mm) was put into a thick vinyl bag, and sealed after deairing. That was put into a molding part (inside size: inside diameter 350 mm×H120 mm) of a cold isostatic pressing (CIP) device. Clean water was filled into the space between the vinyl bag with this press molded body therein and the molding part of the CIP device and isostatic pressing was conducted at a molding pressure of 4 MPa, resulting in a CIP molded body (size of about 218 mm×218 mm×t75 mm). Preliminary sintering at 550° C. for 5 hours in an air atmosphere was conducted on this molded body, so as to obtain a preliminary sintered body of 211 mm×211 mm×t72.5 mm. This preliminary sintered body was heated from room temperature to 740° C. at a fixed rate for 6 hours in a helium gas atmosphere, and the temperature was held there for 6 hours. It was then raised to 900° C. at a fixed rate for 2 hours and held there for 1 hour. Heating was then stopped, and the temperature was lowered by self-cooling (furnace cooling) for about 20 hours to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The bulk density of the sintered body calculated from the rough size (198 mm×198.5 mm×t67.5 mm) and the weight thereof was 2.89 g/cm3 (relative density of 91.7%). The sintering state was slightly porous. As the evaluation results of the neutron moderation performance and characteristics of every kind, as shown in Table 2, a large quantity of fast neutrons having possibilities of adversely influencing the body remained in the neutron flux after moderation. There was a problem left that the moderation effect could not be sufficiently obtained. In addition, there was a problem of low mechanical strength. [Comparative Material: CaF2] A high-purity CaF2 raw material (mean particle diameter of 20 μm and purity of 99.9% by weight or more) was pulverized using the pot mill and alumina balls to a high-purity CaF2 powder (mean particle diameter of 1.4 μm and purity of 99.9% by weight or more). To the powder, a carboxymethyl cellulose (CMC) solution was added as a sintering aid in the proportion of 0.2% by weight to 100 of the CaF2 powder, and mixed in the pot mill for 12 hours to be a starting raw material. This raw material was filled into a mold form (mold size of 220 mm×220 mm×H150 mm) using a uniaxial press device and compressed at a uniaxial press pressure of 10 MPa to be molded. This press molded body (size of about 220 mm×220 mm×t85 mm), which was put into a thick vinyl bag and sealed after deairing, was put into a molding part (inside size: inside diameter 350 mm×H120 mm) of a cold isostatic pressing (CIP) device. Clean water was filled into the space between the vinyl bag with this press molded body therein and the molding part of the CIP device, and isostatic pressing was conducted at a molding pressure of 20 MPa, leading to a CIP molded body (size of about 215 mm×215 mm×t75 mm). Preliminary sintering at 600° C. for 6 hours in an air atmosphere was conducted on the molded body, so as to obtain a preliminary sintered body having a size of about 208 mm×28 mm×t72 mm. This preliminary sintered body was heated from room temperature to 870° C. at a fixed rate for 6 hours in a nitrogen atmosphere, and the temperature was held there for 6 hours. It was then raised to 1100° C. at a fixed rate for 2 hours and held there for 1 hour. Heating was then stopped, and the temperature was lowered by self-cooling (furnace cooling) for about 20 hours to 100° C. at which time it was previously set to take out the sintered body, after which it was taken out. The bulk density of the CaF2 sintered body was calculated at 3.05 g/cm3 (relative density of 95.9%, and the true density of CaF2 is 3.18 g/cm3) from the rough size (193 mm×193 mm×t62 mm) and the weight thereof. The sintering state was good. As the evaluation results, a sintered body in a compact sintering state could be obtained and the mechanical strength was sufficient as shown in Table 2. However, since a large quantity of fast neutrons remained, there was a big problem of the moderation performance to neutrons left. This result indicated that a CaF2 sintered body was inferior to a MgF2 sintered body in characteristics as a moderator even if the CaF2 sintered body was sufficiently compact. It is possible to be used as a moderator to restrict the radiation velocity of radioactive rays of every kind such as neutrons.

abstract

A support grid for a nuclear fuel assembly, the fuel rod assembly having a generally cylindrical fuel rod with a diameter, wherein the support grid includes a frame assembly having a plurality of generally uniform cells, each the cell having at least one wall and a width and at least one generally cylindrical tubular member having a cell contact portion with a greater diameter and at least one helical fuel rod contact portion with a lesser diameter, the cell contact portion and the fuel rod contact portion joined by a transition portion, the greater diameter being generally equivalent to the cell width, and the lesser diameter being generally equivalent to the fuel rod diameter such that a fuel rod disposed in the tubular member would engage the inner diameter. Wherein the least one tubular member disposed in one cell of the plurality of generally square cells so that the cell contact portion engages the at least one cell sidewall.

050376012

summary

BACKGROUND OF THE INVENTION The glass-pool, air-cycle nuclear power plant of this invention is designed as an isolated system that requires minimal monitoring and is of a "walk-away" type, that is, one that can be shut down and decommissioned without any external intervention other then the poisoning of the nuclear reaction. In such event, the containment structure that contains the glass matrix pool and reaction core solidifies into a glass solid that can remain in place or be removed to a storage site. Recent disasters and near disasters in the operation of existing nuclear power plants of large size have required a reevaluation of the technology of nuclear power plant design. Far greater attention has been placed on power plants that are considered "passively-safe," that is, which do not require the intervention of an operator during a nuclear crisis in order to return the plant to a safe operating condition. The expense and complexity of current and future designs of light water reactor plants have required the nuclear industry to rethink its nuclear energy goals and have generated renewed interest in smaller, modular type plants that operate without the use of water as a coolant or as a steam generating medium. Renewed interest in more inherently safe designs such as liquid sodium systems, including static designs that do not require sodium pumps, such as that proposed in my prior patent, entitled "Nuclear Power Plant With On-Site Storage Capabilities," U.S. Pat. No. 4,313,795, issued Feb. 2, 1982. In that patent there is disclosed a nuclear reactor power plant having a gas cycle that utilizes superheated steam in its superheated state throughout the cycle. The use of a gas cycle reactor avoids a motive substance that must undergo a phase change. The use of a substance that has a phase change between liquid and gas, can typically result in emergency conditions. For example, when quantities of water contact high temperature core material the explosive reaction releases large volumes of contaminated steam. This is the heart of the traditional disaster scenario. Operating the reactor core in the very material that is to constitute its entombment on decommissioning, provides an attractive safety feature that other plants of advanced design appear to lack. This feature can provide a attractive solution to the problem of decommissioning and disposal of reactor cores. The use of new reactor fuel sources utilizing thorium/uranium.sup.233 in encapsulated fuel pellets with neutron moderation and containment by graphite shells and casings, provides the basis for advanced designs of walk-away nuclear power plants that require little or no monitoring during the life of operation of the plants. By use of smaller modular systems that are standardized with lower power goals which do not include failure prone internal or external liquid circulation pumps, the goal of a passively-safe or a walk-away nuclear power plant can realistically be achieved. One of the crucial problems facing the nuclear power industry in the United States is the fact that, all of the nuclear plants that have been constructed to date are different from one another. In addition to the huge capital cost, large scale, custom power plants cause difficulty in staffing and safe monitoring of plant operation. Furthermore, at the time of decommissioning, each plant must be considered as a separate entity for which a decommissioning plan must be devised that in many cases can result in decommissioning costs that exceed the original cost of construction. With a lower ultimate power goal for each plant, the system design can be standardized. By simply multiplying the number of identical plants, any desired greater power capacity can be obtained. Given a substantial flexibility in power rating and design, small inexpensive plants under one megawatt can be placed in operation to test operating parameters over a larger number of units at minimal financial and safety risk. The glass-pool, aircycle, nuclear power plant described and claimed herein resolves many of the current problems in the design of a safe power plant that utilizes fissionable nuclear materials that will not adversely impact the environment during operation or after shut-down. SUMMARY OF THE INVENTION This invention relates to a nuclear power plant and in particular to a glass-pool, gas-cycle plant having a thorium/uranium.sup.233 reactor in a glass matrix that is designed to constitute the heat dissipating core during operation, and, the inert tomb upon deactivation. The nuclear power plant of this invention couples a safe thermal source with a safe conversion means for converting thermal energy of a nuclear reaction to useful power, for example, electricity. Because the design of the power plant is directed to lower power goals, the thermal energy can also be converted directly to mechanical work useable on-site, for example, in pumping irrigation water. The design concept is such that the plant can be operated in an isolated environment as a self-contained system that requires no external support to either monitor operations or respond to an emergency situation. Key to the isolated system concept is the combination of an energy core that is immersed in a glass matrix that provides a heat sink to allow operation of the core at maximum temperature with the molten pool becoming the entombment matrix on solidification. The glass matrix includes in its composition fertile thorium material that is reduced in proportion to inert silicates as the distance from the central fissile core increases. During nuclear reaction, the glass matrix is in a molten state with a viscosity that increases as the distance from the core increases. The core and glass pool are encapsulated in a containment structure that is of a neutron reflecting substance such as graphite. The containment structure has a thermally conductive casing that provides a heat exchange from the glass-pool, thermal sink to a closed-cycle gas system. The other primary feature that insures the safety of the device is the use of a power extraction system that has a drive medium that does not undergo a phase change from liquid to gas. The use of a liquid to gas drive medium has been a significant contributor to the safety problems of prior art devices. In the preferred embodiment the gas is simply air. A unique divided cycle enables the effective use of air to comprise the motive force in an enclosed system. The unique, dual-path, air-cycle system utilizes a common compressor for each of two paths, with the compressor outlet coupled to a first path that communicates with the nuclear thermal source and a second path that communicates with an intercooler before being supplied to a turbine. Preferably, the compressed air from both sources drives a common turbine with the air from both sources combining in a common collector where the divergent temperatures are effectively moderated for return to the compressor. The nuclear reaction is preferably accomplished by utilizing a thorium/U.sup.233 breeding reaction in a glass matrix that on activation provides both a starting fissile material and a fertile feed material to continue a long term nuclear reaction preferably without the addition of more fuel. The life of the reaction can be determined at the time the plant is commissioned. At the time of decommissioning, when the fuel reaction is diminishing to the point that adversely affects the thermodynamic efficiency of the plant, the reduced-level, nuclear reaction is finally poisoned with a probe of a neutron absorbing material such as boron, allowing the glass matrix and core to cease reaction and gradually cool to a solid glass block. The entire core and encapsulation structure can either be removed for easy transportation as a vitrified solid to a central storage location, or can be entombed on site. If entombed on site, the volume of open space in the heat exchange area, between the pressure vessel and the encapsulation structure can be filled with a solidifying substance such as concrete, doped with a neutron absorber such that the outer containment structure totally entombs the decommissioned reactor capsule and shields any low level residual radiation that may be emitted from the core. These and other features of the preferred embodiment of this invention will be considered in greater detail in the detailed description of the preferred embodiments that follows.

claims

1. An optical element comprising a substrate and at least a pair of alternate layers provided on the substrate, the alternate layers each having an Mo layer and an Si layer,wherein the Mo layer contains 90% or more of 98Mo and the Si layer contains 99% or more of 23Si. 2. An optical element comprising a substrate and at least a pair of multilayer films of a four-layer structure provided on the substrate, each of the at least the pair of the multilayer films having an Si/B4C/Mo/B4C structure in this order from the substrate,wherein the Mo layer contains 90% or more of 98Mo, the Si layer contains 99% or more of 23Si and the B4C layer contains 99% or more of 11B. 3. An X-ray mirror comprising the optical element according to claim 1. 4. An X-ray mirror comprising the optical element according to claim 2.

047479949

description

DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention is illustrated in FIG. 1 which utilizes a switchgear mechanism 10 as a reactor trip breaker RTB. The switchgear mechanism 10 receives power from an AC power bus 12 in a reactor control system and supplies power to a rod positioner 14 which controls the position of control rods in a pressurized light water nuclear reactor. The switchgear 10 can be a conventional switchgear mechanism, such as Westinghouse Part No. DS206 or DS4l6. Such a switchgear mechanism 10 conventionally includes an undervoltage trip coil 16 which is de-energized while the shunt trip coil 18 is energized, when an undesirable condition is detected in the nuclear reactor. According to the present invention, the shunt trip coil 18 in the switchgear 10 is provided power via a potential transformer 20, such as a Westinghouse type PXA, style No. 592A78lG0A, and a rectifier 22 which may comprise diodes 28, each diode may be a 1N3990, available from Westinghouse Electric Corporation. The shunt trip coil 18 is energized by activation of either a manual trip switch 24 or an automatic trip switch 26 connected to an automatic protection system. Since the potential transformer 20 is supplied with power by the switchgear 10, when the shunt trip coil 18 is energized to interrupt the supply of power to the rod positioner 14, the supply of power to the potential transformer 20 is also interrupted, thereby de-energizing the shunt trip coil 18. The rectifier 22 outputs a DC voltage which can be monitored to determine the ability of the trip coil control system to activate the shunt trip coil 18 and the condition of the power supplied to the rod positioner 14. The DC voltage will have a ripple, as illustrated in FIG. 1, if just three diodes 28 are used in the rectifier 22. One embodiment of the present invention includes a power monitoring device 30 to monitor the DC voltage output by the rectifier 22. The power monitoring device 30 comprises a voltage/optical converter 32, such as a Hewlett-Packard # HFBR-1201, which provides isolation between the trip coil control system and monitoring devices in the reactor control system. The voltage/optical converter 32 outputs a light signal which can be tranmitted over an optical cable 34, such as a Hewlett-Packard # HFBR-300. The light signal generated by a simple voltage/optical converter 32 is sufficient to transmit information regarding whether the rectifier 22 is outputting a DC voltage and further provides an indication regarding the condition of the power supply to the rod positioner 14, such as missing phases in the AC power. If additional information, such as voltage level, is desired, an analog/digital converter 36 can be added to the monitoring device 30. The monitoring device 30 may also include additional components at a remote distance from the switchgear 10. Such components are illustrated in FIG. 2 as receiving the light signal via the optical cable 34. An optical/voltage converter 40, such as a Hewlett-Packard # HFBR-2201, converts the light signal back into a DC voltage which is supplied to a microprocessor board 42, such as an Intel 88/40. The microprocessor board 42 includes a signal conditioner 44, microprocessor 46 and an output interface 48 for interfacing with other devices 50 in the reactor control system. Each reactor trip breaker 10 in a conventional reactor control system may be connected to several signal processing units such as the microprocessor board 42 illustrated in FIG. 2. With the addition of more voltage optical voltage/converters 32 to receive the output of the rectifier 22, several microprocessor boards 42 can be connected to monitor a single reactor trip breaker 10. The many features and advantages of the present invention are apparent from the detailed specification, and thus it is intended by the appended claims to cover all such features and advantages of the control system which fall within the true spirit and scope of the invention. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation illustrated and described, accordingly, all suitable modifications and equivalents may be resorted to, falling within the scope and spirit of the invention.

claims

1. A segmented waste rod comprising:a plurality of burnt rod segments,the rod segments being removably mated to each other in an axial direction,the rod segments being individually cladded, andthe rod segments forming a continuous multi-segment waste rod; andat least one of the rod segments being a waste rod segment containing at least one piece of non-fuel waste sealed within the waste rod segment after harvesting isotopes produced in the waste rod segment in a nuclear reactor from the waste rod. 2. The segmented waste rod of claim 1, wherein the at least one piece of waste includes material from a harvested burnt rod segment. 3. The segmented waste rod of claim 2, wherein the at least one piece of waste is selected from the group consisting of a cladding, a container assembly, a male end plug, and a female end plug. 4. The segmented waste rod of claim 2, wherein the segmented waste rod has a length and outer diameter substantially similar to the burnt segmented rod. 5. The segmented waste rod of claim 1, wherein at least one of the rod segments not containing waste contains spent nuclear fuel. 6. The segmented waste rod of claim 1, further comprising:a lower extension removably mated to a first rod segment of the plurality of rod segments at a first end of the segmented waste rod; andan upper extension removably mated to a second rod segment of the plurality of rod segments at a second end of the segmented waste rod, the upper extension and the lower extension being recycled from a burnt segmented rod. 7. The segmented waste rod of claim 1, wherein the rod segments are removably mated via a male end plug and a female end plug. 8. A method for handling nuclear waste, the method comprising:harvesting isotopes produced in a rod segment in a nuclear reactor from the rod segment;placing the waste into the rod segment so as to form a waste rod segment;sealing the waste rod segment; andplacing the waste rod segment into a segmented waste rod by axially mating the waste rod segment to at least one of an upper extension, a lower extension, a rod segment containing spent nuclear fuel, and another waste rod segment. 9. The method of claim 8, further comprising:preparing the waste for placement into the waste rod segment before placing the waste into the waste rod segment. 10. The method of claim 8, wherein the waste includes material from a harvested burnt rod segment. 11. The method of claim 10, wherein the waste includes at least one of a cladding, a container assembly, a male end plug, and a female end plug of the harvested burnt rod segment. 12. The method of claim 8, further comprising:placing the segmented waste rod into a fuel bundle. 13. The method of claim 8, wherein placing the waste into the waste rod segment includes compressing the waste into the waste rod segment. 14. The method of claim 8, wherein the sealing the waste rod segment includes welding one of a female end plug and a male end plug to an open end of the waste rod segment. 15. A method of handling waste generated from a process of harvesting isotopes from a burnt segmented fuel rod, the method comprising:rolling, cutting, and curling cladding from a rod segment harvested for isotopes;crushing at least one end plug removed from the rod segment harvested for isotopes;placing the cladding, at least one end plug, a container assembly removed from the rod segment harvested for isotopes, and a cap of the container assembly into a waste rod segment;sealing the waste rod segment; andplacing the waste rod segment in the burnt segmented fuel rod in a location from which the rod segment harvested for isotopes was taken so as to form a segmented waste rod. 16. The method of claim 15, further comprising:inserting the segmented waste rod into a burnt fuel bundle in a location from which the burnt segmented fuel rod was taken.

description

The present invention generally relates to a debris mitigation system and a lithographic apparatus that includes the debris mitigation system. More specifically, the invention relates to a debris mitigation system for trapping contaminant material coming from a debris-generating radiation source. A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. comprising part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate. In addition to EUV radiation, radiation sources used in EUV lithography tend to generate contaminant material that may be harmful for the optics and the working environment in which the lithographic process is carried out. Hence, in EUV lithography, a desire exists to limit the contamination of the optical system that is arranged to condition the beams of radiation coming from an EUV source. To this end, it is known to use a so-called rotating foil trap, for instance, as disclosed in U.S. Pat. No. 6,838,684. A typical foil trap uses a high number of closely packed foils that are aligned generally parallel to the direction of the radiation generated by the EUV source. Contaminant debris, such as micro-particles, nano-particles and ions can be trapped in walls provided by foil plates. Thus, the foil trap may function as a contamination barrier that traps contaminant material from the source. Generally, these foil traps are designed to have a sufficiently large dimension to trap virtually any contaminant particle traveling through the trap. Indeed, a large fraction of debris is captured since the velocity directions are mostly non-parallel to the foil plates so that impact of the contaminant material follows eventually. Also, smaller particles travel in typical random diffusion-like paths in which most of the particles are trapped eventually. However, a small fraction of particles travel in a direction and at a velocity that allows the particles to travel through the foil trap, which may cause undesired contamination of the optics. These are mostly micro and nanometer sized particles traveling at speeds <1000 m/s. Such particles may be stopped using a rotating foil trap. However, some of these particles have a velocity that is too high to be stopped by the rotating foil trap (typically this is the case for nanometer sized particles and for ions/fast neutrals). To improve the debris mitigating function of the foil trap, electromagnetic deflecting fields have been proposed. However, a rotating foil trap functions as a rotor in a static electromagnetic field, which may impede the function thereof and cause undesired inhibiting of the foil trap rotation. It is an aspect of the present invention to reduce the inhibiting effect of an electromagnetic field while improving the debris mitigating effect of the rotating foil trap. According to an embodiment of the invention, a debris mitigation system for trapping contaminant material coming from a debris-generating radiation source is provided. The system includes a contamination barrier constructed and arranged to rotate about an axis, and a magnet structure constructed and arranged to provide a magnetic field for deflecting charged debris from the radiation source. The magnet structure is constructed and arranged to provide a magnetic field through the contamination barrier. The magnetic field, when passing through the contamination barrier, is oriented along planes generally coinciding with the axis of rotation of the contamination barrier. According to an embodiment of the invention, a lithographic apparatus is provided. The apparatus includes a patterning device constructed and arranged to pattern a beam of radiation, a projection system constructed and arranged to project the patterned beam of radiation onto a substrate, and a debris mitigation system constructed and arranged to trap contaminant material generated by a debris-generating radiation source. The debris mitigation system includes a contamination barrier constructed and arranged to rotate about an axis, and a magnet structure constructed and arranged to provide a magnetic field for deflecting charged debris from the radiation source. The magnet structure is constructed and arranged to provide a magnetic field through the contamination barrier. The magnetic field, when passing through the contamination barrier, is oriented along planes generally coinciding with the axis of rotation of the contamination barrier. FIG. 1 schematically depicts a lithographic apparatus according to one embodiment of the invention. The apparatus comprises: an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. UV radiation or EUV radiation); a support structure (e.g. a mask table) MT constructed to support a patterning device (e.g. a mask) MA and connected to a first positioner PM configured to accurately position the patterning device in accordance with certain parameters; a substrate table (e.g. a wafer table) WT constructed to hold a substrate (e.g. a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate in accordance with certain parameters; and a projection system (e.g. a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g. comprising one or more dies) of the substrate W. The illumination system may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof, for directing, shaping, or controlling radiation. The support structure supports, i.e. bears the weight of, the patterning device. It holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions, such as for example whether or not the patterning device is held in a vacuum environment. The support structure can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The support structure may be a frame or a table, for example, which may be fixed or movable as required. The support structure may ensure that the patterning device is at a desired position, for example with respect to the projection system. Any use of the terms “reticle” or “mask” herein may be considered synonymous with the more general term “patterning device.” The term “patterning device” used herein should be broadly interpreted as referring to any device that can be used to impart a radiation beam with a pattern in its cross-section such as to create a pattern in a target portion of the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so called assist features. Generally, the pattern imparted to the radiation beam will correspond to a particular functional layer in a device being created in the target portion, such as an integrated circuit. The patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography, and include mask types such as binary, alternating phase-shift, and attenuated phase-shift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted so as to reflect an incoming radiation beam in different directions. The tilted mirrors impart a pattern in a radiation beam which is reflected by the mirror matrix. The term “projection system” used herein should be broadly interpreted as encompassing any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system”. As here depicted, the apparatus is of a reflective type (e.g. employing a reflective mask). Alternatively, the apparatus may be of a transmissive type (e.g. employing a transmissive mask). The lithographic apparatus may be of a type having two (dual stage) or more substrate tables (and/or two or more mask tables). In such “multiple stage” machines the additional tables may be used in parallel, or preparatory steps may be carried out on one or more tables while one or more other tables are being used for exposure. The lithographic apparatus may also be of a type wherein at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, e.g. water, so as to fill a space between the projection system and the substrate. An immersion liquid may also be applied to other spaces in the lithographic apparatus, for example, between the mask and the projection system. Immersion techniques are well known in the art for increasing the numerical aperture of projection systems. The term “immersion” as used herein does not mean that a structure, such as a substrate, must be submerged in liquid, but rather only means that liquid is located between the projection system and the substrate during exposure. Referring to FIG. 1, the illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus may be separate entities, for example when the source is an excimer laser. In such cases, the source is not considered to form part of the lithographic apparatus and the radiation beam is passed from the source SO to the illuminator IL with the aid of a beam delivery system comprising, for example, suitable directing mirrors and/or a beam expander. In other cases the source may be an integral part of the lithographic apparatus, for example when the source is a mercury lamp. The source SO and the illuminator IL, together with the beam delivery system if needed, may be referred to as a radiation system. The illuminator IL may comprise an adjuster for adjusting the angular intensity distribution of the radiation beam. Generally, at least the outer and/or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may comprise various other components, such as an integrator and a condenser. The illuminator may be used to condition the radiation beam, to have a desired uniformity and intensity distribution in its cross-section. The radiation beam B is incident on the patterning device (e.g., mask MA), which is held on the support structure (e.g., mask table MT), and is patterned by the patterning device. Having traversed the mask MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and position sensor IF2 (e.g. an interferometric device, linear encoder or capacitive sensor), the substrate table WT can be moved accurately, e.g. so as to position different target portions C in the path of the radiation beam B. Similarly, the first positioner PM and another position sensor IF1 can be used to accurately position the mask MA with respect to the path of the radiation beam B, e.g. after mechanical retrieval from a mask library, or during a scan. In general, movement of the mask table MT may be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which form part of the first positioner PM. Similarly, movement of the substrate table WT may be realized using a long-stroke module and a short-stroke module, which form part of the second positioner PW. In the case of a stepper (as opposed to a scanner) the mask table MT may be connected to a short-stroke actuator only, or may be fixed. Mask MA and substrate W may be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks as illustrated occupy dedicated target portions, they may be located in spaces between target portions (these are known as scribe-lane alignment marks). Similarly, in situations in which more than one die is provided on the mask MA, the mask alignment marks may be located between the dies. The depicted apparatus could be used in at least one of the following modes: 1. In step mode, the mask table MT and the substrate table WT are kept essentially stationary, while an entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e. a single static exposure). The substrate table WT is then shifted in the X and/or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C imaged in a single static exposure. 2. In scan mode, the mask table MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The velocity and direction of the substrate table WT relative to the mask table MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width (in the non-scanning direction) of the target portion in a single dynamic exposure, whereas the length of the scanning motion determines the height (in the scanning direction) of the target portion. 3. In another mode, the mask table MT is kept essentially stationary holding a programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, generally a pulsed radiation source is employed and the programmable patterning device is updated as required after each movement of the substrate table WT or in between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography that utilizes programmable patterning device, such as a programmable mirror array of a type as referred to above. Combinations and/or variations on the above described modes of use or entirely different modes of use may also be employed. FIG. 2 shows a basic configuration for a radiation system according to embodiments of the invention. In the Figure, the dashed lines represent EUV radiation 1 coming from an EUV source 2, which may be a discharge produced or a laser induced plasma source such as a tin, lithium or xenon source, which are known per se. The foil trap 3 functions as a contamination barrier for trapping contaminant material coming from the radiation source 2. To this end, the foil trap 3 is provided with a plurality of closely packed foil plates 4, typically about 100 arranged at a distance of about 0.3-5 mm (depending on radial distance). The foil plates 4 may have a length dimension in substantially the radial direction from the source 2 of about a few cm, for example. Preferably, the foil plates 4 lengths ranging from about 1.5-5 cm. Along a central axis, the source 2 may be shielded by a heat shield 5. The foil trap, also referenced as a contamination barrier, comprises a plurality of foil plates 4 positioned in respective planes which are parallel to a propagation direction of radiation 9. As is schematically indicated in FIG. 2, in the downstream direction of the radiation, a collector element 6 is present and has a converging power for collecting and converging the EUV radiation from the EUV source 2 to further EUV optics. Such a collector element 6 may generally be cylinder symmetric along a central axial direction and comprises concentrically curved shell formed reflective surfaces 7 that are stacked at a distance ranging between about 1 and 7 cm. As illustrated in FIG. 2, a magnetic field 8 may be arranged in the area between the source 2 and a foil trap 3. The magnetic field 8 may function to deflect charged particles from a trajectory that would leave the particles unhindered through the foil trap 3. However, when rotating the foil trap 3 through the magnetic field 8, the flux of magnetic field lines on the platelets 4 will change. As a result, a current may be induced, which in turn will induce a magnetic field that results in a force opposite to the force driving the foil trap 3. This may make it difficult to rotate the foil trap 3 at the desired speed. According to an aspect of the invention, a magnet structure is used to provide the magnetic field 8 through the contamination barrier 3. When passing through the contamination barrier 3 (see FIG. 3), the magnet field is oriented along planes generally coinciding with the axis of rotation 10 of the foil trap 3. Although the foil trap 3 can have any form and a magnetic flux through the foil trap 3 can be defined as a sum of fluxes passing through all constituent parts of the foil trap, in the embodiment of FIG. 2, the plates 4 are preferably oriented parallel to the magnetic field 8. In this respect, the magnetic field 8 is created so that magnetic field lines traverse the plates 4 in an axial direction, relative to the axis of rotation of the foil trap 3. In another respect, the magnetic field 8 may be provided to have magnetic field lines traversing the plates 4 in a radial direction, relative to the axis of rotation. According to another aspect of the invention, an outer magnet structure 11 is arranged providing a passage to the radiation, in addition to provide a magnetic field 8 for deflecting charged debris. The magnet structure 11 is preferably arranged to provide a magnetic field having a symmetry axis generally coinciding with the axis of rotation. In particular, the symmetry can be rotational symmetry about the symmetry axis and/or reflection symmetry in one or more planes passing through the symmetry axis. Preferably, the magnetic field 8 is provided generally invariant for a rotation of the rotating contamination barrier, that is, a rotation, less than 360° over a specified number of angles. More preferably, the magnetic field is provided generally invariant for any rotation angle of the rotating contamination barrier. In addition, another debris mitigation system may be present in this area between the source 2 and the foil trap 3, or between foil trap 3 and collector 6, for instance, using a buffer gas for thermalizing the ions coming from the EUV source. Then, the ions may be stopped by a stationary foil trap, in the same way as normal atomic debris is stopped. The magnetic field may rotate along with the foil trap 3 or may be stationary relative to that trap 3. FIG. 3 shows a further detailing of the magnetic structure 9, 11 for the magnetic field 8 shown in FIG. 2. The embodiment uses an outer magnet structure 11 and a central magnet structure 9 opposed relative to each other to provide a generally radially oriented magnetic field. In the current example, the outer magnet structure 11 is a hollow structure comprising axially opposed magnetic poles, that is, having a magnetic axis substantially parallel to the axis of rotation 10. A central magnet structure 9 is provided having magnetic poles for providing a magnetic axis generally parallel to the rotation axis 10, and having poles opposite to the poles of the hollow structure. Accordingly, at least on the axial outer ends of the magnetic structure, a generally radially oriented magnetic field is provided. The first magnet structure 9 is incorporated into the rotation axis 10 of the foil trap 3 and therefore it will rotate along with the foil trap 3. It should be noted that it is also possible to keep the magnet 9 stationary, and have a rotating foil trap 3 surrounding the axial magnet. The advantage of this is that it may be easier to equip the magnet with cooling. For the same reason, the magnet structure 9 is preferably stationary, but it may also be incorporated into the rotating part of the rotating foil trap 3, for example, to increase the structural strength. The second magnet structure 11 may be placed at a distance from the foil trap 3, but surrounding it and causing magnetic field lines to run in radial directions. FIG. 4 shows a cross-sectional view, in the viewing direction of the rotation axis, for an alternative embodiment. Here, the magnetic field is not fully rotation symmetric, but the magnetic field is provided generally invariant for a rotation of the rotating contamination barrier over an angle of 180°. The magnetic structure comprises an outer hollow magnet structure 11 that comprise semicircular radially opposed poles, and a central magnet structure 9 is provided that comprises radially opposed magnetic poles opposite to the poles of the hollow structure 11. The outer structure 11 is preferably an integral structure of radially aligned oppositely arranged curved magnetic structures 10 and 11 to produce a magnetic field that is radially aligned relative to the central axis of rotation. Due to limited rotational symmetry of the magnetic field, components surrounding the rotating foil trap may to some extent be exposed to a varying magnetic field, if the magnetic structures 10 and 11 rotate along with the foil trap. If structures 10 and 11 are stationary, the rotating foil trap may to some extent be exposed to a varying magnetic field. In another embodiment depicted in FIG. 5, a magnetic structure is shown for incorporation into the rotating foil trap 3 or for providing stationary relative thereto. The structure 11 is arranged concentrically relative to an axis of rotation, for example, as a static ring provided around the contamination barrier. The structure comprises a plurality of linear magnets having a magnetic axis aligned and arranged radially relative to a center axis of the contamination barrier. By increasing the number of magnets provided on the rotation axis and provided in a ring 12 concentric thereto at a distance, the magnetic field can be made more rotationally invariant. Typically, the number of magnets on the rotation axis and in the ring 12 may differ; for example, the number of magnets arranged in the ring 12 may be larger. Also, one of the magnetic structures 9, 11, respectively arranged axially or on a ring surrounding the rotational axis may be omitted. In the embodiment illustrated in FIG. 5, the radially aligned magnets may be provided fixed relative to the center axis. Also, the magnets may be provided as a static ring provided around the rotating foil trap 3. FIG. 6 shows an embodiment wherein a magnetic deflecting field is formed by two opposing linear magnets 13 that have a magnetic axis located on the rotation axis. Thus, in this embodiment, the magnet structure may comprise linear magnets having a magnetic axis oriented concentric with the axis of rotation of the rotating contamination barrier. This magnetic field may be perfectly rotationally symmetric around the rotation axis of the rotational foil trap 3. Similarly, a symmetric magnetic field may be formed using two opposing hollow cylindrical magnets surrounding the rotating foil trap 3, or even using a single magnet instead of two opposing magnets. FIG. 7 shows calculation results for magnetic field strengths in an embodiment that includes a rotating foil trap having an axial length of 30 mm; and FIG. 8 shows the results in combination with a stationary foil trap serially aligned respective to the optical axis having a length of 40 mm. A foil spacing was taken to be about 2 mm and an average ionization degree of high energy ions (E/Z=2.5 kV and E/Z=3 kV) is taken to be about 8+. It is shown in FIG. 8 that using a magnetic field strength of about 0.15 T, ions with energy up to Ekin of about 400 keV can be stopped using a combined rotating foil trap and stationary foil trap. Without the stationary foil trap, ions with energy up to Ekin of about 10 keV can be stopped, as shown in FIG. 7; based on deflection of ions with minimum charge Z=6. In FIG. 7, a vertical deflection x(L) is given for a given magnetic field strength B and ion charge Z. The bold horizontal line indicates the foil trap spacing b. For values of x(L)>b, the ion will have a collision with the foil. In FIG. 8, a vertical deflection y(L) is given for a given magnetic field strength B and ion charge Z. The bold horizontal line indicates the foil trap spacing b. For values of y(L)>b, the ion will have a collision with the foil. Although the embodiment of FIG. 2 shows a rotating foil trap having a rotation axis directed towards the pinch of the radiation source, that is, in line with an optical axis, the rotation axis may also have a certain angle relative to a line of sight coming from the radiation source. Although specific reference may be made in this text to the use of lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein may have other applications, such as the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, liquid-crystal displays (LCDs), thin-film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “wafer” or “die” herein may be considered as synonymous with the more general terms “substrate” or “target portion”, respectively. The substrate referred to herein may be processed, before or after exposure, in for example a track (a tool that typically applies a layer of resist to a substrate and develops the exposed resist), a metrology tool and/or an inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. Further, the substrate may be processed more than once, for example in order to create a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers. Although specific reference may have been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention may be used in other applications, for example imprint lithography, and where the context allows, is not limited to optical lithography. In imprint lithography a topography in a patterning device defines the pattern created on a substrate. The topography of the patterning device may be pressed into a layer of resist supplied to the substrate whereupon the resist is cured by applying electromagnetic radiation, heat, pressure or a combination thereof. The patterning device is moved out of the resist leaving a pattern in it after the resist is cured. The terms “radiation” and “beam” used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g. having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) and extreme ultra-violet (EUV) radiation (e.g. having a wavelength in the range of 5-20 nm), as well as particle beams, such as ion beams or electron beams. The term “lens”, where the context allows, may refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic and electrostatic optical components. While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described. For example, the invention may take the form of a computer program containing one or more sequences of machine-readable instructions describing a method as disclosed above, or a data storage medium (e.g. semiconductor memory, magnetic or optical disk) having such a computer program stored therein. The descriptions above are intended to be illustrative, not limiting. Thus, it will be apparent to one skilled in the art that modifications may be made to the invention as described without departing from the scope of the claims set out below.

050080709

description

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The inventors have studied the fuel assembly shown in U.S. Pat. No. 4,587,090, i.e., the fuel assembly in which not only an enrichment but also an amount of a burnable poison in the upper region is larger than that in the lower region, and then found that the conventional fuel assembly suffers from the following new problems. Namely, the conventional fuel assembly suffers from a problem such that, in the case where it is desired to increase the spectral shift effect, as the burnable poison in the lower region of the fuel assembly is decreased, a maximum linear heat rating of fuel rods is considerably increased. If the number of the fuel rods that contains the burnable poison in the lower region or the concentration of the burnable poison contained in the fuel rods would be reduced, a neutron infinite multiplication factor would be increased in the lower region, so that the reactivity difference between the upper and lower portions of the reactor core becomes large. In addition, the thermal neutron flux density would be increased in the lower region of the reactor core so that the burning of the burnable poison would be hastened to further increase the reactivity difference between the upper and lower regions. For that reason, there would be a fear that the operational limit for the maximum linear heat rating would be exceeded because of the lower region peak in the axial power distribution at a certain period during the operational cycle. A variety of arrangements of the fuel assembly for overcoming the above-described new problems have been studies. The results of such studies will be explained hereinunder. The inherent function of the burnable poison is to control the excess reactivity at the initial stage of the operational cycle. Since the burnable poison is a strong neutron absorption material, the material should be prevented from being unburnt at the final stage of the operational cycle. Also, in the burnable poison such as gadolinia, the undue absorption of the neutron by the nuclides after the neutron absorption is not negligible. It is, therefore, important to reduce the burnable poison within the range where the reactivity at the initial stage of the cycle can be moderated in view of the economical point of the neutron. In view of the above-described point, it is very effective to reduce the amount of the burnable poison in the lower region of the fuel assembly. FIGS. 1A to 1D show the differences of operation changes, respectively, in the case (1) where the amount of gadolinia (Gd.sub.2 O.sub.3), i.e., the burnable poison is decreased in the upper region of the fuel assembly, in the case (2) where the amount of gadolinia is kept constant between the upper and lower regions of the fuel assembly, and in the case (3) where the amount of gadolinia is decreased in the lower region of the fuel assembly. In the case (1) where the amount of gadolinia in the lower region is decreased, the reactivity increment in the final stage of the operational cycle is remarkable due to the spectral shift effect as described above and shown in FIG. 1A. Since the void fraction in the initial stage in the operational cycle is increased, the excess reactivity is rather suppressed to a low level irrespective of the small amount of gadolinia (FIG. 1B). Also, since the reactivity increment in the reactor core is decreased when the operation state is in the transient stage from the operation state to the cold condition, the shutdown margin of the reactor is increased as shown in FIG. 1C. As described above, it is possible to enhance the fuel utilization without degradation of the shutdown margin of the reactor or the excess reactivity by reducing the amount of the gadolinia in the lower region of the fuel assembly. However, if the reduction of the amount of the gadolinia in the lower region of the fuel assembly is performed simply by decreasing the concentration of the gadolinia in the lower region or by decreasing the number of the fuel rods containing in the lower region thereof the gadolinia, the maximum linear heat rating is considerably increased as shown in FIG. 1D. The above-mentioned features of the present invention can be achieved on the basis of the concept to optimize the change in burning of power distribution in the reactor core axial direction power and of the burnable poison amount in the lower region of the fuel assembly in which the maximum spectral shift effect may be obtained without remarkably increasing the maximum linear heat rating. FIG. 2 shows a typical burning change at the axial power peaking. FIG. 3 shows the power distribution in the axial direction of the reactor core with respect to each burnup at the points A to E shown in FIG. 2. In FIG. 2, the lower peak of the axial power distribution at the initial of the operational cycle (point A) is weakened once at the point B and again strengthened most at the point C. Thereafter, the axial power distribution is rapidly flattened and weakened, and past the point D, the upward peaked power distribution is provided. With respect to such a change, as shown in FIG. 4, the peaking of the lower region is kept at a high level before the middle of the operational cycle while the axial power peaking maximum is being kept constant (in the right side condition of FIG. 4). As a result it is possible to increase the spectral shift effect without increasing the maximum linear heat rating. A plurality of groups of fuel assemblies that have different operational cycles are installed in the reactor core. According to the inventors' analyses, the action of the axial power peaking in the initial stage of the operational cycle mainly depends upon the burnup change in reactivity ratio between the upper region and lower region of the fuel assemblies in the first and the second operational cycles, and depends upon a relative power ratio of the fuel assemblies in the first and the second operational cycles. The local maximum peaking value of the axial output in the intermediate stage of the operational cycle depends upon the maximum value of the reactivity ratio between the upper and the lower regions of the fuel assemblies in the first operational cycle. Therefore, if the change of the neutron infinite multiplication factor in the initial burnup stage is adjusted by the amount of gadolinia of the fuel assemblies to suitably set the burnup change of the reactivity ratio of the upper and the lower regions of the first cycle fuel assemblies, a desired axial power peaking change as shown in the right portion of FIG. 4 may be obtained. The reactivity value of the strong neutron absorption material such as gadolinia depends upon a surface area thereof. The more the number of the fuel rods containing the gadolinia becomes, the more the reactivity moderating effect becomes. FIG. 5 shows the relationship between the number of the fuel rods containing the gadolinia and the neutron infinit multiplication factor. The neutron infinite multiplication factor of a fuel assembly composed of twelve fuel rods containing gadolinia by 4.5 wt% and four fuel rods containing gadolinia by 3.5 wt% is, in the initial state of the operational cycle, smaller by 3.3% .DELTA.k than that of a fuel assembly in which the number of the fuel rods containing gadolinia by 3.5 wt% is less by two than that of the former case. However, at the final stage when gadolinia is burnt up, there is only difference in maximum value of the neutron initiate multiplication factor only by 0.3% .DELTA.k because the value does not have a direct relationship with the number of the fuel rods containing the gadolinia in the case where the gadolinia concentration is kept constant in the fuel rods. When the number of the fuel rods containing the gadolinia in the lower portion of the fuel assembly is decreased, the lower region power peaking of the fuel assembly is raised, as shown in FIG. 6A, in particular at the initial stage of the operational cycle. In accordance with this phenomenon, the burnup rate difference between the upper and the lower regions of the fuel assembly is more enlarged, so that the lower region power peaking will be somewhat raised during the intermediate stage of the operational cycle. The concentration of the gadolinia contained in a single fuel rod will affect the burnup period of gadolinia. As shown in FIG. 7, the neutron infinite multiplication factor at the initial burnup stage may be kept within a short range of about 1.2% .DELTA.k according to the gadolinia concentration. However, if the concentration of gadolinia is low, the gadolinia will quickly be burnt up, so that the burnup reaching the maximum value of the infinite multiplication factor will be accelerated to provide a difference of 1.8% .DELTA.k in the maximum value of the neutron infinite multiplication factor. Therefore, the concentration of the gadolinia will affect the magnitude of the lower region peaking in particular in the intermediate stage of the operational cycle. When the concentration of gadolinia in the lower region of the fuel rod is increased, as shown in FIG. 6B, the power peaking in the lower region of the fuel assembly may be lowered mainly in the intermediate stage of the operational cycle. The solid line in FIG. 7 indicates the characteristics of the fuel assembly composed of twelve fuel rods containing gadolinia by 4.5 wt% and four fuel rods containing gadolinia by 3.5 wt%. The dotted line indicates the characteristics of the fuel assembly composed of sixteen fuel rods containing the gadolinia by 3.5 wt%. The dot and dash line indicates the characteristics of the fuel assembly composed of twelve fuel rods containing gadolinia by 5.5 wt% and four fuel rods containing gadolinia by 3.5 wt%. The axial power peaking control effect may be ensured by the combination of the number of the fuel rods containing the gadolinia and the gadolinia concentration to obtain the axial power peaking change close to the right portion shown in FIG. 4. Namely, the number of the fuel rods containing the gadolinia is decreased in the lower region of the fuel assembly, and the gadolinia concentration in that region is increased, so that the portion corresponding to the trough in the axial power peaking change may be raised in the initial stage in the operational cycle and the portion corresponding to the crest in the axial power peaking change may be lowered in the intermediate stage of the operational cycle. The adjustment of the gadolinia amount at which such characteristics may be obtained corresponds to the case where the gadolinia concentration which is lowest in the lower region of the fuel rods is kept at zero. However, the above-described fuel assembly is not constructed so as to control the axial power peaking at the very initial stage of the operational cycle. Namely, since the number of the fuel rods containing the gadolinia in the lower region of the fuel assembly is reduced, the power distribution in the transverse cross-section of the fuel assembly is made uniform to reduce the local power peaking. Therefore, the increment of the linear heat rating is small relative to the increment of the power peaking in the lower region of the fuel assembly. However, as the number of the fuel rods containing the gadolinia in the lower region of the fuel assembly is decreased, the peaking of the power in the lower region in the initial stage of the operational cycle is rapidly increased. For that reason, if the number of the fuel rods containing the gadolinia in the lower region of the fuel assembly is decreased to exceed some lower limit, the linear heat rating will be at maximum in the initial stage of the operational cycle. In order to improve this, it is preferable to reduce the lowest gadolinia concentration in the lower region to a rather small level that is not zero. Namely, the gadolinia at the lowest concentration (but not zero) in the lower region of the fuel rods only functions to suppress the power in the lower region at the very initial stage of the operational cycle. Thus, it is possible to shift the change of the axial power peaking relative to the burnup further to an ideal one. Subsequently, the fuel rods containing the gadolinia at minimum concentration in the lower region among the gadolinia containing fuel rods should be located as follows. (i) The reactivity in the lower region of the fuel assembly should be effectively reduced in the very initial stage of the operational cycle. (ii) Where the neutron spectrum is soft and the neutron importance is high, the amount of the burnable poison should be decreased as much as possible. Namely, it is preferable that the concentration of gadolinia should be low in the region close to the saturated water region such as locations adjacent to the water rods. In a region where the neutron flux density is high and the spectrum is soft, the reactivity moderating effect at the initial stage of burnup is remarkable even with a small amount of gadolinia. The small amount of gadolinia will be burnt rapidly, so that it is possible to readily attain an object to moderate the reactivity at the very initial stage of the operational cycle. Also, in view of the neutron absorption by the gadolinia nuclides after the neutron has been absorbed thereby, it is possible to enhance the reactivity after the burnup of the gadolinia by decreasing the amount of the gadolinia in the region adjacent to the saturated water region. In order to make, among the fuel assemblies, a wide region where the neutron spectrum is soft as described above, available is the fuel assembly where the water rod region is increased (that is, the number of the water rods is increased or the outer diameter of the water rods is increased). Incidentally, with respect to the enrichment of the upper and lower regions of the fuel assembly, if the upper region enrichment is higher than the lower region enrichment as shown in U.S. Pat. No. 4,229,258, the axial power distribution is made uniform to reduce the lower region power peaking. Since such a decreased amount of the power peaking in the lower region of the fuel assembly is not substantially related to the burnup of the operational cycle, it is effective to keep the axial power peaking substantially in a uniform state over the entire period of the operational cycle without largely changing the burnup of the axial power peaking. An embodiment which is obtained on the basis of the above mentioned inventors' study will be explained hereinunder. The preferred embodiment of the invention applied to a boiling water reactor will now be described with reference to FIGS. 8 and 9. A fuel assembly 10 according to the embodiment comprises an upper tie plate 11, a lower tie plate 12, a plurality of fuel rods 13, a plurality of fuel spacers 14 and two water rod WR. Each of the fuel rods 13 and the water rods WR are supported at its upper end portion to the upper tie plate 11 and at its lower end portion to the lower tie plate 12, respectively. Dioxide uranium pellets are filled in the fuel rods 13. The fuel spacers 14 are used to support the respective fuel rods 13 so that a space between the adjacent fuel rods 13 is kept at a predetermined distance. A channel box 15 is mounted on the upper tie plate 11 to surround the periphery of the fuel rod bundle supported by the fuel spacer 14. Six kinds of fuel rods 1 to 4, G1 and G2 are used as the fuel rods 13. The fuel rods are arranged in a regular square matrix of 9 rows and 9 columns. The two water rods WR are located in the central portion of the transverse cross-section of the fuel assembly and close to each other on a straight line connecting a pair of opposite corners of the channel box 15. An outer diameter of the water rod WR is larger than a pitch of the fuel rods. The two water rods WR occupies an area corresponding to the seven fuel rods 13 arranged at the same fuel rod pitch. Namely, seven fuel rods 13 are replaced by the two water rods WR. The fuel assembly having such an arrangement is shown in FIGS. 1, 7 and 8 of Japanese Patent Unexamined Publication No. 62-217186. The enrichment in the axial direction of the fuel rods 1 to 4, G1 and G2 and the gadolinia concentration distribution are shown in FIG. 10. Each fuel rod is filled with natural uranium in a range between a lower end of the effective length portion of the fuel and 1/24 of the effective length thereof, and in a range between 22/24 and 24/24 of the effective length portion with reference to the lower end of the effective length portion. The hatched regions of each fuel rod in FIG. 10 show the natural uranium filled portion. The fuel effective length portion means the region in which the fuel pellets are filled. None of the fuel rods 1 to 4 contain gadolinia. The fuel rods G1 and G2 contain gadolinia to be used as the gadolinia containing fuel rods. The average gadolinia concentration of the fuel rod G2 is lower than that of the fuel rod G1. The enriched uranium filling region of the fuel rods 1 to 4, G1 and G2 are in the range of 1/24 to 22/24 of the axial entire length of the fuel effective length portion with reference to the lower end of the fuel effective length. In the fuel rods 1, 3, 4, G1 and G2, the enrichment in the axial direction is uniformed in the enriched uranium filling region. The enrichments in the enriched uranium filling region of the fuel rods 1, 3, 4, G1 and G2 are as follows. The enrichment of the fuel rod 1 is at 4.85 %, the enrichment of the fuel rod 3 is at 3.90 %, the enrichment of the fuel rod 4 is at 3.20 wt%, the enrichment of the fuel rod G1 is at 4.20 wt% and the enrichment of the fuel rod G2 is at 3.8 wt%. The enrichment in the enriched uranium region of the fuel rod 2 is at 4.20 wt% in the range of 1/24 to 11/24 of the axial entire length of the fuel effective length portion with reference to the lower end of the fuel effective length portion, and at 4.85 % in the range of 11/24 to 22/24 of the axial entire length of the fuel effective length portion. The gadolinia concentration distributions of the fuel rods G1 and G2 are as follows. The gadolinia concentration of the fuel rod G1 is at 5.0 wt% in the range of 1/24 to 11/24 of the axial entire length of the fuel effective length portion with reference to the lower end of the fuel effective length portion, and the gadolinia concentration thereof is at 4.5 wt% in the range of 11/24 to 22/24 of the axial entire length of the fuel effective length portion. The gadolinia concentration of the fuel rod G2 is at 0.0 % in the range of 1/24 to 11/24 of the entire axial length of the fuel effective length portion, and the gadolinia concentration thereof is at 3.5 wt% in the range of 11/24 to 22/24 of the entire axial length of the fuel effective length portion. It is unnecessary to fill the natural uranium filling region with gadolinia since the power thereat is inherently small. If the gadolinia would be filled in this region, the gadolinia would be left after the completion of the operational cycle. The upper region is located above the position of 11/24 of the axial entire length of the fuel effective length portion from the lower end of the fuel effective length portion, whereas the lower region is located below that position. In the embodiment, twelve fuel rods G1 and four fuel rods G2 are used. The four fuel rods G2 are arranged at the position adjacent to the water rods WR that form the saturated water region therebetween. The twelve fuel rods G1 are arranged radially inward from the outermost periphery but are not arranged close to the water rods WR or the channel box 15. The channel box 15 is used to define the cooling water flow path within the fuel assembly 10 and to define a water gap (saturated water region) formed between the fuel assembly 10 when the fuel assembly 10 is installed within the reactor core. Namely, the fuel rods G1 are not arranged close to the saturated water region which is formed when the fuel assembly 10 is installed within the reactor core. With respect to the gadolinia within the fuel assembly 10, the amount of the gadolinia in the upper region of the fuel assembly 10 is expressed by the equation, 4.5 wt%.times.12+3.5 wt%.times.4=68, whereas the amount in the lower region of the fuel assembly 10 is smaller and expressed by the equation, 5.0 wt%.times.12+0.0 wt%.times.4=60. When the fuel rods G1 and G2 are divided into upper and lower regions, the maximum gadolinia concentration (5 %) portion and the minimum gadolinia concentration (0.0 %) portion are both present in the lower region in the gadolinia containing fuel rods. The above-described maximum and minimum gadolinia concentration portions are not present in the enriched uranium filling region in the upper region of the fuel assembly 10. Further, the fuel rods G2 containing the gadolinia at the minimum concentration are arranged in the vicinity of the water rods WR for enhancing the reactivity moderating effect by the converted nuclear seeds from the gadolinia after the burnup of the gadolinia, thereby keep the reactivity moderation at a minimum level. In the embodiment, to reduce the maximum heat rating, the average enrichment of the lower region of the fuel assembly is lower by 0.2 wt% than that of the upper region. FIG. shows the fuel assembly used for illustrating the effect of the embodiment, which fuel assembly is shown in Japanese Patent Unexamined Publication 62-217186, the gadolinia concentration and the enrichment distribution are kept uniform in both of regions. The fuel rods 1, 22, 23, 4, G3 and G4 shown in FIG. 12 are arranged to form a fuel assembly 16. The enrichments of the fuel rods 1, 22, 23, 4, G3 and G4 are at 4.85, 4.40, 3.80, 3.20, 4.40 and 3.80 wt%, respectively in the regions in the natural uranium filling region between the upper and the lower end portions thereof. The fuel rods G3 and G4 contain gadolinia with gadolinia concentrations of 4.50 and 3.50 wt%, respectively. FIG. 13 shows a change, relative to the burnup, of the maximum linear heat rating of the reactor core to which each of the fuel assemblies 10 and 16 is loaded. FIG. 14 shows a change, relative to the burnup, of the reactor average void fraction. In the fuel assembly 10 according to this embodiment, the amount of gadolinia in the upper region in the axial direction is larger than that in the lower region. Within the gadolinia containing fuel rods, the maximum and minimum gadolinia concentration portions are present only in the lower regions. Therefore, it is possible to keep the power peaking in the lower region at a high level in comparison with the fuel assembly 16 before the middle stage of the operational cycle. It is possible to keep the reactor core average void fraction in the first half of the operational cycle at a constant level that is larger than that of the fuel assembly 16, as shown in FIG. 14 in solid line. Thus, the spectral shift effect in the fuel assembly 10 is increased. The neutron effective multiplication factor at the final stage of the cycle according to this embodiment is higher than that of the fuel assembly 16 by 0.3% .DELTA.k. This shows the effect of 1% reduction of the necessary natural uranium amount. In the fuel assembly 10, it is possible to make the maximum linear heat rating smaller than the maximum linear heat rating ML that is at maximum in the fuel assembly 16. The case will be explained where the concept is applied to the fuel assembly 16, in which the fuel rods G2 with the gadolinia concentration of 4.5 wt% in the lower region and the gadolinia concentration of 3.5 wt% in the upper region and the fuel rods G3 with the gadolinia concentration of 0.0 % in the lower region and the gadolinia concentration of 4.5 wt% in the upper region are used as shown in FIG. 3B of U.S. Pat. No. 4,587,090. Namely, assume that, in the fuel assembly 16, the distribution of the gadolinia concentration of the fuel rods G3 is changed as the fuel rod G3 of U.S. Pat. No. 4,587,090, and the distribution of the gadolinia concentration of the fuel rod G4 is changed as the fuel rod G3 of U.S. Pat. No. 4,587,090. On the basis of this as the assumption, if the operation is started with the thus assumed fuel assembly being loaded on the reactor core, the maximum linear heat rating and the average void fraction are changed as follows. Namely, the maximum linear heat rating is changed between the solid line and the dotted line until reaching the position of about 6GWd/t (the intersection P between the solid line and the dotted line) in FIG. 13 and is changed along the dotted line after the point P. The reactor average void fraction of the assumed fuel assembly is changed in the same manner as the maximum linear heat rating. The reason why such characteristics are obtained in the assumed fuel assembly is that the maximum gadolinia concentration (4.5 wt%) within the gadolinia containing fuel rods is present in the lower region of the fuel rod G2 and the upper region of the fuel rod G3. In the fuel assembly 10 according to the embodiment, the maximum gadolinia concentration portion Gmax (for example, 5.0 wt%) within the gadolinia containing fuel rod is present in the lower portion of the fuel rod G1 (more exactly in the enriched uranium filling region within the lower region), the minimum gadolinia concentration Gmin portion (for example, 0.0 %) within the gadolinia containing fuel rod is present in the lower region of the fuel rod G2 (more exactly in the enriched uranium filling region of the lower region) and none of the maximum gadolinia concentration Gmax portion and the minimum gadolinia concentration Gmin portion within the gadolinia containing fuel rods are present in the upper region of the fuel rods G1 and G2 (more exactly in the enriched uranium filling region within the upper region). Accordingly, it is possible for the fuel assembly 10 to lower the maximum linear heat rating having the largest value exceeding that of the above-described fuel assembly assumed on the basis on FIG. 3B of U.S. Pat. No. 4,587,090. Also, since it is also possible for the fuel assembly 10 to keep the power peaking in the lower region of the first half of the operational cycle and the reactor void fraction at high levels than those of the assumed fuel assembly, the spectral shift effect is more enhanced than that of the assumed fuel assembly. Incidentally, the gadolinia concentration of the upper region (in particular in the enriched uranium filling region in the upper region) of each gadolinia containing fuel rod (G1 and G2) in the embodiment is between the maximum gadolinia concentration Gmax and the minimum gadolinia concentration Gmin. Since the fuel rods G1 having the maximum gadolinia concentration Gmax in the lower region thereof are disposed in the radial inner region from the outer periphery of the fuel assembly and away from the saturated water region, in which the neutron spectrum is hard, it is possible to effect the function of the gadolinia within the fuel rods G1 until the final stage of the operational cycle. The gadolinia in the upper and the lower regions of the fuel rods G1 is consumed in the final stage of the operational cycle. In the case where, as in the embodiment, the fuel rods G2 having the gadolinia concentration lower than that of the fuel rods G1 and having the gadolinia concentration in the upper region rather higher than in the lower region are disposed adjacent to the water rods WR, it is possible to enhance the shutdown margin of the reactor and effect the spectral shift at a maximum level. The fuel rods G2 have the function to increase the gadolinia amount in the upper region of the fuel assembly higher than that of the lower region. The function to generate the spectral shift is imparted to the fuel assembly 10. The natural uranium region located in the upper and the lower ends of each fuel rod has an effect to reduce the amount of neutron leaked downwardly and outwardly of the reactor core to enhance the economical aspect. In the embodiment, the fuel rods 13 are arranged in triplex closed loops from the outermost periphery of the fuel assembly to surround the two water rods WR. The two water rods WR are arranged in the central portion of the transverse cross-section of the fuel assembly and occupy an area corresponding to the area of the fuel rods 13 in a matrix of 3 rows and 3 columns. A diameter of the water rod WR is selected so that the water rods may be arranged in the above-described area. Thus, although the two water rods WR are disposed in such area, two fuel rods 13 may be further disposed besides the two water rods WR in the direction perpendicular to the straight line connecting the centers of the two water rods WR in the area where the fuel rods of 3 rows and 3 columns may be disposed. Therefore, the number of the replaced fuel rods 13 is reduced to seven (7=9-2). Also, since the two water rods WR are disposed in the central portion of the fuel assembly, it is possible to well moderate the fission neutron generated in the central portion of the fuel assembly 10 to enlarge the thermal neutron flux. Therefore, the thermal neutron flux in the central portion of the fuel assembly is enhanced and the thermal neutron flux distribution is flatted in the fuel assembly 10. Also, the fuel rods 13 and the water rods WR within the fuel assembly 10 are not considerably displaced from the symmetric arrangement thereof with respect to the center of the fuel assembly 10, so that it is possible to arrange the fuel rods having the same enrichment in a substantial symmetric arrangement. Another embodiment will be explained with reference to FIGS. 15 and 16, which is applied to the boiling water reactor. The fuel assembly 17 is substantially identical to the fuel assembly 10 with respect to the arrangement thereof. The differences therebetween reside in that the fuel rods 2 of the fuel assembly 10 are replaced by fuel rods 22 in which the enrichment of the enriched uranium filling region is uniform in the axial direction at 4.40 wt%, and the fuel rods G1 are replaced by fuel rods G5 that have a higher enrichment of 4.40 wt%. The other structure of the fuel assembly 17 is the same as the fuel assembly 10. The fuel assembly 17 has the same effect as that of the fuel assembly 10. Since the fuel assembly 17 uses the fuel rods 22, the maximum linear heat rating is increased by 2% in comparison with the fuel assembly 10. Also, the spectral shift effect is increased to enhance the effective multiplication in the final stage of the operational cycle by 0.05% .DELTA.k. Also, the shutdown margin of the reactor is enhanced according to the fuel assembly 17 rather than the fuel assembly 10. The reason for this is that since the enrichment of the upper region of the fuel assembly 17 is lower than that of the fuel assembly 10, the reactivity increment during the cold stop state becomes small. It should be noted that, according to this embodiment, the shutdown margin of the reactor is enhanced over the case where the enrichment and the gadolinia distribution are kept uniform in the axial direction in the fuel assembly 10. Under the condition that the enrichment distribution is kept constant in the axial direction and the gadolinia distribution in the upper region is kept constant, if the amount of the gadolinia in the lower region is decreased, the reactivity of the lower region is enhanced, so that the shutdown margin of the reactor is ensured. Still another embodiment of the invention will now be described hereinunder with reference to FIGS. 17 and 18. In this fuel assembly 18, the minimum gadolinia concentration Gmin is changed from 0.0 % to 1.0 wt%. Namely, in the fuel assembly 18, the fuel rods G6 are used instead of the fuel rods G2, the gadolinia concentration of the lower region of which is kept at 1.0 wt%. The four fuel rods G6 are arranged in the vicinity of the water rods WR in the same manner as the fuel assembly 10, that is, are confronted with the saturated water region. Thus, the thermal neutron flux density is kept at a high level. Therefore, it is possible to ensure the relatively large reactivity moderating effect even with a small amount of gadolinia. Also, the gadolinia concentration of the upper region of the fuel rods G6 is smaller than the gadolinia concentration of the upper region of the other gadolinia containing, fuel rods (G1) so that the gadolinia is fully burnt and is not left in the final stage of the operational cycle. An object of the arrangement of the plurality of water rods WR is to make uniform the power distribution within the fuel assembly. To this end, the gadolinia within the fuel rods G6 in the vicinity of the water rods WR is adapted to be burnt up fully when almost gadolinia is burnt up to increase the power. As a result, it is possible to increase the reactivity moderating effect at the initial stage of the operational cycle without sacrificing the effect on the power distribution uniformity. In this embodiment, the gadolinia amount in the upper region of the fuel assembly 18 is expressed by the equation, 4.5 wt%.times.12+3.5 wt%.times.4=68 and the gadolinia amount in the lower region thereof is expressed by the equation, 5.0 wt%.times. 12+1.0 wt%.times.4=64. The gadolinia amount in the lower portion is smaller than that in the upper portion. The fuel assembly 18 has the same effect as the fuel assembly 10. In particular, it is possible for the fuel assembly 18 to moderate the axial power peaking in the initial stage of the operational cycle by means of the fuel rods G6 in comparison with the fuel assembly 10. The linear heat rating of the fuel assembly 18 is then lowered. As a result, the maximum linear heat rating is lower by 3% than the fuel assembly 10 throughout the operational cycle. On the other hand the spectral shift effect is weakened since the gadolinia of the lower region of the fuel assembly 18 is somewhat increased, and the power distribution is made uniform as a whole. Therefore, the effective multiplication in the final stage of the operational cycle is lowered by about 0.1% .DELTA.k. However, on the basis of the fuel assembly 16 in which the enrichment is kept constant in the axial direction as shown in FIG. 11, although the maximum linear heat rating is lowered by 3%, the effective multiplication at the final stage of the operational cycle is increased by 0.2% k. Still another embodiment of the invention will now be described with reference to FIGS. 19 and 20. In this fuel assembly 19, a water rod WR1 having a cruciform cross section is arranged in the central portion of the fuel assembly 19. The fuel rods 1, 2, 23, 4, G1 and G7 are arranged in the fuel assembly 19 so as to surround the water rod WR1. The water rod WR1 sufficiently occupy a space corresponding to the space of the five fuel rods to keep the same water area as the fuel assembly 18. The number of the gadolinia containing fuel rods of G1 and G7 is sixteen. The twelve fuel rods G1 contains 4.5 wt% gadolinia in the upper region and 5.0 wt% gadolinia in the lower region. The other four fuel rods G7 are disposed close to the water rod WR1 and contain only in the upper region thereof the gadolinia of 3.5 wt%. The maximum gadolinia concentration 5.0 wt% portion and the minimum gadolinia concentration 0.0 % portion are present in the lower region of the fuel assembly 19 but not present in the upper region of the fuel assembly 19. Also, the gadolinia amount is smaller in the lower region of the fuel assembly 19. The enrichment of the lower region is lower than the upper region. However, the average of the enrichment difference between the upper and lower regions is at 0.2 wt% and is the same as the fuel assembly 10. The fuel assembly 19 has the same effect as the fuel assembly 10. However, in this embodiment, since the number of the fuel rods is larger by two than that of the fuel assembly 10, the average linear heat rating is lowered by about 2%. For that reason, it is possible to suppress the maximum linear heat rating relative to the fuel assembly 10. The characteristics of the reactor core on which the fuel assembly 19 is loaded are substantially the same as those of the fuel assembly 10. The improved effect of the characteristics relative to the uniform axial distribution and the enrichment in the fuel assembly 19 is also substantially the same as those of the fuel assembly 10. In the case where a large amount of recycle fuel may be used in a commercial light water reactor, it is possible to obtain the same effect with the plutonium instead of the uranium fuel. Further another embodiment of the invention will be described hereinunder with reference to FIGS. 21 and 22. This fuel assembly 20 is constituted by replacing all of fuel rods in the fuel assembly 10 with new set of fuel rods 31 to 35, and G8 to G11 shown in FIG. 22. These nine kinds of fuel rods are arranged in the fuel assembly as shown in FIG. 21. Each fuel rods is filled with natural uranium in a range between a lower end of the effective length portion and 1/24 of an entire effective length thereof. Further, in the fuel rods except for the fuel rods 32, natural uranium is further filled in a range between 22/24 of the entire effective length of the effective length portion and an upper end thereof. These upper and lower ends of the fuel rods 31, 34, 35, and G8 to G11 are the enriched uranium filling regions. The enrichments in the enriched uranium filling regions in the fuel rods 31, 34, 35 and G8 to G11 are 4.8 wt%, 3.7 wt%, 3.0 wt%, 3.7 wt% 3.9 wt%, 3.9 wt% and 3.9 wt%, respectively. The enrichment in each of the fuel rods is uniform in an axial direction thereof. The enriched uranium filling region in the fuel rod 33 is divided into an upper region and a lower region at a separating point of 11/24 of the axial entire length of the fuel effective length portion from the lower end thereof. The enrichment in the upper region of the enriched uranium filling region is 4.8 wt% and that in the lower region thereof is 4.1 wt%. The fuel rods G8 to G11 contain gadolinia in the enriched uranium filling regions. The fuel rod G9 contains gadolinia of 3.5 wt% allower the enriched uranium filling region thereof. The enriched uranium filling region of each of the fuel rods G8, G10 and G11 is divided into an upper region and a lower region at the same separating point as the fuel rod 33. The fuel rod G8 contains gadolinia of 4.5 wt% in the upper region thereof and gadolinia of 5.5 wt% in the lower region thereof. The fuel rod G10 contains gadolinia of 3.5 wt% in the upper region thereof and gadolinia of 1.0 wt% in the lower region thereof. The fuel rod G11 contains gadolinia of 4.5 wt% in the upper region thereof and no gadolinia in the lower region thereof. The fuel rod 32 has an upper end of the effective length portion which is located in 15/24 of the axial entire length of the fuel effective length portion from the lower end of another fuel rod. The fuel rod 32 has an axial length which is smaller than that of the other fuel rods. All of fuel rods 32 are located in an inner closed loop adjacent the outermost periphery of the fuel assembly 20. The use of the short length fuel rods are disclosed in Japanese Unexamined Publication Nos. 52-50498 and 60-2240092. This embodiment has the same effect as that of the fuel assembly 10, because a region of upper and lower regions in the fuel rods containing a maximum gadolinia concentration and a region of upper and lower regions in the fuel rods containing a minimum gadolinia concentration are located in the lower region in the fuel assembly, and the amount of gadolinia in the upper region in the fuel assembly is larger that in the lower region in the fuel assembly. Further, the short length fuel rod can lower the pressure loss in the upper region in the fuel assembly and improve the shutdown margin of the reactor.

description

This application is a national phase of International Application No. PCT/EP2006/066710 entitled “Sealing Means, Transfer Device Comprising Such a Sealing Means, Arrangement Comprising Such a Transfer Device and a Method for Producing Said Sealing Means”, which was filed on Sep. 25, 2006, and which claims priority of French Patent Application No. 05 52938, filed Sep. 28, 2005. This invention mainly concerns a sealing means, in particular between two radioactive environments, a transfer device in a nuclear fuel production plant comprising means of tight insulation, a production plant comprising such a device and a method for producing such a sealing means. It is known, for example in document FR-1364102, a revolving or barrel door to transfer a radioactive object from one enclosed area to another, with the door providing when operating and when at rest, a tight seal between the two spaces. The seal is obtained thanks to an inflatable seal mounted on a wall partially surrounding the drum. The sealing means must resist hot gases and flames in the event of fire, in order to limit the propagation of contaminated gases and flames. However, the seals that are currently in use which are fixed on the door, or on the wall separating the two confined areas, do not ensure sufficient resistance to hot gases and flames or a tight seal against contamination during a long period. In addition these seals are fragile and quickly become brittle since they are solicited with each rotation of the barrel door. Thus major problems appear in terms of maintaining this type of transfer device, which can cause stoppages of installations for a long duration. It is consequently a purpose of this invention to provide a sealing means that offers the guarantees of safety that are required for this type of device. It is also a purpose of this invention to provide a transfer device that can operate in conditions that are safe for the environment and for people working in this type of installation. It is also a purpose of this invention to offer a method for producing said sealing means. The previously mentioned purposes are attained by a means making it possible to tightly insulate two chambers, formed by a seal and a seal carrier, with the seal able to insulate flames and hot gases and is sufficiently resistant to radiation to be suitable for such devices. The seal carrier is easily removable, thus making it possible to replace the seal easily when the latter shows signs of deterioration. By seal is meant the property of confining for a determined length of time flames and hot gases in a first chamber in order to avoid them passing into a second chamber. Thus, it is not necessary to have a seal that is resistant to flames, hot gases and radiation over a long period of time, since the latter can be changed quickly and easily. This replacement does not impose a prolonged stoppage of the device. The subject-matter of the present invention is mainly a sealing means for a transfer device of a nuclear installation comprising a seal carrier and a seal connected thereto, wherein the seal carrier is removably fixable between two areas insulated from each other. The seal carrier comprises for example a T groove receiving the seal. Advantageously, the seal carrier is made of stainless steel. The seal is made of a material that resists flames, hot gases and radiation, and advantageously intumescent material. In an embodiment, the seal carrier is made of several parts, for example three parts. The invention also relates to a transfer device of a nuclear installation between two chambers separated by a wall, wherein said transfer device comprises a transfer mechanism and at least one sealing means according to the invention, said sealing means being positioned between the wall and the transfer mechanism. Furthermore, the seal carrier and the seal are arranged substantially along the wall according to a generatrix of a cylinder forming the outer periphery of the transfer mechanism. In an embodiment, the transfer mechanism is of the barrel door type mobile around an axis, comprising a cylindrical body defining an inner space wherein an object can be positioned, with this space being accessible by an opening that can be oriented either on the side of a first chamber or on the side of a second chamber. Advantageously, the transfer device according to the invention comprises a first pressure drop means able to increase the travel of the gases between the chambers, said first means being mounted on an upper end of the door substantially according to a plane orthogonal to the axis of rotation of the door. The first pressure drop means is, for example, formed by a steel angle assembly and, advantageously, by several arcs of a circle placed end to end. The transfer device can also comprise a second pressure drop means positioned along a generatrix of the outer periphery of the transfer mechanism. This second means comprises for example an elongated element made of steel, with a substantially circular transversal section. In an embodiment, the door comprises a first axis projecting from an upper side and a second axis projecting from a lower side around which the door is able to rotate. The door can be driven in rotation by an electric motor. The subject-matter of the present invention is also a production or treatment installation, for example of nuclear fuel, for example of the MOX-type (mixture of uranium oxide and plutonium oxide) comprising a main chamber and at least one secondary chamber separated by the wall, an opening for communication between the chambers arranged in the wall, a transfer device according to the invention, insulating the chambers. The seal carrier is fixed by screw-bolt connection on the wall separating the two chambers. The production installation according to the invention can comprise a first curved recess with inner radius substantially equal to the outer radius of the door and receiving a portion of this door. The second pressure drop means is for example welded in a groove defined by the wall and a safety caisson defining the first recess, a second curved recess surrounding the door, over approximately 180°. The subject-matter of the present invention is also a method of producing the sealing means according to the invention, comprising the steps: installing shutters on the longitudinal and transversal ends of the groove of the seal carrier, injecting a flame- and hot gas-resistant material into the groove, removing shutters. In the description that follows, the invention is applied to a nuclear fuel production installation, but it also applies to an installation that uses said fuel or that treats it. Furthermore, the transfer device according to the invention can be used in any installation requiring a transfer between two areas between which a tight seal is expected. In FIG. 9, a workshop is shown schematically wherein a nuclear fuel is produced. This workshop comprises a main chamber 2 equipped for example with a means of transporting or conveying materials intended for the production of the nuclear fuel, and secondary chambers 4 wherein the different operations of transforming the basic materials of the nuclear fuel are executed. The basic operations are for example the proportioning of the primary mixture, milling, the proportioning of the final mixture, homogenisation, granulation and the production of nuclear fuel pellets which will then be placed in ducts in order to form fuel rods. The main chamber 2 has the shape of a rectangular corridor and the secondary chambers 4 are distributed on either side of the main chamber 2. Openings 18 allow for communication between chamber 2 and chambers 4. In order to provide maximum protection in use and in operation, the main chamber 2 and the secondary chambers 4 are insulated from each other in order to reduce the risk of propagation of flames and hot gases in the event of fire in one of the chambers. However, in order to allow for the transfer of the materials between the secondary chambers by the intermediary of the main chamber 2, transfer devices 6 are disposed between the main chamber 2 and the secondary chambers 4, at openings 18. In FIG. 1, this transfer device can be seen, comprising a barrel door 8 rotatable about the axis X of rotation and making it possible to transfer objects from the main chamber 2 to secondary chambers 4 and vice versa. The main chamber 2 is separated from secondary chambers 4 by an insulation wall 10. Since all of the transfer devices of the installation are substantially the same, only a transfer device 6 and a secondary chamber 4 will be described. The barrel door 8 substantially has the form of a regular cylinder, defining an inner space 12, communicating with the outside via an opening 14 that is substantially rectangular in the example shown. The barrel door 8 comprises a body 9 formed, for example, of a jacket 11 made of stainless steel filled with a material comprising cast iron and binders of the resin type, such as MP2. The jacket comprises, advantageously arms penetrating into the fill material in such a way as to ensure proper fixation of the shell 11 in the material. The wall 10 is made from, for example, concrete and covered with a shielding 16 in such a way as to form a fire-proof seal. The opening 18 is of substantially likewise dimension as that of opening 14 arranged in barrel door 8, in such a way that when the opening 14 of the barrel door is facing the opening 18 of the wall, openings 14 and 18 match up. The wall 10 comprises a recess 20 defined by a curved surface, with an inner radius that is substantially equal to the outer radius of barrel door 8, and receiving a portion of said barrel door 8. The barrel door penetrates into wall 10 and sealing means 22 are provided between the cylindrical periphery of the door and the curved surface of wall 10, in such a way as to provide a seal between the barrel door and the wall, and thus between the main chamber 2 and the secondary chamber 4. A sealing means 22 according to the invention is positioned along a generatrix (FIG. 1) of the cylindrical body 9 in such a way that it is in contact with the outer periphery of barrel door 8. Means 22 is, for example fixed to the wall 10, in particular to an end of the curved recess 20. This sealing means 22 comprises, according to this invention and as shown in FIGS. 3 and 4, a seal carrier 24 and a seal 26, with seal carrier 24 being fixed on the wall 10, and the seal being in contact with the outer periphery of barrel door 8. The seal carrier 24 has a substantially trapezoidal form, with the large base comprising a groove 25 wherein is placed seal 26. The particular form of the seal carrier ensures guidance for the mounting of the seal carrier, facilitating its accurate installation and the alignment of the seal with the outside cylindrical wall of the barrel door. The groove 25 advantageously has a T-shaped section in order to improve the holding of the seal 26. Advantageously, the seal carrier is provided with a handgrip handle 31 for the installation and mounting of the seal carrier on the wall 10 and the element 27. This handle 31 can be removable, it is used to mount the seal carrier, and for this it is fixed on the seal carrier. After the mounting of the seal carrier on the barrel door 8, it is removed for the operation of the barrel door. For the removal of the seal carrier, the handle 31 is again fixed to the latter. Advantageously, the seal carrier 24 is made from stainless steel by casting, and the groove 25 wherein is injected the material of the seal, is machine tooled. The seal is advantageously made from an intumescent material, which has the property of inflating when heated thus providing a tight seal for hot and flammable gases. Advantageously, it also provides heat insulation. For example the material of the seal can be chosen in order to provide its sealing function for more than 2 hours. The seal is for example made from bi-component mastic, such as a 335s of the Mécatiss® brand. The groove can have any other form that retains the seal in the groove, for example a trapezium form, with the large base corresponding to the bottom of the groove 25. The seal carrier 24 is fixed to the wall 10 in a removable way, for example by screw-bolt connection. Bolts 29 are for example welded on the shielding 16 (FIG. 2) wherein the seal carrier can be fixed using nuts. Any other means of removable fixation can be used to attach the seal carrier 24 to the wall 10. In the example shown, the seal carrier 24 is made from several pieces which are placed end to end in order to form the seal between the wall 10 and the barrel door 8 across the entire height of the barrel door 8. The transfer device 6 according to the invention comprises also, advantageously, a first means 28 shown in FIGS. 6A and 6B, able to provoke a pressure drop for hot gases. This first means 28 is positioned at an upper end of the barrel door 8. This means 28 is carried out in the form of an angle assembly or annular ring. The ring 28 as a cross-section in FIG. 6B, comprises a first 41 and a second 43 sides substantially at a right angle, the first side 41 being flush with an upper surface 36 of the drum 8 and the second side 43 being in line with the outer periphery of the drum 8, thus extending towards the top of drum 8. The angle assembly 28 is for example made of steel, comprising several arcs of a circle, for example six, placed end to end via welding. The arcs of a circle have an inner radius substantially equal to that of the barrel door. These sectors are advantageously non-jointed. The angle assembly 28 is, for example, fixed by its first side 41 on the barrel door 8 by a welded pin, washer and nut assembly 47. Advantageously, means (not shown) to adjust the position of the angle assembly can be provided on the angle assembly 28. The latter make it possible to fix a defined spacing between the recess 20 and the second side 43 of the angle assembly 28. These means of adjustment are advantageously removable and are mounted on the angle assembly 28 only for its positioning. The angle assembly 28 forms a baffle system, which makes it possible to substantially improve the seal by creating a pressure drop for hot gases. Furthermore, the addition of this angle assembly 28 on the barrel door 8 increases the total height of the barrel door, lengthening the travel of the hot gases to emerge on the upper side of the barrel door 8. The device according to the invention also comprises, more preferably, a second pressure drop means 30, positioned substantially along a generatrix of the cylindrical body 9, between the wall 10 and a safety caisson 32. The safety caisson 32 comprises a recess 34 of substantially curved form, with inner radius substantially equal to the outer radius of the barrel door 8 and defining with the recess 20 of the wall 10, a housing extending substantially at 180° around the barrel door 8. The caisson 32 avoids communication between chambers 2 and 4 during the rotation of the door 8 by providing a minimum overlap between the opening 14 of the door 8 and the caisson 32. As such it avoids the propagation of the fire during the rotation of the door. The caisson 32 is for example formed of a stainless steel jacket filled with MP2 as mentioned previously. The second pressure drop means 30, shown in FIG. 5, is disposed between the safety caisson 32 and the wall 10. In the example shown, the second pressure drop means 30 is formed of an elongated element, for example made of steel and of circular transversal section, of the round steel type, welded in a groove 34 arranged between the wall 10 and the caisson 32. Advantageously, the second means 30 is made of several sections, for example two, advantageously welded in a housing defined between the shielding covering the wall 10 and the caisson 32, for example via intermittent point weld. In the example shown, the upper and lower ends of the round steel (not shown) are folded to 90° towards the wall by moving the barrel door away, which makes it possible to remove the spacing of the emerging groove 34. The round steel is adjusted so as to guarantee a maximum spacing, for example of about 2 mm, with the outer periphery of the door. This makes it possible to obtain a pressure drop sufficient to limit a propagation of hot gases. In FIG. 10, a door 8 can be seen for a transfer device according to this invention, comprising a first upper surface 36 and a second lower surface 38, and first 40 and second 42 axes respectively projecting from surfaces 36 and 38, arranged according to the direction X and forming the axis of rotation of the door 8. In the example shown, the arms are maintained axially in relation to the wall 10 using a lower support 44 projecting transversally from the wall in the secondary chamber 2 and an upper support 46 also projecting transversally from the wall 10. The first axis 40 is fixed in rotation in relation to the door and mobile in rotation in relation to the upper support 46 by means of a bearing 48. The second axis is, in the example shown, fixed in rotation on the lower support 44 and mobile by means of a bearing 50 in relation to the door 8. The door is driven in rotation by an electric motor positioned at one end of the axis 40. The motor can be controlled from the exterior of the installation. The motor can also be positioned on the second axis 42. Several motors can also be provided. The operation of said transfer device shall now be explained. In FIG. 1, the drum can be seen, especially the inner space 12 open onto the main chamber 2. In this position, an object for example a bottle (not shown) containing one or several materials in order to produce nuclear fuel is introduced into space 12. The barrel door 8 is then driven in rotation around the X axis. After having completed a 180° rotation, the interior volume 12 is open onto the secondary chamber 4. The bottle contained in space 12 can thus be transferred into the secondary chamber 4. The transfer device can also be provided so that the rotation in one direction of the barrel door is less than 180°. We shall now describe a method of producing the seal and seal carrier unit according to this invention, in relation to FIGS. 7 and 8. Such a method comprises the following steps: installing shutters on the longitudinal and transversal ends of the groove (25) of the seal carrier, injecting a flame- and hot gas-resistant material into the groove, removing shutters. In the FIGS. 7 and 8, the step of injecting the material forming the seal in the seal carrier can be seen. In order to carry out the injection, the longitudinal ends 60, 62 of the groove, as well as its open end 64 are shut by plates 66, 68, 70 respectively, in such a way as to define the location and the form of the seal 26. The plates 66, 68 are maintained attached to the seal carrier, for example by screwing on the ends of the seal carrier. The plate 70 is, in the example shown, maintained by tightening between transversal elements 72 connected by the tightening elements 74, such as threaded rods and nuts. An orifice 76 is provided in plate 70 for the injection of the material of the seal via a nozzle 78 in the groove 25. When the material has the desired texture, the plates 66, 68 and 70 are removed. The seal carrier provided with the seal is ready to be mounted. At the transversal end 64 of the groove 25, a knitted sheet of Kevlar® and a sheet of Milard® can be provided in order to provide the seal of the mould when the material is injected. The latter are removed during demoulding.

045129215

description

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT In order to decontaminate the coolant system of a water cooled nuclear power reactor, the reactor must first be shut down and the coolant allowed to cool below 100.degree. C. The decontamination solution is prepared by adding concentrated solutions to the coolant to make the coolant about 0.01M in oxalic acid and about 0.005M in citric acid, by adjusting the pH to about 3 with ammonia, and by adding and maintaining about 0.75 ppm dissolved oxygen in the coolant. The decontamination solution is then circulated at a temperature of about 90.degree. C., throughout the coolant system. As the decontamination solution circulates, the metal oxide films on the surface of the system dissolve and are complexed by the oxalic acid and to a lesser extent by the citric acid. In addition to the complexed metal ions, other particulate matter may be loosened and swept along by the decontamination solution. As the decontamination process proceeds, the dissolved metallic ions are continuously removed and the complexing power of the reagents renewed by passing a portion of the coolant containing the metal-ion complexes through a strong-base anion-exchange resin bed which has been presaturated with oxalic and citric acids in about the same ratio and about the same pH as these reagents are present in the circulating coolant. As the contaminated decontamination solution, which contains a mixture of unutilized or metal-ion-free organic anions and complexed divalent and trivalent metal ions, is passed through the presaturated anion-exchange resin bed wherein the metallic-ion complexes are exchanged for the metal-ion-free organic anions on the resin while any unutilized, metal-ion-free organic anions pass through the resin bed unaffected, whereby this portion of the decontamination solution is renewed and is ready for recirculation throughout the cooling system. The coolant may be made from 0.005 to 0.02M in oxalic acid with about 0.01M being the preferred concentration; lower concentrations result in much slower dissolution rates. Citric acid concentration may vary from about 0.002 to 0.01M with 0.005M being the preferred concentration. The ratio of oxalic acid to citric acid may vary from 1:1 to 10:1 with a ratio of about 2:1 preferred. The citric acid acts as a pH buffer and to retard the formation of ferrous oxalate which may otherwise precipitate and may be difficult to resolubilize. The citric acid may also act as a minor complexing agent. The oxalic and citric acids may be injected together or separately into the coolant as concentrated solutions. The pH of the coolant may vary from about 2.5 to 4.0, preferably 2.8 to 3.5 and most preferably about 3.0 and may be controlled by adjusting the pH with ammonia. Control of pH is important to obtain the highest dissolution rate with the minimum amount of corrosion. Coolant temperature during decontamination may vary from about 60.degree. to 100.degree. C. with 90.degree. C. being preferred. Temperatures above 100.degree. C. cause the organic reagents to decompose while below about 60.degree. C. the dissolution rate is very slow. A small amount of dissolved oxygen should also be added to the circulating coolant during decontamination to ensure complete oxidation of the Fe.sup.+2 to Fe.sup.+3. This is important to prevent formation of ferrous oxalate precipitate. The concentration of oxygen may vary from about 0.2 to 4.0 ppm, preferably about 0.5 to 1.0 ppm. The oxygen may be added by any convenient method, such as the addition of hydrogen peroxide to the coolant, or preferably, by gas injection into one of the flowing coolant systems. The anion-exchange resin may be any commercially available strong base anion exchange resin such as Bio Rad AG-1 or Amberlite IR-400. The resin, which is generally received in hydroxide form must be loaded with oxalate and citrate anions so that the anions on the resin are in chemical equilibrium with the reagents in the decontamination solution. This can best be accomplished by first loading the organic anion on the resin bed from a concentrated solution of the reagents. The resin can then be equilibrated in a stepwise matter with a dilute flushing solution of the same composition as the decontamination solution until the effluent from the bed has about the same concentration of reagents and pH as the decontamination solution. For example, a concentrated oxalic acid-citric acid solution is prepared in which the oxalate-citrate ratio is the desired ratio of the two reagents on the resin when it is in chemical equilibrium with the decontamination solution. This concentrated solution is added to the resin at a controlled rate until the pH is about that desired for the decontamination solution. A dilute oxalic acid-citric acid flushing solution is prepared having the same composition and pH as the decontamination solution. The resin is then flushed in a column with large quantities of the flushing solution until the effluent is the same pH as the decontamination solution. At this time the resin is presaturated and ready for use in regenerating the reagents in the coolant. When the coolant decontamination solution, containing a mixture of the unutilized metal-ion free organic anions and the metallic-ion complexes, is passed through the presaturated anion-exchange resin, the metallic-ion complexes are exchanged for the metal-ion-free organic ions in the resin. The unutilized reagents pass through the resin bed unaffected. Using oxalic acid as an example, the exchange reactions for the Fe.sup.+3 oxalate and Co.sup.+2 oxalic complexes are: EQU Fe(C.sub.2 O.sub.4).sub.3.sup.-3 +3RHC.sub.2 O.sub.4 .fwdarw.R.sub.3 Fe(C.sub.2 O.sub.4).sub.3 +3HC.sub.2 O.sub.4.sup.-, and EQU Co(C.sub.2 O.sub.4).sub.2.sup.-2 +2RHC.sub.2 O.sub.4 .fwdarw.R.sub.2 Co(C.sub.2 O.sub.4).sub.2 +2HC.sub.2 O.sub.4.sup.-, where R stands for the cationic species affixed to molecular structure of the resin. Although these are reversible, equilibirum reactions, they are driven to the right by the thermodynamic preference of the resin for the multicharged metallic-complex ion over the single-charged binoxalate anion and by the multistage sorption effect of the anion-exchange column. The decontamination reagents can be easily removed from the reactor coolant system by passing the coolant containing the reagents, either complexed or uncomplexed through a mixed ion-exchage resin bed, i.e. both anion- and cation-exchange resins, until the conductivity of the solution drops to about 1 .mu.mho. At this point, the coolant is essentially free of reagent and reactor start-up can be commenced. While the method of the invention as described, is applied only to the regeneration of oxalic acid and citric acid systems, the technology could potentially be applied to the regeneration of solutions of a variety of other metal complexing organic chemicals which might be used as decontaminating agents. These include nitrilotriacetic acid (NTA) and hydroxyethylethylenediaminetriacetic acid (HEDTA). The addition of a small amount (5 to 10% by volume) of cation-exchange resin to the presaturated anion-exchange resin could potentially provide a margin of additional capacity for the removal of divalent ions. Since the cation-exchange resin does not sorb appreciable amounts of Fe.sup.+3 from oxalate and citrate solutions, its capacity for removing the divalent metallic ions from the decontaminating solution is essentially independent of the Fe.sup.+3 concentration. Thus, even though it is less efficient initially than the anion-exchange resin for the removal of divalent ions, the cation-exchange resin may become more efficient as the anion-exchange resin reaches saturation with the Fe.sup.+3 complexes. EXAMPLE I To compare the effectiveness of the anion- and cation-exchange resins on the removal of iron and cobalt from a decontamination solution, a typical laboratory ion-exchange column (1 cm.times.30 cm) was loaded with strong-base anion-exchange resin (Bio Rad AG-1) to a height of 20 cm. To presaturate the resin, a solution of 0.02M oxalic acid, adjusted to a pH of 3.0 with NH.sub.4 OH, was passed through the column until the column effluent had the same concentration and pH as the feed. A simulated decontamination solution, consisting of 0.02M oxalic acid with 1.51.times.10.sup.-3 M Fe.sup.+3 and 4.0.times.10.sup.-5 M Co.sup.+2 (6.8.times.10.sup.-3 .mu.Ci/ml Co-60), was passed through the column, and the effluent was sampled periodically. The effluent samples were analyzed for the concentrations of Fe.sup.+3 and Co-60. The Fe.sup.+3 and Co-60 concentrations in the effluent are shown in FIG. I. The anion-exchange resin, presaturated with binoxalate anions, was essentially 100% efficient at removing Co-60 for about 500 bed-void volumes and at removing Fe.sup.+3 for about 550 bed-void volumes. This demonstrates the efficiency of the anion-exchange process for removing the metallic-ion complexes from the solution. Similar experiments to evaluate the cation regeneration process were conducted with hydrogen-ion-form cation-exchange resin and a pH 3 solution of 0.02M oxalic acid with 1.55.times.10.sup.-3 M Fe.sup.+3 and 5.7.times.10.sup.-5 M Co.sup.+2 (7.7.times.10.sup.-3 .mu.Ci/ml Co-60). The results of the Fe.sup.+3 and Co-60 are plotted in FIG. II. These data readily indicate that the Fe.sup.+3 -oxalate complex is not efficiently removed by cation-exchange resin (breakthrough after about one bed-void volume) and efficiency of the cation-exchange resin for removal of Co.sup.+2 decreases after only about 150 bed-void volumes of solution is passed through the column. This premature cobalt breakthrough occurred even though the ion-exchange column was not saturated with the metallic ions. EXAMPLE II An anion exchange resin was presaturated with oxalate and citrate anion in the following manner: A concentrated solution of oxalic acid and citric acid was prepared by dissolving 83.6 g oxalic acid and 33.5 g in citric acid in 1070 ml H.sub.2 O to form a solution 0.62M in oxalate and 0.149M in citrate. The concentrated solution was added to a beaker containing 780 ml of a strong base anion resin in the OH.sup.- form at a controlled rate of 12 ml/min and stirred, until a pH of 3 was achieved. This required about 625 ml of solution. The resin was then loaded into a standard ion exchange column and flushed with a solution of 0.012M oxalic acid and 0.005M citric acid at pH3 until the column effluent had about the same pH and oxalate-citrate concentration as the flushing solution. Table I below shows the correlation between solution volume and oxalate-citrate concentration. TABLE I ______________________________________ Total Solution Oxalate-Citrate Volume ml pH Concentration ______________________________________ 800 4.11 Not Determined 6200 4.10 Not Determined 18200 3.43 Oxalate-0.0085 M Citrate-0.008 M 29900 3.19 Not Determined 40900 2.98 Oxalate-0.0116 M Citrate 0.0049 M ______________________________________ The resin was then presaturated and ready for regeneration of the decontamination solution. EXAMPLE III An ion-exchange column breakthrough experiment was conducted to evaluate the elution sequence and the capacity of a mixed-bed of cation and presaturated anion resin used for the regeneration process. A solution of 0.01M oxalic acid and 0.005M citric acid at pH 3 containing 0.003M Fe.sup.+3 and 0.0001M Cr.sup.+3, Ni.sup.+2, Co.sup.+2, Zn.sup.+2, Mn.sup.+2, Cu.sup.+2, and Fe.sup.+2 was passed through a 90/10 mixture of anion and cation resins until the effluent and feed concentrations were similar. The effluent was sampled periodically and analyzed for metal ion concentrations by plasma spectrometry; the Fe.sup.+2 concentrations were determined spectrophotometrically. The elution sequence was (Fe.sup.+3,Cr.sup.+3), Cu.sup.+2, (Ni.sup.+2, Zn.sup.+2, Co.sup.+2), Mn.sup.+2 and Fe.sup.+2, which is in agreement with the oxalate complex stabilities for the various ions. These data indicate the quantity of cation resin added to the pre-saturated anion resin to provide back-up Co-60 capacity for the regeneration process must have sufficient capacity to adsorb all of the divalent corrosion products except Cu. In addition, these data indicated the Fe.sup.+3 and Cr.sup.+3 oxalate complexes have similar affinities for the anion-exchange resin since their breakthroughs occurred simultaneously and their final concentrations on the resin were proportional to their solution concentrations. The capacity of the presaturated anion-exchange resin for trivalent ions was determined to be 0.47 moles/liter, which is equivalent to the theoretical capacity. The capacity of the cation-exchange resin for divalent-ions was determined to be 0.33 moles/liter, which is approximately 40% of the theoretical capacity. EXAMPLE IV A circulating test loop was prepared to study the effects of the decontamination reagents on the removal of iron oxides and cobalt from reactor coolant system piping and to determine the efficiency of the reagent regeneration. A solvent consisting of 0.01M oxalic acid and 0.005M citric acid at pH3 was circulated through the loop. The dissolved oxygen content of the solvent was maintained within the specification of 0.75.+-.0.25 ppm. No ferrous oxalate precipitation was observed. Approximately 85% of the Co-60 activity was removed over the 12-hour dissolution cycle. Within a few minutes after the initial injection of the reagents, the loop chemistry and operating conditions were stabilized. All of the operating parameters were maintained within specification for the remainder of the run. The Co-60 activity in solution increased to a maximum during the first few hours of the test and then it decreased as the oxide film dissolution rate decreased and was exceeded by the solvent regeneration rate. The maximum Co-60 concentration obtained was equal to approximately 6.7% of the total Co-60 dissolved during the test. The oxalic acid and citric acid concentrations were maintained within specification during the decontamination cycle. The iron concentration in solution was maintained below 6% of the total iron dissolved. As can be seen from the preceeding discussion and Examples, the process of this invention provides an effective method for the decontamination of the coolant systems of water cooled nuclear power reactors by providing an efficient and effective method for continuously regenerating the reagents used for the decontamination process.

summary

046831142

description

DETAILED DESCRIPTION According to the present invention, a composition and method are provided for combining a boron-containing burnable absorber with a nuclear fuel pellet, with the burnable absorber coated on the pellet, encased in a boron-containing glass. The nuclear fuel pellets are preferably comprised of uranium dioxide which is enriched in U-235 isotope. Other such nuclear fuels, however, may be used in the formation of the pellets, such as a mixture of uranium-plutonium dioxide. The fuel pellets are generally formed by enriching the uranium dioxide and, either alone or in mixture with plutonium dioxide, compacting the material to the desired shape and size, and sintering the same to produce dense pellets for use in a nuclear fuel rod. The sintered pellets are then coated according to the present invention. The coating formed on the nuclear fuel pellets is a boron-containing burnable absorber encased in a boron-containing glass, which coating is resistant to peeling and exhibits exceptionally low moisture or hydrogen adsorption. The boron-containing burnable absorber is preferably boron carbide (B.sub.4 C) but other known boron-containing absorbers such as zirconium diboride (ZrB.sub.2), and the like, which are stable at temperatures in excess of about 1000.degree. C. may also be used. The second component of the coating composition of the present invention is a specially developed boron-containing glass composition. The boron-containing glass composition has a melting temperature between 900.degree.-1100.degree. C. and contains boron oxide (B.sub.2 O.sub.3); silicon dioxide (SiO.sub.2); at least one alkali oxide such as sodium oxide (Na.sub.2 O); or potassium oxide (K.sub.2 O); at least one alkaline earth oxide such as calcium oxide (CaO) or barium oxide (BaO); and a stabilizer such as aluminum oxide (Al.sub.2 O.sub.3); within specified amounts by weight of the boron-containing glass composition. The amounts, by weight, of the various components of the glass composition that is usable are: B.sub.2 O.sub.3 : 20-30 percent PA1 SiO.sub.2 : 30-60 percent PA1 Na.sub.2 O: 5-15 percent PA1 BaO: 5-15 percent PA1 CaO: 5-15 percent PA1 Al.sub.2 O.sub.3 : 5-15 percent PA1 B.sub.2 O.sub.3 : 20 PA1 SiO.sub.2 : 40 PA1 Na.sub.2 O: 10 PA1 BaO: 10 PA1 CaO: 10 PA1 Al.sub.2 O.sub.3 : 10 PA1 SiO.sub.2 -40 gr PA1 B.sub.2 O.sub.3 -20 gr PA1 Na.sub.2 CO.sub.3 -17 gr (10 g Na.sub.2 O) PA1 BaCO.sub.3 -13 gr (10 g BaO) PA1 CaCO.sub.3 -18 gr (10 g CaO) PA1 Al.sub.2 O.sub.3 -10 gr The amount of boron oxide present must be between 20-30 percent by weight. If less than about 20 percent by weight of the boron oxide is present, insufficient encapsulation and entrapment of the boron-containing burnable absorber results, while use of more than about 30 percent by weight in unacceptable due to reaction with water and, hence, moisture adsorption from the atmosphere which must be avoided. Since borosilicate glasses usually have very low thermal expansion coefficients (.alpha.), the alkali oxide having a high .alpha., in excess of that of uranium dioxide, is added in order to obtain an adequate .alpha. of the coating to match or exceed that of the uranium dioxide fuel pellet (.alpha.=10.times.10.sup.-6 /.degree.C.). Since B.sub.4 C, which is added to the glass, has a low .alpha.(4.times.10.sup.-6 /.degree.C.), the boron-containing glass component should have a higher .alpha. such that the resulting mixture has an expansion commensurate with the amount of B.sub.4 C present. Amounts of alkali metal oxide between 5-15 percent by wieght will give the desired expansion. The alkaline earth oxides are used to adjust the melting temperature of the glass composition, with a melting temperature of the glass composition, with a melting temperature of about 1000.degree. C. being preferred. The aluminum oxide is added as a stabilizer for the glass composition. A preferred glass composition has the composition, in percent by weight: This composition, when melted in a silica crucible at about 1100.degree. C. and quenched, gives a clear glass. The glass, after being immersed in water for 24 hours and dried, showed no weight change indicating that the glass does not react with water. In application of the present coating, the boron-containing burnable absorber and boron-containing glass are ground or otherwise provided in a finely divided particulate state, and first mixed together. Both these components should be provided in a particle size finer than 325 mesh, U.S. Standard Sieve. It is preferred, however, that the particle size of the boron carbide be smaller, with at least 90 percent of the particles being of a diameter less than about 10 microns. It is also preferred that the particle size of the boron-containing glass be smaller, with those particles being of a diameter of about 5 microns or less. These smaller particle sizes provide more intimate mixing of the particles and the ability to incorporate a higher amount of boron carbide in the coating, with the resultant coating still exhibiting exceptional bond strength and resistance to peeling and to hydrogen adsorption. In mixing of the two components, the boron carbide content of the mixture must be within a range of 20 to 80 percent by weight, while the boron-containing glass is in an amount of 80 to 20 percent by weight of the mixture. The use of less than about 20 percent by weight of boron carbide would not provide the desired absorption capabilities within a tolerable thickness of the resultant coating, while use of in excess of about 80 percent of boron carbide results in incomplete incorporation of the boron carbide in the resultant coating and possible peeling of the same from the pellets. Amounts of up to 80 percent boron carbide in the coating are achievable when the particle sizes of both components of the mixture are of a size in the above-mentioned preferred ranges. In instances where less than about 40 percent of the composition is boron carbide, particle sizes which are somewhat larger but still below 325 mesh are usable, with formation of a coating that incorporates the boron carbide sufficiently to prevent peeling or hydrogen adsorption. The mixture of boron-containing burnable absorber and boron-containing glass may be applied to the surface of the nuclear fuel pellets by various techniques, such as dipping the pellets in a slurry of the mixture, wet spraying a slurry of the mixture on the pellets, rolling the pellets in a slurry of the mixture, or dry spraying the mixture as a powder on the surface of the pellets using electrostatic charge spraying techniques. In the dipping, wet spraying and rolling applications, the finely ground mixture of boron-containing burnable absorber and boron-containing glass is formed into a slurry with a liquid such as acetone, an alcohol, water, or a liquid hydrocarbon medium such as toluene, to the consistency desired, with a dispersant or surface active agent added to provide the desired dispersion of the particles in the liquid as a slurry. The thickness of the boron carbide-containing coating should be kept at or below a thickness of about 1 mil. Because of the close tolerance required upon loading of fuel pellets in a metallic cladding, the application should also provide a controlled, uniform, thin coating of 1 mil or less. Also, since any coating thickness will remove some of the gap between the pellet and cladding, the coating thickness should be kept to a minimum to avoid a reduction in fuel inventory, and also to provide sufficient space for the liberation of helium, during irradiation, from the B.sup.10 such that the desired fuel rod pressure is not exceeded. The minimum thickness of the coating will be that thickness which contains the desired amount of B.sup.10 to provide sufficient neutron absorption during reactor operation. In general, an amount of about 1 to 2 mg, preferably 1.5 mg, of B.sup.10 per inch of length of pellet, having a constant diameter of about 0.3 inch, has been determined to be a preferred amount. The thickness of the coating should thus be that which will provide an amount of boron, including the boron in the boron-containing burnable absorber and the boron in the boron-containing glass, that results in a B.sup.10 quantity of about 1 to 2 mg per inch of pellet. The coating is applied to the circumferential surface of the pellets and the ends of the pellets are uncoated. In dipping, or otherwise applying the coating where the whole pellet may be coated, the coating is removed from the ends of the pellet to leave the coating only on the circumferential surface. After coating the nuclear fuel pellets with the coating composition of the present invention, the coated pellets are dried and then heated to an elevated temperature to melt the boron-containing glass and incorporate the boron carbide particles therein. The coated pellets are heated to a temperature of between 900.degree.-1100.degree. C., preferably 1000.degree.-1050.degree. C. for a short period of time, under an atmosphere that is inert relative to the uranium dioxide of the fuel pellets and to the boron carbide powder. The temperature range of 900.degree.-1100.degree. C., is important in that the temperature must be high enough to melt the glass and effect encapsulation of the boron carbide, while temperatures in excess of about 1100.degree. C. are avoided to prevent reaction between the boron of the boron-containing burnable absorber with the components of the boron-containing glass, which would, in effect, cause a loss of boron-containing absorber that is needed in the finished pellets. The melting of the glass and encapsulation of the boron-containing absorber in the glass at the above temperatures is effected by heating the coated pellets for only about 5 to 15 minutes, preferably about 10 minutes. The heating is effected in an atmosphere that is inert relative to the uranium dioxide, such as an atmosphere of hydrogen, argon, or mixtures thereof, or a vacuum, with oxygen being excluded from the atmosphere. A short holding time at the required temperature is believed to be a key factor for obtaining an ideal coated pellet. The coated pellets, after the heating step, are cooled and the result is a nuclear fuel pellet coated with a strong, adherent coating of a boron-containing burnable absorber that is encapsulated in a boron-containing glass. The invention is further illustrated by reference to the following example, wherein parts or percentages are by weight unless otherwise indicated. EXAMPLE I As an example of the coating composition and process of the present invention, a series of coated pellets were made using the following composition and procedure. A boron-containing glass composition was prepared by combining the following for 100 g of glass: The above powders were mixed in a plastic bottle with Al.sub.2 O.sub.3 balls on a roller overnight. The mixture was then melted in a pot furnace using a silica crucible at 1200.degree. C. After the melt was clear, containing no bubbles, the melt was quenched into a cold stainless steel crucible which was surrounded with an ice water bath. The glass was then vibra-milled in a plastic bottle with Al.sub.2 O.sub.3 balls and screened to -325 mesh. Thirty-five (35) grams of the above glass composition, milled to a particle size, such that about 95 percent of the particles were less than 10 microns, were mixed with 65 grams of boron carbide (Tetrabor, about 96 percent of particles less than 10 microns). This mixture was formed into a slurry by combining the mixture with 67.71 grams toluene and 11.90 grams of a binder (A-20, acryloid resin sold by Rohm & Haas Co.). The coating composition resulting was sprayed onto uranium dioxide pellets, dried and the coated pellets fired in a hydrogen furnace at 1000.degree. C. for 5 minutes. The resultant coated pellets were subjected to a peel test wherein a piece of Scotch tape was wrapped around the circumference of the pellet, pressed firmly onto the coating, and then removed. The coated pellets passed the peel test, with no coating removed, showing good adhesion of the coating. The coated pellets had a hydrogen content of less than 1 ppm (part per million by weight) indicating resistance to moisture adsorption. The pellets showed the coating weight in thicknesses listed in Table I: TABLE I ______________________________________ Original Weight of Pellet Weight of Coated, Fired Weight of Thickness of No. Pellet (gr) Pellet (gr) Coating (gr) Coating (mil) ______________________________________ 1 7.4909 7.4992 0.0083 0.9-1.00 2 7.3812 7.3894 0.0082 0.85-0.95 3 7.4943 7.5024 0.0081 0.75-1.00 4 7.4808 7.4888 0.0080 0.90-1.00 5 7.3750 7.3829 0.0079 0.85-1.00 ______________________________________ As is evident from the results listed in Table I, the thickness of the coating was one mil or less and the resulting coated pellets contained a desired amount of B.sup.10. A theoretical amount of about 8.04 mg B.sup.10 is desired, with the actual amounts listed being between about 7.9 mg to 8.3 mg. The actual amount of B.sup.10 is calculated by combining the amount of B.sup.10 in the glass and the amount of B.sup.10 in the boron carbide (about 18.9 percent of boron being the B.sup.10 isotope in natural boron). EXAMPLE II A further series of pellets were coated as follows. Powdered boron-containing glass was prepared having the following composition, by weight: SiO.sub.2 -40; B.sub.2 O.sub.3 -20; Al.sub.2 O-10; BaO-10; CaO-10; and Na.sub.2 O-10. The glass was then vibra-milled into a powder (<325 mesh) for mixing with B.sub.4 C to prepare the coating slurry. Several slurries were made by mixing the powdered boron-containing glass and B.sub.4 C powders (Norton Company B.sub.4 C powder, about 90 percent of particles less than 15 microns) in different proportions (20, 30, 40 and 50 percent by weight B.sub.4 C) using acetone as the liquid medium and a dispersing agent (a solution containing 13 volume percent of Tamol and 1 volume percent of Triton from Rohm & Haas Co.). Uranium dioxide pellets were coated with these slurries either by dipping or spraying methods. A uniform layer of coating was obtained and dried quickly. The coated uranium dioxide pellets were fired in a hydrogen furnace at 950.degree. C. for 10-15 minutes. The glass melted and the B.sub.4 C particles became immersed in the melt, but did not react with the glass. The coating containing 30 percent by weight B.sub.4 C or less showed a shiny, adherent, glassy surface which passed the peel test (aforedescribed) without any evidence of coating removal. The coating containing 40 percent by weight B.sub.4 C showed a dull but still adherent coating and also passed the peel test. However, the coating containing 50 percent by weight B.sub.4 C failed to peel test. This is believed to be a result of the glass particles not being in a sufficiently finely divided state to encapsulate all of the B.sub.4 C particles. The moisture content of the coated pellets was measured and showed hydrogen contents in the range of 0.3-0.7 ppm. This low hydrogen content is considered to be due to the smooth, non-porous nature of the surface resulting in less surface area of the coating and the passive nature of the boron-containing glass to moisture. Metallographic sections, at two magnifications, of a pellet so produced are illustrated in FIGS. 1 and 2. It is clear that the coating is adherent, uniform and continuous. There are no cracks in the coating or at the pellet/coating interface. The encapsulated boron carbide particles show as white spots in the glass matrix. EXAMPLE III A series of pellets were coated according to the procedure of Example II, wherein the coating contained 40 percent by weight B.sub.4 C. Before firing of the pellets, a second coating containing only the boron-containing glass, without any added B.sub.4 C was applied to the initially coated pellets, as an overcoat. The dual-coated pellets, after drying, containing a major thickness of boron carbide containing glass and a minor thickness of glass overlay, were then fired as described in Example II. The resultant dual-coated pellets had a shiny and glassy coating and passed the peel test. The moisture content of the dual-coated pellets also showed hydrogen contents in the range of 0.3-0.6 ppm. Metallographic sections of a dual-coated pellet so produced are illustrated at two magnifications, in FIGS. 3 and 4. Again, an adherent, uniform and continuous coating with no cracks either in the coating or at the pellet/coating interface are indicated. The extremely smooth surface of the top, glass layer (without any B.sub.4 C particles) is also visible in FIGS. 3 and 4. It should be noted that the two coating layers merged at their interface such that no bond line is apparent between the two layers, although the bottom layer containing the boron carbide is seen as being covered by a thin glass layer free of boron carbide particles. Again, the boron carbide particles show as white spots in the glass matrix. EXAMPLE IV A series of coated pellets were made according to the procedure of Example I, except that the coating composition comprised 80 grams of boron carbide (Tetrabor, about 96 percent of particles less than 10 microns) and 20 grams of the glass composition, that had been ground to a particle size of less than about 5 microns in diameter. Coated pellets, after drying, were fired at about 1000.degree. C. for 5 to 15 minutes. The thickness of the final coating was between about 0.5 to 0.7 mil. The fired pellets passed the peel test, indicating that up to 80 percent boron carbide can be present in the glazed coating when the boron carbide particles are finely divided and the glass particles are also finely divided. The coatings prepared according to the present invention, wherein a burnable absorber is encapsulated in a boron-containing glass exhibit very low hydrogen (moisture) adsorption (<1 ppm) and have a strong bond with the pellet without any cracks in either the glass, the coating, or at the interface. The coating also provides a smooth surface which could act as a lubricant, and is provided by a process tht is relatively simple, quick, and requires less capital expediture than other processes. Both the thickness of the coating and the B.sup.10 content in the coating can be varied and controlled to fit the exact needs of the user.

claims

1. A method of irradiating comprising: moving items through a charged particle beam; determining a kinetic energy of the charged particle beam entering the item; and, measuring a kinetic energy of the charged particle beam exiting the item. 2. The method as set forth in claim 1 , further including: claim 1 determining a difference between the energy of the charged particle beam entering and exiting the item; and, determining an absorbed dosage of the charged particle beam from the difference. 3. The method as set forth in claim 2 , further including: claim 2 controlling at least one of a speed with which the items move through the charged particle beam and the energy of the charged particle beam in accordance with the determined absorbed dose. 4. The method as set forth in claim 1 , wherein: claim 1 the items are conveyed through the charged particle beam in a first direction; and, the charged particle beam is swept back and forth in a plane perpendicular to the first direction. 5. The method as set forth in claim 1 , wherein the charged particle beam is an electron beam. claim 1 6. The method as set forth in claim 1 , further including: claim 1 determining a beam current absorbed by the irradiated product. 7. The method as set forth in claim 1 , further including: claim 1 scanning the charged particle beam; and, measuring beam current pulses as the beam current scans past a measurement point. 8. A method of irradiating comprising: irradiating items with a charged particle beam; determining an energy of the charged particle beam entering the item including measuring changes in a charged particle beam current; and determining an energy of the charged particle beam exiting the item including measuring changes in a charged particle beam current. 9. The method as set forth in claim 8 , further including: claim 8 measuring the charged particle beam current at a plurality of locations along the item. 10. The method as set forth in claim 9 , further including: claim 9 determining reductions in the charged particle beam current at the various points along the item and determining an absorbed dose for a plurality of regions of the item from the reduced current. 11. The method as set forth in claim 8 , wherein the measuring of the charged particle beam current includes: claim 8 concentrating magnetic flux changes attributable to the changing current; and with concentrated magnetic flux changes, inducing electrical currents in windings of a coil. 12. A method of detecting energy of an electron beam, the method comprising: collimating an electron beam to a preselected cross-section; inducing a first electromotive force with the collimated electron beam; attenuating the collimated electron beam; inducing a second electromotive force with the attenuated electron beam; and, comparing the first and second electromotive forces. 13. The method as set forth in claim 12 , wherein: claim 12 inducing the first electromotive force includes pulsing the collimated electron beam through a first annular winding; attenuating the collimated electron beam includes passing the electron beam through a metal layer of preselected thickness; and, inducing the second electromotive force includes pulsing the collimated electron beam through a second annular winding, the second annular winding being disposed closely adjacent the metal layer. 14. An irradiation apparatus comprising: a charged particle beam generator for generating and aiming a charged particle beam of a first kinetic energy along a preselected path; a conveyor which conveys items to be irradiated through the beam; and, a beam kinetic energy monitor for monitoring a second kinetic energy of the beam after it has passed through the item. 15. The apparatus as set forth in claim 14 , further including: claim 14 a processor for comparing the first and second beam energies and determining a dose of the charged particle beam absorbed by the item. 16. The apparatus as set forth in claim 15 , wherein the processor is disposed remote from the monitors and further including: claim 15 a transducer for converting an output of the monitors into optical signals, the transducer being disposed adjacent the monitor such that the output from the monitor is conveyed from the irradiation region in an optical format. 17. The apparatus as set forth in claim 15 , wherein the beam generator includes a beam strength control circuit for controlling at least one of charged particle beam voltage and current and wherein the conveyor includes a speed control circuit for controlling a speed with which the items are moved through the charged particle beam, and further including: claim 15 a parameter adjustment processor which compares the determined absorbed doses with target absorbed doses and selectively adjusts at least one of the beam strength control circuit and the conveyor speed control circuit. 18. The apparatus as set forth in claim 17 , wherein the charged particle beam generator further includes a sweep control circuit for sweeping the charged particle beam back and forth across at least one of a planar region and a volumetric region and wherein the beam strength monitor includes: claim 17 first and second current transformers in which a current is induced by the electron beam; a metal absorbing foil disposed between the first and second current transformers whereby the current induced the second current transformer is less than the current induced the first current transformer; and, a vacuum chamber in which the first and second current transformers and the absorbing foil are disposed. 19. The apparatus as set forth in claim 14 , wherein the charged particle beam generator includes an electron accelerator. claim 14 20. An energy detector comprising: first and second inductive coils in which currents are induced by an electron beam; a metal layer of preselected thickness disposed between the first and second inductive coils; a beam collimator upstream of the inductive coils which collimates the electron beam to a preselected cross-section. 21. The energy detector as set forth in claim 20 , further including: claim 20 a vacuum chamber in which the inductive coils and the metal foil are disposed. 22. A method of irradiating comprising: moving items through a charged particle beam; determining a kinetic energy of the charged particle beam entering the item; measuring a kinetic energy of the charged particle beam exiting the item; determining an absorbed kinetic energy by subtracting the kinetic energy of the charged particle beam exciting the item from the kinetic energy of the beam before entering the item; dividing the determined absorbed kinetic energy by a mass of the item irradiated by the charged particle beam. 23. The method as set forth in claim 22 , further including: claim 22 determining a charge deposited in the irradiated item by the absorbed charged particle beam. 24. The method as set forth in claim 23 , further including: claim 23 multiplying the absorbed kinetic energy by the deposited charge. 25. The method as set forth in claim 24 , wherein determining the deposited charge includes: claim 24 measuring a beam current of the charged particle beam after irradiating the product. 26. An irradiating method including: collimating a charged particle beam to a preselected cross-section; passing the charged particle beam through an item; determining the energy of the beam entering the item by inducing a first electromotive force with the collimated beam; attenuating the collimated beam with the item; determining the energy of the beam exiting the item by inducing a second electromotive force with the attenuated electron beam; and, comparing the first and second electromotive forces. 27. A method of determining an absorbed dose deposited by an electron beam in an irradiated product comprising: determining an absorbed kinetic energy by subtracting a final kinetic energy of the electron beam exciting the product from an initial kinetic energy of the beam before entering the product; dividing the determined absorbed kinetic energy by a mass of the product irradiated by the electron beam. 28. An irradiation apparatus comprising: a charged particle beam generator for generating and aiming a charged particle beam of a first energy along a preselected path; a conveyor which conveys items to be irradiated through the beam; and, a beam strength monitor for monitoring a second energy of the beam after it has passed through the item, the monitor including: a vacuum chamber; first and second current transformers; a foil having known absorption characteristics disposed between of the first current transformer and the second current transformer. 29. The apparatus as set forth in claim 28 , further including: claim 28 a collimator disposed upstream of the current transformers for collimating the charged particle beam before it passes through the first current transformer, foil, and the second current transformer. 30. The apparatus as set forth in claim 28 , further including: claim 28 a comparitor which compares the currents induced in the first and second current transformers and determines therefrom the energy of the charged particle beam. 31. An apparatus for detecting energy of an electron beam, the apparatus comprising: a means for collimating an electron beam to a preselected cross-section; a first means in which the collimated electron beam induces a first electromotive force before being attenuated; a second means in which the electron beam induces a second electromotive force after the collimated electron beam has been attenuated; and, a means for comparing the first and second electromotive forces. 32. An apparatus for determining an absorbed dose deposited by an electron beam in an irradiated product comprising: a means for subtracting a final kinetic energy of the electron beam exciting the product from an initial kinetic energy of the beam before entering the product; a means for dividing the difference between the initial and final kinetic energy by a mass of the product irradiated by the electron beam.

summary

description

The invention relates generally to collimators for use in diagnostic imaging and, more particularly, to a two dimensional reflector and collimator assembly and method of manufacturing thereof. Typically, in computed tomography (CT) imaging systems, an x-ray source emits a fan-shaped beam toward a subject or object, such as a patient or a piece of luggage. Hereinafter, the terms “subject” and “object” shall include anything capable of being imaged. The beam, after being attenuated by the subject, impinges upon an array of radiation detectors. The intensity of the attenuated beam radiation received at the detector array is typically dependent upon the attenuation of the x-ray beam by the subject. Each detector element of the detector array produces a separate electrical signal indicative of the attenuated beam received by each detector element. The electrical signals are transmitted to a data processing system for analysis which ultimately produces an image. Generally, the x-ray source and the detector array are rotated about the gantry within an imaging plane and around the subject. X-ray sources typically include x-ray tubes, which emit the x-ray beam at a focal point. X-ray detectors typically include a collimator for collimating x-ray beams received at the detector, a scintillator for converting x-rays to light energy adjacent the collimator, and photodiodes for receiving the light energy from the adjacent scintillator and producing electrical signals therefrom. The outputs of the photodiodes are then transmitted to the data processing system for image reconstruction. As stated above, typical x-ray detectors include a collimator for collimating x-ray beams such that collection of scattered x-rays is minimized. As such, the collimators operate to attenuate off-angle scattered x-rays from being detected by a scintillator cell. Reducing this scattering reduces noise in the signal and improves the final reconstructed image. Therefore, it is necessary that the scintillator array and the collimator, typically plates extending along one dimension above the scintillator array, are uniformly aligned. That is, exact mechanical alignment is required between the collimator plates and the cast reflector lines in the array of scintillators. Known manufacturing processes attempt this exact alignment by constructing a continuous collimator that is sized to dimensionally match the width and length of the entire detector array. That is, the collimator plates are arranged or arrayed in a continuous consistent pattern or pitch that spans the entire detector length and is placed and attached to the detector rail structure. As such, individual scintillator arrays or packs must then be exactly aligned to the continuous collimator to ensure that all scintillator cells and collimator cells are aligned exactly; otherwise the collimator must be discarded or repaired, or the scintillator packs must be discarded. This process requires excessively tight tolerancing and requires great operator skill and patience to assemble. Accordingly, these known processes are susceptible to waste of parts, material, and labor. A known CT detector 1 fabricated according to known manufacturing processes is shown in FIG. 1. The CT detector 1 includes a series of tungsten collimator plates 2 configured and position to collimate, in one dimension, x-rays projected toward scintillator cells 3 of a scintillator array 4. As shown, each of the collimator plates 2 is generally aligned with a reflector line 5 disposed between adjacent scintillators 3. The reflector lines 5 prevent light from being emitted between adjacent scintillators. The scintillator array is coupled to a photodiode array 6 that detects light emissions from the scintillator array and transmits corresponding electrical signals to a data acquisition system for signal processing. As readily shown, the collimator plates are not integrated with the individual scintillator elements 3. That is, an air gap 7 exists between the collimator plates and the scintillator cells 3. The air gap 7 typically results in a separation between the collimator plates and the scintillator array of approximately two to four thousandths of an inch. This air gap occurs as a result of the manufacturing process whereupon the collimator plates are formed as a single collimator assembly that accepts and aligns an array of scintillators. The air gap, however, makes the CT detector susceptible to x-rays received between two collimator plates impinging upon an adjacent scintillator thereby resulting in undesirable anomalies in the final reconstructed CT image. Additionally, and as shown in FIG. 1, the collimator plates 2 serve to collimate x-rays projected toward scintillator cells 3 in only one dimension, which places limitations on the effectiveness of the collimator assembly. Therefore, it would be desirable to design a reflector and collimator assembly and method of manufacturing thereof that provides for easy alignment between the scintillator array and the collimator assembly and that effectively prevents cross-talk between adjacent scintillators. It would further be desirable to provide a reflector and collimator assembly and method of manufacturing thereof that provides for two-dimensional collimation of x-rays. Embodiments of the invention are directed to a two dimensional reflector and collimator assembly and a method of manufacturing thereof. In accordance with one aspect of the invention, a collimator assembly for a CT imaging system positioned between an object to be scanned and a CT detector includes a wall structure constructed to form a two dimensional array of channels to collimate x-rays. The wall structure further includes a first portion positioned proximate the object to be scanned and configured to absorb scattered x-rays and a second portion formed integrally with the first portion and extending out from the first portion away from the object to be scanned, with a height of the first portion being greater than a height of the second portion. The second portion of the wall structure includes a reflective material coated on the wall structure in each of the channels forming the two dimensional array of channels. In accordance with another aspect of the invention, a method of fabricating a collimator assembly for a CT medical imaging system includes providing a powder material having a density and atomic number that is sufficient to substantially absorb x-rays, providing a binding agent, and mixing the powder material and the binding agent to form a collimator material. The method also includes the step of extruding the collimator material through a collimator extrusion die to form a honeycomb collimator assembly, with the honeycomb collimator assembly comprising a two dimensional array of channels formed therethrough. In accordance with yet another aspect of the invention, a CT imaging system includes a rotatable gantry having an opening to receive an object to be scanned, a high frequency electromagnetic energy projection source configured to project a high frequency electromagnetic energy beam toward the object, and a scintillator array positioned on the gantry opposite the high frequency electromagnetic energy projection source, the scintillator array including a plurality of scintillator cells configured to detect high frequency electromagnetic energy passing through the object. The CT imaging system also includes a collimator assembly positioned between the object and the scintillator array, with the collimator assembly comprising a honeycomb wall structure configured to form a two dimensional array of channels to collimate x-rays. A portion of the collimator assembly is formed about the scintillator array such that each of the plurality of scintillator cells is housed within a respective channel in the two dimensional array of channels. Various other features and advantages will be made apparent from the following detailed description and the drawings. The operating environment of the invention is described with respect to a sixty-four-slice computed tomography (CT) system. However, it will be appreciated by those skilled in the art that the invention is equally applicable for use with other multi-slice configurations. Moreover, the invention will be described with respect to the detection and conversion of x-rays. However, one skilled in the art will further appreciate that the invention is equally applicable for the detection and conversion of other high frequency electromagnetic energy. The invention will be described with respect to a “third generation” CT scanner, but is equally applicable with other CT systems. Referring to FIG. 2, a computed tomography (CT) imaging system 10 is shown as including a gantry 12 representative of a “third generation” CT scanner. Gantry 12 has an x-ray source 14 that projects a beam of x-rays toward a detector assembly or collimator 18 on the opposite side of the gantry 12. Referring now to FIG. 3, detector assembly 18 is formed by a plurality of detectors 20 and data acquisition systems (DAS) 32. The plurality of detectors 20 sense the projected x-rays 16 that pass through a medical patient 22, and DAS 32 converts the data to digital signals for subsequent processing. Each detector 20 produces an analog electrical signal that represents the intensity of an impinging x-ray beam and hence the attenuated beam as it passes through the patient 22. During a scan to acquire x-ray projection data, gantry 12 and the components mounted thereon rotate about a center of rotation 24. Rotation of gantry 12 and the operation of x-ray source 14 are governed by a control mechanism 26 of CT system 10. Control mechanism 26 includes an x-ray controller 28 that provides power and timing signals to an x-ray source 14 and a gantry motor controller 30 that controls the rotational speed and position of gantry 12. An image reconstructor 34 receives sampled and digitized x-ray data from DAS 32 and performs high speed reconstruction. The reconstructed image is applied as an input to a computer 36 which stores the image in a mass storage device 38. Computer 36 also receives commands and scanning parameters from an operator via console 40 that has some form of operator interface, such as a keyboard, mouse, voice activated controller, or any other suitable input apparatus. An associated display 42 allows the operator to observe the reconstructed image and other data from computer 36. The operator supplied commands and parameters are used by computer 36 to provide control signals and information to DAS 32, x-ray controller 28 and gantry motor controller 30. In addition, computer 36 operates a table motor controller 44 which controls a motorized table 46 to position patient 22 and gantry 12. Particularly, table 46 moves patients 22 through a gantry opening 48 of FIG. 2 in whole or in part. As shown in FIG. 4, detector assembly 18 includes rails 17 having a plurality of reflector-collimator assemblies 19, hereinafter generally referred to as “collimator assemblies,” placed thereon and having detectors 20 secured thereto. Collimator assemblies 19 are positioned on rail to collimate x-rays 16 before such beams impinge upon, for instance, detector elements 50 of FIG. 5 positioned within the collimator assembly. In one embodiment, detector assembly 18 includes 57 detectors 20, each detector 20 having an array size of 64×16 of pixel elements 50. As a result, detector assembly 18 has 64 rows and 912 columns (16×57 detectors) which allows 64 simultaneous slices of data to be collected with each rotation of gantry 12. A detector 20 is shown in FIG. 5 for use with embodiments of the invention. Each detector 20 includes a number of detector elements 50 (i.e., scintillator pixels) forming an array 51 (i.e., scintillator array). Scintillator array 51 is optically coupled to a backlit diode array 53 having a plurality of diodes 59, with backlit diode array 53 in turn being positioned on, and electrically coupled to, multi-layer substrate 54. While scintillator array 51 is described as forming part of detector 20, scintillator pixels 50 are in fact positioned within a portion of collimator assembly 19, which is then positioned relative to diode array 53 and the remainder of detector 20, as is explained in greater detail below. As further shown in FIG. 5, detectors 20 also include pins 52 positioned relative to scintillator array 51 and spacers 55 positioned on multi-layer substrate 54. Flex circuits 56 are attached to face 57 of multi-layer substrate 54 and to DAS 32. Detectors 20 are positioned within detector assembly 18 by use of pins 52. In the operation of one embodiment, x-rays impinging within detector elements 50 generate photons which traverse scintillator array 51, thereby generating an analog signal which is detected on a diode within backlit diode array 53. The analog signal generated is carried through multi-layer substrate 54, through flex circuits 56, to DAS 32 wherein the analog signal is converted to a digital signal. Referring now to FIG. 6, collimator assembly 19 is shown according to an embodiment of the present invention. Collimator assembly 19 is configured as a “two dimensional collimator” in that a wall structure 60 forming the collimator assembly 19 has a honeycomb structure. A plurality of walls 62 forming wall structure 60 are arranged to define a two dimensional array of channels 64 that collimate x-rays attenuated by subject 22, for example, prior to the x-rays impinging upon detector 20 (FIG. 5). The wall structure 60 of collimator assembly 19 is formed and arranged such that a pitch of channels 64 is identical to a pitch of detector elements 50 (FIG. 5), which according to one embodiment are formed as scintillator pixels. According to an exemplary embodiment, walls 62 of wall structure 60 are thus formed to have a thickness of 0.10 to 0.20 mm and walls 62 are spaced apart to have a pitch of 1.0 to 1.2 mm, for example. According to an exemplary embodiment of the invention, wall structure 60 of collimator assembly 19 is composed of a mixed metal and binder material having a density and atomic number that is sufficient to substantially absorb x-rays. According to an exemplary embodiment, a powder composed of a heavy metal, heavy metal alloy powder, or heavy metal oxide is mixed with an organic polymer or thermoplastic material to provide a mixed collimator forming material, hereinafter referred to generally as a “mixed metal-binder material.” Thus, wall structure 60 may be formed of Pb, Ta, W, Au, or Pt powder, for example, that is bonded with an organic polymer or thermoplastic material. The mixed metal-binder material is extruded through a collimator extrusion die (not shown) to form the wall structure 60 and the channels 64 therein. A cross-sectional view of a portion of collimator assembly 19 is shown in FIG. 7. While collimator assembly 19 is shown as having a wall structure 60 defining only four channels 64, it is noted that FIG. 7 is for illustrative purposes only and that collimator assembly 19 would be formed to include a wall structure 60 that defines a greater number of channels arranged in a two-dimensional array, such as shown in FIG. 6. As shown in FIG. 7, wall structure 60 is generally defined as including a first portion 66 and a second portion 68 stacked in a vertical arrangement, according to an exemplary embodiment of the invention. While wall structure 60 of collimator assembly 19 is formed as an integral structure, and thus first and second portions 66, 68 are in fact formed as a single unitary structure, the first portion 66 of the collimator assembly 19 is identified as functioning as a collimator to collimate x-rays, while the second portion 68 is identified as functioning as a reflective grid that separates individual detector cells 50 (i.e., scintillator pixels) from each other to prevent cross-talk therebetween. As shown in FIG. 7, scintillator pixels 50 having a reflective material 71 coated on a top surface thereof are positioned within second portion 68 of wall structure 60, such that each scintillator pixel is housed within a respective channel 64 of the array of channels in collimator assembly 19. The first portion 66 of collimator assembly 19 is positioned proximate subject 22 (FIG. 1) so as to receive x-rays 16 attenuated therefrom. As set forth above, wall structure 60 is formed of a mixed metal-binder material having a density and atomic number that is sufficient to substantially absorb x-rays. Thus, as shown in FIG. 7, x-rays entering collimator assembly 19 at an undesired scatter angle are absorbed by first portion 66 of wall structure 60. The second portion 68 of wall structure 60 extends out from the first portion 66 away from the subject (i.e., downstream of x-rays) so as to receive x-rays 16 that pass through first portion 66. The second portion 68 of wall structure 60 includes a reflective material 70 that is coated on walls 62 such that each of the channels 64 forming the two dimensional array of channels is coated with the reflective material 70. The reflective material 70 and 71 may be composed of Al, Ag, Au, TiO2, BaSO4, and MgO, or some other similar material that acts to reflect light thereoff. That is, as collimated x-rays 16 pass through first portion 66 of wall structure 60 and impinge on the scintillator material of detector cells 50 housed in second portion 68 of wall structure 60, photons are generated. The reflective material 70 coated on walls 62 and reflective material 71 coated on the top of scintillator pixels 50 act to reflect these photons, such that they are trapped within a particular detector cell 50, allowing for readout thereof by diode array 53 (FIG. 5) without cross-talk interference from adjacent detector cells. As shown in FIG. 7, first portion 66 of wall structure 60 is formed to have a height 72 that is greater than a height 74 of second portion 68 of wall structure 60. According to an exemplary embodiment, a height of first portion 66 is at least twice a height of second portion 68. Thus, a height of first portion 66 may be approximately 8 mm and a height of second portion 68 may be approximately 1.5-3 mm, for example. A height ratio between first and second portions 66, 68 such as the one set forth above provides for first portion 66 of wall structure 60 to properly collimate x-rays 16 passing therethrough, while still allowing for a desired dose of x-rays to reach detector cells 50. Referring now to FIG. 8, a technique 76 for manufacturing collimator assembly 19 is set forth according to an embodiment of the invention. The technique 76 begins with the providing of materials for forming the collimator assembly at block 77. The materials include a metal or ceramic material having a density and atomic number that is sufficient to substantially absorb x-rays, as well as a binder material that is mixed with the metal/ceramic material in order to form a collimator assembly having sufficient rigidity and structural strength. According to an exemplary embodiment, the metal/ceramic material is in the form of a powder composed of a heavy metal, heavy metal alloy, heavy metal oxide, or ceramic, examples of which include Pb, Ta, W, Au, Pt, WO3, BiO3, Ta2O5, PbO, and heavy rare earth metal oxides such as Gd2O3, Lu2O3, etc. The metal/ceramic powder is then mixed with the binder material at block 78, which according to the embodiment of FIG. 8, is in the form of an organic polymer such as silicone, epoxy, or polyimide, for example. A mixed metal-binder material is formed upon combination of the metal/ceramic powder and the binding material. The mixed metal-binder material is extruded through a collimator extrusion die at block 79 to form the honeycomb wall structure of the collimator assembly having the two-dimensional array of channels therein. In a next step of the manufacturing technique 76, the extruded wall structure is sintered at block 80 so as to increase the mechanical strength of the wall structure to a desired level. In order to reduce surface roughness of the wall structure resulting from the sintering process, the wall structure is chemically polished at block 81. Upon chemical polishing of the wall structure, a reflective material is coated on the wall structure within each of the channels at block 82. According to an exemplary embodiment, the reflective material is coated on only a bottom or “second” portion of each channel (i.e., a portion adjacent to detector 20). The reflective material may be composed of Al, Ag, Au, TiO2, BaSO4, and MgO, or some other similar material that acts to reflect photons (i.e., light) thereoff. The manufacturing technique 76 continues with positioning of detector elements relative to the collimator assembly at block 83. Detector elements, in the form of scintillator pixels or crystals having a reflective material coated on a top surface thereof, are positioned relative to the collimator assembly such that an individual detector element is positioned within each of the channels in the collimator assembly. That is, a scintillator pixel/crystal is positioned within each of the channels in the collimator assembly in the bottom or “second” portion of the channel, such that the scintillator pixel/crystal is within that portion of the channel that has been coated with the reflective material. Accordingly, as x-rays pass through upper or “first” portion of the wall structure to impinge on the scintillator material housed in the bottom/second portion of the channel, photons generated by the scintillator material will be contained in each pixel by the reflection provided by the reflective material coated within the channels of the wall structure and on the top of the scintillator pixels. Referring now to FIG. 9, a technique 90 for manufacturing collimator assembly 19 is set forth according to another embodiment of the invention. The technique 90 begins with the providing of materials for forming the collimator assembly at block 91. The materials include a metal or ceramic material having a density and atomic number that is sufficient to substantially absorb x-rays, as well as a binder material that is mixed with the metal/ceramic material in order to form a collimator assembly having sufficient rigidity and structural strength. According to an exemplary embodiment, the metal/ceramic material is in the form of a powder composed of a heavy metal, heavy metal alloy, heavy metal oxide, or ceramic. The metal/ceramic powder is then mixed with the binder material at block 92, which according to the embodiment of FIG. 9 is in the form of a thermoplastic material. A mixed metal-binder material is formed upon combination of the metal/ceramic powder and the thermoplastic. The mixed metal-binder material is extruded through a collimator extrusion die at block 93 to form the honeycomb wall structure of the collimator assembly having the two-dimensional array of channels therein. Based on the structural rigidity and strength provided by the thermoplastic binding material, no sintering or further strengthening process need be applied to the extruded wall structure. Thus, the manufacturing technique continues with the application of a reflective material on the wall structure within each of the channels at block 94. According to an exemplary embodiment, the reflective material is coated on only a bottom or “second” portion of each channel (i.e., a portion adjacent to detector 20). The reflective material may be composed of Al, Ag, Au, TiO2, BaSO4, and MgO, or some other similar material that acts to reflect photons (i.e., light) thereoff. The manufacturing technique continues with positioning of detector elements relative to the collimator assembly at block 95. Detector elements, in the form of scintillator pixels or crystals having a reflective material coated on a top surface thereof, are positioned relative to the collimator assembly such that an individual detector element is positioned within each of the channels in the collimator assembly. That is, a scintillator pixel/crystal is positioned within each of the channels in the collimator assembly in the bottom or “second” portion of the channel, such that the scintillator pixel/crystal is within that portion of the channel that has been coated with the reflective material. Accordingly, as x-rays pass through upper or “first” portion of the wall structure to impinge on the scintillator material housed in the bottom/second portion of the channel, photons generated by the scintillator material will be contained in each pixel by the reflection provided by the reflective material coated within the channels of the wall structure and on the top of the scintillator pixels. Beneficially, the manufacturing techniques shown and described in each of FIGS. 8 and 9 allow for fine-tuning of the properties of the collimator assembly. That is, the properties of the collimator assembly can be tuned by the die design, the ratio of metal/ceramic to binder in the collimator formation mixture, and the thickness and height of the wall of the honeycomb collimator assembly. Additionally, the manufacturing techniques shown and described in each of FIGS. 8 and 9 eliminate an air gap that typically exists between collimator plates and scintillator cells by positioning the scintillator cells/pixels into the two-dimensional array of channels in the collimator assembly. Furthermore, the manufacturing techniques shown and described in each of FIGS. 8 and 9 provide for a collimator assembly that allows for higher spatial resolution in generated CT images. Referring now to FIG. 10, a package/baggage inspection system 100 is shown that can incorporate a collimator assembly 19 (FIGS. 6 and 7) and that includes a rotatable gantry 102 having an opening 104 therein through which packages or pieces of baggage may pass. The rotatable gantry 102 houses a high frequency electromagnetic energy source 106 as well as a detector assembly 108 having scintillator arrays comprised of scintillator cells similar to that shown in FIG. 6 or 7. A conveyor system 110 is also provided and includes a conveyor belt 112 supported by structure 114 to automatically and continuously pass packages or baggage pieces 116 through opening 104 to be scanned. Objects 116 are fed through opening 104 by conveyor belt 112, imaging data is then acquired, and the conveyor belt 112 removes the packages 116 from opening 104 in a controlled and continuous manner. As a result, postal inspectors, baggage handlers, and other security personnel may non-invasively inspect the contents of packages 116 for explosives, knives, guns, contraband, etc. Therefore, according to one embodiment of the invention, a collimator assembly for a CT imaging system positioned between an object to be scanned and a CT detector includes a wall structure constructed to form a two dimensional array of channels to collimate x-rays. The wall structure further includes a first portion positioned proximate the object to be scanned and configured to absorb scattered x-rays and a second portion formed integrally with the first portion and extending out from the first portion away from the object to be scanned, with a height of the first portion being greater than a height of the second portion. The second portion of the wall structure includes a reflective material coated on the wall structure in each of the channels forming the two dimensional array of channels. According to another embodiment of the invention, a method of fabricating a collimator assembly for a CT medical imaging system includes providing a powder material having a density and atomic number that is sufficient to substantially absorb x-rays, providing a binding agent, and mixing the powder material and the binding agent to form a collimator material. The method also includes the step of extruding the collimator material through a collimator extrusion die to form a honeycomb collimator assembly, with the honeycomb collimator assembly comprising a two dimensional array of channels formed therethrough. According to yet another embodiment of the invention, a CT imaging system includes a rotatable gantry having an opening to receive an object to be scanned, a high frequency electromagnetic energy projection source configured to project a high frequency electromagnetic energy beam toward the object, and a scintillator array positioned on the gantry opposite the high frequency electromagnetic energy projection source, the scintillator array including a plurality of scintillator cells configured to detect high frequency electromagnetic energy passing through the object. The CT imaging system also includes a collimator assembly positioned between the object and the scintillator array, with the collimator assembly comprising a honeycomb wall structure configured to form a two dimensional array of channels to collimate x-rays. A portion of the collimator assembly is formed about the scintillator array such that each of the plurality of scintillator cells is housed within a respective channel in the two dimensional array of channels. This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.

summary

claims

1. A method of manufacturing an integrated circuit (IC) device, the method comprising:forming a photoresist layer on a substrate; andexposing the photoresist layer to light by using a photolithographic apparatus including a light generator,wherein the light generator includes:a chamber having a plasma generation space,an optical collector in the chamber, the optical collector having an aperture, anda debris shielding assembly between the optical collector and the plasma generation space in the chamber,wherein the debris shielding assembly includes:a protective film facing the optical collector and being spaced apart from the optical collector with a protected space therebetween, the protected space including an optical path, the protective film having a through hole in a center region of the protective film, and the through hole being spaced apart from the aperture with the protected space therebetween, anda protective frame attaching the protective film to the optical collector, the protective frame to support the protective film and to shield the protected space from the plasma generation space. 2. The method as claimed in claim 1, wherein the protective film includes a material that is transparent with respect to a laser beam having a wavelength of about 1064 nm, a laser beam having a wavelength of about 10.6 μm, and extreme ultraviolet (EUV) light having a wavelength of about 13.5 nm. 3. The method as claimed in claim 1, wherein the protective film includes carbon nanotube, diamond, graphite, graphene, fullerene, or a combination thereof. 4. The method as claimed in claim 1, wherein the protective film includes a carbon nanotube film having single-wall carbon nanotubes (SWCNT), multiwall carbon nanotubes (MWCNT), or a combination thereof. 5. The method as claimed in claim 1, wherein the protective frame includes a metal. 6. The method as claimed in claim 1, wherein the protective frame includes:a support portion in contact with an edge portion of the optical collector; anda shield portion integrally connected with the support portion, the shield portion extending between the support portion and the protected film to shield the protective space from the plasma generation space. 7. The method as claimed in claim 1, wherein the protective frame includes:a support portion in contact to an edge portion of the optical collector;a shield portion extending between the support portion and the protective film to shield the protected space from the plasma generation space; andan outer fixing portion facing the shield portion with the protective film therebetween and supporting the protective film in cooperation with the shield portion. 8. The method as claimed in claim 7, wherein the protective frame further includes at least one of a first buffer film that is between the shield portion and the protective film, and a second buffer film that is between the protective film and the outer fixing portion. 9. The method as claimed in claim 7, wherein the shield portion includes an elliptic surface facing the protected space. 10. The method as claimed in claim 7, wherein the shield portion includes a reflective surface facing the protected space, and the reflective surface is an elliptic surface. 11. A method of manufacturing an integrated circuit (IC) device, the method comprising:forming a photoresist layer on a substrate; andexposing the photoresist layer to light by using a photolithographic apparatus including a light generator,wherein the light generator includes:a chamber having a plasma generation space,an optical collector in the chamber, the optical collector having an aperture and a reflective surface, anda debris shielding assembly between the optical collector and the plasma generation space in the chamber,wherein the debris shielding assembly includes:a protective film spaced apart from the reflective surface with a protected space therebetween and facing the reflective surface, the protected space including an optical path, the protective film having a through hole at a position corresponding to the optical path in the protective film, and the through hole being spaced apart from the aperture with the protected space therebetween, anda protective frame that is in contact with an edge portion of the optical collector and supports the protective film. 12. The method as claimed in claim 11, wherein the protective frame includes:a support portion in contact with the edge portion of the optical collector;a shield portion integrally connected with the support portion and having an inner surface between the support portion and the protective film, the inner surface facing the protected space; andan outer fixing portion facing the shield portion with the protective film therebetween and supporting the protective film in cooperation with the shield portion. 13. The method as claimed in claim 12, wherein the support portion includes a ring member extending from the shield portion, the ring member having a straight cross-sectional shape or an L-like cross-sectional shape. 14. The method as claimed in claim 12, wherein the shield portion includes a shield frame and a reflective layer on the shield frame, the reflective layer being exposed to the protected space, and the reflective layer defining an elliptic surface together with the reflective surface of the optical collector. 15. The method as claimed in claim 11, wherein the protective frame has widths varying in a circumferential direction with respect to a central axis of the debris shielding assembly. 16. The method as claimed in claim 11, wherein the debris shielding assembly further includes a fixing member that couples the protective film and the protective frame. 17. A method of manufacturing an integrated circuit (IC) device, the method comprising:forming a photoresist layer on a substrate; andexposing the photoresist layer to light by using a photolithographic apparatus including a light generator,wherein the light generator includes:a chamber having a plasma generation space;an optical collector in the chamber, the optical collector having an aperture and a reflective surface; anda debris shielding assembly between the optical collector and the plasma generation space in the chamber,wherein the debris shielding assembly includes:a protective film facing the reflective surface with a protected space therebetween, the protected space including an optical path, the protective film having a through hole at a position corresponding to the optical path in the protective film, and the through hole being spaced apart from the aperture with the protected space therebetween, anda protective frame attaching the protective film to an edge of the optical collector, the protective frame extending along an entire perimeter of the edge of the optical collector. 18. The method as claimed in claim 17, wherein exposing the photoresist layer includes using EUV light generated in the light generator.

abstract

A multi-layered cladding material including a ceramic matrix composite and a metallic material, and a tube formed from the cladding material. The metallic material forms an inner liner of the tube and enables hermetic sealing of thereof. The metallic material at ends of the tube may be exposed and have an increased thickness enabling end cap welding. The metallic material may, optionally, be formed to infiltrate voids in the ceramic matrix composite, the ceramic matrix composite encapsulated by the metallic material. The ceramic matrix composite includes a fiber reinforcement and provides increased mechanical strength, stiffness, thermal shock resistance and high temperature load capacity to the metallic material of the inner liner. The tube may be used as a containment vessel for nuclear fuel used in a nuclear power plant or other reactor. Methods for forming the tube comprising the ceramic matrix composite and the metallic material are also disclosed.

claims

1. An optical apparatus for radiation having a wavelength xe2x89xa6160 nm, comprising: a mirror with a mirror surface; and a device for producing elastic oscillations on said mirror surface, wherein said elastic oscillations cause radiation impinging on said mirror surface to be diffracted. 2. The optical apparatus of claim 1 , wherein said device generates surface acoustical waves on said mirror surface produce said elastic oscillations. claim 1 3. The optical apparatus of claim 2 , wherein said surface acoustical waves produce a diffraction grid on said mirror surface. claim 2 4. The optical apparatus of claim 2 , wherein said surface acoustical waves have a wavelength in the range of about 1 xcexcm to 50 xcexcm. claim 2 5. The optical apparatus of claim 2 , wherein said surface acoustical waves have an amplitude in the range of about 1 nm to 100 nm. claim 2 6. The optical apparatus of claim 2 , wherein said surface acoustical waves have a frequency that is varied. claim 2 7. The optical apparatus of claim 2 , claim 2 wherein said device is a first device and said surface acoustical waves are first surface acoustical waves, and wherein said optical apparatus further comprises: a second device for generating second acoustical waves on said mirror surface, wherein said second surface acoustical waves are parallel to said first surface acoustical waves. 8. The optical apparatus of claim 7 , wherein said mirror surface comprises a plurality of individual mirror surfaces. claim 7 9. The optical apparatus of claim 2 , claim 2 wherein said device is a first device and said surface acoustical waves are first surface acoustical waves, and wherein said optical apparatus further comprises: a second device for generating second acoustical waves on said mirror surface, wherein said second surface acoustical waves are not parallel to said first surface acoustical waves. 10. The optical apparatus of claim 9 , wherein said mirror surface comprises a plurality of individual mirror surfaces. claim 9 11. A method, using the optical apparatus of claim 2 , for illuminating a predetermined range of angles (xcex1) with said radiation, said method comprising: claim 2 generating said surface acoustical waves; and varying a frequency of said surface acoustical waves, wherein said surface acoustical waves produce a plurality of grid lines on said mirror surface, wherein said radiation impinges two or more of said plurality of grid lines, and wherein said radiation is diffracted in said predetermined range of angles (xcex1) and, when averaged over time, homogeneously illuminates said predetermined range of angles (xcex1). 12. The method of claim 11 , wherein said predetermined range of angles (xcex1) is about xe2x88x9212.0 mrad xe2x89xa6xcex1xe2x89xa612.0 mrad. claim 11 13. The optical apparatus of claim 1 , wherein said device comprises a piezoelectric foil. claim 1 14. The optical apparatus of claim 13 , wherein said piezoelectric foil is a PZT film. claim 13 15. The optical apparatus of claim 1 , wherein said device comprises a piezoeleetne crystal. claim 1 16. The optical apparatus of claim 1 , wherein said device comprises a point-like or linear-form electrode. claim 1 17. The optical apparatus of claim 1 , wherein the optical apparatus is a component in an exposure device for lithography. claim 1 18. The optical apparatus of claim 17 , wherein said exposure device comprises a source of said raditation, and wherein the optical apparatus broadens a beam of said source. claim 17 19. The optical apparatus of claim 17 , wherein said exposure device comprises an illumination system, and wherein the optical apparatus varies an illumination setting of said illumination system. claim 17 20. The optical apparatus of claim 17 , wherein the optical apparatus homogenizes an illumination of a pupil of said exposure device. claim 17 21. A method for producing the optical apparatus of claim 1 , comprising: claim 1 superpolishing a side of a substrate to yield a surface roughness of less than about 0.5 nm; and attaching an electrode to said substrate, wherein said mirror surface comprises said side of said substrate, and wherein said device comprises said electrode. 22. The method of claim 21 , wherein said electrode is attached to said superpolished side of said substrate. claim 21 23. The optical apparatus of claim 1 , wherein said device comprises a piezoelectric foil. claim 1 24. The optical apparatus of claim 1 , wherein said elastic oscillations generate a plurality of diffraction grids on said mirror surface. claim 1 25. The optical apparatus of claim 24 , wherein said plurality of diffraction grids are provided by varying a frequency of said elastic oscillations. claim 24 26. The optical apparatus of claim 1 , wherein said device is a first device, and wherein said optical apparatus further comprises a second device for producing elastic oscillations on said mirror surface. claim 1 27. The optical apparatus of claim 26 , wherein said first and second devices are arranged on said mirror surface so that a beam of said radiation impinging on said mirror surface is modified in two dimensions. claim 26 28. The optical apparatus of claim 1 , wherein said device comprises an interdigital transformer. claim 1 29. An illumination system for microlithography having a radiation source for emitting radiation having a wavelength xe2x89xa6160 nm, comprising the optical apparatus of claim 1 . claim 1 30. A projection exposure apparatus for microlithography, comprising: the illumination system of claim 29 , for illuminating an object; and claim 29 a projection objective for imaging said object onto a light sensitive substrate. 31. An optical apparatus for radiation having a wavelength xe2x89xa6160 nm, comprising: a mirror with a mirror surface; and a device for producing elastic oscillations on said mirror surface, wherein said elastic oscillations cause radiation impinging on said mirror surface to be diffracted in a predetermined range of angles (xcex1), and wherein said predetermined range of angles (xcex1) is about xe2x88x9212 mrad=xcex1=mrad.

abstract

A scintillator panel includes a substrate having a substrate main surface, a substrate rear surface, and a substrate side surface; and a scintillator layer having a scintillator rear surface formed of a plurality of columnar crystals, a scintillator main surface, and a scintillator side surface. The substrate side surface and the scintillator side surface are substantially flush with each other. In the substrate, an angle between the substrate rear surface and the substrate side surface is smaller than 90 degrees.

abstract

A hazardous material storage repository includes a drillhole extending into the Earth and including an entry at least proximate a terranean surface, the drillhole including a substantially vertical drillhole portion, a transition drillhole portion coupled to the substantially vertical drillhole portion, and a hazardous material storage drillhole portion, at least one of the transition drillhole portion or the hazardous material storage drillhole portion including an isolation drillhole portion; a storage canister positioned in the hazardous material storage drillhole portion, the storage canister sized to fit from the drillhole entry through the substantially vertical drillhole portion, the transition drillhole portion, and into the hazardous material storage drillhole portion of the drillhole, the storage canister including an inner cavity sized enclose hazardous material; and a seal positioned in the drillhole, the seal isolating the hazardous material storage drillhole portion of the drillhole from the entry of the drillhole.

claims

1. A radiological barrier material comprising a matrix and a particulate having a cross sectional dimension of about 500 micrometers or less contained within the matrix, the particulate comprising a radiation absorber that absorbs either one or both of alpha and beta radiation, the particulate comprising a defined nanostructure, the defined nanostructure comprising an aluminosilicate nanotube, the radiation absorber comprising a metal oxide, the radiation absorber further comprising an energy absorbing chromophore on the surface of the particulate. 2. The radiological barrier material of claim 1, wherein the radiation absorber further comprises a semiconductor. 3. The radiological barrier material of claim 1, wherein the matrix comprises an organic matrix. 4. The radiological barrier material of claim 1, wherein the matrix comprises an inorganic matrix. 5. The radiological barrier material of claim 4, wherein the inorganic matrix comprises a glass or a ceramic. 6. The radiological barrier material of claim 1, wherein the radiological barrier material is in the form of a fiber or a sheet. 7. A container for radiation emitting material, the container comprising the radiological barrier material of claim 1. 8. The container of claim 7, wherein the container comprises a flexible bag. 9. The container of claim 8, wherein the container is a single-layer flexible bag. 10. Personal protective equipment comprising the radiological barrier material of claim 1. 11. The personal protective equipment of claim 10, wherein the personal protective equipment comprises a glove. 12. The personal protective equipment of claim 10, wherein the personal protective equipment comprises a face shield or a body suit. 13. The radiological barrier material of claim 1, wherein the metal oxide comprises TiO2, FeO2, AlO2, CeO2, WO4, Cr2O3, SiO2, MgO2, CaO2, BaO2, CoO, VO2, NiO2, CuO2, ZnO, YO2, Na2WO2, ZrO2 or a combination of one or more metal oxides. 14. The radiological barrier material of claim 1, wherein the particulate is formed of the metal oxide.

045432317

summary

BACKGROUND OF THE INVENTION This invention relates generally to plasma devices and particularly to the confinement and stabilization of plasmas in fusion devices by means of average magnetic well. More particularly, the present invention relates to the combination of multipole fields and the plasma pinch effect for the production of average magnetic well, most particularly in a toroidal system. Toroidal plasma devices are devices in which plasma is created in a topologically toroidal space, usually axisymmetric, and is confined therein by appropriate confining magnetic fields. Toroidal plasma devices are useful in the generation, confinement, heating, study and analysis of plasmas. In particular, such devices are useful for the reaction of deuterium and tritium, deuterium and deuterium or other nuclear fusible mixtures, with the production of high energy neutrons and energetic charged particles as products of the nuclear fusion reactions. The problems in nuclear fusion devices are largely to heat the plasma to a high enough temperature to enable the desired reactions to occur and to confine the heated plasma for a time long enough to release energy in excess of that required to heat the plasma to reaction temperature. The present invention is directed to the magnetic confinement of such plasma and finds particular utility in such devices and their applications, including experimental devices and the use thereof in experimentation and investigation with respect to toroidal plasma devices. A number of toroidal plasma devices have been suggested and built. The ones most closely related to the present invention are: tokamak devices, including doublet devices; multipole devices; and z-pinch devices, including reversed field pinch (RFP) devices. In such devices, gas is confined in a toroidal confinement vessel and is heated to form a plasma which is generally held away from the walls of the confinement vessel by appropriate magnetic fields. Such devices are all topologically toroidal and are usually axisymmetric. A topological torus is any geometric solid figure that can be produced by an imagined elastic deformation of an initial circular torus. An axisymmetric torus is obtained by rotating any plane geometric figure about the major toroidal axis. An axisymmetric toroidal device is one in which all quantities are invariant to rotation about the major toroidal axis. A necessary condition for the toroidal magnetic confinement of plasmas is that the complete set of magnetic field components results in a set of nested, toroidally closed magnetic surfaces. A magnetic surface is defined as a mathematical surface on which the magnetic field has no component normal thereto. The magnetic surface enclosing zero volume in the center of the nest is called an elliptic magnetic axis. Most devices have only a single elliptic magnetic axis and a single set of nested surfaces. However, doublet devices have two elliptic magnetic axes, and multipole devices have two or more sets of nested surfaces. In some toroidal devices, such as tokamak and pinch devices, the confining magnetic field includes magnetic field components produced by currents flowing through the confined plasma itself. When nested magnetic surfaces are present, this current is significantly concentrated into those magnetic surfaces closer to elliptic magnetic axes. Such regions of greater current density relative to the remainder of the plasma are called current channels. In those toroidal devices where it is required, a toroidal plasma current is usually produced by a transformer with the toroidal confined plasma acting as the secondary and with the primary being a central solenoid. Upon change of the current in the solenoid, a toroidal electric field is produced to ionize the gas and drive plasma current around the torus. A pinch effect takes place when electric current flowing through the plasma is acted upon by its own magnetic field to exert a confining pressure on the plasma. The large current simultaneously heats the plasma ohmically. However, this simplest configuration by itself, called the Bennett pinch, is unstable, and most of the plasma soon strikes the confinement vessel, hence cooling the plasma and impeding any reaction. For this reason, additional measures are taken to improve the stability of the system. The magnetohydrodynamic (MHD) stability of a magnetically confined plasma is dependent on the pitch of the magnetic field lines encircling the magnetic axis or axes. This pitch P is defined by ##EQU1## where .DELTA..zeta. is the distance traversed along the direction of the magnetic axis and k the number of times the axis is encircled, both while following a field line. This limit is the same for all possible field lines on a given magnetic surface. In toroidal plasma devices it is customary to use instead the safety factor q where EQU q=P/<R>. (2) Here <R> is the average major radius of the magnetic surface in question. For a general topological torus <R>=<C>/2.pi., where <C> is the average major circumference of the nonaxisymmetric magnetic surface in question. There is a corresponding relationship between P and safety factor q for still more general systems. In order to be magnetohydrodynamically stable, toroidal plasma devices must satisfy certain necessary conditions on q. If r is the mean minor radius, then these conditions are: (a) .vertline.q.vertline..noteq.1; and PA1 (b) ##EQU2## must be large enough to satisfy relevant criteria, including the Mercier and the Robinson criteria; in particular, dq/dr must not change sign within the plasma, and it may be zero only at a magnetic axis. Conditions (a) and (b) taken together require that in plasmas with current channels, such as tokamaks and z-pinches, either .vertline.q.vertline..gtoreq.1 on axis and increases monotonically everywhere else in the plasma; or else .vertline.q.vertline.<1 everywhere, decreases monotonically with increasing distance from the magnetic axis, passes smoothly through zero, and then increases monotonically with increasing distance from the magnetic axis in the outside regions of the plasma. The .vertline.q.vertline..gtoreq.1 case is realized in tokamaks, and the .vertline.q.vertline.<1 case in reversed field pinches. Condition (a) above is necessary to avoid a serious kink instability that arises when q.apprxeq.1. In the case of substantially circular flux surfaces in axisymmetric tori, Eq. (2) can be written in the easily applied form ##EQU3## where B.sub.T is the toroidal and B.sub.p the poloidal magnetic field intensity. The quantity s appearing in condition (b) above is the magnetic shear, which exerts a stabilizing effect on many classes of instabilities, particularly on ideal MHD interchange instabilities and on many microinstabilities. Another important property, which enhances stability by suppressing those MHD instabilities that are excited specifically by plasma pressure, is average magnetic well or minimum average B, where B is the magnetic field intensity. A review of the advantages of average magnetic well and of many configurations that have this property is given by H. P. Furth in Advances in Plasma Physics, Simon and Thompson, eds., 1 (Interscience Publishers, New York, 1968), pp. 67-100. The average square of the magnetic field intensity <B.sup.2 > on a flux surface is calculated by ##EQU4## where the integration is taken by following a magnetic field line for a sufficient distance to sample all of the magnetic surface. The simplest definition of average magnetic well in the limit where the plasma pressure is small is a minimum of <B.sup.2 > within the plasma. More generally, it has been shown by J. L. Johnson and J. M. Greene, Plasma Phys. 9 (1967), pp. 611-629, that magnetic well exists if V**<0, where ##EQU5## In the above equations, the integrations are over the volume enclosed by the flux surface, d.tau. is a differential volume, and V is the volume so enclosed. L, U, V and plasma pressure p are functions of flux, and the primes indicate differentiation with respect to flux. When p'=0, V**<0 is the same as having a minimum of <B.sup.2 > within the plasma. A magnetic well implies that the average of the magnitude of the magnetic field increases outwardly from the center of the device. Therefore, if the plasma is driven outward by an incipient instability, it encounters a stronger magnetic field which opposes its outward motion. The most commonly used toroidal magnetic confinement configuration at present is the tokamak, whose principal defining characteristic is to satisfy the q stability requirements by operating with .vertline.q.vertline.>1 and s.gtoreq.0 by supplying a sufficiently large toroidal magnetic field intensity B.sub.T, in accordance with Eq. (3). Because the aspect ratio A.ident.R/r is generally .gtoreq.3, the toroidal field, which must be provided by a large toroidal field coil system disposed around the confinement vessel, must be large. Typically, B.sub.T =5 B.sub.P to 10 B.sub.P. Therefore, the maximum toroidal current I.sub.p flowing in the plasma, which is related to poloidal magnetic field intensity B.sub.P by the formula B.sub.P =.mu..sub.o I.sub.p /2.pi.r, and with it the ohmic heating of the plasma, are limited by the maximum possible toroidal field intensity B.sub.T that can be withstood in a practical magnet system. A small magnetic well, which is also important for tokamak stability, is obtained by toroidal effects. The theoretically predicted maximum plasma pressure that can be confined is limited to .beta..ltorsim.0.10 and may well be less, where .beta..ident.<p>/(B.sup.2 /2.mu..sub.o) is the ratio of the volume averaged plasma pressure to the magnetic pressure of the confining field. (Here and throughout the remainder of this disclosure the SI mks system of units is used.) Because of the small .beta. of the tokamak, fusion reactor concepts based on it either must be large or must employ extraordinarily high toroidal magnetic field strength. Z-pinches are most readily distinguished form tokamaks, which they superficially resemble, by having .vertline.q.vertline.<1 everywhere throughout the plasma, and usually they have .vertline.q.vertline.>>1. The only toroidal z-pinch previously known to satisfy the necessary conditions on q is the reversed field pinch (RFP). A recent review of the RFP art has been given by H. A. B. Bodin and A. A. Newton, Nucl. Fusion 20 (1980), pp. 1255-1324. The RFP is a diffuse z-pinch in which the magnetic field component sensibly parallel to the magnetic axis has a direction in the outside region of the plasma opposite to that in the inner region, and as a result, q(r) passes through zero and changes sign within the plasma. In fact, greatly reduced instability is observed in z-pinch experiments when the reversed q(r) profile is established. The field and q reversal is achieved by trapping a toroidal field in a pinched plasma and providing external boundary conditions such that a toroidal field of the opposite sign can exist between the plasma and the wall. A conducting shell is also required for stability. The combination of toroidal current and reversed toroidal magnetic field achieved in RFPs produces an equilibrium state of very low free energy, which is stable at low .beta.. This stability is independent of toroidal effects. Therefore, RFP aspect ratios can be chosen at will to optimize engineering and reactor parameters. In the RFP the externally acting toroidal field is smaller than B.sub.P. Therefore, unlike in the tokamak, I.sub.p is limited only by the maximum intensity of B.sub.P that can be withstood in the device, and large ohmic heating of the plasma is possible. Furthermore, the maximum .beta. achievable in RFP devices will probably be greater than in tokamaks. Therefore, fusion reactor concepts based on the RFP can either be smaller or use lower magnetic fields than with tokamaks. Unfortunately, the RFP does not possess a magnetic well, and it has been predicted theoretically and observed in computer plasma simulations that an m=0 resistive interchange instability grows into a large convective cell near the q=0 surface and limits plasma confinement. Here m is the poloidal mode number of the instability in question. There are data suggesting that this instability is present in contemporary RFP experiments. Resistive interchange instabilities are among those that can be stabilized by magnetic well. Multipole plasma confinement devices take a different approach to toroidal plasma confinement. In multipole devices, the toroidal plasma current is replaced by two or more solid conducting rings located internal to the plasma, which produce a set of nested closed magnetic surfaces around each ring. By convention the number of poles is equal to twice of the number of conductors. Thus, for example a device with two internal conductors is termed a quadrupole; four an octopole, etc. Since the current flows through rigid conductors, the current flow is stable. There is no necessity for a strong toroidal magnetic field. The current rings are placed so as to generate a multipolar magnetic field and at least one hyperbolic magnetic axis within the space roughly enclosed poloidally by the rings. Furthermore, these rings and the hyperbolic axis or axes are surrounded by an outer set of nested closed magnetic surfaces. The magnetic surface or surfaces passing through the hyperbolic axis and separating the outer magnetic surfaces from those magnetic surfaces that enclose only a single ring are called separatrix magnetic surfaces. Excellent confinement has been demonstrated in experimental multipole devices. Shear can be added by means of only a small toroidal field. Multipole devices have a number of serious difficulties for high temperature plasma and fusion applications associated with the placement of conducting rings internal to the plasma. The rings require support structure, which intercepts charged particles, destroys the symmetry of the device, and leads to reduced confinement of plasma. Alternatively, the support structure can be eliminated by use of superconducting rings which are levitated by use of magnetic fields, but requirements to shield the superconductor from the high energy fusion neutrons are formidable. SUMMARY OF THE INVENTION The present invention involves a fundamentally different confinement principle, obtaining the best advantages of internal ring multipole and RFP devices in a multipole pinch device. The basic invention can be considered as a multipole device in which the solid internal rings have been replaced by high current z-pinch plasma current channels. Just as in the solid ring multipole devices, approximately equal currents flowing in parallel through the plasma current channels generate a hyperbolic magnetic axis and separatrix magnetic surfaces internal to the plasma. This produces an average magnetic well, provided the component of magnetic field in the direction of the hyperbolic axis is not too large in the vicinity of the hyperbolic axis, which can always be achieved by operating the plasma current channels like reversed field pinches so that q=0 occurs in the vicinity of said hyperbolic axis. Because z-pinch plasmas have a strong tendency to keep a nearly circular poloidal cross section, means are provided to prevent the multiple current channels from coalescing into a single, circular cross section RFP. Furthermore, the precise shape of the plasma can be adjusted and optimized, if necessary, by means of small currents in toroidal coils exterior to the conducting shell. Stability in the multipole pinch invention is obtained by a q profile and conducting shell as in the RFP, plus the average magnetic well. In particular, when the q=0 surface coincides with the hyperbolic magnetic axis in the plasma, q varies monotonically outwardly from the elliptic axes. The magnetic well is then centered on the q=0 surface. This is the optimal theoretical location for the suppression of the m=0 resistive interchange instability that threatens to limit RFP .beta.. In general terms, the average magnetic well increases the maximum .beta. that can be accommodated. The well in multipole pinch devices is independent of toroidal effects, and so the toroidal aspect ratio of such devices can be chosen at will. Like the RFP, the multipole pinch needs only small toroidal fields; thus, plasma current and ohmic heating are limited only by the maximum poloidal fields that can be withstood in the device. The device of the present invention is distinctly different from prior art multipole devices in that the magnetic well is achieved without the use of solid rings immersed in the plasma and the problems that such rings entail. It is distinctly different from prior art RFP devices by provision of means to make plasmas with an average magnetic well by an internal hyperbolic magnetic axis. Furthermore, it is distinctly different from prior art helical pinches as in T. Ohkawa U.S. Pat. No. 4,302,284, sometimes referred to as OHTE, whose multiple hyperbolic axes are at the plasma surface rather than internal. The device of the present invention is also distinctly different from the prior art doublet device, as in T. Ohkawa U.S. Pat. No. 3,692,626, which it superficially resembles. The doublet device is essentially a quadrupole in which the two solid internal conductors have been replaced by two tokamak current channels. The present invention, in its quadrupole form, replaces the two solid conductors by z-pinch current channels. The magnetic fields and currents within the two devices are very different. The most critical difference, from the viewpoint of the efficiency and construction of the device, is that the tokamak current channels of the doublet device require toroidal magnetic fields many times greater than the field produced by the plasma current, whereas in the z-pinch current channels, the fields are comparable. Furthermore, with a given toroidal field it is possible to drive a much larger current through the present device than through the doublet device, and the heating associated with this current drastically reduces the auxiliary heating requirements relative to the doublet device. The multipole pinch also differs from the doublet device in how the magnetic well is generated. Because of the large toroidal magnetic field, the average magnetic well in doublet devices arises from toroidal effects, as in the tokamak, and not because of a hyperbolic magnetic axis. In the low toroidal field environment of the multipole pinch device, average magnetic well is produced by its hyperbolic axis. The multipole pinch device is further differentiated from the doublet device by their different q profiles. The doublet q profile is everywhere greater than unity and passes through infinity at its internal separatrix magnetic surface; wheras in the multipole pinch device, q is much less than unity, is monotonically varying and passes through zero at its separatrix magnetic surface. Finally, the toroidal field in doublet devices varies only slightly throughout the plasma volume, whereas in multipole pinch devices it reverses direction between the elliptic magnetic axes and the boundary of the plasma. Therefore, a doublet device is built with a small aspect ratio A and with very strong toroidal field coils supplied with large currents; whereas a multipole pinch device is built with any convenient aspect ratio, usually A.gtoreq.5, and with toroidal field coils designed for lesser magnetic fields and currents. Furthermore, a preferred multipole pinch device has an induction coil and associated power system designed to induce a toroidal electric field of at least 100 V/m during the plasma pinch formation phase of the discharge cycle; whereas a doublet device is usually designed to induce a weaker toridal electric field, such as less than 25 V/m in the Doublet III device at the General Atomic Company. Thus, it is a primary object of the present invention to provide for magnetic pinch confinement of plasma with an average magnetic well obtained using at least one hyperbolic magnetic axis generated by multipolar magnetic fields produced by multiple z-pinch current channels. Other objects and advantages of the present invention will become evident from the consideration of the following detailed description, particularly when taken in conjunction with the accompanying drawings.

claims

1. A device for characterizing surfaces, the device comprising:means for generating a beam of neutral atoms or molecules, the means being arranged to direct said beam towards a surface for characterizing; anddetector means that are sensitive to position for detecting the neutral atoms or molecules of said beam that have been diffused forwards by said surface for characterizing;wherein:said means for generating a beam of neutral atoms or molecules produces a beam having energy lying in the range 50 eV to 5 keV with divergence no greater than 0.05°; andsaid means for generating a beam of neutral atoms or molecules directs said beam towards said surface for characterizing at an angle of incidence no greater than 10° relative to the plane of said surface;in such a manner that a diffraction pattern of said neutral atoms or molecules diffused forwards by said surface for characterizing is detectable by said position-sensitive detector means. 2. A device according to claim 1, wherein said means for generating a beam of neutral atoms or molecules produces a beam having energy lying in the range 100 eV to 2 keV. 3. A device according to claim 1, wherein said means for generating a beam of neutral atoms or molecules produces a beam having energy lying in the range 100 eV to 1 keV. 4. A device according to claim 1, wherein said means for generating a beam of neutral atoms or molecules produces a beam having energy dispersion no greater than 5%. 5. A device according to claim 1, wherein said means for generating a beam of neutral atoms or molecules directs said beam towards said surface for characterizing with an angle of incidence lying in the range 0.5° to 3°. 6. A device according to claim 1, wherein the angle of incidence θinc and the energy E0 of said beam of atoms or molecules are selected such that E0 sin2 θinc≦1 eV. 7. A device according to claim 1, wherein said means for generating a beam of neutral atoms or molecules generates a beam constituted by particles having atomic mass lying in the range 1 au to 20 au. 8. A device according to claim 7, wherein said means for generating beam of neutral atoms or molecules generates a beam constituted by a chemical species selected from H, H2, and 3He, and isotopes thereof. 9. A device according to claim 1, wherein said means for generating a beam of neutral atoms or molecules comprise:means for generating a beam of atomic or molecular ions;means for neutralizing said beam of atomic or molecular ions; andmeans for collimating the beam of neutral atoms or molecules obtained by neutralizing said beam of atomic or molecular ions. 10. A device according to claim 9, wherein said means for generating a beam of neutral atoms or molecules also comprise means for filtering said atomic or molecular ions by mass. 11. A device according to claim 9, wherein said means for generating a beam of neutral atoms or molecules comprise chopper means for generating a pulsed beam. 12. A device according to claim 11, wherein said position-sensitive detector means also present time sensitivity, with resolution of not more than 50 ns, so as to determine the energy loss of the neutral atoms or molecules of said beam as a result of being diffused by said surface, by measuring flight time. 13. A device according to claim 12, wherein said position-sensitive detector means present time sensitivity, with resolution of not more than 10 ns. 14. A device according to claim 1, also comprising secondary detector means for detecting neutral or ionized atoms or molecules, said secondary detector means having time resolution no greater than 1 μs, and being arranged in such a manner as to detect neutral or ionized atoms or molecules that leave the surface for characterizing on a trajectory that forms relative to said surface an angle that is greater than the specular reflection angle of said beam of neutral atoms or molecules. 15. A machine for molecular jet epitaxy, the machine including a surface characterizing device according to claim 1, arranged to characterize the surface of a crystal that is being grown. 16. A method of characterizing surfaces, the method comprising the steps of:directing a beam of neutral atoms or molecules on the surface to be characterized; anddetecting in position-sensitive manner the neutral atoms or molecules of said beam that have been diffused forwards by said surface for characterizing;wherein:said beam of neutral atoms or molecules has energy lying in the range 50 eV to 5 keV, and divergence no greater than 0.05°; andthe angle of incidence of said beam on said surface for characterizing is no greater than 10° relative to the plane of said surface;in such a manner that at least some of said forwardly-diffused neutral atoms or molecules are diffracted by said surface for characterizing. 17. A method of characterizing surfaces according to claim 16, wherein said beam of neutral atoms or molecules presents energy lying in the range 100 eV to 2 keV. 18. A method of characterizing surfaces according to claim 17, wherein said beam of neutral atoms or molecules presents energy lying in the range 100 eV to 1 keV. 19. A method of characterizing surfaces according to claim 16, wherein said beam of neutral atoms or molecules presents energy dispersion no greater than 5%. 20. A method of characterizing surfaces according to claim 16, wherein the angle of incidence of said beam on said surface for characterizing lies in the range 0.5° to 3°. 21. A method of characterizing surfaces according claim 16, wherein the angle of incidence θinc and the energy E0 of said beam of atoms or molecules are selected such that E0 sin2 θinc<1 eV. 22. A method of characterizing surfaces according to claim 16, wherein said beam is constituted by particles presenting atomic mass lying in the range 1 au to 20 au. 23. A method of characterizing surfaces according to claim 22, wherein said beam is constituted by a chemical species selected from H, H2, and 3He, and isotopes thereof. 24. A method according to claim 16, also including a step for determining at least one crystallographic parameter of said surface for characterizing from a detected diffraction pattern of said neutral atoms or molecules diffused forwards by said surface for characterizing. 25. A method according to claim 24, implemented during fabrication of a crystal by molecular beam epitaxy, the method also including:a step of observing oscillatory behavior over time of said diffraction pattern; anda step of extracting information relating to the epitaxial growth of successive layers of atoms forming said crystal on the basis of said observation of oscillatory behavior over time of said diffraction pattern.

abstract

It is possible to improve the workability and the stress corrosion resistance by easily performing a repairing operation in a nozzle repairing method and a nuclear reactor vessel. The repairing method includes: removing a first connection portion ((trepanned portion) 208) with respect to an in-core instrument tube (204) in a groove-welding portion (206); removing the in-core instrument tube (204) from a lower mirror (66); leaving and grooving a second connection portion ((existing welding portion) 211) with respect to the lower mirror (66) in the groove-welding portion (206); inserting a new in-core instrument tube (204A) into an attachment hole (203); and groove-welding (so as to form a new groove-welding portion (213)) the inner side of the lower mirror (66) so as to fix the new in-core instrument tube (204A).

description

In the various drawings, like parts are indicated by like references. FIG. 1 schematically depicts a lithographic projection apparatus according to a particular embodiment of the invention. The apparatus comprises: a radiation system Ex, IL, for supplying a projection beam PB of radiation (e.g. EUV radiation), which in this particular case also comprises a radiation source LA; a first object table (mask table) MT provided with a mask holder for holding a mask MA (e.g. a reticle), and connected to first positioning means PM for accurately positioning the mask with respect to item PL; a second object table (substrate table) WT provided with a substrate holder for holding a substrate W (e.g. a resist-coated silicon wafer), and connected to second positioning means PW for accurately positioning the substrate with respect to item PL; a projection system (xe2x80x9clensxe2x80x9d) PL (e.g. a mirror group) for imaging an irradiated portion of the mask MA onto a target portion C (e.g. comprising one or more dies) of the substrate W. As here depicted, the apparatus is of a reflective type (i.e. has a reflective mask). However, in general, it may also be of a transmissive type, for example (with a transmissive mask). Alternatively, the apparatus may employ another kind of patterning structure, such as a programmable mirror array of a type as referred to above. The source LA (e.g. a discharge or laser-produced plasma source) produces a beam of radiation. This beam is fed into an illumination system (illuminator) IL, either directly or after having traversed conditioning means, such as a beam expander Ex, for example. The illuminator IL may comprise adjusting means AM for setting the outer and/or inner radial extent (commonly referred to as "sgr"-outer and "sgr"-inner, respectively) of the intensity distribution in the beam. In addition, it will generally comprise various other components, such as an integrator IN and a condenser CO. In this way, the beam PB impinging on the mask MA has a desired uniformity and intensity distribution in its cross-section. It should be noted with regard to FIG. 1 that the source LA may be within the housing of the lithographic projection apparatus (as is often the case when the source LA is a mercury lamp, for example), but that it may also be remote from the lithographic projection apparatus, the radiation beam which it produces being led into the apparatus (e.g. with the aid of suitable directing mirrors); this latter scenario is often the case when the source LA is an excimer laser. The current invention and Claims encompass both of these scenarios. The beam PB subsequently intercepts the mask MA, which is held on a mask table MT. Having been selectively reflected by the mask MA, the beam PB passes through the lens PL, which focuses the beam PB onto a target portion C of the substrate W. With the aid of the second positioning means PW (and interferometric measuring means IF), the substrate table WT can be moved accurately, e.g. so as to position different target portions C in the path of the beam PB. Similarly, the first positioning means PM can be used to accurately position the mask MA with respect to the path of the beam PB, e.g. after mechanical retrieval of the mask MA from a mask library, or during a scan. In general, movement of the object tables MT, will be realized with the aid of a long-stroke module (course positioning) and a short-stroke module (fine positioning), which are not explicitly depicted in FIG. 1. However, in the case of a wafer stepper (as opposed to a step-and-scan apparatus) the mask table MT may just be connected to a short stroke actuator, or may be fixed. The depicted apparatus can be used in two different modes: 1. In step mode, the mask table MT is kept essentially stationary, and an entire mask image is projected at once (i.e. a single xe2x80x9cflashxe2x80x9d) onto a target portion C. The substrate table WT is then shifted in the x and/or y directions so that a different target portion C can be irradiated by the beam PB; 2. In scan mode, essentially the same scenario applies, except that a given target portion C is not exposed in a single xe2x80x9cflashxe2x80x9d. Instead, the mask table MT is movable in a given direction (the so-called xe2x80x9cscan directionxe2x80x9d, e.g. the y direction) with a speed v, so that the projection beam PB is caused to scan over a mask image; concurrently, the substrate table WT is simultaneously moved in the same or opposite direction at a speed V=Mv, in which M is the magnification of the lens PL (typically, M={fraction (1/4)} or {fraction (1/5)}). In this manner, a relatively large target portion C can be exposed, without having to compromise on resolution. Mirror System Classification According to the present invention, a mirror system of n mirrors is classified by reference to the direction of the reflected beam compared to the incident beam at each mirror surface. Having defined the object height to be positive along a Y-axis and a suitable reference plane, e.g. the plane containing the optical axis Z of the projection system and the Y-axis (as shown in FIG. 1), the chief ray CR at a mirror is defined as having a positive angle of incidence xcex1, if the angle between the normal of the surface and the incident ray is counterclockwise (as shown in FIG. 2) and a negative angle of incidence if the angle between the normal and the incident ray is clockwise. Further, one should view this reference plane along a positive X direction, the X, Y, Z directions making up a right-handed orthogonal coordinate system, as shown in FIG. 1. The chief ray is defined as that ray emerging from the object point, which goes through the center of the stop and therefore also through the center of the entrance and exit pupils, i.e. at a height equal to zero from the optical axis. (NB this assignment is arbitrary, the scheme can be implemented with either relative direction of reflection regarded as positive, provided that the assignment is consistent.) By assigning the binary digit xe2x80x9c1xe2x80x9d to a negative angle of incidence and xe2x80x9c0xe2x80x9d to a positive angle of incidence of the chief ray, a mirror system is assigned a binary number defined by the sequence of binary digits assigned to each mirror in the system in sequence along the optical path of the beam from object to source. For convenience, this binary number is expressed in decimal notation. The various classes of the incidence angle classification system are further characterized by indicating the sign of the magnification of the system. Herein, this is indicated by the appropriate sign in parentheses after the class number, e.g. 6(xe2x88x92). The sign is obtained by dividing the magnification M by its absolute value |M|. A system has a positive magnification if the object and image are the same side of the optical axis and a negative magnification if they are opposite sides. The decimal incidence angle classification, C, can thus be expressed as: C = ∑ i = 1 n ⁢ a i · 2 ( n - i ) ⁢ ( M "LeftBracketingBar" M "RightBracketingBar" ) ( 1 ) where: ai=1 if the angle of incidence of the chief ray at mirror i is negative, ai=0 if the angle of incidence of the chief ray at mirror i is positive, M is the magnification of the projection system, and index i numbers the mirrors of the system in series from object to source. FIG. 2 shows the four possible arrangements of incident chief rays CR and mirrors M. In A the incident chief ray is travelling left to right and has an angle of incidence xcex1 greater than 0, so ai=0. In B the incident chief ray is travelling right to left and has an angle of incidence xcex1 less than 0, so ai=1. In C the incident chief ray is travelling right to left and has an angle of incidence xcex1 greater than 0, so ai=0. In D the incident chief ray is travelling left to right with an angle of incidence xcex1 less than 0, so ai=1. Note that although convex mirrors are shown, the same assignments apply with concave or plane mirrors. While the incidence angle classification C does not wholly define a mirror system, the basic layout of a system is inherent in its incidence angle classification. By reference to whether the reflection at a given mirror is positive or negative, the orientation of that mirror and the position of the succeeding mirror, above or below the beam, can be determined. Thus a given classification number can be used by the designer of a mirror system to set out the system prior to optimization of that system, e.g. using commercially available ray tracing software such as CODE V(TM) by Optical Research Associates, Pasadena, Calif., USA. It should be noted that previous classifications of mirror systems based on whether the curvature, and hence power, of each mirror in the system is positive or negative, do not give any information as to the layout of a mirror system. It will also be noted that the incidence angle classification of a given mirror system can readily be determined from simple inspection of the beam path. Using the above classification system and numerical simulations, the present inventors have determined that only certain classes contain mirror systems usable as the projection system in a lithographic projection system. For four-mirror systems, feasible projection systems exist in classes 2(xe2x88x92), 6(xe2x88x92), 9(+), 9(xe2x88x92) and 10(xe2x88x92). For six-mirror systems, feasible projection systems exist in classes 5(+), 6(xe2x88x92), 9(+), 13(+), 18(xe2x88x92), 21(+), 22(xe2x88x92), 25(+), 26(xe2x88x92), 29(+), 34(xe2x88x92), 37(+), 38(xe2x88x92), 41(+), 42(xe2x88x92), 45(+) and 54(xe2x88x92). For eight-mirror systems, feasible projection systems exist in class 2(+), 5(+), 9(+), 12(+), 13(+), 18(+), 18(xe2x88x92), 19(+), 20(+), 21(+), 22(+), 23(+), 25(+), 26(+), 34(xe2x88x92), 36(+), 37(+), 38(xe2x88x92), 45(+), 46(+), 49(+), 52(+), 53(+), 54(+), 54(xe2x88x92), 55(xe2x88x92), 58(xe2x88x92), 68(+), 69(+), 73(+), 74(+), 77(+), 82(+), 82(xe2x88x92), 85(+), 88(+), 89(+), 90(xe2x88x92), 92(+), 93(+), 97(+), 100(xe2x88x92), 101(+), 102(xe2x88x92), 104(+), 105(+), 106(+), 106(xe2x88x92), 107(+), 108(+), 109(+), 109(xe2x88x92), 110(+), 110(xe2x88x92), 111(+), 113(+), 116(+), 117(+), 118(+), 118(xe2x88x92), 120(+), 121(+), 122(xe2x88x92), 123(xe2x88x92), 132(+), 133(+), 134(xe2x88x92), 137(+), 138(+), 141(+), 145(+), 145(xe2x88x92), 146(+), 146(xe2x88x92), 147(+), 148(+), 148(xe2x88x92), 149(+), 150(+), 150(xe2x88x92), 151(+), 151(xe2x88x92), 152(xe2x88x92), 153(+), 154(+), 154(xe2x88x92), 155(+), 155(xe2x88x92), 156(+), 157(+), 159(+), 161(+), 162(xe2x88x92), 163(xe2x88x92), 164(+), 165(+), 166(+), 166(xe2x88x92), 167(+), 168(+), 169(+), 170(+), 170(xe2x88x92), 171(+), 172(+), 173(+), 174(+), 175(+), 176(+), 177(+), 178(xe2x88x92), 179(+), 180(+), 180(xe2x88x92), 181(+), 181(xe2x88x92), 182(+), 182(xe2x88x92), 183(+), 183(xe2x88x92), 184(+), 185(+), 185(xe2x88x92), 186(xe2x88x92), 187(+), 187(xe2x88x92), 188(xe2x88x92), 189(+), 196(+), 197(+), 201(+), 203(+), 205(+), 209(+), 214(xe2x88x92), 216(+), 217(+), 218(+), 218(xe2x88x92), 225(+), 228(+), 229(+), 230(+), 232(+), 233(+), 235(+), 236(+), 237(+), 238(xe2x88x92), 243(+), 246(+), 247(+), 248(+), 250(xe2x88x92). Design Methodology As mentioned above, a given class defines an outline layout for a mirror system for which a functional projection system can be designed. A methodology according to the present invention for such a design process is described below. In the design process according to the invention, the mirrors in a system are defined by xe2x80x9cthicknessesxe2x80x9d and curvatures, defined as shown in FIG. 3. (NB the term xe2x80x9cthicknessxe2x80x9d is used by analogy to refractive systems which are conventionally defined in terms of surface curvatures, thicknesses between surfaces and the refractive indices of the media between surfaces.) Thus, thickness d1 is the distance between the object, the mask MA in the present case of a projection system in a lithographic apparatus, and the intersection of the (imaging extended) first mirror M1 with the optical axis OA. The distance between the intersections of the (imaging extended) first mirror M1 and the (imaging extended) second mirror M2 with the optical axis OA is d1. Note that since the second mirror is situated between the first mirror M1 and the object (mask MA), thickness d1 is negative. In general, thickness di is the distance between the intersections of mirror Mi and mirror Mi+1 with the optical axis OA. For an n-mirror system, the thickness dn is the distance between the last mirror Mn and the image plane, where the substrate W is positioned in a lithographic projection apparatus. In specific embodiments described below, an additional thickness dn+1 is given, this represents the distance between the position of the image calculated using a first order approximation and using a real ray tracing algorithm. In a first step the design method identifies conceivable systems under a number of constraints by using a paraxial approach described below. Those systems should not present obscuration, as is also described further below. The paraxial approach and the constraints yield a limited number of variables that are sampled to identify solutions. In a further step those solutions are checked using a real ray tracing method, referred to above, in which the paraxial assumptions are not present and in which also multilayer coatings of the reflectors may be modelled. Paraxial Approach The present inventors have developed an approach to designing mirror systems which starts with a paraxial approximation of a mirror system using matrix formalism. In a paraxial approximation the sine of an angle is approximated as the angle, i.e. sin xcex1=xcex1, and are the mirrors considered as being flat, while the actual curvature of a mirror is considered only to affect the angle of an incident ray, not its point of intersection with the supposedly xe2x80x98flatxe2x80x99 surface. In a matrix formalism, such as described in xe2x80x9cIntroduction to Opticsxe2x80x9d by Frank and Leno Pedrotti, Prentice Hall 1993; ISBN: 0135015456, incorporated herein by reference, the description of an optical system consist of an accumulation of translation and reflection (and/or refraction in a catadioptric or refractive system) matrices Mtrans,Mrefl which are defined as follows: M trans = [ 1 d i 0 1 ] ( 2 ) M refl = [ 1 0 - 2 · c i - 1 ] ( 3 ) where di is the distance to the next surface and ci the curvature of the surface, which is positive if the center of the sphere is on the right side of the surface. The path of a ray is given by a vector made of a height (distance from the optical axis) and an angle: [height, angle]. The multiplication of the vector with one or more matrices gives the ray after the corresponding translations or reflections. The system matrix is the multiplication of all the matrices in the system. The first matrix is the reflection matrix of the first surface, the penultimate matrix is the translation matrix of the thickness preceding the last reflective surface and the last matrix is the reflection matrix of the last reflective surface. The effective focal length, the back focal length, the front focal length and the paraxial image distance can be derived from the system matrix as follows. If the system matrix is defined as: M system = [ a b c d ] ( 4 ) then the effective focal length is given by: efl = - 1 c ( 5 ) the back focal length is given by: bfl = - a c ( 6 ) the front focal length is given by: ffl = d c ( 7 ) and the paraxial image distance, i.e. the distance between the last reflective surface and the image plane, is given by: d n = a · d 0 + b c · d 0 + d ( 8 ) where d 0 = ad - cb - magn · d magn · c and magn is the magnification of the system. The system matrix for the first part of the system, from the object plane to the stop (pupil) can be represented as: M 1 ⁢ st = [ a 1 ⁢ st b 1 ⁢ st c 1 ⁢ st d 1 ⁢ st ] ( 9 ) so that the distance, Lenpup, to the entrance pupil is given by: [ a 1 ⁢ st b 1 ⁢ st c 1 ⁢ st d 1 ⁢ st ] · [ 1 L enpup 0 1 ] · [ 0 A enpup ] = "AutoLeftMatch" xe2x80x83 ⁢ [ "AutoLeftMatch" ( a 1 ⁢ st · L enpup + b 1 ⁢ st ) · A enpup ( c 1 ⁢ st · L enpup + d 1 ⁢ st ) · A enpup ] = [ 0 A stop ] ( 10 ) The second part of the system, from stop to image surface can be represented as: M 2 ⁢ nd = [ a 2 ⁢ nd b 2 ⁢ nd c 2 ⁢ nd d 2 ⁢ nd ] ( 11 ) so that the distance, Lexpup, to the exit pupil is given by: [ 1 L exp ⁢ xe2x80x83 ⁢ up 0 1 ] · [ a 2 ⁢ nd b 2 ⁢ nd c 2 ⁢ nd d 2 ⁢ nd ] · [ 0 A stop ] = "AutoLeftMatch" [ ( b 2 ⁢ nd + L exp ⁢ xe2x80x83 ⁢ up · d 2 ⁢ nd ) · A stop D 2 ⁢ nd · A stop ] = [ 0 A exp ⁢ xe2x80x83 ⁢ up ] ( 12 ) The distances to the entrance and exit pupils, if xcex9enpupxe2x89xa00, are then given by: L enpup = - b 1 ⁢ st a 1 ⁢ st ⁢ xe2x80x83 ⁢ and ⁢ xe2x80x83 ⁢ xe2x80x83 ⁢ L exp ⁢ xe2x80x83 ⁢ up = - b 2 ⁢ nd d 2 ⁢ nd ( 13 ) Constraints Given the above, various constraints that must be applied to the system can be used to determine equations for the curvatures and thicknesses of certain surfaces of the system as functions of the constraints and other curvatures and thicknesses. Some example constraints G1 to G4 are shown in FIG. 5. A first constraint G1 is minimum deviation from telecentricity on the object side that still enables obscuration-free illumination of the object, which may determine the curvature of the first surface or the thickness between mirrors 1 and 2. Another constraint G3, is perfect telecentricity on the image side, which may determine the curvature of the last surface or the thickness between the final and penultimate mirrors. This telecentricity requirement is equivalent to the requirement that the exit pupil is at infinity. The requirement that the object and the image are conjugated and have a prescribed value of the transverse magnification fixes the values of the object (G2) and image (G4) distances. The object distance G2, the first thickness, can be solved as a function of the desired magnification of the system: the paraxial image distance is inserted in the thickness of the surface immediately preceding the image plane and the object distance is modified to satisfy: M = Image ⁢ xe2x80x83 ⁢ Height Object ⁢ xe2x80x83 ⁢ Height ( 14 ) In current lithography apparatus, M is usually set as xc2x10.20 or xc2x10.25, i.e. reduction by a factor of 5 or 4 respectively. A minimum deviation from telecentricity at the object side is an important requirement in lithography. The reflective object (mask MA) is illuminated with a beam coming from the radiation system. The chief ray angle at the object must be such that the incident illuminating beam does not interfere with the beam reflected from the object and going into the projection system. The angle of the chief ray together with the numerical aperture on the object side should be almost zero and the angles of all rays must be smaller or larger than zero, to fulfill these two requirements. For telecentricity on the image side, the angle of the chief ray relative to the optical axis has to be zero. The size of the last mirror increases quickly as a function of the distance between the image and the last mirror, due to the relatively large numerical aperture. A system with zero or an even number of intermediate images has a negative magnification. To have an overall system with a positive magnification the number of intermediate images has to be odd. The working distance at the object side is the minimum distance between the object plane and the surface closest to the object, most of the time the second mirror. On the image side the working distance is the minimum distance between the image plane and the plane closest to the image, most often the penultimate mirror. The working distances provide room for mirror supports and for mechanical movements of the object and the image and must not be too small. An example of applying the above constraints in a six-mirror system is described below. This may be carried out in practice using software such as Maple(TM) produced by Waterloo Maple Inc. 57 Erb Street W. Waterloo, Ontario Canada N2L 6C2. First is a derivation of the formulas used for a six-mirror system, but the formulas are also valid for other numbers of mirrors, using the paraxial approach. In the matrix notation a ray is defined by the vector: [height, angle in radians]. After a distance di the ray [y,a] will be: [ y + d i ⁢ a a ] ( 15 ) using the matrix given in equation (2). After a mirror with curvature ci the ray [y,a] will have the same height but a different angle: [ v - 2 c i ⁢ v - a ] ( 16 ) using the matrix given in equation (3). To derive formulas used later on, firstly the distance between mirror 5 and 6 is solved by requiring telecentricity in the image of the ray going through the optical axis in the stop surface. The following matrix A is from the stop surface to after the 5th mirror, as we don""t now where we will locate the stop surface we take an unknown 2 by 2 matrix: A := [ a b c d ] ( 17 ) From the 5th mirror we travel a distance la to the 6th mirror, la is the variable to solve now. L6 := [ 1 la 0 1 ] ( 18 ) Matrix MC is of the 6th mirror surface: MC := [ 1 0 - 2 ⁢ c6 - 1 ] ( 19 ) The ray going through the center of the stop with an arbitrary angle ap is: Y := [ 0 ap ] ( 20 ) That ray after the 6th mirror will be: Y_image := [ ( b + la ⁢ xe2x80x83 ⁢ d ) ⁢ ap ( - 2 ⁢ c6 + ( - 2 ⁢ c6 ⁢ xe2x80x83 ⁢ la - 1 ) ⁢ d ) ⁢ ap ] ( 21 ) in which the angle is equal to zero since telecentricity is required and the solution opl for the distance la between mirror five and six is now opl := - 1 2 ⁢ 2 ⁢ c6 ⁢ xe2x80x83 ⁢ b + d c6 ⁢ xe2x80x83 ⁢ d ( 22 ) The matrix from the stop surface to after the 6th mirror is now: B := [ 1 2 ⁢ 2 ⁢ c6 ⁢ xe2x80x83 ⁢ ad - 2 ⁢ c6 ⁢ xe2x80x83 ⁢ bc - cd c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ d c6 - 2 ⁢ xe2x80x83 ⁢ c6 ⁡ ( da - bc ) d 0 ] ( 23 ) The next solve is the distance d between the object and the first mirror and the solve ya for the angle of the chief ray (going through the center of the stop) between the object and the first mirror. The ray Ya in the object point yob with the desired angle ya is given by the vector: Ya := [ yob ya ] ( 24 ) and the distance l between the object and the first mirror surface by the matrix: L := [ 1 l 0 1 ] ( 25 ) The first mirror surface is given by: MC := [ 1 0 - 2 ⁢ cl - 1 ] ( 26 ) The distance m between the first mirror and the second mirror is given by: M := [ 1 m 0 1 ] ( 27 ) The unknown matrix from the second mirror surface to the stop position is defined as A := [ e f g h ] ( 28 ) The chief ray in the stop surface is now: Y_stop := xe2x80x83 ⁢ ⁢ xe2x80x83 ⁢ [ xe2x80x83 ⁢ ( e - 2 ⁢ xe2x80x83 ⁢ ( e ⁢ xe2x80x83 ⁢ m + f ) ⁢ xe2x80x83 ⁢ c1 ) ⁢ yob + ( ( e - 2 ⁢ ( e ⁢ xe2x80x83 ⁢ m + f ) ⁢ xe2x80x83 ⁢ c1 ) ⁢ l - em - f ) ⁢ ya ( g - 2 ⁢ ( g ⁢ xe2x80x83 ⁢ m + h ) ⁢ xe2x80x83 ⁢ c1 ) ⁢ yob + ( ( g - 2 ⁢ ( g ⁢ xe2x80x83 ⁢ m + h ) ⁢ c1 ) ⁢ l - g ⁢ xe2x80x83 ⁢ m - h ) ⁢ ya ⁢ xe2x80x83 ] ( 29 ) and in the image the chief ray is: Y_image := xe2x80x83 ⁢ [ ( 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ e c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g c6 - xe2x80x83 ⁢ 2 ⁢ ( ( 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ e c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g c6 ) ⁢ m + xe2x80x83 ⁢ 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ f c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h c6 ) c1 ) ⁢ yob + xe2x80x83 ⁢ ( ( 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ e c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g c6 - xe2x80x83 ⁢ 2 ⁢ ( ( 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ e c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g c6 ) ⁢ m + xe2x80x83 ⁢ 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ f c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h c6 ) c1 ) l - xe2x80x83 ⁢ ( 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ e c6 ⁢ xe2x80x83 ⁢ d - 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g c6 ) ⁢ m - xe2x80x83 ⁢ 1 2 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - c ⁢ xe2x80x83 ⁢ d ) ⁢ f c6 ⁢ xe2x80x83 ⁢ d + 1 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h c6 ) ⁢ yz ] xe2x80x83 ⁢ [ ( - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ e d - 2 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c6 ⁡ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ e ⁢ xe2x80x83 ⁢ m d - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ f d ) c1 ) yob + ( ( - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ e d - xe2x80x83 ⁢ 2 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ m d - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ f d ) ⁢ c1 ) ⁢ l + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ m d + 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ f d ) ⁢ yz ] ( 30 ) The height of the chief ray in the image is by definition magn*height in the object surface (yob), we solve l from equation (30) to impose this reduction to the system giving: Y_image ⁢ _l := xe2x80x83 ⁢ - ( 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d - xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ g - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d + 4 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d + 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ g - 4 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c + 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d + 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ h - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d + 2 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c + ya ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d + xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ g - 2 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d + 2 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c + ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d + xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ h - 2 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d ) / xe2x80x83 ⁢ ( ( 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d - 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c - e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d - d 2 ⁢ g - 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c + 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d + 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ m ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ g - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d + 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c + 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d + 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ d 2 ⁢ h ) ⁢ ya ) ( 31 ) and we force the height of the chief ray to be zero in the stop surface in equation (29), as it should be by definition to solve the distance m Y_stop ⁢ _m := - xe2x80x83 ⁢ - yob ⁢ xe2x80x83 ⁢ e + 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c1 - ya ⁢ xe2x80x83 ⁢ l ⁢ xe2x80x83 ⁢ e + 2 ⁢ ya ⁢ xe2x80x83 ⁢ l ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c1 + ya ⁢ xe2x80x83 ⁢ f e ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 + 2 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ l + ya ) ( 32 ) The solution for the distance m between the first and the second mirror now becomes: Y_stop ⁢ _m := 1 4 ⁢ xe2x80x83 ⁢ xe2x80x83 ⁢ - 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - e ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h + ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g e ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ( 33 ) The solution for the distance m between the object and the first mirror now is: Y_image ⁢ _l := - 1 2 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g + 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g - e ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h - 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ h + 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ya ⁢ xe2x80x83 ⁢ ( f ⁢ xe2x80x83 ⁢ g - e ⁢ xe2x80x83 ⁢ h ) ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ d ( 34 ) We substitute the just derived expressions in the matrices L and M of equations (25) and (27). M := [ 1 1 4 ⁢ xe2x80x83 ⁢ xe2x80x83 ⁢ - 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - e ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h + ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g e ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 0 1 ] ( 35 ) L := [ 1 - 1 2 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g + 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g - e ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h - 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ h + 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ya ⁢ xe2x80x83 ⁢ ( f ⁢ xe2x80x83 ⁢ g - e ⁢ xe2x80x83 ⁢ h ) ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ d 0 1 ] ( 36 ) And as a check we calculate the chief ray after the 6th surface with the new expressions. We see that the angle is always zero and that the height is the object height multiplied with magnification. Y_image := [ magn ⁢ xe2x80x83 ⁢ yob 0 ] ( 37 ) The final solve is the distance n between the last mirror surface and the image surface. In the image surface all rays from the same object point come together in a point with a height=magnification*object height. First we define a ray Yb from the object point yob and an arbitrary angle yb. Yb := [ yob yb ] ( 38 ) N := [ 1 n 0 1 ] ( 39 ) In the image this ray Yb will become: Y_image := xe2x80x83 ⁢ [ - 1 4 ⁢ ( - f ⁢ xe2x80x83 ⁢ g 2 ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ ya 2 + g ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ ya 2 ⁢ xe2x80x83 ⁢ h - g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h - 4 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ e - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + 4 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya 2 ⁢ xe2x80x83 ⁢ h - 4 ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya 2 ⁢ xe2x80x83 ⁢ h + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ ya 2 ⁢ xe2x80x83 ⁢ h + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya 2 ⁢ xe2x80x83 ⁢ h - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya 2 ⁢ xe2x80x83 ⁢ h - 2 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ h + 4 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ h ⁢ xe2x80x83 - xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + f ⁢ xe2x80x83 ⁢ g 2 ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ ya + f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ d ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ ya 2 + 2 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya 2 - 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya 2 + 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya 2 - f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya 2 + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ ya - 4 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ n ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ yb ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ) / ( ya ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 2 ) ] xe2x80x83 ⁢ [ - xe2x80x83 ⁢ ( - ya + yb ) ⁢ ( f ⁢ xe2x80x83 ⁢ g - e ⁢ xe2x80x83 ⁢ h ) ⁢ ( d ⁢ xe2x80x83 ⁢ a - b ⁢ xe2x80x83 ⁢ c ) magn ] ( 40 ) The expression for the image distance n is, given that the image height is equal to magn. yob: Y_image ⁢ _n := xe2x80x83 ⁢ - 1 4 ⁢ ( - d 2 ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + 2 ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ e + 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - 2 ⁢ xe2x80x83 ⁢ e 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 + 4 ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ h ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob - e 2 ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ h + xe2x80x83 ⁢ d 2 ⁢ xe2x80x83 ⁢ g 2 ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ f - 2 ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ ya ⁢ xe2x80x83 ⁢ f ⁢ xe2x80x83 ⁢ g ) / xe2x80x83 ⁢ ( ( - e ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ a ⁢ xe2x80x83 ⁢ h + e ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ h + f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ d ⁢ xe2x80x83 ⁢ a - f ⁢ xe2x80x83 ⁢ g ⁢ xe2x80x83 ⁢ b ⁢ xe2x80x83 ⁢ c ) ⁢ xe2x80x83 ⁢ e ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ ya ) ( 41 ) 6-mirror system, stop on mirror 2 Now we use these derivations in the first part: solving the variables of a six-mirror system with the stop position on mirror two, defining thicknesses as d:=[d0,d1,d2,d3,d4,d5,d6] and the curvatures as c=[c1,c2,c3,c4,c5,c6]. The stop (pupil) position is on the second surface. A limitation on the Petzval sum (i.e. the sum of curvatures in the system, curvatures of odd surfaces being subtracted from curvatures of even surfaces, or vice versa), e.g. to be zero, can be introduced and used to solve the curvature of the stop surface. However, a zero Petzval sum is not essential and an non-zero value can be accommodated. Now we define all the matrices in the system, the reflectance (even subscripts) and translation (odd subscripts) matrices, from the object to the image. M 1 := [ 1 d0 0 1 ] M 2 := [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c1 - 1 ] M 3 := [ 1 d1 0 1 ] M 4 := [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c2 - 1 ] M 5 := [ 1 d2 0 1 ] M 6 := [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c3 - 1 ] M 7 := [ 1 d3 0 1 ] M 8 := [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c4 - 1 ] M 9 := [ 1 d4 0 1 ] M 10 := [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c5 - 1 ] M 11 := [ 1 d5 0 1 ] M 12 := [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c6 - 1 ] M 13 := [ 1 d6 0 1 ] xe2x80x83 ( 42 ) The first solve is the exit pupil in infinity or telecentricity in the image. The angle of the ray going through the optical axis in the stop surface should be zero in the image. The matrix from the stop surface to the fifth mirror generated by multiplication of the appropriate M matrices derived just above, is given by: | 1 - 2 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ) + 2 ⁢ xe2x80x83 ⁢ c3 ) , d2 + d3 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + d4 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) | ⁢ [ - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ) + 2 ⁢ xe2x80x83 ⁢ c3 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ( 1 - 2 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 - 2 ⁢ c3 . - 2 ⁢ xe2x80x83 ⁢ c5 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 | ( 43 ) The matrix from the second mirror surface to the stop surface is given by: [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c2 - 1 ] ( 44 ) So as we derived the distance between mirror 5 and 6, we solve this new found value in the appropriate matrix and the vector of distances. d5 := xe2x80x83 ⁢ - 1 2 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d2 - 4 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d3 - 4 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 + xe2x80x83 ⁢ 8 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d3 + 4 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d4 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d3 + 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 - xe2x80x83 ⁢ 8 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) / ( c6 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d2 - 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d3 - 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 + 8 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 + 4 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 + 4 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d3 + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) ( 45 ) The distance between mirror one and two is derived as: d1 := - 1 4 ⁢ - 2 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ( 46 ) and the distance between the object and the first mirror is: d0 := xe2x80x83 ⁢ 1 2 ⁢ ( - angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) - 2 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) / ( angle ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - xe2x80x83 ⁢ 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( d2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) ( 47 ) The distance between mirror six and the image surface is: d6 := xe2x80x83 ⁢ - 1 4 ⁢ ( 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d3c3 + d4 ( - "AutoLeftMatch" 2 ⁢ c4 ⁡ ( 1 - "AutoLeftMatch" xe2x80x83 ⁢ 2 ⁢ d3c3 ) + xe2x80x83 ⁢ 2 ⁢ c3 ) ) ⁢ xe2x80x83 ⁢ c6 ( xe2x80x83 ⁢ - 2 ⁢ c5 ( d2 + "AutoLeftMatch" xe2x80x83 ⁢ "AutoLeftMatch" d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + d4 ( - 2 ⁢ c4 ( d2 + xe2x80x83 ⁢ d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) + 2 ⁢ c4 ( d2 + xe2x80x83 ⁢ d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) - 2 ⁢ c3d2 - 1 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d3c3 + d4 ⁡ ( - 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d3c3 ) + 2 ⁢ c3 ) ) + xe2x80x83 ⁢ 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d3c3 ) - 2 ⁢ c3 ) ⁢ c6 ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) - xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d3c3 + d4 ⁡ ( - 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d3c3 ) + 2 ⁢ c3 ) ) + xe2x80x83 ⁢ 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d3c3 ) - 2 ⁢ c3 ) ⁢ ( - 2 ⁢ c5 ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) + xe2x80x83 ⁢ 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) - 2 ⁢ c3d2 - 1 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) + xe2x80x83 ⁢ "AutoLeftMatch" 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) - 2 ⁢ c3d2 - 1 ) "AutoRightMatch" 2 ⁢ c2 + xe2x80x83 ⁢ 4 ⁢ c1 ( - 2 ⁢ c5 ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) + xe2x80x83 ⁢ 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) - 2 ⁢ c3d2 - 1 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ magn 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 2 ) / ( ( ( - 2 ⁢ c5 ( 1 - 2 ⁢ d3c3 + d4 ( - 2 ⁢ c4 ( 1 - xe2x80x83 ⁢ 2 ⁢ d3c3 ) + 2 ⁢ c3 ) ) + 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d3c3 ) - 2 ⁢ c3 ) ⁢ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) - xe2x80x83 ⁢ ( - 2 ⁢ c5 ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) + d4 ( - 2 ⁢ c4 ( d2 + xe2x80x83 ⁢ d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) + 2 ⁢ c3d2 + 1 ) ) + 2 ⁢ c4 ⁡ ( d2 + d3 ⁡ ( - 2 ⁢ c3d2 - 1 ) ) - xe2x80x83 ⁢ 2 ⁢ c3d2 - 1 ) ⁢ ( 1 - 2 ⁢ d3c3 + d4 ⁡ ( - 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d3c3 ) + 2 ⁢ c3 ) ) ) ⁢ c6 2 ⁢ xe2x80x83 ⁢ angle ) ( 48 ) The variable angle is identical to ya introduced in equation (24) above. 6-Mirror System, Stop on Mirror 3 The original derivations can similarly be used to solve the variables of a six-mirror system with the stop position on mirror three, as will now be shown. The first solve is pupil in infinity or telecentricity in the image. The angle of the ray going through the optical axis in the stop surface should be zero in the image. The matrix from the stop surface to the fifth mirror generated by multiplication of the appropriate M matrices derived just above, is given by: [ 1 - 2 ⁢ d4c4 d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d4c4 ) + 2 ⁢ c4 - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ] ( 50 ) The matrix from the second mirror surface to the stop surface is given by: [ 1 - 2 ⁢ d2c2 - d2 - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 2 ⁢ c3d2 + 1 ] ( 51 ) So, as derived above, the distance between mirror 5 and 6 is, solved this new found value in the appropriate matrix and the vector of distances: d5 := - 1 2 ⁢ xe2x80x83 ⁢ 2 ⁢ c6d3 - 4 ⁢ c6d4c4d3 - 2 ⁢ c6d4 - 2 ⁢ c5d3 + 4 ⁢ c5d4c4d3 + 2 ⁢ c5d4 + 2 ⁢ c4d3 + 1 c6 ⁡ ( - 2 ⁢ c5d3 + 4 ⁢ c5d4c4d3 + 2 ⁢ c5d4 + 2 ⁢ c4d3 + 1 ) ( 51 ) The distance between mirror one and two was: d1 := xe2x80x83 ⁢ - 1 4 ⁢ ( - 4 ⁢ d2c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - 2 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ c4d3 + 1 ) ⁢ ( 2 ⁢ c3d2 + 1 ) + angle ⁢ xe2x80x83 ⁢ d2 ( - 2 ⁢ c5 ( d3 + d4 ( - 2 ⁢ c4d3 - xe2x80x83 ⁢ 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) / ( ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 ) ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) ( 52 ) And the distance between the object and the first mirror: d0 := xe2x80x83 ⁢ - 1 2 ⁢ ( ( 1 - 2 ⁢ d2c2 ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ c4d3 + 1 ) ⁢ ( 2 ⁢ c3d2 + 1 ) + angle ⁢ xe2x80x83 ⁢ d2 ( - 2 ⁢ c5 ( d3 + d4 ( - 2 ⁢ c4d3 - xe2x80x83 ⁢ 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ d2 ( - 2 ⁢ c5 ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( - 2 ⁢ c3 ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 ) + 2 ⁢ c2 ) + 2 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ ( - 2 ⁢ c5 ( d3 + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( 2 ⁢ c3d2 + 1 ) - xe2x80x83 ⁢ 2 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) / ( angle ⁢ xe2x80x83 ⁢ ( ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) ⁢ d2 + ( 2 ⁢ c3d2 + 1 ) ⁢ ( 1 - 2 ⁢ d2c2 ) ) ⁢ c1 ( - 2 ⁢ c5 ( d3 + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ) ( 53 ) And the distance between mirror six and the image surface: d6 := xe2x80x83 ⁢ - xe2x80x83 ⁢ 1 4 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) 2 ⁢ ( 1 - 2 ⁢ d4c4 ) ⁢ c6 ( - 2 ⁢ c5 ( d3 + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( 2 ⁢ c3d2 + xe2x80x83 ⁢ 1 ) - 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ ( 1 - 2 ⁢ d4c4 ) ⁢ c6 ( - 2 ⁢ c5 ( d3 + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ d2 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) 2 ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d4c4 ) + xe2x80x83 ⁢ 2 ⁢ c4 ) ⁢ c6 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) ⁢ ( 2 ⁢ c3d2 + 1 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d4c4 ) + 2 ⁢ c4 ) ⁢ c6 ( d3 + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) ⁢ d2 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) + xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) 2 ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d4c4 ) + xe2x80x83 ⁢ 2 ⁢ c4 ) ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( 2 ⁢ c3d2 + 1 + xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d4c4 ) + 2 ⁢ c4 ) ⁢ ( - 2 ⁢ c5 ( d3 + xe2x80x83 ⁢ d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ d2 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) + angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + xe2x80x83 ⁢ 1 ) 2 ⁢ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ ( 2 ⁢ c3d2 + 1 ) + xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) 2 ⁢ ( - 2 ⁢ c3 ( 1 - "AutoLeftMatch" xe2x80x83 ⁢ 2 ⁢ d2c2 ) + 2 ⁢ c2 ) "AutoRightMatch" 2 ⁢ d2 - 4 ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ c4d3 + 1 ) ⁢ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ⁢ d2c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - xe2x80x83 ⁢ 4 ⁢ c1 ⁡ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + 1 ) ⁢ ( 2 ⁢ c3d2 + xe2x80x83 ⁢ 1 ) ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + 4 ⁢ xe2x80x83 ⁢ magn 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 2 ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 ) ) / ( ( ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + xe2x80x83 ⁢ 1 ) ⁢ ( 1 - 2 ⁢ d4c4 ) ⁢ d2 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) - ( - 2 ⁢ c5 ( 1 - xe2x80x83 ⁢ 2 ⁢ d4c4 ) + 2 ⁢ c4 ) ⁢ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) ⁢ d2 ( - 2 ⁢ c3 ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 ) + 2 ⁢ c2 ) - ( 2 ⁢ c3d2 + 1 ) ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ ( - 2 ⁢ c5 ⁡ ( 1 - 2 ⁢ d4c4 ) + xe2x80x83 ⁢ 2 ⁢ c4 ) ⁢ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + ( 2 ⁢ c3d2 + 1 ) ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 ) ⁢ ( - 2 ⁢ c5 ⁡ ( d3 + d4 ⁡ ( - 2 ⁢ c4d3 - 1 ) ) + 2 ⁢ c4d3 + xe2x80x83 ⁢ 1 ) ⁢ ( 1 - 2 ⁢ d4c4 ) ) ⁢ ( 1 - 2 ⁢ d2c2 ) ⁢ c6 2 ⁢ xe2x80x83 ⁢ angle ) ( 54 ) 6-Mirror System, Stop on Mirror 4 Similarly, the original derivations can be used to solve the variables of a six-mirror system with the stop position on mirror four. Again, the first solve is pupil in infinity or telecentricity in the image. The angle of the ray going through the optical axis in the stop surface should be zero in the image. The matrix from the stop surface to the fifth mirror generated by multiplication of the appropriate M matrices derived above is given by: [ 1 d4 - 2 ⁢ c5 - 2 ⁢ c5d4 - 1 ] ( 55 ) The matrix from the second mirror surface to the stop surface is given by: [ 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) - d2 + d3 ⁡ ( 2 ⁢ c3d2 + 1 ) - 2 ⁢ c4 ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) + 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) - 2 ⁢ c2 - 2 ⁢ c4 ( - d2 + d3 ( 2 ⁢ c3d2 + 1 ) ) - 2 ⁢ c3d2 - 1 ] ( 56 ) So, as derived above, the distance between mirror 5 and 6, solved in the appropriate matrix and the vector of distances, is: d5 := - xe2x80x83 ⁢ 1 2 ⁢ xe2x80x83 ⁢ - 2 ⁢ c6d4 + 2 ⁢ c5d4 + 1 c6 ⁡ ( 2 ⁢ c5d4 + 1 ) ( 57 ) The distance between mirror one and two is: d1 := xe2x80x83 ⁢ - xe2x80x83 ⁢ 1 4 ⁢ ( 4 ⁢ ( - d2 + d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - 2 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 + d3 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + xe2x80x83 ⁢ ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5d4 - 1 ) ⁢ ( - 2 ⁢ c4 ( - d2 + d3 ( 2 ⁢ c3d2 + xe2x80x83 ⁢ 1 ) ) - 2 ⁢ c3d2 - 1 ) - angle ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) ⁢ ( - 2 ⁢ c5d4 - xe2x80x83 ⁢ 1 ) ⁢ ( - 2 ⁢ c4 ⁡ ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) - 2 ⁢ c2 ) ) / ( ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) ( 58 ) And the distance between the object and the first mirror: d0 := xe2x80x83 ⁢ - 1 2 ⁢ ( ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ c5d4 - 1 ) ⁢ ( - 2 ⁢ c4 ( - d2 + xe2x80x83 ⁢ d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) - 2 ⁢ c3d2 - 1 ) - angle ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) ⁢ ( - 2 ⁢ c5d4 - 1 ) ⁢ ( - 2 ⁢ c4 ( 1 - 2 ⁢ d2c2 + xe2x80x83 ⁢ d3 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) + 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) - xe2x80x83 ⁢ 2 ⁢ c2 ) - 2 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) ⁢ ( - 2 ⁢ c5d4 - xe2x80x83 ⁢ 1 ) ⁢ ( - 2 ⁢ c4 ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) ) + 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) - 2 ⁢ c2 ) + 2 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 + d3 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) ⁢ ( - 2 ⁢ c5d4 - xe2x80x83 ⁢ 1 ) ⁢ ( - 2 ⁢ c4 ⁡ ( - d2 + d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) - 2 ⁢ c3d2 - 1 ) - xe2x80x83 ⁢ 2 ⁢ ( 1 - 2 ⁢ d2c2 + d3 ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + xe2x80x83 ⁢ 2 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) / ( angle ⁢ xe2x80x83 ⁢ ( - ( - 2 ⁢ c4 ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 + d3 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) - 2 ⁢ c2 ) ⁢ ( - d2 + d3 ( 2 ⁢ c3d2 + xe2x80x83 ⁢ 1 ) ) + ( - 2 ⁢ c4 ⁡ ( - d2 + d3 ⁡ ( 2 ⁢ c3d2 + 1 ) ) - 2 ⁢ c3d2 - 1 ) ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ d2c2 + d3 ⁡ ( - 2 ⁢ c3 ⁡ ( 1 - 2 ⁢ d2c2 ) + 2 ⁢ c2 ) ) ) ⁢ c1 ⁡ ( - 2 ⁢ c5d4 - 1 ) ) ( 59 ) And the distance between mirror six and the image surface: d6 := xe2x80x83 ⁢ - xe2x80x83 ⁢ 1 4 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) 2 xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) - 4 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d4 xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 ⁢ xe2x80x83 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + 4 ⁢ xe2x80x83 ⁢ angle xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + ⁢ xe2x80x83 xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) 2 xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) xe2x80x83 ⁢ c5 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) + angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) 2 xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 - 1 ) - xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) 2 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + ( xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) 2 xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 + 1 ) ) ⁢ xe2x80x83 xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁡ ( - d2 + d3 ⁡ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + 4 ⁢ xe2x80x83 ⁢ magn 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 2 ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) ) / ( ( - ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ⁢ xe2x80x83 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 + ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ d4 - 1 ) ) xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ angle ) ( 60 ) 6-Mirror System, Stop on Mirror 5 Again, we use the original derivations to solve the variables of a six-mirror system with the stop position on mirror five. As before, the first solve is pupil in infinity or telecentricity in the image. The angle of the ray going through the optical axis in the stop surface should be zero in the image. The matrix from the stop surface to the fifth mirror generated by multiplication of the appropriate M matrices derived above is given by: [ 1 0 0 1 ] ( 61 ) The matrix from the second mirror surface to the stop surface is given by: [ 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) , - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + "AutoLeftMatch" d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + "AutoLeftMatch" 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - xe2x80x83 ⁢ "AutoLeftMatch" 1 ) ] [ xe2x80x83 ⁢ - "AutoLeftMatch" 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) + "AutoLeftMatch" d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + "AutoLeftMatch" d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 , - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ "AutoLeftMatch" "AutoRightMatch" ⁢ "AutoLeftMatch" 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ] ( 62 ) So, as derived above, the distance between mirror 5 and 6, solved in the appropriate matrix and the vector of distances: is: d5 := - xe2x80x83 ⁢ 1 2 ⁢ 1 c6 ( 63 ) The distance between mirror one and two was: d1 := xe2x80x83 ⁢ - 1 4 ⁢ ( 4 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) - angle ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) / ( ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) ( 64 ) And the distance between the object and the first mirror: d0 := xe2x80x83 ⁢ - 1 2 ⁢ ( ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ angle xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) - xe2x80x83 ⁢ angle ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ⁢ xe2x80x83 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ⁢ xe2x80x83 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 + 1 ) - xe2x80x83 ⁢ 2 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 ) / xe2x80x83 ⁢ ( angle ⁢ xe2x80x83 ⁢ ( - ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) xe2x80x83 ⁢ ( - d2 ⁢ xe2x80x83 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ) ⁢ c1 ) ( 65 ) And the distance between mirror six and the image surface: d6 := xe2x80x83 ⁢ - 1 4 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) 2 ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ c6 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + xe2x80x83 ⁢ 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) - angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) 2 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 + 4 ⁢ xe2x80x83 ⁢ magn 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) ) / ( ( - ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + ( - 2 ⁢ xe2x80x83 ⁢ c5 ⁢ xe2x80x83 ⁢ ( - d2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ) + 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - d2 + d3 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - 2 ⁢ xe2x80x83 ⁢ c2 ) ) ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + d4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ d3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ) + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ xe2x80x83 ⁢ c6 2 ⁢ xe2x80x83 ⁢ angle ) ( 66 ) 4-Mirror System, Stop on mirror 2 Yet again, we can use these derivations to solve the variables of a four-mirror system with the stop position on mirror two. As usual, the first solve is pupil in infinity or telecentricity in the image. The angle of the ray going through the optical axis in the stop surface should be zero in the image. The matrix from the stop surface to the third mirror generated by multiplication of the appropriate M matrices derived above, is given by: [ 1 d2 - 2 ⁢ xe2x80x83 ⁢ c3 - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ] ( 67 ) The matrix from the second mirror surface to the stop surface is given by: [ 1 0 - 2 ⁢ xe2x80x83 ⁢ c2 - 1 ] ( 68 ) So as derived above, the distance between mirror 3 and 4, solved in the appropriate matrix and the vector of distances is: d3 := - 1 2 - 2 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 + 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 c4 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ( 69 ) The distance between mirror one and two was: d1 := - 1 4 - 2 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 - angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 ( 70 ) And the distance between the object and the first mirror: d0 := 1 2 ⁢ - angle ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 - 1 ) - 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 - 1 ) - 2 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 angle ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 - 1 ) ( 71 ) And the distance between mirror four and the image surface: d4 := xe2x80x83 ⁢ - 1 4 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + 4 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 + xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) + 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) 2 ⁢ xe2x80x83 ⁢ c2 + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 - 1 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 + 4 ⁢ xe2x80x83 ⁢ magn 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 2 ) / xe2x80x83 ⁢ ( c4 2 ⁢ xe2x80x83 ⁢ angle ) ( 72 ) 4-Mirror System, Stop on Mirror 3 Again, we use the original derivations to solve the variables of a four-mirror system with the stop position on mirror three. The first solve is pupil in infinity or telecentricity in the image. The angle of the ray going through the optical axis in the stop surface should be zero in the image. The matrix from the stop surface to the third mirror generated by multiplication of the appropriate M matrices derived above is given by: "AutoLeftMatch" [ 1 0 0 1 ] ( 73 ) The matrix from the second mirror surface to the stop surface is given by: "AutoLeftMatch" [ 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 - d2 - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ] ( 74 ) So as we derived the distance between mirror 3 and 4 is: d3 := - 1 2 ⁢ 1 c4 ( 75 ) And we solve this new found value in the appropriate matrix and the vector of distances. The distance between mirror one and two was: d1 := - 1 4 ⁢ - 4 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 - 2 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 + ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + angle ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 ( 76 ) And the distance between the object and the first mirror: d0 := xe2x80x83 ⁢ - 1 2 ⁢ ( ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) - 2 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 ) / xe2x80x83 ⁢ ( angle ⁢ xe2x80x83 ⁢ ( ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁡ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ d2 + xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ) ⁢ c1 ) ( 77 ) And the distance between mirror four and the image surface: d4 := xe2x80x83 ⁢ - 1 4 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) 2 ⁢ c4 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( 1 - xe2x80x83 ⁢ 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ c4 ⁢ xe2x80x83 ⁢ d2 ⁡ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) + xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) + xe2x80x83 ⁢ angle ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) 2 ⁢ d2 - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 - xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ c1 ⁢ xe2x80x83 ⁢ ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ xe2x80x83 ⁢ magn ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 + xe2x80x83 ⁢ 4 ⁢ xe2x80x83 ⁢ magn 2 ⁢ xe2x80x83 ⁢ yob ⁢ xe2x80x83 ⁢ c4 2 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ) / xe2x80x83 ⁢ ( ( ( - 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) + 2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ d2 + ( 2 ⁢ xe2x80x83 ⁢ c3 ⁢ xe2x80x83 ⁢ d2 + 1 ) ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ) xe2x80x83 ⁢ ( 1 - 2 ⁢ xe2x80x83 ⁢ d2 ⁢ xe2x80x83 ⁢ c2 ) ⁢ c4 2 ⁢ xe2x80x83 ⁢ angle ) ( 78 ) Obscuration A particular problem in designing mirror systems, not encountered in refractive lens systems, is ensuring that the beam is not obscured in its zigzag course by other mirrors. Because of the necessary zigzag path, as the projection beam proceeds between successive mirrors I and I+1 on the optical path in many cases it will pass by at least one other mirror J. Thus, for an optical system not to be obscured it is necessary to ensure that the position and extent of the intervening mirror J is such that it does not intersect any part of the beam between mirrors I and I+1. This is shown in FIG. 4 in which it can be seen that mirror lies wholly below the beam between I and I+1 whereas mirror Jxe2x80x2 partially intersects the beam. The arrangement of mirror is not permitted. In a model of a potential projection system, obscuration can be detected by the following procedure: 1. For each pair of successive mirrors I, I+1 on the optical path, check if there exists a 20 mirror J (with J not equal to I, I+1) having a position on the optical axis (Z axis) between I and I+1 2. If J exists, calculate the distance from the optical axis (Y position) of the extreme rays from I to I+1 at the position of mirror j on the optical axis. 3. Check that the top and bottom of mirror J are both above (i.e. have greater Y position) or both below (i.e. have smaller Y position) both the extreme rays from I to I+1. If the check in (3) fails, then mirror at least partially obscures the beam from I to I+1 and the mirror system must be modified or rejected. Preferred Four-mirror Systems FIG. 6 shows a mirror system in class 9(+) which can be used in the lithography apparatus of FIG. 1. In this class, the stop can be positioned on mirror 2 or 3; in the system of FIG. 6, the stop position is on surface 2. The ring field of this system is defined on the object side, between 114 and 118 arbitrary units, with a numerical aperture of 0.25 (0.05 on the object side). The magnification is 0.2 and an intermediate image is formed between mirrors 3 and 4. The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 1 below. The values found for the curvatures and thicknesses can be re-scaled using a scaling factor. If the thicknesses are multiplied by that factor, the curvatures should be divided by it, and vice versa. FIG. 7 also shows a mirror system in class 9(+). In this case the stop is on mirror 3 and the intermediate image is between mirrors 1 and 2. The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 2 below. FIG. 8 shows an example of a class 2(xe2x88x92) system having the stop located on the third mirror. From the object (mask MA, surface 0) all the rays go, with a negative angle (a zero angle is parallel to the optical axis), to the first convex mirror M1. The convex mirror M1 reflects the beam upward to a large concave mirror M2. The position of the second mirror M2 has to be above the beam between the object (mask MA) and mirror M1. The beam then goes under mirror M1 to the stop surface mirror M3. From the stop surface the beam is reflected to concave mirror M4. Mirror M4 takes care of a telecentric illumination of the image (surface 5). The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 3 below. A class 6(xe2x88x92) system, shown in FIG. 9, consists of two mirror pairs, in a symmetrical design. From the object (mask MA, surface 0) all the rays go, with a negative angle (a zero angle is parallel to the optical axis), to the first convex mirror M1. The object is illuminated as telecentric as possible, this being a requirement for lithography. The convex mirror M1 reflects the beam upward to a large concave mirror M2. The position of this mirror has to be above the beam between the object and mirror M1. So far this design resembles the class 2(xe2x88x92) design (shown in FIG. 8). The beam then goes over mirror M1 to the stop surface on mirror M3, limited by the top of mirror M1. From the stop surface M3 the beam is reflected to concave mirror M4. Mirror M4 takes care of a telecentric illumination of the image (surface 5). The ring field of this system is defined on the image side, between xe2x88x9222.8 and xe2x88x9223.8, resulting in a Strehl ratio of at least 0.972 with a numerical aperture of 0.15. The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 4 below. A class 9(xe2x88x92) system with a stop on the second surface is shown in FIG. 10. The ring field of this system is defined on the object side, between 114 and 118 arbitrary units, with a numerical aperture of 0.2 (0.05 on the object side). The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 5 below. FIG. 11 shows a system in class 10(xe2x88x92). The ring field of this system is defined on the object side, between 114 and 118 arbitrary units, with a numerical aperture of 0.2 (0.05 on the object side). The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 6 below. Preferred Six-mirror Systems All the six-mirror systems found to be feasible have, as they have a positive magnification, an intermediate image. FIG. 12 shows a six-mirror system in class 9(+) in which the stop can be positioned on mirror 2, 3, 4 and 5. The system has the intermediate image located between mirror 2 and five. The ring field of this system is defined on the object side, between 114 and 118 arbitrary units, with a numerical aperture of 0.24 (0.06 on the object side). The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 7 below. A class 37(+) six-mirror system can have the stop positioned on mirror 2, 3, 4 or 5 and has the intermediate image located between mirror 2 and five. The ring field of such a system is defined on the image side, between 27 and 30 arbitrary units, with a numerical aperture of 0.24. The system shown in FIG. 13 has the stop on surface 2. This system consists of a mirror pair near the object and four-mirrors grouped near the image. From the object (mask MA, surface 0) all the rays go, with a negative angle, to the first concave mirror M1. The concave mirror M1 reflects the beam downward to mirror M2 which is almost flat. The top of mirror M2 is restricted to be below the beam between the object and mirror M,. The beam between mirror M2 and M3 limits the bottom of the small mirror M4, while the beam between mirror M4 and M5 limits the top of mirror M4. Finally, the beam between the last mirror M6 and the image limits the top of mirror M5. The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 8 below. For comparison, FIG. 14 shows a class 37(+) six-mirror system with the stop on surface 5. The ring field of this system is defined on the image side, between 27 and 30 arbitrary units, with a numerical aperture of 0.24. The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 9 below. Preferred Eight-mirror System An eight-mirror system in class 165(+) with stop on surface 3 is shown in FIG. 15. The ring field of this system is defined on the object side, between 116 and 124 arbitrary units, with a numerical aperture of 0.24 (0.06 on the object side). The first order curvatures and thicknesses of this system, in arbitrary units, are given in Table 10 below. An eight mirror system in class 169(+) is shown in FIG. 16, the curvatures and thicknesses of its elements are shown in Table 11. This system has a ring field in the object side between 114 and 118 arbitrary units, a numerical aperture of 0.4, distortion less than 2.9 nm and an rms wavefront error less than 0.3xcex. An eight mirror system in class 181(+) is shown in FIG. 17, the curvatures and thicknesses of its elements are shown in Table 12. Again, the ring field on the object side is between 114 and 118 units and the numerical aperture is 0.4. However, the distortion is less than 1.9 nm and the rms wavefront error less than 0.5xcex. An eight mirror system in class 150(xe2x88x92) is shown in FIG. 18, the curvatures and thicknesses of its elements are shown in Table 13. This system provides a distortion less than 2.6 nm and an rms wavefront error less than 0.19xcex. An eight mirror system in class 182(xe2x88x92) is shown in FIG. 19, the curvatures and thicknesses of its elements are shown in Table 14. This system likewise has a ring field on the object side between 114 and 118 arbitrary units, a numerical aperture of 0.4, an rms wavefront error of less than 1xcex and a distortion less than 2.18 nm. While we have described above specific embodiments of the invention it will be appreciated that the invention may be practiced otherwise than described. The description is not intended to limit the invention.

claims

1. An under vessel automated work platform assembly for remotely servicing a lower portion of a vessel, the platform assembly comprising:a horizontal generally circular work platform extending in a first plane;a generally circular rail extending in a second plane substantially parallel to the first plane, the rail supporting an orbital track on which the work platform is rotationally supported to rotate the work platform in the first plane and the orbital track includes a circumferential drive ring having gear teeth and extending in a third plane substantially parallel to the second plane;a pin gear structured to interact with the gear teeth of the circumferential drive;a remotely controlled motor for rotating the work platform on the orbital track by driving the pin gear;a linear track extending across a diameter of the work platform;a remotely controlled carriage moveable on the linear track across the diameter of the work platform;an automated tool programed to perform at least part of a reactor maintenance task, attached to the remotely controlled carriage and moveable therewith, the automated tool having a vertically extending member moveable in a direction perpendicular to the first plane; anda controller for remotely inputting an in-vessel cell coordinate and automatically positioning the automated tool under the in-vessel cell coordinate by controlling the rotation of the work platform on the orbital track and movement of the remotely controlled carriage on the linear track. 2. The under vessel automated work platform assembly of claim 1 including a hand wheel for manually moving the work platform around the orbital track. 3. The under vessel automated work platform assembly of claim 1 wherein the automated tool is a swappable task robot. 4. The under vessel automated work platform assembly of claim 1 wherein the automated work platform assembly is sized to fit under the vessel. 5. The under vessel automated work platform assembly of claim 1 wherein the work platform supports a camera generally focused on the distal end of the vertically extending member. 6. The under vessel automated work platform assembly of claim 5 wherein the camera has a remote controlled panning capability. 7. The under vessel automated work platform assembly of claim 5 wherein the camera has a remote controlled tilt capability. 8. The under vessel automated work platform assembly of claim 1 for servicing a nuclear reactor having a nuclear core and a refueling system command station for refueling the core, and the remotely controlled motor and the remotely controlled carriage are structured to communicate with the controller that is structured to control the rotation of the work platform and the movement of the remotely controlled carriage and provide an output identifying a position of the remotely controlled carriage in a form that can be received and understood by the refueling system command station so the refueling system command station is notified of the position of the remotely controlled carriage so that proper work processes can be adhered to.

045267448

summary

TECHNICAL FIELD The present invention relates to a fuel assembly for a boiling water reactor, the fuel assembly comprising a plurality of vertical fuel rods, which are surrounded by a fuel channel device with a vertical longitudinal axis, the fuel rods constituting four partial bundles or subassemblies, the fuel rods in each partial bundle being positioned by means of a corresponding group of spacers arranged vertically one after the other, each of the partial bundles resting on a corresponding bottom grid. BACKGROUND ART A fuel assembly of this kind is known from U.K. Patent Specification No. 931,676. In the known fuel assembly the fuel rods are distributed among four partial bundles, each of which is provided with a bottom grid and with a top grid. Each fuel rod is provided with slotted end portions and arranged with the slots in engagement with and hard-soldered to the top grid and the bottom grid, respectively. Further, such a fuel assembly is known from U.S. Patent No. 3,389,056. Which discloses a fuel assembly in which the fuel rods are distributed among four partial bundles, which are positioned with respect to each other by means of a plurality of upwardly-directed fixing members, disposed outside the fuel channel device and extending from one partial bundle each, said fixing members being attached to the top grid of the reactor core. With conventional boiling water reactor fuel assemblies of the kind comprising several partial bundles, it is not possible to lift all the partial bundles out of the fuel channel device in one and the same lifting operation. DISCLOSURE OF THE INVENTION The invention aims to provide a four-part fuel assembly which permits simplified and less time-consuming fuel handling than what is possible when using the above-mentioned prior art fuel assemblies. According to the invention, the majority of the fuel rods in each partial bundle is arranged in the bottom grid freedom of movememnt in a direction vertically upwards. At least one fuel rod in each partial bundle is a tie rod which is detachably arranged in a tensile force transmitting connection with the bottom grid of the partial bundle. The partial bundles are positioned in relation to each other by means of a common top tie plate, positioned above the fuel rods and surrounded by an upper portion of said fuel channel device. The top tie plate is detachably arranged in a tensile force transmitting connection with the bottom grids by means of the tie rods and is provided with a lifting loop adapted for lifting all the partial bundles of the fuel assembly in one and the same lifting operation. A simultaneous lifting is time-saving in case of inspection of the fuel and when, at a certain burnup stage, it is desirec to change the positions and/or orientations of the various partial bundles with a view to achieving better fuel economy.

039430375

abstract

In a nuclear reactor which is housed in a round building and which has a reactor pressure vessel in a reactor pool, a fuel element storage pool of arcuate outline, a gate-controlled channel interconnecting the two pools and an operating platform adjacent the pools, there is provided a fuel element exchange system which has a first fuel element exchange gantry supported on a column disposed in the center of the reactor building and on a rail which is held by the building wall and which is situated above the level of the operating platform, and a second fuel element exchange gantry supported under the first gantry in such a manner that the second gantry may freely pass under the first gantry. There is further provided a fuel element box-stripping machine at the storage pool immediately across from the channel within the operational range of both the first and the second gantries.

039473198

summary

The invention relates to a nuclear reactor plant intended for supplying heat to a steam generator, which plant comprises at least two circuits for conveying this heat, these circuits being hydraulically separated but thermally coupled to each other by means of heat exchangers, specifically one water-steam-circuit equipped with a steam generator, a feed water pump which is included in a feed water conduit with a feed controlling valve as well as with a steam turbine, and one reactor-circuit equipped with a primary circulation pump and charged with a non-water, heat-transferring medium, in such a way that the heat exchangers in the operative state exhibit a relatively small pressure drop. The control systems hitherto known for such a reactor system have been marked by a high degree of complexity. Applicant has arrived at the insight that it is also possible to attain very good results with a control system of very simple design. According to the invention, this aim is reached by dimensioning the feed water conduit with the feed water control valve contained therein in such a way that the pressure drop along this feed water conduit at full load is greater than 10 bars. In proportion as the pump characteristic is steeper, this pressure drop can become somewhat smaller without any objection. If a pump is selected having a steep curve indicating the correlation between lift and output, this will furthermore provide the advantage of such a pump being lower in price. In a given design, use may be made, for example, of a feed pump marked by an almost linear correlation between lift and output. This curve may be actually curved or may be a virtually straight line which, at a constant pump speed, indicates the correlation between lift (=pump pressure) and output, and is in this connection called steeper in proportion as, with a given drop in output, the lift of the pump rises. This curve is in the following sometimes designated as "pump characteristic." Since it is sometimes not a simple matter to realize a fairly appreciable pressure drop in a control valve, use may be made, if required, of a hydraulic turbine. In this liquid turbine, at least part of the pressure drop can be realized which is necessary for the stability of the system. An additional advantage of this is that energy is recovered in the liquid turbine. The liquid turbine, which often needs to comprise only one step, can advantageously be accommodated in the housing of the feed water pump, the blade wheel of this turbine being fastened on the rotor of the pump. A bypass valve, arranged in a bypass of the turbine, in such case regulates the amount of feed water flowing through the turbine. In many cases, the aforementioned hydraulically separated but thermally coupled circuits are separated from each other not only by heat exchangers but also by an additional heat-transferring circuit. This measure will be taken specifically in the case of a nuclear reactor plant provided with a sodium-cooled reactor. In such a case, the precaution is taken of providing an additional heat-transferring circuit for hydraulically separating the primary circuit and the steam-water-circuit; said additional or so-called secondary circuit being equipped with a secondary circulating pump and containing a non-water heat-transferring medium. The three hydraulically separated circuits then are thermally coupled by means of an intermediate heat exchanger for conveying heat from the primary or reactor-circuit to the secondary circuit and the steam generator. For a correct understanding of the following, it is pointed out that a sodium-cooled reactor, on account of the secondary cooling circuits with prolonged dead times (time lags) for heat transportation, gives rise to processes which are difficult to control. In this respect, it has been considered that the use of a steam-water-separator in the sodium-heated steam generator presents advantages with respect to the control of temperature in the steam generator. A consequence of using such a water-steam-separator, however, is that this steam generator gives rise to the formation of a positive feedback between live steam pressure and feed water flow. An important element of the present invention is the insight that this undesired feedback can be simply eliminated by taking the required measures for the pressure drop through the feed water conduit and the control valve, to have a value of at least 10 bars. The aforementioned steam separator is necessary, because the evaporator of the steam generator produces somewhat wet steam. The excess water is separated from the mixture in the steam-water-separator, so as to return it to the feed water preheaters. It has been found in practice that several factors are decisive for the stability of the control system of the steam generator. This steam generator system, consisting of a feed water pump, a control valve, an evaporator, a steam-water-separator, a superheater and a turbine-inlet-valve exhibits -- without the control circuits -- a negative feedback effect on account of the thermal behaviour thereof. In certain circumstances, however, the same system exhibits a positive feedback effect on account of the hydraulic behaviour. The presence of a negative thermal feedback (back coupling) can be observed by an increase in the flow of feed water through the evaporator. Since, in this case, more water must be heated to boiling temperature, less steam will be produced, resulting in a drop of the flow of steam through the superheater. Since the conditions of steam admission to the superheater through the steam water separator must be kept constant, the power transmitted from the sodium to the steam is proportional to the quantity of steam flowing per unit of time through the superheater. A reduced steam production gives a higher sodium outlet temperature at the superheater, causing more power to become available for producing steam in the evaporator. As a result, the entire system will rapidly find its new state of equilibrium. The fact, however, that a positive hydraulic feedback can also arise can be understood by realizing that a change occurs in the position of the turbine inlet valve. An increase in the valve passage of the turbine causes an increase in the amount of steam flowing through the steam conduit, as well as a pressure drop in this steam conduit, in the superheater and in the steam-water-separator. Now the mass flow through the evaporator is directly proportional to the square root of the pressure difference that prevails between the steam-water-separator and the feed water pump. This pressure difference increases as a result of the decrease of pressure in the steam-water-separator. The eventual increase of the feed water flow causes a decrease in the steam flow through the superheater, which in turn causes a decrease of the live steam pressure. In this manner, variations can occur in the steam pressure without leading to a new stable state. It is a fortunate circumstance that the increase in the amount of feed water likewise produces a decrease of the feed water pump pressure as a result of the pressure output characteristic of this pump. If this decrease is of the same order of magnitude as the decrease in pressure of the steam-water-separator, a new, stable adjustment can indeed be reached in operation. The output characteristic of the great majority of feed water pumps exhibits a slight inclination at low outputs. Accordingly, the opposing effect is too small for our purpose. Measures must therefore be taken for the increase in feed water flow, resulting from the pressure drop in the steam-water-separator, to be reduced at low loads. This can be done in a simple manner by introducing an extra pressure drop or resistance in the feed water conduit. According to calculations, a pressure drop of 20 bars at a load of 30 percent is sufficient for ensuring a stable behaviour of the steam generator. This pressure drop should be about 10 bars at full load for attaining the same stabilizing effect. According to the invention, the control system is furthermore so designed that a control impulse coming from the measured amount of water separated in the external water separator gives an impulse to the feed water control valve. A steam generator system equipped with such a control circuit exhibits the following behaviour: A drop of the live steam pressure owing for instance to a greater turbine steam flow, causes an increase in the feed water flow. This causes an increase in the draining of condensate collected in the steam-water-separator. The control circuit over this condensate drainage will slightly close the feed water valve, resulting in a decrease of the feed water flow as well as in a decrease of the steam condensate drainage and an increase in pressure, because of an increase both in the flow of steam to the superheater and the supply of heat. This pressure increase brings about a further decrease of the feed water flow, and thus a still further decrease in the drainage from the water separator. This decrease will again induce the control circuit to open the feed water valve still further, until a correct and stable state has fairly rapidly been established. Now if the coupling factor between the live steam pressure changes and the change in the drainage of condensate from the steam water separator is too high, this control circuit can become unstable. This can be remedied by reducing the coupling factor by increasing the pressure drop in the feed water conduit. It has already been explained in the above that other considerations have also led to the finding that a pressure drop of 20 bars will ensure at all loads a stabilizing dynamic behaviour of this control circuit. According to a preferred embodiment of the invention, the set-point controls of the regulators for the tertiary and for the primary circuit are disconnected, whereby the process has become well regulable. This is preferably accomplished by taking such measures that a control impulse coming from the measured steam pressure, or the measured amount of steam per unit of time, or a combination of these measured values, corrects the mass flow of the secondary circuit, by influencing the speed of the secondary circulating pump. This measure can be effectively supplemented by causing a control impulse from the mass flow measured in the secondary circuit to correct the mass flow of the reactor circuit by influencing the speed of the primary circulating pump. Finally, it has been found effective to cause a control impulse from the mass flow measured in the secondary circuit to adjust the set point of the reactor temperature regulator. With the use of the control method described, according to which the reactor outlet temperature changes as a function of load, the temperature of the live steam does not have to be separately regulated. Calculations have shown that this temperature during very fast load changes, such as, for example, 10 percent of load in 5 seconds, changes by only about 6.degree.C, during a very short time, approximately 30 seconds. The control system according to the invention can be load-following as well as load-forcing. According to the latter method, the secondary sodium pump is controlled with a desired power signal, and the live steam pressure is constantly controlled with the turbine valve, so-called prepressure (initial pressure) control. With the aid of the following figures, two embodiments of the invention will be explained in further detail.

abstract

This invention relates to a system for regulating a liquid in a circuit, with the system comprising: a plug valve comprising at least one inlet and one outlet, the plug comprising an internal passage through which is intended to pass the liquid flowing from the inlet to the outlet of the valve when the valve is open at least partially, an expansion reservoir in communication with the liquid flowing in the circuit and intended to contain liquid and a compensating gas, characterized in that the plug comprises at least partially an expansion channel which has at least one lateral opening located on a lateral face of the plug and which is conformed to provide a permanent communication between said lateral opening and the expansion reservoir, the valve being conformed in such a way that: at least when the valve is closed: the lateral opening is in direct communication with the liquid coming from the inlet or from the outlet of the valve, when the valve is open at least partially, the lateral opening cooperates with an inner wall integral with a body of the valve in such a way as to form a conduit in communication on the one hand with the expansion reservoir and on the other hand with the internal passage. The invention also relates to a circuit integrating this system as well as a use of this system.

summary

abstract

A technique for processing a workpiece is disclosed. In accordance with one exemplary embodiment, the technique is realized as a method for processing a substrate, where the method comprises: providing the workpiece in the chamber; providing a plurality of electrodes between a wall of the chamber and the workpiece; generating a plasma containing ions between the plurality of electrodes and the workpiece, ion density in an inner portion of the plasma being greater than the ion density in an outer portion of the plasma portion, the outer portion being between the inner portion and the wall of the chamber; and providing a bias voltage to the plurality of electrodes and dispersing at least a portion of the ions in the inner portion until the ion density in the inner portion is substantially equal to the ion density in the periphery plasma portion.

description

The present application claims foreign priority based on Japanese Patent Application No. 2005-150832, filed May 24, 2005, the content of which is incorporated herein by reference. 1. Technical Field The present invention relates to an ion beam irradiation apparatus so constructed as to irradiate a substrate held by a substrate holding surface of a holder with an ion beam that travels in the horizontal direction. Particularly, the invention relates to means for controlling non-uniformity of ion implantation due to a divergent angle of the ion beam applied onto the substrate. This ion beam irradiation apparatus is, for example, an ion implantation apparatus. 2. Related Art FIG. 4 shows a schematic side view of this type of related-art ion beam irradiation apparatus, showing an example of the constitution in which the substrate held by the holder is irradiated with the ion beam. An ion beam irradiation apparatus having the nearly similar structure to this structure has been disclosed in FIG. 13 in JP-A-2003-110012. Three axes that are orthogonal to each other at one point are taken as an X-axis, a Y-axis and a Z-axis. Generally, an ion beam 58 traveling in the direction along the Z-axis is scanned in the direction along the X-axis by an electric filed or a magnetic field, and applied onto a substrate 54 held by a substrate holding surface 6 of a holder 4. The holder 4 is, for example, an electrostatic chuck. In this example, both the X-axis and the Z-axis are imaginary axes in the horizontal direction. Further, as the ion beam 58, in place of the ion beam scanned in the direction along the X-axis, there is also an ion beam which is long in the shape of a strip from its base without scanning in the direction along the X-axis, and travels in the direction along the Z-axis. In this specification, “direction along an axis” means a direction substantially parallel to its axis. Further, “substantially parallel” includes a parallel state. This ion beam irradiation apparatus includes a counter-rotatable type of irradiation angle setting motor 14 which controls an irradiation angle θ of the ion beam 58 to the substrate holding surface 6 of the holder 4 supported by a rotation shaft 46 through a coupling member 48, that is, to a surface 56 of the substrate 54 by rotating the holder 4 around the rotation shaft 46 substantially parallel to the X-axis in the direction of an arrow A in FIG. 4; and an elevator unit 50 which causes the holder 4 supported by this motor 14 to ascend and descend in the direction along the Y-axis thereby to scan the substrate 54 for the ion beam 58. When ion beam 58 irradiation processing for the substrate 54, for example, ion implantation processing is performed, the irradiation angle θ is usually set in a range of 0° to 60°. This irradiation angle θ is an angle made by a perpendicular line 62 to the substrate holding surface 6 and the traveling direction of the ion beam 58. For example, in the ion implantation apparatus, this angle is referred to as an implantation angle. As described above, in the related-art ion beam irradiation apparatus, in case that the irradiation angle θ is set to an angle that is larger than 0°, the substrate 54 supported by the holder 4, in a tilting state in the irradiation direction of the ion beam 58 (that is, direction along the Z-axis), is scanned in the direction along the Y-axis. However, in case that the substrate 54, in the tilting state in the irradiation direction Z of the ion beam 58, is scanned in the direction along the Y-axis, there is a problem that the density of the ion beam 58 applied onto the substrate 54 becomes non-uniform in the surface 56 of the substrate 54. The cause of this problem will be described with reference to FIG. 5. In this figure, for convenience, the irradiation angle setting motor 14, the rotation shaft 46, the coupling member 48 and the elevator unit 50 are omitted. The ion beam 58 that has passed through a beam slit 52 is applied toward the substrate holding surface 6 of the holder 4 arranged in a vacuum chamber (not shown), that is, the surface 56 of the substrate 54. The substrate 54, by the reciprocating movement of a center O1 on the surface 56 of the substrate 54 together with the holder 4 between a position α and a position γ, is scanned for the ion beam 58. In a position β, the center O1 on the surface 56 of the substrate 54 coincides with the path of the ion beam 58 traveling in the direction along the Z-axis. On the other hand, the ion beam 58 is applied in a state where it diverges to some extent in the direction along the Y-axis due to the space-charge effect. Here, the angle at which the ion beam 58 diverges in the direction along the Y-axis is referred to as a divergent angle ξ. In case that the ion beam 58 is thus applied onto the surface 56 of the substrate 54 in the state where it diverges to some extent in the direction along the Y-axis, according to the distance L from an arbitrary point on the path of the ion beam 58 (for example, an exit point of the beam slit 52) to the surface 56 of the substrate 56, the size of the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 is different. Namely, as the distance becomes longer, the size of the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 becomes larger. Specifically, the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 when the center O1 on the surface 56 of the substrate 54 is in the position α is taken as G1, the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 when the center O1 on the surface 56 of the substrate 54 is in the position β is taken as G2, and the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 when the center O1 on the surface 56 of the substrate 54 is in the position γ is taken as G3. In this case, among the area of the region G1, the area of the region G2 and the area of the region G3, the relation of G1<G2<G3 holds. Regarding the density of the ion beam 58 applied onto the surface 56 of the substrate 54, as the area of the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 becomes larger, the density becomes lower; and as the area of the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 becomes smaller, the density becomes higher. Therefore, in case that the substrate 54 is scanned in the direction along the Y-axis in the titling state in the irradiation direction of the ion beam 58, the distance L changes during irradiation processing of the ion beam 58 onto the surface 56 of the substrate 54. Therefore, a phenomenon is produced in which the density of the ion beam 58 applied onto the substrate 54 becomes non-uniform in the surface 56 of the substrate 54. In result, uniformity of ion implantation in the surface 56 of the substrate 54 worsens. Therefore, it is an object of the invention to prevent, even in case that the substrate is scanned in the tiling state in the irradiation direction of the ion beam, the density of the ion beam applied onto the substrate from becoming non-uniform in the surface of the substrate. However, the present invention need not achieve the above objects, and other objects not described herein may also be achieved. Further, the invention may achieve no disclosed objects without affecting the scope of the invention. An ion beam irradiation apparatus according to a first aspect of this invention is so constructed as to scan, when three axes that are orthogonal to each other at one point are taken as an X-axis, a Y-axis and a Z-axis, in the direction along the X-axis, an ion beam traveling in the direction along the Z-axis, and applies the ion beam onto a substrate held by a substrate holding surface of a holder. This ion beam irradiation apparatus includes: an irradiation angle setting motor which holds the holder, and can set an irradiation angle of the ion beam with respect to the substrate holding surface by rotating the holder around a center axis that is substantially parallel to the X-axis; a Y-axis linear motor which supports the irradiation angle setting motor, and causes the holder and the irradiation angle setting motor to ascend and descend in the direction along the Y-axis; a Z-axis linear motor which supports the Y-axis linear motor, and moves the holder, the irradiation angle setting motor and the Y-axis linear motor in the direction along the Z-axis; and a control unit which operation-controls synchronously the Y-axis linear motor and the Z-axis linear motor so that the substrate holding surface of the holder reciprocates and scans linearly along an S-axis that is substantially parallel to the substrate holding surface and substantially orthogonal to the X-axis. An ion beam irradiation apparatus according to a second aspect of the invention is so constructed as to scan, when three axes that are orthogonal to each other at one point are taken as an X-axis, a Y-axis and a Z-axis, in the direction along the X-axis, an ion beam traveling in the direction along the Z-axis, and applies the ion beam onto a substrate held by a substrate holding surface of a holder. This ion beam irradiation apparatus includes: an irradiation angle setting motor which holds the holder, and can set an irradiation angle of the ion beam with respect the substrate holding surface by rotating the holder around a center axis that is substantially parallel to the X-axis; a Z-axis linear motor which supports the irradiation angle setting motor, and moves the holder and the irradiation angle setting motor in the direction along the Z-axis; a Y-axis linear motor which supports the Z-axis linear motor, and causes the holder, the irradiation angle setting motor and the Z-axis linear motor to ascend and descend in the direction along the Y-axis; and a control unit which operation-controls synchronously the Z-axis linear motor and the Y-axis linear motor so that the substrate holding surface of the holder reciprocates and scans linearly along an S-axis that is substantially parallel to the substrate holding surface and substantially orthogonal to the X-axis. An ion beam irradiation apparatus according to a third aspect of the invention is so constructed as to apply, when three axes that are orthogonal to each other at one point are taken as an X-axis, a Y-axis and a Z-axis, an ion beam that is long in the shape of a strip in the direction along the X-axis direction and travels in the direction along the Z-axis, onto a substrate held by a substrate holding surface of a holder. This ion beam irradiation apparatus includes: an irradiation angle setting motor which holds the holder, and can set an irradiation angle of the ion beam with respect to the substrate holding surface by rotating the holder around a center axis that is substantially parallel to the X-axis; a Y-axis linear motor which supports the irradiation angle setting motor, and causes the holder and the irradiation angle setting motor to ascend and descend in the direction along the Y-axis; a Z-axis linear motor which supports the Y-axis linear motor, and moves the holder, the irradiation angle setting motor and the Y-axis linear motor in the direction along the Z-axis; and a control unit which operation-controls synchronously the Y-axis linear motor and the Z-axis linear motor so that the substrate holding surface of the holder reciprocates and scans linearly along an S-axis that is substantially parallel to the substrate holding surface and substantially orthogonal to the X-axis. An ion beam irradiation apparatus according to a fourth aspect of the invention is so constructed as to apply, when three axes that are orthogonal to each other at one point are taken as an X-axis, a Y-axis and a Z-axis, an ion beam that is linearly long in the shape of a strip in the direction along the X-axis direction and travels in the direction along the Z-axis, onto a substrate held by a substrate holding surface of a holder. This ion beam irradiation apparatus includes: an irradiation angle setting motor which holds the holder, and can set an irradiation angle of the ion beam with respect to the substrate holding surface by rotating the holder around a center axis that is substantially parallel to the X-axis; a Z-axis linear motor which supports the irradiation angle setting motor, and moves the holder and the irradiation angle setting motor in the direction along the Z-axis; a Y-axis linear motor which supports the Z-axis linear motor, and causes the holder, the irradiation angle setting motor and the Z-axis linear motor to ascend and descend in the direction along the Y-axis; and a control unit which operation-controls synchronously the Z-axis linear motor and the Y-axis linear motor so that the substrate holding surface of the holder reciprocates and scans linearly along an S-axis that is substantially parallel to the substrate holding surface and substantially orthogonal to the X-axis. According to these ion beam irradiation apparatuses, the holder is linearly reciprocated and scanned so that the substrate holding surface of the holder is along the S-axis. Therefore, during irradiation processing of the ion beam onto the substrate held by the holder, while the distance from an arbitrary point on the path of the ion beam to the substrate holding surface of the holder, that is, to the surface of the substrate is kept substantially constant, the substrate held by the holder can be scanned in a tiling state in the irradiation direction of the ion beam. It is preferable that the control unit operation-controls synchronously the Y-axis linear motor and the Z-axis linear motor so that: when the control unit causes the Y-axis linear motor to ascend along the Y-axis by the distance Δy, the relation of Δz=Δy tan θ is satisfied or the relation mathematically equivalent to this relation is satisfied; and when the control unit causes the Y-axis linear motor to descend along the Y-axis by the distance Δy, the relation of −Δz=Δy tan θ is satisfied or the relation mathematically equivalent to this relation is satisfied, in which θ represents an irradiation angle of the ion beam applied to the substrate, and Δz represents distance by which the linear motor is moved along the Z-axis (The direction in which the ion beam travels is taken as a positive direction.). According to the invention, while the distance from the arbitrary point on the path of the ion beam to the surface of the substrate is kept substantially constant, the substrate held by the holder can be scanned in the tiling state in the irradiation direction of the ion beam. Therefore, the area of the irradiation region of the ion beam applied onto the substrate becomes always substantially constant. Thus, it is possible to prevent the density of the ion beam applied onto the substrate from becoming non-uniform in the surface of the substrate. In result, uniformity of ion implantation in the surface of the substrate improves. FIG. 1 is a schematically plan view showing one exemplary, non-limiting example of an ion beam irradiation apparatus according to this invention, and FIG. 2 is a schematically side view of the ion beam irradiation apparatus shown in FIG. 1. The same or corresponding parts as or to those in the related art shown in FIGS. 4 and 5 are denoted by the same reference numerals, and the different points from the related art will be mainly described below. In this ion beam irradiation apparatus, an arm 8 for supporting a holder 4 is supported by a disc-shaped turn table 12. At this time, a center O2 of the turn table 12 is on an imaginary center axis 60 that passes through a center O1 of a substrate holding surface 6 of the holder 4 and is substantially parallel to an X-axis (refer to FIG. 1). The shown substrate 54, though it has the same thickness as thickness of the holder 4 for convenience, is very thin actually. Therefore, it can be said that the center axis 60 substantially passes through a surface 56 of the substrate 54. This turn table 12 turns around the center axis 60. Further, in this ion beam irradiation apparatus, an orientation flat angle control motor 10, which is not an essential component, is incorporated in the arm 8. Hereby, step implantation in which an orientation flat angle is changed every time the holder 4, that is, the substrate 54 is scanned once with respect to an irradiation direction Z of the ion beam 58 thereby to perform ion implantation can be executed. Here, the “orientation flat angle” indicates an angle with respect to the predetermined direction, which is made by an orientation flat (that is, a notch (not shown)) formed in the substrate 54. Further, this ion beam irradiation apparatus includes, in place of the related-art counter-rotatable type of irradiation angle setting motor 14 and the elevator unit 50 (refer to FIG. 4), includes a counter-movable type of irradiation angle setting motor 14a and a counter-movable type of Y-axis linear motor 20. The irradiation angle setting motor 14a includes an irradiation angle setting mover 16 which is coupled to the turntable 12, and an irradiation angle setting stator 18 which is opposed to this irradiation angle setting mover 16 and fixed to a Y-axis mover 28. The irradiation angle setting mover 16 is provided for a part of the peripheral portion of the turn table 12, and formed in the shape of a fan along the peripheral surface of the turn table 12, viewed in the direction of the X-axis (refer to FIG. 2). When the irradiation angle setting motor 14a rotates the turn table 12 around the center axis 60, the holder 4 supported through the arm 8 by the turn table 12 is rotated around the center axis 60. Thus, the irradiation angle θ (refer to FIG. 2) of the ion beam 58 with respect to the substrate holding surface 6 of the holder 4, that is, the surface 56 of the substrate 54 can be set. The irradiation angle θ shown in FIG. 2 is an angle with respect to the surface 56 of the substrate 54 which is shown by a chain double-dashed line. The Y-axis linear motor 20 includes a Y-axis stator 22 and a Y-axis mover 28 opposed to this Y-axis stator 22. The Y-axis stator 22 includes a fixing plate 24 that is long in the direction along the Y-axis, and a guide rail 26 that is fixed to this fixing plate 24 and long in the direction along the Y-axis. The Y-axis mover 28 supports the irradiation angle setting motor 14a, and ascends and descends linearly along the guide rail 26. Therefore, when the Y-axis mover 28 ascends and descends in the direction along the Y-axis, the holder 4 and the irradiation angle setting motor 14a ascend and descend linearly with the movement of the mover 28 in the direction along the Y-axis. Further, this ion beam irradiation apparatus includes a counter-movable type of Z-axis linear motor 30. This Z-axis linear motor 30 includes a Z-axis stator 32, and a Z-axis mover 38 (refer to FIG. 1) opposed to this Z-axis stator 32. However, the Y-axis stator 22 and the Z-axis mover 38, and more particularly the fixing plate 24 and the Z-axis mover 38 may be formed as one member to hold these functions simultaneously. The Z-axis stator 32 includes a fixing plate 34 that is long in the direction along the Z-axis, and a guide rail 36 that is fixed to this fixing plate 34 and long in the direction along the Z-axis. In this embodiment, though the fixing plate 34 is fixed to a vacuum chamber 2 and supported as shown in FIG. 1, for example, a table for fixing the fixing plate 34 may be set in the vacuum chamber 2. The Z-axis mover 38 (refer to FIG. 1) supports the Y-axis linear motor 20, and more particularly the fixing plate 24, and moves linearly along the guide rail 36 in the direction along the Z-axis. Therefore, when the Z-axis mover 38 (refer to FIG. 1) moves in the direction along the Z-axis, the holder 4, the irradiation angle setting motor 14a and the Y-axis linear motor 20 move linearly with this movement in the direction along the Z-axis. The irradiation angle setting motor 14a, the Y-axis linear motor 20 and the Z-axis linear motor 30 are arranged in the vacuum chamber 2 that is kept in a vacuum state. As shown in FIG. 2, on the outside of the vacuum chamber 2, a control unit 40 is provided. This control unit 40 controls the irradiation angle setting motor 14a through a field through 64 penetrating a wall surface of the vacuum chamber 2, and is electrically connected to the Y-axis linear motor 20 and the Z-axis linear motor 30 through field throughs 64so as to operation-control synchronously these motors. The control unit 40, when the irradiation angle θ is set or input, causes the irradiation angle setting motor 14a to turn the turn table 12 so that the irradiation angle of the ion beam 58 with respect to the substrate holding surface 6 of the holder 4 becomes θ. Thereafter, the ion beam 58 is applied to the substrate 54 held by the holder 4. Hereby, the substrate 54 receives the ion implantation processing. Next, the operations of the Y-axis linear motor 20 and the Z-axis linear motor 30 controlled by the control unit 40 will be described with reference to FIG. 3. When the distance by which the Y-axis liner motor 20 is caused to ascend in the direction along the Y-axis is taken as Δy, and the distance by which the Z-axis linear motor 30 is moved in the direction along the Z-axis is taken as Δz, the control unit 40 (refer to FIG. 2) operation-controls synchronously the Y-axis linear motor 20 and the Z-axis linear motor 30 so that the relation expression of Expression 1 is satisfied or the relation mathematically equivalent to this relation expression is satisfied.Δz=Δy tan θ [Expression 1] On the other hand, when the distance by which the Y-axis liner motor 20 is caused to descend in the direction along the Y-axis is taken as Δy, and the distance by which the Z-axis linear motor 30 is moved in the direction along the Z-axis is taken as Δz, the control unit 40 (refer to FIG. 2) operation-controls synchronously the Y-axis linear motor 20 and the Z-axis linear motor 30 so that the relation expression of Expression 2 is satisfied or the relation mathematically equivalent to this relation expression is satisfied.−Δz=Δy tan θ [Expression 2] The direction in which the ion beam 58 travels is taken as a positive direction of the Z-axis, and the opposite direction to that direction is taken as a negative direction of the Z-axis. Further, the “distance by which the Y-axis linear motor 20 is caused to ascend in the direction along the Y-axis”, and the “distance by which the Z-axis linear motor 30 is moved in the direction along the Z-axis” are specifically “distance by which the Y-axis mover 28 is caused to ascend in relation to the Y-axis stator 22 in the direction along the Y-axis”, and “distance by which the Z-axis mover 38 (refer to FIG. 1) is moved in relation to the Z-axis stator 32 in the direction along the Z-axis”, respectively. When the control unit 40 (refer to FIG. 2) operation-controls synchronously the Y-axis linear motor 20 and the Z-axis linear motor 30 (namely, when the control unit 40 operates the both motors 20 and 30 substantially simultaneously, the holder 4 reciprocates and scans linearly so that the substrate holding surface 6 of the holder 4is along an S-axis. The “S-axis” is a direction that is substantially parallel to the substrate holding surface 6 of the holder 4 and substantially orthogonal to the X-axis. Further, “substantially orthogonal” includes an orthogonal state. Therefore, even if the holder 4, that is, the substrate 54 is scanned in a tiling state in the irradiation direction Z of the ion beam 58, the distance L from an arbitrary point (for example, an exit point of the beam slit 52) on the path of the ion beam 58 to the surface 56 of the substrate 54 becomes substantially constant. In result, the area of the irradiation region of the ion beam 58 applied onto the surface 56 of the substrate 54 becomes always substantially constant. Therefore, it is possible to prevent the density of the ion beam 58 applied onto the surface 56 of the substrate 54 from becoming non-uniform. Thus, uniformity of the ion implantation in the surface 56 of the substrate 54 improves. Further, since the holder 4 can be moved in the direction along the Y-axis and in the direction along the Z-axis, and can be turned around the center axis 60, the degree of freedom in transport of the substrate 54 improves. Namely, the substrate 54 can be moved to the position where the substrate 54 is easy to be transported. Further, it is also thought that using a ball screw, the holder 4 and the substrate 54 are scanned in the tilting state in the irradiation direction Z of the ion beam 58. However, as the case in this embodiment, the use of the Y-axis linear motor 20 and the Z-axis linear motor 30 can simplify the structure more while keeping the accuracy. Further, this case can prevent occurrence of particles (contaminants) from the screw portion. Further, since both the center O1 of the substrate holding surface 6 of the holder 4 and the center O2 of the turn table 12 are on the center axis 60, by only turning the turn table 12 around the center axis 60, the irradiation angle θ can be set. Namely, it is not necessary to operate the Y-axis linear motor 20 or the Z-axis linear motor 30. Therefore, the control becomes easy, the structure can be simplified and the cost can be reduced. However, even in case that the center O2 of the turn table 12 is shifted from the center axis 60, the object of the invention can be achieved. Namely, in case that the center O2 of the turn table 12 is shifted from the center axis 60, when the turn table 12 is turned, though the position of the holder 4 in the directions along the Y-axis and the Z-axis changes, this position change can be corrected by the Y-axis linear motor 20 and the Z-axis linear motor 30. In the embodiment, the irradiation angle setting motor 14a is supported by the Y-axis linear motor, and this Y-axis linear motor is supported by the Z-axis linear motor. However, the invention is not limited to this. For example, the Y-axis linear motor 20 and the Z-axis linear motor 30 may be replaced. Namely, the irradiation angle setting motor 14a may be supported by the Z-axis linear motor 30, and this Z-axis linear motor 30 may be supported by the Y-axis linear motor 20. In this case, the Z-axis linear motor 30 moves the holder 4 and the irradiation angle setting motor 14a in the direction along the Z-axis. The Y-axis linear motor 20 is fixed to the vacuum chamber 2, and causes the holder 4, the irradiation angle setting motor 14a and the Z-axis linear motor 30 to ascend and descend in the direction along the Z-axis. It will be apparent to those skilled in the art that various modifications and variations can be made to the described preferred embodiments of the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention cover all modifications and variations of this invention consistent with the scope of the appended claims and their equivalents.

042785006

claims

1. A pressurized water reactor comprising: a primary fluid circuit, at least one circulating pump for circulating primary fluid within at least one primary loop of said primary circuit, said primary circuit including a steam generator, a pressure vessel which contains a reactor core, and a bundle of tubes in said steam generator, a secondary fluid circuit containing fluid which enters the steam generator in a liquid state and is discharged therefrom in the form of steam which is returned into the generator after expansion within main turbines and recovery in a condenser, said primary circuit including a driving turbine supplied with steam taken from the steam generator, and fluid circulating pumps each driven by said driving turbine, a feed tank of a water supply unit, an auxiliary turbine, a storage tank and a pump drivingly connected to said auxiliary turbine, each main turbine having an outlet connected to said feed tank by means of conduit means provided with isolating valves and by means of bypass conduit means, for permitting a flow of steam for driving said auxiliary turbine in the event of closure of said isolating valves, and means for injecting high-pressure emergency water into said primary circuit from said storage tank by means of said pump. 2. A pressurized water reactor according to claim 1, comprising at least two injectors, means for passing water under pressure in said feed tank in the event of failure of the primary circuit into said injectors to perform the function of a driving fluid within said injectors, driven fluid within one injector being water derived from a storage tank of a low-pressure safety injection circuit, and driven fluid within the second injector being secondary water derived from a storage tank and fed into an emergency feed circuit of one of the steam generators. 3. A pressurized water reactor according to claim 1, comprising at least two injectors, means for passing water under pressure in said feed tank in the event of failure of the primary circuit into said injectors to perform the function of a driving fluid within said injectors, driven fluid within one injector being primary water in a sump to be recycled to the reactor core, and driven fluid within the second injector being secondary water derived from a storage tank and fed into an emergency feed circuit of one of the steam generators. 4. A pressurized water reactor according to claim 1, wherein the turbine for driving the primary fluid circulating pump is of the back-pressure type and comprises a regulating valve having at least two positions such that a first of said positions permits a minimum flow of steam while a second position permits a normal flow, means being provided for automatically returning the regulating valve to the first position when in the second position in the event of overstepping of a predetermined threshold.

description

Embodiment 1 As described above, the void coefficient is influenced mainly by the water rod area, and by number and length and further by positions of the short length fuel rods. However, in the conventional example described above, effect of the void coefficient on the core stability depending on number and length of the short length fuel rods has not be quantitatively evaluated. From the viewpoint of backfitting a newly designed fuel assembly to an existing nuclear core, it is necessary to keep the core stability in nearly the same level compared to the case of using conventional fuel assemblies. Therefore, when the void coefficient described above is insufficiently evaluated, it can not be said that evaluation of the core stability (area of water rods, number and length of the short length fuel rods) attainable high burn-up is sufficient. Further, the effect on the pressure loss of assembly important for backfitting, that is, the effect of area of water rods and the effects of number and length of short length fuel rods on the pressure loss are not considered. A preferred embodiment of a fuel assembly in accordance with the present invention will be described below, referring to FIG. 1 and FIG. 2. The fuel assembly 1 is loaded in a reactor core of a boiling water reactor. In the fuel assembly 1, fuel rods 2 are arranged in a square array of 10 rows by 10 columns. The fuel rods 2 include fuel rods 2A having a long axial length and short length fuel rods 2B having an axial length shorter than that of the fuel rod 2A. In the center of the horizontal section of the fuel assembly 1, two water rods 3 are arranged. Each of the water rods 3 has a circular horizontal cross section the area of which occupies a region capable of arranging the four fuel rods. The two water rods 3 are arranged so that a center axis of each of the water rods is positioned on one diagonal line of the fuel assembly 1. These water rods 3 are arranged in a region of the fourth tier from the outer side of the fuel rod array, and arranged in the symmetrical positions with respect to the other diagonal line (the diagonal line which passes through a corner portion 8 facing a control rod when the fuel assembly 1 is loaded into the core of the boiling water reactor). The upper end portions of the fuel rods 2A and the water rods 3 are held by an upper tie plate 4 and the lower end portions are held by a lower tie plate 5. The lower end portions of the short length fuel rods 2B are held by the lower tie plate 5. The fuel rods 2A, 2B and the water rods 3 are held with a spacing one another by fuel spacers 6. These fuel rods are contained in a channel box 7 attached to the upper tie plate 4. Twelve rods among the sixteen short length fuel rods 2B are arranged in the second tier from the outer side of the fuel rod array. In the second tier of the fuel rod array, the twelve short length fuel rods 2B are arranged at positions in each of the corners and in two rods away from each of the corners. The remainder of the four short length fuel rods 2B are arranged adjacent to the water rods 3. In the present embodiment, the inner width Dcb of the channel box 7 is approximately 134 mm, the outer diameter Df of the fuel rods 2A and 2B is 10.26 mm, the fuel rod pitch Pf is 12.95 mm, and the effective fuel length Lf of the fuel rod 2A is approximately 3.7 m. In the present embodiment, the short length fuel rods 2B are not arranged in the outermost tier of the fuel rod array. The present embodiment of the fuel assembly 1 is constructed so that the effective fuel length Lp of the short length fuel rod 1B and the total horizontal sectional area Awr of the water rods 2 satisfy the conditions of Equation 1 to Equation 6. The conditions of Equation 1 to Equation 6 are found from a study performed by the inventors of the present invention. The results of the study will be described in detail below. Firstly, Equation 6 determined from the pressure loss of the fuel assembly will be described. The inventors of the present invention calculated a total horizontal sectional area of water rods 3 in the 10-by-10 fuel assembly having a pressure loss equal to that of a conventional 9-by-9 fuel assembly disclosed in Japanese Patent Application Laid-Open No.7-234293 (hereinafter, simply referred to as the conventional fuel assembly) by varying number of the short length fuel rods and effective fuel length of the short length fuel rod as parameters, and found the relationships between the number of the short length fuel rods, the effective fuel length Lp of the short length fuel rod and the total horizontal sectional area of all the water rods. The relationships are shown in FIG. 3. In FIG. 3, the abscissa indicates a ratio (Lp/Lf) of the effective fuel length Lp of the short length fuel rod 2B to the effective fuel length Lf of the fuel rod 2A, and the ordinate indicates a ratio (Awr/Ach) of the total horizontal sectional area Awr of all the water rods in the fuel assembly to the area Ach of the coolant flow passage of the fuel assembly in the lower portion of the fuel assembly. Therein, the coolant channel area Ach can be roughly expressed by the following equation. The coolant flow passage of the fuel assembly is a region inside the channel box 7 and outside the fuel rods 2 and the water rods 3. Ach=Dcb2xe2x88x92xcfx80/4xc3x97Df2xc3x97(100xe2x88x928)xe2x88x92Awrxe2x80x83xe2x80x83(Equation 20) By substituting the numerical values corresponding to the present embodiment described above into Equation 20, the following equation can be obtained. Ach=10350xe2x88x92Awr(mm2)xe2x80x83xe2x80x83(Equation 21) The diagram means that when a value of the abscissa is 0.5, the effective fuel length of the short length fuel rod 2B is approximately 1.85 m (3.7 mxc3x970.5). Referring to FIG. 3, the reference characters L1, L2, L3 are boundary lines depending on number of the short length fuel rods 2B. The boundary line L1 indicates a case where number of the short length fuel rods 2B is 12, the boundary line L2 indicates a case where number of the short length fuel rods 2B is 16, and the boundary line L3 indicates a case where number of the short length fuel rods 2B is 20. In the case where number of the short length fuel rods 2B is 16, the boundary line L2 in the diagram is a boundary satisfying the condition that the pressure loss is equal to the pressure loss of the conventional fuel assembly. In the case where number of the short length fuel rods 2B is 16, on the boundary line L2 and the zone below the boundary line L2 are a zone where the pressure loss is not larger than the pressure loss of the conventional fuel assembly. Therefore, by constructing the fuel assembly so that the total horizontal sectional area of all the water rods falls in the zone below the boundary line L2 including on the boundary line L2, The pressure loss of the present embodiment of the fuel assembly can be equal to and smaller than that of the conventional fuel assembly. That is, the value Awr/Ach should satisfy Equation 6. Each of the boundary lines depending on number of the short length fuel rods 2B in the fuel assembly is expressed by Equation 6 including number n of the short length fuel rods as the parameter. In addition, the dotted line K in FIG. 3 indicates the maximum value of the total horizontal sectional area of all the water rods occupying a region for 8 rods of the fuel rods, and can be expressed by the following equation. xe2x80x83Awr=Pf2xc3x978xe2x80x83xe2x80x83(Equation 22) Therefore, the value Awr/Ach to the upper limit value of the total horizontal sectional area of all the water rods becomes as follows. Awr/Ach=1342/(10350xe2x88x921342)=0.149xe2x80x83xe2x80x83(Equation 23) Therefore, the value Awr/Ach must be smaller than 0.149, that is, Equation 3. Further, the value corresponding to the abscissa of the dotted line J corresponds to a length that the effective fuel length of the short length fuel rod 2B becomes 11/24 (=0.458) of the effective fuel length of the fuel rod 2A. In this length, the upper end portion of the short length fuel rods including a length of the gas plenum (formed in the fuel rod) are supported by one of the fuel spacers placed in the nearly middle portion in the axial direction of the fuel assembly. However, if the effective fuel length of the short length fuel rod 2B is further shortened, it is necessary from the viewpoint of flow-induced vibration of the short length fuel rod that the effective fuel length of the short length fuel rod is formed about 8/24 of the effective fuel length of the fuel rod 2A. When the effective fuel length of the short length fuel rod 2B is made shorter than 11/24 as described above, the uranium inventory becomes too small to deteriorate the fuel cycle cost. Therefore, the value Lp/Lf must be larger than 11/24 (Equation 4). Next, Equation 5 determined from the core stability will be described below. The core stability is a characteristic relating to fluctuation of the core flow rate and the reactor output power of the whole core after a disturbance is added to the reactor core. Here, it is assumed that a disturbance of sinusoidal core flow rate is added to the reactor core. Further, it is also assumed that the fluctuation of the core flow rate in the reactor core after adding the disturbance is as shown in FIG. 4. In the fluctuation of FIG. 4, the amplitude of the fluctuation is decreased with time and the core flow rate returns to a stable state in a short time. Therein, letting an amplitude of the disturbance added to the reactor core be y0, and an amplitude one cycle after that time be y1, the amplitude damping ratio is defined as the value y1/y0. In the case of FIG. 4, the amplitude damping ratio is smaller than 1, and the reactor core is returned to a stable state (a normal state). In such a case, it is said that the reactor core is stable. On the other hand, in the case of FIG. 5, the amplitude damping ratio is larger than 1, and the fluctuation of the core flow rate in the reactor core is increased as the time elapses. This is not preferable state from the viewpoint of reactor operation. Therefore, the core stability can be evaluated as stable when the amplitude damping ratio is smaller than 1, and as unstable when the amplitude damping ratio is larger than 1. Therefore, although the core stability can be evaluated as stable when the amplitude damping ratio is smaller than 1, design is practically performed by setting the amplitude damping ratio to 0.8 for taking a margin. The inventors of the present invention calculated a horizontal sectional area of water rods in the 10-by-10 fuel assembly satisfying the amplitude damping ratio of 0.8 by varying number of the short length fuel rods and effective fuel length of the short length fuel rod as parameters, and found the relationships between the number of the short length fuel rods, the effective fuel length of the short length fuel rod and the horizontal sectional area of the water rods. Further, in order attain a high burn-up higher than the average unloading burn-up 45 Gwd/t of the conventional 9-by-9 fuel assembly, the average unloading burn-up was set to 60 GWd/t. FIG. 6 shows the analysis results. The ordinate and the abscissa of FIG. 6 are the same as those of FIG. 3. Similarly to the analysis results of the pressure loss, the boundary line is drawn for each number of the short length fuel rods. The boundary line M1 is the result for the case where number of the short length fuel rods is 12, the boundary line M2 is the result for the case where number of the short length fuel rods is 16, and the boundary line M3 is the result for the case where number of the short length fuel rods is 20. In the case of 16 rods of the short length fuel rods, the boundary line M2 is the boundary satisfying the amplitude damping ratio of 0.8, and the zone on the boundary line M2 and above the boundary line M2 is the zone where the amplitude damping ratio is below 0.8. Therefore, when the fuel assembly is constructed so that the total horizontal sectional area of all the water rods falls in the zone above the solid line M2 including on the solid line M2, the average unloading burn-up of 60 GWd/t can be attained, and the allowable core stability can be maintained. That is, Awr/Ach should satisfy Equation 5. Each of the boundary lines depending on number of the short length fuel rods 2B in the fuel assembly is expressed by Equation 5 including number n of the short length fuel rods as the parameter. The boundary lines for the pressure loss shown in FIG. 3, the boundary lines for the core stability shown in FIG. 6 and the boundary lines J and K are shown in FIG. 7. In the case of 12 rods of the short length fuel rods, the boundary line M1 expressing the minimum required total horizontal sectional area of all the water rods determined from the core stability is positioned above the dotted line K. Accordingly, the case of 12 rods of the short length fuel rods requires a total horizontal sectional area of all the water rods larger than the maximum total horizontal sectional area of all the water rods in the region occupied by eight fuel rods in the present embodiment. Therefore, in the case of 12 rods of the short length fuel rods, the core stability can not be satisfied under the condition of average unloading burn-up of 60 GWd/t. As described above, in the case where the water rods are arranged in the region capable of being occupied by 8 fuel rods and the short length fuel rods are arranged in the fuel rod array except the outermost tier, required number of the short length fuel rods is larger than 15 rods. On the other hand, when number of the short length fuel rods is increased above 21, the void coefficient is improved, but the uranium inventory is excessively reduced. In addition, it is not preferable from the viewpoint of the mechanical strength of the fuel spacers for holding the fuel rods with a spacing between one another which are positioned above the upper end of the short length fuel rod. Therefore, number of the short length fuel rods should be smaller than 20. Thus, the number n of the short length fuel rods should satisfy the condition of 15xe2x89xa6nxe2x89xa620, that is, Equation 2. In FIG. 7, the hatched zone is a zone where Equation 1, Equation 3 to Equation 6 are satisfied to the 10-by-10 fuel assembly of the present embodiment having 16 rods of the short length fuel rods. The ratio Lp/Lf and the horizontal sectional area of the water rods 3 are set so as to fall into this zone. However, even in a case of 15xe2x89xa6nxe2x89xa620, there is a zone where Equation 1, Equation 3 to Equation 6 are satisfied. According to the present embodiment, the average unloading burn-up of 60 GWd/t can be attained, and the allowable core stability can be attained without increasing the pressure loss compared to that of the conventional fuel assembly. Further, the fuel assemblies of the present embodiment can be applied to the existing boiling water reactor. In Japanese Patent Application Laid-Open No.5-232273 there is no description that the burn-up above 60 GWd/t is attained using the fuel assembly having a fuel rod array of 10 rows by 10 columns. The fuel assembly of the present embodiment can attain the burn-up above 60 GWd/t by 10 columns by satisfying the conditions of Equation 1 to Equation 6, and in the fuel assembly having the fuel rod array of 10 rows, the allowable core stability can be attained without increasing the pressure loss larger than that of the conventional fuel assembly. In the present embodiment, the same effects can be obtained even in a case where the short length fuel rods are arranged in different positions from those of FIG. 1 unless the short length fuel rods are arranged in the outermost tier. Further, the same effects can be obtained the water rod is changed to a rectangular water rod 3A as shown in FIG. 8 or to a water rod having another shape if the total horizontal sectional area is the same. Since Equation 20 includes the channel box inner width Dcb and the fuel rod outer diameter Df, the present embodiment can also cope with small changes in the channel box inner width and the fuel rod outer diameter. Embodiment 2 A second embodiment of a fuel assembly in accordance with the present invention will be described below, referring to FIG. 9. The present embodiment of the fuel assembly 1C is loaded in a reactor core of a boiling water reactor. In the fuel assembly 1C, the two water rods 3 of the fuel assembly 1 shown in FIG. 1 are replaced with one water rod 3C. The other structure of the present embodiment is the same as that of the fuel assembly shown in FIG. 1. The water rod 3C has a circular horizontal section, and occupies a region capable of arranging 9 fuel rods. The center axis of the water rod 3C is arranged at a position dislocated from a center axis of the fuel assembly toward a side opposite to a corner portion 8 facing a control rod under a condition that the fuel assembly 1C is loaded in the core of the boiling water reactor. Consequently, there exist four tiers of the fuel rod array in the side of the corner portion 8 between the water rod 3C and the channel box 7. On the other hand, there exist three tiers of the fuel rod array in the opposite side of the corner portion 8 between the water rod 3C and the channel box 7. In the second tier from the outer side of the fuel rod array, the twelve short length fuel rods 2B are arranged at positions in each of the corners and in two rods away from each of the corners. The dimensions of the inner width Dcb of the channel box 7, the outer diameter Df of the fuel rod 2, the fuel rod pitch Pf and the effective fuel length Lf of the fuel rod 2A are the same as those of the fuel assembly 1. In the present embodiment, the short length fuel rods 2B are not arranged in the outermost tier of the fuel rod array either. The present embodiment of the fuel assembly 1C is constructed so that the effective fuel length Lp of the short length fuel rod 1B and the total horizontal sectional area Awr of the water rod 3C satisfy the conditions of Equation 1, Equation 4, and Equation 7 to Equation 10. The conditions of Equation 7 to Equation 10 are found from a study performed by the inventors of the present invention. An example of a boundary line derived from individual analyses of the pressure loss and the core stability in the present embodiment of the fuel assembly 1C similarly to Embodiment 1 is shown in FIG. 10. The boundary line L4 shown in FIG. 10 is a boundary line for the pressure loss when 12 rods of the short length fuel rods 2B are arranged in the fuel rod array of the fuel assembly 1C except the outermost tier. Similarly, the boundary line M4 is a boundary line for the core stability when 12 rods of the short length fuel rods 2B are arranged. Therein, the coolant channel area Ach in the fuel assembly 1C can be roughly expressed by the following equation. Ach=Dcb2xe2x88x92xcfx80/4xc3x97Df2xc3x97(100xe2x88x929)xe2x88x92Awrxe2x80x83xe2x80x83(Equation 24) By substituting the numerical values corresponding to the present embodiment described above into Equation 24, the following equation can be obtained. xe2x80x83Ach=10432xe2x88x92Awr(mm2)xe2x80x83xe2x80x83(Equation 25) In addition, the dotted line K1 in FIG. 10 indicates the maximum value of the total horizontal sectional area of all the water rods occupying a region for 9 rods of the fuel rods, and can be expressed by the following equation. Awr=Pf2xc3x979xe2x80x83xe2x80x83(Equation 26) Therefore, the value Awr/Ach to the upper limit value of the total horizontal sectional area of all the water rods becomes as follows. Awr/Ach=1509/(10432xe2x88x921509)=0.169xe2x80x83xe2x80x83(Equation 27) Therefore, the value Awr/Ach must be smaller than 0.169, that is, Equation 8. Further, in this embodiment, the required number of the short length fuel rods 2B is within a range of 10 to 20 which is obtained from a study similar to that of Embodiment 1. In FIG. 10, Equation 8 corresponds to the zone lower than the dotted line K1 including the dotted line K1, and Equation 4 corresponds to the zone in right hand side from the dotted line J including the dotted line J. In FIG. 10, the hatched zone is a zone where Equation 1, Equation 4, and Equation 8 to Equation 10 are satisfied to the fuel assembly having 12 rods of the short length fuel rods 2B arranged as shown in FIG. 9. The ratio Lp/Lf and the horizontal sectional area of the water rod 3 are set so as to fall into this zone. However, even in a case of satisfying Equation 7, that is, 10xe2x89xa6nxe2x89xa620, there is a zone where Equation 1, Equation 4, and Equation 8 to Equation 10 are satisfied. According to the present embodiment, the same effects similar to those of Embodiment 1 can be obtained. The short length fuel rods may be arranged in different positions from those of FIG. 9 unless the short length fuel rods are arranged in the outermost tier, and further, the fuel assembly 1D shown in FIG. 11 may be used. The fuel assembly 1D is a fuel assembly that in the fuel assembly 1C, the water rod 3C is replaced with a water rod 3D having a rectangular horizontal cross section. Embodiment 3 A third embodiment of a fuel assembly in accordance with the present invention will be described below, referring to FIG. 12. The present embodiment of the fuel assembly 1E is loaded in a reactor core of a boiling water reactor. In the fuel assembly 1E, the two water rods 3 of the fuel assembly 1 (FIG. 1) are replaced with three water rods 3E. The three water rods 3E are positioned on one diagonal line intersecting at right angle with the other diagonal line passing through the corner portion 8 of the fuel assembly 1E facing a control rod, and are adjacent to each other. One middle rod among the water rods 3E is also placed on the diagonal line passing through the corner position 8. That is, this one middle rod among the water rods 3E is placed at the axis of the fuel assembly 1E. The three water rods 3E occupy a region capable of arranging 10 rods of the fuel rods 2. The outer diameter of the water rods 3E is smaller than the outer diameter of the water rod 3 (FIG. 1). 10 rods of the short length fuel rods 2B are arranged. 8 rods among the 10 short length fuel rods 2B are arranged in the second tier in the fuel rod array. Each of the remaining 2 short length fuel rods 2B is placed at the corner in the fourth tier of the fuel rod array. In the second tier of the fuel rod array, the short length fuel rod 2B is placed at each of the corners. The dimensions of the inner width Dcb of the channel box 7, the outer diameter Df of the fuel rod 2, the fuel rod pitch Pf and the effective fuel length Lf of the fuel rod 2A in the present embodiment are the same as those of the fuel assembly 1. In the present embodiment, the short length fuel rods 2B are not arranged in the outermost tier of the fuel rod array either. The fuel assembly 1E is constructed so that the effective fuel length Lp of the short length fuel rod 2B and the total horizontal sectional area Awr of the water rod 3E satisfy the conditions of Equation 1, Equation 4, and Equation 11 to Equation 14. The conditions of Equation 11 to Equation 14 are found from a study performed by the inventors of the present invention. An example of a boundary line derived from individual analyses of the pressure loss and the core stability in the present embodiment of the fuel assembly 1E similarly to Embodiment 1 is shown in FIG. 13. The boundary line L5 shown in FIG. 13 is a boundary line for the pressure loss when 10 rods of the short length fuel rods 2B are arranged in the fuel rod array of the fuel assembly 1E except the outermost tier. Similarly, the boundary line M5 is a boundary line for the core stability when 10 rods of the short length fuel rods 2B are arranged. Therein, the coolant channel area Ach in the fuel assembly 1E can be roughly expressed by the following equation. Ach=Dcb2xe2x88x92xcfx80/4xc3x97Df2xc3x97(100xe2x88x9210)xe2x88x92Awrxe2x80x83xe2x80x83(Equation 28) By substituting the numerical values corresponding to the present embodiment described above into Equation 27, the following equation can be obtained. Ach=10515xe2x88x92Awr(mm2)xe2x80x83xe2x80x83(Equation 29) In addition, the dotted line K2 in FIG. 13 indicates the maximum value of the total horizontal sectional area of all the water rods occupying a region for 10 rods of the fuel rods, and can be expressed by the following equation. Awr=Pf2xc3x9710xe2x80x83xe2x80x83(Equation 30) Therefore, the value Awr/Ach to the upper limit value of the total horizontal sectional area of all the water rods becomes as follows. Awr/Ach=1677/(10515xe2x88x921677)=0.190xe2x80x83xe2x80x83(Equation 31) Therefore, the value Awr/Ach must be smaller than 0.190, that is, Equation 12. Further, in this embodiment, the required number of the short length fuel rods 2B is within a range of 9 to 20 which is obtained from a study similar to that of Embodiment 1. In FIG. 13, Equation 12 corresponds to the zone lower than the dotted line K2 including the dotted line K1, and Equation 4 corresponds to the zone in right hand side from the dotted line J including the dotted line J. In FIG. 13, the hatched zone is a zone where Equation 1, Equation 4, and Equation 12 to Equation 14 are satisfied to the fuel assembly having 10 rods of the short length fuel rods 2B arranged as shown in FIG. 12. The ratio Lp/Lf and the horizontal sectional area of the water rods 3 are set so as to fall into this zone. However, even in a case of satisfying Equation 11, that is, 10xe2x89xa6nxe2x89xa620, there is a zone where Equation 1, Equation 4, and Equation 12 to Equation 14 are satisfied. According to the present embodiment, the same effects similar to those of Embodiment 1 can be obtained. The short length fuel rods may be arranged in different positions from those of FIG. 12 unless the short length fuel rods are arranged in the outermost tier, and further, the fuel assembly 1F shown in FIG. 14 may be used. The fuel assembly 1F is a fuel assembly that in the fuel assembly 1E, the water rods 3E are integrated into a single rod of water rod 3F. The water rod 3F is placed at the same position of the three water rods 3C. Embodiment 4 A fourth embodiment of a fuel assembly 1G in accordance with the present invention will be described below, referring to FIG. 15. The present embodiment of the fuel assembly 1G is loaded in a reactor core of a boiling water reactor. The fuel assembly 1G has a construction that in the fuel assembly 1 shown in FIG. 1, the arrangement of the short length fuel rods 2B is changed. That is, the short length fuel rods 2B are not arranged in the second tier of the fuel rod array from the outer side, but arranged in the outermost tier of the fuel rod array. In the outermost tier, two rods of the short length fuel rods 2B are arranged in the middle portion of each side adjacent to each other. The other structure of the fuel assembly 1G is the same as that of Embodiment 1. The dimensions of the inner width Dcb of the channel box 7, the outer diameter Df of the fuel rod 2, the fuel rod pitch Pf and the effective fuel length Lf of the fuel rod 2A are the same as those of the fuel assembly 1. The fuel assembly 1G is constructed so that the effective fuel length Lp of the short length fuel rod 2B and the total horizontal sectional area Awr of the water rod 3E satisfy the conditions of Equation 1, Equation 3, Equation 4, Equation 6, Equation 11 and Equation 15. The conditions expressed by these equations are found from a study performed by the inventors of the present invention. An example of a boundary line derived from individual analyses of the pressure loss and the core stability in the present embodiment of the fuel assembly 1G similarly to Embodiment 1 is shown in FIG. 16. The boundary line L6 shown in FIG. 16 is a boundary line for the pressure loss when 12 rods of the short length fuel rods 2B are arranged in the fuel rod array of the fuel assembly 1G including the outermost tier. Similarly, the boundary line M6 is a boundary line for the core stability when 12 rods of the short length fuel rods 2B are arranged. In the present embodiment, because all the short length fuel rods 2B are arranged at the positions where the effect of improving the void coefficient is large, that is, at the positions in the outermost tier of the fuel rod array and adjacent to the water rods, the condition for the core stability, that is, Equation 15 is different from the condition for the core stability in Embodiment 1, that is, Equation 5. The total horizontal sectional area of the water rods in the present embodiment is smaller than that of Embodiment 1 when the core stability is the same. On the other hand, the condition determined from the pressure loss in the present embodiment, that is, Equation 6 is not influenced by the arrangement of the short length fuel rods, and is the same as that of Embodiment 1. Further, the upper limit value for Awr/Ach is a value shown by Equation 23 similarly to Embodiment 1. In the present embodiment, the required number of the short length fuel rods 2B is within a range of 9 to 20 which is obtained from a study similar to that of Embodiment 1. In FIG. 16, the hatched zone is a zone where Equation 1, Equation 3, Equation 4, Equation 6 and Equation 15 are satisfied to the fuel assembly having 12 rods of the short length fuel rods 2B arranged as shown in FIG. 15. The ratio Lp/Lf and the horizontal sectional area of the water rods 3 are set so as to fall into this zone. However, even in a case of satisfying Equation 11, that is, 10xe2x89xa6nxe2x89xa620, there is a zone where Equation 1, Equation 3, Equation 4, Equation 6 and Equation 15 are satisfied. By arranging the short length fuel rods 2B in the outermost tier, the void coefficient is reduced to more than one half as small as that in the case where the short length fuel rods 2B are arranged in the second tier of the fuel rod array from the outer side. When the short length fuel rods 2B are arranged at the corners of the outermost tier, the reducing rate of the void coefficient becomes maximum. However, in the case where the short length fuel rods 2B are arranged at the corners of the outermost tier, both of the reactivity loss and the local power peaking factor of the short length fuel rods arranged at the corners become large. Therefore, arranging of the short length fuel rods 2B at the corners should be avoided. The reactivity loss can be reduced by arranging the short length fuel rods 2B at positions other than the corner in the outermost tier. Further, by arranging the short length fuel rods at the positions in the outermost tier of the fuel rod array intersecting with a row or a column of the fuel rod array on which each of the water rod 3 is arranged (in concrete, at the four fuel rod positions at middle portions in the individual sides of the outermost tier), the reactivity loss and the local power peaking can be reduced. According to the present embodiment, the same effects as those of the first embodiment can be obtained, and further the void coefficient can be reduced. In addition, the reactivity loss and the local power peaking can be also reduced. The short length fuel rods may be arranged differently from the arrangement of FIG. 15 if the short length fuel rods are arranged both in the positions in the outermost tier and in the positions adjacent to the water rods, or arranged only in the outermost tier, and further the fuel assembly 1H shown in FIG. 17 may be acceptable. The fuel assembly 1H is that in the fuel assembly 1G, the water rods 3 are replaced with the water rods 3A having a rectangular horizontal section. The two water rods 3A are arranged at the same positions as those of the two water rods 3. Embodiment 5 A fifth embodiment of a fuel assembly 1I in accordance with the present invention will be described below, referring to FIG. 18. The present embodiment of the fuel assembly 1I is loaded in a reactor core of a boiling water reactor. The fuel assembly 1I has a construction that in the fuel assembly 1C shown in FIG. 9, the arrangement of the short length fuel rods 2B is changed. The other construction of the fuel assembly 1I is the same as that of the fuel assembly 1C. The arrangement of the water rod 3C of the fuel assembly 1I is also the same as that of the fuel assembly 1C. The present embodiment has 12 rods of the short length fuel rods 2B. These short length fuel rods 2B are not arranged in the second tier from the outer side of the fuel rod array. Eight rods of the short length fuel rods 2B are arranged in the outermost tier of the fuel rod array, and two rods are arranged in the middle portion on each side of the fuel rod array adjacent to each other. The remainder of four rods of the short length fuel rods 2B are arranged in the fourth tier from the outer side of the fuel rod array in the side of the corner portion 8 side facing a control rod under the state when the fuel assembly 1I is loaded in the reactor core of the boiling water and in the third tier from the outer side of the fuel rod array in the opposite side of the corner portion 8 side. Each of these four short length fuel rods 2B is adjacent to the water rod 3C. The dimensions of the inner width Dcb of the channel box 7, the outer diameter Df of the fuel rod 2, the fuel rod pitch Pf and the effective fuel length Lf of the fuel rod 2A are the same as those of the fuel assembly 1. The fuel assembly 1I is constructed so that the effective fuel length Lp of the short length fuel rod 2B and the total horizontal sectional area Awr of the water rod 3 satisfy the conditions of Equation 1, Equation 4, Equation 8, Equation 10, Equation 16 and Equation 17. The conditions expressed by these equations are found from a study performed by the inventors of the present invention. An example of a boundary line derived from individual analyses of the pressure loss and the core stability in the present embodiment of the fuel assembly 1I similarly to Embodiment 1 is shown in FIG. 19. The boundary line L7 shown in FIG. 19 is a boundary line for the pressure loss when 12 rods of the short length fuel rods 2B are arranged in the fuel rod array of the fuel assembly 1I including the outermost tier. Similarly, the boundary line M7 is a boundary line for the core stability when 12 rods of the short length fuel rods 2B are arranged. In the present embodiment, because all the short length fuel rods 2B are arranged at the positions where the effect of improving the void coefficient is large, that is, at the positions in the outermost tier of the fuel rod array and adjacent to the water rods, the condition for the core stability, that is, Equation 17 is different from the condition for the core stability in Embodiment 2, that is, Equation 9. The total horizontal sectional area of the water rods in the present embodiment is smaller than that of Embodiment 2 when the core stability is the same. On the other hand, the condition determined from the pressure loss in the present embodiment, that is, Equation 10 is not influenced by the arrangement of the short length fuel rods, and is the same as that of Embodiment 2. Further, the upper limit value for Awr/Ach is a value shown by Equation 27 similarly to Embodiment 2. In the present embodiment, the required number of the short length fuel rods 2B is within a range of 8 to 20 which is obtained from a study similar to that of Embodiment 1. In FIG. 19, the hatched zone is a zone where Equation 1, Equation 4, Equation 8, Equation 10 and Equation 17 are satisfied to the fuel assembly having 12 rods of the short length fuel rods 2B arranged as shown in FIG. 18. The ratio Lp/Lf and the horizontal sectional area of the water rods 3 are set so as to fall into this zone. However, even in a case of satisfying Equation 16, that is, 8xe2x89xa6nxe2x89xa620, there is a zone where Equation 1, Equation 4, Equation 8, Equation 10 and Equation 17 are satisfied. According to the present embodiment, the effects similar to those of Embodiment 4 can be obtained. Further, the short length fuel rods may be arranged differently from the arrangement of FIG. 18 if the short length fuel rods are arranged both in the positions in the outermost tier and in the positions adjacent to the water rods, or arranged only in the outermost tier, and further the fuel assembly 1J shown in FIG. 20 may be acceptable. The fuel assembly 1J is that in the fuel assembly 1I, the water rod 3C is replaced with the water rod 3D having a rectangular horizontal section. The water rod 3D is arranged at the same positions as those of the two water rod 3C. Embodiment 6 A sixth embodiment of a fuel assembly 1K in accordance with the present invention will be described below, referring to FIG. 21. The present embodiment of the fuel assembly 1K is loaded in a reactor core of a boiling water reactor. The fuel assembly 1K has a construction that in the fuel assembly 1E shown in FIG. 12, the arrangement of the short length fuel rods 2B is changed. The other construction of the fuel assembly 1K is the same as that of the fuel assembly 1E. The arrangement of the water rod 3E of the fuel assembly 1K is also the same as that of the fuel assembly 1E. The present embodiment has 10 rods of the short length fuel rods 2B. These short length fuel rods 2B are not arranged in the second tier from the outer side of the fuel rod array. Eight rods of the short length fuel rods 2B are arranged in the outermost tier of the fuel rod array similarly to the fourth embodiment, and two rods are arranged in the middle portion on each side of the fuel rod array adjacent to each other. The remainder of 2 rods of the short length fuel rods 2B are arranged in the fourth tier from the outer side of the fuel rod array, and each of these 2 short length fuel rods 2B is adjacent to the water rods 3E. The dimensions of the inner width Dcb of the channel box 7, the outer diameter Df of the fuel rod 2, the fuel rod pitch Pf and the effective fuel length Lf of the fuel rod 2A are the same as those of the fuel assembly 1. The fuel assembly 1K is constructed so that the effective fuel length Lp of the short length fuel rod 2B and the total horizontal sectional area Awr of the water rods 3 satisfy the conditions of Equation 1, Equation 4, Equation 12, Equation 14, Equation 18 and Equation 19. The conditions expressed by these equations are found from a study performed by the inventors of the present invention. An example of a boundary line derived from individual analyses of the pressure loss and the core stability in the present embodiment of the fuel assembly 1K similarly to Embodiment 1 is shown in FIG. 22. The boundary line L8 shown in FIG. 22 is a boundary line for the pressure loss when 10 rods of the short length fuel rods 2B are arranged in the fuel rod array of the fuel assembly 1K including the outermost tier. Similarly, the boundary line M8 is a boundary line for the core stability when 12 rods of the short length fuel rods 2B are arranged. In the present embodiment, because all the short length fuel rods 2B are arranged at the positions where the effect of improving the void coefficient is large, that is, at the positions in the outermost tier of the fuel rod array and adjacent to the water rods, the condition for the core stability, that is, Equation 19 is different from the condition for the core stability in Embodiment 3, that is, Equation 13. The total horizontal sectional area of the water rods 3C in the present embodiment is smaller than that of Embodiment 2 when the core stability is the same. On the other hand, the condition determined from the pressure loss in the present embodiment, that is, Equation 14 is not influenced by the arrangement of the short length fuel rods, and is the same as that of Embodiment 3. Further, the upper limit value for Awr/Ach is a value shown by Equation 31 similarly to Embodiment 3. In the present embodiment, the required number of the short length fuel rods 2B is within a range of 7 to 20 which is obtained from a study similar to that of Embodiment 1. In FIG. 22, the hatched zone is a zone where Equation 1, Equation 4, Equation 12, Equation 14 and Equation 19 are satisfied to the fuel assembly having 10 rods of the short length fuel rods 2B arranged as shown in FIG. 21. The ratio Lp/Lf and the horizontal sectional area of the water rods 3E are set so as to fall into this zone. However, even in a case of satisfying Equation 18, that is, 7xe2x89xa6nxe2x89xa620, there is a zone where Equation 1, Equation 4, Equation 12, Equation 14 and Equation 19 are satisfied. According to the present embodiment, the effects similar to those of Embodiment 4 can be obtained. Further, the short length fuel rods may be arranged differently from the arrangement of FIG. 21 if the short length fuel rods are arranged both in the positions in the outermost tier and in the positions adjacent to the water rods, or arranged only in the outermost tier, and further the fuel assembly 1L shown in FIG. 22 may be acceptable. The fuel assembly 1L is that in the fuel assembly 1K, the water rods 3E are replaced with a water rod 3F having a rectangular horizontal section. The water rod 3F is arranged at the same positions as those of the water rods 3E. The fuel assembly in accordance with the present invention is suitable for loading into a core of a boiling water reactor.

056132395

description

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS In the drawing, an electrical conduction tank 1 contains a solution composed of a chelating solution and/or an organic acid containing radioactive metal ions. Suitable chelating agents for preparation of a chelating solution include ethylenediamine tetraacetic acid, ethylenenitrilodiamine triacetic acid, hydroxyethylethylenediamine tetraacetic acid and the like. Suitable organic acids include citric acid, oxalic acid, acetic acid and the like. The chelating solution and organic acid may be used singly or in combination and contain radioactivity-laden metal ions such as Fe ions, Mn ions, Co ions and other metal ions. Denoted by numeral 9 is an alkaline agent-feeding device from which a NaOH or KOH solution is supplied. An alkaline agent used here is a hydroxide of an alkali metal or of an alkaline earth metal. Numeral 10 is a stirrer, numeral 11 is a pump, and numeral 12 is a filtration device, which is, as an example, a cartridge filter in this embodiment. A filtrate tank is denoted by numeral 13. An electrolytic device 3 is composed of an electrolyzer 14 and a plurality of electrodes 15 designed to flow direct current. An air pump 16 of an electromagnetic type is provided to feed air which removes or blows off various gases. A tank 17 is provided to store a solution electrolyzed in the electrolyzation device 3. A filtration device 4 communicates with the electrolyzer 14 and filters metal hydroxides which are little soluble in water coming out of the electrolyzer 14, to discharge the metal hydroxides as a filter cake and to convey the resultant filtrate to the tank 17. An ultraviolet irradiation device 6 has an elongate tank 18 to which an ultraviolet lamp 19 is secured. The filtrate comes into the device 6 from an inlet 20 and comes out from an inlet 21. A pump 22 is arranged to feed air and provided with an air inlet 23 and an air outlet 24. The air thus fed generates ozone upon irradiation with ultraviolet rays, to promote oxidation of the filtrate. Numeral 25 is a tank. A separation device 5, which is as an example of a reverse osmosis type, is provided to separate organic matter and water resulting from decomposition in the ultraviolet irradiation device 6. The organic matter so decomposed is near mineral, and the water so separated may be recycled as clean water or discharged. The separation device 5 may also be of an ion-exchange resin type. The operation of the apparatus which is constructed as described above will be described hereunder. Firstly, an organic solution composed of a chelating solution and/or an organic acid is applied to radioactive metals laden with radioactivity, to form an organic metal solution. In this embodiment, a mixture of a chelating solution and an organic acid is used. For example, a mixture of ethylenediamine tetraacetic acid and citric acid, each being a 1% aqueous solution, is used. Contained in the metal solution are metal ions such as Fe ions, Mn ions and the like, and here explanation will be made as to Fe ions as an example. The metal solution contained in the electrical conduction tank 1 is applied with a NaOH solution as an example from the alkaline agent-feeding device 9, and stirred by the stirrer 10. For example, the ratio of NaOH to a metal solution is 4 g/liter. Then iron hydroxides are formed in the metal solution and precipitated in colloid. The same kind of action occurs as to metals other than iron, too. Being a typical coprecipitant, iron helps precipitation of other radioactive metal ions. The metal solution is thereafter filtered in the filtration device 2 so that the iron hydroxides are separated and removed, while the resulting filtrate is fed into the electrolytic device 3 where the filtrate is electrolyzed. Efficient electrolyzation is made because the filtrate treated with an alkaline agent has markedly high electrical conductivity. With respect to electrical conductivity of the metal solution treated with an alkaline agent, as an example, the following are the current densities as measured. before addition of an alkaline agent: 0. 8 A/dm2 PA1 after addition of an alkaline agent: 10 A/dm2 Most of Fe ions are lost, and the chelating effect of the chelating solution is lost, presumably due to hydrolysis. For instance, using disodium ethylenediamine tetraacetic acid, C.sub.10 H.sub.14 N.sub.2 O.sub.8 Na.sub.2 +16H.sub.2 O.fwdarw.10CO.sub.2 +2NO+2NaOH+22H.sub.2. CO.sub.2 and NaOH are formed by anode oxidation and H.sub.2 is formed at a cathode side. The organic acid is also decomposed by electrolysis to form CO.sub.2, H.sub.2 and the like. Prior to electrolysis, most of the metal ions are removed in the treatment in the electrical conduction tank 1 and the filtration device 12 so that radioactive metals left to be deposited on the electrodes 15 of the electrolytic device 3 can be reduced greatly. Much deposition on the electrodes 15 is responsible for poor electrolysis efficiency. Moreover, radioactivity of the electrodes 15 is kept low because just a small extent of radioactive metal ions are still remaining. Thus troublesome post-treatment can be minimized. According to the invention, although a chelating solution and/or an organic acid containing radioactive ions are generally little conductive and difficult to be electrolyzed, they can be easily electrolyzed by increasing electrical conductivity by addition of an alkaline agent. This ensures easy collection of radioactive metal ions contained in such solutions. In the above electrolytic treatment, in addition to the decomposition through the anode oxidation, a material convertible by electrolysis into highly oxidative matter, such as NaOH for example, may also be used to take advantage of its high oxidative action. As a result of electrolysis, radioactive metal ions are converted into little-water-soluble hydroxides in the electrolyzer 14. The filtrate in the electrolyzer 14 is filtered in the filtration device 4 where the hydroxides are separated and removed. The separated filtrate is allowed to enter the ultraviolet irradiation device 6 from the lower inlet 20 and to be discharged out of the upper outlet 21 while being supplied with air bubbles. Oxygen in the bubbles generates ozone upon exposure to ultraviolet rays, and ozone acts to decompose any remaining organic matter, promoting decomposition of such organic matter by ultraviolet rays. The organic matter decomposed by ultraviolet irradiation is near mineral and sent to the separation device 5 that is of a reverse osmosis type for example. In the device 5, the irradiated filtrate put inside a translucent membrane (not shown) is brought in pressurized condition so that water alone iscaused to pass through the membrane outside in clean water and thus separated from the decomposed organic matter. The separation device 5 may be an ion-exchange resin type. The solution containing the matter decomposed in the ultraviolet irradiation device 6 is sent to the ion-exchange resin device, where the decomposed matter is absorbed by the ion-exchange resin, while water free from the decomposed matter is separated as cleanwater. The water may be discharged or recycled to the first stage of the apparatus. Being constructed as described above, the present invention enables the following available: It is available to electrolyze a solution composed of a chelating solution and/or an organic acid containing a radioactive metal ions, which is little soluble in water and difficult to be electrolyzed, by increasing electrical conductivity thereof by adding an alkaline agent, and to collect without difficulty radioactive metals contained in the solution. It is also available in collecting radioactive metals by way of dissolution to decrease mass volume of the radioactive matter required to be stored in safety quite significantly because there is no need to store radioactive chelating solutions and/or organic acids. Therefore, it is available to realize a quite high extent of reduction of storage space for radioactive matter. It is also available to make cementing treatment of the chelating solution and the organic solution after electrolysis because carboxyl groups therein have been decomposed. It is available to collect radioactive metal ions dissolved in the chelating solution and/or the organic acid, as hydroxides easily, because inherent activities of such solutions are lost by decomposition by electrolysis. Prior to electrolysis, the radioactive metal ions in the chelating solution and/or the organic acid have already been considerably reduced, through convertion into little-water-soluble matter by addition of an alkaline agent and filtration thereafter. Therefore loading on the electrodes can be minimized, metals to deposit on the electrodes can be minimized, lowering of electrolytic efficiency can be prevented, and further, necessity to remove radioactive metals, which is dangerous to handle, from the electrodes can be minimized. The alkaline agent which is added prior to electrolysis in order to decrease radioactive metal ions through conversion into matter poorly soluble in water and filtration thereafter serves to increase electrical conductivity of the electrolytic solution, and therefore realizes quite effective electrolysis. This may be well understood from the fact that electrical conductivity of the chelating solution and/or the organic acid is low before the treatment. Furthermore, it is available in the invention to collect most of radioactive metal ions through formation of matter poorly soluble in water by alkaline treatment combined with the electrolytic treatment. Further, it is available in the invention to collect almost all of radioactive metal ions by additional ultraviolet irradiation treatment and separation step. Furthermore, it is available in the invention to collect radioactive metal ions almost completely because an additional separation device is that by use of reverse osmosis or ion-exchange resin.

summary

claims

1. A charged beam exposure apparatus comprising: a charged beam generating source; a first flat board which has a plurality of first aperture sections having rectangular apertures arranged close to one another and electrodes for deflecting the beam passing through the first aperture sections at the respective apertures; and a second flat board which is arranged parallel with said first flat board and has second aperture sections having basic figure apertures for shaping the beam, which passes or passed through the first aperture sections, wherein a ratio of a width of the first aperture sections to an interval between the first aperture sections is larger than a ratio of a width of the second aperture sections to an interval between the second aperture sections. 2. The charged beam exposure apparatus as in claim 1 , further comprising: claim 1 a first deflector to emit the beam passed through the first aperture sections to the second aperture section; a second deflector to emit the beam passed through the second aperture section to an arbitrary position of a sample; and a lens to image the beam passed through the second aperture section onto the sample. 3. The charged beam exposure apparatus as in claim 1 , wherein the first aperture sections are arranged cyclically. claim 1 4. The charged beam exposure apparatus as in claim 1 , wherein said first flat board has the aperture sections and the electrodes according to LSI wiring pitches. claim 1 5. The charged beam exposure apparatus as in claim 1 , wherein said second flat board has the basic figures according to LSI wiring pitches. claim 1 6. The charged beam exposure apparatus as in claim 1 , wherein a form of the apertures of the second aperture sections has linear wiring patterns in vertical and horizontal directions. claim 1 7. The charged beam exposure apparatus as in claim 6 , wherein a form of the apertures of the second aperture sections further has a connection pattern which connects vertical and horizontal wirings. claim 6 8. The charged beam exposure apparatus as in claim 1 , wherein a form of the apertures of the second aperture sections has a linear wiring pattern in a direction where a vertical direction and a horizontal direction do not form a right angle. claim 1 9. The charged beam exposure apparatus as in claim 1 , wherein a form of the apertures of the second aperture sections has a standard cell pattern. claim 1 10. The charged beam exposure apparatus as in claim 1 , wherein the second aperture sections comprises: claim 1 first slits which are arranged parallel with vertical sides of the rectangles and opposed to one another with equal intervals; and second slits which are arranged parallel with horizontal sides of the rectangles and opposed to one another with equal intervals. 11. The charged beam exposure apparatus as in claim 10 , wherein lengths of the first slits are equal, and both end portions are arranged on a line, and their number is the same as a number of lines of the first aperture sections, the first aperture sections being arranged cyclically. claim 10 12. The charged beam exposure apparatus as in claim 10 , wherein lengths of the second slits are equal, and both end portions are arranged on a line, and their number is the same as a number of rows of the first aperture sections, the first aperture sections being arranged cyclically. claim 10

description

This application is a national phase application of International Application No. PCT/EP2011/058926, filed May 31, 2011, designating the United States and claiming priority to European Patent Application No. 10164664.4, filed Jun. 1, 2010, which is incorporated by reference herein. The present invention relates to an apparatus for producing a radioisotope by irradiating a target fluid comprising a precursor of said radioisotope with a particle beam produced by a particle accelerator. More particularly, the present invention relates to an apparatus comprising means for an improved maintenance, and a method of maintenance of said apparatus. Radioisotopes used for medicine are generally produced by irradiation of a precursor of radioisotope by a particle beam. The particle beam is produced by a particle accelerator, generally a linear accelerator or a cyclotron able to produce a beam in an energy range of 10 to 50 MeV. When the precursor is under liquid or gaseous state, the precursor is comprised into a housing forming a target cavity, the housing having an opening which is closed by a metal foil. The metal foil is generally made of Havar, Molybdenum or Niobium and has a thickness from about ten to about hundred micrometers for supporting the thermal and mechanical stress and allowing the passage of the particle beam to reach the inside of the cavity with sufficient energy for initiating nuclear reactions with the precursor. The metal foil is advantageously comprised between the said target cavity and a cooling cavity in which is able to flow a cooling fluid directed towards the said metal foil. The cooling cavity is closed by a second foil made of any metal separating the cooling cavity from the vacuum of the particle accelerator. Document WO2000019787 describes a target body having parts fitting with the exit of a particle accelerator, the target body comprising three target body portions: a first target body portion having a target cavity comprising the precursor of the radioisotope; a second target body portion comprising a cooling cavity closed by two metallic foils, said second target body portion in which flows a cooling fluid directed towards the said metallic foils, a first foil separating the said cooling cavity from the said target cavity, and a second foil in contact with a third target body portion; a third target body portion having a cavity under vacuum, said third target body portion fitting with the particle accelerator, the cavity of the third target body portion being separated from the cooling cavity by the said second foil.The said first, second and third target body portions are screwed together by means of bolts. In case of any leakage, for example after the breaking of a metallic foil, the user has to dismantle a lot of parts of the target body for changing the broken window while an important loss of precursor gas and radioisotope occurs. During the exchange of the said foil, the user is exposed to radiations coming from the produced radioisotope and from activated parts of the target body such as the metallic foils. Such operation is time consuming and usually need long cooling down time of the target for decay of the by-product. An apparatus named Kipros 120, for producing iodine-123 by irradiating 124-Xe with an accelerated proton beam, is manufactured and provided by ZAG Zyklotron AG, Hermann-von-Helmoltz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany. Said apparatus comprises a target housing having an opening for allowing the passage of the particle beam and comprising gaseous 124-Xe as radioisotope precursor, a dual foil flange for closing the opening of the said target housing, and a rotatable robot arm for positioning the said dual foil flange in an in-line position in front of the opening of the target housing. A dual foil flange is an appellation for a device comprising two irradiation foils able to allow the passage of a particle beam, a first and a second foil being located respectively on a first and a second side of a hollowed standoff, said first and second foil covering the hole of the standoff and forming a cooling cavity. The said first and second foils are maintained on the said standoff respectively by a first and a second flange. The dual foil flange further comprises an inlet channel for bringing a cooling fluid into said cooling cavity and an outlet channel for the evacuation of the said cooling fluid outside of the said cooling cavity. In the said apparatus named Kipros 120, the inlet and outlet channels are located on the said standoff. Flexible cooling gas pipelines, for flowing a cooling gas through the said cooling cavity, are fixed on the branches of said robot arm. The branches of said robot arm are actuated by means of an air-compressed system for clutching the standoff of said dual foil flange or for releasing the dual foil flange. The said robot arm is rotatable around an axis parallel to the axis of the particle beam for bringing the said dual foil flange from a first loading position to a in-line position in front of the target cavity and from said in-line position to a third position wherein the branches of the robot arm release the said dual foil flange into a shielded box. After the releasing of the dual foil flange, the robot arm returns to its initial loading position. In case of a production run of a radioisotope, if a window foil gets broken, a cryogenic system traps the target fluid and the dual foil flange is evacuated to said shielded box. Then a user has to enter into the room comprising the apparatus for replacing a new dual foil flange into the branches of the robot arm of said apparatus. The replacement of an irradiation foil is faster with such an apparatus since no part has to be dismantled manually. Nevertheless, a first drawback is that the user has to enter in an unsafe high radiation area enclosing the said apparatus, comprising an amount of produced radioisotope in the target or trap. A second drawback is that the time during which the user replaces a dual foil flange is still time consuming. A third drawback is that the said robot arm of the apparatus is a complicated and encumbered device comprising: an air-compressed system comprising two flexible gas ducts adapted to maintain a pressure on the said branches for maintaining the dual foil flange and; the said flexible cooling pipelines.Flexible ducts and pipelines are subject to move and are submitted to some mechanicals constraints. Therefore some leaks could occur in those pieces during the use of the apparatus. These flexible ducts and pipeline are not easily accessible and the detection and reparation of a leak in the apparatus is also time-consuming. It is an object of our invention to provide an apparatus for producing a radioisotope wherein the maintenance of a dual foil flange is safer. It is a further object of our invention to provide an apparatus wherein the maintenance of a dual foil flange is faster than in the apparatuses of the prior art. It is a further object of our invention to provide an apparatus for producing a radioisotope having simplified means for changing a dual foil flange avoiding down time in production. According to a first aspect, the invention relates to an apparatus for producing a radioisotope by irradiating a target fluid comprising a precursor of said radioisotope with a particle beam produced by a particle accelerator, the apparatus comprising: a housing comprising a target cavity for receiving said target fluid, said housing having an opening for allowing the passage of the said particle beam into the said cavity; a dual foil flange for closing said opening of the target cavity, said dual foil flange comprising: a standoff comprising a central hole; a first and a second foil able to allow the passage of the said particle beam and located respectively on a first side and a second side of the said standoff, covering the said central hole and forming a cooling cavity; a first flange and a second flange for sealing respectively the said first and second foil on said standoff; at least an inlet channel and at least an outlet channel, for flowing a cooling fluid through the cavity of the dual foil flange; guiding means for positioning said dual foil flange in an in-line position in which a said foil is facing said opening of said housing;the apparatus being characterized in that the said guiding means are adapted to transfer said dual foil flange through a translation movement, from a stand-by position to the said in-line position. In a preferred embodiment of the invention, said guiding means are adapted to evacuate a defective or dated dual foil flange through translation movements towards a discard position. Preferably, said guiding means comprise parallel elongated parts in which a dual foil flange is able to slide. Advantageously, the apparatus comprises means for moving the said housing following a direction parallel to the axis of the particle beam, said means for moving the said housing being able to position the said housing in two positions: a first position wherein the said opening of the housing is at a distance from the beam exit of the particle accelerator larger than the longitudinal length of the said dual foil flange, in order to have a space for inserting said dual foil flange in the said in-line position or for evacuating said dual foil flange from said in-line position; a second position wherein the said housing presses the said dual foil flange against the said beam exit of the particle accelerator. Preferably, said means for moving the said housing comprise a lever being maintained at rest by a spring and being actionable by a piston able to exert a force opposite to the force exerted by the spring, in order to induce a movement on the said housing for retracting the said housing from the beam exit of the particle accelerator or from the said dual foil flange. Preferably, said guiding means comprise means for moving the said parallel elongated parts following a direction parallel to the axis of the particle beam for providing a first space between said dual foil flange and the said beam exit of the particle accelerator and a second space between said dual foil flange and the opening of the said housing, when said housing is positioned at said first location. Preferably, said inlet and outlet of the said dual foil flange have their first extremity located on a flange and their second extremity located on the standoff, said second extremities being directed towards the inside of the said cooling cavity. Advantageously, the apparatus comprises a first fixed gas pipeline having a fixed extremity connectable with the extremity of the said inlet channel of said dual foil flange and a second fixed gas pipeline connectable with the extremity of the said outlet channel of the said dual foil flange for flowing the said cooling fluid inside the said cooling cavity when said dual foil flange is compressed between said beam exit of the particle accelerator and the said opening of the housing. Advantageously, the apparatus comprises a charger having the capacity for containing at least one dual foil flange and able to position the said dual foil flange into the said parallel elongated parts. Advantageously, the apparatus comprises monitoring means able to detect any leakage. More advantageously, the apparatus comprises means for trapping the said target fluid in case of any detection of a leakage by the said monitoring means. Preferably, the apparatus comprises a program able to start in case of any leakage detected by the said monitoring means, said program being adapted for performing the steps of: actuating the said means for trapping the said target fluid; when the said target fluid is trapped, transferring the said dual foil flange to the said discard position; transferring a new dual foil flange from the said stand-by position to the said in-line position. A second aspect of the present invention relates to a dual foil flange for closing the opening of a housing destined to contain a fluid comprising a precursor of radioisotope, said dual foil flange comprising: a standoff comprising a central hole; a first and a second foil able to allow the passage of a particle beam, located respectively on a first and a second side of the said standoff, covering the said central hole and forming a cooling cavity; a first flange and a second flange for sealing respectively the said first and second foil on said standoff; an inlet channel and an outlet channel for flowing a cooling fluid through the said cooling cavity;characterized in that the said inlet and outlet channels have their first extremity located on a flange and their second extremity located on the said standoff, said second extremities being directed towards the inside of the cooling cavity. The invention also relates to a method for replacing a dual foil flange closing the opening of a housing comprising a target material, comprising the steps of: Trapping the said target fluid; Evacuating the said dual foil flange from its position closing the said opening of the housing to a storage position; Transferring another dual foil flange from another storage position to the said position closing the said opening of the housing;characterized in that the said method is fully automated. Advantageously, said dual foil flanges are evacuated or transferred using a gravity effect. Preferably, the method according to the invention uses a dual foil flange an apparatus as detailed hereabove. FIG. 1 shows a three-dimensional view of an apparatus 100 for producing a radioisotope by irradiating a target fluid comprising a precursor of said radioisotope with a particle beam 102 produced by a particle accelerator. FIG. 2 shows a cross sectional view along the axis of the particle beam 102 of some parts of the apparatus of our invention. The apparatus of our invention comprises: a housing 104 enclosing a target cavity 105 for receiving said target fluid, said housing 104 having an opening 106 for allowing the passage of the said particle beam 102 into the said cavity 105; a dual foil flange 107 for closing said opening 106 of the cavity, guiding means for positioning said dual foil flange 107 in an in-line position 117 between said opening 106 of said housing 104 and the beam exit 118 of the particle accelerator. FIG. 3 shows a cross sectional view of a dual foil flange 107 for use in the apparatus of our invention. Said dual foil flange comprises: a standoff 108 comprising a central hole; a first and a second foil 109, 110 able to allow the passage of a particle beam 102, located respectively on a first and a second side of the said standoff 108, covering the said central hole and forming a cooling cavity 103; a first flange 111 and a second flange 111′ for sealing respectively the said first and second foil 109, 110 on said standoff; an inlet channel 112 and an outlet channel 113, for flowing a cooling fluid through the said cooling cavity 103.The said dual foil flange 107 is characterized in that the said inlet channel 112 and outlet channels 113 have a first extremity respectively 130, 131 located on a flange 111 and/or 111′ and at least another extremity respectively 132, 133 located on the standoff 108 and directed through the inside of the cooling cavity 103. FIG. 4 shows a view in the direction of arrow A of FIG. 2 of a first dual foil flange 107 and a second dual foil flange 107′ into the said guiding means. Said guiding means are adapted for transferring said dual foil flanges 107, 107′ through translation movements from a stand-by position 116 to an in-line position 117 and from said in-line position 117 to a discard position 128. Said guiding means comprises parallel elongated parts 114 in which a dual foil flange 107 is able to slide. Said guiding means further comprises actionable blocking means 134′, for blocking a dual foil flange 107′ in said stand-by position 116 and blocking means 134 for blocking a dual foil flange 107 into said in-line position 117. In an embodiment of our invention, the said dual foil flange comprises notches 135 for allowing the said blocking means 134, 134′ to maintain the said dual foil flange 107, 107′. Various means for blocking said dual foil flange 107, 107′ may be easily realized by a man skilled in the art. Said guiding means are adapted to evacuate a defective or dated dual foil flange through translation movements towards a discard position 128, advantageously into a shielded enclosure. The apparatus of our invention further comprises a means for moving the said housing 104 following a direction parallel to the axis of the said particle beam 102. Said means for moving the said housing 104 is able to position the said housing 104 in two positions: a first position (actuated position) as shown on FIG. 6, wherein the said opening 106 of the housing 104 is at a distance from the beam exit 118 of the particle accelerator, said distance being longer than the longitudinal length 144 of the dual foil flange 107, in order to have sufficient space to insert said dual foil flange 107 in the said in-line position 117 or to evacuate said dual foil flange from said in-line position 117 to said discard position 128; a second position (rest position) as shown on FIG. 5, wherein the said housing 104 presses the said dual foil flange 107 against the said beam exit 118 of the particle accelerator. Said means for moving the said housing may comprise for example a piston located backwards the said housing, following the arrow A of FIG. 2. FIG. 5 shows an embodiment of our invention wherein said means for moving the said housing comprises a lever 121 being maintained at rest by a spring 122 and being actionable by a piston 123. Said piston 123 is able to exert a force opposite to the force exerted by the spring 122, in order to induce a movement on the said housing 104 for retracting the said housing 104 from the said dual foil flange 107. Both said spring 122 and said piston 123 are fixed near the extremity of the said lever 121. Said lever 121 has a main elongated part 141 having a longitudinal axis 138 inclined respect to the longitudinal axis 140 of the housing 104, and a shorter part 142 comprising a pivot 120 and having a longitudinal axis 139 perpendicular to the longitudinal axis 140 of the housing 104. The housing 104 comprises a member 119 able to slide between two abutments 136. Said member 119 comprises a notch 137 in which is inserted the said smaller part 142 of the lever 121. FIG. 6 shows an enlarged view of the said smaller part 142 of the lever 121 and the said member 119 in a configuration in which the lever 121 is actuated by the said piston 123. The said longitudinal axis 139 of the said smaller part 142 of the lever 121 makes an angle of less than 90° with the axis of the said housing, retracting the said housing 104 from the said dual foil flange 107. Said guiding means comprises means for moving the said parallel elongated parts 114 in the direction of the axis of the particle beam. When the said housing is in the said first position (actuated position), said parallel elongated parts 114 are located in a manner that a first side of the said dual foil flange is separated from the said beam exit 118 of the particle accelerator and the second side of the said dual foil flange is separated from the opening of the housing, in order that the insertion in the said in-line position or the evacuation from said in-line position of a dual foil flange is facilitated. When the housing 104 is in the second position (rest position), pressing the said dual foil flange, the said parallel elongated members 114 are moved towards the said beam exit 118 of the particle accelerator, in a manner that the said dual foil flange 107 is tightly compressed between the said housing 104 and the said beam exit 118 of the particle accelerator. For example, said means for moving the said elongated parts 114 may comprise a motor moving the said parallel elongated parts 114 following both direction along the axis of the particle beam 102, or may comprise a spring 115 having a first extremity fixed on said parallel elongated parts 114 and a second extremity fixed in a plan parallel to the said beam exit 118 of the particle accelerator. Referring to FIGS. 2, 3 and 4, the apparatus of our invention further comprises a first fixed gas pipeline 124 having a fixed extremity 143 connectable with the extremity 130 of the inlet channel 112 of the said dual foil flange, and a second fixed gas pipeline 124′ having a fixed extremity 143′ connectable with the extremity 131 of the outlet channel 113 of the said dual foil flange 107. Said fixed gas pipelines 124, 124′ provide a flow of cooling fluid inside said cooling cavity 103 when said dual foil flange is compressed between said beam exit 118 of the particle accelerator and said opening 106 of the housing 104. Advantageously, said fixed connections 143 are located on a surface in the plan of said beam exit 118 of the particle accelerator, in a manner that the compression of the dual foil flange 107 between the said housing 104 and the said beam exit 118, provides a tight sealing between the extremities 143, 143′ of the fixed gas pipelines 124, 124′ with the extremities 130, 131 of the inlet and outlet channels of the dual foil flange 107. The apparatus of our invention further comprises a charger 125 having the capacity for containing at least one dual foil flange 107′ in a stand-by position 116. Said charger 125 is able to position the said dual foil flange 107 into the said parallel elongated parts 114. Advantageously, said charger comprises the said elongated parts 114 and the said actionable blocking means 134′, for blocking a dual foil flange 107′ into said stand-by position 116. Referring to FIGS. 2 and 3, the apparatus of our invention further comprises monitoring means 126 able to detect any leakage. Said monitoring means 126 may be a pressure controller or a radiation monitor connected to the cooling cavity 103 of the dual foil flange and/or to the target cavity 105 of the housing 104. Advantageously, both a pressure controller and a radiation monitor are used as monitoring means. The apparatus of our invention further comprises means for trapping 127 the target fluid comprised into the target cavity 105 of the housing 104. Said means for trapping 127 is actionable in case of any leakage detected by the said monitoring means 126, in order to avoid the dispersion of precursor and radioisotope in the apparatus and the atmosphere. The apparatus of our invention further comprises a program able to start in case of any leakage detected by the said monitoring means 126. Said program is adapted for performing the steps of: actuating the said means for trapping 127 the said target fluid; when the when the said target fluid is trapped, transferring the said dual foil flange 107 to the said discard position 128; transferring a new dual foil flange 107 from the said stand-by position to the said in-line position. A first dual foil flange 107 is located in the said stand-by position 116 in a charger 125. In a first step, the means for moving the said housing 104 is actuated in order to retract the said housing 104 from the said beam exit 118 of the particle accelerator. Said parallel elongated parts 114 are maintained separated from the said beam exit 118 of the particle accelerator by a spring 115. In a second step, the said blocking means 134′ blocking said dual foil flange 107′ into said stand-by position 116 are deactivated while the said blocking means 134 for blocking said dual foil flange 107 into the said in-line position 117 are actuated. Said dual foil flange 107 slides into the said parallel elongated members 114 and falls down in the said in-line position by gravity. In a third step, said means for moving the said housing 104 is deactivated in order to press the said housing 104 against the said dual foil flange 107, pressing in the same time the said dual foil flange 107 against the beam exit 118 of the particle accelerator. In this configuration, both extremities 130, 131 of respectively the inlet channel 112 and the outlet channel 113, located on the flange 111 are connected to the said fixed gas connections 143, 143′. Then, said apparatus is ready for flowing a cooling fluid through the cooling cavity 103 of the dual foil flange and for the introduction of a target fluid into the target cavity 105 of the housing 104. Advantageously, a second dual foil flange 107′ is positioned into said charger 125. Advantageously, the said target fluid is in gaseous state and comprises a precursor of a radioisotope. For example, said target fluid may be 124-Xe for the production of 123-I by proton irradiation or 18-O for the production of 18-F by proton irradiation. A cooling fluid, for example helium, is able to flow through the cooling cavity of said dual foil flange 107, cooling the irradiation foils 109, 110 when they are submitted to the irradiation by the particle beam 102. During a production run of radioisotope, if a monitoring means 126 detects a leakage coming from the dual foil flange 107, the means for trapping 127 the target fluid are actuated. Said means for trapping 127 the target fluid comprises for example a cryopump or storage vessel. Then, the means for moving the housing 104 are actuated in order to retract the said housing 104 from the said dual foil flange 107. Said spring 115 moves away the said parallel elongated members 114 from the beam exit 118 of the particle accelerator in order that the said dual foil flange 107 is separated from the said beam exit 118 and from the opening 106 of the housing 104. The said blocking means 134 maintaining the dual foil flange 107 into the said in-line position 117 are deactivated and the damaged dual foil flange falls down into a discard position 128, advantageously into a shielded enclosure. The said second dual foil flange 107′ already located into the said charger 125 is ready to be positioned in the in-line position in the same manner as the used first dual foil flange 107. When the said second dual foil flange 107′ is in a ready position for restarting the production run of radioisotope, the trapping means reintroduces the trapped target fluid from the cryopump or storage vessel to the target cavity 105 of the housing 104. Then, the production run can restart. The user can also choose a program for changing a dual foil flange periodically in order to avoid that a leakage in the dual foil flange occurs. The apparatus of our invention provides some advantages respect to the prior art. Firstly the maintenance of the apparatus is improved since the method for replacing a dual foil flange is fully automated and does not require any manual intervention of the user. For that reason, said apparatus is safer for the user since he does not need to enter anymore in the high radiation area room enclosing the apparatus. The user is thus less susceptible to be submitted to radiations. A second advantage is that the method provided by the apparatus for replacing a dual foil flange is fast due to the simplification of the guiding means for positioning the dual foil flange in the said in-line position. The time for changing a dual foil flange is also reduced due to the fully automation of the method. Finally, the guiding means and cooling means for a dual foil flange are simplified and does not comprises any flexible gas pipelines. The dual foil flange is safely maintained into the said in-line position with the inlet and outlet channels tightly connected to fixed gas connections for flowing a cooling fluid though said dual foil flange.

abstract

A method to determine a global core reactivity bias and the corresponding estimated critical conditions of a nuclear reactor core prior to achieving reactor criticality. The method first requires collection and evaluation of the inverse count rate ratio (ICRR) data; specifically, fitting measured ICRR vs. predicted ICRR data. The global core reactivity bias is then determined as the amount of uniform reactivity adjustment to the prediction that produces an ideal comparison between the measurement and the prediction.

claims

1. A nuclear reactor including: a nuclear reactor vessel containing a body of coolant liquid defining a coolant liquid surface therein, a guard vessel spaced from said nuclear reactor vessel to form an annulus space therebetween, and a thermal load reducing system for controlling thermal stresses in said nuclear reactor vessel comprising: partition members disposed in said annulus space at a position above the surface of the coolant liquid body in said reactor vessel, means for circulating a low temperature gas via the annulus space and above the partition members to cool down the adjacent reactor vessel wall disposed above said coolant liquid surface, and means for circulating a higher temperature gas via the annulus space from a level lower than the surface of the coolant liquid body to the partition members for raising the temperature of the reactor vessel wall disposed below the surface of the coolant liquid body within the reactor vessel. 2. The thermal load reducing system in a nuclear reactor vessel according to claim 1 , wherein said low-temperature gas is circulated at a constant flow velocity during normal operation of said nuclear reactor, and said high-temperature gas is circulated only during starting operation of said nuclear reactor. claim 1

abstract

Method of optimizing output of sensor for indicating location of metallic object. Sensor having primary electromagnetic coil to generate time varying magnetic field; secondary electromagnetic coil to detect time varying magnetic field as affected, by object to output, on basis of detected time varying magnetic field, signal indicative of location of object. Method includes steps of: supplying primary coil with alternating-current to result generated time varying magnetic field; locating object in first-position and recording signal output by secondary electromagnetic coil for range of frequencies of supplied alternating-current; locating object in second-position and recording signal output by secondary electromagnetic coil for range of frequencies of supplied alternating-current; calculating, for each of frequencies, a value for span to offset ratio of measured signals on basis of respective signals measured for object in first and second positions; determining frequency of supplied alternating-current which provides maximum span to offset ratio on basis of calculations.

abstract

A collimator is provided with an adjustable focal length, particularly in X-ray testing systems, comprising an outer part with a conical inner surface and with a inner part having an conical outer surface, which are connected to one another at a fixed distance, as well as with at least one cone sliding part situated between the inner part and outer part in a manner that enables it to move.

abstract

Methods of producing and isolating 68Ga, 89Zr, 64Cu, 63Zn, 86Y, 61Cu, 99mTc, 45Ti, 13N, 52Mn, or 44Sc and solution targets for use in the methods are disclosed. The methods of producing 68Ga, 89Zr, 64Cu, 63Zn, 86Y, 61Cu, 99mTc, 45Ti, 13N, 52Mn, or 44Sc include irradiating a closed target system with a proton beam. The closed target system can include a solution target. The methods of producing isolated 68Ga, 89Zr, 64Cu, 63Zn, 86Y, 61CU, 99mTC, 45-Ti, 52Mn, or 44Sc by ion exchange chromatography. An example solution target includes a target body including a target cavity for receiving the target material; a housing defining a passageway for directing a particle beam at the target cavity; a target window for covering an opening of the target cavity; and a coolant gas flow path disposed in the passageway upstream of the target window.

046718982

summary

TECHNICAL AREA The present invention relates to a process for the treatment of a spent, radioactive, organic ion exchange resin to reduce the volume thereof and to obtain a stable final product. In the context ion exchange resin primarily means a cationic exchange resin but also an anionic exchange resin and an exchange resin of the mixed bed type, containing cation exchanger as well as anion exchanger, can be advantageously treated in accordance with the invention. The invention primarily relates to the treatment of such ion exchange resins which have been utilized to purify cooling water in a nuclear reactor, and the water in a pool for the storage of spent nuclear fuel. TECHNICAL BACKGROUND It is previously known to solidify a spent ion exchange resin in cement or bitumen. However, by such a measure the volume is heavily increased. Furthermore, in the case of solidification in cement, the stability against leaching is not very good. In the case of solidification in bitumen the fire hazards thereof is a problem. Moreover, it is previously known, for instance from Swedish patent specification No. 8101801-2, that the volume of a spent ion exchange resin can be reduced by an incineration thereof. According to said Swedish patent specification the incineration residue is then heated to sintering or melting, a stable product being obtained thereby. The measure of cementing the incineration residue has been considered improper due to the bad stability against leaching which has been observed when solidifying a non-incinerated ion exchange resin in cement.

050770004

summary

CROSS REFERENCE TO RELATED APPLICATIONS Reference is hereby made to the following copending applications dealing with related subject matter and assigned to the assignee of the present invention: 1. "Sealing Devices For The Drive Shaft Of A High Pressure Fluid Pump" by N. Bonhomme, assigned U.S. Ser. No. 379,196 and filed May 17, 1982, now U.S. Pat. No. 4,587,076, issued May 6, 1986. 2. "Nuclear Reactor Coolant Pump Impeller/Shaft Assembly" by L. S. Jenkins, assigned U.S. Ser. No. 761,447 and filed Aug. 1, 1985, now U.S. Pat. No. 4,690,612, issued Sept. 1, 1987. 3. "Improved Shaft Seal" by K. P. Quinn, assigned U.S. Ser. No. 739,745 and filed May 31, 1985, now U.S. Pat. No. 4,693,481, issued Sept. 15, 1987. 4. "Reactor Coolant Pump Hydrostatic Sealing Assembly With Improved Hydraulic Balance" by R. F. Guardiani et al, assigned U.S. Ser. No. 063,331 and filed June 17, 1987, now U.S. Pat. No. 4,838,559, issued June 13, 1989. 5. "Reactor Coolant Pump Sealing Surface With Titanium Nitride Coating" by G. Zottola, assigned U.S. Ser. No. 035,832 and filed Apr. 8, 1987, now U.S. Pat. No. 4,871,297, issued Oct. 3, 1989. 6. "Reactor Coolant Pump Hydrostatic Sealing Assembly With Externally Pressurized Hydraulic Balance Chamber" by R. F. Guardiani, assigned U. S. Ser. No. 091,224 and filed Aug. 31, 1987, now U.S. Pat. No. 4,848,774, issued July 18, 1989. 7. "Reactor Coolant Pump Shaft Seal Utilizing Shape Memory Metal" by D. J. Janacko assigned U.S. Ser. No. 197,174 and filed May 23, 1988. 8. "Reactor Coolant Pump Auxiliary Seal For Reactor Coolant System Vacuum Degasification" by J. D. Fornof, assigned U.S. Ser. No. 222,649 and filed July 21, 1988. BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates generally to shaft seals and, more particularly, is concerned with a reactor coolant pump auxiliary flexible vacuum seal for reactor coolant system vacuum degasification. 2. Description of the Prior Art In pressurized water nuclear power plants, a reactor coolant system is used to transport heat from the reactor core to steam generators for the production of steam. The steam is then used to drive a turbine generator. The reactor coolant system includes a plurality of separate cooling loops, each connected to the reactor core and containing a steam generator and a reactor coolant pump. The reactor coolant pump typically is a vertical, single stage, centrifugal pump designed to move large volumes of reactor coolant at high temperatures and pressures, for example 550 degrees F. and 2500 psi. The pump basically includes three general sections from bottom to top--hydraulic, shaft seal and motor sections. The lower hydraulic section includes an impeller mounted on the lower end of a pump shaft which is operable within the pump casing to pump reactor coolant about the respective loop. The upper motor section includes a motor which is coupled to drive the pump shaft. The middle shaft seal section includes three tandem sealing assemblies--lower primary, middle secondary and upper tertiary sealing assemblies. The sealing assemblies are located concentric to, and near the top end of, the pump shaft. Their combined purpose is to mechanically contain the high positive pressure coolant of the reactor coolant system from leakage along the pump shaft to the containment atmosphere during normal operating condition. Representative examples of pump shaft sealing assemblies known in the prior art are the ones disclosed in U.S. Pat. Nos. to MacCrum (3,522,948), Singleton (3,529,838), Villasor (3,632,117), Andrews et al (3,720,222) and Boes (4,275,891) and in the first three patent applications cross-referenced above, all of which are assigned to the same assignee as the present invention. Thus, the sealing assemblies in the reactor coolant pumps are designed to hold high positive coolant pressures. This fact has raised some concerns about possibility of damage being done to the reactor coolant pumps during reactor coolant system vacuum degasification. Procedures for vacuum degasification of the reactor coolant system are described in U.S. Pat. No. 4,647,425 to Battaglia et al, which is assigned to the same assignee as the present invention and is hereby incorporated by reference. Basically, in vacuum degasification of the reactor coolant system a vacuum or negative pressure is imposed on the system and thus on the reactor coolant pumps. This, in effect, pressurizes the pumps in reverse. One major concern is that reverse pressurization might draw the water used to cool the pump sealing assemblies back into the pump sealing assemblies by a reverse flow of the water through filters which might bring contamination in the form of dirt and foreign matter along with the water from the filters into the sealing assemblies. Then, when the pumps are restarted after conclusion of vacuum degasification, the sealing assemblies may become damaged by the presence of the contamination therein. Consequently, a need exists for an effective way to prevent reverse pressurization of the reactor coolant pumps so as to eliminate these concerns about possible damage to the pump sealing assemblies. SUMMARY OF THE INVENTION The present invention provides a reactor coolant pump auxiliary flexible vacuum seal designed to satisfy the aforementioned needs. The auxiliary flexible vacuum seal of the present invention provides a simple and effective way to prepare the reactor coolant pumps so that the reactor coolant system can be vacuum degasified without applying a reverse pressure to the pump sealing assemblies. The auxiliary flexible vacuum seal is an external, temporary seal that would be installed prior to the start of vacuum degasification between the pump sealing housing and shaft, and then removed after degasification is completed. The auxiliary seal accepts the entire reverse pressure, thus preventing any possible damage to the primary, secondary and tertiary pump sealing assemblies of the pump. The auxiliary flexible vacuum seal of the present invention is an alternative to the invention illustrated and described in the eighth patent application cross-referenced above. The flexible vacuum seal offers several advantages over the rigid segmented seal of the cross-referenced application. First, the flexible seal is embodied primarily in the form of a single flexible split boot member with a pair of axially-spaced integral sealing portions, preferably in the form of ring elements, resulting in fewer parts to handle and less sealing length to be concerned with. Second, all parts of the flexible seal are disposable, thus minimizing decontamination and storage requirements. Third, the flexible seal is easier to manipulate within the limited space of the motor stand. Fourth, deviations in concentricity between the shaft and seal housing would be of no concern with the flexible seal. Fifth, the flexible seal fits with the shaft in either its axially-displaced coupled or uncoupled positions. Sixth, the flexible seal can be installed without the need to remove any of the parts of the pump other than some piping and associated coonections. Accordingly, the present invention is directed to an auxiliary flexible vacuum seal useful in a reactor coolant pump ,for preparing the pump for vacuum degasification of the reactor coolant system. The flexible vacuum seal comprises: (a) a flexible boot member having a pair of longitudinally-displaced opposite open end portions and a pair of side-by-side longitudinally-extending side portions defining a split in the boot member along a side thereof and extending between the open end portions for allowing flexing of the boot member between open and closed side configurations to permit its installation and removal on and from the pump; (b) means for releasably and sealably clamping together the side portions of the at the split to retain the boot member in its closed configuration; and (c) a pair of circumferentially-extending sealably portions on the interior of the boot member at the opposite open end portions thereof for sealably engaging the pump when the boot member is installed and flexed to its closed configuration to thereby permit generation of a vacuum seal condition between the boot member and the pump. Further, the flexible seal includes a boot support member disposable within the boot member between the boot member and the pump for supporting the boot member when in its closed configuration. More particularly, the boot support member is annular in shape and composed of a pair of semi-annular parts. The support member also has an upper surface conformed in shape to that of an intermediate portion of the boot member located between its opposite end portions for engagably supporting the boot member at its intermediate portion. Further, the boot support member has a lower surface conformed in shape to that of the pump for mounting the support member thereon. The boot member of the flexible seal includes a bowl-shaped body having the opposite end portions and defining a hollow cavity. The cavity is open at the opposite end portions and openable at the split defined in the body by the side portions of the boot member. The sealably engaging portions on the boot member at the opposite open end portions thereof are preferably rings projecting radially inwardly and formed integrally on the body of the boot member. In the alternative, these sealably engaging portions may be the interior surface of the boot member itself at its opposite open end portions. The side portions of the boot member are in the form of a pair of radially outward-projecting and longitudinally-extending flanges on the body along opposite sides of the split and disposed in side-by-side contacting relation when the boot member is in its closed configuration. The clamping means of the flexible seal includes a pair of brackets mountable along outer sides of said flanges on the boot member body, and a plurality of fasteners extendible through the brackets and flanges therebetween and being operable for drawing the brackets toward one another and withdrawing the brackets away from one another for clamping and releasing the flanges. The present invention is also directed to a method of preparing a reactor coolant pump for vacuum degasification of a reactor coolant system. The preparing method comprises the steps of: (a) sealing a seal housing of the reactor coolant pump by installing a longitudinally split boot member about a portion of the seal housing and about a shaft extending through the housing; (b) reversing the pressure of the reactor coolant system at start of vacuum degasification of the reactor coolant system, the sealing of the pump seal housing preventing damage to sealing assemblies therein by the reversing of reactor coolant system pressure; (c) terminating reversing of the reactor coolant system pressure at completion of vacuum degasification of the reactor coolant system; and (d) unsealing the pump seal housing of the reactor coolant pump by removing the split boot member. Further, the sealing includes stretching the split boot member. These and other features and advantages of the present invention will become apparent to those skilled in the art upon a reading of the following detailed description when taken in conjunction with the drawings wherein there is shown and described an illustrative embodiment of the invention.

abstract

An apparatus for use in the field of dentistry consisting of a rotatable c-arm assembly having a housing with an emitter on one end and a fluoroscopic image receptor at another end, a control panel, three mechanical arms connecting the housing and the control panel to each other, an intraoral image receptor and a plastic holder device for the intraoral image receptor. The apparatus has the improved feature of having two modes of operation, a fluoroscopic mode or a conventional radiographic mode. The mode of operation is selected by the operator by a foot pedal for use in fluoroscopic mode, or a hand activator control for use in conventional mode. A beam of x-rays or gamma rays is emitted from the housing corresponding to the selected mode. The beam is incident on the fluoroscopic image receptor or on the intraoral image receptor and the image is converted to visible light, amplified and transmitted to a computer monitor and/or television set and VCR, thus allowing the observation of dental procedures in real time.

description

This application: is a continuation-in-part of U.S. patent application Ser. No. 12/425,683 filed Apr. 17, 2009, now U.S. Pat. No. 7,939,809 which claims the benefit of: U.S. provisional patent application No. 61/055,395 filed May 22, 2008; U.S. provisional patent application No. 61/137,574 filed Aug. 1, 2008; U.S. provisional patent application No. 61/192,245 filed Sep. 17, 2008; U.S. provisional patent application No. 61/055,409 filed May 22, 2008; U.S. provisional patent application No. 61/203,308 filed Dec. 22, 2008; U.S. provisional patent application No. 61/188,407 filed Aug. 11, 2008; U.S. provisional patent application No. 61/188,406 filed Aug. 11, 2008; U.S. provisional patent application No. 61/189,815 filed Aug. 25, 2008; U.S. provisional patent application No. 61/201,731 filed Dec. 15, 2008; U.S. provisional patent application No. 61/205,362 filed Jan. 21, 2009; U.S. provisional patent application No. 61/134,717 filed Jul. 14, 2008; U.S. provisional patent application No. 61/134,707 filed Jul. 14, 2008; U.S. provisional patent application No. 61/201,732 filed Dec. 15, 2008; U.S. provisional patent application No. 61/198,509 filed Nov. 7, 2008; U.S. provisional patent application No. 61/134,718 filed Jul. 14, 2008; U.S. provisional patent application No. 61/190,613 filed Sep. 2, 2008; U.S. provisional patent application No. 61/191,043 filed Sep. 8, 2008; U.S. provisional patent application No. 61/192,237 filed Sep. 17, 2008; U.S. provisional patent application No. 61/201,728 filed Dec. 15, 2008; U.S. provisional patent application No. 61/190,546 filed Sep. 2, 2008; U.S. provisional patent application No. 61/189,017 filed Aug. 15, 2008; U.S. provisional patent application No. 61/198,248 filed Nov. 5, 2008; U.S. provisional patent application No. 61/198,508 filed Nov. 7, 2008; U.S. provisional patent application No. 61/197,971 filed Nov. 3, 2008; U.S. provisional patent application No. 61/199,405 filed Nov. 17, 2008; U.S. provisional patent application No. 61/199,403 filed Nov. 17, 2008; and U.S. provisional patent application No. 61/199,404 filed Nov. 17, 2008; claims the benefit of U.S. provisional patent application No. 61/209,529 filed Mar. 9, 2009; claims the benefit of U.S. provisional patent application No. 61/208,182 filed Feb. 23, 2009; claims the benefit of U.S. provisional patent application No. 61/208,971 filed Mar. 3, 2009; claims the benefit of U.S. provisional patent application No. 61/270,298, filed Jul. 7, 2009; and claims priority to PCT patent application serial No.: PCT/RU2009/00015, filed Mar. 4, 2009, all of which are incorporated herein in their entirety by this reference thereto. 1. Field of the Invention This invention relates generally to treatment of solid cancers. More particularly, the invention relates to an X-ray system synchronized to patient respiration, where the synchronized system is used in conjunction with charged particle cancer therapy beam injection, acceleration, extraction, and/or targeting methods and apparatus. 2. Discussion of the Prior Art Cancer Treatment Proton therapy systems typically include: a beam generator, an accelerator, and a beam transport system to move the resulting accelerated protons to a plurality of treatment rooms where the protons are delivered to a tumor in a patient's body. Proton therapy works by aiming energetic ionizing particles, such as protons accelerated with a particle accelerator, onto a target tumor. These particles damage the DNA of cells, ultimately causing their death. Cancerous cells, because of their high rate of division and their reduced ability to repair damaged DNA, are particularly vulnerable to attack on their DNA. Due to their relatively enormous size, protons scatter less easily than X-rays or gamma rays in the tissue and there is very little lateral dispersion. Hence, the proton beam stays focused on the tumor shape without much lateral damage to surrounding tissue. All protons of a given energy have a certain range, defined by the Bragg peak, and the dosage delivery to tissue ratio is maximum over just the last few millimeters of the particle's range. The penetration depth depends on the energy of the particles, which is directly related to the speed to which the particles were accelerated by the proton accelerator. The speed of the proton is adjustable to the maximum rating of the accelerator. It is therefore possible to focus the cell damage due to the proton beam at the very depth in the tissues where the tumor is situated. Tissues situated before the Bragg peak receive some reduced dose and tissues situated after the peak receive none. Patents related to the current invention are summarized here. Proton Beam Therapy System F. Cole, et. al. of Loma Linda University Medical Center “Multi-Station Proton Beam Therapy System”, U.S. Pat. No. 4,870,287 (Sep. 26, 1989) describe a proton beam therapy system for selectively generating and transporting proton beams from a single proton source and accelerator to a selected treatment room of a plurality of patient treatment rooms. Respiration K. Matsuda “Radioactive Beam Irradiation Method and Apparatus Taking Movement of the Irradiation Area Into Consideration”, U.S. Pat. No. 5,538,494 (Jul. 23, 1996) describes a method and apparatus that enables irradiation even in the case of a diseased part changing position due to physical activity, such as breathing and heart beat. Initially, a position change of a diseased body part and physical activity of the patient are measured concurrently and a relationship therebetween is defined as a function. Radiation therapy is performed in accordance to the function. Patient Positioning Y. Nagamine, et. al. “Patient Positioning Device and Patient Positioning Method”, U.S. Pat. No. 7,212,609 (May 1, 2007) and Y. Nagamine, et. al. “Patient Positioning Device and Patient Positioning Method”, U.S. Pat. No. 7,212,608 (May 1, 2007) describe a patient positioning system that compares a comparison area of a reference X-ray image and a current X-ray image of a current patient location using pattern matching. D. Miller, et. al. “Modular Patient Support System”, U.S. Pat. No. 7,173,265 (Feb. 6, 2007) describe a radiation treatment system having a patient support system that includes a modularly expandable patient pod and at least one immobilization device, such as a moldable foam cradle. K. Kato, et. al. “Multi-Leaf Collimator and Medical System Including Accelerator”, U.S. Pat. No. 6,931,100 (Aug. 16, 2005); K. Kato, et. al. “Multi-Leaf Collimator and Medical System Including Accelerator”, U.S. Pat. No. 6,823,045 (Nov. 23, 2004); K. Kato, et. al. “Multi-Leaf Collimator and Medical System Including Accelerator”, U.S. Pat. No. 6,819,743 (Nov. 16, 2004); and K. Kato, et. al. “Multi-Leaf Collimator and Medical System Including Accelerator”, U.S. Pat. No. 6,792,078 (Sep. 14, 2004) all describe a system of leaf plates used to shorten positioning time of a patient for irradiation therapy. Motor driving force is transmitted to a plurality of leaf plates at the same time through a pinion gear. The system also uses upper and lower air cylinders and upper and lower guides to position a patient. Computer Control A. Beloussov et. al. “Configuration Management and Retrieval System for Proton Beam Therapy System”, U.S. Pat. No. 7,368,740 (May 6, 2008); A. Beloussov et. al. “Configuration Management and Retrieval System for Proton Beam Therapy System”, U.S. Pat. No. 7,084,410 (Aug. 1, 2006); and A. Beloussov et. al. “Configuration Management and Retrieval System for Proton Beam Therapy System”, U.S. Pat. No. 6,822,244 (Nov. 23, 2004) all describe a multi-processor software controlled proton beam system having treatment configurable parameters that are easily modified by an authorized user to prepare the software controlled system for various modes of operation to insure that data and configuration parameters are accessible if single point failures occur in the database. J. Hirota et. al. “Automatically Operated Accelerator Using Obtained Operating Patterns”, U.S. Pat. No. 5,698,954 (Dec. 16, 1997) describes a main controller for determining the quantity of control and the control timing of every component of an accelerator body with the controls coming from an operating pattern. Problem There exists in the art of particle beam therapy of cancerous tumors a need for an X-ray system that is synchronized with patient respiration. Preferably, the synchronized system is used in conjunction with a negative ion beam source, synchrotron, and/or targeting method apparatus to provide an X-ray timed with patient respiration and performed immediately prior to and/or concurrently with particle beam therapy irradiation to ensure targeted and controlled delivery of energy relative to a patient position. Further, there exists a need in the art to control the charged particle cancer therapy system in terms of specified energy, intensity, and/or timing of charged particle delivery relative to a patient position. Still further, there exists a need for efficient, precise, and/or accurate noninvasive, in-vivo treatment of a solid cancerous tumor with minimization of damage to surrounding healthy tissue in a patient using the proton beam position verification system. The invention comprises an X-ray method and apparatus operating in conjunction with patient respiration monitoring. The invention relates generally to treatment of solid cancers. More particularly, the invention relates to an X-ray system capable of collecting X-rays of a patient (1) during a period of a respiration cycle and (2) in a positioning system for cancer therapy. Novel design features of a charged particle beam cancer therapy system are described. Particularly, a negative ion beam source with novel features in the negative ion source, ion source vacuum system, ion beam focusing lens, and tandem accelerator is described. Additionally, turning magnets, edge focusing magnets, magnetic field concentration magnets, winding and correction coils, flat magnetic field incident surfaces, and extraction elements are described that minimize the overall size of the synchrotron, provide a tightly controlled proton beam, directly reduce the size of required magnetic fields, directly reduce required operating power, and allow continual acceleration of protons in a synchrotron even during a process of extracting protons from the synchrotron. The ion beam source system and synchrotron are preferably computer integrated with a patient imaging system and a patient interface including respiration monitoring sensors and patient positioning elements. Further, intensity control of a charged particle beam acceleration, extraction, and/or targeting method and apparatus used in conjunction with charged particle beam radiation therapy of cancerous tumors are described. More particularly, intensity, energy, and timing control of a charged particle stream of a synchrotron is described. The synchrotron control elements allow tight control of the charged particle beam, which compliments the tight control of patient positioning to yield efficient treatment of a solid tumor with reduced tissue damage to surrounding healthy tissue. In addition, the system reduces the overall size of the synchrotron, provides a tightly controlled proton beam, directly reduces the size of required magnetic fields, directly reduces required operating power, and allows continual acceleration of protons in a synchrotron even during a process of extracting protons from the synchrotron. All of these systems are preferably used in conjunction with an X-ray system capable of collecting X-rays of a patient in (1) a positioning system for proton treatment and (2) at a specified moment of the patient's respiration cycle. In one embodiment, a treatment delivery control system (TDCS) or main controller is used to control multiple aspects of the cancer therapy system, including one or more of: an imaging system, such as a CT or PET; a positioner, such as a couch or patient interface module; an injector or injection system; a ring accelerator or synchrotron; an extraction system; an irradiation plan; and a display system. The TDCS is preferably a control system for automated cancer therapy once the patient is positioned. The TDCS integrates output of one or more of the above described cancer therapy system elements with inputs of one or more of the above described cancer therapy system elements. More generally, the TDCS controls or manages input and/or output of imaging, an irradiation plan, and charged particle delivery. Charged Particle Beam Therapy Throughout this document, a charged particle beam therapy system, such as a proton beam, hydrogen ion beam, or carbon ion beam, is described. Herein, the charged particle beam therapy system is described using a proton beam. However, the aspects taught and described in terms of a proton beam are not intended to be limiting to that of a proton beam and are illustrative of a charged particle beam system. Any of the techniques described herein are equally applicable to any charged particle system. Referring now to FIG. 1, a charged particle beam system 100 is illustrated. The charged particle beam preferably comprises a number of subsystems including any of: a main controller 110; an injection system 120; a synchrotron 130 that typically includes: (1) an accelerator system 132 and (2) an extraction system 134; a scanning/targeting/delivery system 140; a patient interface module 150; a display system 160; and/or an imaging system 170. An exemplary method of use of the charged particle beam system 100 is provided. The main controller 110 controls one or more of the subsystems to accurately and precisely deliver protons to a tumor of a patient. For example, the main controller 110 obtains an image, such as a portion of a body and/or of a tumor, from the imaging system 170. The main controller 110 also obtains position and/or timing information from the patient interface module 150. The main controller 110 then optionally controls the injection system 120 to inject a proton into a synchrotron 130. The synchrotron typically contains at least an accelerator system 132 and an extraction system 134. The main controller preferably controls the proton beam within the accelerator system, such as by controlling speed, trajectory, and timing of the proton beam. The main controller then controls extraction of a proton beam from the accelerator through the extraction system 134. For example, the controller controls timing, energy, and/or intensity of the extracted beam. The controller 110 also preferably controls targeting of the proton beam through the scanning/targeting/delivery system 140 to the patient interface module 150. One or more components of the patient interface module 150 are preferably controlled by the main controller 110. Further, display elements of the display system 160 are preferably controlled via the main controller 110. Displays, such as display screens, are typically provided to one or more operators and/or to one or more patients. In one embodiment, the main controller 110 times the delivery of the proton beam from all systems, such that protons are delivered in an optimal therapeutic manner to the patient. Herein, the main controller 110 refers to a single system controlling the charged particle beam system 100, to a single controller controlling a plurality of subsystems controlling the charged particle beam system 100, or to a plurality of individual controllers controlling one or more sub-systems of the charged particle beam system 100. Synchrotron Herein, the term synchrotron is used to refer to a system maintaining the charged particle beam in a circulating path. Further, the charged particle beam is referred to herein as circulating along a circulating path about a central point of the synchrotron. The circulating path is alternatively referred to as an orbiting path; however, the orbiting path does not refer to a perfect circle or ellipse, rather it refers to cycling of the protons around a central point or region. Referring now to FIG. 2, an illustrative exemplary embodiment of one version of the charged particle beam system 100 is provided. The number, position, and described type of components is illustrative and non-limiting in nature. In the illustrated embodiment, an injector system 210 or ion source or charged particle beam source generates protons. The protons are delivered into a vacuum tube that runs into, through, and out of the synchrotron. The generated protons are delivered along an initial path 262. Focusing magnets 230, such as quadrupole magnets or injection quadrupole magnets, are used to focus the proton beam path. A quadrupole magnet is a focusing magnet. An injector bending magnet 232 bends the proton beam toward the plane of the synchrotron 130. The focused protons having an initial energy are introduced into an injector magnet 240, which is preferably an injection Lamberson magnet. Typically, the initial beam path 262 is along an axis off of, such as above, a circulating plane of the synchrotron 130. The injector bending magnet 232 and injector magnet 240 combine to move the protons into the synchrotron 130. Main bending magnets 250 or dipole magnets or circulating magnets are used to turn the protons along a circulating beam path 264. A dipole magnet is a bending magnet. The main bending magnets 250 bend the initial beam path 262 into a circulating beam path 264. In this example, the main bending magnets 250 or circulating magnets are represented as four sets of four magnets to maintain the circulating beam path 264 into a stable circulating beam path. However, any number of magnets or sets of magnets are optionally used to move the protons around a single orbit in the circulation process. The protons pass through an accelerator 270. The accelerator accelerates the protons in the circulating beam path 264. As the protons are accelerated, the fields applied by the magnets are increased. Particularly, the speed of the protons achieved by the accelerator 270 are synchronized with magnetic fields of the main bending magnets 250 or circulating magnets to maintain stable circulation of the protons about a central point or region 280 of the synchrotron. At separate points in time the accelerator 270/main bending magnet 250 combination is used to accelerate and/or decelerate the circulating protons while maintaining the protons in the circulating path or orbit. An extraction element of the inflector/deflector system 290 is used in combination with a Lamberson extraction magnet 292 to remove protons from their circulating beam path 264 within the synchrotron 130. One example of a deflector component is a Lamberson magnet. Typically the deflector moves the protons from the circulating plane to an axis off of the circulating plane, such as above the circulating plane. Extracted protons are preferably directed and/or focused using an extraction bending magnet 237 and extraction focusing magnets 235, such as quadrupole magnets along a transport path 268 into the scanning/targeting/delivery system 140. Two components of a scanning system 140 or targeting system typically include a first axis control 142, such as a vertical control, and a second axis control 144, such as a horizontal control. In one embodiment, the first axis control 142 allows for about 100 mm of vertical scanning of the proton beam 268 and the second axis control 144 allows for about 700 mm of horizontal scanning of the proton beam 268. A nozzle system 146 is used for imaging the proton beam and/or as a vacuum barrier between the low pressure beam path of the synchrotron and the atmosphere. Protons are delivered with control to the patient interface module 150 and to a tumor of a patient. All of the above listed elements are optional and may be used in various permutations and combinations. Ion Beam Generation System An ion beam generation system generates a negative ion beam, such as a hydrogen anion or H− beam; preferably focuses the negative ion beam; converts the negative ion beam to a positive ion beam, such as a proton or H+ beam; and injects the positive ion beam into the synchrotron 130. Portions of the ion beam path are preferably under partial vacuum. Each of these systems are further described, infra. Referring now to FIG. 3, an exemplary ion beam generation system 300 is illustrated. As illustrated, the ion beam generation system 300 has four major elements: a negative ion source 310, a first partial vacuum system 330, an optional ion beam focusing system 350, and a tandem accelerator 390. Still referring to FIG. 3, the negative ion source 310 preferably includes an inlet port 312 for injection of hydrogen gas into a high temperature plasma chamber 314. In one embodiment, the plasma chamber includes a magnetic material 316, which provides a magnetic field barrier 317 between the high temperature plasma chamber 314 and a low temperature plasma region on the opposite side of the magnetic field barrier. An extraction pulse is applied to a negative ion extraction electrode 318 to pull the negative ion beam into a negative ion beam path 319, which proceeds through the first partial vacuum system 330, through the ion beam focusing system 350, and into the tandem accelerator 390. Still referring to FIG. 3, the first partial vacuum system 330 is an enclosed system running from the hydrogen gas inlet port 312 to the tandem accelerator 390 foil 395. The foil 395 is sealed directly or indirectly to the edges of the vacuum tube 320 providing for a higher pressure, such as about 10−5 torr, to be maintained on the first partial vacuum system 330 side of the foil 395 and a lower pressure, such as about 10−7 torr, to be maintained on the synchrotron side of the foil 390. By only pumping first partial vacuum system 330 and by only semi-continuously operating the ion beam source vacuum based on sensor readings, the lifetime of the semi-continuously operating pump is extended. The sensor readings are further described, infra. Still referring to FIG. 3, the first partial vacuum system 330 preferably includes: a first pump 332, such as a continuously operating pump and/or a turbo molecular pump; a large holding volume 334; and a semi-continuously operating pump 336. Preferably, a pump controller 340 receives a signal from a pressure sensor 342 monitoring pressure in the large holding volume 334. Upon a signal representative of a sufficient pressure in the large holding volume 334, the pump controller 340 instructs an actuator 345 to open a valve 346 between the large holding volume and the semi-continuously operating pump 336 and instructs the semi-continuously operating pump to turn on and pump to atmosphere residual gases out of the vacuum line 320 about the charged particle stream. In this fashion, the lifetime of the semi-continuously operating pump is extended by only operating semi-continuously and as needed. In one example, the semi-continuously operating pump 336 operates for a few minutes every few hours, such as 5 minutes every 4 hours, thereby extending a pump with a lifetime of about 2,000 hours to about 96,000 hours. Further, by isolating the inlet gas from the synchrotron vacuum system, the synchrotron vacuum pumps, such as turbo molecular pumps can operate over a longer lifetime as the synchrotron vacuum pumps have fewer gas molecules to deal with. For example, the inlet gas is primarily hydrogen gas but may contain impurities, such as nitrogen and carbon dioxide. By isolating the inlet gases in the negative ion source system 310, first partial vacuum system 330, ion beam focusing system 350 and negative ion beam side of the tandem accelerator 390, the synchrotron vacuum pumps can operate at lower pressures with longer lifetimes, which increases the efficiency of the synchrotron 130. Still referring to FIG. 3, the ion beam focusing system 350 includes two or more electrodes where one electrode of each electrode pair partially obstructs the ion beam path with conductive paths 372, such as a conductive mesh. In the illustrated example, two ion beam focusing system sections are illustrated, a two electrode ion focusing section 360 and a three electrode ion focusing section 370. In a given electrode pair, electric field lines, running between the conductive mesh of a first electrode and a second electrode, provide inward forces focusing the negative ion beam. Multiple such electrode pairs provide multiple negative ion beam focusing regions. Preferably the two electrode ion focusing section 360, first three electrode ion focusing section 370, and a second three electrode ion focusing section are placed after the negative ion source and before the tandem accelerator and/or cover a space of about 0.5, 1, or 2 meters along the ion beam path 319. Ion beam focusing systems are further described, infra. Still referring to FIG. 3, the tandem accelerator 390 preferably includes a foil 395, such as a carbon foil. The negative ions in the negative ion beam path 319 are converted to positive ions, such as protons, and the initial ion beam path 262 results. The foil 395 is preferably sealed directly or indirectly to the edges of the vacuum tube 320 providing for a higher pressure, such as about 10−5 torr, to be maintained on the side of the foil 395 having the negative ion beam path 319 and a lower pressure, such as about 10−7 torr, to be maintained on the side of the foil 390 having the proton ion beam path 262. Having the foil 395 physically separating the vacuum chamber 320 into two pressure regions allows for a system having fewer and/or smaller pumps to maintain the lower pressure system in the synchrotron 130 as the inlet hydrogen and its residuals are extracted in a separate contained and isolated space by the first partial vacuum system 330. Negative Ion Source An example of the negative ion source 310 is further described herein. Referring now to FIG. 4, a cross-section of an exemplary negative ion source system 400 is provided. The negative ion beam 319 is created in multiple stages. During a first stage, hydrogen gas is injected into a chamber. During a second stage, a negative ion is created by application of a first high voltage pulse, which creates a plasma about the hydrogen gas to create negative ions. During a third stage, a magnetic field filter is applied to components of the plasma. During a fourth stage, the negative ions are extracted from a low temperature plasma region, on the opposite side of the magnetic field barrier, by application of a second high voltage pulse. Each of the four stages are further described, infra. While the chamber is illustrated as a cross-section of a cylinder, the cylinder is exemplary only and any geometry applies to the magnetic loop containment walls, described infra. In the first stage, hydrogen gas is injected through the inlet port 312 into a high temperature plasma region 490. The injection port 442 is open for a short period of time, such as less than about 1, 5, or 10 microseconds to minimize vacuum pump requirements to maintain vacuum chamber 320 requirements. The high temperature plasma region is maintained at reduced pressure by the partial vacuum system 330. The injection of the hydrogen gas is optionally controlled by the main controller 110, which is responsive to imaging system 170 information and patient interface module 150 information, such as patient positioning and period in a respiration cycle. In the second stage, a high temperature plasma region is created by applying a first high voltage pulse across a first electrode 422 and a second electrode 424. For example a 5 kV pulse is applied for about 20 microseconds with 5 kV at the second electrode 424 and about 0 kV applied at the first electrode 422. Hydrogen in the chamber is broken, in the high temperature plasma region 490, into component parts, such as any of: atomic hydrogen, H0, a proton, H+, an electron, e−, a hydrogen anion, and H−. In the third stage, the high temperature plasma region 490 is at least partially separated from a low temperature plasma region 492 by a magnetic field or magnetic field barrier 430. High energy electrons are restricted from passing through the magnetic field barrier 430. In this manner, the magnetic field barrier 430 acts as a filter between, zone A and zone B, in the negative ion source. Preferably, a central magnetic material 410 is placed within the high temperature plasma region 490, such as along a central axis of the high temperature plasma region 490. Preferably, the first electrode 422 and second electrode 424 are composed of magnetic materials, such as iron. Preferably, the outer walls 450 of the high temperature plasma region, such as cylinder walls, are composed of a magnetic material, such as a permanent magnet, ferric, or iron based material, or a ferrite dielectric ring magnet. In this manner a magnetic field loop is created by: the central magnetic material 410, first electrode 422, the outer walls 450, the second electrode 424, and the magnetic field barrier 430. Again, the magnetic field barrier 430 restricts high energy electrons from passing through the magnetic field barrier 430. Low energy electrons interact with atomic hydrogen, H0, to create a hydrogen anion, H−, in the low temperature plasma region 492. In the fourth stage, a second high voltage pulse or extraction pulse is applied at a third electrode 426. The second high voltage pulse is preferentially applied during the later period of application of the first high voltage pulse. For example, an extraction pulse of about 25 kV is applied for about the last 5 microseconds of the first creation pulse of about 20 microseconds. The potential difference, of about 20 kV, between the third electrode 426 and second electrode 424 extracts the negative ion, H−, from the low temperature plasma region 492 and initiates the negative ion beam 390, from zone B to zone C. The magnetic field barrier 430 is optionally created in number of ways. An example of creation of the magnetic field barrier 430 using coils is provided. In this example, the elements described, supra, in relation to FIG. 4 are maintained with several differences. First, the magnetic field is created using coils. An isolating material is preferably provided between the first electrode 422 and the cylinder walls 450 as well as between the second electrode 424 and the cylinder walls 450. The central material 410 and/or cylinder walls 450 are optionally metallic. In this manner, the coils create a magnetic field loop through the first electrode 422, isolating material, outer walls 450, second electrode 424, magnetic field barrier 430, and the central material 410. Essentially, the coils generate a magnetic field in place of production of the magnetic field by the magnetic material 410. The magnetic field barrier 430 operates as described, supra. Generally, any manner that creates the magnetic field barrier 430 between the high temperature plasma region 490 and low temperature plasma region 492 is functionally applicable to the ion beam extraction system 400. Ion Beam Focusing System Referring now to FIG. 5, the ion beam focusing system 350 is further described. In this example, three electrodes are used. In this example, the first electrode 510 and third electrode 530 are both negatively charged and each is a ring electrode circumferentially enclosing or at least partially enclosing the negative ion beam path 319. The second electrode 520 is positively charged and is also a ring electrode circumferentially enclosing the negative ion beam path. In addition, the second electrode includes one or more conducting paths 372 running through the negative ion beam path 319. For example, the conducting paths are a wire mesh, a conducting grid, or a series of substantially parallel conducting lines running across the second electrode. In use, electric field lines run from the conducting paths of the positively charged electrode to the negatively charged electrodes. For example, in use the electric field lines 540 run from the conducting paths 372 in the negative ion beam path 319 to the negatively charged electrodes 510, 530. Two ray trace lines 550, 560 of the negative ion beam path are used to illustrate focusing forces. In the first ray trace line 550, the negative ion beam encounters a first electric field line at point M. Negatively charged ions in the negative ion beam 550 encounter forces running up the electric field line 571, illustrated with an x-axis component vector 572. The x-axis component force vectors 572 alters the trajectory of the first ray trace line to a inward focused vector 552, which encounters a second electric field line at point N. Again, the negative ion beam 552 encounters forces running up the electric field line 573, illustrated as having an inward force vector with an x-axis component 574, which alters the inward focused vector 552 to a more inward focused vector 554. Similarly, in the second ray trace line 560, the negative ion beam encounters a first electric field line at point O. Negatively charged ions in the negative ion beam encounter forces running up the electric field line 575, illustrated as having a force vector with an x-axis force 576. The inward force vectors 576 alters the trajectory of the second ray trace line 560 to an inward focused vector 562, which encounters a second electric field line at point P. Again, the negative ion beam encounters forces running up the electric field line 577, illustrated as having force vector with an x-axis component 578, which alters the inward focused vector 562 to a more inward focused vector 564. The net result is a focusing effect on the negative ion beam. Each of the force vectors 572, 574, 576, 578 optionally has x and/or y force vector components resulting in a 3-dimensional focusing of the negative ion beam path. Naturally, the force vectors are illustrative in nature, many electric field lines are encountered, and the focusing effect is observed at each encounter resulting in integral focusing. The example is used to illustrate the focusing effect. Still referring to FIG. 5, optionally any number of electrodes are used, such as 2, 3, 4, 5, 6, 7, 8, or 9 electrodes, to focus the negative ion beam path where every other electrode, in a given focusing section, is either positively or negatively charged. For example, three focusing sections are optionally used. In the first ion focusing section 360, a pair of electrodes are used where the first electrode encountered along the negative ion beam path is negatively charged and the second electrode is positively charged, resulting in focusing of the negative ion beam path. In the second ion focusing section 370, two pairs of electrodes are used, where a common positively charged electrode with a conductive mesh running through the negatively ion beam path 319 is used. Thus, in the second ion focusing section 370, the first electrode encountered along the negative ion beam path is negatively charged and the second electrode is positively charged, resulting in focusing of the negative ion beam path. Further, in the second ion focusing section, moving along the negative ion beam path, a second focusing effect is observed between the second positively charged electrode and a third negatively charged electrode. In this example, a third ion focusing section is used that again has three electrodes, which acts in the fashion of the second ion focusing section, describe supra. Referring now to FIG. 6, the central regions of the electrodes in the ion beam focusing system 350 are further described. Referring now to FIG. 6A, the central region of the negatively charged ring electrode 510 is preferably void of conductive material. Referring now to FIGS. 6B-D, the central region of positively charged electrode ring 520 preferably contains conductive paths 372. Preferably, the conductive paths 372 or conductive material within the positively charged electrode ring 520 blocks about 1, 2, 5, or 10 percent of the area and more preferably blocks about 5 percent of the cross-sectional area of the negative ion beam path 319. Referring now to FIG. 6B, one option is a conductive mesh 610. Referring now to FIG. 6C, a second option is a series of conductive lines 620 running substantially in parallel across the positively charged electrode ring 520 that surrounds a portion of the negative ion beam path 319. Referring now to FIG. 6D, a third option is to have a foil 630 or metallic layer cover all of the cross-sectional area of the negative ion beam path with holes punched through the material, where the holes take up about 90-99 percent and more preferably about 95 percent of the area of the foil. More generally, the pair of electrodes are configure to provide electric field lines that provide focusing force vectors to the negative ion beam when the ions in the negative ion beam translate through the electric field lines, as described supra. In an example of a two electrode negative beam ion focusing system having a first cross-sectional diameter, d1, the negative ions are focused using the two electrode system to a second cross-sectional diameter, d2, where d1>d2. Similarly, in an example of a three electrode negative beam ion focusing system is provided having a first cross-sectional diameter, d1, the negative ions are focused using the three electrode system to a third cross-sectional diameter, d3, where d1>d3. For like potentials on the electrodes, the three electrode system provides tighter or stronger focusing compared to the two-electrode system, d3<d2. In the examples provided, supra, of a multi-electrode ion beam focusing system, the electrodes are rings. More generally, the electrodes are of any geometry sufficient to provide electric field lines that provide focusing force vectors to the negative ion beam when the ions in the negative ion beam translate through the electric field lines, as described supra. For example, one negative ring electrode is optionally replaced by a number of negatively charged electrodes, such as about 2, 3, 4, 6, 8, 10, or more electrodes placed about the outer region of a cross-sectional area of the negative ion beam probe. Generally, more electrodes are required to converge or diverge a faster or higher energy beam. In another embodiment, by reversing the polarity of electrodes in the above example, the negative ion beam is made to diverge. Thus, the negative ion beam path is optionally focused and expanded using combinations of electrode pairs. For example, if the electrode having the mesh across the negative ion beam path is made negative, then the negative ion beam path is made to defocus. Hence, combinations of electrode pairs are used for focusing and defocusing a negative ion beam path, such as where a first pair includes a positively charged mesh for focusing and a where a second pair includes a negatively charged mesh for defocusing. Tandem Accelerator Referring now to FIG. 7A, the tandem accelerator 390 is further described. The tandem accelerator accelerates ions using a series of electrodes 710, 711, 712, 713, 714, 715. For example, negative ions, such as H−, in the negative ion beam path are accelerated using a series of electrodes having progressively higher voltages relative to the voltage of the extraction electrode 426, or third electrode 426, of the negative ion beam source 310. For instance, the tandem accelerator 390 optionally has electrodes ranging from the 25 kV of the extraction electrode 426 to about 525 kV near the foil 395 in the tandem accelerator 390. Upon passing through the foil, the negative ion, H−, loses two electrons to yield a proton, H+, according to equation 1.H−→H++2e− (eq. 1) The proton is further accelerated in the tandem accelerator using appropriate voltages at a multitude of further electrodes 713, 714, 715. The protons are then injected into the synchrotron 130 as described, supra. Still referring to FIG. 7, the foil 395 in the tandem accelerator 390 is further described. The foil 395 is preferably a very thin carbon film of about 30 to 200 angstroms in thickness. The foil thickness is designed to both: (1) not block the ion beam and (2) allow the transfer of electrons yielding protons to form the proton beam path 262. The foil 395 is preferably substantially in contact with a support layer 720, such as a support grid. The support layer 720 provides mechanical strength to the foil 395 to combine to form a vacuum blocking element 725. The foil 395 blocks nitrogen, carbon dioxide, hydrogen, and other gases from passing and thus acts as a vacuum barrier. In one embodiment, the foil 395 is preferably sealed directly or indirectly to the edges of the vacuum tube 320 providing for a higher pressure, such as about 10−5 torr, to be maintained on the side of the foil 395 having the negative ion beam path 319 and a lower pressure, such as about 10−7 torr, to be maintained on the side of the foil 395 having the proton ion beam path 262. Having the foil 395 physically separating the vacuum chamber 320 into two pressure regions allows for a vacuum system having fewer and/or smaller pumps to maintain the lower pressure system in the synchrotron 130 as the inlet hydrogen and its residuals are extracted in a separate contained and isolated space by the first partial vacuum system 330. The foil 395 and support layer 720 are preferably attached to the structure 750 of the tandem accelerator 390 or vacuum tube 320 to form a pressure barrier using any mechanical means, such as a metal, plastic, or ceramic ring 730 compressed to the walls with an attachment screw 740. Any mechanical means for separating and sealing the two vacuum chamber sides with the foil 395 are equally applicable to this system. Referring now to FIG. 7B, the support structure 720 and foil 395 are individually viewed in the x-, y-plane. Referring now to FIG. 8, another exemplary method of use of the charged particle beam system 100 is provided. The main controller 110, or one or more sub-controllers, controls one or more of the subsystems to accurately and precisely deliver protons to a tumor of a patient. For example, the main controller sends a message to the patient indicating when or how to breath. The main controller 110 obtains a sensor reading from the patient interface module, such as a temperature breath sensor or a force reading indicative of where in a respiration cycle the subject is. The main controller collects an image, such as a portion of a body and/or of a tumor, from the imaging system 170. The main controller 110 also obtains position and/or timing information from the patient interface module 150. The main controller 110 then optionally controls the injection system 120 to inject hydrogen gas into a negative ion beam source 310 and controls timing of extraction of the negative ion from the negative ion beam source 310. Optionally, the main controller controls ion beam focusing the ion beam focusing lens system 350; acceleration of the proton beam with the tandem accelerator 390; and/or injection of the proton into the synchrotron 130. The synchrotron typically contains at least an accelerator system 132 and an extraction system 134. The synchrotron preferably contains one or more of: turning magnets, edge focusing magnets, magnetic field concentration magnets, winding and correction coils, and flat magnetic field incident surfaces, some of which contain elements under control by the main controller 110. The main controller preferably controls the proton beam within the accelerator system, such as by controlling speed, trajectory, and/or timing of the proton beam. The main controller then controls extraction of a proton beam from the accelerator through the extraction system 134. For example, the controller controls timing, energy, and/or intensity of the extracted beam. The controller 110 also preferably controls targeting of the proton beam through the targeting/delivery system 140 to the patient interface module 150. One or more components of the patient interface module 150 are preferably controlled by the main controller 110, such as vertical position of the patient, rotational position of the patient, and patient chair positioning/stabilization/control elements. Further, display elements of the display system 160 are preferably controlled via the main controller 110. Displays, such as display screens, are typically provided to one or more operators and/or to one or more patients. In one embodiment, the main controller 110 times the delivery of the proton beam from all systems, such that protons are delivered in an optimal therapeutic manner to the patient. Circulating System A synchrotron 130 preferably comprises a combination of straight sections 910 and ion beam turning sections 920. Hence, the circulating path of the protons is not circular in a synchrotron, but is rather a polygon with rounded corners. In one illustrative embodiment, the synchrotron 130, which as also referred to as an accelerator system, has four straight elements and four turning sections. Examples of straight sections 910 include the: inflector 240, accelerator 270, extraction system 290, and deflector 292. Along with the four straight sections are four ion beam turning sections 920, which are also referred to as magnet sections or turning sections. Turning sections are further described, infra. Referring now to FIG. 9, an exemplary synchrotron is illustrated. In this example, protons delivered along the initial proton beam path 262 are inflected into the circulating beam path with the inflector 240 and after acceleration are extracted via a deflector 292 to a beam transport path 268. In this example, the synchrotron 130 comprises four straight sections 910 and four bending or turning sections 920 where each of the four turning sections use one or more magnets to turn the proton beam about ninety degrees. As is further described, infra, the ability to closely space the turning sections and efficiently turn the proton beam results in shorter straight sections. Shorter straight sections allows for a synchrotron design without the use of focusing quadrupoles in the circulating beam path of the synchrotron. The removal of the focusing quadrupoles from the circulating proton beam path results in a more compact design. In this example, the illustrated synchrotron has about a five meter diameter versus eight meter and larger cross-sectional diameters for systems using a quadrupole focusing magnet in the circulating proton beam path. Referring now to FIG. 10, additional description of the first bending or turning section 920 is provided. Each of the turning sections preferably comprises multiple magnets, such as about 2, 4, 6, 8, 10, or 12 magnets. In this example, four turning magnets 1010, 1020, 1030, 1040 in the first turning section 20 are used to illustrate key principles, which are the same regardless of the number of magnets in a turning section 920. A turning magnet 1010 is a particular type of main bending or circulating magnet 250. In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. The Lorentz force is given by equation 2 in terms of magnetic fields with the election field terms not included.F=q(v×B) eq. 2 In equation 2, F is the force in newtons; B is the magnetic field in Teslas; and v is the instantaneous velocity of the particles in meters per second. Referring now to FIG. 11, an example of a single magnet bending or turning section 1010 is expanded. The turning section includes a gap 1110 through which protons circulate. The gap 1110 is preferably a flat gap, allowing for a magnetic field across the gap 1110 that is more uniform, even, and intense. A magnetic field enters the gap 1110 through a magnetic field incident surface and exits the gap 1110 through a magnetic field exiting surface. The gap 1110 runs in a vacuum tube between two magnet halves. The gap 1110 is controlled by at least two parameters: (1) the gap 1110 is kept as large as possible to minimize loss of protons and (2) the gap 1110 is kept as small as possible to minimize magnet sizes and the associated size and power requirements of the magnet power supplies. The flat nature of the gap 1110 allows for a compressed and more uniform magnetic field across the gap 1110. One example of a gap dimension is to accommodate a vertical proton beam size of about 2 cm with a horizontal beam size of about 5 to 6 cm. As described, supra, a larger gap size requires a larger power supply. For instance, if the gap 1110 size doubles in vertical size, then the power supply requirements increase by about a factor of 4. The flatness of the gap 1110 is also important. For example, the flat nature of the gap 1110 allows for an increase in energy of the extracted protons from about 250 to about 330 MeV. More particularly, if the gap 1110 has an extremely flat surface, then the limits of a magnetic field of an iron magnet are reachable. An exemplary precision of the flat surface of the gap 1110 is a polish of less than about five microns and preferably with a polish of about one to three microns. Unevenness in the surface results in imperfections in the applied magnetic field. The polished flat surface spreads unevenness of the applied magnetic field. Still referring to FIG. 11, the charged particle beam moves through the gap 1110 with an instantaneous velocity, v. A first magnetic coil 1120 and a second magnetic coil 1130 run above and below the gap 1110, respectively. Current running through the coils 1120, 1130 results in a magnetic field, B, running through the single magnet turning section 1010. In this example, the magnetic field, B, runs upward, which results in a force, F, pushing the charged particle beam inward toward a central point of the synchrotron, which turns the charged particle beam in an arc. Still referring to FIG. 11, a portion of an optional second magnet bending or turning section 1020 is illustrated. The coils 1120, 1130 typically have return elements 1140, 1150 or turns at the end of one magnet, such as at the end of the first magnet turning section 1010. The turns 1140, 1150 take space. The space reduces the percentage of the path about one orbit of the synchrotron that is covered by the turning magnets. This leads to portions of the circulating path where the protons are not turned and/or focused and allows for portions of the circulating path where the proton path defocuses. Thus, the space results in a larger synchrotron. Therefore, the space between magnet turning sections 1160 is preferably minimized. The second turning magnet is used to illustrate that the coils 1120, 1130 optionally run along a plurality of magnets, such as 2, 3, 4, 5, 6, or more magnets. Coils 1120, 1130 running across multiple turning section magnets allows for two turning section magnets to be spatially positioned closer to each other due to the removal of the steric constraint of the turns, which reduces and/or minimizes the space 1160 between two turning section magnets. Referring now to FIGS. 12 and 13, two illustrative 90 degree rotated cross-sections of single magnet bending or turning sections 1010 are presented. The magnet assembly has a first magnet 1210 and a second magnet 1220. A magnetic field induced by coils, described infra, runs between the first magnet 1210 to the second magnet 1220 across the gap 1110. Return magnetic fields run through a first yoke 1212 and second yoke 1222. The combined cross-section area of the return yokes roughly approximates the cross-sectional area of the first magnet 1210 or second magnet 1220. The charged particles run through the vacuum tube in the gap 1110. As illustrated, protons run into FIG. 12 through the gap 1110 and the magnetic field, illustrated as vector B, applies a force F to the protons pushing the protons towards the center of the synchrotron, which is off page to the right in FIG. 12. The magnetic field is created using windings. A first wire is used to construct a first winding coil 1250 and a second wire is used to construct a second winding coil 1260. Isolating or concentrating gaps 1230, 1240, such as air gaps, isolate the iron based yokes from the gap 1110. The gap 1110 is approximately flat to yield a uniform magnetic field across the gap 1110, as described supra. Still referring to FIG. 13, the ends of a single bending or turning magnet are preferably beveled. Nearly perpendicular or right angle edges of a turning magnet 1010 are represented by dashed lines 1374, 1384. The dashed lines 1374, 1384 intersect at a point 1390 beyond the center of the synchrotron 280. Preferably, the edge of the turning magnet is beveled at angles alpha, α, and beta, β, which are angles formed by a first line 1372, 1382 going from an edge of the turning magnet 1010 and the center 280 and a second line 1374, 1384 going from the same edge of the turning magnet and the intersecting point 1390. The angle alpha is used to describe the effect and the description of angle alpha applies to angle beta, but angle alpha is optionally different from angle beta. The angle alpha provides an edge focusing effect. Beveling the edge of the turning magnet 1010 at angle alpha focuses the proton beam. Multiple turning magnets provide multiple magnet edges that each have edge focusing effects in the synchrotron 130. If only one turning magnet is used, then the beam is only focused once for angle alpha or twice for angle alpha and angle beta. However, by using smaller turning magnets, more turning magnets fit into the turning sections 920 of the synchrotron 130. For example, if four magnets are used in a turning section 920 of the synchrotron, then for a single turning section there are eight possible edge focusing effect surfaces, two edges per magnet. The eight focusing surfaces yield a smaller cross-sectional beam size. This allows the use of a smaller gap 1110. The use of multiple edge focusing effects in the turning magnets results in not only a smaller gap 1110, but also the use of smaller magnets and smaller power supplies. For a synchrotron 130 having four turning sections 920 where each turning sections has four turning magnets and each turning magnet has two focusing edges, a total of thirty-two focusing edges exist for each orbit of the protons in the circulating path of the synchrotron 130. Similarly, if 2, 6, or 8 magnets are used in a given turning section, or if 2, 3, 5, or 6 turning sections are used, then the number of edge focusing surfaces expands or contracts according to equation 3. TFE = NTS * M NTS * FE M eq . ⁢ 3 where TFE is the number of total focusing edges, NTS is the number of turning sections, M is the number of magnets, and FE is the number of focusing edges. Naturally, not all magnets are necessarily beveled and some magnets are optionally beveled on only one edge. The inventors have determined that multiple smaller magnets have benefits over fewer larger magnets. For example, the use of 16 small magnets yields 32 focusing edges whereas the use of 4 larger magnets yields only 8 focusing edges. The use of a synchrotron having more focusing edges results in a circulating path of the synchrotron built without the use of focusing quadrupoles magnets. All prior art synchrotrons use quadrupoles in the circulating path of the synchrotron. Further, the use of quadrupoles in the circulating path necessitates additional straight sections in the circulating path of the synchrotron. Thus, the use of quadrupoles in the circulating path of a synchrotron results in synchrotrons having larger diameters, circulating beam pathlengths, and/or larger circumferences. In various embodiments of the system described herein, the synchrotron has any combination of: at least 4 and preferably 6, 8, 10, or more edge focusing edges per 90 degrees of turn of the charged particle beam in a synchrotron having four turning sections; at least about 16 and preferably about 24, 32, or more edge focusing edges per orbit of the charged particle beam in the synchrotron; only 4 turning sections where each of the turning sections includes at least 4 and preferably 8 edge focusing edges; an equal number of straight sections and turning sections; exactly 4 turning sections; at least 4 edge focusing edges per turning section; no quadrupoles in the circulating path of the synchrotron; a rounded corner rectangular polygon configuration; a circumference of less than 60 meters; a circumference of less than 60 meters and 32 edge focusing surfaces; and/or any of about 8, 16, 24, or 32 non-quadrupole magnets per circulating path of the synchrotron, where the non-quadrupole magnets include edge focusing edges. Referring now to FIG. 12, the incident magnetic field surface 1270 of the first magnet 1210 is further described. FIG. 12 is not to scale and is illustrative in nature. Local imperfections or unevenness in quality of the finish of the incident surface 1270 results in inhomogeneities or imperfections in the magnetic field applied to the gap 1110. Preferably, the incident surface 1270 is flat, such as to within about a zero to three micron finish polish, or less preferably to about a ten micron finish polish. Referring now to FIG. 14, additional optional magnet elements, of the magnet cross-section illustratively represented in FIG. 12, are described. The first magnet 1210 preferably contains an initial cross-sectional distance 1410 of the iron based core. The contours of the magnetic field are shaped by the magnets 1210, 1220 and the yokes 1212, 1222. The iron based core tapers to a second cross-sectional distance 1420. The magnetic field in the magnet preferentially stays in the iron based core as opposed to the gaps 1230, 1240. As the cross-sectional distance decreases from the initial cross-sectional distance 1410 to the final cross-sectional distance 1420, the magnetic field concentrates. The change in shape of the magnet from the longer distance 1410 to the smaller distance 1420 acts as an amplifier. The concentration of the magnetic field is illustrated by representing an initial density of magnetic field vectors 1430 in the initial cross-section 1410 to a concentrated density of magnetic field vectors 1440 in the final cross-section 1420. The concentration of the magnetic field due to the geometry of the turning magnets results in fewer winding coils 1250, 1260 being required and also a smaller power supply to the coils being required. In one example, the initial cross-section distance 1410 is about fifteen centimeters and the final cross-section distance 1420 is about ten centimeters. Using the provided numbers, the concentration of the magnetic field is about 15/10 or 1.5 times at the incident surface 1270 of the gap 1110, though the relationship is not linear. The taper 1460 has a slope, such as about 20, 40, or 60 degrees. The concentration of the magnetic field, such as by 1.5 times, leads to a corresponding decrease in power consumption requirements to the magnets. Referring now to FIG. 15, an additional example of geometry of the magnet used to concentrate the magnetic field is illustrated. As illustrated in FIG. 14, the first magnet 1210 preferably contains an initial cross-sectional distance 1410 of the iron based core. The contours of the magnetic field are shaped by the magnets 1210, 1220 and the yokes 1212, 1222. In this example, the core tapers to a second cross-sectional distance 1420 with a smaller angle theta, θ. As described, supra, the magnetic field in the magnet preferentially stays in the iron based core as opposed to the gaps 1230, 1240. As the cross-sectional distance decreases from the initial cross-sectional distance 1410 to the final cross-sectional distance 1420, the magnetic field concentrates. The smaller angle, theta, results in a greater amplification of the magnetic field in going from the longer distance 1410 to the smaller distance 1420. The concentration of the magnetic field is illustrated by representing an initial density of magnetic field vectors 1430 in the initial cross-section 1410 to a concentrated density of magnetic field vectors 1440 in the final cross-section 1420. The concentration of the magnetic field due to the geometry of the turning magnets results in fewer winding coils 1250, 1260 being required and also a smaller power supply to the winding coils 1250, 1260 being required. Still referring to FIG. 15, optional correction coils 1510, 1520 are illustrated that are used to correct the strength of one or more turning magnets. The correction coils 1520, 1530 supplement the winding coils 1250, 1260. The correction coils 1510, 1520 have correction coil power supplies that are separate from winding coil power supplies used with the winding coils 1250, 1260. The correction coil power supplies typically operate at a fraction of the power required compared to the winding coil power supplies, such as about 1, 2, 3, 5, 7, or 10 percent of the power and more preferably about 1 or 2 percent of the power used with the winding coils 1250, 1260. The smaller operating power applied to the correction coils 1510, 1520 allows for more accurate and/or precise control of the correction coils. The correction coils are used to adjust for imperfection in the turning magnets. Optionally, separate correction coils are used for each turning magnet allowing individual tuning of the magnetic field for each turning magnet, which eases quality requirements in the manufacture of each turning magnet. Referring now to FIG. 16, an example of winding coils and correction coils about a plurality of turning magnets 1610, 1620 in an ion beam turning section 920 is illustrated. One or more high precision magnetic field sensors are placed into the synchrotron and are used to measure the magnetic field at or near the proton beam path. For example, the magnetic sensors are optionally placed between turning magnets and/or within a turning magnet, such as at or near the gap 1110 or at or near the magnet core or yoke. The sensors are part of a feedback system to the correction coils. Thus, the system preferably stabilizes the magnetic field in the synchrotron elements rather than stabilizing the current applied to the magnets. Stabilization of the magnetic field allows the synchrotron to come to a new energy level quickly. This allows the system to be controlled to an operator or algorithm selected energy level with each pulse of the synchrotron and/or with each breath of the patient. The winding and/or correction coils correct 1, 2, 3, or 4 turning magnets, and preferably correct a magnetic field generated by two turning magnets. In the illustrated example, in one case a first correction coil 1610 wraps around a single magnet and in a second case a separately used second correction coil wraps around two or more magnets. A winding or correction coil covering multiple magnets reduces space between magnets as fewer winding or correction coil ends are required, which occupy space. Referring now to FIG. 17A and FIG. 17B, the accelerator system 270, such as a radio-frequency (RF) accelerator system, is further described. The accelerator includes a series of coils 1710-1719, such as iron or ferrite coils, each circumferentially enclosing the vacuum system 320 through which the proton beam 264 passes in the synchrotron 130. Referring now to FIG. 17B, the first coil 1710 is further described. A loop of standard wire 1730 completes at least one turn about the first coil 1710. The loop attaches to a microcircuit 1720. Referring again to FIG. 17A, an RF synthesizer 1740, which is preferably connected to the main controller 110, provides a low voltage RF signal that is synchronized to the period of circulation of protons in the proton beam path 264. The RF synthesizer 1740, microcircuit 1720, loop 1730, and coil 1710 combine to provide an accelerating voltage to the protons in the proton beam path 264. For example, the RF synthesizer 1740 sends a signal to the microcircuit 1720, which amplifies the low voltage RF signal and yields an acceleration voltage, such as about 10 volts. The actual acceleration voltage for a single microcircuit/loop/coil combination is about 5, 10, 15, or 20 volts, but is preferably about 10 volts. Preferably, the RF-amplifier microcircuit and accelerating coil are integrated. Still referring to FIG. 17A, the integrated RF-amplifier microcircuit and accelerating coil presented in FIG. 17B is repeated, as illustrated as the set of coils 1711-1719 surrounding the vacuum tube 320. For example, the RF-synthesizer 1740 under main controller 130 direction, sends an RF-signal to the microcircuits 1720-1729 connected to coils 1710-1719, respectively. Each of the microcircuit/loop/coil combinations generate a proton accelerating voltage, such as about 10 volts each. Hence, a set of five microcircuit/loop/coil combinations generate about 50 volts for proton acceleration. Preferably about 5 to 20 microcircuit/loop/coil combinations are used and more preferably about 9 or 10 microcircuit/loop/coil combinations are used in the accelerator system 270. As a further clarifying example, the RF synthesizer 1740 sends an RF-signal, with a period equal to a period of circulation of a proton about the synchrotron 130, to a set of ten microcircuit/loop/coil combinations, which results in about 100 volts for acceleration of the protons in the proton beam path 264. The 100 volts is generated at a range of frequencies, such as at about 1 MHz for a low energy proton beam to about 15 MHz for a high energy proton beam. The RF-signal is optionally set at an integer multiple of a period of circulation of the proton about the synchrotron circulating path. Each of the microcircuit/loop/coil combinations are optionally independently controlled in terms of acceleration voltage and frequency. Integration of the RF-amplifier microcircuit and accelerating coil, in each microcircuit/loop/coil combination, results in three considerable advantages. First, for synchrotrons, the prior art does not use microcircuits integrated with the accelerating coils but rather uses a set of long cables to provide power to a corresponding set of coils. The long cables have an impedance/resistance, which is problematic for high frequency RF control. As a result, the prior art system is not operable at high frequencies, such as above about 10 MHz. The integrated RF-amplifier microcircuit/accelerating coil system is operable at above about 10 MHz and even 15 MHz where the impedance and/or resistance of the long cables in the prior art systems results in poor control or failure in proton acceleration. Second, the long cable system, operating at lower frequencies, costs about $50,000 and the integrated microcircuit system costs about $1000, which is 50 times less expensive. Third, the microcircuit/loop/coil combinations in conjunction with the RF-amplifier system results in a compact low power consumption design allowing production and use of a proton cancer therapy system is a small space, as described supra, and in a cost effective manner. Referring now to FIG. 18, an example is used to clarify the magnetic field control using a feedback loop 1800 to change delivery times and/or periods of proton pulse delivery. In one case, a respiratory sensor 1810 senses the respiration cycle of the subject. The respiratory sensor sends the information to an algorithm in a magnetic field controller 1820, typically via the patient interface module 150 and/or via the main controller 110 or a subcomponent thereof. The algorithm predicts and/or measures when the subject is at a particular point in the respiration cycle, such as at the bottom of a breath. Magnetic field sensors 1830 are used as input to the magnetic field controller, which controls a magnet power supply 1840 for a given magnetic field 1850, such as within a first turning magnet 1010 of a synchrotron 130. The control feedback loop is thus used to dial the synchrotron to a selected energy level and deliver protons with the desired energy at a selected point in time, such as at the bottom of the breath. More particularly, the main controller injects protons into the synchrotron and accelerates the protons in a manner that combined with extraction delivers the protons to the tumor at a selected point in the respiration cycle. Intensity of the proton beam is also selectable and controllable by the main controller at this stage. The feedback control to the correction coils allows rapid selection of energy levels of the synchrotron that are tied to the patient's respiration cycle. This system is in stark contrast to a system where the current is stabilized and the synchrotron deliver pulses with a period, such as 10 or 20 cycles per second with a fixed period. The feedback or the magnetic field design coupled with the correction coils allows for the extraction cycle to match the varying respiratory rate of the patient. Traditional extraction systems do not allow this control as magnets have memories in terms of both magnitude and amplitude of a sine wave. Hence, in a traditional system, in order to change frequency, slow changes in current must be used. However, with the use of the feedback loop using the magnetic field sensors, the frequency and energy level of the synchrotron are rapidly adjustable. Further aiding this process is the use of a novel extraction system that allows for acceleration of the protons during the extraction process, described infra. Referring again to FIG. 16, an example of a winding coil 1630 that covers two turning magnets 1010, 1020 is provided. Optionally, a first winding coil 1640 covers two magnets and a second winding coil covers another two magnets. As described, supra, this system reduces space between turning section allowing more magnetic field to be applied per radian of turn. A first correction coil 1610 is illustrated that is used to correct the magnetic field for the first turning magnet 1010. A second correction coil 1620 is illustrated that is used to correct the magnetic field for a winding coil 1630 about two turning magnets. Individual correction coils for each turning magnet are preferred and individual correction coils yield the most precise and/or accurate magnetic field in each turning section. Particularly, the individual correction coil 1610 is used to compensate for imperfections in the individual magnet of a given turning section. Hence, with a series of magnetic field sensors, corresponding magnetic fields are individually adjustable in a series of feedback loops, via a magnetic field monitoring system, as an independent coil is used for each turning section. Alternatively, a multiple magnet correction coil is used to correct the magnetic field for a plurality of turning section magnets. Flat Gap Surface While the gap surface is described in terms of the first turning magnet 1010, the discussion applies to each of the turning magnets in the synchrotron. Similarly, while the gap 1110 surface is described in terms of the magnetic field incident surface 1270, the discussion additionally optionally applies to the magnetic field exiting surface 1280. The magnetic field incident surface 1270 of the first magnet 1210 is preferably about flat, such as to within about a zero to three micron finish polish or less preferably to about a ten micron finish polish. By being very flat, the polished surface spreads the unevenness of the applied magnetic field across the gap 1110. The very flat surface, such as about 0, 1, 2, 4, 6, 8, 10, 15, or 20 micron finish, allows for a smaller gap size, a smaller applied magnetic field, smaller power supplies, and tighter control of the proton beam cross-sectional area. Proton Beam Extraction Referring now to FIG. 19, an exemplary proton extraction process from the synchrotron 130 is illustrated. For clarity, FIG. 19 removes elements represented in FIG. 2, such as the turning magnets, which allows for greater clarity of presentation of the proton beam path as a function of time. Generally, protons are extracted from the synchrotron 130 by slowing the protons. As described, supra, the protons were initially accelerated in a circulating path 264, which is maintained with a plurality of main bending magnets 250. The circulating path is referred to herein as an original central beamline 264. The protons repeatedly cycle around a central point in the synchrotron 280. The proton path traverses through a radio frequency (RF) cavity system 1910. To initiate extraction, an RF field is applied across a first blade 1912 and a second blade 1914, in the RF cavity system 1910. The first blade 1912 and second blade 1914 are referred to herein as a first pair of blades. In the proton extraction process, an RF voltage is applied across the first pair of blades, where the first blade 1912 of the first pair of blades is on one side of the circulating proton beam path 264 and the second blade 1914 of the first pair of blades is on an opposite side of the circulating proton beam path 264. The applied RF field applies energy to the circulating charged-particle beam. The applied RF field alters the orbiting or circulating beam path slightly of the protons from the original central beamline 264 to an altered circulating beam path 265. Upon a second pass of the protons through the RF cavity system, the RF field further moves the protons off of the original proton beamline 264. For example, if the original beamline is considered as a circular path, then the altered beamline is slightly elliptical. The applied RF field is timed to apply outward or inward movement to a given band of protons circulating in the synchrotron accelerator. Each orbit of the protons is slightly more off axis compared to the original circulating beam path 264. Successive passes of the protons through the RF cavity system are forced further and further from the original central beamline 264 by altering the direction and/or intensity of the RF field with each successive pass of the proton beam through the RF field. The RF voltage is frequency modulated at a frequency about equal to the period of one proton cycling around the synchrotron for one revolution or at a frequency than is an integral multiplier of the period of one proton cycling about the synchrotron. The applied RF frequency modulated voltage excites a betatron oscillation. For example, the oscillation is a sine wave motion of the protons. The process of timing the RF field to a given proton beam within the RF cavity system is repeated thousands of times with each successive pass of the protons being moved approximately one micrometer further off of the original central beamline 264. For clarity, the approximately 1000 changing beam paths with each successive path of a given band of protons through the RF field are illustrated as the altered beam path 265. With a sufficient sine wave betatron amplitude, the altered circulating beam path 265 touches or traverses a material 1930, such as a foil or a sheet of foil. The foil is preferably a lightweight material, such as beryllium, a lithium hydride, a carbon sheet, or a material of low nuclear charge. A material of low nuclear charge is a material composed of atoms consisting essentially of atoms having six or fewer protons. The foil is preferably about 10 to 150 microns thick, is more preferably 30 to 100 microns thick, and is still more preferably about 40 to 60 microns thick. In one example, the foil is beryllium with a thickness of about 50 microns. When the protons traverse through the foil, energy of the protons is lost and the speed of the protons is reduced. Typically, a current is also generated, described infra. Protons moving at a slower speed travel in the synchrotron with a reduced radius of curvature 266 compared to either the original central beamline 264 or the altered circulating path 265. The reduced radius of curvature 266 path is also referred to herein as a path having a smaller diameter of trajectory or a path having protons with reduced energy. The reduced radius of curvature 266 is typically about two millimeters less than a radius of curvature of the last pass of the protons along the altered proton beam path 265. The thickness of the material 1930 is optionally adjusted to created a change in the radius of curvature, such as about ½, 1, 2, 3, or 4 mm less than the last pass of the protons 265 or original radius of curvature 264. Protons moving with the smaller radius of curvature travel between a second pair of blades. In one case, the second pair of blades is physically distinct and/or are separated from the first pair of blades. In a second case, one of the first pair of blades is also a member of the second pair of blades. For example, the second pair of blades is the second blade 1914 and a third blade 1916 in the RF cavity system 1910. A high voltage DC signal, such as about 1 to 5 kV, is then applied across the second pair of blades, which directs the protons out of the synchrotron through an extraction magnet 292, such as a Lamberson extraction magnet, into a transport path 268. Control of acceleration of the charged particle beam path in the synchrotron with the accelerator and/or applied fields of the turning magnets in combination with the above described extraction system allows for control of the intensity of the extracted proton beam, where intensity is a proton flux per unit time or the number of protons extracted as a function of time. For example, when a current is measured beyond a threshold, the RF field modulation in the RF cavity system is terminated or reinitiated to establish a subsequent cycle of proton beam extraction. This process is repeated to yield many cycles of proton beam extraction from the synchrotron accelerator. Because the extraction system does not depend on any change in magnetic field properties, it allows the synchrotron to continue to operate in acceleration or deceleration mode during the extraction process. Stated differently, the extraction process does not interfere with synchrotron acceleration. In stark contrast, traditional extraction systems introduce a new magnetic field, such as via a hexapole, during the extraction process. More particularly, traditional synchrotrons have a magnet, such as a hexapole magnet, that is off during an acceleration stage. During the extraction phase, the hexapole magnetic field is introduced to the circulating path of the synchrotron. The introduction of the magnetic field necessitates two distinct modes, an acceleration mode and an extraction mode, which are mutually exclusive in time. Charged Particle Beam Intensity Control Control of applied field, such as a radio-frequency (RF) field, frequency and magnitude in the RF cavity system 1910 allows for intensity control of the extracted proton beam, where intensity is extracted proton flux per unit time or the number of protons extracted as a function of time. Referring still to FIG. 19, when protons in the proton beam hit the material 1930 electrons are given off resulting in a current. The resulting current is converted to a voltage and is used as part of a ion beam intensity monitoring system or as part of an ion beam feedback loop for controlling beam intensity. The voltage is optionally measured and sent to the main controller 110 or to a controller subsystem 1940. More particularly, when protons in the charged particle beam path pass through the material 1930, some of the protons lose a small fraction of their energy, such as about one-tenth of a percent, which results in a secondary electron. That is, protons in the charged particle beam push some electrons when passing through material 1930 giving the electrons enough energy to cause secondary emission. The resulting electron flow results in a current or signal that is proportional to the number of protons going through the target material 1930. The resulting current is preferably converted to voltage and amplified. The resulting signal is referred to as a measured intensity signal. The amplified signal or measured intensity signal resulting from the protons passing through the material 1930 is preferably used in controlling the intensity of the extracted protons. For example, the measured intensity signal is compared to a goal signal, which is predetermined in an irradiation of the tumor plan. The difference between the measured intensity signal and the planned for goal signal is calculated. The difference is used as a control to the RF generator. Hence, the measured flow of current resulting from the protons passing through the material 1930 is used as a control in the RF generator to increase or decrease the number of protons undergoing betatron oscillation and striking the material 1930. Hence, the voltage determined off of the material 1930 is used as a measure of the orbital path and is used as a feedback control to control the RF cavity system. Alternatively, the measured intensity signal is not used in the feedback control and is just used as a monitor of the intensity of the extracted protons. As described, supra, the photons striking the material 1930 is a step in the extraction of the protons from the synchrotron 130. Hence, the measured intensity signal is used to change the number of protons per unit time being extracted, which is referred to as intensity of the proton beam. The intensity of the proton beam is thus under algorithm control. Further, the intensity of the proton beam is controlled separately from the velocity of the protons in the synchrotron 130. Hence, intensity of the protons extracted and the energy of the protons extracted are independently variable. For example, protons initially move at an equilibrium trajectory in the synchrotron 130. An RF field is used to excite the protons into a betatron oscillation. In one case, the frequency of the protons orbit is about 10 MHz. In one example, in about one millisecond or after about 10,000 orbits, the first protons hit an outer edge of the target material 130. The specific frequency is dependent upon the period of the orbit. Upon hitting the material 130, the protons push electrons through the foil to produce a current. The current is converted to voltage and amplified to yield a measured intensity signal. The measured intensity signal is used as a feedback input to control the applied RF magnitude, RF frequency, or RF field. Preferably, the measured intensity signal is compared to a target signal and a measure of the difference between the measured intensity signal and target signal is used to adjust the applied RF field in the RF cavity system 1910 in the extraction system to control the intensity of the protons in the extraction step. Stated again, the signal resulting from the protons striking and/or passing through the material 130 is used as an input in RF field modulation. An increase in the magnitude of the RF modulation results in protons hitting the foil or material 130 sooner. By increasing the RF, more protons are pushed into the foil, which results in an increased intensity, or more protons per unit time, of protons extracted from the synchrotron 130. In another example, a detector external to the synchrotron 130 is used to determine the flux of protons extracted from the synchrotron and a signal from the external detector is used to alter the RF field or RF modulation in the RF cavity system 1910. Here the external detector generates an external signal, which is used in a manner similar to the measured intensity signal, described in the preceding paragraphs. In yet another example, when a current from material 130 resulting from protons passing through or hitting material is measured beyond a threshold, the RF field modulation in the RF cavity system is terminated or reinitiated to establish a subsequent cycle of proton beam extraction. This process is repeated to yield many cycles of proton beam extraction from the synchrotron accelerator. In still yet another embodiment, intensity modulation of the extracted proton beam is controlled by the main controller 110. The main controller 110 optionally and/or additionally controls timing of extraction of the charged particle beam and energy of the extracted proton beam. The benefits of the system include a multi-dimensional scanning system. Particularly, the system allows independence in: (1) energy of the protons extracted and (2) intensity of the protons extracted. That is, energy of the protons extracted is controlled by an energy control system and an intensity control system controls the intensity of the extracted protons. The energy control system and intensity control system are optionally independently controlled. Preferably, the main controller 110 controls the energy control system and the main controller simultaneously controls the intensity control system to yield an extracted proton beam with controlled energy and controlled intensity where the controlled energy and controlled intensity are independently variable. Thus the irradiation spot hitting the tumor is under independent control of: time; energy; intensity; x-axis position, where the x-axis represents horizontal movement of the proton beam relative to the patient, and y-axis position, where the y-axis represents vertical movement of the proton beam relative to the patient. In addition, the patient is optionally independently rotated relative to a translational axis of the proton beam at the same time. Referring now to FIG. 20, a proton beam position verification system 2000 is described. A nozzle 2010 provides an outlet for the second reduced pressure vacuum system initiating at the foil 395 of the tandem accelerator 390 and running through the synchrotron 130 to a nozzle foil 2020 covering the end of the nozzle 2010. The nozzle expands in cross-sectional area along the z-axis of the proton beam path 268 to allow the proton beam 268 to be scanned along the x- and y-axes by the vertical control element 142 and horizontal control element 144, respectively. The nozzle foil 2020 is preferably mechanically supported by the outer edges of an exit port of the nozzle 2010. An example of a nozzle foil 2020 is a sheet of about 0.1 inch thick aluminum foil. Generally, the nozzle foil separates atmosphere pressures on the patient side of the nozzle foil 2020 from the low pressure region, such as about 10−5 to 10−7 torr region, on the synchrotron 130 side of the nozzle foil 2020. The low pressure region is maintained to reduce scattering of the proton beam 264, 268. Still referring to FIG. 20, the proton beam verification system 2000 is a system that allows for monitoring of the actual proton beam position 268, 269 in real-time without destruction of the proton beam. The proton beam verification system 2000 preferably includes a proton beam position verification layer 2030, which is also referred to herein as a coating, luminescent, fluorescent, phosphorescent, radiance, or viewing layer. The verification layer or coating layer 2030 is preferably a coating or thin layer substantially in contact with an inside surface of the nozzle foil 2020, where the inside surface is on the synchrotron side of the nozzle foil 2020. Less preferably, the verification layer or coating layer 2030 is substantially in contact with an outer surface of the nozzle foil 2020, where the outer surface is on the patient treatment side of the nozzle foil 2020. Preferably, the nozzle foil 2020 provides a substrate surface for coating by the coating layer, but optionally a separate coating layer support element, on which the coating 2030 is mounted, is placed anywhere in the proton beam path 268. Still referring to FIG. 20, the coating 2030 yields a measurable spectroscopic response, spatially viewable by the detector 2040, as a result of transmission by the proton beam 268. The coating 2030 is preferably a phosphor, but is optionally any material that is viewable or imaged by a detector where the material changes spectroscopically as a result of the proton beam path 268 hitting or transmitting through the coating 2030. A detector or camera 2040 views the coating layer 2030 and determines the current position of the proton beam 268 by the spectroscopic differences resulting from protons passing through the coating layer. For example, the camera 2040 views the coating surface 2030 as the proton beam 268 is being scanned by the horizontal 144 and vertical 142 beam position control elements during treatment of the tumor 2120. The camera 2040 views the current position of the proton beam 268 as measured by spectroscopic response. The coating layer 2030 is preferably a phosphor or luminescent material that glows or emits photons for a short period of time, such as less than 5 seconds for a 50% intensity, as a result of excitation by the proton beam 268. Optionally, a plurality of cameras or detectors 2040 are used, where each detector views all or a portion of the coating layer 2030. For example, two detectors 2040 are used where a first detector views a first half of the coating layer and the second detector views a second half of the coating layer. Preferably, the detector 2040 is mounted into the nozzle 2010 to view the proton beam position after passing through the first axis and second axis controllers 142, 144. Preferably, the coating layer 2030 is positioned in the proton beam path 268 in a position prior to the protons striking the patient 2130. Still referring to FIG. 20, the main controller 130, connected to the camera or detector 2040 output, compares the actual proton beam position 268 with the planned proton beam position and/or a calibration reference to determine if the actual proton beam position 268 is within tolerance. The proton beam verification system 2000 preferably is used in at least two phases, a calibration phase and a proton beam treatment phase. The calibration phase is used to correlate, as a function of x-, y-position of the glowing response the actual x-, y-position of the proton beam at the patient interface. During the proton beam treatment phase, the proton beam position is monitored and compared to the calibration and/or treatment plan to verify accurate proton delivery to the tumor 2120 and/or as a proton beam shutoff safety indicator. Patient Positioning Referring now to FIG. 21, the patient is preferably positioned on or within a patient positioning system 2110 of the patient interface module 150. The patient positioning system 2110 is used to translate the patient and/or rotate the patient into a zone where the proton beam can scan the tumor using a scanning system 140 or proton targeting system, described infra. Essentially, the patient positioning system 2110 performs large movements of the patient to place the tumor near the center of a proton beam path 268 and the proton scanning or targeting system 140 performs fine movements of the momentary beam position 269 in targeting the tumor 2120. To illustrate, FIG. 21 shows the momentary proton beam position 269 and a range of scannable positions 2140 using the proton scanning or targeting system 140, where the scannable positions 2140 are about the tumor 2120 of the patient 2130. This illustratively shows that the y-axis movement of the patient occurs on a scale of the body, such as adjustment of about 1, 2, 3, or 4 feet, while the scannable region of the proton beam 268 covers a portion of the body, such as a region of about 1, 2, 4, 6, 8, 10, or 12 inches. The patient positioning system and its rotation and/or translation of the patient combines with the proton targeting system to yield precise and/or accurate delivery of the protons to the tumor. Referring still to FIG. 21, the patient positioning system 2110 optionally includes a bottom unit 2112 and a top unit 2114, such as discs or a platform. Referring now to FIG. 21A, the patient positioning unit 2110 is preferably y-axis adjustable 2116 to allow vertical shifting of the patient relative to the proton therapy beam 268. Preferably, the vertical motion of the patient positioning unit 2110 is about 10, 20, 30, or 50 centimeters per minute. Referring now to FIG. 21B, the patient positioning unit 2110 is also preferably rotatable 2117 about a rotation axis, such as about the y-axis, to allow rotational control and positioning of the patient relative to the proton beam path 268. Preferably the rotational motion of the patient positioning unit 2110 is about 360 degrees per minute. Optionally, the patient positioning unit rotates about 45, 90, or 180 degrees. Optionally, the patient positioning unit 2110 rotates at a rate of about 45, 90, 180, 360, 720, or 1080 degrees per minute. The rotation of the positioning unit 2117 is illustrated about the rotation axis at two distinct times, t1 and t2. Protons are optionally delivered to the tumor 2120 at n times where each of the n times represent different directions of the incident proton beam 269 hitting the patient 2130 due to rotation of the patient 2117 about the rotation axis. Any of the semi-vertical, sitting, or laying patient positioning embodiments described, infra, are optionally vertically translatable along the y-axis or rotatable about the rotation or y-axis. Preferably, the top and bottom units 2112, 2114 move together, such that they rotate at the same rates and translate in position at the same rates. Optionally, the top and bottom units 2112, 2114 are independently adjustable along the y-axis to allow a difference in distance between the top and bottom units 2112, 2114. Motors, power supplies, and mechanical assemblies for moving the top and bottom units 2112, 2114 are preferably located out of the proton beam path 269, such as below the bottom unit 2112 and/or above the top unit 2114. This is preferable as the patient positioning unit 2110 is preferably rotatable about 360 degrees and the motors, power supplies, and mechanical assemblies interfere with the protons if positioned in the proton beam path 269 Proton Beam Position Control Referring now to FIG. 22, a beam delivery and tissue volume scanning system is illustrated. Presently, the worldwide radiotherapy community uses a method of dose field forming using a pencil beam scanning system. In stark contrast, FIG. 22 illustrates a spot scanning system or tissue volume scanning system. In the tissue volume scanning system, the proton beam is controlled, in terms of transportation and distribution, using an inexpensive and precise scanning system. The scanning system is an active system, where the beam is focused into a spot focal point of about one-half, one, two, or three millimeters in diameter. The focal point is translated along two axes while simultaneously altering the applied energy of the proton beam, which effectively changes the third dimension of the focal point. The system is applicable in combination with the above described rotation of the body, which preferably occurs in-between individual moments or cycles of proton delivery to the tumor. Optionally, the rotation of the body by the above described system occurs continuously and simultaneously with proton delivery to the tumor. For example, in the illustrated system in FIG. 22A, the spot is translated horizontally, is moved down a vertical, and is then back along the horizontal axis. In this example, current is used to control a vertical scanning system having at least one magnet. The applied current alters the magnetic field of the vertical scanning system to control the vertical deflection of the proton beam. Similarly, a horizontal scanning magnet system controls the horizontal deflection of the proton beam. The degree of transport along each axes is controlled to conform to the tumor cross-section at the given depth. The depth is controlled by changing the energy of the proton beam. For example, the proton beam energy is decreased, so as to define a new penetration depth, and the scanning process is repeated along the horizontal and vertical axes covering a new cross-sectional area of the tumor. Combined, the three axes of control allow scanning or movement of the proton beam focal point over the entire volume of the cancerous tumor. The time at each spot and the direction into the body for each spot is controlled to yield the desired radiation does at each sub-volume of the cancerous volume while distributing energy hitting outside of the tumor. The focused beam spot volume dimension is preferably tightly controlled to a diameter of about 0.5, 1, or 2 millimeters, but is alternatively several centimeters in diameter. Preferred design controls allow scanning in two directions with: (1) a vertical amplitude of about 100 mm amplitude and frequency up to 200 Hz; and (2) a horizontal amplitude of about 700 mm amplitude and frequency up to 1 Hz. More or less amplitude in each axis is possible by altering the scanning magnet systems. In FIG. 22A, the proton beam is illustrated along a z-axis controlled by the beam energy, the horizontal movement is along an x-axis, and the vertical direction is along a y-axis. The distance the protons move along the z-axis into the tissue, in this example, is controlled by the kinetic energy of the proton. This coordinate system is arbitrary and exemplary. The actual control of the proton beam is controlled in 3-dimensional space using two scanning magnet systems and by controlling the kinetic energy of the proton beam. The use of the extraction system, described supra, allows for different scanning patterns. Particularly, the system allows simultaneous adjustment of the x-, y-, and z-axes in the irradiation of the solid tumor. Stated again, instead of scanning along an x,y-plane and then adjusting energy of the protons, such as with a range modulation wheel, the system allows for moving along the z-axes while simultaneously adjusting the x- and or y-axes. Hence, rather than irradiating slices of the tumor, the tumor is optionally irradiated in three simultaneous dimensions. For example, the tumor is irradiated around an outer edge of the tumor in three dimensions. Then the tumor is irradiated around an outer edge of an internal section of the tumor. This process is repeated until the entire tumor is irradiated. The outer edge irradiation is preferably coupled with simultaneous rotation of the subject, such as about a vertical y-axis. This system allows for maximum efficiency of deposition of protons to the tumor, as defined using the Bragg peak, to the tumor itself with minimal delivery of proton energy to surrounding healthy tissue. Combined, the system allows for multi-axes control of the charged particle beam system in a small space with a small power supply. For example, the system uses multiple magnets where each magnet has at least one edge focusing effect in each turning section of the synchrotron and/or multiple magnets having concentrating magnetic field geometry, as described supra. The multiple edge focusing effects in the circulating beam path of the synchrotron combined with the concentration geometry of the magnets and described extraction system yields a synchrotron having: a small circumference system, such as less than about 50 meters; a vertical proton beam size gap of about 2 cm; corresponding reduced power supply requirements associated with the reduced gap size; an extraction system not requiring a newly introduced magnetic field; acceleration or deceleration of the protons during extraction; and control of z-axis energy during extraction. The result is a 3-dimensional scanning system, x-, y-, and z-axes control, where the z-axes control resides in the synchrotron and where the z-axes energy is variably controlled during the extraction process inside the synchrotron. Referring now to FIG. 22B, an example of a proton scanning or targeting system 140 used to direct the protons to the tumor with 4-dimensional scanning control is provided, where the 4-dimensional scanning control is along the x-, y-, and z-axes along with intensity control, as described supra. A fifth axis is time. Typically, charged particles traveling along the transport path 268 are directed through a first axis control element 142, such as a vertical control, and a second axis control element 144, such as a horizontal control and into a tumor 2120. As described, supra, the extraction system also allows for simultaneous variation in the z-axis. Further, as describe, supra, the intensity or dose of the extracted beam is optionally simultaneously and independently controlled and varied. Thus instead of irradiating a slice of the tumor, as in FIG. 22A, all four dimensions defining the targeting spot of the proton delivery in the tumor are simultaneously variable. The simultaneous variation of the proton delivery spot is illustrated in FIG. 22B by the spot delivery path 269. In the illustrated case, the protons are initially directed around an outer edge of the tumor and are then directed around an inner radius of the tumor. Combined with rotation of the subject about a vertical axis, a multi-field irradiation process is used where a not yet irradiated portion of the tumor is preferably irradiated at the further distance of the tumor from the proton entry point into the body. This yields the greatest percentage of the proton delivery, as defined by the Bragg peak, into the tumor and minimizes damage to peripheral healthy tissue. Imaging/X-Ray System Herein, an X-ray system is used to illustrate an imaging system. Timing An X-ray is preferably collected either (1) just before or (2) concurrently with treating a subject with proton therapy for a couple of reasons. First, movement of the body, described supra, changes the local position of the tumor in the body relative to other body constituents. If the subject has an X-ray taken and is then bodily moved to a proton treatment room, accurate alignment of the proton beam to the tumor is problematic. Alignment of the proton beam to the tumor using one or more X-rays is best performed at the time of proton delivery or in the seconds or minutes immediately prior to proton delivery and after the patient is placed into a therapeutic body position, which is typically a fixed position or partially immobilized position. Second, the X-ray taken after positioning the patient is used for verification of proton beam alignment to a targeted position, such as a tumor and/or internal organ position. Positioning An X-ray is preferably taken just before treating the subject to aid in patient positioning. For positioning purposes, an X-ray of a large body area is not needed. In one embodiment, an X-ray of only a local area is collected. When collecting an X-ray, the X-ray has an X-ray path. The proton beam has a proton beam path. Overlaying the X-ray path with the proton beam path is one method of aligning the proton beam to the tumor. However, this method involves putting the X-ray equipment into the proton beam path, taking the X-ray, and then moving the X-ray equipment out of the beam path. This process takes time. The elapsed time while the X-ray equipment moves has a couple of detrimental effects. First, during the time required to move the X-ray equipment, the body moves. The resulting movement decreases precision and/or accuracy of subsequent proton beam alignment to the tumor. Second, the time required to move the X-ray equipment is time that the proton beam therapy system is not in use, which decreases the total efficiency of the proton beam therapy system. X-Ray Source Lifetime It is desirable to have components in the particle beam therapy system that require minimal or no maintenance over the lifetime of the particle beam therapy system. For example, it is desirable to equip the proton beam therapy system with an X-ray system having a long lifetime source, such as a lifetime of about 20 years. In one system, described infra, electrons are used to create X-rays. The electrons are generated at a cathode where the lifetime of the cathode is temperature dependent. Analogous to a light bulb, where the filament is kept in equilibrium, the cathode temperature is held in equilibrium at temperatures at about 200, 500, or 1000 degrees Celsius. Reduction of the cathode temperature results in increased lifetime of the cathode. Hence, the cathode used in generating the electrons is preferably held at as low of a temperature as possible. However, if the temperature of the cathode is reduced, then electron emissions also decrease. To overcome the need for more electrons at lower temperatures, a large cathode is used and the generated electrons are concentrated. The process is analogous to compressing electrons in an electron gun; however, here the compression techniques are adapted to apply to enhancing an X-ray tube lifetime. Referring now to FIG. 23, an example of an X-ray generation device 2300 having an enhanced lifetime is provided. Electrons 2320 are generated at a cathode 2310, focused with a control electrode 2312, and accelerated with a series of accelerating electrodes 2340. The accelerated electrons 2350 impact an X-ray generation source 2348 resulting in generated X-rays that are then directed along an X-ray path 2470 to the subject 2130. The concentrating of the electrons from a first diameter 2315 to a second diameter 2316 allows the cathode to operate at a reduced temperature and still yield the necessary amplified level of electrons at the X-ray generation source 2348. In one example, the X-ray generation source is the anode coupled with the cathode 2310 and/or the X-ray generation source is substantially composed of tungsten. Still referring to FIG. 23, a more detailed description of an exemplary X-ray generation device 2300 is described. An anode 2314/cathode 2310 pair is used to generated electrons. The electrons 2320 are generated at the cathode 2310 having a first diameter 2315, which is denoted d1. The control electrodes 2312 attract the generated electrons 2320. For example, if the cathode is held at about −150 kV and the control electrode is held at about −149 kV, then the generated electrons 2320 are attracted toward the control electrodes 2312 and focused. A series of accelerating electrodes 2340 are then used to accelerate the electrons into a substantially parallel path 2350 with a smaller diameter 2316, which is denoted d2. For example, with the cathode held at −150 kV, a first, second, third, and fourth accelerating electrodes 2342, 2344, 2346, 2348 are held at about −120, −90, −60, and −30 kV, respectively. If a thinner body part is to be analyzed, then the cathode 2310 is held at a smaller level, such as about −90 kV and the control electrode, first, second, third, and fourth electrode are each adjusted to lower levels. Generally, the voltage difference from the cathode to fourth electrode is less for a smaller negative voltage at the cathode and vise-versa. The accelerated electrons 2350 are optionally passed through a magnetic lens 2360 for adjustment of beam size, such as a cylindrical magnetic lens. The electrons are also optionally focused using quadrupole magnets 2370, which focus in one direction and defocus in another direction. The accelerated electrons 2350, which are now adjusted in beam size and focused strike an X-ray generation source 2348, such as tungsten, resulting in generated X-rays that pass through an optional blocker 2462 and proceed along an X-ray path 2370 to the subject. The X-ray generation source 2348 is optionally cooled with a cooling element 2349, such as water touching or thermally connected to a backside of the X-ray generation source 2348. The concentrating of the electrons from a first diameter 2315 to a second diameter 2316 allows the cathode to operate at a reduced temperature and still yield the necessary amplified level of electrons at the X-ray generation source 2348. More generally, the X-ray generation device 2300 produces electrons having initial vectors. One or more of the control electrode 2312, accelerating electrodes 2340, magnetic lens 2360, and quadrupole magnets 2370 combine to alter the initial electron vectors into parallel vectors with a decreased cross-sectional area having a substantially parallel path, referred to as the accelerated electrons 2350. The process allows the X-ray generation device 2300 to operate at a lower temperature. Particularly, instead of using a cathode that is the size of the electron beam needed, a larger electrode is used and the resulting electrons 2320 are focused and/or concentrated into the required electron beam needed. As lifetime is roughly an inverse of current density, the concentration of the current density results in a larger lifetime of the X-ray generation device. A specific example is provided for clarity. If the cathode has a 15 mm radius or d1 is about 30 mm, then the area (π r2) is about 225 mm2 times pi. If the concentration of the electrons achieves a radius of 5 mm or d2 is about 10 mm, then the area (π r2) is about 25 mm2 times pi. The ratio of the two areas is about 9 (225π/257π). Thus, there is about 9 times less density of current at the larger cathode compared to the traditional cathode having an area of the desired electron beam. Hence, the lifetime of the larger cathode approximates 9 times the lifetime of the traditional cathode, though the actual current through the larger cathode and traditional cathode is about the same. Preferably, the area of the cathode 2310 is about 2, 4, 6, 8, 10, 15, 20, or 25 times that of the cross-sectional area of the substantially parallel electron beam 2350. In another embodiment of the invention, the quadrupole magnets 2370 result in an oblong cross-sectional shape of the electron beam 2350. A projection of the oblong cross-sectional shape of the electron beam 2350 onto the X-ray generation source 2348 results in an X-ray beam that has a small spot in cross-sectional view, which is preferably substantially circular in cross-sectional shape, that is then passed through the patient 2330. The small spot is used to yield an X-ray having enhanced resolution at the patient. Referring now to FIG. 24, in one embodiment, an X-ray is generated close to, but not in, the proton beam path. A proton beam therapy system and an X-ray system combination 2400 is illustrated in FIG. 24. The proton beam therapy system has a proton beam 268 in a transport system after the Lamberson extraction magnet 292 of the synchrotron 130. The proton beam is directed by the scanning/targeting/delivery system 140 to a tumor 2120 of a patient 2130. The X-ray system 2405 includes an electron beam source 2305 generating an electron beam 2350. The electron beam is directed to an X-ray generation source 2348, such as a piece of tungsten. Preferably, the tungsten X-ray source is located about 1, 2, 3, 5, 10, 15, or 20 millimeters from the proton beam path 268. When the electron beam 2350 hits the tungsten, X-rays are generated in all directions. X-rays are blocked with a port 2462 and are selected for an X-ray beam path 2470. The X-ray beam path 2470 and proton beam path 268 run substantially in parallel as they progress to the tumor 2120. The distance between the X-ray beam path 2470 and proton beam path 269 preferably diminishes to near zero and/or the X-ray beam path 2470 and proton beam path 269 overlap by the time they reach the tumor 2120. Simple geometry shows this to be the case given the long distance, of at least a meter, between the tungsten and the tumor 2120. The distance is illustrated as a gap 2480 in FIG. 24. The X-rays are detected at an X-ray detector 2490, which is used to form an image of the tumor 2120 and/or position of the patient 2130. As a whole, the system generates an X-ray beam that lies in substantially the same path as the proton therapy beam. The X-ray beam is generated by striking a tungsten or equivalent material with an electron beam. The X-ray generation source is located proximate to the proton beam path. Geometry of the incident electrons, geometry of the X-ray generation material, and/or geometry of the X-ray beam blocker 262 yield an X-ray beam that runs either in substantially in parallel with the proton beam or results in an X-ray beam path that starts proximate the proton beam path an expands to cover and transmit through a tumor cross-sectional area to strike an X-ray detector array or film allowing imaging of the tumor from a direction and alignment of the proton therapy beam. The X-ray image is then used to control the charged particle beam path to accurately and precisely target the tumor, and/or is used in system verification and validation. Referring now to FIG. 25, additional geometry of the electron beam path 2350 and X-ray beam path 2470 is illustrated. Particularly, the electron beam 2350 is shown as an expanded electron beam path 2352, 2354. Also, the X-ray beam path 2470 is shown as an expanded X-ray beam path 2472, 2474. Referring now to FIG. 26, a 3-dimensional (3-D) X-ray tomography system 2600 is presented. In a typical X-ray tomography system, the X-ray source and detector rotationally translate about a stationary subject. In the X-ray tomography system described herein, the X-ray source and detector are stationary and the patient 2130 rotates. The stationary X-ray source allows a system where the X-ray source 2348 is proximate the proton therapy beam path 268, as described supra. In addition, the rotation of the patient 2130 allows the proton dosage to be distributed around the body, rather than being concentrated on one static entrance side of the body. Further, the 3-D X-ray tomography system allows for simultaneous updates of the tumor position relative to body constituents in real-time during proton therapy treatment of the tumor 2120 in the patient 2130. The X-ray tomography system is further described, infra. In a first step of the X-ray tomography system 2600, the patient 2130 is positioned relative to the X-ray beam path 2470 and proton beam path 268 using a patient semi-immobilization/placement system 2800, described infra. After patient 2130 positioning, a series of reference 2-D X-ray images are collected, on a detector array 2490 or film, of the patient 2130 and tumor 2120 as the subject is rotated about a y-axis 2117. For example, a series of about 50, 100, 200, or 400 X-ray images of the patient are collected as the patient is rotated. In a second example, an X-ray image is collected with each n degrees of rotation of the patient 2130, where n is about ½, 1, 2, 3, or 5 degrees of rotation. Preferably, about 200 images are collected during one full rotation of the patient through 360 degrees. Subsequently, using the reference 2-D X-ray images, an algorithm produces a reference 3-D picture of the tumor 2120 relative to the patient's constituent body parts. A tumor 2120 irradiation plan is made using the 3-D picture of the tumor 2120 and the patient's constituent body parts. Creation of the proton irradiation plan is optionally performed after the patient has moved from the X-ray imaging area. In a second step, the patient 2130 is repositioned relative to the X-ray beam path 2470 and proton beam path 268 using the patient semi-immobilization/placement system 2800. Just prior to implementation of the proton irradiation plan, a few comparative X-ray images of the patient 2130 and tumor 2120 are collected at a limited number of positions using the X-ray tomography system 2600 setup. For example, a single X-ray image is collected with the patient positioned straight on, at angles of plus/minus forty-five degrees, and/or at angles of plus/minus ninety degrees relative to the proton beam path 268. The actual orientation of the patient 2130 relative to the proton beam path 268 is optionally any orientation. The actual number of comparative X-ray images is also optionally any number of images, though the preferable number of comparative X-ray images is about 2 to 5 comparative images. The comparative X-ray images are compared to the reference X-ray images and differences are detected. A medical expert or an algorithm determines if the difference between the reference images and the comparative images is significant. Based upon the differences, the medical expert or algorithm determines if: proton treatment should commence, be halted, or adapted in real-time. For example, if significant differences in the X-ray images are observed, then the treatment is preferably halted and the process of collecting a reference 3-D picture of the patient's tumor is reinitiated. In a second example, if the differences in the X-ray images are observed to be small, then the proton irradiation plan commences. In a third example, the algorithm or medical expert can adapt the proton irradiation plan in real-time to adjust for differences in tumor location resulting from changes in position of the tumor 2120 in the patient 2130 or from differences in the patient 2130 placement. In the third example, the adaptive proton therapy increases patient throughput and enhances precision and accuracy of proton irradiation of the tumor 2120 relative to the healthy tissue of the patient 2130. Patient Immobilization Accurate and precise delivery of a proton beam to a tumor of a patient requires: (1) positioning control of the proton beam and (2) positioning control of the patient. As described, supra, the proton beam is controlled using algorithms and magnetic fields to a diameter of about 0.5, 1, or 2 millimeters. This section addresses partial immobilization, restraint, and/or alignment of the patient to insure the tightly controlled proton beam efficiently hits a target tumor and not surrounding healthy tissue as a result of patient movement. In this section an x-, y-, and z-axes coordinate system and rotation axis is used to describe the orientation of the patient relative to the proton beam. The z-axis represent travel of the proton beam, such as the depth of the proton beam into the patient. When looking at the patient down the z-axis of travel of the proton beam, the x-axis refers to moving left or right across the patient and the y-axis refers to movement up or down the patient. A first rotation axis is rotation of the patient about the y-axis and is referred to herein as a rotation axis, bottom unit 2112 rotation axis, or y-axis of rotation. In addition, tilt is rotation about the x-axis, yaw is rotation about the y-axis, and roll is rotation about the z-axis. In this coordinate system, the proton beam path 269 optionally runs in any direction. As an illustrative matter, the proton beam path running through a treatment room is described as running horizontally through the treatment room. In this section, three examples of positioning systems are provided: (1) a semi-vertical partial immobilization system 2700; (2) a sitting partial immobilization system 2800; and (3) a laying position 2900. Elements described for one immobilization system apply to other immobilization systems with small changes. For example, a head rest will adjust along one axis for a reclined position, along a second axis for a seated position, and along a third axis for a laying position. However, the headrest itself is similar for each immobilization position. Vertical Patient Positioning/Immobilization The semi-vertical patient positioning system 2700 is preferably used in conjunction with proton therapy of tumors in the torso. The patient positioning and/or immobilization system controls and/or restricts movement of the patient during proton beam therapy. In a first partial immobilization embodiment, the patient is positioned in a semi-vertical position in a proton beam therapy system. As illustrated, the patient is reclining at an angle alpha, α, about 45 degrees off of the y-axis as defined by an axis running from head to foot of the patient. More generally, the patient is optionally completely standing in a vertical position of zero degrees off the of y-axis or is in a semi-vertical position alpha that is reclined about 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, or 65 degrees off of the y-axis toward the z-axis. Patient positioning constraints 2715 are used to maintain the patient in a treatment position, including one or more of: a seat support 2720, a back support 2730, a head support 2740, an arm support 2750, a knee support 2760, and a foot support 2770. The constraints are optionally and independently rigid or semi-rigid. Examples of a semi-rigid material include a high or low density foam or a visco-elastic foam. For example the foot support is preferably rigid and the back support is preferably semi-rigid, such as a high density foam material. One or more of the positioning constraints 2715 are movable and/or under computer control for rapid positioning and/or immobilization of the patient. For example, the seat support 2720 is adjustable along a seat adjustment axis 2722, which is preferably the y-axis; the back support 2730 is adjustable along a back support axis 2732, which is preferably dominated by z-axis movement with a y-axis element; the head support 2740 is adjustable along a head support axis 2742, which is preferably dominated by z-axis movement with a y-axis element; the arm support 2750 is adjustable along an arm support axis 2752, which is preferably dominated by z-axis movement with a y-axis element; the knee support 2760 is adjustable along a knee support axis 2762, which is preferably dominated by y-axis movement with a z-axis element; and the foot support 2770 is adjustable along a foot support axis 2772, which is preferably dominated by y-axis movement with a z-axis element. If the patient is not facing the incoming proton beam, then the description of movements of support elements along the axes change, but the immobilization elements are the same. An optional camera 2780 is used with the patient immobilization system. The camera views the patient/subject creating an video image. The image is provided to one or more operators of the charged particle beam system and allows the operators a safety mechanism for determining if the subject has moved or desires to terminate the proton therapy treatment procedure. Based on the video image, the operators optionally suspend or terminate the proton therapy procedure. For example, if the operator observes via the video image that the subject is moving, then the operator has the option to terminate or suspend the proton therapy procedure. An optional video display 490 is provided to the patient. The video display optionally presents to the patient any of: operator instructions, system instructions, status of treatment, or entertainment. Motors for positioning the constraints 2715, the camera 2780, and video display 2790 are preferably mounted above or below the proton path. Respiration control is optionally performed by using the video display. As the patient breathes, internal and external structures of the body move in both absolute terms and in relative terms. For example, the outside of the chest cavity and internal organs both have absolute moves with a breath. In addition, the relative position of an internal organ relative to another body component, such as an outer region of the body, a bone, support structure, or another organ, moves with each breath. Hence, for more accurate and precise tumor targeting, the proton beam is preferably delivered at point a in time where the position of the internal structure or tumor is well defined, such as at the bottom of each breath. The video display is used to help coordinate the proton beam delivery with the patient's respiration cycle. For example, the video display optionally displays to the patient a command, such as a hold breath statement, a breath statement, a countdown indicating when a breath will next need to be held, or a countdown until breathing may resume. Sitting Patient Positioning/Immobilization In a second partial immobilization embodiment, the patient is partially restrained in a seated position 2800. The sitting restraint system has support structures that are similar to the support structures used in the semi-vertical positioning system, described supra with the exception that the seat support is replaced by a chair and the knee support is not required. The seated restraint system generally retains the adjustable support, rotation about the y-axis, camera, video, and breath control parameters described in the semi-vertical embodiment, described supra. Referring now to FIG. 28, a particular example of a sitting patient semi-immobilization system 2800 is provided. The sitting system is preferably used for treatment of head and neck tumors. As illustrated, the patient is positioned in a seated position on a chair 2810 for particle therapy. The patient is further immobilized using any of the: the head support 2740, the back support 2730, a hand support 2750, the knee support 2760, and the foot support 2770. The supports 2720, 2730, 2740, 2750, 2760, 2770 preferably have respective axes of adjustment 2722, 2732, 2742, 2752, 2762, 2772 as illustrated. The chair 2810 is either readily removed to allow for use of a different patient constraint system or adapts to a new patient position, such as the semi-vertical system. Laying Patient Positioning/Immobilization In a third partial immobilization embodiment, the patient is partially restrained in a laying position. The laying restraint system 2900 has support structures that are similar to the support structures used in the sitting positioning system and semi-vertical positioning system, described supra. In the laying position, optional restraint, support, or partial immobilization elements include one or more of: the head support 2740 and the back support, hip, and shoulder 2730 support. The supports preferably have respective axes of adjustment that are rotated as appropriate for a laying position of the patient. The laying position restraint system generally retains the adjustable supports, rotation about the y-axis, camera, video, and breath control parameters described in the semi-vertical embodiment, described supra. If the patient is very sick, such as the patient has trouble standing for a period of about one to three minutes required for treatment, then being in a partially supported system can result in some movement of the patient due to muscle strain. In this and similar situations, treatment of a patient in a laying position on a support table 2920 is preferentially used. The support table has a horizontal platform to support the bulk of the weight of the patient. Preferably, the horizontal platform is detachable from a treatment platform. In a laying positioning system 2900, the patient is positioned on a platform 2910, which has a substantially horizontal portion for supporting the weight of the body in a horizontal position. Optional hand grips are used, described infra. In one embodiment, the platform 2910 affixes relative to the table 2920 using a mechanical stop or lock element 2930 and matching key element 2935 and/or the patient 2130 is aligned or positioned relative to a placement element 2960. Additionally, upper leg support 2944, lower leg support 2940, and/or arm support 2950 elements are optionally added to raise, respectively, an arm or leg out of the proton beam path 269 for treatment of a tumor in the torso or to move an arm or leg into the proton beam path 269 for treatment of a tumor in the arm or leg. This increases proton delivery efficiency, as described infra. The leg supports 2940, 2944 and arm support 2950 are each optionally adjustable along support axes 2942, 2946, 2952. One or more leg support elements are optionally adjustable along an arc to position the leg into the proton beam path 269 or to remove the leg from the proton beam path 269, as described infra. An arm support element is preferably adjustable along at least one arm adjustment axis or along an arc to position the arm into the proton beam path 269 or to remove the arm from the proton beam path 269, as described infra. Preferably, the patient is positioned on the platform 2910 in an area or room outside of the proton beam path 269 and is wheeled or slid into the treatment room or proton beam path area. For example, the patient is wheeled into the treatment room on a gurney where the top of the gurney, which is the platform, detaches and is positioned onto a table. The platform is preferably lifted onto the table or slid onto the table so that the gurney or bed need not be lifted onto the table. The semi-vertical patient positioning system 2700 and sitting patient positioning system 2800 are preferentially used to treatment of tumors in the head or torso due to efficiency. The semi-vertical patient positioning system 2700, sitting patient positioning system 2800, and laying patient positioning system 2900 are all usable for treatment of tumors in the patient's limbs. Support System Elements Positioning constraints 2715 include all elements used to position the patient, such as those described in the semi-vertical positioning system 2700, sitting positioning system 2800, and laying positioning system 2900. Preferably, positioning constraints or support system elements are aligned in positions that do not impede or overlap the proton beam path 269. However, in some instances the positioning constraints are in the proton beam path 269 during at least part of the time of treatment of the patient. For instance, a positioning constraint element may reside in the proton beam path 269 during part of a time period where the patient is rotated about the y-axis during treatment. In cases or time periods that the positioning constraints or support system elements are in the proton beam path, then an upward adjustment of proton beam energy is preferably applied that increases the proton beam energy to offset the positioning constraint element impedance of the proton beam, this time period and energy is a function of rotational orientation of the patient. In one case, the proton beam energy is increased by a separate measure of the positioning constraint element impedance determined during a reference scan of the positioning constraint system element or set of reference scans of the positioning constraint element as a function of rotation about the y-axis. For clarity, the positioning constraints 2715 or support system elements are herein described relative to the semi-vertical positioning system 2700; however, the positioning elements and descriptive x-, y-, and z-axes are adjustable to fit any coordinate system, to the sitting positioning system, or the laying positioning system. An example of a head support system is described to support, align, and/or restrict movement of a human head. The head support system preferably has several head support elements including any of: a back of head support, a right of head alignment element, and a left of head alignment element. The back of head support element is preferably curved to fit the head and is optionally adjustable along a head support axis, such as along the z-axis. Further, the head supports, like the other patient positioning constraints, is preferably made of a semi-rigid material, such as a low or high density foam, and has an optional covering, such as a plastic or leather. The right of head alignment element and left of head alignment elements or head alignment elements, are primarily used to semi-constrain movement of the head. The head alignment elements are preferably padded and flat, but optionally have a radius of curvature to fit the side of the head. The right and left head alignment elements are preferably respectively movable along translation axes to make contact with the sides of the head. Restricted movement of the head during proton therapy is important when targeting and treating tumors in the head or neck. The head alignment elements and the back of head support element combine to restrict tilt, rotation or yaw, roll and/or position of the head in the x-, y-, z-axes coordinate system. Referring now to FIG. 30 another example of a head support system 3000 is described for positioning and/or restricting movement of a human head 2102 during proton therapy of a solid tumor in the head or neck. In this system, the head is restrained using 1, 2, 3, 4, or more straps or belts, which are preferably connected or replaceably connected to a back of head support element 3010. In the example illustrated, a first strap 3020 pulls or positions the forehead to the head support element 3010, such as by running predominantly along the z-axis. Preferably a second strap 3030 works in conjunction with the first strap 3020 to prevent the head from undergoing tilt, yaw, roll or moving in terms of translational movement on the x-, y-, and z-axes coordinate system. The second strap 3030 is preferably attached or replaceable attached to the first strap 3020 at or about: (1) a forehead position 3032; (2) at a position on one or both sides of the head 3034; and/or (3) at or about the support element position 3036. A third strap 3040 preferably orientates the chin of the subject relative to the support element 3010 by running dominantly along the z-axis. A fourth strap 3050 preferably runs along a predominantly y- and z-axes to hold the chin relative to the head support element 3010 and/or proton beam path. The third 3040 strap preferably is attached to or is replaceably attached to the fourth strap 3050 during use at or about the patient's chin position 3042. The second strap 3030 optionally connects to the fourth strap 3050 at or about the support element 3010. The four straps 3020, 3030, 3040, 3050 are illustrative in pathway and interconnection. Any of the straps optionally hold the head along different paths around the head and connect to each other in separate fashion. Naturally, a given strap preferably runs around the head and not just on one side of the head. Any of the straps 3020, 3030, 3040, and 3050 are optionally used independently or in combinations or permutations with the other straps. The straps are optionally indirectly connected to each other via a support element, such as the head support element 3010. The straps are optionally attached to the head support element 3010 using hook and loop technology, a buckle, or fastener. Generally, the straps combine to control position, front-to-back movement of the head, side-to-side movement of the head, tilt, yaw, roll, and/or translational position of the head. The straps are preferably of known impedence to proton transmission allowing a calculation of peak energy release along the z-axis to be calculated, such as an adjustment to the Bragg peak is made based on the slowing tendency of the straps to proton transport. Referring now to FIG. 28, still another example of a head support system 2740 is described. The head support 2740 is preferably curved to fit a standard or child sized head. The head support 2740 is optionally adjustable along a head support axis 2742. Further, the head supports, like the other patient positioning constraints, is preferably made of a semi-rigid material, such as a low or high density foam, and has an optional covering, such as a plastic or leather. Elements of the above described head support, head positioning, and head immobilization systems are optionally used separately or in combination. Still referring to FIG. 31, an example of the arm support 2750 is further described. The arm support preferably has a left hand grip 3110 and a right hand grip 3120 used for aligning the upper body of the patient 2130 through the action of the patient 2130 gripping the left and right hand grips 3110, 3120 with the patient's hands 2134. The left and right hand grips 3110, 3120 are preferably connected to the arm support 2750 that supports the mass of the patient's arms. The left and right hand grips 3110, 3120 are preferably constructed using a semi-rigid material. The left and right hand grips 3110, 3120 are optionally molded to the patient's hands to aid in alignment. The left and right hand grips optionally have electrodes, as described supra. Positioning System Computer Control One or more of the patient positioning unit components and/or one of more of the patient positioning constraints are preferably under computer control, where the computer control positioning devices, such as via a series of motors and drives, to reproducibly position the patient. For example, the patient is initially positioned and constrained by the patient positioning constraints. The position of each of the patient positioning constraints is recorded and saved by the main controller 110, by a sub-controller or the main controller 110, or by a separate computer controller. Then, medical devices are used to locate the tumor 2120 in the patient 2130 while the patient is in the orientation of final treatment. The imaging system 170 includes one or more of: MRI's, X-rays, CT's, proton beam tomography, and the like. Time optionally passes at this point where images from the imaging system 170 are analyzed and a proton therapy treatment plan is devised. The patient may exit the constraint system during this time period, which may be minutes, hours, or days. Upon return of the patient to the patient positioning unit, the computer can return the patient positioning constraints to the recorded positions. This system allows for rapid repositioning of the patient to the position used during imaging and development of the treatment plan, which minimizes setup time of patient positioning and maximizes time that the charged particle beam system 100 is used for cancer treatment. Proton Delivery Efficiency A Bragg peak energy profile shows that protons deliver their energy across the entire length of the body penetrated by the proton up to a maximum penetration depth. As a result, energy is being delivered to healthy tissue, bone, and other body constituents before the proton beam hits the tumor. It follows that the shorter the pathlength in the body prior to the tumor, the higher the efficiency of proton delivery efficiency, where proton delivery efficiency is a measure of how much energy is delivered to the tumor relative to healthy portions of the patient. Examples of proton delivery efficiency include:(1) a ratio proton energy delivered the tumor and proton energy delivered to non-tumor tissue; (2) pathlength of protons in the tumor versus pathlength in the non-tumor tissue; and (3) damage to a tumor compared to damage to healthy body parts. Any of these measures are optionally weighted by damage to sensitive tissue, such as a nervous system element, heart, brain, or other organ. To illustrate, for a patient in a laying position where the patient is rotated about the y-axis during treatment, a tumor near the hear would at times be treated with protons running through the head-to-heart path, leg-to-heart path, or hip-to-heart path, which are all inefficient compared to a patient in a sitting or semi-vertical position where the protons are all delivered through a shorter chest-to-heart; side-of-body-to-heart, or back-to-heart path. Particularly, compared to a laying position, using a sitting or semi-vertical position of the patient, a shorter pathlength through the body to a tumor is provided to a tumor located in the torso or head, which is a higher or better proton delivery efficiency. Herein proton delivery efficiency is separately described from the time efficiency or synchrotron use efficiency, which is a fraction of time that the charged particle beam apparatus is in operation. Patient Placement Preferably, the patient 2130 is aligned in the proton beam path 269 in a precise and accurate manner. Several placement systems are described. The patient placement systems are described using the laying positioning system, but are equally applicable to the semi-vertical and sitting positioning systems. In a first placement system, the patient is positioned in a known location relative to the platform. For example, one or more of the positioning constraints position the patient in a precise and/or accurate location on the platform. Optionally, a placement constraint element connected or replaceably connected to the platform is used to position the patient on the platform. The placement constraint element(s) is used to position any position of the patient, such as a hand, limb, head, or torso element. In a second placement system, one or more positioning constraints or support element, such as the platform, is aligned versus an element in the patient treatment room. Essentially a lock and key system is optionally used, where a lock fits a key. The lock and key elements combine to locate the patient relative to the proton beam path 269 in terms of any of the x-, y-, and z-position, tilt, yaw, and roll. Essentially the lock is a first registration element and the key is a second registration element fitting into, adjacent to, or with the first registration element to fix the patient location and/or a support element location relative to the proton beam path 269. Examples of a registration element include any of a mechanical element, such as a mechanical stop, and an electrical connection indicating relative position or contact. In a third placement system, the imaging system, described supra, is used to determine where the patient is relative to the proton beam path 269 or relative to an imaging marker placed in an support element or structure holding the patient, such as in the platform. When using the imaging system, such as an X-ray imaging system, then the first placement system or positioning constraints minimize patient movement once the imaging system determines location of the subject. Similarly, when using the imaging system, such as an X-ray imaging system, then the first placement system and/or second positioning system provide a crude position of the patient relative to the proton beam path 269 and the imaging system subsequently determines a fine position of the patient relative to the proton beam path 269. X-Ray Synchronization with Patient Respiration In one embodiment, X-ray images are collected in synchronization with patient respiration. The synchronization enhances X-ray image clarity by removing position ambiguity due to the relative movement of body constituents during a patient respiration cycle. In a second embodiment, an X-ray system is orientated to provide X-ray images of a patient in the same orientation as viewed by a proton therapy beam, is synchronized with patient respiration, is operable on a patient positioned for proton therapy, and does not interfere with a proton beam treatment path. Preferably, the synchronized system is used in conjunction with a negative ion beam source, synchrotron, and/or targeting method apparatus to provide an X-ray timed with patient respiration and performed immediately prior to and/or concurrently with particle beam therapy irradiation to ensure targeted and controlled delivery of energy relative to a patient position resulting in efficient, precise, and/or accurate noninvasive, in-vivo treatment of a solid cancerous tumor with minimization of damage to surrounding healthy tissue in a patient using the proton beam position verification system. An X-ray delivery control algorithm is used to synchronize delivery of the X-rays to the patient 2130 within a given period of each breath, such as at the top or bottom of a breath when the subject is holding their breath. For clarity of combined X-ray images, the patient is preferably both accurately positioned and precisely aligned relative to the X-ray beam path 2470. The X-ray delivery control algorithm is preferably integrated with the respiration control module. Thus, the X-ray delivery control algorithm knows when the subject is breathing, where in the respiration cycle the subject is, and/or when the subject is holding their breath. In this manner, the X-ray delivery control algorithm delivers X-rays at a selected period of the respiration cycle. Accuracy and precision of patient alignment allow for (1) more accurate and precise location of the tumor 2120 relative to other body constituents and (2) more accurate and precise combination of X-rays in generation of a 3-dimensional X-ray image of the patient 2130 and tumor 2120. Referring now to FIG. 32, an example of generating an X-ray image 3200 of the patient 2130 and tumor 2120 using the X-ray generation device 2300 or 3-dimensional X-ray generation device 2300 as a known function of time of the patient's respiration cycle is provided. In one embodiment, as a first step the main controller 110 instructs, monitors, and/or is informed of patient positioning 3210. In a first example of patient positioning 3210, an automated patient positioning system, under main controller 110 control, is used to align the patient 2130 relative to the X-ray beam path 2470. In a second example of patient positioning, the main controller 110 is told via sensors or human input that the patient 2130 is aligned. In a second step, patient respiration is then monitored 3220, as described infra. As a first example of respiration monitoring, an X-ray is collected 3240 at a known point in the patient respiration cycle. In a second example of respiration monitoring, the patient's respiration cycle is first controlled in a third step of controlling patient respiration 3220 and then as a fourth step an X-ray is collected 3240 at a controlled point in the patient respiration cycle. Preferably, the cycle of patient positioning 3210, patient respiration monitoring 3220, patient respiration control 3230, and collecting an X-ray 3240 is repeated with different patient positions. For example, the patient 2130 is rotated about an axis 2117 and X-rays are collected as a function of the rotation. In a fifth step, a 3-dimensional X-ray image of the patient 2130, tumor 2120, and body constituents about the tumor is generated using the collected X-ray images, such as with the 3-dimensional X-ray generation device 2300, described supra. The patient respiration monitoring and control steps are further described, infra. Patient Respiration Monitoring Preferably, the patient's respiration pattern is monitored 3220. When a subject, also referred to herein as a patient, is breathing many portions of the body move with each breath. For example, when a subject breathes the lungs move as do relative positions of organs within the body, such as the stomach, kidneys, liver, chest muscles, skin, heart, and lungs. Generally, most or all parts of the torso move with each breath. Indeed, the inventors have recognized that in addition to motion of the torso with each breath, various motion also exists in the head and limbs with each breath. Motion is to be considered in delivery of a proton dose to the body as the protons are preferentially delivered to the tumor and not to surrounding tissue. Motion thus results in an ambiguity in where the tumor resides relative to the beam path. Protons are preferentially delivered at the same point in each of a series of respiration cycles. Initially a rhythmic pattern of breathing of a subject is determined 3220. The cycle is observed or measured. For example, an X-ray beam operator or proton beam operator can observe when a subject is breathing or is between breaths and can time the delivery of the protons to a given period of each breath. Alternatively, the subject is told to inhale, exhale, and/or hold their breath and the protons are delivered during the commanded time period. Preferably, one or more sensors are used to determine the respiration cycle of the individual. Two examples of a respiration monitoring system are provided: (1) a thermal monitoring system and (2) a force monitoring system. Referring again to FIG. 30, a first example of the thermal respiration monitoring system is provided. In the thermal respiration monitoring system, a sensor is placed by the nose and/or mouth of the patient. As the jaw of the patient is optionally constrained, as described supra, the thermal respiration monitoring system is preferably placed by the patient's nose exhalation path. To avoid steric interference of the thermal sensor system components with proton therapy, the thermal respiration monitoring system is preferably used when treating a tumor not located in the head or neck, such as a when treating a tumor in the torso or limbs. In the thermal monitoring system, a first thermal resistor 3070 is used to monitor the patient's respiration cycle and/or location in the patient's respiration cycle. Preferably, the first thermal resistor 3070 is placed by the patient's nose, such that the patient exhaling through their nose onto the first thermal resistor 3070 warms the first thermal resistor 3070 indicating an exhale. Preferably, a second thermal resistor 3060 operates as an environmental temperature sensor. The second thermal resistor 3060 is preferably placed out of the exhalation path of the patient but in the same local room environment as the first thermal resistor 3070. Generated signal, such as current from the thermal resistors 3070, 3060, is preferably converted to voltage and communicated with the main controller 110 or a sub-controller of the main controller. Preferably, the second thermal resistor 3060 is used to adjust for the environmental temperature fluctuation that is part of a signal of the first thermal resistor 3070, such as by calculating a difference between the values of the thermal resistors 3070, 3060 to yield a more accurate reading of the patient's respiration cycle. Referring again to FIG. 28, a second example of the force/pressure respiration monitoring system is provided. In the force respiration monitoring system, a sensor is placed by the torso. To avoid steric interference of the force sensor system components with proton therapy, the force respiration monitoring system is preferably used when treating a tumor located in the head, neck, or limbs. In the force monitoring system, a belt or strap 2850 is placed around an area of the patient's torso that expands and contracts with each respiration cycle of the patient. The belt 2850 is preferably tight about the patient's chest and is flexible. A force meter 2852 is attached to the belt and senses the patients respiration pattern. The forces applied to the force meter 2852 correlate with periods of the respiration cycle. The signals from the force meter 2852 are preferably communicated with the main controller 110 or a sub-controller of the main controller. Respiration Control Once the rhythmic pattern of the subject's breathing is determined, a signal is optionally delivered to the subject to more precisely control the breathing frequency 3230. For example, a display screen 2790 is placed in front of the subject directing the subject when to hold their breath and when to breath. Typically, a respiration control module uses input from one or more of the breathing sensors. For example, the input is used to determine when the next breath exhale is to complete. At the bottom of the breath, the control module displays a hold breath signal to the subject, such as on a monitor, via an oral signal, digitized and automatically generated voice command, or via a visual control signal. Preferably, a display monitor 2790 is positioned in front of the subject and the display monitor displays at least breathing commands to the subject. Typically, the subject is directed to hold their breath for a short period of time, such as about one-half, one, two, or three seconds. The period of time the subject is asked to hold their breath is less than about ten seconds. The period of time the breath is held is preferably synchronized to the delivery time of the proton beam to the tumor, which is about one-half, one, two, or three seconds. While delivery of the protons at the bottom of the breath is preferred, protons are optionally delivered at any point in the respiration cycle, such as upon full inhalation. Delivery at the top of the breath or when the patient is directed to inhale deeply and hold their breath by the respiration control module is optionally performed as at the top of the breath the chest cavity is largest and for some tumors the distance between the tumor and surrounding tissue is maximized or the surrounding tissue is rarefied as a result of the increased volume. Hence, protons hitting surrounding tissue is minimized. Optionally, the display screen tells the subject when they are about to be asked to hold their breath, such as with a 3, 2, 1, second countdown so that the subject is aware of the task they are about to be asked to perform. Proton Beam Therapy Synchronization with Respiration A proton delivery control algorithm is used to synchronize delivery of the protons to the tumor within a given period of each breath, such as at the top or bottom of a breath when the subject is holding their breath. The proton delivery control algorithm is preferably integrated with the respiration control module. Thus, the proton delivery control algorithm knows when the subject is breathing, where in the respiration cycle the subject is, and/or when the subject is holding their breath. The proton delivery control algorithm controls when protons are injected and/or inflected into the synchrotron, when an RF signal is applied to induce an oscillation, as described supra, and when a DC voltage is applied to extract protons from the synchrotron, as described supra. Typically, the proton delivery control algorithm initiates proton inflection and subsequent RF induced oscillation before the subject is directed to hold their breath or before the identified period of the respiration cycle selected for a proton delivery time. In this manner, the proton delivery control algorithm can deliver protons at a selected period of the respiration cycle by simultaneously or nearly simultaneously delivering the high DC voltage to the second pair of plates, described supra, which results in extraction of the protons from the synchrotron and subsequent delivery to the subject at the selected time point. Since the period of acceleration of protons in the synchrotron is constant or known for a desired energy level of the proton beam, the proton delivery control algorithm is used to set an AC RF signal that matches the respiration cycle or directed respiration cycle of the subject. Multi-Field Irradiation The 3-dimensional scanning system of the proton spot focal point, described supra, is preferably combined with a rotation/raster method. The method includes layer wise tumor irradiation from many directions. During a given irradiation slice, the proton beam energy is continuously changed according to the tissue's density in front of the tumor to result in the beam stopping point, defined by the Bragg peak, to always be inside the tumor and inside the irradiated slice. The novel method allows for irradiation from many directions, referred to herein as multi-field irradiation, to achieve the maximal effective dose at the tumor level while simultaneously significantly reducing possible side-effects on the surrounding healthy tissues in comparison with existing methods. Essentially, the multi-field irradiation system distributes dose-distribution at tissue depths not yet reaching the tumor. Although the invention has been described herein with reference to certain preferred embodiments, one skilled in the art will readily appreciate that other applications may be substituted for those set forth herein without departing from the spirit and scope of the present invention. Accordingly, the invention should only be limited by the Claims included below.

description

1. Field of the Invention The present invention relates to a nuclear reactor building that houses a pressure containment vessel (PCV) of a nuclear power plant and a construction method thereof. 2. Description of the Related Art A conventional nuclear reactor building (or merely reactor building, called hereinafter) of a nuclear power plant has been constructed by a frame made of reinforced concrete in order to meet earthquake resistant design criteria and achieve radiation shielding. The reinforced concrete building is constructed by first arranging a grid of reinforcing bars in a formwork and then pouring concrete into the formwork. After completion of the construction of the building, a pressure containment vessel and other equipment are installed in the building. These works are carried out mainly at the site of the construction of the plant, so that on-site construction work takes long time, and it may sometimes take four or more years to construct the whole of a nuclear power plant. Recently, it is strongly demanded to reduce time and cost for constructing a building of a nuclear power plant, and in order to reduce the construction period, it is contemplated to eliminate the reinforcing bar arranging work and the concrete casting work by adopting a steel plate reinforced concrete structure composed of a combination of a steel plate and concrete (referred to as an SC structure hereinafter) or a steel structure composed mainly of steel members to construct the building, rather than the conventional reinforced concrete structure. However, reducing only the period of construction of the frame of the reactor building is not enough to reduce the total period of construction of the entire nuclear power plant, and it is also required to reduce the period of installation of various equipments into the building. In view of such circumstances, recently, there has been provided a construction method that reduces the construction period by applying the SC structure to the frame of the reactor building, in which a composite module composed of an SC steel plate structure serving as the formwork of the frame and piping and other equipment installed or mounted on the structure is previously manufactured, and then the composite module is placed at the site of installation (see Patent Document 1: Japanese Patent Laid-Open No. 2003-167086, for example). In addition, requirements on the security of the nuclear power plant have become severe in recent years, and there is a demand for including provision not only for design basis accidents but also for unexpected events, such as severe accidents, in the design criteria of plant facilities of nuclear power plants. For example, if a loss of coolant accident (LOCA), which is a design basis accident, occurs, and reactor cooling fails, hydrogen may be generated in the PCV, increasing the pressure in the PCV beyond the design value. In such a case, for a pressure suppression type PCV, a steel PCV is more advantageous than a reinforced concrete PCV in points that thermal deterioration of concrete does not occur and the surface of the PCV can be externally cooled, for example. Thus, it is expected that the superiority of the steel PCV will be appreciated in the future. The reactor building needs a biological shielding wall (which may be called BSW hereinafter) serving as a radiological countermeasure that is made of reinforced concrete and placed outside the steel PCV at a certain distance (1 m or less) so that the wall is not in contact with the PCV. In construction of the reactor building having the steel PCV, the PCV and the surrounding BSW need to be separately independently constructed. Besides, the PCV has outwardly protruding PCV penetration portions, such as pipes for external connection, and in addition, it is also needed to form openings, in the BSW, for the PCV penetration portions so as to pass through the BSW in such a manner that the openings are not in contact with the PCV penetration portions, but the gap between the openings and the PCV penetration portions is made minimal so as to ensure the radiation shielding effect. Thus, when the steel PCV is used, in order to ensure the positional relationship between the PCV and the BSW, the PCV has to be constructed before the construction of the concrete frame of the BSW, and therefore, a downtime waiting for completion of the construction of the PCV may occur. According to another recent method for reducing the construction period based on building modularization, the BSW is constructed as an SC building module by applying the SC structure to the BSW and integrating the BSW with the SC building. In this case, the SC building module is installed vertically from the upper side, which may cause a case that the SC building module inevitably interferes with the PCV penetration ports extending from the PCV. In this regard, the reinforced concrete PCV and the steel plate concrete PCV are advantageous over the steel PCV. These PCVs combine the pressure resistant and confinement capabilities of the steel PCV and the shielding capability of the BSW and do not have the above-described defects or problems with the PCV penetration portion of the steel PCV because the PCV penetration portion and the BSW are previously integrated. A structure of a reactor building of a nuclear power plant and a construction method thereof according to the prior art will be described hereunder with reference to the accompanying drawings. FIG. 7 is a cross-sectional view of a reactor building under construction according to the prior art. This drawing illustrates modularization at the time of the reactor building being constructed. FIG. 8 is a diagram for illustrating mounting of SC building modules of the reactor building. In FIG. 7 a reactor building 2 is constructed of steel PCV blocks 60 and steel plate concrete (SC) building modules 80 and houses a steel pressure containment vessel (PCV) 1. PCV penetration portions 3 protrude to the outside of the PCV and penetrate a biological shielding wall (BSW) 4 made of reinforced concrete disposed outside the PCV. The steel PCV 1 is divided into steel PCV blocks 60 (A to F) by horizontal dividing planes 50, and the reactor building 2 is divided into SC building modules 80 ((i) to (iv)) by horizontal dividing planes 70. FIG. 8 shows interference of an SC building module 80 with the PCV penetration portion 3 of a steel PCV block 60. As described above, in the construction of the reactor building and the steel PCV according to the conventional SC building modularization, the modules are mounted vertically from the upper side. Therefore, the SC building module inevitably interferes with the PCV penetration port protruding form the PCV. This poses an obstacle to reduction in the construction period, and a solution thereto has been required. In view of the above circumstances encountered in the prior art mentioned above, an object of the present invention is to provide a nuclear rector building and a construction method thereof intended to prevent interference between a PCV penetration portion of a steel PCV and an SC building module and reduce the construction period. The above object can be achieved according to the present invention by providing, in one aspect, a reactor building having a steel plate concrete structure that houses a pressure containment vessel formed with a plurality of pressure containment vessel penetration ports in the periphery thereof and includes a biological shielding wall disposed outside the pressure containment vessel, wherein the pressure containment vessel is vertically divided into a plurality of blocks, each of the blocks has one or more pressure containment vessel penetration ports arranged on a same horizontal plane, and the reactor building including the biological shielding wall is divided into a plurality of modules by the horizontal plane. The above object can be also achieved according to the present invention by providing, in another aspect, a nuclear reactor building having a steel plate concrete structure that houses a pressure containment vessel formed of a plurality of pressure containment vessel penetration ports in the periphery thereof and includes a biological shielding wall disposed outside the pressure containment vessel, wherein the pressure containment vessel is vertically divided into a plurality of blocks, each of the blocks has one or more pressure containment vessel penetration ports arranged on a same horizontal plane, and the biological shielding wall is divided into a plurality of modules by the horizontal plane. In the above aspects, the modules may be further divided by a vertical plane. The above object can be also achieved according to the present invention by providing, in a further aspect, a construction method of a nuclear reactor building having a steel plate concrete structure that houses a pressure containment vessel formed with a plurality of pressure containment vessel penetration ports in the periphery thereof and includes a biological shielding wall disposed outside the pressure containment vessel, the construction method comprising the steps of: vertically dividing the pressure containment vessel into a plurality of blocks so that each block has one or more pressure containment vessel penetration ports arranged on a same horizontal plane; dividing the reactor building including the biological shielding wall into a plurality of modules by the horizontal plane; and alternately stacking the blocks of the pressure containment vessel and the modules of the reactor building. 6. The above object can be also achieved according to the present invention by providing, in a still further aspect, a construction method of a nuclear reactor building having a steel plate concrete structure that houses a pressure containment vessel formed with a plurality of pressure containment vessel penetration ports in the periphery thereof and includes a biological shielding wall disposed outside the pressure containment vessel, the construction method comprising the steps of: vertically dividing the pressure containment vessel into a plurality of blocks so that each block has one or more pressure containment vessel penetration ports arranged on a same horizontal plane; dividing the biological shielding wall into a plurality of modules by the horizontal plane; and alternately stacking the blocks of the pressure containment vessel and the modules of the biological shielding wall. According to the present invention having the characteristics described above, when assembling workings of the steel PCV blocks and the SC building modules including the BSW are carried out at the same time, interference between the PCV penetration ports and the SC building modules can be prevented from occurring. Thus, the waiting for completion of the construction of the PCV can be reduced, and the construction period of the reactor building having the steel PCV can be reduced. Structures of and construction methods of a reactor building of a nuclear power plant according to embodiments of the present invention will be described. In the following description, terms indicating directions, such as “upper”, “lower”, “left” and “right”, are used herein with reference to the illustration on the accompanying drawings or in the actual installation state. In the following, a first embodiment of the present invention will be described with reference to FIGS. 1 to 4. FIG. 1 is a cross-sectional view of a reactor building according to the first embodiment of the present invention. This drawing illustrates modularization of a nuclear reactor pressure containment vessel into mounting blocks and of an SC reactor building into SC building blocks during construction. The same parts as those in the prior art described in FIGS. 7 and 8 are denoted by the same reference numerals. A reactor building 2 of the SC structure houses a steel PCV 1, which is formed with a plurality of penetration ports 3 penetrating a wall portion of the PCV (called PCV penetration ports herein) on the periphery of the PCV, and includes a BSW 4 disposed outside the PCV. The steel PCV 1 is vertically divided into a plurality of steel PCV block 61 (A to H) by horizontal steel PCV dividing planes 51, and each block has one or more PCV penetration ports 3 arranged on the same horizontal plane. The reactor building 2 is vertically divided into SC building modules 81 ((i) to (vii)) by horizontal SC building dividing planes 71 passing through the PCV penetration ports 3. The BSW 4 disposed outside the PCV has the SC structure and is divided into modules by the same horizontal planes that pass through the PCV penetration ports 3 and divide the reactor building 2 into the SC building modules 81. FIG. 2 is a diagram showing PCV penetration ports of the steel PCV in the reactor building and building modules of the reactor building viewed from the direction of an arrow A in FIG. 1. The reactor building 2 is divided into modules by the horizontal planes passing through the PCV penetration ports 3. The steel PCV blocks 61 and the SC building modules 81 are alternately stacked. More specifically, the steel PCV blocks 61 and the SC building modules 81 are mounted in the order: A→(i)→B→(ii)→C→(iii)→D→(iv)→E→(v)→F→(vi)→G→(vii)→H. Thus, the steel PCV blocks 61 and the SC building modules 81 can be assembled without interference between the PCV penetration ports 3 and the SC building modules 81. FIG. 3 is a diagram illustrating mounting of the SC building modules of the reactor building. As can be seen from this drawing, interference between the PCV penetration ports 3 and the SC building modules 81 is avoided. FIG. 4 is a diagram illustrating horizontal division of the SC building module. The SC building module 81 is horizontally divided into four parts by vertical SC building module dividing planes 9 that pass through the center of the steel PCV 1, for example. The number of the divisional parts can be arbitrarily selected depending on the capacity of the crane used on the construction site. Furthermore, different horizontally divided parts of the nuclear rector building may be vertically divided into different number of SC building modules. The vertical position of the boundary between the SC building modules 81 passing through the PCV penetration ports 3 (the position of the horizontal SC building dividing plane 71) may not be the center of the penetration ports as far as it is ensured that interference between the PCV penetration ports 3 and the SC building modules 81 does not occur. In the following, a second embodiment of the present invention will be described with reference to FIGS. 5 and 6. FIG. 5 is a cross-sectional view of a reactor building according to the second embodiment of the present invention. This drawing illustrates modularization of a nuclear reactor pressure containment vessel into mounting blocks and of an SC reactor building into SC building blocks during construction. The same parts as those in the prior art shown in FIGS. 7 and 8 are denoted by the same reference numerals. FIG. 6 is a diagram showing a part of a steel PCV in which the PCV penetration ports are concentrated and the SC building modules of the reactor building viewed from the direction of the arrow B in FIG. 5. As in the first embodiment, a reactor building 2 of the SC structure houses a steel PCV 1, which is formed with a plurality of the penetration ports 3 in the periphery the PCV, and includes a BSW 4 disposed outside the PCV. The steel PCV 1 is vertically divided into a plurality of steel PCV block 62 (A to H) by a plurality of horizontal steel PCV dividing planes 51, and each block has one or more PCV penetration ports 3 arranged on the same horizontal plane. The reactor building 2 is vertically divided into SC building modules 82 ((i) to (iv)) by horizontal SC building dividing planes 72 in the same manner as the prior art shown in FIG. 7. Furthermore, with the SC building module 82, a part of the BSW 4 is cut off, and the SC building module 82 is divided into BSW modules 10 ((v) to (vi)) by horizontal planes passing through the PCV penetration ports 3. In this embodiment, the BSW 4 in which PCV penetration ports 3 are concentrated is divided into the same number of parts as the number of different levels of the PCV penetration ports 3 by horizontal planes passing through the PCV penetration ports 3, thereby preventing interference between the PCV penetration ports 3 and the steel PCV 1. Thus, the number of SC building modules can be reduced. The steel PCV blocks 62 and the BSW modules 10 are alternately stacked. More specifically, in the portion in which the PCV penetration ports 3 are concentrated, the steel PCV blocks 62 and the SC building modules 82 including the BSW modules 10 are mounted in the order: D→(iii)→E→(v)→F→(vi)→G→(iv)→H. As a result, the number of mountings of the SC building modules 82, which are heavy and take much time to be mounted in precise alignment, can be reduced, thus reducing the construction period. It is to be noted that the present invention is not limited to the embodiments described above, and many other changes and modifications may be made without departing form the scope of the appended claims. For example, although a portion of the BSW 4 in which PCV penetration ports 3 are concentrated is divided, the whole of the BSW 4 may be divided. Furthermore, the vertical position of the boundary between the BSW modules 10 passing through the PCV penetration ports 3 (the position of the horizontal plane) may not be the center of the penetration ports as far as it is ensured that the PCV penetration ports 3 and the BSW modules 10 have dimensions which do not cause any interference therebetween. Furthermore, as in the first embodiment, the BSW module 10 may be further divided into divisional modules by vertical planes as shown in FIG. 4.

abstract

The present disclosure relates to a process for recycling a sodium salt by decomposition of a sodium nitride liquid waste, comprising a neutralization step in which a nitric acid liquid waste or an off-gas having nitric acid dissolved therein which is produced through a wet reprocessing process comprising a dissolution step for dissolving a spent nuclear fuel in nitric acid is neutralized by adding or contacting the nitrate liquid waste or the off-gas to or with at least one sodium salt selected from the group consisting of sodium hydroxide, sodium hydrogencarbonate and sodium carbonate, thereby yielding a sodium nitrate liquid waste; a sodium nitrate-decomposition step in which the sodium nitrate liquid waste is reductively decomposed with a reducing agent, thereby decomposing sodium nitrate into a nitrogen gas and the sodium salt; and a recycle step for recycling the sodium salt into the neutralization step or wet reprocessing process.

abstract

In one aspect, it is disclosed a detection system comprising: a plurality of detectors, each detector being configured to detect radiation scattered by an associated respective portion of a load to inspect, the radiation being scattered in response to the respective portion being irradiated by radiation transmitted through the portion; and a plurality of collimators associated with the plurality of detectors, each collimator of the plurality of collimators being associated with a respective detector of the plurality of detectors and being configured to, for each detector of the plurality of detectors: enable radiation scattered by the respective portion of the load to reach the associated detector of the plurality of detectors, and inhibit other scattered radiation from reaching the associated detector.

062401556

summary

BACKGROUND OF THE INVENTION The present invention relates to a preventive maintenance apparatus for structural members in a nuclear pressure vessel and, more particularly, to a preventive maintenance apparatus for structural members in a nuclear pressure vessel capable of preventing occurrence of stress corrosion cracks of structural members by adding compressive remaining stress to surfaces of the structural members. The present invention relates to a preventive maintenance apparatus for structural members in a nuclear pressure vessel suitable for adding compressive residual stress to a surface of a welded portion and a heat affected zone in each of core internals of, preferably, a boiling water reactor (BWR) such as a core shroud, a shroud support cylinder, a shroud support leg, a shroud support plate and a jet pump diffuser. Japanese Patent Application Laid-Open No.62-63614 discloses a method of releasing tensile remaining stress in a welded portion which may become a cause of occurrence of stress corrosion cracks. In the method, a high pressure water shot peening apparatus is inserted inside of a heat transfer tube of a heat exchanger to peen an inner surface of the heat transfer tube by axial kinetic pressure energy of a high pressure water jet (kinetic pressure energy of a confined water jet in the axial direction). Tensile remaining stress having existed near the inner surface of the heat transfer tube is converted into compressive remaining stress by the peening. The high pressure water shot peening apparatus comprises a rotating nozzle portion for discharging a high pressure liquid jet. Further, Japanese Patent Application Laid-Open No.5-78738 discloses an improving method of converting tensile remaining stress on a surface of a core shroud in a reactor pressure vessel into compressive remaining stress by water jet peening. The water jet peening is performed by arranging a traveling cart mounting a vertical driving apparatus on a flange in a top end portion of the reactor pressure vessel. An upper mast and a lower mast having a water jet discharging head in the top end are mounted onto the vertical driving apparatus. A high pressure water jet is discharged from a water jet discharging nozzle of the water jet discharging head to generate cavitation. Air bubbles generated by the cavitation are hit on a surface of the shroud. Furthermore, Japanese Patent Application Laid-Open No.7-270591 discloses a method in which preventive maintenance apparatuses comprising a nozzle unit having an upper attachment, a lower attachment and a drive mechanism for a discharging nozzle and a main apparatus body are arranged in a top end portion of a CRD housing and a lower core support plate inside a reactor pressure vessel to generate cavitation bubbles by discharging a high pressure jet from the discharging nozzle. The method also discloses a method of improving remaining stress by water jet peening. The cavitation bubbles are hit onto the surfaces of a lower barrel of the core shroud, a core shroud support cylinder and so on. Tensile remaining stress in the surfaces of the lower barrel of the core shroud, the core shroud support cylinder and so on is converted to compressive remaining stress. The method of the prior art disclosed in Japanese Patent Application Laid-Open No.62-63614 is effective as a method of releasing the remaining stress in a heat exchanger and the like. The axial kinetic pressure of the water jet in this method can be effectively used in the work under atmospheric pressure. However, when the high pressure shot peening apparatus of the prior art is used under water, an effective peening effect cannot be obtained because the axial kinetic pressure of the water jet is substantially decayed under water. In order to obtain an axial kinetic pressure equivalent to that under a condition of air atmosphere under a condition of water using the high pressure shot peening apparatus, a water jet of ultra high pressure discharge is necessary. Accordingly, the pump and the related components used need to have structures capable of withstanding the ultra high pressure. In order to avoid such structures, it is required to discharge the high pressure liquid jet under air atmosphere by lowering a core water level inside the reactor pressure vessel. Since lowering of the core water level causes an increase in the environmental radiation dose, radiation exposure to workers may be increased. On the other hand, the method of improving remaining stress by the water jet peening disclosed in Japanese Patent Application Laid-Open No.5-78738 is effective as a method of improving remaining stress in core internals such as a core shroud. However, since the traveling cart having the mast is placed on the top end portion of the reactor pressure vessel, the mast becomes long in order to apply the method of improving remaining stress by water jet peening to the lower barrel of the core shroud, the core shroud support cylinder and so on. In addition to this, the apparatus is difficult to be handled. It cannot be said that this is preferable from the viewpoint of workability. The method of improving remaining stress by the water jet peening disclosed in Japanese Patent Application Laid-Open No.7-270591 is an effective technology aiming to improve the workability which is the problem in the method of improving remaining stress described in Japanese Patent Application Laid-Open No.5-78738 since the apparatus does not have any long mast. However, application of the method in Japanese Patent Application Laid-Open No.7-270591 is limited within a small field of preventive maintenance work since the preventive maintenance apparatus is attached to the top end portion of the CRD housing and the lower core support plate inside the reactor pressure vessel. Therefore, it is necessary that the preventive maintenance apparatus is detached and moved from one CRD housing after completion of the preventive maintenance work to a portion existing in the inner surface of the core shroud to be set to another CRD housing. SUMMARY OF THE INVENTION An object of the present invention is to provide a preventive maintenance apparatus for structural members in a reactor pressure vessel which is capable of being easily arranged on a core shroud and easily moving a discharging nozzle to a portion to perform preventive maintenance. A first invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel which comprises a ring-shaped guide rail having a plurality of lugs, the guide rail being placed on an upper flange of a core shroud provided inside a reactor pressure vessel, at least one of the plurality of lugs engaging with a plurality of guide rods provided on an inner surface of the reactor pressure vessel; a turntable rotatable on the guide rail; a discharging nozzle moving apparatus for moving a discharging nozzle in a radial direction of the core shroud and in an axial direction of the core shroud, the discharging nozzle moving apparatus being placed on the turntable; and a high pressure water supply apparatus for supplying high pressure water to the discharging nozzle. Since the guide rail has the plurality of lugs engaging with the plurality of guide rods provided in the inner surface of the reactor pressure vessel, the guide rail can be easily moved downward up to the upper portion of the core shroud along the guide rods. Therefore, the guide rail can be easily placed on the upper flange without being interfered with main steam line plugs which are inserted into opening portions of main steam pipes. In addition to this, since the turntable can be rotated, the discharging nozzle can be easily moved to a portion to perform preventive maintenance. Since the turntable is rotated on the guide rail placed on the upper flange, the turntable does not contact the upper flange. Accordingly, the upper flange can be prevented from being damaged by the rotation of the turntable. A second invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel which comprises a first discharging nozzle moving apparatus for moving a discharging nozzle in a radial direction of the core shroud and in an axial direction of the core shroud, the discharging nozzle discharging high pressure water to add compressive remaining stress to an outer surface of the core shroud, the discharging nozzle moving apparatus being placed on the turntable; and a second discharging nozzle moving apparatus for moving a discharging nozzle in a radial direction of the core shroud and in an axial direction of the core shroud, the discharging nozzle discharging high pressure water to add compressive remaining stress to an inner surface of the core shroud, the discharging nozzle moving apparatus being placed on the turntable. Since the first and the second discharging nozzle moving apparatuses are installed in the turntable, compressive remaining stress can be added to both of the outer surface and the inner surface of the core shroud. Therefore, it is possible to shorten the time for performing preventive maintenance to the core shroud. A third invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel in which the second discharging nozzle moving apparatus comprises an arm member movable in a horizontal direction; a pole member movable in an axial direction of the core shroud provided in the arm member; a multi-joint arm attached to the pole member; and the discharging nozzle provided in a top end portion of the multi-joint arm. Since the multi-joint arm is provided, it is possible to insert the discharging nozzle into a narrow portion formed between the core shroud and an upper core grid plate placed on the core shroud. Therefore, compressive remaining stress can be added to the inner surface of the core shroud in the narrow portion. A fourth invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel in which the first discharging nozzle moving apparatus comprises an arm member movable in a horizontal direction; a pole member movable in an axial direction of the core shroud provided in the arm member, the pole member being inserted between the reactor pressure vessel and the core shroud; a vertically moved body attached to the pole member, the vertically moved body being movable in a vertical direction; and the discharging nozzle provided in a top end portion of the vertically moved body. Since the vertically moved body having the discharging nozzle can be vertically moved along the pole member, it is possible to easily add compressive remaining stress to a welded portion of the core shroud and the vicinity. A fifth invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel which comprises a water supply apparatus for cleaning reactor water and supplying the water to a high pressure water supply apparatus. Since the reactor water is cleaned to be supplied to the high pressure supply apparatus, the water discharged from the discharging nozzle becomes the reactor water again. Accordingly, an amount of the reactor water inside the reactor pressure vessel and the reactor well is never increased even when the high pressure water is discharged from the discharging nozzle during preventive maintenance work. Therefore, radioactive disposal liquid cannot be produced even when the high pressure water is discharged from the discharging nozzle. A sixth invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel which comprises a crud sucking apparatus for sucking crud suspending in reactor water. Since it is possible to remove crud suspended in the reactor water during preventive maintenance work, visibility under the reactor water can be improved. Therefore, it is possible to clearly monitor a portion under preventive maintenance work using an image in a monitoring camera. A seventh invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel which comprises a bubble collecting apparatus for collecting bubbles reaching a water surface in a reactor well, the bubble collecting apparatus being placed near the water surface. Since the bubble collecting apparatus is provided, it is possible to prevent radioactive materials floating up in the reactor water accompanied by the bubbles from being dispersed. Therefore, it is possible to suppress radiation exposure to workers. An eighth invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel in which the first discharging nozzle moving apparatus comprises an arm member movable in a horizontal direction; a plurality of pole members provided in the arm member, the pole members being inserted between the reactor pressure vessel and the core shroud; vertically moved bodies respectively attached to the pole members, the vertically moved body being movable in a vertical direction; and the discharging nozzles respectively provided in the vertically moved bodies. Since the vertically moved bodies capable of respectively and vertically moving the plurality of pole members are provided, it is possible to perform preventive maintenance work to different positions on the outer surface of the core shroud at the same time. Therefore, it is possible to further shorten the time required for the preventive maintenance work. A ninth invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel which comprises a rotating apparatus for rotating a metal fitting for bundling a plurality of hoses and a plurality of cables, the plurality of hoses and the plurality of cables being connected to the first discharging nozzle moving apparatus and the second discharging nozzle moving apparatus. Since the rotating apparatus for rotating the metal fitting for bundling the plurality of hoses and the plurality of cables is provided, the rotating apparatus can be rotated when the turntable mounting the first discharging nozzle moving apparatus and the second discharging nozzle moving apparatus is rotated during preventive maintenance work. Therefore, it is possible to prevent the plurality of hoses and the plurality of cables from being intertwined by rotation of the turntable. A tenth invention to attain the above-mentioned object is characterized by a preventive maintenance apparatus for structural members inside a reactor pressure vessel in which the first discharging nozzle moving apparatus and the second discharging nozzle moving apparatus respectively comprise a discharging nozzle for discharging high pressure water for adding compressive remaining stress to an outer surface of the core shroud and a discharging nozzle for discharging high pressure water for adding compressive remaining stress to an inner surface of the core shroud, and the preventive maintenance apparatus further comprises an apparatus for moving the discharging nozzles. Since the first discharging nozzle moving apparatus and the second discharging nozzle moving apparatus respectively comprise the discharging nozzle for discharging high pressure water for adding compressive remaining stress to an outer surface of the core shroud and the discharging nozzle for discharging high pressure water for adding compressive remaining stress to an inner surface of the core shroud, it is possible to perform preventive maintenance work to four positions in the inner and outer surfaces of the core shroud at the same time. Therefore, it is possible to substantially shorten the time required for the preventive maintenance work to the core shroud.

description

This application claims the benefit of U.S. Provisional Patent Application No. 61/195,639, filed Oct. 9, 2008, entitled “Four-dimensional Electron Microscope,” U.S. Provisional Patent Application No. 61/236,745, filed Aug. 25, 2009, entitled “4D Nanoscale Diffraction Observed by Convergent-Beam Ultrafast Electron Microscopy,” and U.S. Provisional Patent Application No. 61/240,946, filed Sep. 9, 2009, entitled “4D Attosecond Imaging with Free Electrons: Diffraction Methods and Potential Applications,” which are commonly assigned, the disclosures of which are hereby incorporated by reference in their entirety. The following two regular U.S. patent applications (including this one) are being filed concurrently, and the entire disclosure of the other application is hereby incorporated by reference into this application for all purposes: application Ser. No. 12/575,285, filed Oct. 7, 2009, entitled “4D Imaging in an Ultrafast Electron Microscope”; and application Ser. No. 12/573,312, filed Oct. 7, 2009, entitled “Characterization of Nanoscale Structures Using an Ultrafast Electron Microscope”. The U.S. Government has certain rights in this invention pursuant to Grant No. GM081520 awarded by the National Institutes of Health, Grant No. FA9550-07-1-0484 awarded by the Air Force (AFOSR) and Grant No(s). CME0549936 & DMR0504854 awarded by the National Science Foundation. Electrons, because of their wave-particle duality, can be accelerated to have picometer wavelength and focused to image in real space. With the impressive advances made in transmission electron microscopy (TEM), STEM, and aberration-corrected TEM, it is now possible to image with high resolution, reaching the sub-Angstrom scale. Together with the progress made in electron crystallography, tomography, and single-particle imaging, today the electron microscope has become a central tool in many fields, from materials science to biology. For many microscopes, the electrons are generated either thermally by heating the cathode or by field emission, and as such the electron beam is made of random electron bursts with no control over the temporal behavior. In these microscopes, time resolution of milliseconds or longer, being limited by the video rate of the detector, can be achieved, while maintaining the high spatial resolution. Despite the advances made in TEM techniques, there is a need in the art for improved methods and novel systems for ultrafast electron microscopy. According to embodiments of the present invention, methods and systems for 4D ultrafast electron microscopy (UEM) are provided—in situ imaging with ultrafast time resolution in TEM. Thus, 4D microscopy provides imaging for the three dimensions of space as well as the dimension of time. In some embodiments, single electron imaging is introduced as a component of the 4D UEM technique. Utilizing one electron packets, resolution issues related to repulsion between electrons (the so-called space-charge problem) are addressed, providing resolution unavailable using conventional techniques. Moreover, other embodiments of the present invention provide methods and systems for convergent beam UEM, focusing the electron beams onto the specimen to measure structural characteristics in three dimensions as a function of time. Additionally, embodiments provide not only 4D imaging of specimens, but characterization of electron energy, performing time resolved electron energy loss spectroscopy (EELS). The potential applications for 4D UEM are demonstrated using examples including gold and graphite, which exhibit very different structural and morphological changes with time. For gold, following thermally induced stress, the atomic structural expansion, the nonthermal lattice temperature, and the ultrafast transients of warping/bulging were determined. In contrast, in graphite, striking coherent transients of the structure were observed in the selected-area image dynamics, and also in diffraction, directly measuring the resonance period of Young's elastic modulus. Measurement of the Young's elastic modulus for the nano-scale dimension, the frequency is found to be as high as 30 gigahertz, hitherto unobserved, with the atomic motions being along the c-axis. Both materials undergo fully reversible dynamical changes, retracing the same evolution after each initiating impulsive stress. Thus, embodiments of the present invention provide methods and systems for performing imaging studies of dynamics using UEM. Other embodiments of the present invention extend four-dimensional (4D) electron imaging to the attosecond time domain. Specifically, embodiments of the present invention are used to generate attosecond electron pulses and in situ probing with electron diffraction. The free electron pulses have a de Broglie wavelength on the order of picometers and a high degree of monochromaticity (ΔE/E0≈10−4); attosecond optical pulses have typically a wavelength of 20 nm and ΔE/E0≈0.5, where E0 is the central energy and ΔE is the energy bandwidth. Diffraction, and tilting of the electron pulses/specimen, permit the direct investigation of electron density changes in molecules and condensed matter. This 4D imaging on the attosecond time scale is a pump-probe approach in free space and with free electrons. As described more fully throughout the present specification, some embodiments of the present invention utilize single electron packets in UEM, referred to as single electron imaging. Conventionally, it was believed that the greater number of electrons per pulse, the better the image produced by the microscope. In other words, as the signal is increased, imaging improves. However, the inventor has determined that by using single electron packets and repeating the imaging process a number of times, images can be achieved without repulsion between electrons. Unlike photons, electrons are charged and repel each other. Thus, as the number of electrons per pulse increases, the divergence of the trajectories increases and resolution decreases. Using single electron imaging techniques, atomic scale resolution of motion is provided once the space-charge problem is addressed. According to an embodiment of the present invention, a four-dimensional electron microscope for imaging a sample is provided. The four-dimensional electron microscope includes a stage assembly configured to support the sample, a first laser source capable of emitting a first optical pulse of less than 1 ps in duration, and a second laser source capable of emitting a second optical pulse of less than 1 ns in duration. The four-dimensional electron microscope also includes a cathode coupled to the first laser source and the second laser source. The cathode is capable of emitting a first electron pulse less than 1 ps in duration in response to the first optical pulse and a second electron pulse of less than 1 ns in response to the second optical pulse. The four-dimensional electron microscope further includes an electron lens assembly configured to focus the electron pulse onto the sample and a detector configured to capture one or more electrons passing through the sample. The detector is configured to provide a data signal associated with the one or more electrons passing through the sample. The four-dimensional electron microscope additionally includes a processor coupled to the detector. The processor is configured to process the data signal associated with the one or more electrons passing through the sample to output information associated with an image of the sample. Moreover, the four-dimensional electron microscope includes an output device coupled to the processor. The output device is configured to output the information associated with the image of the sample. According to another embodiment of the present invention, a convergent beam 4D electron microscope is provided. The convergent beam 4D electron microscope includes a laser system operable to provide a series of optical pulses, a first optical system operable to split the series of optical pulses into a first set of optical pulses and a second set of optical pulses and a first frequency conversion unit operable to frequency double the first set of optical pulses. The convergent beam 4D electron microscope also includes a second optical system operable to direct the frequency doubled first set of optical pulses to impinge on a sample and a second frequency conversion unit operable to frequency triple the second set of optical pulses. The convergent beam 4D electron microscope further includes a third optical system operable to direct the frequency tripled second set of optical pulses to impinge on a cathode, thereby generating a train of electron packets. Moreover, the convergent beam 4D electron microscope includes an accelerator operable to accelerate the train of electron packets, a first electron lens operable to de-magnify the train of electron packets, and a second electron lens operable to focus the train of electron packets onto the sample. According to a specific embodiment of the present invention, a system for generating attosecond electron pulses is provided. The system includes a first laser source operable to provide a laser pulse and a cathode optically coupled to the first laser source and operable to provide an electron pulse at a velocity v0 directed along an electron path. The system also includes a second laser source operable to provide a first optical wave at a first wavelength. The first optical wave propagates in a first direction offset from the electron path by a first angle. The system further includes a third laser source operable to provide a second optical wave at a second wavelength. The second optical wave propagates in a second direction offset from the electron path by a second angle and the interaction between the first optical wave and the second optical wave produce a standing wave copropagating with the electron pulse. According to another specific embodiment of the present invention, a method for generating a series of tilted attosecond pulses is provided. The method includes providing a femtosecond electron packet propagating along an electron path. The femtosecond electron packet has a packet duration and a direction of propagation. The method also includes providing an optical standing wave disposed along the electron path. The optical standing wave is characterized by a peak to peak wavelength measured in a direction tilted at a predetermined angle with respect to the direction of propagation. The method further includes generating the series of tilted attosecond pulses after interaction between the femtosecond electron packet and the optical standing wave. According to a particular embodiment of the present invention, a method of operating an electron energy loss spectroscopy (EELS) system is provided. The method includes providing a train of optical pulses using a pulsed laser source, directing the train of optical pulses along an optical path, frequency doubling a portion of the train of optical pulses to provide a frequency doubled train of optical pulses, and frequency tripling a portion of the frequency doubled train of optical pulses to provide a frequency tripled train of optical pulses. The method also includes optically delaying the frequency doubled train of optical pulses using a variable delay line, impinging the frequency doubled train of optical pulses on a sample, impinging the frequency tripled train of optical pulses on a photocathode, and generating a train of electron pulses along an electron path. The method further includes passing the train of electron pulses through the sample, passing the train of electron pulses through a magnetic lens, and detecting the train of electron pulses at a camera. According to an embodiment of the present invention, a method of imaging a sample is provided. The method includes providing a stage assembly configured to support the sample, generating a train of optical pulses from a laser source, and directing the train of optical pulses along an optical path to impinge on a cathode. The method also includes generating a train of electron pulses in response to the train of optical pulses impinging on the cathode. Each of the electron pulses consists of a single electron. The method further includes directing the train of electron pulses along an imaging path to impinge on the sample, detecting a plurality of the electron pulses after passing through the sample, processing the plurality of electron pulses to form an image of the sample, and outputting the image of the sample to an output device. According to another embodiment of the present invention, a method of capturing a series of time-framed images of a moving nanoscale object is provided. The method includes a) initiating motion of the nanoscale object using an optical clocking pulse, b) directing an optical trigger pulse to impinge on a cathode, and c) generating an electron pulse. The method also includes d) directing the electron pulse to impinge on the sample with a predetermined time delay between the optical clocking pulse and the electron pulse, e) detecting the electron pulse, f) processing the detected electron pulse to form an image, and g) increasing the predetermined time delay between the optical clocking pulse and the electron pulse. The method further includes repeating steps a) through g) to capture the series of time-framed images of the moving nanoscale object. According to a specific embodiment of the present invention, a method of characterizing a sample is provided. The method includes providing a laser wave characterized by an optical wavelength (λ0) and a direction of propagation and directing the laser wave along an optical path to impinge on a test surface of the sample. The test surface of the sample is tilted with respect to the direction of propagation of the laser by a first angle (α). The method also includes providing a train of electron pulses characterized by a propagation velocity (vel), a spacing between pulses ( λ 0 ⁢ v el c ) ,and a direction of propagation tilted with respect to the direction of propagation of the laser by a second angle (β). The method further includes directing the train of electron pulses along an electron path to impinge on the test surface of the sample. The first angle, the second angle, and the propagation velocity are related by sin ⁢ ⁢ ( α ) sin ⁡ ( α - β ) = c v el . According to another specific embodiment of the present invention, a method of imaging chemical bonding dynamics is provided. The method includes positioning a sample in a reduced atmosphere environment, providing a first train of laser pulses, and directing the first train of laser pulses along a first optical path to impinge on a sample. The method also includes providing a second train of laser pulses, directing the second train of laser pulses along a second optical path to impinge on a photocathode, and generating a train of electron pulses. One or more of the electron pulses consist of a single electron. The method further includes accelerating the train of electron pulses and transmitting a portion of the train of electron pulses through the sample. Numerous benefits are achieved by way of the present invention over conventional techniques. For example, the present systems provide temporal resolution over a wide range of time scales. Additionally, unlike spectroscopic methods, embodiments of the present invention can determine a structure in 3-D space. Such capabilities allow for the investigation of phase transformation in matter, determination of elastic and mechanical properties of materials on the nanoscale, and the time evolution of processes involved in materials and biological function. Depending upon the embodiment, one or more of these benefits may be achieved. These and other benefits will be described in more detail throughout the present specification and more particularly below. These and other objects and features of the present invention and the manner of obtaining them will become apparent to those skilled in the art, and the invention itself will be best understood by reference to the following detailed description read in conjunction with the accompanying drawings. DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS Ultrafast imaging, using pulsed photoelectron packets, provides opportunities for studying, in real space, the elementary processes of structural and morphological changes. In electron diffraction, ultrashort time resolution is possible but the data is recorded in reciprocal space. With space-charge-limited nanosecond (sub-micron) image resolutions ultrashort processes are not possible to observe. In order to achieve the ultrafast resolution in microscopy, the concept of single-electron pulse imaging was realized as a key to the elimination of the Coulomb repulsion between electrons while maintaining the high temporal and spatial resolutions. As long as the number of electrons in each pulse is much below the space-charge limit, the packet can have a few or tens of electrons and the temporal resolution is still determined by the femtosecond (fs) optical pulse duration and the energy uncertainty, on the order of 100 fs, and the spatial resolution is atomic-scale. However, the goal of full-scale dynamic imaging can be attained only when in the microscope the problems of in situ high spatiotemporal resolution for selected image areas, together with heat dissipation, are overcome. FIG. 1 is a simplified diagram of a 4D electron microscope system according to an embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims herein. One of ordinary skill in the art would recognize many variations, modifications, and alternatives. As illustrated in FIG. 1, a femtosecond laser 110 or a nanosecond laser 105 is directed through a Pockels cell 112, which acts as a controllable shutter. A Glan polarizer 114 is used in some embodiments, to select the laser power propagating in optical path 115. A beam splitter (not shown) is used to provide several laser beams to various portions of the system. Although the system illustrated in FIG. 1 is described with respect to imaging applications, this is not generally required by the present invention. One of skill in the art will appreciate that embodiments of the present invention provide systems and methods for imaging, diffraction, crystallography, electron spectroscopy, and related fields. Particularly, the experimental results discussed below yield insight into the varied applications available using embodiments of the present invention. The femtosecond laser 110 is generally capable of generating a train of optical pulses with predetermined pulse width. One example of such a laser system is a diode-pumped mode-locked titanium sapphire (Ti:Sapphire) laser oscillator operating at 800 nm and generating 100 fs pulses at a repetition rate of 80 MHz and an average power of 1 Watt, resulting in a period between pulses of 12.5 ns. In an embodiment, the spectral bandwidth of the laser pulses is 2.35 nm FWHM. An example of one such laser is a Mai Tai One Box Femtosecond Ti:Sapphire Laser, available from Spectra-Physics Lasers, of Mountain View, Calif. In alternative embodiments, other laser sources generating optical pulses at different wavelengths, with different pulse widths, and at different repetition rates are utilized. One of ordinary skill in the art would recognize many variations, modifications, and alternatives. The nanosecond laser 105 is also generally capable of generating a train of optical pulses with a predetermined pulse width greater than that provided by the femtosecond laser. The use of these two laser systems enables system miniaturization since the size of the nanosecond laser is typically small in comparison to some other laser systems. By moving one or more mirrors, either laser beam is selected for use in the system. The ability to select either laser enables scanning over a broad time scale—from femtoseconds all the way to milliseconds. For short time scale measurement, the femtosecond laser is used and the delay stage (described below) is scanned at corresponding small time scales. For measurement of phenomena over longer time scales, the nanosecond laser is used and the delay stage is scanned at corresponding longer time scales. A first portion of the output of the femtosecond laser 110 is coupled to a second harmonic generation (SHG) device 116, for example a barium borate (BaB2O4) crystal, typically referred to as a BBO crystal and available from a variety of doubling crystal manufacturers. The SHG device frequency doubles the train of optical pulses to generate a train of 400 nm, 100 fs optical pulses at an 80 MHz repetition rate. SHG devices generally utilize a nonlinear crystal to frequency double the input pulse while preserving the pulse width. In some embodiments, the SHG is a frequency tripling device, thereby generating an optical pulse at UV wavelengths. Of course, the desired output wavelength for the optical pulse will depend on the particular application. The doubled optical pulse produced by the SHG device propagates along electron generating path 118. A cw diode laser 120 is combined with the frequency doubled optical pulse using beam splitter 122. The light produce by the cw diode laser, now collinear with the optical pulse produced by the SHG device, serves as an alignment marker beam and is used to track the position of the optical pulse train in the electron generating path. The collinear laser beams enter chamber 130 through entrance window 132. In the embodiment illustrated in FIG. 1, the entrance window is fabricated from materials with high transparency at 400 nm and sufficient thickness to provide mechanical rigidity. For example, BK-7 glass about 6 mm thick with anti-reflection coatings, e.g. MgF2 or sapphire are used in various embodiments. One of ordinary skill in the art would recognize many variations, modifications, and alternatives. An optical system, partly provided outside chamber 130 and partly provided inside chamber 130 is used to direct the frequency doubled optical pulse train along the electron-generating path 134 inside the chamber 130 so that the optical pulses impinge on cathode 140. As illustrated, the optical system includes mirror 144, which serves as a turning mirror inside chamber 130. In embodiments of the present invention, polished metal mirrors are utilized inside the chamber 130 since electron irradiation may damage mirror coatings used on some optical mirrors. In a specific embodiment, mirror 144 is fabricated from an aluminum substrate that is diamond turned to produce a mirror surface. In some embodiments, the aluminum mirror is not coated. In other embodiments, other metal mirrors, such as a mirror fabricated from platinum is used as mirror 144. In an embodiment, the area of interaction on the cathode was selected to be a flat 300 μm in diameter. Moreover, in the embodiment illustrated, the frequency doubled optical pulse was shaped to provide a beam with a beam waist of a predetermined diameter at the surface of the cathode. In a specific embodiment, the beam waist was about 50 μm. In alternative embodiments, the beam waist ranged from about 30 μm to about 200 μm. Of course, the particular dimensions will depend on the particular applications. The frequency doubled optical pulse train was steered inside the chamber using a computer controlled mirror in a specific embodiment. In a specific embodiment, the optical pulse train is directed toward a front-illuminated photocathode where the irradiation of the cathode by the laser results in the generation of electron pulses via the photoelectric effect. Irradiation of a cathode with light having an energy above the work function of the cathode leads to the ejection of photoelectrons. That is, a pulse of electromagnetic energy above the work function of the cathode ejects a pulse of electrons according to a preferred embodiment. Generally, the cathode is maintained at a temperature of 1000 K, well below the thermal emission threshold temperature of about 1500 K, but this is not required by the present invention. In alternative embodiments, the cathode is maintained at room temperature. In some embodiments, the cathode is adapted to provide an electron pulse of predetermined pulse width. The trajectory of the electrons after emission follows the lens design of the TEM, namely the condenser, the objective, and the projector lenses. Depending upon the embodiment, there may also be other configurations. In the embodiment illustrated, the cathode is a Mini-Vogel mount single crystal lanthanum hexaboride (LaB6) cathode shaped as a truncated cone with a flat of 300 μm at the apex and a cone angle of 90°, available from Applied Physics Technologies, Inc., of McMinnville, Oreg. As is often known, LaB6 cathodes are regularly used in transmission and scanning electron microscopes. The quantum efficiency of LaB6 cathodes is about 10−3 and these cathodes are capable of producing electron pulses with temporal pulse widths on the order of 10−13 seconds. In some embodiments, the brightness of electron pulses produced by the cathode is on the order of 109 A/cm2/rad2 and the energy spread of the electron pulses is on the order of 0.1 eV. In other embodiments, the pulse energy of the laser pulse is reduced to about 500 pJ per pulse, resulting in approximately one electron/pulse Generally, the image quality acquired using a TEM is proportional to the number of electrons passing through the sample. That is, as the number of electrons passing through the sample is increased, the image quality increases. Some pulsed lasers, such as some Q-switched lasers, reduce the pulse count to produce a smaller number of pulses characterized by higher peak power per pulse. Thus, some laser amplifiers operate at a 1 kHz repetition rate, producing pulses with energies ranging from about 1 μJ to about 2 mJ per pulse. However, when such high peak power lasers are used to generate electron pulses using the photoelectric effect, among other issues, both spatial and temporal broadening of the electron pulses adversely impact the pulse width of the electron pulse or packet produced. In some embodiments of the present invention, the laser is operated to produce low power pulses at higher repetition rates, for example, 80 MHz. In this mode of operation, benefits available using lower power per pulse are provided, as described below. Additionally, because of the high repetition rate, sufficient numbers of electrons are available to acquire high quality images. In some embodiments of the present invention, the laser power is maintained at a level of less than 500 pJ per pulse to prevent damage to the photocathode. As a benefit, the robustness of the photoemitter is enhanced. Additionally, laser pulses at these power levels prevent space-charge broadening of the electron pulse width during the flight time from the cathode to the sample, thus preserving the desired femtosecond temporal resolution. Additionally, the low electron count per pulse provided by some embodiments of the present invention reduces the effects of space charge repulsion in the electron pulse, thereby enhancing the focusing properties of the system. As one of skill in the art will appreciated, a low electron count per pulse, coupled with a high repetition rate of up to 80 MHz provided by the femtosecond laser, provides a total dose as high as one electron/Å2 as generally utilized in imaging applications. In alternative embodiments, other suitable cathodes capable of providing a ultrafast pulse of electrons in response to an ultrafast optical pulse of appropriate wavelength are utilized. In embodiments of the present invention, the cathode is selected to provide a work function correlated with the wavelength of the optical pulses provided by the SHG device. The wavelength of radiation is related to the energy of the photon by the familiar relation λ(μm)≈1.24÷v(eV), where λ is the wavelength in microns and v is the energy in eV. For example, a LaB6 cathode with a work function of 2.7 eV is matched to optical pulses with a wavelength of 400 nm (v=3.1 eV) in an embodiment of the present invention. As illustrated, the cathode is enclosed in a vacuum chamber 130, for example, a housing for a transmission electron microscope (TEM). In general, the vacuum in the chamber 130 is maintained at a level of less than 1×10−6 torr. In alternative embodiments, the vacuum level varies from about 1×10−6 torr to about 1×10−10 torr. The particular vacuum level will be a function of the varied applications. In embodiments of the present invention, the short duration of the photon pulse leads to ejection of photoelectrons before an appreciable amount of the deposited energy is transferred to the lattice of the cathode. In general, the characteristic time for thermalization of the deposited energy in metals is below a few picoseconds, thus no heating of the cathode takes place using embodiments of the present invention. Electrons produced by the cathode 140 are accelerated past the anode 142 and are collimated and focused by electron lens assembly 146 and directed along electron imaging path 148 toward the sample 150. The electron lens assembly generally contains a number of electromagnetic lenses, apertures, and other elements as will be appreciated by one of skill in the art. Electron lens assemblies suitable for embodiments of the present invention are often used in TEMs. The electron pulse propagating along electron imaging path 148 is controlled in embodiments of the present invention by a controller (not shown, but described in more detail with reference to certain Figures below) to provide an electron beam of predetermined dimensions, the electron beam comprising a train of ultrafast electron pulses. The relationship between the electron wavelength (λde Broglie) and the accelerating voltage (U) in an electron microscope is given by the relationship λde Broglie=h/(2m0eU)1/2, where h, m0, e are Planck's constant, the electron mass, and an elementary charge. As an example, the de Broglie wavelength of an electron pulse at 120 kV corresponds to 0.0335 Å, and can be varied depending on the particular application. The bandwidth or energy spread of an electron packet is a function of the photoelectric process and bandwidth of the optical pulse used to generate the electron packet or pulse. Electrons passing through the sample or specimen 150 are focused by electron lens assembly 152 onto a detector 154. Although FIG. 1 illustrates two electron lens assemblies 146 and 152, the present invention is not limited to this arrangement and can have other lens assemblies or lens assembly configurations. In alternative embodiments, additional electromagnets, apertures, other elements, and the like are utilized to focus the electron beam either prior to or after interaction with the sample, or both. Detection of electrons passing through the sample, including single-electron detection, is achieved in one particular embodiment through the use of an ultrahigh sensitivity (UHS) phosphor scintillator detector 154 especially suitable for low-dose applications in conjunction with a digital CCD camera. In a specific embodiment, the CCD camera was an UltraScan™ 1000 UHS camera, manufactured by Gatan, Inc., of Pleasanton, Calif. The UltraScan™ 1000 CCD camera is a 4 mega-pixel (2048×2048) camera with a pixel size of 14 μm×14 μm, 16-bit digitization, and a readout speed of 4 Mpixels/sec. In the embodiment illustrated, the digital CCD camera is mounted under the microscope in an on-axis, below the chamber position. In order to reduce the noise and picture artifacts, in some embodiments, the CCD camera chip is thermoelectrically cooled using a Peltier cooler to a temperature of about −25° C. The images from the CCD camera were obtained with DigitalMicrograph™ software embedded in the Tecnai™ user interface, also available from Gatan, Inc. Of course, there can be other variations to the CCD camera, cooler, and computer software, depending upon the embodiment. FIG. 2 is a simplified perspective diagram of a 4D electron microscope system according to an embodiment of the present invention. The system illustrated in FIG. 2 is also referred to as an ultrafast electron microscope (UEM2) and was built at the present assignee. The integration of two laser systems with a modified electron microscope is illustrated, together with a representative image showing a resolution of 3.4 Å obtained in UEM2 without the field-emission-gun (FEG) arrangement of a conventional TEM. In one embodiment of the system illustrated in FIG. 2, the femtosecond laser system (fs laser system) is used to generate the single-electron packets and the nanosecond laser system (ns laser system) was used both for single-shot and stroboscopic recordings. In the single-electron mode of operation, the coherence volume is well defined and appropriate for image formation in repetitive events. The dynamics are fully reversible, retracing the identical evolution after each initiating laser pulse; each image is constructed stroboscopically, in seconds, from typically 106 pulses and all time-frames are processed to make a movie. The time separation between pulses can be varied to allow complete heat dissipation in the specimen. Without limiting embodiments of the present invention, it is believed that the electrons in the single electron packets have a transverse coherence length that is comparable to the size of the object that is being imaged. Since the subsequent electrons have a coherence length on the order of the size of the object, the electrons “see” the whole object at once. To follow the area-specific changes in the hundreds of images collected for each time scan, we obtained selected-area-image dynamics (SAID) and selected-area-diffraction dynamics (SADD); for the former, in real space, from contrast change and for the latter, in Fourier space, from changes of the Bragg peak separations, amplitudes, and widths. It is the advantage of microscopy that allows us to perform this parallel-imaging dynamics with pixel resolution, when compared with diffraction. As shown below, it would not have been possible to observe the selected temporal changes if the total image were to be averaged over all pixels, in this case 4 millions. As illustrated in FIG. 2, a TEM is modified to provide a train of electron pulses used for imaging in addition to the thermionic emission source used for imaging of samples. Merely by way of example, an FEI Tecnai™ G2 12 TWIN, available from FEI Company in Hillsboro, Oreg., may be modified according to embodiments of the present invention. The Tecnai™ G2 12 TWIN is an all-in-one 120 kV (λde Broglie=0.0335 Å) high-resolution TEM optimized for 2D and 3D imaging at both room and liquid-nitrogen temperatures. Embodiments of the present invention leverage capabilities provided by commercial TEMs such as automation software, detectors, data transfer technology, and tomography. In particular, in some embodiments of the present invention, a five-axis, motor-driven, precision goniometer is used with computer software to provide automated specimen tilt combined with automated acquisition of images as part of a computerized tomography (CT) imaging system. In these embodiments, a series of 2D images are captured at various specimen positions and combined using computer software to generate a reconstructed 3D image of the specimen. In some embodiments, the CT software is integrated with other TEM software and in other embodiments, the CT software is provided off-line. One of ordinary skill in the art would recognize many variations, modifications, and alternatives. In certain embodiments in which low-electron content electron pulses are used to image the sample, the radiation damage is limited to the transit of the electrons in the electron pulses through the sample. Typically, samples are on the order of 100 nm thick, although other thicknesses would work as long as certain electrons may traverse through the sample. Thus, the impact of radiation damage on these low-electron content electron pulse images is limited to the damage occurring during this transit time. Radiation induced structural damage occurring on longer time scales than the transit time will not impact the collected image, as these damage events will occur after the structural information is collected. Utilizing the apparatus described thus far, embodiments of the present invention provide systems and methods for imaging material and biological specimens both spatially and temporally with atomic-scale spatial resolution on the order of 1 nm and temporal resolution on the order of 100 fs. At these time scales, energy randomization is limited and the atoms are nearly frozen in place, thus methods according to the present invention open the door to time-resolved studies of structural dynamics at the atomic scale in both space and time. Details of the present computer system according to an embodiment of the present invention may be explained according to the description below. Referring to FIG. 2, a photograph of a UEM2 in accordance with embodiments of the present invention is illustrated, together with a high-resolution image of graphitized carbon. As illustrated, two laser systems (fs and ns) are utilized to provide a wide range of temporal scales used in 4D electron imaging. A 200-kV TEM is provided with at least two ports for optical access to the microscope housing. Using one or more mirrors (e.g., two mirrors), it is possible to switch between the laser systems to cover both the fs and ns experiments. The optical pulses are directed to the photocathode to generate electron packets, as well as to the specimen to initiate (clock) the change in images with a well-defined delay time Δt. The time axis is defined by variable delay between the electron generating and clocking pulses using the delay stage 170 illustrated in FIG. 1. Details of development of ultrafast electron microscopy with atomic-scale real-, energy-, and Fourier-space resolutions is now provided. The second generation UEM2 described in FIG. 2 provides images, diffraction patterns, and electron-energy spectra, and has application for nanostructured materials and organometallic crystals. The separation between atoms in direct images, and the Bragg spots/Debye-Scherrer rings in diffraction, are clearly resolved, and the electronic structure and elemental energies in the electron-energy-loss spectra (EELS) and energy-filtered-transmission-electron microscopy (EFTEM) are obtained. The development of 4D ultrafast electron microscopy and diffraction have made possible the study of structural dynamics with atomic-scale spatial resolution, so far in diffraction, and ultrashort time resolution. The scope of applications is wide-ranging with studies spanning diffraction of isolated structures in reactions (gas phase), nanostructures of surfaces and interfaces (crystallography), and imaging of biological cells and materials undergoing first-order phase transitions. Typically, for microscopy the electron was accelerated to 120 keV and for diffraction to 30 keV, respectively, and issues of group velocity mismatch, in situ clocking (time zero) of the change, and frame referencing were addressed. One powerful concept implemented is that of “tilted pulses,” which allow for the optimum resolution to be reached at the specimen. For ultrafast electron microscopy, the concept of “single-electron” imaging is fundamental to some embodiments. The electron packets, which have a well-defined picometer-scale de Broglie wave length, are generated in the microscope by femtosecond optical pulses (photoelectric effect) and synchronized with other optical pulses to initiate the change in a temperature jump or electronic excitation. Because the number of electrons in each packet is one or a few, the Coulomb repulsion (space charge) between electrons is reduced or eliminated and the temporal resolution can reach the ultimate, that of the optical pulse. The excess energy above the work function determines the electron energy spread and this, in principle, can be minimized by tuning the pulse energy. The spatial resolution is then only dependent on the total number of electrons because for each packet the electron “interferes with itself” and a coherent buildup of the image is achievable. The coherence volume, given by:Vc=λde Broglie2(R/a)2ve(h/ΔE)establishes that the degeneracy factor is much less than one and that each Fermionic electron is independent, without the need of the statistics commonly used for Bosonic photons. The volume is determined by the values of longitudinal and transverse coherences; Vc is on the order of 106 nm3 for typical values of R (distance to the source), a (source dimension), ve (electron velocity), and ΔE (energy spread). Unlike the situation in transmission electron microscopy (TEM), coherence and image resolution in UEM are thus determined by properties of the optical field, the ability to focus electrons on the ultrashort time scale, and the operational current density. For both “single electron” and “single pulse” modes of UEM, these are important considerations for achieving the ultimate spatio-temporal resolutions for studies of materials and biological systems. Atomic-scale resolution in real-space imaging can be achieved utilizing the second generation ultrafast electron microscopy system (UEM2) of FIG. 2. With UEM2, which operates at 200 keV (λde Broglie=2.507 pm), energy-space (electron-energy-loss spectroscopy, EELS) and Fourier-space (diffraction) patterns of nanostructured materials are possible. The apparatus can operate in the scanning transmission electron microscope (STEM) mode, and is designed to explore the vast parameter space bridging the gap between the two ideal operating modes of single-electron and single-pulse imaging. With these features, UEM2 studies provide new limits of resolution, image mapping, and elemental analysis. Here, demonstrated are the potential by studying gold particles and islands, boron nitride crystallites, and organometallic phthalocyanine crystals. FIG. 2A displays the conceptual design of UEM2, which, as with the first generation (UEM1—described generally in FIG. 1), comprises a femtosecond laser system and an electron microscope modified for pulsed operation with femtosecond electron packets. A schematic representation of optical, electric, and magnetic components are shown. The optical pulse train generated from the laser, in this case having a variable pulse width of 200 fs to 10 ps and a variable repetition rate of 200 kHz to 25 MHz, is divided into two parts, after harmonic generation, and guided toward the entries of the design hybrid electron microscope. The frequency-tripled optical pulses are converted to the corresponding probe electron pulses at the photocathode in the hybrid FEG, whereas the other optical pump beam excites (T-jump or electronic excitation) in the specimen with a well-defined time delay with respect to the probe electron beam. The probe electron beam through the specimen can be recorded as an image (normal or filtered, EFTEM), a diffraction pattern, or an EEL spectrum. The STEM bright-field detector is retractable when it is not in use. The laser in an embodiment is a diode-pumped Yb-doped fiber oscillator/amplifier (Clark-MXR; in development), which produces ultrashort pulses of up to 10 μJ at 1030 nm with variable pulse width (200 fs-10 ps) and repetition rate (200 kHz-25 MHz). The output pulses pass through two successive nonlinear crystals to be frequency doubled (515 nm) and tripled (343 nm). The harmonics are separated from the residual infrared radiation (IR) beam by dichroic mirrors, and the frequency-tripled pulses are introduced to the photocathode of the microscope for generating the electron pulse train. The residual IR fundamental and frequency-doubled beams remain available to heat or excite samples and clock the time through a computer-controlled optical delay line for time-resolved applications. The electron microscope column is that of a designed hybrid 200-kV TEM (Tecnai 20, FEI) integrated with two ports for optical access, one leading to the photocathode and the other to the specimen. The field emission gun (FEG) in the electron-generation assembly adapts a lanthanum hexaboride (LaB6) filament as the cathode, terminating in a conical electron source truncated to leave a flat tip area with a diameter of 16 μm. The tip is located in a field environment controlled by suppressor and extractor electrodes. The gun can be operated as either a thermal emission or a photoemission source. The optical pulses are guided to the photocathode as well as to the specimen by a computer-controlled, fine-steering mirror in an externally-mounted and x-ray-shielded periscope assembly. Each laser beam can be focused to a spot size of <30 μm full width at half maximum (FWHM) at its respective target when the beam is expanded to utilize the available acceptance angle of the optical path. Various pulse-energy, pulse-length, and focusing regimes have been used in the measurements reported here. For UEM measurements, the cathode was heated to a level below that needed to produce detectible thermal emission, as detailed below, and images were obtained using both the TEM and the UEM2 mode of operation. For applications involving EELS and energy-filtered-transmission-electron microscopy (EFTEM), the Gatan Imaging Filter (GIF) Tridiem, of the so-called post-column type, was attached below the camera chamber. The GIF accepts electrons passing through an entrance aperture in the center of the projection chamber. The electron beam passes through a 90° sector magnet as shown in FIG. 2A, which bends the primary beam through a 10 cm bending radius and thereby separates the electrons according to their energy into an energy spectrum. An energy resolution of 0.87 eV was measured for the EELS zero-loss peak in thermal mode operation of the TEM. A retractable slit is located after the magnet followed by a series of lenses. The lenses restore the image or diffraction pattern at the entrance aperture and finally it can be recorded on a charge-coupled device (CCD) camera (UltraScan 1000 FT) at the end of the GIF with the Digital Micrograph software. The digital camera uses a 2,048×2,048 pixel CCD chip with 14 μm square pixels. Readout of the CCD is done as four independent quadrants via four separate digitizing signal chains. This 4-port readout camera combines single-electron sensitivity and 16-bit pixel depth with high-speed sensor readout (4 Mpix/s). Additionally, for scanning-transmission-electron microscopy (STEM), the UEM2 is equipped with a bright-field (BF) detector with a diameter of 7 mm and an annular dark-field (ADF) detector with an inner diameter of 7 mm and an outer diameter of 20 mm. Both detectors are located in the near-axis position underneath the projection chamber. The BF detector usually collects the same signal as the TEM BF image, i.e., the transmitted electrons, while the ADF detector collects an annulus at higher angle where only scattered electrons are detected. The STEM images are recorded with the Tecnai Imaging & Analysis (TIA) software. To observe the diffraction pattern, i.e., the back focal plane of the objective lens, we inserted a selected area aperture into the image plane of the objective lens, thus creating a virtual aperture in the plane of the specimen. The result is a selected area diffraction (SAD) pattern of the region of interest only. Adjustment of the intermediate and projector lens determines the camera length. Diffraction patterns are processed and analyzed for crystal structure determination. Several features of the UEM2 system are worthy of note. First, the high repetition rate amplified laser source allows us to illuminate the cathode with 343 nm pulses of energies above 500 nJ, compared with typical values of 3 nJ near 380 nm for UEM1. Thus, a level of average optical power for electron generation comparable to that of UEM1 operating at 80 MHz, but at much lower repetition rates, was able to be delivered. The pulse energy available in the visible and IR beams is also at least two orders of magnitude greater than for UEM1, allowing for exploration of a much greater range in the choice of sample excitation conditions. Second, the hybrid 200-kV FEG, incorporating an extractor/suppressor assembly providing an extractor potential of up to 4 kV, allows higher resolving power and greater flexibility and control of the conditions of electron generation. Third, with simple variation of optical pulse width, the temporal and spatial resolution can be controlled, depending on the requirements of each experiment. Fourth, with variation of spacing between optical pulses without loss of pulse energy, a wide range of samples can be explored allowing them to fully relax their energy after each excitation pulse and rewind the clock precisely; with enough electrons, below the space-charge limit, single-pulse recording is possible. Finally, by the integration of the EELS spectrometer, the system is empowered with energy resolution in addition to the ultrafast time resolution and atomic-scale space resolution. The following results demonstrate the capabilities of UEM2 in three areas: real-space imaging, diffraction, and electron energy resolution. Applications of the present invention are not limited to these particular examples. First discussed are the images recorded in the UEM mode, of gold particles and gold islands on carbon films. FIGS. 2Ba-f are UEM2 images obtained with ultrafast electron pulses. Shown are gold particles (a, d) and gold islands (c, f) on carbon films. UEM2 background images (b, e) obtained by blocking the photoelectron-extracting femtosecond laser pulses. For the UEM2 images of gold particles, we used the objective (contrast) aperture of 40 μm to eliminate diffracted beams, while no objective aperture was used for the gold-island images. FIGS. 2Aa and 2Ad show gold particles of uniform size dispersed on a carbon film. From the higher magnification image of FIG. 2Ad, corresponding to the area indicated by the black arrow in FIG. 2Aa, it is found that the gold particles have a size of 15 nm, and the minimum particle separation seen in the image is 3 nm. It should be noted that FIGS. 2Ab and 2Ae were recorded under identical conditions to FIGS. 2Aa and 2Ad, respectively, but without cathode irradiation by the femtosecond laser pulses. No images were observed, demonstrating that non-optically generated electrons from our warm cathode were negligible. Similar background images with the light pulses blocked were routinely recorded and checked for all cathode conditions used in this study. The waffle (cross line) spacing of the cross grating replica (gold islands) seen in FIG. 2Ac is known to be 463 nm. The gold islands are observed in FIG. 2Af, where the bright regions correspond to the amorphous carbon support film and the dark regions to the nanocrystalline gold islands. It is found that the islands may be interconnected or isolated, depending on the volume fraction of the nanocrystalline phases. To test the high-resolution capability of UEM utilizing phase contrast imaging, an organometallic compound, chlorinated copper phthalocyanine (hexadecachlorophthalocyanine, C32Cl16CuN8), was investigated. The major spacings of lattice fringes of copper of this molecule in projection along the c-axis are known to be 0.88, 1.30, and 1.46 nm, with atomic spacings of 1.57 and 1.76 nm. FIGS. 2Ca-b are high-resolution, phase-contrast UEM images. Shown are an image in FIG. 2Ca and digital diffractogram in FIG. 2Cb of an organometallic crystal of chlorinated copper phthalocyanine. The diffractogram was obtained by the Fourier transform of the image in FIG. 2Ca. The high-resolution image was taken near the Scherzer focus for optimum contrast, which was calculated to be 90.36 nm for a spherical aberration coefficient Cs of the objective lens of 2.26 mm. The objective aperture was not used. FIG. 2Da exhibits the lattice fringes observed by UEM, where the black lines correspond to copper layers parallel to the c-axis. The Fourier transform of FIG. 2Da is shown in FIG. 2Db, discussed below, and the clear reciprocity (without satellite peaks in the F.T.) indicates the high degree of order in crystal structure. FIG. 2D shows high-resolution, phase-contrast UEM image and structure of chlorinated copper phthalocyanine The high-resolution image shown in FIG. 2Da is a magnified view of the outlined area in FIG. 2Ca. The representation of the crystal structure shown in FIG. 2Db is shown in projection along the c axis, and the assignment of the copper planes observed in FIG. 2Da is indicated by the gray lines. The spheres are the copper atoms. FIG. 2Da is an enlargement of the area outlined in FIG. 2Ca, clearly showing the lattice fringe spacing of 1.46 nm, corresponding to the copper planes highlighted in gray in FIG. 2Db, in which a unit cell is shown in projection along the c-axis. Regions without lattice fringes are considered to correspond to crystals with unfavorable orientation, or amorphous phases of phthalocyanine, or the carbon substrate. It is known that in high resolution images, the lattice fringes produced by the interference of two waves passing through the back focal plane, i.e., the transmitted and diffracted beams, are observed only in crystals where the lattice spacing is larger than the resolution of the TEM. In the profile inset of FIG. 2Da, it should be noted that the FWHM was measured to be approximately 7 Å, directly indicating that our UEM has the capability of sub-nanometer resolution. The digital diffractogram obtained by the Fourier transform of the observed high-resolution image of FIG. 2Ca is shown in FIG. 2Cb. In the digital diffractogram, the peaks represent the fundamental spatial frequency of the copper layers (0.69 nm−1), and higher harmonics thereof. A more powerful means of obtaining reciprocal-space information such as this is the direct recording of electron diffraction, also available in UEM. FIGS. 2Ea-f show measured and calculated electron diffraction patterns of gold islands and boron nitride (BN) on carbon films, along with the corresponding real-space images of each specimen, all recorded by UEM. Shown are images and measured and calculated electron diffraction patterns of gold islands (a,b,c) and boron nitride (BN) (d,e,f) on carbon films. The incident electron beam is parallel to the [001] direction of the BN. All diffraction patterns were obtained by using the selected-area diffraction (SAD) aperture, which selected an area 6 μm in diameter on the specimen. Representative diffraction spots were indexed as indicated by the arrowheads. In FIG. 2Eb, the electron diffraction patterns exhibit Debye-Scherrer rings formed by numerous diffraction spots from a large number of face-centered gold nanocrystals with random orientations. The rings can be indexed as indicated by the white arrowheads. The diffraction pattern of BN in FIG. 2Ee is indexed by the hexagonal structure projected along the [001] axis as shown in FIG. 2Ef. It can be seen that there are several BN crystals with different crystal orientations, besides that responsible for the main diffraction spots indicated by the white arrowheads. In order to explore the energy resolution of UEM, we investigated the BN specimen in detail by EELS and EFTEM. FIG. 2F shows energy-filtered UEM images and spectrum. FIG. 2F shows a zero-loss filtered image (FIG. 2Fa), boron K-edge mapping image (FIG. 2Fb), thickness mapping image (FIG. 2Fc), and corresponding electron-energy-loss (EEL) spectrum (FIG. 2Fd) of the boron nitride (BN) sample. The 5.0- and 1.0-mm entrance aperture were used for mapping images and EEL spectrum, respectively. The thickness at the point indicated by the asterisk in FIG. 2Fc is estimated to be 41 nm. ZL stands for zero-loss. The boron map was obtained by the so-called three-window method. In the boron map of FIG. 2Fb, image intensity is directly related to areal density of boron. In the thickness map of FIG. 2Fc, the brightness increases with increasing thickness: d (thickness)=λ(β)ln(It/I0), where λ is the mean free path for inelastic scattering under a given collection angle β, I0 is the zero-loss (ZL) peak intensity, and It is the total intensity. The thickness in the region indicated by the asterisk in FIG. 2Fc was estimated to be 41 nm. In the EEL spectrum of FIG. 2Fd, the boron K-edge, carbon K-edge, and nitrogen K-edge are observed at the energy of 188, 284, and 401 eV, respectively. In the boron K-edge spectrum, sharp π* and σ* peaks are visible. The carbon K-edge spectrum is considered to result from the amorphous carbon film due to the existence of small and broad peaks at the position π* and σ*, being quite different from spectra of diamond and graphite. With the capabilities of the UEM2 system described herein, structural dynamics can be studied, as with UEM1, but with the new energy and spatial resolution are achieved here. Specimens will be excited in a T-jump or electronic excitation by the femtosecond laser pulses (FIG. 2A) scanned in time with respect to the electron packets which will probe the changes induced in material properties through diffraction, imaging, or electron energy loss in different regions, including that of Compton scattering. Also planned to be explored is the STEM feature in UEM, particularly the annular dark-field imaging, in which compositional changes are evident in the contrast (Z contrast). Such images are known to offer advantages over high-resolution TEM (relative insensitivity to focusing errors and ease of interpretation). Electron fluxes will be optimized either through changes of the impinging pulse fluence or by designing new photocathode materials. In this regard, with higher brightness the sub-angstrom limit should be able to be reached. The potential for applications in materials and biological research is rich. FIG. 3 is a simplified diagram of a computer system 310 that is used to oversee the system of FIGS. 1 and 2 according to an embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims herein. One of ordinary skill in the art would recognize many other modifications, alternatives, and variations. As shown, the computer system 310 includes display device 320, display screen 330, cabinet 340, keyboard 350, and mouse 370. Mouse 370 and keyboard 350 are representative “user input devices.” Mouse 370 includes buttons 380 for selection of buttons on a graphical user interface device. Other examples of user input devices are a touch screen, light pen, track ball, data glove, microphone, and so forth. The system is merely representative of but one type of system for embodying the present invention. It will be readily apparent to one of ordinary skill in the art that many system types and configurations are suitable for use in conjunction with the present invention. In a preferred embodiment, computer system 310 includes a Pentium™ class based computer, running Windows™ NT, XP, or Vista operating system by Microsoft Corporation. However, the system is easily adapted to other operating systems such as any open source system and architectures by those of ordinary skill in the art without departing from the scope of the present invention. As noted, mouse 370 can have one or more buttons such as buttons 380. Cabinet 340 houses familiar computer components such as disk drives, a processor, storage device, etc. Storage devices include, but are not limited to, disk drives, magnetic tape, solid-state memory, bubble memory, etc. Cabinet 340 can include additional hardware such as input/output (I/O) interface cards for connecting computer system 310 to external devices external storage, other computers or additional peripherals, which are further described below. FIG. 4 is a more detailed diagram of hardware elements in the computer system of FIG. 3 according to an embodiment of the present invention. This diagram is merely an example, which should not unduly limit the scope of the claims herein. One of ordinary skill in the art would recognize many other modifications, alternatives, and variations. As shown, basic subsystems are included in computer system 310. In specific embodiments, the subsystems are interconnected via a system bus 375. Additional subsystems such as a printer 374, keyboard 378, fixed disk 379, monitor 376, which is coupled to display adapter 382, and others are shown. Peripherals and input/output (I/O) devices, which couple to I/O controller 371, can be connected to the computer system by any number of means known in the art, such as serial port 377. For example, serial port 377 can be used to connect the computer system to a modem 381, which in turn connects to a wide area network such as the Internet, a mouse input device, or a scanner. The interconnection via system bus allows central processor 373 to communicate with each subsystem and to control the execution of instructions from system memory 372 or the fixed disk 379, as well as the exchange of information between subsystems. Other arrangements of subsystems and interconnections are readily achievable by those of ordinary skill in the art. System memory, and the fixed disk are examples of tangible media for storage of computer programs, other types of tangible media include floppy disks, removable hard disks, optical storage media such as CD-ROMS and bar codes, and semiconductor memories such as flash memory, read-only-memories (ROM), and battery backed memory. Although the above has been illustrated in terms of specific hardware features, it would be recognized that many variations, alternatives, and modifications can exist. For example, any of the hardware features can be further combined, or even separated. The features can also be implemented, in part, through software or a combination of hardware and software. The hardware and software can be further integrated or less integrated depending upon the application. Further details of the functionality, which may be carried out using a combination of hardware and/or software elements, of the present invention can be outlined below according to the figures. Embodiments of the present invention enable ultrafast imaging with applications in studies of structural and morphological changes in single-crystal gold and graphite films, which exhibit entirely different dynamics, as discussed below. For both, the changes were initiated by in situ femtosecond impulsive heating, while image frames and diffraction patterns were recorded in the microscope at well-defined times following the temperature-jump. The time axis in the microscope is independent of the response time of the detector, and it is established using a variable delay-line arrangement; a 1-μm change in optical path of the initiating (clocking) pulse corresponds to a time step of 3.3 fs. FIG. 5 illustrates both time-resolved images and diffraction. In this example, the images in FIGS. 5A and 5B were obtained stroboscopically at several time delays after heating with the fs pulse (fluence of 1.7 mJ/cm2). The specimen is a gold single crystal film mounted on a standard 3-mm 400-mesh grid. Shown are the bend contours (dark bands), {111} twins (sharp straight white lines) and holes in the sample (bright white circles). The insets in FIG. 5B are image-difference frames Im(tref; t) with respect to the image taken at −84 ps. The gold thickness was determined to be 8 nm by electron energy loss spectroscopy (EELS). FIG. 5C illustrates the time dependence of image cross-correlations of the full image from four independent scans taken with different time steps. A fit to biexponential rise of the 1 ps step scan is drawn, yielding time constants of 90 ps and 1 ns. FIG. 5D illustrates the time dependence of image cross-correlations at 1 ps time steps for the full image and for selected regions of interest SAI #1, #2, and #3, as shown in FIG. 5A. FIGS. 5E and 5F are diffraction patterns obtained using a single pulse of 6×106 electrons at high peak fluence (40 mJ/cm2) and selected-area aperture of 25 μm diameter. Two frames are given to indicate the change. Diffraction spots were indexed and representative indices are shown as discussed below. FIGS. 5A and 5B illustrate representative time-framed images of the gold nanocrystal using the fs excitation pulses at a repetition rate of 200 kHz and peak excitation fluence of ˜1.7 mJ/cm2. In FIG. 5A, taken at −84 ps, before the clocking pulse (t=0), typical characteristic features of the single crystal gold in the image are observed: twins and bend contours. Bend contours, which appear as broad fuzzy dark lines in the image, are diffraction contrast effects occurring in warped or buckled samples of constant thickness. In the dark regions, the zone axis (the crystal [100]) is well aligned with the incident electron beam and electrons are scattered efficiently, whereas in the lighter regions the alignment of the zone axis deviates more and the scattering efficiency is lower. Because bend contours generally move when deformation causes tilting of the local crystal lattice, they provide in images a sensitive visual indicator of the occurrence of such deformations. At positive times, following t=0, visual dynamical changes are observed in the bend contours with time steps from 0.5 ps to 50 ps. A series of such image frames with equal time steps provide a movie of the morphological dynamics. To more clearly display the temporal evolution, image-difference frames were constructed. Depicted as insets in the images of FIG. 5B, are those obtained when referencing to the −84 ps frame; for t=+66 ps and +151 ps. In the difference images, the regions of white or black directly indicate locations of surface morphology change (bend contour movement), while gray regions are areas where the contrast is unchanged from that of the reference frame. It is noted that the white and black features in the difference images are nm-scale dynamical change, indicating the size of the induced deformations. Care was taken to insure the absence of long-term specimen drifts as they can cause apparent contrast change. To quantify the changes in the image the following method of cross-correlation was used. The normalized cross correlation of an image at time t with respect to that at time t′ is expressed as: γ ⁡ ( t ) = ∑ x , y ⁢ C x , y ⁡ ( t ) ⁢ C x , y ⁡ ( t ′ ) ∑ x , y ⁢ C x , y ⁡ ( t ) 2 ⁢ ∑ x , y ⁢ C x , y ⁡ ( t ′ ) 2 where the contrast Cx,y(t)=[Ix,y(t)−Ī(t)]/Ī(t); Ix,y(t) and Ix,y(t′) are the intensities of pixels at the position of (x,y) at times t and t′, and Ī(t) and Ī(t′) are the means of Ix,y(t) and Ix,y(t′), respectively. This correlation coefficient γ(t) is a measure of the temporal change in “relief pattern” between the two images being compared, which can be used as a guide to image dynamics as a function of time. Two types of cross-correlation plots were made, those referenced to a fixed image frame before t=0 and others that show correlation between adjacent time points. (Another quantity that shows time dependence qualitatively similar to that of the image cross-correlation is the standard deviation of pixel intensity in difference images). FIGS. 5C and 5D show the cross-correlation values between the image at each measured time point and a reference image recorded before the arrival of the clocking pulse. The experiments were repeated, for different time-delay steps (500 fs, 1 ps, 5 ps, and 50 ps), and similar results were obtained, showing that morphology changes are completely reversible and reproducible over each 5 μs inter-pulse interval. The adjacent-time cross-correlations reveal the timescales for intrinsic changes in the images, which disappear for time steps below 5 ps, consistent with full-image rise in time. Over all pixels, the time scale for image change covers the full range of time delay, from ps to ns, indicating the collective averaging over sites of the specimen; as shown in FIG. 5C the overall response can be fit to two time constants of 90 ps and 1 ns. The power of selected area image dynamics (SAID) is illustrated when the dynamics of the bend contours are followed in different selected areas of the image, noted in the micrographs as SAI #1, 2, and 3. The corresponding image cross-correlations (FIG. 5D) have different shape and amplitude from each other and from the full image correlation. The large differences observed here and for other data sets, including onsets delayed in time and sign reversals, indicate the variation in local deformation dynamics. In FIGS. 5G-L, a time-resolved SAI at higher magnification is depicted. A broad and black “penguin-like” contour is observed as the dominant feature of this area. As shown in the frames, a colossal response to the fs heating is noted. The gray region inside the black contour appears and broadens with time. Also, a new black contour above the large central white hole begins to be evident at 1200 ps, and gains substantial intensity over the following 50 ps. All frames taken can be used to construct a movie of SAID. The observed SAID changes correspond to diffraction contrast (bright-field) effects in bend contours, as mentioned above. It is known that the shape of bend contours can be easily altered by sample tilting or heating inside the microscope. However, here in the ultrafast electron microscope (UEM) measurements, the changes in local tilt are transient in nature, reflecting the temporal changes of morphology and structure. Indeed, when the experiments were repeated in the TEM mode of operation, i.e., for the same heating laser pulse and same scanning time but with continuous electron probe beam, no image change was observed. This is further supported by the change in diffraction observed at high fluences and shown in FIGS. 5E and 5F for two frames, at negative time and at +50 ns; in the latter, additional Bragg spots are visible, a direct evidence of the transient structural change due to bulging at longer times. Whereas real-space imaging shows the time-dependent morphology, the selected area diffraction dynamics (SADD) patterns provide structural changes on the ultrashort timescale. Because the surface normal of the film is parallel to the [100] zone axis, the diffraction pattern of the sample was properly indexed by the face-centered-cubic (fcc) structure projected along the [100] zone axis at zero tilt angle (see FIG. 5E). From the positions of the spots in FIG. 5F, which are reflections from the {113} and {133} planes, forbidden in the [100] zone-axis viewing, we measured the interplanar spacings to be 1.248 and 0.951 Å, respectively. With selected area diffraction, Bragg peak separations, amplitudes, and widths were obtained as a function of time. The results indicate different timescales from those of image dynamics. FIG. 6A illustrates structural dynamics and heat dissipation in gold and FIG. 6B illustrates coherent resonance of graphite. Referring to FIG. 6A, SADD for fs excitation at 1.7 mJ/cm2 peak fluence (519 nm) is illustrated. The Bragg separation for all peaks and the amplitude of the {042} peaks are shown in the main panel; the inset gives the 2.2 μs recovery (by cooling) of the structure obtained by stroboscopic ns excitation at 7 mJ/cm2. The peak amplitude has been normalized to the transmitted beam amplitude, and the time dependence of amplitude and separation is fit as an exponential rise, and a delay with rise, respectively. Referring to FIG. 6B, resonance oscillations are observed for the Bragg (1 22) peak in the diffraction pattern of graphite; the amplitudes are similar in magnitude to those in FIG. 6A. The sample was tilted at 21° angle to the microscope axis and the diffraction pattern was obtained by using the SAD aperture of 6 μm diameter on the specimen. The graphite thickness is 69 nm as determined by EELS; the oscillation period (τp) is measured to be 56.3 ps. For a thickness of 45 nm, the period is found to be τp=35.4 ps. FIGS. 6D-G illustrate, for selected areas, time dependence of intensity difference (dark-field) for graphite. The image change displays the oscillatory behavior with the same τp as that of diffraction. The dark-field (DF) images were obtained by selecting the Bragg (1 22) peak. In FIG. 6H, each line corresponds to the difference in image intensities, Im(t−30 ps; t), for selected areas of 1×100-pixel slices parallel to contrast fringes in the DF image. The average amplitude of {042} diffraction peaks drop significantly; the rise time is 12.9 ps, whereas the change in separations of all planes is delayed by 31 ps and rises in 60 ps. The delay in the onset of separation change with respect to amplitude change is similar to the timescale for the amplitude to reach its plateau value of 15% reduction in the case of the {042} amplitude shown. In order to determine the recovery time of the structure, we carried out stroboscopic (and also single-pulse) experiments over the timescale of microseconds. The recovery transient in the inset of FIG. 6A (at 7 mJ/cm2) gives a time constant of 2.2 μs; we made calculations of 2D lateral heat transport with thermal conductivity (λ=3.17 W/(cm K) at 300 K) and reproduced the observed timescale. For this fluence, the maximum lattice spacing change of 0.08% gives the temperature increase ΔT to be 60 K, knowing the thermal expansion coefficient of gold (α=14.2×10−6 K−1). The atomic-scale motions, which lead to structural and morphological changes, can now be elucidated. Because the specimen is nanoscale in thickness, the initial temperature induced is essentially uniform across the atomic layers and heat can only dissipate laterally. It is known that for metals the lattice temperature is acquired following the large increase in electron temperature. The results in FIG. 6A give the temperature rise to be 13 ps; from the known electron and lattice heat-capacity constants [C1=70 J/(m3 K2) and C2=2.5×106 J/(m3 K), respectively] and the electron-phonon coupling [g=2×1016 W/(m3 K)] we obtained the initial heating time to be ˜10 ps for electron temperature T1=2500 K, in good agreement with the observed rise. Reflectivity measurements do not provide structural information, but they give the temperature rise. For bulk material, the timescale for heating (˜1 ps) is shorter than that of the nano-scale specimen (˜10 ps), due to confinement in the latter, which limits the ballistic motion of electrons in the specimen, and this is evident in the UEM studies. Because the plane separation is 0.4078 nm, the change of the average peak separation (0.043%), at the fluence of 1.7 mJ/cm2, gives a lattice constant change of 0.17 pm. Up to 30 ps the lattice is hot but, because of macroscopic lattice constraint, the atomic stress cannot lead to changes in lateral separations, which are the only separations visible for the [100] zone-axis probing. However, the morphology warping change is correlated with atomic (lateral) displacements in the structure as it relieves the structural constraint. Indeed the time scale of the initial image change is similar to that of plane separations in diffraction (60-90 ps). This initial warping, which changes image contrast, is followed by longer time (ns) minimization of surface energy and bulging, as shown in FIG. 5D. Given the picometer-scale structural change (0.17 pm), the stress over the 8-nanometer specimen gives the total expansion to be 3.4 pm over the whole thickness. Considering the influence of lateral expansion, the maximum bulge reaches 1 to 10 nm depending on the lateral scale. Finally, the calculated Debye-Waller factor for structural changes gives a temperature of 420 K (ΔT=125 K), in excellent agreement with lattice temperature derived under similar conditions, noting that for the nanoscale material the temperature is higher than in the bulk. Graphite was another study in the application of the UEM methodology. In contrast to the dynamics of gold, in graphite, because of its unique 2D structure and physical properties, we observed coherent resonance modulations in the image and also in diffraction. The damped resonance of very high frequency, as shown below, has its origin in the nanoscale dimension of the specimen and its elasticity. The initial fs pulse induces an impulsive stress in the film and the ultrafast electron tracks the change of the transient structure, both in SAID and SADD. In FIG. 6B, the results obtained by measuring changes of the diffraction spot (1 22) are displayed and in FIGS. 6D-G those obtained by dark-field (DF) imaging with the same diffraction spot being selected by the objective aperture and the specimen tilted, as discussed below. For both the image and diffraction, a strong oscillatory behavior is evident, with a well defined period and decaying envelope. When the transients were fitted to a damped resonance function [(cos 2πt/τp)exp(−t/τdecay)], we obtained τp=56.3±1 ps for the period. The decay of the envelope for this particular resonance is significantly longer, τdecay=280 ps. This coherent transient decay, when Fourier transformed, indicates that the length distribution of the film is only ±2 nm as discussed in relation to the equation below. The thickness of the film was determined (L=69 nm) using electron energy loss spectra (EELS). In order to test the validity of this resonance behavior we repeated the experiments for another thickness, L=45 nm. The period indeed scaled with L, giving τp=35.4 ps. These, hitherto unobserved, very high frequency resonances (30 gigahertz range) are unique to the nanoscale length of graphite. They also reflect the (harmonic) motions due to strain along the c-axis direction, because they were not observed when we repeated the experiment for the electron to be along the [001] zone axis. The fact that the period in the image is the same as that of the diffraction indicates the direct correlation between local atomic structure and macroscopic elastic behavior. Following a fs pulse of stress on a freely vibrating nanofilm, the observed oscillations, because of their well-defined periods, are related to the velocity (C) of acoustic waves between specimen boundaries, which in turn can be related to Young's modulus (Y) of the elastic stress-strain profile: 1 τ p = nC 2 ⁢ L = n 2 ⁢ L ⁢ ( Y ρ ) 1 / 2 ,where n is a positive integer, with n=1 being the fundamental resonance frequency (higher n are for overtones). Knowing the measured τp and L, we obtained C=2.5×105 cm/s. For graphite with the density ρ=2.26 g/cm3, Y=14.6 gigapascal for the c-axis strain in the natural specimen examined. Pyrolytic graphite has Y values that range from about 10 to 1000 gigapascal depending on the orientation, reaching the lowest value in bulk graphite and the highest one for graphene. The real-time measurements reported here can now be extended to different length scales, specimens of different density of dislocations, and orientations, exploring their influence at the nanoscale on C, Y, and other properties. We note that selected-area imaging was critical as different regions have temporally different amplitudes and phases across the image. Uniting the power of spatial resolution of EM with the ultrafast electron timing in UEM provides an enormous advantage when seeking to unravel the elementary dynamics of structural and morphological changes. With total dissipation of specimen heat between pulses, selected-area dynamics make it possible to study the changes in seconds of recording and for selected pixels of the image. In the applications given here, for both gold and graphite, the difference in timescales for the nonequilibrium temperature (reaching 1013 K/s), the structural (pm scale) and morphological (nm scale) changes, and the ultrafast coherent (resonance) behavior (tens of gigahertz frequency) of materials structure illustrate the potential for other applications, especially when incorporating the different and valuable variants of electron microscopy as we have in our UEM. Embodiments of the present invention extend ultrafast 4D diffraction and microscopy to the attosecond regime. As described herein, embodiments use attosecond electron diffraction to observe attosecond electron motion. Pulses are freely generated, compressed, and tilted. The approach can be implemented to extend previous techniques including, for example phase transformations, chemical reactions, nano-mechanical processes, and surface dynamics, and possibly to other studies of melting processes, coherent phonons, gold particles, and molecular alignment. As described herein, the generation of attosecond resolution pulses and in situ probing through imaging with free electrons. Attosecond diffraction uses near mono-energetic attosecond electron pulses for keV-range of energies in free space and thus space charge effects are considered. Additionally, spatiotemporal synchronization of the electron pulses to the pump pulses is made along the entire sample area and with attosecond precision. Diffraction orders are shown to be sensitive to the effect of electron displacement and conclusive of the four-dimensional dynamics. A component of reaching attosecond resolution with electron diffraction is the generation of attosecond electron pulses in “free space,” so that diffraction from freely chosen samples of interest can take place independent of the mechanisms of pulse generation. Electrons with energies of 30-300 keV are ideal for imaging and diffraction, because of their high scattering cross sections, convenient diffraction angles, and the appropriate de Broglie wavelength (0.02 to 0.07 Å) to resolve atomic-scale changes. Moreover, they have a high degree of monochromaticity. For example, electrons accelerated to E0=30-300 keV with pulse duration of 20 attoseconds (bandwidth of ΔE≈30 eV) have ΔE/E0≈10−3-10−4, making diffraction and imaging possible without a spread in angle and resolution. Optical attosecond pulses have typically ΔE/E0≈0.5 and because of this reach of ΔE to E0, their duration is Fourier-limited to ˜100 attoseconds. Free electron pulses of keV central energy can, in principle, have much shorter duration, down to sub-attoseconds, while still consisting of many wave cycles. Pulses with a large number of electrons suffer from the effect of space charge, which determines both the spatial and the temporal resolutions. This can be avoided by using packets of single, or only a few, electrons in a high repetition rate, as demonstrated in 4D microscopy imaging. FIG. 7A depicts the relation of single electron packets to the effective envelope due to statistics. Each single electron (blue) is a coherent packet consisting of many cycles of the de Broglie wave and has different timing due to the statistics of generation. On average, multiple single electron packets form an effective electron pulse (dotted envelope). It will be appreciated that there is high dispersion for electrons of nonrelativistic energy. The small but unavoidable bandwidth of an attosecond electron pulse causes the pulse to disperse during propagation in free space, even when no space charge forces are present. For example, a 20-attosecond pulse with ΔE/E0≈10−3 would stretch to picoseconds after just a few centimeters of propagation. Embodiments of the present invention provide methods and systems for the suppression of dispersion and the generation of free attosecond electron pulses based on the initial preparation of negatively-chirped electron packets. As described herein, femtosecond electron pulses are generated by photoemission and accelerated to keV energies in a static electric field. Preceding the experimental interaction region, optical fields are used to generate electron packets with a velocity distribution, such that the higher-energy parts are located behind the lower-energy ones. With a proper adjustment of this chirp, the pulse then self-compresses to extremely short durations while propagating towards the point of diffraction. To achieve attosecond pulses, the chirp must be imprinted to the electron pulse on a nanometer length scale. Optical waves provide such fields. However, non-relativistic electrons move significantly slower than the speed of light (e.g. ˜0.3 c for 30 keV). The direct interaction with an optical field will, therefore, cancel out over time and can not be used to accelerate and decelerate electrons for compression. In order to overcome this limitation, we make use of the ponderomotive force, which is proportional to the gradient of the optical intensity to accelerate electrons out of regions with high intensity. By optical wave synthesis, intensity profiles can be made that propagate with less than the speed of light and, therefore, allow for co-propagation with the electrons. FIG. 7B illustrates a schematic of attosecond pulse generation according to an embodiment of the present invention. A synthesized optical field of two counter-propagating waves of different wavelengths results in an effective intensity grating, similar to a standing wave, which moves with a speed slower than the speed of light. Electrons can, therefore, co-propagate with a matched speed and are accelerated or decelerated by the ponderomotive force according to their position within the wave. After the optical fields have faded away, this velocity distribution results in self-compression; the attosecond pulses are formed in free space. Depending on the optical pulse intensity, the electron pulse duration can be made as short as 15 attoseconds, and, in principle, shorter durations are achievable. If the longitudinal spatial width of the initial electron pulse is longer than the wavelength of the intensity grating, multiple attosecond pulses emerge that are located with well-defined spacing at the optical minima. This concept of compression can be rigorously described analytically as a “temporal lens effect.” The temporal version of the Kapitza-Dirac effect has an interesting analogy. Some of our initial work was based on an effective ponderomotive force in a collinear geometry. In order to extend the approach to more complex arrangements, here we generalize the approach and consider the full spatiotemporal (electric and magnetic) fields of two colliding laser waves with an arbitrary angle and polarization. The transversal and longitudinal fields of a Gaussian focus were applied. We simulated electron trajectories by applying the Lorentz force with a fourth-order Runge-Kutta algorithm using steps of 100 attoseconds. Space charge effects were taken into account by calculating the Coulomb interactions between all single electrons for each time step (N-body simulations). FIG. 7B illustrates temporal optical gratings for the generation of free attosecond electron pulses for use in diffraction. (a) A femtosecond electron packet (blue) is made to co-propagate with a moving optical intensity grating (red). (b) The ponderomotive force pushes electron towards the minima and thus creates a temporal lens. (c) The induced electron chirp leads to compression to attosecond duration at later time. (d) The electron pulse duration from 105 trajectories reaches into the domain of few attoseconds. FIG. 7C depicts the compression of single electron packets in the combined field of two counter-propagating laser pulses with durations of 300 fs at wavelengths of 1040 nm and 520 nm. The pulse is shown just before, at, and after the time of best compression; the center along Z is shifted for clarity. The plotted pulse shape is a statistical average over 105 packets of single electrons. The beam diameter of the initial electron packet was 10 μm and the beam diameters of the laser pulses were 60 μm; the resulting compression dynamics is depicted before, just at, and some time after the time of best compression to a duration of 15 attoseconds (see FIG. 7C(b)). These results show that an optical wave with a beam diameter of only several times larger than that of the electron packet is sufficient to result in almost homogeneous compression along the entire electron beam. The characteristic longitudinal spread after the point of best compression, as depicted in FIG. 7C is the result of an “M”-shaped energy spectrum of the electrons after interactions with the sinusoidal intensity grating. Coulomb forces prevent concentration of a large number of electrons in a limited volume, and a compromise between electron flux and laser repetition rate must be found to achieve sufficiently intense diffraction. The laser pulses for compression have energies on the order of 5 μJ and can, therefore, be generated at MHz repetition rates with the resulting flux of 106 electrons/s, which is sufficient for conclusive diffraction. Nevertheless, having more than one electron per attosecond pulse is beneficial for improving the total flux. In order to investigate the influence of space charge on the performance in our attosecond compression scheme, we considered electron packets of increasing electron density and evaluated the resulting pulse durations and effective electron density per attosecond pulse. Two findings are relevant with the results shown in FIG. 8. First, the duration of individual attosecond electron pulses increases relatively insignificantly with the number of electrons contained within. Even for 40 electrons in a single pulse, the duration increases only from 15 to 25 attoseconds (see FIG. 8(a)). The reasons for this are the highly oblate shape of the electron pulses, and the approximate linearity of space charge forces in the longitudinal direction, which are compensated for by somewhat longer interaction in the ponderomotive forces of the optical waves. Secondly, for a train of pulses, there is an effect on synchronization. When the initial femtosecond electron packet covers several optical cycles of the compression wave, a train of attosecond pulses results as shown in FIG. 7B. Perfect synchronization to the optical wave is provided, because all attosecond pulses are located at the same optical phase of the fundamental laser wave. This phase matching relation, which permits attosecond resolution, despite the presence of multiple pulses, is altered under space charge conditions. The attosecond pulses repel each other and a temporal spreading of the comb-like train results. For a train of near 10 attosecond pulses, FIG. 8(b) displays the difference in timing for an adjacent attosecond pulse in relation to the central one, which is always locked to the optical phase because the space charge forces cancel out. The total timing mismatch is the product of the plotted value with the number of attosecond pulses in the entire electron packet (near 10 for this example). In order to keep the total mismatch to the optical wave below 20 attoseconds, 10 electrons per attosecond electron pulse represent an optimum value. The total pulse train then consists of 200 electrons for that group of pulses; of course the total flux of electrons is determined by the repetition rate. Note that mismatch to the compression wave is absent with isolated attosecond electron pulses, which are generated when the initial uncompressed electron packet is shorter than a few femtoseconds, or with optical fields of longer wavelength. Numerous imaging experiments have been successful with single electron packets. In state-of-the-art electron crystallography experiments, typically 500 electrons per pulse were used at a repetition rate of kHz to produce the needed diffraction. This is equivalent to having 5 electrons per attosecond pulse at 100 kHz, which is a convenient repetition rate for optical wave synthesis, and provides enough time for letting the material under investigation to cool back to the initial state. Laser systems with MHz repetition rates will provide even higher fluxes. Applications of attosecond electron pulses for diffraction and microscopy use synchronization of events in the pump-probe arrangement with an accuracy that is equal or better than the individual pulse durations. In contrast to recompression concepts that are based on time-dependent microwave fields, the application of laser waves for attosecond electron pulse generation provides exact temporal synchronization when the pump pulses are derived by phase-locking from the same laser system. Many common optical techniques, such as nonlinear frequency conversion, continuum generation in solids, or high-harmonic generation, all provide a phase lock in the sense that the outcome has the same relative phase and timing in relation to the incoming optical wave for each single pulse of the laser. A second requirement for reaching into the temporal resolution of attoseconds is the realization of spatial delay matching along extended areas of the diffraction. The use of large samples, for example with up to millimeters in size in some electron diffraction experiments, provides enhanced diffraction efficiency and offers the possibility to use electron beams with large diameter, in order to maximize the coherence and flux. In this case, the time resolution is limited by differences in the arrival times of pump and probe pulses at different points within the involved beam diameters (group velocity mismatch). Electron pulses at keV energies travel with significantly less than the speed of light (e.g. vel=0.3 c for 30 keV electrons) and are, therefore, “overtaken” by the laser wave. Embodiments of the present invention provide two arrangements for matching the group velocity of electrons with the phase velocity of optical pulses. Both arrangements are suitable for applications in noncollinear, ultrafast electron microscopy and diffraction. FIG. 9(a) presents a concept for the transmission geometry of diffraction and microscopy in which two angles are introduced, one between the laser beam and the electron beam (β), and another one (α) for the tilt angle of the sample (black) to the phase fronts of the laser wave. Total synchrony is achieved if the relative delay between the optical wave and the attosecond electron pulses is made identical for all points along the entire sample surface. Each small volume of the sample is then subject to an individual pump-probe-type experiment with the same time delay. The above condition is found when we match the coincidence along the entire width of the specimen. The effective surface velocity vsurface of the laser and of the electron pulses must be identical. From FIG. 9A, this requirement is expressed by the following equation: sin ⁡ ( α ) sin ⁡ ( α - β ) = c v el . ( 1 ) It follows that an angle of β=10°, for example, results in an optimum angle for the sample tilt of α=14.8°, which are both easily achievable angles in a real experiment. The effective tilt of the sample with respect to the electron direction is then α−β=4.8°. Naturally, if this value is not coincident with a zone axis direction, a complete rocking curve should be obtained in order to optimize α and β with tilt requirements. Although different portions of the laser wavefront impinge on the surface of the sample at different times, this behavior is matched by the electron pulse, resulting in all portions of the surface of the sample being phase matched. As illustrated in FIG. 9(a), the laser beam, also referred to as a laser wave, is used to activate the sample, for example, to heat the sample, cause motion of the sample, or to effect the chemical bonds present in the sample. The timing of the laser wave and the electron pulses are synchronized using the delay stage discussed in relation to FIG. 1. The train of electron pulses can be generated using the configuration illustrated in FIG. 10(a). Another option for synchronization along extended surfaces is the use of tilted electron pulses, for that the electron density makes an angle with respect to the propagation direction. Tilted optical pulses have been used for reaching femtosecond resolution in reflection geometry, but here tilted electron pulses are introduced for effective spatiotemporal synchronization to the phase velocity of the excitation pulses along the entire sample surface. FIG. 9B depicts the concept. If an angle γ is chosen between the laser (red) and the attosecond electron pulses (blue), the electron pulses need to be tilted likewise. The sample is located parallel to the optical phase fronts and its entire surface is illuminated by the attosecond electron pulse at once and at the same time of incidence relative to the optical pulse wave. Because the incidence is delay-free for all points along the surface, velocity matching is provided for the whole probed area. The generation of tilted attosecond electron pulses is outlined in FIG. 10(a). The introduction of an angle between the intensity grating (red) and the electron beam (blue) leads to formation of electron pulses with a tilt. As described above, a femtosecond electron packet (blue) is first generated by conventional photoelectron generation and accelerated in a static electric field. By intersecting the counter-propagating intensity grating at an angle, tilted electron pulses result with attosecond duration. The ponderomotive force accelerates the electrons towards the planes of destructive interference in the intensity wave and they form attosecond pulses that are compressed along the optical beam axis; but the pulses propagate in the original direction. Only a slight adjustment of the electrons' central energy is required to achieve phase matching to the moving optical grating. Based on this concept, we simulated the tilting effect by using 31-keV electron pulses with an initial duration of ˜15 femtoseconds and a spatial beam diameter of ˜10 μm. FIG. 10(b) illustrates the simulation results for an initial packet of 15-femtosecond duration (left) and an intersection angle of 5°. The tilted attosecond pulses have duration of ˜20 attoseconds when measured perpendicular to the tilt (note the different scale of Z and X). The optical intensity wave is synthesized by two counter-propagating laser pulses of 100-fs duration and wavelengths of 1040 and 520 nm. The angle between the electron beam and the laser wave is 5°. The results of compression are shown in FIG. 10(b): The attosecond electron pulses are formed at the minima of the optical intensity wave and, therefore, are tilted by 5° with respect to the electron propagation direction. For other incidence angles of the laser, the electron pulses are tilted accordingly. Perpendicular to the attosecond pulses, the measured duration is ˜20 attoseconds, given as the full width at half maximum. Based on the methodology for generation and synchronization of attosecond electron pulses described above, the diffraction and manifestation of electron dynamics in the patterns are described. By way of two different examples, embodiments of the present invention are utilized to observe electronic motions in molecules and materials with attosecond electron packets. We consider first the physics of electron scattering and the change in scattering factors which characterize individual atoms and the electron density involved. Diffraction from molecular crystals or other crystalline structures provides two distinct advantages over that obtained for gas phase ensembles. First, the sample density is many orders of magnitudes higher (1021 molecules/cm3 as compared to 1010 to 1016/cm3 in gas jets); diffraction is, therefore, more intense. Second, the crystalline order results in Bragg scatterings and they are concentrated into well-defined “spots” for ordered crystals; the patterns become rods for surfaces and narrow rings for amorphous substances. The diffraction results in intensities which are proportional to the square of the diffraction amplitude. As discussed below, coherence in diffraction is used in observing the changes of interest. The diffraction from molecular crystals, or other crystalline materials of interest, is defined by the summation over the contributions of all scatterers in a unit cell. The intensity I of a Bragg spot with the Miller indices (hkl) is determined by the positions (xyz) of the scatterers j the unit cell: I ⁡ ( hkl ) ∝  ∑ j ⁢ f j ⁢ exp ⁡ [ - 2 ⁢ π ⁢ ⁢ ⅈ ⁡ ( hkl ) · ( xyz ) j ]  2 , ( 2 ) where fj are the atomic scattering factors. Electron diffraction is the result of Coulomb interaction between the incoming electrons and the potential formed by nuclei and electrons. The factors fj account for the effective scattering amplitude of atoms and are derived from quantum calculations that take into account the specific electron density distribution around the nuclei, including core electrons. The scattering we are considering here is the elastic one. In order to estimate the influence of electron dynamics on contributions to time-resolved diffraction patterns, we consider typical densities of electrons in chemical bonds, and the possible change. Static electron density maps show that typical covalent bonds consist of about one electron/Å3 and that this density is delocalized over volumes with diameters in the order of 1 Å. For estimating an effective scattering factor of such electron density, we consider a Gaussian sphere with a diameter of 1 Å, consisting of one electron. The electric potential is derived by Gauss' law and results in a radial dependence that is represented in FIG. 11, dotted line. The total scattering amplitude of free charges diverges at small angles, because of the long-range behavior of the potential. Since in real crystals the potential is localized in unit cells, we use a Gaussian distribution of the same magnitude in order to restrict the range to about ±1.5 Å. For potential of spherical symmetry, an effective scattering factor can be calculated from the radial potential Φ(r) according to f el ⁡ ( s ) = 8 ⁢ π 2 ⁢ m e ⁢ e h 2 ⁢ ∫ 0 ∞ ⁢ r 2 ⁢ Φ ⁡ ( r ) ⁢ sin ⁡ ( 4 ⁢ π ⁢ ⁢ sr ) 4 ⁢ π ⁢ ⁢ sr ⁢ ⅆ r , ( 3 ) where s=sin(υ/2)/λel is the scattering parameter for a diffraction angle υ and λel is the de Broglie wavelength of the incident electrons. The result for our delocalized electron density is shown in FIG. 11(b); for comparison we plot also the tabulated scattering factor of neutral hydrogen. Both have comparable magnitude, which is expected because of their similar sizes. Here, we consider the iodine molecule as a model case and invoke the transition from a bonding to an anti-bonding orbital. The crystal structure of iodine consists of nearly perpendicular iodine pairs with a bond length of ˜2.7 Å. Two electrons contribute to the intramolecular σ bond; the intermolecular bond is weaker. FIG. 12 depicts the system under study and the two cases considered. The effect of antibonding excitation is made by comparing the Bragg intensities for the iodine structure, including the binding electrons, to a hypothetical iodine crystal consisting only of isolated atoms (see FIG. 12(a)). In Table 1, we give the results of the calculations following equation 2 with the values off f tabulated for iodine atoms and from equation (3) for the electronic distribution changes. Despite the large difference in f of the iodine nuclei and the electron (about 50:1), the changes of Bragg spot intensity are significant, being on an order of 10-30%. TABLE 1Effects of Electron Motion on Selected Molecular Bragg SpotsMiller Indices (hkl)(a) ΔITransition(b) ΔIMovement(0.08 Å)100, 010, 001(forbidden)(forbidden)200, 400, 60000002−35%0020 (weak)+100% −17%40000040−18%+13%00400111+15% −2%331−20%+15% In column (a), the mMagnitude of Bragg spot intensity change ΔI of crystalline iodine as a result of bonding to antibonding transition is given. In column (b), the magnitude of Bragg spot intensity change as a result of field interaction with charge density, also in iodine. This large change is for two reasons. First, the bonding electrons are located in-between iodine atoms and contribute, therefore, strongly to the enhancement or suppression of all Bragg spots that project from the inter-atomic distances of the molecular units. Second, the large effect is result of the intrinsic “heterodyne detection” scheme of diffraction; the total intensity of a Bragg spot scales with the square of the coherent sum of individual contributions (see equation (2)). Although the total contribution to the intensity of a Bragg spot from bonding electrons is lower by a factor of several hundreds than the intensity contributions from the iodine atoms, the modulation is on the order of several percents as a result of the coherence of diffraction on a nanometer scale. Symmetry in the crystal is evident in the absence of change in certain Bragg orders. From measurements of the dynamics of multiple spots, it follows that electron density movies could be made. This is best achieved in an electron microscope in diffraction geometry; however conventional diffraction is also suitable to simultaneously monitor many Bragg spots and is advantageous for the study of ordered bulk materials. The example given is not far from an experimental observation made on a metal-to-insulator transition for which a σ*-type excitation was induced with a femtosecond pulse. As a second model case we consider the reaction of bonded electron density to external electric fields, such as the ones from laser fields. Depending on the restoring force and the resonance, an electron density will oscillate with the driving field in phase or with a phase delay. This charge oscillation re-radiates and is responsible for the refractive index of a dielectric material. In order to estimate the magnitude of charge displacement, we must take into account the polarizability, α, and the electric field strength, Elaser. In the limit of only one moving charge, the displacement D is approximately given by D ≈ α e ⁢ E laser . The polarizability of molecular iodine along the bond is α≈130 ∈0Å3 (˜70 a.u.) in the static limit and a similar magnitude is expected for the crystal for optical frequencies away from the strong absorption bands; the anisotropy of polarizability indicates the role of the bonding electrons. With femtosecond laser pulses, a field of Elaser=109 V/m is possible for intensities below the damage threshold. With these parameters, one expects a charge displacement of D≈0.08 Å, or about 3% of the bond length. FIG. 12(b) is a schematic for the change in charge distribution by an electric field. We assume an active role of only the bonded electrons, and take the polarization of the laser field to be along the b axis of solid iodine. This axis is chosen because it has the least symmetry; a is perpendicular to the bonds. Table 1 gives the intensity changes of selected Bragg spots; the change is in the range of ±20% for some of the indices. The total energy delivered to the molecular system by the laser field is only on the order of 0.01 eV. Nevertheless the changes of charge displacements on sub-angstrom scales are evident. This marks a central advantage of electron diffraction over spectroscopic approaches, which require large energy changes in order to have projections on dynamics. In contrast, diffraction allows for the direct visualization of a variety of ultrafast electron dynamics with combined spatial and temporal resolutions, and independent of the resolution of internal energy levels. The “temporal lens” concept can be used for the focus and magnification of ultrashort electron packets in the time domain. The temporal lenses are created by appropriately synthesizing optical pulses that interact with electrons through the ponderomotive force. With such an arrangement, a temporal lens equation with a form identical to that of conventional light optics is derived. The analog of ray diagrams, but for electrons, are constructed to help the visualization of the process of compressing electron packets. It is shown that such temporal lenses not only compensate for electron pulse broadening due to velocity dispersion but also allow compression of the packets to durations much shorter than their initial widths. With these capabilities ultrafast electron diffraction and microscopy can be extended to new domains, but, as importantly, electron pulses are delivered directly on the target specimen. With electrons, progress has recently been made in imaging structural dynamics with ultrashort time resolution in both microscopy and diffraction. Earlier, nuclear motions in chemical reactions were shown to be resolvable on the femtosecond (fs) time scale using pulses of laser light, and the recent achievement of attosecond (as) light pulses has opened up this temporal regime for possible mapping of electron dynamics. Electron pulses of femtosecond and attosecond duration, if achievable, are powerful tools in imaging. The “electron recombination” techniques used to generate such attosecond electron pulses require the probing electron to be created from the parent ions (to date no attosecond electron pulses have been delivered on an arbitrary target) and for general applications it is essential that the electron pulse be delivered directly to the specimen. In ultrafast electron microscopy (UEM), the electron packet duration is determined by the initiating laser pulse, the dispersion of the electron packet due to an initial energy spread and electron-electron interactions. Since packets with a single electron can be used to image, and the initiating laser pulse can in principle be made very short (sub-10 fs), the limiting factor for the electron pulse duration is the initial energy spread. In photoelectron sources this spread is primarily due to the excess energy above the work function of the cathode, and is inherent to both traditional photocathode sources and optically-induced field emission sources. Energy-time uncertainty will also cause a measurable broadening of the electron energy spread, when the initiating laser pulse is decreased below ˜10 fs. For ultrafast imaging techniques to be advanced into the attosecond temporal regime, methods for dispersion compensation and new techniques to further compress electron pulses to the attosecond regime need to be developed. As described herein techniques for compressing free electron packets, from durations of hundreds of femtoseconds to tens of attoseconds, using spatially-dependent ponderomotive potentials are provided by embodiments of the present invention. Thus, a train of attosecond pulses can be created and used in ultrafast electron imaging. Because they are generated independent of the target they can be delivered to a specimen for studies of transient structures and electronic excitations on the attosecond time scale. The deflection of electrons (as in the Kapitza-Dirac effect) by the ponderomotive potential of intense lasers and the diffraction of electrons in standing waves of laser light have been observed, and so is the possibility (described through computer modeling) of spatial/temporal focusing with combined time-dependent electric and static magnetic fields. The “temporal lens” description analytically expresses how ponderomotive compression can be used to both compensate for the dispersion and magnify, in this case compress, the temporal duration of electron packets. We obtain simple lens equations which have analogies in optics and the results of “electron ray optics” of temporal lenses allows for analytical expressions and for the design of different schemes using geometrical optics. Here, we consider two types of temporal lenses, thin and thick. For the realization of the temporal thin lens, a laser beam with a Laguerre-Gaussian transverse mode, radial index ρ=0 and azimuthal index l=0 (or, in common nomenclature, a “donut” mode, is utilized. In the center of the donut mode, electrons will experience a spatially-varying ponderomotive potential (intensity) that is approximately parabolic. This potential corresponds to a linear spatial force which, for chirped electron pulses, can lead to compression from hundreds of fs to sub-10 fs. The second type, that of a thick lens, is based on the use of two counter-propagating laser beams in order to produce a spatially-dependent standing wave that co-propagates with the electrons. A train of ponderomotive potential wells are produced at the nodes of the standing wave, leading to compression but now with much “tighter focus” (thick lens). Because the electron co-propagates with the laser fields, velocity is matched. Analytical expressions are derived showing that this lens has the potential to reach foci with attosecond duration. Finally, we discuss methods for creating tunable standing waves for attosecond pulse compression, and techniques for measuring the temporal durations of the compressed pulses. Space-charge dispersed packets of electrons that have a linear spatial velocity chirp may also be compressed with the temporal lenses described here. All electron sources, both cw and pulsed, have an initial energy spread. For pulsed electron sources this is particularly relevant as electron packets created in a short time disperse as they propagate. The initial energy spread leads to an initial spread in velocities. These different velocities cause the initial packet to spread temporally, with the faster electrons traveling a further distance and the slower electrons traveling a shorter distance in a given amount of time. The dispersion leads to a correlation between position (along the propagation direction) and electron velocity as described in relation to FIG. 14. The linear spatial velocity “chirp” can be corrected for with a spatially-dependent linear impulsive force (or a parabolic potential). Thus, if a pulsed, spatially-dependent parabolic potential can be made to coincide appropriately with the dispersed electron packet, the slow trailing electrons can be sped up and the faster leading electrons can be slowed down. The trailing electrons, now traveling faster, can catch the leading electrons and the electron pulse will thus be compressed. FIG. 13 illustrates dispersion of an ultrashort electron packet. At t=to the packet is created from a photocathode and travels with a velocity v0. As it propagates along the x-axis it disperses, with the faster electrons traveling further, and the slower ones trailing for a given propagation time t. At t=0 a parabolic potential is pulsed on, giving an impulsive “kick” to the dispersed electron packet. After the potential is turned off, t>τ, the trailing electrons now have a greater velocity than the leading electrons. After a propagation time t=ti, the pulse is fully compressed. Consider a packet of electrons, propagating at a speed v0 along the x-axis, with a spread in positions of Δxo=v0Δto, at time t=to. At t=0, a potential of the form U(x)=½Kx2 interacts with the electron packet for a duration τ in the lab frame. The waist, or spatial extent of the potential (temporal lens) is chosen to be w, while the duration τ is chosen such that it is short compared to w/v0. When this condition is met the impulse approximation holds, and the change in velocity is Δv=−τ/m(dU(x)/dx)=−τKx/m, for |x|<w, where m is the electron mass. After the potential is turned off, t>τ, the electrons will pass through the same position, xf−x=(v0+Δv)tf, at the focal time tf=−x/Δv=m/(Kτ). To include an initial velocity spread around v0 (due to an initial ΔE), consider electrons that all emanate from a source located at a fixed position on the x-axis. An electron traveling exactly at v0 will take a time t0 to reach the center of the potential well at x=0. Electrons leaving the source with other velocities v0+vk will reach a location x=vkto at t=0. The image is formed at a location where electrons traveling with a velocity v0 and a velocity v0+vk intersect, this is, when v0ti=x+(v0+Δv+vk)ti. The image time ti is then ti=−x/(Δv+vk). FIG. 14 illustrates ray diagrams for spatial and temporal lenses. The top figure in FIG. 14 depicts three primary rays for an optical thin spatial lens. The object is located at yo, and the spatial lens has a focal length, f. A real image of the object is created at the image plane, position yi. The bottom figure in FIG. 14 is a ray diagram for a temporal thin lens. The diagram is drawn in a frame moving with the average speed v0 of the electron packet. The slopes of the different rays in the temporal diagram correspond to different initial velocities that are present in the electron packet. As shown in the diagram, a temporal image of the original electron packet is created at the image time ti. The initial packet (object) is created at a time to with Δto=Δxo/v0, where the spatial extend of the pulse is directly related to the temporal duration of the object. The lens is pulsed on at t=0 and the temporal focal length of the lens is tf. The lens represents the ponderomotive potential and in this case is on for the very short time τ. For the object time, to=x/vk, image time ti=−x/(Δv+vk) and the focal time tf=−x/Δv, the temporal lens equation holds, 1 t o + 1 t i ⁢ = 1 t f ⁢ . ( 4 ) Ray tracing for optical lenses is often used to visualize how different ray paths form an image, and is also useful for visualizing how temporal lenses work as shown in FIG. 14. As derived in later sections, the magnification M is defined as the ratio of the electron pulse duration (Δti) at the image position to the electron pulse duration (Δto), and is directly proportional to the ratio of the object and image times (−ti/to) and distances (−xi/xo). In polar coordinates, a Laguerre-Gaussian (LG01) mode has a transverse intensity profile given by, I(r,φ)=I0exp(1)2r2exp(−2(r/w)2)/w2 where w is the waist of the focus and I0 the maximum intensity. This “donut” mode has an intensity maximum located at r=√{square root over (2)} w/2 with a value of I0=2EP(√{square root over (1n 2/π3)}/(w2τ) where EP is the energy of the laser pulse and τ is the full-width-at-half-maximum of the pulse duration, assuming a Gaussian temporal profile given by exp(−4 ln 2(t/τ)2). The ponderomotive energy UP(x) is proportional to intensity, U P ⁡ ( x ) = 1 2 [ ⅇ 2 ⁢ λ 2 ⁢ exp ⁡ ( 1 ) ⁢ I 0 2 ⁢ π 2 ⁢ m ⁢ ⁢ ɛ 0 ⁢ c 3 ⁢ w ⁢ 2 ⁢ ln ⁢ ⁢ 2 π ] ⁢ x 2 ≡ 1 2 ⁢ Kx 2 , ( 5 ) where m is the electron mass, e is the electron charge and λ the central wavelength of the laser radiation and replacing r with x. Near the center of the donut mode focus (or x<<w) the intensity distribution is approximately parabolic, and hence the ponderomotive energy near the donut center is also parabolic. In analogy with a mechanical harmonic oscillator, the quantity in the square brackets of equation (5) can be referred to as the stiffness K; it has units of J/m2=N/m, and at 800 nm has the numerical value of, K≈3.1×10−36EP/(w4τ). For this parabolic approximation to be applicable, the spatial extent of the dispersed electron pulse, at t=0, Δx(0)=v0Δto+Δvoto must be much smaller than the laser waist, where the object velocity spread is Δvo=ΔE/√{square root over (2mE)}. The effect of this parabolic potential on an ensemble of electrons emitted from a source will now be analyzed. The velocity distribution of the ensemble is centered around v0, with an emission time distribution centered on −to, where all electrons are emitted from the same location xo=−v0to. Assuming a single donut-shaped laser pulse is applied at t=0, and centered at x=0, the electron ensemble is then influenced by the potential U(x)=½Kx2. The kth electron in the ensemble has an initial velocity v0+vk and emission time −to+tk. Using a Galilean transformation to a frame moving with velocity v0, the propagation coordinate x (lab frame) is replaced with the moving frame coordinate {tilde over (x)}=x−v0t. At t=0 the potential exists for the ultrashort laser pulse duration τ, giving the electron an impulse (or “kick”) dependent on its instantaneous position in the parabolic potential. In both frames, the position of the electron at t=0 is xk(0)={tilde over (x)}k(0)≡−v0tk+vkto−vktk, where xk(t) and {tilde over (x)}k (t) are in the lab and moving frames, respectively. Using the impulse approximation the electron trajectory immediately after the potential is turned off becomes,{tilde over (x)}k(t)=vkt+{tilde over (x)}k(0)(1−t/tf), (6)where tf=m/(Kτ) is the focal time. The electron trajectories, before and after t=0, can be plotted in both frames to give the equivalent of a ray diagram as illustrated in FIG. 15. Electrons emitted at the same time, i.e. tk=0, but with different velocities, will meet at the image position, {tilde over (x)}k=0 in the moving frame at the image time ti. The image time is found by setting {tilde over (x)}k(ti)=0, from equation (6), with tk=0, {tilde over (x)}k(ti)=vkti+vkto(1−ti/tf)=0 which is equivalent to the lens equation, equation (4): to−1+ti−1=tf−1. An expression for the magnification can be obtained when electrons that are emitted at different times tk and different velocities vk are considered. If the magnification is defined as M=−ti/to then the temporal duration at the image time becomes,Δti=MΔto, (7)where Δto and Δti are the duration of the electron packet at the object and image time, respectively. Durations achievable with a thin temporal lens follow from equation (7). An experimentally realistic temporal lens would use a 50 fs, 800 nm laser pulse with 350 μJ energy, focused to a waist of w=25 μm. These values result in a stiffness of K=5.5×10−8 N/m and a focal time of tf=0.3 ns; tf=m/(Kτ). If the lens is applied 10 cm from the source, electrons emitted at v0=c/10 (3 keV) would have an object time of to=xo/v0=0.1/(c/10)=3.0 ns. Using the temporal lens equation, equation (4), ti is obtained to be 0.33 ns. Hence, a magnification of M=−ti/to=0.1. Consequently, a thin temporal lens can compress an electron packet with an initial temporal duration of Δto≈100 fs, after it has dispersed, to an image duration of Δti≈10 fs. While the example presented here is for 3 keV electrons, the thin lens approximation holds for higher energy electrons as long as τ is chosen to be short compared to w/v0. Experimentally, the thin temporal lens can be utilized in ultrafast diffraction experiments which operate at kHz repetition rates with lasers that typically possess power that exceeds the value needed for the ponderomotive compression. Referring to FIG. 15, thin lens temporal ray diagrams for the lab and co-propagating frames are illustrated. The upper left panel is a ray diagram drawn in the lab frame showing how different initial velocities can be imaged to a single position/time. The gray lines are rays representing electrons with different velocities. The lower left panel is a ray diagram drawn in a frame moving with the average velocity v0 of the electron packet. The rays represent velocities of v0/67, v0/100 and 0. In the co-propagating frame, the relationship between Δto and Δti can be visualized as Δti=−Δtoti/to. One major difference between the lab frame and the moving frame is that in the latter the position of the object and image are moving. The lines representing the object and the image positions are drawn with slopes of −v0. The upper right panel depicts the experimental geometry for the implementation of a thin temporal lens. Note that the laser pulse and electron packet propagate perpendicular to each other, and that the interception point between the electrons and photons is at x=0 and t=0. The lower right panel shows how the parabolic (idealized) potential compares to the experimentally realizable donut potential. The colored dots indicate the position of electrons following the rays indicated in the left bottom diagram. Above, it was analytically shown that free electron packets can be compressed from hundreds to tens of femtoseconds using a temporal thin lens, which would correspond to a magnification of ˜0.1. Co-propagating standing wave can be created by using two different optical frequencies, constructed by having a higher frequency (ω1) optical pulse traveling in the same direction as the electron packet and a lower frequency (ω2) traveling in the opposite direction. When the optical frequencies ω1, ω2, and the electron velocity v0 are chosen according to v0=c(ω1−ω2)/(ω1+w2), a standing wave is produced in the rest frame of the electron as illustrated in FIG. 16. If the electron has a velocity v=c/3, and ω1=2ω2 then the co-propagating standing wave has a ponderomotive potential of the form, U P ⁡ ( x ) = 1 2 ⁢ ( ⅇ 2 ⁢ λ ~ 2 ⁢ E 0 2 8 ⁢ π 2 ⁢ m ⁢ ⁢ c 2 ) ⁢ cos 2 ( k ~ ⁢ x ) , ( 8 ) where E0 is the peak electric field, {tilde over (λ)} the Doppler shifted wavelength. The envelopes of the laser pulses are ignored in this derivation, but they can be engineered so that the standing wave contrast is optimized. The standing waves can be provided outside the microscope housing or inside the microscope housing. The presence of the standing wave copropagating with the electron pulse or packet inside the microscope housing can produce a series of attosecond electron pulses as illustrated in FIG. 7B and FIG. 16. Depending on the geometry with which the laser beams interact, the standing wave and the electron pulse can overlap adjacent to the sample, providing attosecond electron pulse generation at distances close to the sample. The attosecond electron pulses can be single electron pulses. To find an analytic solution in the thick lens geometry, each individual potential well in the standing wave is approximated by a parabolic potential that matches the curvature of the sinusoidal potential, UP(x)=½[e2E02/(2mc2]x2≡½Kx2. Using the exact solution to the harmonic oscillator the focal time is,tf=cot(ωPτ)/ωP+τ, (9)where ωp=√{square root over (Km)} and τ is the duration that the lens is on. For τ→0, tf→m/(K τ), which is identical to the thin lens definition. The image time, ti, has a form,ti=(1/ωP2+totf−tfτ+τ2)/(to−tf+τ), (10)and after the two assumptions, τ→0 and to>>1/(tfωP2) becomes equivalent to equation (4), the lens equation: to−1+ti−1=tf−1. The standard deviation of the compressed electron pulse at arbitrary time ta is, Δ ⁢ ⁢ t a = t f 2 ( λ ~ 2 + 4 ⁢ t a 2 ⁢ Δ ⁢ ⁢ v o 2 ) + t a 2 ⁢ λ ~ 2 - 2 ⁢ t f ⁢ t a ⁢ λ ~ 2 48 ⁢ t f 2 ⁢ v 0 2 , ( 11 ) which is valid for an individual well. The time when the minimum pulse duration occurs is ta=tf{tilde over (λ)}2/({tilde over (λ)}2+4tf2Δvo2)≈tf and for experimentally realistic parameters is equal to tf. This implies that the thick lens does not image the initial temporal pulse; it temporally focuses the electrons that enter each individual well. Since there is no image in the thick lens regime, the minimum temporal duration is not determined by the magnification M as in the thin lens section, but is a given by, Δ ⁢ ⁢ t f = t f 2 ⁢ λ ~ 2 ⁢ Δ ⁢ ⁢ v o 2 12 ⁢ v 0 2 ( λ ~ 2 + 4 ⁢ t f 2 ⁢ Δ ⁢ ⁢ v o 2 ) ≃ t f ⁢ Δ ⁢ ⁢ v o v 0 ⁢ 2 ⁢ 3 . ( 12 ) It should be noted that neither the temporal focal length nor the temporal duration are directly dependent on the Doppler shifted wavelength {tilde over (λ)}, as long as the condition to<v0Δto/Δvo is met. An example illustrates what temporal foci are obtainable. A source emits electrons with an energy distribution of 1 eV and a temporal distribution of 100 fs. Electrons traveling at v0=c/3 and having an energy E=31 keV gives a velocity distribution of Δvo=1670 m/s. If the distance between the source and the temporal lens is 10 cm, to=1.0 ns is less than v0Δto/Δvo≈6.0 ns, satisfying the condition to<v0Δto/Δvo and equation (12) is then valid. If the two colors used for the laser beams are 520 nm and 1040 nm, the Doppler-shifted wavelength is {tilde over (λ)}=740 nm. For a laser intensity of 3×1012 Wcm−2 (available with repetition rates up to megahertz), the oscillation frequency in the potential well is ωp≈2×1012 rad/s, which gives a focal time of tf≈1 ps. With these parameters, equation (12) gives a temporal duration at the focus of Δtf≈5 as. To support this ˜5 as electron pulse, time-energy uncertainty demands an energy spread of ˜50 eV. The ponderomotive compression imparts an energy spread to the electron pulse which can be estimated from ΔE˜mv0{tilde over (λ)}(2tf), giving ˜50 eV similar to the uncertainty limit. This ΔE is very small relative to the accelerating voltage in microscopy (200 keV) and only contributes to a decrease of the temporal coherence. In optical spectroscopy such pulses can still be used as attosecond probes despite the relatively large ΔE when the chirp is well characterized. Combining the anharmonicity broadening of 15 as, we conclude that ultimately temporal pulse durations in the attosecond regime can be reached. In the temporal thick lens case, the use of ω and 2ω to create a co-propagating standing wave requires v0=c/3. However, the velocity of the electrons, v0, can be tuned by changing the angle of the two laser pulses. A co-propagating standing wave can still be obtained by forcing the Doppler-shifted frequencies of both tilted laser pulses to be equal. A laser pulse that propagates at an angle θ with the respect to the electron propagation direction has a Doppler-shifted frequency {tilde over (ω)}=γω(1±(v/c)cos θ), where ω is the angular frequency in the lab frame, {right arrow over (v)}=v{circumflex over (x)} is the electron velocity, and γ=1/√{square root over (1−v2/c2)}. When the two laser pulses are directed as shown in FIG. 16, a co-propagating standing wave occurs for an electron with a velocity v0=c(k1−k2)/(k1 cos θ1+k2 cos θ2), where the laser pulse travelling with the electron packet has a wave vector of magnitude k1 and makes an angle of θ1 with the electron propagation axis; the second laser pulse traveling against has a wave vector magnitude of k2 and angle θ2, in the lab frame. An electron moving at v0 will see a standing wave with an angular frequency, ω ~ = 2 ⁢ ( cos ⁢ ⁢ θ 1 + cos ⁢ ⁢ θ 2 ) 2 ⁢ cos ⁢ ⁢ θ 1 + cos ⁢ ⁢ θ 2 ⁢ γ ⁢ ⁢ ω ⁡ ( 1 - β ) , ( 13 ) where 2k=k1=2k2 for experimental convenience, ω=kc, and the wavelength is {tilde over (λ)}=2πc/{tilde over (ω)}=2π/{tilde over (k)}. The standing wave created with arbitrary angles θ1 and θ2 will be tilted with respect to the electron propagation direction, which will temporally smear the electron pulse. This tilting of the standing wave can be corrected for by constraining the angles θ1 and θ2 to be: θ2=arcsin(2 sin θ1). For θ1=150(forcing θ2≈310), electrons with velocity v0=0.36c (E≈33 keV) see a standing wave. A 1 eV electron energy distribution at the source gives a velocity distribution of Δv0≈1630 m/s, at 33 keV. Using the same laser intensity as in the thick lens case, and the new v0 and Δvo, the condition to<v0Δto/Δvo is still satisfied, allowing equation (13) to be used, resulting in a duration at the focus of Δtf≈4.6 as. Using the tunable thick lens makes the experimental realization more practical, allowing for easy optical access and electron energy tuning, while at the same time keeping Δtf approximately the same. For additional tunability, an optical parametric amplifier can be used so that the laser pulse frequencies are not restricted to ω and 2ω. The ability to create electron pulses with duration from ˜10 fs to ˜10 as raises a challenge regarding the measuring of their duration and shape. Two different schemes are presented here for measuring pulses compressed by thick and thin temporal lenses. For measuring the thin lens compressed electron packet, the focused packet could be intersected by a laser pulse with a Gaussian spatial focus as illustrated in FIG. 17. An optical delay line would control the time delay between the measuring laser pulse and the compressed electron packet. As the time delay, Δt, is varied, so is the average energy of the electrons, as shown in FIG. 17. If the delay time is zero, then the average electron energy will be unaffected, as there is no force. If the delay line is changed so that the Gaussian pulse arrives early (late), then the average energy will decrease (increase). The change in the average energy is dependent on the duration of the electron pulse, and the intensity of the probing laser pulse. If the electron pulse is longer than the duration of the measuring laser pulse, then the change in the average energy will be reduced. The steepness of the average energy as a function of delay time, Ē(Δt), is a direct measure of the electron pulse duration, and using fs-pulsed electron energy loss spectra this scheme can be realized. For the thick lens a similar method is described here. At the focal position and time of the compressed temporal electron packet, a second co-propagating potential is introduced. The positions of the individual wells in the second co-propagating standing wave can be moved by phase shifting one of the two laser beams that create the probing potential (FIG. 17). By varying the phase shift, the potential slope (and hence the force) that the electrons encounter at the focus is changed. If no phase shift is given to the probing standing wave, no average energy shift results. When a phase shift is introduced, the electrons will be accelerated (or decelerated) by the slope of an individual well in the standing wave, and as long as the phase stability between the electrons and the probing standing wave is appropriate, attosecond resolution can be achieved. As the electron pulse duration becomes less than the period of the standing wave, the average electron energy change increases. The electron temporal duration of the compressed electron packet can be determined directly by the steepness of the Ē(φ) curve. Diffraction with focused electron probes is among the most powerful tools for the study of time-averaged nanoscale structures in condensed matter. Embodiments of the present invention provide methods and systems for four-dimensional (4D) nanoscale diffraction, probing specific-site dynamics with ten orders of magnitude improvement in time resolution, in convergent-beam ultrafast electron microscopy (CB-UEM). For applications, we measured the change of diffraction intensities in laser-heated crystalline silicon as a function of time and fluence. The structural dynamics (change in 7.3±3.5 ps), the temperatures (up to 366 K), and the amplitudes of atomic vibrations (up to 0.084 angstroms) are determined for atoms strictly localized within the confined probe area of 50-300 nm; the thickness was varied from 2 to 100 nm. A broad range of applications for CB-UEM and its variants are possible, especially in the studies of single-particles and heterogeneous structures. In fields ranging from cell biology to materials science, structures can be imaged in real-space using electron microscopy. Atomic-scale resolution of structures is usually available from Fourier-space diffraction data, but this approach suffers from the averaging over the selected specimen area which is typically on the micrometer scale. Significant progress in techniques has enabled localization of diffraction to nanometer and even angstrom-sized areas by focusing a condensed electron beam onto the specimen. Parallel illumination with a single electron wavevector is reshaped to a convergent beam with a span of incident wavevectors. T his method of convergent beam electron diffraction (CBED), or electron microdiffraction, and with energy filtering, has made possible determination of structures in 3 dimensions with highly precise localization to areas reaching below one unit cell. The applications have been wide-ranging, from revealing bonding charge distribution and local defects and strains in solids to detecting local atomic vibrations and correlations. Today, aberration-corrected, atomic-sized convergent electron beams enable analytical probing using electron-energy-loss spectroscopy (EELS) and scanning transmission electron microscopy (STEM). In order to resolve structural dynamics with appropriate spatiotemporal resolution, femtosecond (fs) and picosecond (ps) electron pulses are ideal probes because of their picometer wavelength and their large cross section, resulting from the effective Coulomb interaction with atomic nuclei and core/valence electrons of matter. Typically, ultrafast electron diffraction is achieved by initiating the physical or chemical change with a pulse of photons (pump) and observing the ensuing dynamics with electron pulses (probe) at later times. By recording sequentially delayed diffraction frames a “movie” can be produced to reveal the temporal evolution of the transient structures involved in the processes under study. FIG. 18 is a simplified schematic diagram of a CB-UEM set-up (top), and observed low-angle diffraction discs according to an embodiment of the present invention. Femtosecond electron pulses are focused on the specimen to form a nanometer-sized electron beam. Structural dynamics are determined by initiating a change with a laser pulse and then observing the consequences using electron packets delayed in time. Insets (right) show the CB-UEM patterns taken along the Si [011] zone axis at different magnifications. At the high camera length used, only the ZOLZ discs indexed in the figure are visible; the kinematically-forbidden 200 disc appears as a result of dynamic scattering. In the reciprocal space representation of the diffraction process (bottom) the Ewald sphere has an effective thickness of 2α, the convergence angle of the electron beam. The diamond structure of Si forbids any reflections from odd numbered Laue planes when the zone axis is [011]. Embodiments of the present invention provide CB-UEM methods and systems with applications in the study of nanoscale, site-selected structural dynamics initiated by ultrafast laser heating (1014 K/s). Because of the femtosecond pulsed-electron capability, the time resolution is ten orders of magnitude improved from that of conventional TEM, which is milliseconds; and because of beam convergence, high-angle Bragg scatterings are visible with their intensities being very sensitive to both the 3D structural changes and amplitudes of atomic vibrations. The CB-UEM configuration is shown in FIG. 18; our chosen specimen is a crystalline silicon slab, a prototype material for such investigations. From these experiments, it is found that the structural change within the locally probed site occurs with a time constant of 7.3±3.5 ps, which is on the time scale of the rise of lattice temperature known for bulk silicon. For these local sites, the temperatures measured at different laser fluences range from 299° K to 366° K, corresponding to vibrational amplitude changes from 0.077 Å to 0.084 Å, respectively. The reported results would be impossible to obtain with conventional, parallel beam diffraction. The electron microscope is integrated with a fs oscillator/amplifier laser system. The fundamental mode of the laser at 1036 nm was split into two beams: the first was frequency doubled to 518 nm and used to initiate the heating of the specimen, whereas the second, which was frequency tripled, was directed to the microscope for extracting electrons from the cathode. The time delay between pump and probe was adjusted by changing the relative optical path lengths of these two pulses. The pulses were sufficiently separated in time (5 μs) to allow for cooling of the specimen. The electron packets were accelerated to 200 keV (corresponding to a de Broglie wavevector of 39.9 Å−1), de-magnified, and finally focused (with a 6 mrad convergence angle) to an area of 50-300 nm diameter on the wedge-shaped specimen, as shown in FIG. 18. A wide range of thicknesses, starting from ˜2 nm was accessible simply by moving the electron beam laterally. The silicon specimen was prepared by mechanical polishing of a wafer along the (011) planes, followed by Ar ion-milling for final thinning/smoothing; the wedge angle was 2°. In the microscope, Kikuchi lines were observed and used as a guide to orient the specimen with the [011] zone axis either parallel or tilted relative to the incident electron beam direction. FIG. 18 display the typical high-magnification (high-value camera length) CB-UEM patterns of Si obtained when the specimen is unexcited and the zone axis is very close to [011]; the magnification (>10×) cab be seen by comparing the disc length scale in FIG. 18 and ring radius in FIG. 19. Unlike parallel-beam diffraction which yields spots, convergent-beam diffraction produces discs in reciprocal space (back focal plane of the objective lens) with their diameter given by the convergence angle (2α) of the electron pulses. These discs form the Zero Order Laue Zone (ZOLZ) of the pattern; they show white contrast with thin specimens and exhibit the interference patterns displayed in FIG. 18 when the thickness is increased. In the reciprocal space, the effective thickness of the Ewald sphere is 2α (bottom panel of FIG. 18), giving rise to multiple spheres that can intersect with Higher Order Laue Zones (HOLZ) reflections, the focus of this study (see FIG. 19) and the key to 3D structural information; the first and second zones, FOLZ and SOLZ, are examples of such zones or rings. The interference patterns in the disks are the result of dynamical scattering in silicon and are reproduced in our CB-UEM patterns (FIG. 18). The scattering vectors of HOLZ rings (R) are related to the inter-zone spacing in the reciprocal space (hz in Å−1) by the tilt angle from the zone axis (η) and by the magnitude of the incident electron's wavevector (k0). In the plane of the detector and for our tilt geometry, the HOLZ ring scattering vector is given by (equation (14)):R≅(k02 sin2(η)+2k0hz)1/2−k0 sin(η), (14)where, for our case of the [011] zone axis, hz=n/(a√{square root over (2)}) with n=1,2,3 . . . for the different Laue zones. Additionally, for this zone axis, k+l=n, where (hkl) are the Miller indices of the reciprocal space. When k+l=1, for FOLZ, k and l must have different parity, which is forbidden by the symmetry of the diamond Si structure. Therefore, the FOLZ along the [011] zone axis should be absent and the first visible ring should belong to SOLZ; in general, all odd numbered zones will be forbidden. Here, HOLZ indexing is defined according to the fcc unit cell and not to the primitive one [1]. FIG. 19 illustrates temporal frames obtained using CBUED. In FIG. 19(a) high angle SOLZ ring obtained for a tilt angle of 5.15° from the [011] zone axis are shown. Besides SOLZ, Kikuchi lines and periodic bands (due to atomic correlations) are visible. The ZOLZ discs are blocked (top left) to enhance the dynamic range in the area of interest; the disc of the direct beam (the center one in FIG. 18 discs) is indicated by a circle. The intensity scale is logarithmic. In FIG. 19(b,c,d) time frames of the SOLZ ring are shown by color mapping for visualization of dynamics. The intensity of the ring changes within picoseconds, but the surrounding background remains at the same level. FIG. 19(a) presents the HOLZ ring taken with the CB-UEM. In order to reduce the strong on-zone-axis dynamic scattering (and to bring the high scattering angles into the range of the recording camera), the slab was tilted 5.15° away from the [011] zone axis, along the [02 2] direction. The scattering vector of the Bragg points of the ring, from the direct beam position, was measured to be 2.2 Å−1, close to the value of 2.22 Å−1 obtained by using equation (14) for n=2, which identifies the spots shown as part of the SOLZ. From this value, the know lattice separation of 5.4 Å was obtained for silicon. In addition to the SOLZ ring, Kikuchi lines and some oscillatory bands are also visible in the CB-UEM, as seen in FIG. 19(a). Kikuchi lines arise from elastic scatterings of the inelastically scattered electrons, whereas the oscillatory bands in the thermal diffuse scattering (TDS) background result from correlations between the atoms. We also observed deficit HOLZ lines and interference fringes in ZOLZ discs for a two-beam condition. The temporal behavior is displayed in FIG. 19, with three CB-UEM frames taken at time delays of t=−14.8 ps, +5.2 ps, and +38.2 ps, together with a static image; the zero of time is defined by the coincidence of the pump and probe pulses in space and time. The frame at negative time has higher ring intensity than that observed at +38.2 ps, whereas the +5.2 ps frame shows an intermediate intensity value. It is clear from the results that the intensity change is visible within the first 5 ps of the structural dynamics. For quantification, the intensities in each frame were normalized to the area of azimuthally integrated background. The normalization of the HOLZ ring intensities to the TDS background makes the atomic vibration estimations insensitive to the thickness changes of the probed area, which may result from slight beam jittering. FIG. 20 illustrates diffraction intensities at different times and fluences. Normalized, azimuthally-integrated intensity changes of the SOLZ ring are shown with time ranging from −20 ps to +100 ps, for two different laser powers. Whereas the 10 mW response does not show noticeable dynamics, the 107 mW transient has a clear intensity change with a characteristic time of 7.3±3.5 ps. The range of fluences studied was 1.7 to 21 mJ/cm2 (see FIG. 21). The red curve is a mono-exponential fit based on the Debye-Waller effect. The red dashed line through the 10 mW data is an average of the points after +20 ps. The dependence on fluence is given in FIG. 21. FIG. 20 depicts the transient behavior of the SOLZ ring intensity for two different laser power, 10 mW and 107 mW, corresponding to pulse fluence of 1.7 and 19 mJ/cm2, respectively; the heating laser beam diameter on the specimen is 60 μm. The intensities were normalized to the average value obtained at negative times. Whereas the intensity change is essentially absent in the 10 mW data, the results for the 107 mW set shows a transient behavior with a characteristic time of 7.3 ±3.5 ps, obtained from the mono-exponential fit shown in red in the figure. The temporal response of UEM-2 is on the fs time scale, as obtained by EELS, and it is much shorter than the 7 ps illustrated here. The local heating of the lattice is responsible for the SOLZ intensity change with time. A pump laser, in our case at 518 nm (2.4 eV), excites the valance electrons of Si to the conduction band; one-photon absorption occurs through the indirect bandgap at 1.1 eV, and multi-photon absorption excites electron-hole pairs through the direct gap. The excited carriers thermalize within 100 fs, via carrier-carrier scatterings, and then electron cooling takes place in ˜1 ps, by electron-phonon coupling. During this time lattice heating occurs through increased atomic vibration, reducing SOLZ intensity. The effective lattice temperature is ultimately established with a time constant of a few picoseconds depending on density of carriers or fluence. However, in CB-UEM measurements the lattice-temperature rise could be slower than in bulk depending on the dimension of the specimen relative to the mean free path of electrons in the solid. The dynamical change can be quantified by considering a time-dependent Debye-Waller factor with an effective temperature describing the decrease in the Bragg spot intensity with time. If the root-mean-square (rms) displacement of the atoms, 1/2, along one of the three principle axes is denoted by ux for simplicity, and the scattering vector by s, then the HOLZ ring intensity can be expressed as (equation (15)):IRingF(t)=I0(t−)exp[−4π2s2ux2(t)], (15)where IRingF(t) is the measured intensity for a given fluence, F, and the vibrational amplitude is now time dependent. Note that ux is ⅓ of the total, utotal. In the Einstein model of atomic vibrations, which has been used successfully for silicon, the atoms are treated as independent harmonic oscillators, with the three orthogonal components of the vibrations decoupled. As a result, a single frequency (ω) is sufficient to specify the energy eigenstates of the oscillators. The relationship of the vibrational amplitude to temperature can be established by simply considering the Boltzmann average over the populated eigenstates. Consequently, the probability distribution of atomic displacements is derived to be of Gaussian form, with a standard deviation corresponding to the rms (ux) of the vibration involved (equation (16)):ux=[(/2ωm)coth(ω/2kBTeff)]1/2 (16)where is Planck's constant, kB the Boltzmann constant, Teff in our case the effective temperature, and m the mass of the oscillator. In the high temperature limit, i.e. when ω/2kBT<<1, eq. 3 simplifies to mω2ux2=kBT, which is the classical limit for a harmonic oscillator; the zero-point energy, which contributes almost half of the mean vibration amplitude at room temperature, is included in equation (16). The value of ω is 25.3 meV. Despite its simplicity, the Einstein model in equation (16) was remarkably successful in predicting the HOLZ rings and TDS intensities by multi-slice simulations. FIG. 21 illustrates the amplitudes of atomic vibrations (rms) plotted against the observed intensity change at different fluences. The inset shows the mono-exponential temporal behavior, with the asymptotes highlighted (circles) for their values at different fluences. The fluence was varied from 1.7 to 21 mJ/cm2. This comparative study of the effect of the fluence was performed at a slightly different sample tilt (corresponding to s=2.7 Å−1), corresponding to a thickness of ˜80 nm. For each fluence, the temperature represents the effective value for the lattice structural change. The error bars given were obtained from the fits at the asymptotes shown in the inset, and they are determined by the noise level of temporal scans. In FIG. 21, we present the change in the asymptotic intensity with fluence (inset), and the derived vibrational amplitudes for the different temperatures. The amplitudes are directly obtained from equation (15), as s is experimentally measured. The relative temperature change (from t− to t+) is then derived from equation (16), taking the value of ux at room temperature (297° K) to be 0.076 Å. The amplitude of atomic vibrations, and hence the temperature, increases as the fluence of the initiating pulse increases. Although the trend is expected for an increased ux with temperature, the absolute values, from 0.077 to 0.084 Å, correspond to a large 3.2% to 3.6% change in nearest neighbor separation; these values are still well below the 15% criterion for a melting phase transition. The linear thermal expansion coefficient has been accurately determined for silicon, and for a value of 2.6×10−6 K−1 at room temperature the vibrational amplitudes reported here are much higher than the equilibrium thermal values at the same temperature. This is because the effective temperature applies to a lattice arrested in a picosecond time window; at longer times, the vibrations equilibrate to a lower temperature. As such, measuring nanoscale local temperatures on the ultrashort time scale enhances the sensitivity of the probe thermometer by orders of magnitude. Moreover, the excitation per site is significantly enhanced. For a single-photon absorption at the fluence used, we estimate, for a 60 nm-thick specimen, the number of absorbed photons per Si atom (for the fs pulse employed) to be ˜0.01, as opposed to 10−9 photons per atom if the experiments were conducted in the time-averaged mode. The achievement of nanoscale diffraction with convergent-beam ultrafast electron microscopy opens the door to exploration of different structural, morphological, and electronic phenomena. The spatially focused and timed electron packets enable studies of single particles and structures of heterogeneous media. Extending the methodology reported here to other variants, such as EELS, STEM and nanotomography, promises possibilities for mapping individual unit cells and atoms on the ultrashort time scale of structural dynamics. With 4D electron microscopy, in situ imaging of the mechanical drumming of a nanoscale material is measured. The single crystal graphite film is found to exhibit global resonance motion that is fully reversible and follows the same evolution after each initiating stress pulse. At early times, the motion appears “chaotic” showing the different mechanical modes present over the micron scale. At longer time, the motion of the thin film collapses into a well defined fundamental frequency of 0.54 MHz, a behavior reminiscent of mode locking; the mechanical motion damps out after ˜200 μs and the oscillation has a “cavity” quality factor of 150. The resonance time is determined by the stiffness of the material and for the 53-nm thick and 55-μm wide specimen used here we determined Young's modulus to be 0.8 TPa, for the in-plane stress-strain profile. Because of its real-time dimension, this 4D microscopy has applications in the study of these and other types of materials structures. Structural, morphological, and mechanical properties of materials have different length and time scales. The elementary structural dynamics, which involve atomic movements, are typically of picometer length scale and occur on the time scale of femto (fs) to picoseconds (ps). Collective phenomena of such atomic motions, which define morphological changes, are observed on somewhat longer time scale, spanning the ps to nanosecond (ns) time domain, and the length scale encompasses up to sub-micrometers. These microscopic structures are very different in behavior from those involved in the mechanical properties. On the nanoscale, when the membrane-like mechanical properties have high frequencies and complex spatial-mode structures, imaging becomes of great value in displaying the spatiotemporal behavior of the material under stress. Utilizing embodiments of the present invention, we have visualized nanoscale vibrations of mechanical drumming in a single-crystalline graphite film (53-nm thick). To study the transient structures, in both space and time, our method of choice has been 4D ultrafast electron microscopy (UEM). This microscope enables investigation of the atomic structural and morphological changes in graphite on the fs to ns time scale and for nm-scale resolution. Additionally, mechanical properties can be determined in real time, which are evident on the ns and microsecond (μs) time scale. The stress is introduced impulsively using a ns laser pulse while observing the motions in real space (in situ) in the microscope using the stroboscopic electron pulses. Remarkably, at times immediately following the initiating pulse the motion appears “chaotic” in the full image transients, showing the different mechanical modes present in graphite. However, after several μs the motion of the nanofilm collapses into a final global resonance of 0.54 MHz. From this resonance of mechanical drumming of the whole plate, we obtained the in-plane Young's modulus of 0.8 terapascal (Tpa). The reported coherent resonance represents the in-phase build up of a mechanical drumming, which is directly imaged without invasive probes. Graphite was chosen because of its unique material properties; it is made of stacked layers of 2D graphene sheets, in which the atoms of each sheet are covalently bonded in a honeycomb lattice, and the sheets separated by 0.335 nm are weakly held together by van der Waals forces. It displays anisotropic electromechanical properties of high strength, stiffness, and thermal/electric conductivity along the 2D basal planes. More recently, with the rise of graphene, a new type of nano-electromechanical system (NEMS) has been highlighted with a prototypical NEMS being a nanoscale resonator, a beam of material that vibrates in response to an applied external force. With the thicknesses reaching the one atomic layer, graphene remains in a high crystalline order, resulting in a NEMS with extraordinary thinness, large surface area, low mass density, and high Young's modulus. Briefly, the setup for ultrafast (and fast) electron imaging involves the integration of laser optical systems into a modified transmission electron microscope (TEM). Upon the initiation of a structural change by either heating of the specimen or through electronic excitation by the laser pulses, an electron pulse generated by the photoelectric effect is used to probe the specimen with a well-defined time delay. A microscopy image or a diffraction pattern is then taken. A series of time-framed snapshots of the image or the diffraction pattern recorded at a number of delay times provides a movie, which displays the temporal evolution of the structural (morphological) and mechanical motions, using either the fs or ns laser system. Because here the visualization is that of the mechanical modes with resonances on the MHz scale, the ns resolution was sufficient. The electrons are accelerated to 200 kV with a de Broglie wavelength of 2.5079 pm. Two laser pulses were used to generate the clocking, excitation pulse at 532 nm and another at 355 nm for the generation of the electron pulse for imaging. The time delay was controlled by changing the trigger time for electron pulses with respect to that of clocking pulses. The delay can be made arbitrarily long and the repetition rate varies from a single shot to 200 kHz, to allow complete heat dissipation in the specimen. The experiments were carried out with a natural single crystal of graphite flakes on a TEM grid. Graphite flakes were left on the surface, covering some of the grid squares completely. The observed dynamics are fully reversible, retracing the identical evolution after each initiating pulse; each image is constructed stroboscopically, in a half second, from typically 2500 pulses of electrons and completing all time-frames (movies) in twenty minutes. FIG. 22 illustrates images and the diffraction pattern of graphite. (A), an image shows features of fringes in contrast (scale bar: 5 μm). Sample thickness was measured to be 53 nm using electron energy loss spectroscopy (EELS). (B) Magnified view of the indicated square of panel A (scale bar: 1 μm). (C) Diffraction pattern obtained by using a selected area diffraction aperture (SAD), which covered an area of 6 μm in diameter on the specimen. The incident electron beam is parallel to the [001] zone axis. Bragg spots are indexed as indicated for some representative ones. Panels A and B of FIG. 22 show the UEM (bright field) images of graphite, and in panel C, a typical electron diffraction pattern is given. The Bragg spots are indexed according to the hexagonal structure of graphite along the [001] zone axis, with the lattice dimension of a=b=2.46 Å (c=6.71 Å). In FIG. 22A, and at higher magnification in FIG. 22B, contrast fringes are clear, typically consisting of linear fringes having ˜1 μm length and a few hundred-nm spacing. These contrast fringes are the result of physical bucking of the graphene layers by constraints or by nanoscale defects within the film. In the dark regions, the zone axis (the crystal [001]) is well aligned with the incident electron beam and electrons are scattered efficiently, whereas in the lighter regions the alignment of the zone axis deviates more and the scattering efficiency is lower. With these contrast patterns, changes in image provide a sensitive visual indicator of the occurrence of mechanical motions. The black spots are natural graphite particles. FIG. 23 illustrates representative image snapshots and difference frames. (A) Images recorded stroboscopically at different time delays, indicated at the top right corner of each image (t1, t2, t3, t4, and t5), after heating with the initiating pulse (fluence=7 mJ/cm2); t1=200 ns; t2=500 ns; t3=10 μs; t4=30 μs; t5=60 μs; and the negative time frame was taken at −1000 ns. Note the change in position of fringes with time, an effect that can be clearly seen in FIG. 23B. (B) Image difference frames with respect to the image taken at −1 μs, i.e., Im(−1 μs; t), which show the image change with time. The reversal in contrast clearly displays the oscillatory (resonance) behavior. In FIG. 23(A), we display several time-framed images of graphite taken at a repetition rate of 5 kHz and at delay times indicated with respect to the clocking (heating) pulse with the fluence of 7 mJ/cm2. At positive times, following t=0, visual changes are seen in the contrast fringes. With time, the contrast fringes change their location in the images, and with these and other micrographs of equal time steps we made a movie of the mechanical motions of graphite following the ns excitation impulse. To more clearly display the temporal evolution on the nanoscale, image-difference frames were constructed. In FIG. 23(B), depicted are the images obtained when referencing to the −1 μs frame, i.e., Im(−1 μs; t). In the difference images, the regions of white or black indicate locations of surface morphology change (contrast pattern movement), while gray regions are areas where the contrast is unchanged from that of the reference frame. Care was taken to insure the absence of long-term specimen drifts as they can cause apparent contrast change; note that in the difference images, the static features are not present. The image changes, reported in this study, are fully reproducible, retracing the identical evolution after each initiating laser pulse, as mentioned above. The reversal of contrast with time in FIG. 23(B) directly images the oscillatory behavior of the drumming. The image change was quantified by using the method of cross-correlation. The normalized cross correlation of an image at time t with respect to that at time t′ is expressed as γ ⁡ ( t ) = ∑ x , y ⁢ C x , y ⁡ ( t ) ⁢ C x , y ⁡ ( t ′ ) ∑ x , y ⁢ C x , y ⁡ ( t ) 2 ⁢ ∑ x , y ⁢ C x , y ⁡ ( t ′ ) 2 ( 17 ) where the contrast Cx,y(t) is given by [tx,y(t)−Ī(t)]/Ī(t), and Ix,y(t) and Ix,y(t′) are the intensities of pixels at the position of (x,y) at times t and t′; Ī(t) and Ī(t′) are the means of Ix,y(t) and Ix,y(t′), respectively. This correlation coefficient γ(t) is a measure of the temporal change in “relief pattern” between the two images being compared, which can be used as a guide to image dynamics as a function of time. Shown in FIG. 24 are cross-correlation values between the image at each measured time point and a reference image recorded before the arrival of the clocking pulse. FIG. 24 illustrates the time dependence of image cross correlation. The whole scan for 100 μs is made of 2000 images taken at 50-ns steps. Also depicted are the zoomed-in image cross-correlations of three representative time regimes (I, II, and III). In each zoomed-in panel, the selected-area image dynamics of five different regions are included. Note the evolution from the “chaotic” to the global resonance (drumming) behavior at long times. Over all pixels, the time scale for image change covers the full range of time delays, from tens of ns to hundreds of μs, indicating the collective averaging over the sites of the specimen. Upon impulsive heating at t=0, the image cross-correlation changes considerably with an appearance of a “chaotic” behavior, in the ˜5 μs range (regime I in FIG. 24). After 10 μs, e.g., regime II, the cross correlation change begins to exhibit periodicity (regime II), and at longer time, a well-defined resonance oscillation emerges (regime III). This is also evident in the selected-area image dynamics (SAID) in several regions (noted as 1 to 5) where the temporal behavior is of different shapes at early time but converges into a single resonance transient after several tens of μs. The shape of image cross correlation dynamics was robust at different fluences, from 2 to ˜10 mJ/cm2, but the amplitude varies. The overall decay of the transients is on a time scale shorter than the separation between pulses. In fact, we have verified the influence of repetition rate and could establish the full recovery at the time intervals indicated. Heat transfer must occur laterally. With an initial z-independent heat profile by absorption of the heating pulse in graphite, we estimated, using a 2D heat diffusion in a homogeneous medium, the time scale for an in-plane transfer, with thermal conductivity λ=5300 W/(m·K), density ρ=2260 kg/m3, and specific heat cV=707 J/(K·kg). For the radius at half height of the initial pulse heat distribution r0=30 μm, t1/2, the time for the axial temperature to drop to a half of its initial value, is deduced to be ˜720 ns, certainly much shorter than the 200-μs time interval between pulses. It follows that the decay of the oscillation [Q/(π·f0)], as derived below, is determined by the damping of mechanical motions. When the specimen absorbs intense laser light, the lattice energy, converted from carriers (electron energy) by electron-phonon coupling, in a few ps, builds up in the illuminated spot on the surface within the duration of the laser pulse. As a consequence, the irradiated volume will expand rapidly following phonon-phonon interaction on the time scale of tens of ps. The resulting thermal stress can induce mechanical vibration in the material, but a coherent oscillatory behavior, due to the thermoelastic stress, will only emerge in the image if the impulsive stress is on a time scale shorter than the period; probing of images should be over the entire time scale of the process, in this case 100 μs. On the ultrashort time scale we have observed the structural and morphological elastic changes. FIG. 25 illustrates resonance dynamics and FFT of graphite. (Left) Time dependences of image cross correlation of full image (A) and image intensity on the selected area of 4×6 pixels as indicated by the arrowhead (B) in FIG. 24. (Right) Fast Fourier transforms of image cross-correlation (C: 0-100 μs; D: 60-100 μs) and image intensity (E: 0-100 μs; F: 60-100 μs). Asterisks in the panels indicate overtones. Note the emergence of the resonance near 1 MHz in panel F. The resonance modes in graphite are highlighted in FIG. 25 by taking the fast Fourier transform (FFT) of image cross-correlation in the time regime of 0-100 μs. The FFT (FIG. 25C) shows several peaks of different frequencies, among which the strongest one around 2.13 MHz is attributed to the overtone of 1.08 MHz. The overtones, due to the truncated nature of cross-correlation close to the value of 1, are greatly reduced in the FFT of image intensity change (FIGS. 25E and 25F). In a few tens of μs, various local mechanical modes observed at early time damp out and one global mode around 1 MHz survives. The peak when fitted to a Lorentzian yields a resonant frequency of 1.08 MHz, and a “cavity” quality factor Q(=f0/Δf)=150±30. This dominant peak gives the fundamental vibration mode of the plate in graphite. For a period of vibration, the contrast pattern of image would recur twice to its initial feature giving the observed frequency to be twice that of structural vibration; the fundamental frequency is, thus, obtained to be 0.54 MHz. A square mechanical resonator clamped at four edges without tension has a fundamental resonance mode of f0 which is given by f 0 = A ⁢ ⁢ d L 2 ⁡ [ Y ( 1 - v 2 ) ⁢ ρ ] 1 / 2 + f ⁡ ( T ) ( 18 ) where f(T) due to tension T is zero in this case. Y is the Young's modulus; ρis the mass density; v is the Poisson's ratio; L is the dimension of a grid square; d is the thickness of the graphite; and A is a constant, for this case equal to 1.655. We measured d to be 53 nm from EELS. Knowing ρ=2260 kg/m3 (300 K), v=0.16 for graphite, and L=55 μm, we obtained from the observed resonance frequency the Young's modulus to be 0.8 TPa, which is in good agreement with the in-plane value of 0.92 TPa, obtained using stress-strain measurements. This value is different by more than an order of magnitude from the c-axis value we measured using the microscope in the ultrafast mode of operation. Thus, using embodiments of the present invention, we have demonstrated a very sensitive 4D microscopy method for the study of nanoscale mechanical motions in space and time. With selected-area-imaging dynamics, the evolution of multimode oscillations to a coherent resonance (global) mode at long time provides the mapping of local regions in the image and on the nanoscale. The time scale of the resonance is directly related to materials anisotropic elasticity (Young's modulus), density, and tension, and as such the reported real-time observation in imaging can be extended to study mechanical properties of membranes (graphene in the present case) and other nanostructures with noninvasive probing. The emergent properties resolved here are of special interest to us as they represent a well-defined “self-organization” in complex macroscopic systems. The function of many nano and microscale systems is revealed when they are visualized in both space and time. Here, four-dimensional (4D) electron microscopy provided in accordance with an embodiment of the present invention is used to measure nanomechanical motions of cantilevers. From the observed oscillations of nanometer displacements as a function of time, for free-standing beams, we are able to measure the frequency of modes of motion, and determine Young's elastic modulus, the force and energy stored during the optomechanical expansions. The motion of the cantilever is triggered by molecular charge redistribution as the material, single-crystal organic semiconductor, switches from the equilibrium to the expanded structure. For these material structures, the expansion is colossal, typically reaching the micron scale, the modulus is 2 GPa, the force is 600 μN, and the energy is 200 pJ. These values translate to a large optomechanical efficiency (minimum of 1% and up to 10% or more), and a pressure of nearly 1,500 atm. We note that the observables here are real-material changes in time, in contrast to those based on changes of optical/contrast intensity or diffraction. As the physical dimensions of a structure approach the coherence length of carriers, phenomena not observed on the macroscopic scale (e.g., quantization of transport properties) become apparent. The discovery and understanding of these quantization effects requires continued advances in methods of fabrication of atomic-scale structures and, as importantly, in the determination of their structural dynamics in real-time when stimulated into a configuration of a nonequilibrium state. Of particular importance are techniques that are noninvasive and capable of nanoscale visualization in real-time. Examples of the rapid progress in the study of nanoscale structures are numerous in the field of micro and nanoelectromechanical systems (i.e., MEMS and NEMS, respectively). Recent advancements have resulted in structures having single-atom mass detection limits and binding specificities on the molecular level, and especially for biological systems. Beyond mass measurement and analyte detection, changes in the dynamics of these nanoscale structures have been shown to be sensitive to very weak external fields, including electron and nuclear spins, electron charge, and electron and ion magnetization. The response to external stimuli is manifested in deflections of the nanoscale, and a variety of techniques have been used to both actuate and detect the small-amplitude deflections. Optical interference is often used for measurement purposes, wherein the deflections of the structure cause a phase shift in the path-stabilized laser light thus providing detection sensitivities that are much less than the radius of a hydrogen atom. High spatiotemporal resolutions (atomic-scale) can be achieved in 4D ultrafast electron microscopy (UEM). Thus it is possible to image structures, morphologies, as well as nanomechanical motions (e.g., nanogating and nanodrumming) in real-time. Using embodiments of the present invention, we direct visualized nano and microscale cantilevers, and the (resonance) oscillations of their mechanical motions. The static images were constructed from a tomographic tilt series of images, whereas the in situ temporal evolution was determined using the stroboscopic configuration of UEM, which is comprised of an initiating (clocking) laser pulse and a precisely-timed packet of electrons for imaging. The pseudo-one-dimensional molecular material (copper 7,7,8,8-tetracyanoquinodimethane, [Cu(TCNQ)]), which forms single crystals of nanometer and micrometer length scale, is used as a prototype. The optomechanical motions are triggered by charge transfer from the TCNQ radical anion (TCNQ−) to copper (Cu+). More than a thousand frames were recorded to provide a movie of the 3D movements of cantilevers in time. As shown below, the expansions are colossal, reaching the micrometer scale, and the spatial modes are resolved on the nanoscale in the images (and angstrom-scale in diffraction) with resonances of megahertz frequencies for the fixed-free cantilevers. From these results, we obtained the Young's modulus, and force and energy stored in the cantilevers. Here, different crystals were studied and generally are of two types: (1) those “standing”, which are free at one end (cantilevers), and (2) those which are “sleeping” on the substrate bed; the latter will be the subject of another report. For cantilevers, the dimensions of the two crystals studied are 300 nm thick by 4.6 μm long and 2.0 μm thick by 10 μm long (see FIG. 26). As such, they define an Euler-Bernoulli beam, for which we expect the fundamental flexural modes to be prominent, besides the longitudinal one(s) which are parallel to the long axis of the crystal. Our interest in Cu(TCNQ) stems from its highly anisotropic electrical and optical properties, which arise from the nature of molecular stacking in the structure. As illustrated in FIG. 26, Cu(TCNQ) consists of an interpenetrating network of discrete columns of Cu− and TCNQ− running parallel to the crystallographic a-axis. The TCNQ molecules organize so that the π-systems of the benzoid rings are strongly overlapped, and the favorable interaction between stacked TCNQ molecules makes the spacing between the benzoid rings only 3.24 Å, significantly less than that expected from purely van der Waals-type interactions. It is this strong π-stacking that results in the pseudo-one-dimensional macroscale crystal structure and is responsible for the anisotropic properties of the material. With electric field or light, the material becomes mixed in valence with both Cu+(TCNQ) and Cu°(TCNQ°) in the stacks, weakening the interactions and causing the expansion. At high fluences, the reversible structural changes become irreversible due to the reduction of copper from the +1 oxidation state to copper metal and subsequent formation of discrete islands of copper metal driven by Ostwald ripening. The methodology we used here for synthesis resulted in the production of single crystals of phase I. FIG. 26 illustrates atomic to macro-scale structure of phase I Cu(TCNQ). Shown in the upper panel is the crystal structure as viewed along the a-axis (i.e., π-stacking axis) and c-axis. The unit cell is essentially tetragonal (cf. ref 19) with dimensions: a=3.8878 Å, b=c=11.266 Å, α=γ=90°, β=90.00(3)°; gray corresponds to carbon, blue corresponds to nitrogen, and yellow corresponds to copper. The hydrogen atoms on the six-membered rings are not shown for clarity. The lower panel displays a typical selected-area diffraction pattern from Cu(TCNQ) single crystals as viewed down the [011] zone axis along with a micrograph taken in our UEM. The rod-like crystal habit characteristic of phase I Cu(TCNQ) is clearly visible. FIG. 27 illustrates a tomographic tilt series of images. The frames show images (i.e., 2D-projections) of the Cu(TCNQ) single crystals acquired at different tilt angles of the specimen substrate. The highlighted region illustrates a large change in the position of the free-standing microscale crystal relative to another, which is lying flat on the substrate, as we change the tilt angle. The scale bar in the lower left corner measures two micrometers. The tilt angle at which each image was acquired is shown in the lower right corner of each frame in degrees. The tilt angle is defined as zero when the specimen substrate is normal to the direction of electron propagation in the UEM column. The tilt series images shown in FIG. 27 provide the 3D coordinates of the cantilevers. The dimensions and protrusion angles of these free-standing crystals were characterized by taking static frames at different rotational angles of the substrate. By placing the crystal projections into a laboratory frame orthogonal basis and measuring the length of the projections in the x-y (substrate) plane as the crystal is rotated by an angle α about the x-axis, the measured projections were obtained to be Θ of 37.8° and φ of 25.3°, where Θ is the angle the material beam makes with respect to substrate-surface normal and φ is the azimuthal angle with respect to the tilt axis, respectively. Note that the movie of the tilt series clearly shows the anchor point of the crystal to be the substrate. The dimensions and geometries of the crystals are determined from the tilt series images with 5% precision. To visualize real-time and space motions, the microscope was operated at 120 kV and the electron pulses were photoelectrically generated by laser light of 355 nm. The clocking optical pulses (671 nm laser), which are well-suited to induce the charge transfer in Cu(TCNQ), were held constant at 3 μJ, giving a maximum fluence of 160 mJ/cm2. Because the relevant resonance frequencies are on the MHz scale, the ns pulse arrangement of the UEM was more than enough for resolving the temporal changes. The time delay between the initiating laser pulse and probe electron pulse was controlled with precision, and the repetition rate of 100 Hz ensured recovery of the structure between pulses. A typical static image and selected-area diffraction are displayed in FIG. 26. From the selected-area diffraction and macroscopic expansion we could establish the nature of correlation between unit cell and the crystal change. The 4D space-time evolution of cantilevers is shown in FIGS. 28 and 29. The referenced (to negative time, tref=−10 ns; i.e., before the arrival of the clocking pulse) difference images of the microscale (FIG. 28) and nanoscale (FIG. 29) free-standing single crystal clearly display modes of expansion on the MHz scale. Each image illustrates how the spatial location of the crystal has changed relative to the reference image as a function of the time delay, elucidating both the longitudinal and transverse displacements from the at-rest position. In order to accurately measure the positions in space we used a reference particle in the image. These reference particles, which are fixed to the surface of the substrate, do not appear in frame-reference images if drift is absent or corrected for. This is an important indication that the observed crystal dynamics do not arise from motion of the substrate due to thermal drift or photothermal effects. Moreover, there is no significant movement observed in images obtained before the arrival of the excitation pulse, indicating that, during the time of pulse separation, the motion has completely damped out and the crystal has returned to its original spatial configuration. The thermal, charging, and radiation effects of the electron pulses are negligible here and in our previous studies made at higher doses. This is evidenced in the lack of blurring of the images or diffraction patterns; no beam deflection due to sample charging was observed. Lastly, no signs of structural fatigue or plasticity were observed during the course of observation, showing the function of the cantilever to be robust for at least 107 pulse cycles. Shown in FIG. 30 is the displacement of the microscale single crystal as a function of time, in both the longitudinal and transverse directions, along with the fast Fourier transforms (FFT) of the observed spatial oscillations for the time range shown (i.e., 0 to 3.3 μs). The motions in both directions of measurement are characterized by a large initial displacement from the at-rest position. The scale of expansion is enormous. The maximum longitudinal expansion possible (after accounting for the protrusion angle) for the 10 μm crystal would be 720 nm or over 7% of the total length. For comparison, a piezoelectric material such as lead zirconate titanate has typical displacements of less than 1% from the relaxed position, but it is known that molecular materials can show enormous optically-induced elastic structural changes on the order of 10% or more. The large initial motion is transferred into flexural modes in the z and x-y directions, and these modes persist over the microsecond (or longer) scale. The overall relaxation of the crystal to its initial position is not complete until several milliseconds after excitation. From the FFTs of the measured displacements, we obtained the frequency of longitudinal oscillation to be 3.3 MHz, whereas the transverse oscillations are found at 2.5 and 3.3 MHz (FIG. 30). We note that the motion represents coupling of modes with dephasing, so it is not surprising that the FFT gives more than one frequency. In fact, from an analysis consisting of a decomposition of the motion via rotation of a principle axes coordinate system relative to the laboratory frame, we found that the plane of lateral oscillation of the crystal was tilted by 18° relative to the plane of the substrate. The nature of contact with the substrate influences not only the mode structure but also the damping of cantilevers. Because of the boundary conditions of a fixed-free beam, the vibration nodes are not evenly spaced and the overtones are not simple integer multiples of the fundamental flexural frequency (f1), but rather occur at 6.26, 17.5, and 34.4 for f2, f3, and f4, respectively. This is in stark contrast to the integer multiples of the fundamental frequency of a fixed-fixed beam. Taking 3 MHz to be the main fundamental flexural frequency of the microscale crystal, we can deduce Young's elastic modulus of the crystal. The expression for the frequencies of transverse (flexural) vibrations of a fixed-free beam is given by, f n = η ⁢ ⁢ π ⁢ ⁢ κ 8 ⁢ L 2 ⁢ ⁢ c ≡ η ⁢ ⁢ π ⁢ ⁢ κ 8 ⁢ L 2 ⁢ Y ρ ( 19 ) where fn is the frequency of the nth mode in Hz, L is the beam length at rest, Y is Young's modulus, and ρ is the density. The radius of gyration of the beam cross section is κ and is given as t/√{square root over (12)}, where t is the thickness of the beam with rectangular cross section. The value of η for the beam is: 1.1942; 2.9882; 52; 72; . . . ;(2n−1)2, approaching whole numbers for higher η values The overtones are not harmonics of the fundamental, and the numerical terms for f1 and f2, which result from the trigonometric solutions involved in the derivation, must be used without rounding. For the longitudinal modes of fixed-free beam, fn=(2n−1)c/4L. From the above equation, and knowing ρ=1.802 g·cm−3, we obtained Young's modulus to be 2 GPa, with the speed of sound, therefore, being 1,100 m·s−1; we estimate a 12% uncertainty in Y due to errors in t, L, and f. This value of Young's modulus (N·m−2) is very similar to that measured for TTF-TCNQ single crystals using a mm-length vibrating reed under an alternating voltage. Both materials are pseudo-one-dimensional, and the value of the modulus is indicative of the elastic nature along the stacking axis in the direction of weak intercolumn interactions. Young's modulus slowly varies in value in the temperature range of 50 to 300 K but, when extrapolated to higher temperatures, decreases for both TTF-TCNQ and K(TCNQ). From the absorbed laser pulse energy (30 nJ), the amount of material (7.2×10−14 kg), and assuming the heat capacity to be similar to TTF-TCNQ (430 J·K−1·mol−1), the temperature rise in the microscale crystal is expected to be at most 260 K. Finally, we note that for the same modulus reported here, the frequency of longitudinal mode expansion [f=c/4L; n=1] should be nearly 25 MHz, which is not seen in the FFT with the reported resolution, thus suggesting that the observed frequencies in the longitudinal direction are those due to cantilever motion in the z direction; the longitudinal expansion of the crystal is about 1 to 2% of its length, which in this case will be 100 to 200 nm. The potential energy stored in the crystal and the force exerted by the crystal at the moment of full extension along the long axis just after time zero [cf. FIG. 30(A)] can be estimated from the amplitudes and using Hooke's law: V = 1 2 ⁢ ( YA L ) ⁢ Δ ⁢ ⁢ L 2 ( 20 ⁢ a ) F = ( YA L ) ⁢ Δ ⁢ ⁢ L ( 20 ⁢ b ) where V and F are the potential energy and force, respectively, and A is the cross-sectional area of the crystal. The bracketed term in equation (20) is the spring constant (assuming harmonic elasticity, and not the plasticity range), and by simple substitution of the values, we obtained 200 pJ and 600 μN for the potential energy and force, respectively, considering the maximum possible expansion of 720 nm; even when the amplitude is at its half value [see FIG. 30(A)], the force is very large (˜300 μN). For comparison, the average force produced by a single myosin molecule acting on an actin filament, which was anchored by two polystyrene beads, was measured to be a few piconewtons. In other words, because of molecular stacking, the force is huge. Also because of the microscale cross-section, the pressure of expansion translates to 0.1 GPa, only a few orders of magnitude less than pressures exerted by a diamond anvil. Based on the laser fluence, crystal dimensions, and absorptivity of Cu(TCNQ) at 671 nm (3.5×106 m−1), the maximum pulse energy absorbed by the crystal is 30 nJ. This means that, of the initial optical energy, a minimum of ˜1% is converted into mechanical motion of the crystal. But in fact, it could reach 10 or more percent as determined by the projection of the electric field of light on the crystal. In order to verify the trend in frequency shifts, the above studies were extended to another set of crystal beams, namely those of reduced dimensions. Because the resonant frequencies of a fixed-free beam are determined, in part, by the beam dimensions [cf. equation (19)], a Cu(TCNQ) crystal of different length than that shown in FIG. 30 should change the oscillation frequencies by the κ/L2 dependence. With a smaller cantilever beam we measured the oscillation frequencies for a crystal of 300 nm thickness and 4.6 μm length, using the same laser parameters as for the larger crystals, and found them to be at higher values (FIG. 31). This is confirmed by the FFTs of the displacement spanning the range 0 to 3.3 μs [FIGS. 31(C) and (D)]; a strong resonance near 9 MHz with another weaker resonance at 3.6 MHz in the longitudinal direction [FIG. 31(C)] is evident. Within a few microseconds, the only observed frequency in the FFT was near 9 MHz. This oscillation persists up to the time scans of 30 μs, at which point the amplitude was still roughly 40% of the leveling value near 2 μs. By taking this duration (30 μs) to be the decay time (τ) required for the amplitude to fall to 1/e of the original value, the quality factor (Q=πfτ) of the crystal free oscillator becomes near 1,000. However, on longer time scales, and with less step resolution, the crystal recovers to the initial state in a few milliseconds, and if the mechanical motion persists, Q would increase by an order of magnitude. It is clear from the resonance value of the flexural frequency at 9 MHz that as the beam reduces in size, the frequency increases, as expected from equation (19). However, if we use this frequency to predict Young's modulus we will obtain a value of 30 GPa, which is an order of magnitude larger than that for the larger microscale crystal. The discrepancy points to the real differences in modes structure as we reach nanometer-scale cantilevers. One must consider, among other things, the anchor-point(s) of the crystals, the frictional force with substrate and other crystals, and the curvature of the beam (see movie in supporting information). This curvature will cause the crystal to deviate from ideal Euler-Bernoulli beam dynamics, thus shifting resonance frequencies from their expected positions. Interestingly, by using the value of 30 GPa for Young's modulus, the minimum conversion efficiency increases by a factor of 15. These dependencies and the extent of displacement in different directions, together with the physics of modes coupling (dephasing and rephasing), will be the subject of our full account of this work. Thus, with 4D electron microscopy it is possible to visualize in real space and time the functional nanomechanical motions of cantilevers. From tomographic tilt series of images, the crystalline beam stands on the substrate as defined by the polar and azimuthal angles. The resonance oscillations of two beams, micro and nanocantilevers, were observed in situ giving Young's elastic modulus, the force, and the potential energy stored. The systems studied are unique 1D molecular structures, which provide anisotropic and colossal expansions. The cantilever motions are fundamentally of two types, longitudinal and transverse, and have resonance Q factors that make them persist for up to a millisecond. The function is robust, at least for 107 continuous pulse cycles (˜1011 oscillations for the recorded frames), with no damage or plasticity. With these imaging methods in real-time and with other variants, it is now possible to test the various theoretical models involved in MEMS and NEMS. Electron energy loss spectroscopy (EELS) is a powerful tool in the study of valency, bonding and structure of solids. Using our 4D electron microscope, we have performed ultrafast EELS, taking the time resolution in the energy-time space into the femtosecond regime, a 10 order of magnitude increase, and for a table-top apparatus. It is shown that the energy-time-amplitude space of graphite is selective to changes, especially in the electron density of the π+σ plasmon of the collective oscillation of the four electrons of carbon. Embodiments of the present invention related to EELS enable the microscope to be used as an analytical tool. As electrons pass through the specimen, each type of material (e.g., gold, copper, or zinc) will have a different electron energy. Thus, it is possible to “tune” into a particular element and study the dynamic behavior of the material itself. In microscopy, EELS provides rich characteristics of energy bands describing modes of surface atoms, valence- and core-electron excitations, and interferences due to local structural bonding. The scope of applications thus spans surface and bulk elemental analysis, chemical characterization and electronic structure of solids. The static, time-integrated, EEL spectra do not provide direct dynamic information, and with video-rate scanning in the microscope could changes be recorded only with a time resolution of millisecond or longer. Dedicated time-resolved EELS apparatus, without imaging, have obtained millisecond resolution, being determined primarily by detector response and electron counts. However, for studies of dynamics of electronic structure, valency and bonding, the time resolution must increase by at least nine orders of magnitude. We have performed femtosecond resolved EELS (FEELS) using our ultrafast electron microscope (UEM), developed for 4D imaging of structures and morphology. Embodiments of the present invention are conceptually different from time-resolved EELS (termed TREELS) as the time resolution in FEELS is not limited by detector response and sweep rate. Moreover, both real-space images and energy spectra can be recorded in situ in UEM and with energy filtering the temporal resolution can be made optimum. We demonstrate the method in the study of graphite which displays changes on the femtosecond (fs) time scale with the delay steps being 250 fs. Near the photon energy of 2.4 eV (away from the zero energy loss peak), and similarly for the π+σ plasmon band, the change is observed, but it is not as significant for the π plasmon band. Thus it is possible to chart the change from zero to thousands of eV and in 3D plots of time, energy and amplitude; the decrease in EELS intensity at higher energies becomes the limiting factor. This table-top approach using electrons is discussed in relation to recent achievements using soft and hard (optical) X-rays in laboratory and large-scale facilities of synchrotrons and free electron lasers. According to embodiments of the present invention, the probing electrons and the initiating light pulses are generated by a fs laser, and the EEL spectra of the transmitted electrons are recorded in a stroboscopic mode by adjusting the time delay between the pump photons and the probe electron bunches. The concept of single-electron packet used before in imaging is utilized in this approach. When each ultrafast electron packet contains at most one electron, “the single-electron mode,” space-charge broadening of the zero-loss energy peak, which decreases the spectrometer's resolution, is absent. FIG. 32 is a schematic diagram of a microscope used in embodiments of the present invention. A train of 220 fs laser pulses at 1.2 eV was frequency doubled and tripled and then split into two beams. In other embodiments, a range of laser pulse widths could be used, for example from about 10 femtoseconds to about 10 microseconds. The frequency tripled light at 3.6 eV was directed to the microscope photocathode, and the photoelectron probe pulse was accelerated to 200 keV. The 2.4 eV pulses were steered to the specimen, and provided the excitation at a fluence of 5.3 mJ/cm2. In other embodiments, a fluence ranging from about 1 mJ/cm2 to about 20 mJ/cm2 could be utilized. By varying the delay time between the electron and optical pulses, the time dependence of the associated EEL spectrum was followed. The electrons pass through the sample and a set of magnetic lenses to illuminate the CCD camera, forming either a high resolution image of the specimen, a diffraction image, or they can be energy dispersed to provide the EEL spectra. The apparatus is equipped with a Gatan imaging filter (GIF) Tridiem, of the postcolumn type, which is attached below the transmission microscope camera chamber. The energy width of near 1 eV was measured for the EELS zero-loss peak and it is comparable to that obtained in thermal-mode operation of the TEM, but increases significantly in the space-charge limited regime. The experiments were performed at repetition rates of 100 kHz and 1 MHz, and no difference in the EEL spectra or the temporal behavior was observed, signifying a complete recovery of electronic structure changes between subsequent pulses. The reported temporal changes were missed when the scan resolution exceeded 250 fs, and the entire profile of the transient is complete in 2 ps. The electron beam passes through the graphite sample perpendicular to the sample surface while the laser light polarization was parallel to the graphene layers. Finally, the zero of time was determined to the precision of the reported steps, and was observed to track the voltage change in the FEG module of the microscope. The semi-metal graphite is a layered structure, which was prepared as free-standing film. The thickness of the graphite film was estimated from the EEL spectrum to be 106 nm (inelastic mean-free path of ˜150 nm), and the crystallinity of the specimen was verified by observing the diffraction pattern which was indexed as reported. FIG. 33 shows a static EEL spectrum of graphite taken in UEM. The distinct features are observed in the spectrum and indeed are typical of the electronic structure bands of graphite; the in-plane π plasmon is found near 7 eV, while at higher energy, the peak at 27 eV is observed with a shoulder at 15 eV. These latter peaks correspond to the π+σ oscillation of the bulk and surface plasmons, respectively. The results are in agreement with those of literature reports. The bands displayed in different colors (FIG. 33) are the simulations of the profiles with peak positions reproducing the theoretical values near 7, 15 and 27 eV. The 3D FEELS map of the time-energy evolution of the amplitude of the plasmon portion of the spectrum (up to 35 eV) is shown in FIG. 34, together with the EEL spectrum taken at negative time. The spectra were taken at 1 MHz repetition-rate, for a pump fluence of 5.3 mJ/cm2 at room temperature and for ts=250 fs for each difference frame. The map reflects the difference for all energies and as a function of time, made by subtracting a reference EEL spectrum at negative time from subsequent ones. The relatively strong enhancement of the energy loss in the low energy (electron-hole carriers) region is visible and the change is near the energy of the laser excitation. This feature represents the energy loss enhancement due to the creation of carriers by the fs laser excitation in the ππ* band structure, as discussed below. At higher energy, the 7 eV π plasmon peak remains nearly unperturbed by the excitation, and no new features are observed at the corresponding energies. For the 27 eV π+σ bulk plasmon an increased spectral weight at positive time is visible as a peak in the time-resolved spectrum. In order to obtain details of the temporal evolution of the different spectroscopic energy bands, we divided the spectrum into three regions: the low energy region between 2 and 5 eV, the π plasmon region between 6 and 8 eV, and the π+σ plasmon region between 20 and 30 eV. The 3D data are integrated in energy within the specified regions of the spectrum, and the temporal evolution of the different loss features are obtained; see FIG. 35. For regions where changes occur, the time scales involved in the rise and subsequent decay are similar. In FEELS, the shortest decay is 700 fs taken with the steps of 250 fs. The duration of the optical pulse is ˜220 fs, but we generate the UV pulse for electron generation through a non-linear response, and it is possible that the pulses involved are asymmetric in shape and that multiphotons are part of the process; full analysis will be made later. We note that the observed ˜700 fs response indeed reflects the joint response from both the optical and electron pulses and it is an upper limit for the electronic change. It is remarkable that, in FIG. 35, the temporal evolution of the interlayer spacing of graphite obtained by ultrafast electron crystallography (UEC) at a similar fluence, i.e. 3.5 mJ/cm2, the timescale of the ultrafast compression corresponds well to the period in which the bulk plasmon is out of equilibrium; in this plot the zero of time is defined by the change of signal amplitude. In graphite, the characteristic time for the thermalization of photo-excited electrons is known to be near 500 fs at low fluences (a few μJ/cm2). When excited by an intense laser pulse, a strong electrostatic force between graphene layers is induced by the generated electron-hole (carrier) plasma. This causes the structure to be out of equilibrium for nearly 1 ps; a stressful structural rearrangement is imposed on the crystal, which, at very high fluences (above 70 mJ/cm2), has been proposed as a cause of the phase transformation into diamond. Because graphite is a quasi two-dimensional structure, distinct spectral features are visible in EELS. The most prominent and studied peaks are those at 7 eV and the much stronger one at 27 eV. From the solution of the in-plane and out-of-plane components of the dielectric tensor it was shown, for graphite, that the 7 eV band is a π plasmon, resulting from interband ππ* transitions in the energy range of 2-5 eV, whereas the 27 eV band is a π+σ plasmon dominated by σσ* transitions beyond 10 eV (FIG. 5). We note that in this case the plasmon frequencies are not directly given by the ππ* and σσ* transition energies as they constitute tensorial quantities. For example ϖ π + σ 2 = ϖ p 2 + 1 4 ⁢ ( Ω π 2 + 3 ⁢ Ω σ 2 ) ,where ωp=npe2/∈0m)1/2 is the free electron gas plasma frequency; Ωπ and Ωσ are the excitation energies for ππ* and σσ* transitions, respectively. For ωP, the electron density is np, n is the number of valence electrons per atom and p is the density of atoms, and ∈0 is the vacuum dielectric constant. It follows that the density of occupied and empty (π, σ, π*, and σ*) states is critical, and that the π Plasmon is from the collective excitation of the πelectrons (one electron in the p-orbital, with screening corrections) whereas the π+σ plasmon is the result of all 4 valence electrons collectively excited over the coherent length scale of bulk graphite; there are also surface plasmons but at different energies. Recently it was demonstrated, both theoretically and experimentally, that the π and π+σ plasmons are sensitive to the inter-layer separation, but while the former shows some shift of peaks the latter is dramatically reduced in intensity, and, when reaching the grapheme limit, only a relatively small peak at ˜15 eV survives. This is particularly evident when the momentum transfer is perpendicular to the c-axis, the case at hand and for which the EEL spectrum is very similar to ours. With the above in mind, it is now possible to provide, in a preliminary picture, a connection between the selective fs atomic motions, which are responsible for the structural dynamics, and changes in the dielectric properties of Plasmon resonances, the electronic structure. The temporal behavior, and coherent oscillation (shear modes of ˜1 ps), of c-axis expansion display both contraction and expansion on the picometer length scale per unit cell. The contraction precedes the expansion, as shown in FIG. 35, with velocity that depends on the fluence, i.e., the density of carriers. With fs excitation, the electronic bands are populated anisotropically, and, because of energy and momentum conservation, the carriers transiently excite large-momentum phonons, so called strongly coupled phonons. They are formed on the fs time scale (electron-phonon coupling) but decay in ˜7 ps. The initial compression suggests that the process is a cooperative motion and is guided by the out-of-equilibrium structure change dictated by the potential of excited carriers; in this case ππ* excitation which weakens c-axis bonding. The initial atomic compression, when plotted with transient EELS data (FIG. 35), shows that it is nearly in synchrony with the initial change, suggesting that the spacing between layers (c-axis separation) is the rate determining step, and that in the first 1 ps, the compressed ‘hard graphite’ effect is what causes the increase in the amplitude of the π+σ plasmon peak. In other words, the decrease of the spectral weight due to the change of electronic structure upon increasing the interlayer separation (to form graphene) becomes an increase when the plates are compressed, because of the enhanced collectiveness of all four valence electrons of carbon. The change involves shear motions and it is not surprising that the π+σ peak (dominated by σσ* excitation) is very sensitive to such changes. The π peak is less influenced as only one electron is involved, as discussed above, and the amplitude change is relatively small. The faster recovery of EEL peaks in 700 fs is, accordingly, the consequence of expansion which ‘decouples’ the π and σ system. Lastly, the relatively large increase in EEL near the photon energy is due to carrier excitation (π*) which leads to a loss of electron energy at near 3 eV, possibly by electronic excitation involving the cy system (FIG. 36). The created carriers cause an increase in the Drude band as evidenced in the decrease in optical transmission. The demonstration of ultrafast EELS in electron microscopy opens the door to experiments that can follow the ultrafast dynamics of the electronic structure in materials. The fs resolution demonstrates the ability of UEM to probe transients on the relevant sub-picosecond time scale, while keeping the energy resolution of EELS. Moreover, the selectivity of change in the collective electron density (for graphite) suggests future experiments, including those with changes in polarization, shorter optical pulses, core excitation and oxidation sites. We believe that this table-top UEM-EELS should provide the methodology for studies which have traditionally been made using synchrotrons (and free electron lasers) especially in the UV and soft X-ray regions. Chemical bonding dynamics are important to the understanding of properties and behavior of materials and molecules. Utilizing embodiments of the present invention, we have demonstrated the potential of time-resolved, femtosecond electron energy loss spectroscopy (EELS) for mapping electronic structural changes in the course of nuclear motions. For graphite, it is found that changes of milli-electron volts in the energy range of up to 50 electron volts reveal the compression and expansion of layers on the subpicometer scale (for surface and bulk atoms). These nonequilibrium structural features are correlated with the direction of change from sp2 [two-dimensional (2D) grapheme] to sp3 (3D-diamond) electronic hybridization, and the results are compared with theoretical charge-density calculations. The reported femtosecond time resolution of four-dimensional (4D) electron microscopy represents an advance of 10 orders of magnitude over that of conventional EELS method. Bonding in molecules and materials is determined by the nature of electron density distribution between the atoms. The dynamics involve the evolution of electron density in space and the motion of nuclei that occur on the attosecond and femtosecond time scale, respectively. Such changes of the charge distribution with time are responsible for the outcome of chemical reactivity and for phenomena in the condensed phase, including those of phase transitions and nanoscale quantum effects. With convergent-beam electron diffraction, the static pattern of charge-density difference maps can be visualized, and using x-ray absorption and photoemission spectroscopy substantial progress has been made in the study of electronic-state dynamics in bulks and on surfaces. Electron energy loss spectroscopy (EELS) is a powerful method in the study of electronic structure on the atomic scale, using aberration-corrected microscopy, and in chemical analysis of selected sites; the comparison with synchrotron-based near-edge x-ray absorption spectroscopy is impressive. The time and energy resolutions of ultrafast electron microscopy (UEM) provide the means for the study of (combined) structural and bonding dynamics. Here, time-resolved EELS is demonstrated in the mapping of chemical bonding dynamics, which require nearly 10 orders of magnitude increase in resolution from the detector-limited millisecond response. By following the evolution of the energy spectra (up to 50 eV) with femtosecond (fs) resolution, it was possible to resolve in graphite the dynamical changes on a millielectronvolt (subpicometer motion) scale. In this way, we examined the influence of surface and bulk atoms motion and observed correlations with electronic structural changes: contraction, expansion, and recurrences. Because the EEL spectra of a specimen in this energy range contain information about plasmonic properties of bonding carriers, their observed changes reveal the collective dynamics of valence electrons. Graphite is an ideal test case for investigating the correlation between structural and electronic dynamics. Single-layered grapheme, the first two-dimensional (2D) solid to be isolated and the strongest material known, has the orbitals on carbon as sp2 hybrids, and in graphite the π-electron is perpendicular to the molecular plane. Strongly compressed graphite transforms into diamond, whose charge density pattern is a 3D network of covalent bonds with sp3 hybrid orbitals. Thus, any structural perturbation on the ultra-short time scale of the motion will lead to changes in the chemical bonding and should be observable in UEM. Moreover, surface atoms have unique binding, and they too should be distinguishable in their influence from bulk atom dynamics. The experiments were performed on a nm-thick single crystal of natural hexagonal graphite. The sample was cleaved repeatedly until a transparent film was obtained, and then deposited on a transmission electron microscopy (TEM) grid; the thickness was determined from EELS to be 108 nm. The fs-resolved EELS (or FEELS) data were recorded in our UEM, operating in the single-electron per pulse mode to eliminate Boersch's space charge effect. A train of 220 fs infrared laser pulses (λ=1038 nm) was split into two paths, one was frequency-doubled and used to excite the specimen with a fluence of 1.5 mJ/cm2, and the other was frequency-tripled into the UV and directed to the photoemissive cathode to generate the electron packets. These pulses were accelerated in the TEM column and dispersed after transmission through the sample in order to provide the energy loss spectrum of the material. The experimental, static EEL spectra of graphite in our UEM, with grapheme for comparison, are displayed in FIG. 37A; FIG. 37B shows the results of theoretical calculations. The spectral feature around 7 eV is the π Plasmon, the strong peak centered around 26.9 eV is the π+σ bulk plasmon, and the weaker peak on its low energy tail is due to the surface Plasmon. The agreement between the calculated EEL spectra and the experimental ones is satisfactory both for graphite and grapheme. Of relevance to our studies of dynamics is the simulation of the spectra for different c-axis separations, ranging from twice as large as naturally occurring (2c/a; a and c are lattice constraints) to 5 times as large. This thickness dependence is displayed in FIG. 37B. As displayed in FIG. 37, the surface and bulk Plasmon bands (between 13 and 35 eV) can be analyzed using two Voigt functions, thus defining the central position, intensity, and width. At different delay times, we monitored the changes and found that they occur in the intensity and position; the width and shape of the two spectral components are relatively unchanged. FIGS. 37C and 37D, show the temporal changes of the intensity for both the surface and bulk plasmons. As noted, the behavior of bulk dynamics is “out of phase” with that of the surface dynamics, corresponding to an increase in intensity for the former and a decrease for the latter. Each time point represents a 500-fs change. Within the first 1 ps, the bulk Plasmon gains spectral weight with the increase in intensity. With time, the intensity is found to return to its original (equilibrium) value. At longer times, a reverse in sign occurs, corresponding to a decrease and then an increase in intensity—an apparent recurrence or echo occurring with dispersion. The intensity change of the surface plasmon in FIGS. 37C and 37D, shows a π phase-shifted temporal evolution with respect to that of the bulk plasmon. The time dependence of the energy position of the different spectral bands is displayed in FIG. 38. The least-squares fit converges for a value of the surface plasmon energy at 14.3 eV and of the bulk plasmon at 26.9 eV. The temporal evolution of the surface plasmon gives no sign of energy dispersion, whereas the bulk plasmon is found to undergo first a blueshift and then a redshift at longer times (FIGS. 38A and 38B). The overall energy-time changes in the FEEL spectra are displayed in FIG. 39. To make the changes more apparent, the difference between the spectra after the arrival of the initiating laser pulse (time zero) and a reference spectrum taken at ˜20 ps before time zero is shown. The most pronounced changes are observed in the region near the energy of the laser itself (2.39 eV), representing the energy-loss enhancement due to the creation of carriers by the laser excitation, and in the region dominated by the surface and bulk plasmons (between 13 and 35 eV). Clearly evident in the 3D plot are the energy dependence as a function of time, the echoes, and the shift in phase. A wealth of information has been obtained on the spectroscopy and structural dynamics of graphite. Of particular relevance here are the results concerning contraction and expansion of layers probed by diffraction on the ultra-short time scale. Knowing the amplitude of contraction/expansion, which is 0.6 pm at the fluence of 1.5 mJ/cm2, and from the charge of plasmon energy with interlayer distance (FIG. 37), we obtained the results shown in FIG. 38C. The diffraction data, when now translated into energy change, reproduce the pattern in FIG. 38A, with the amplitude being within a factor of two. When the layers are fully separated, that is, reaching grapheme, the bulk plasmon, as expected, is completely suppressed. The dynamics of chemical bonding can now be pictured. The fs optical excitation of graphite generates carriers in the nonequilibrium state. They thermalize by electron-electron and electron-phonon interactions on a time scale found to be less than 1 ps, less than 500 fs, and −200 fs. From our FEELS, we obtained a rise of bulk plasmons in ˜180 fs (FIG. 39). The carriers generated induce a strong electrostatic force between grapheme layers, and ultrafast interlayer contraction occurs as a consequence. In FIG. 37D, the increase of the bulk plasmon spectral weight on the fs time scale reflects this structural dynamics of bond-length shortening because it originates from a denser and more 3D charge distribution. After the compression, a sequence of dilatations and successive expansions along the c axis follows, but, at longer times lattice thermalization dephases the coherent atomic motions; at a higher fluence, strong interlayer distance variations occur, and grapheme sheets can be detached as a result of these interlayer collisions. Thus, the observations reported here reflect the change in electronic structure: contraction toward diamond and expansion toward grapheme. The energy change with time correlates well with the EELS change calculated for different interlayer distances (FIG. 37). We have calculated the charge density distribution for the three relevant structures. The self-consistent density functional theory calculations were made using the linear muffin-tin orbital approximation, and the results are displayed in FIG. 40. To emphasize the nature of the changes observed in FEELS, and their connection to the dynamics of chemical bonding, we pictorially display the evolution of the charge distribution in a natural graphite crystal, a highly compressed one, and the extreme case of diamond. Once can see the transition from a 2D to a 3D electronic structure. The compressed and expanded graphite can pictorially be visualized to deduce the change in electron density as interlayer separations change. With image, energy, and time resolution in 4D UEM, it is possible to visualize dynamical changes of structure and electronic distribution. Such stroboscopic observations require time and energy resolutions of fs and meV, respectively, as evidenced in the case study (graphite) reported here, and for which the dynamics manifest compression/expansion of atomic planes and electronic sp2/sp3-type hybridization change. The application demonstrates the potential for examining the nature of charge density and chemical bonding in the course of physical/chemical or materials phase change. It would be of interest to extend the scale of energy from ˜1 eV, with 100 meV resolution, to the hundreds of eV for exploring other dynamical processes of bonding. The following articles are hereby incorporated by reference for all purposes: 4D imaging of transient structures and morphologies in ultrafast electron microscopy, Brett Barwick, et al., Science, Vol. 322, Nov. 21, 2008, p. 1227. Temporal lenses for attosecond and femtosecond electron pulses, Shawn A. Hibert, et al., PNAS, Vol. 106, No. 26, Jun. 30, 2009, p. 10558. Nanoscale mechanical drumming visualized by 4D electron microscopy, Oh-Hoon Kwon, et al., Nanoletters, Vol. 8, No. 11, November 2008, p. 3557. Nanomechanical motions of cantilevers: direct imaging in real space and time with 4D electron microscopy, David J. Flannigan, et al., Nanoletters, Vol. 9, No. 2 (2009), p. 875. EELS femtosecond resolved in 4D ultrafast electron microscopy, Fabrizio Carbone, et al., Chemical Physics Letters, 468 (2009), p. 107. Dynamics of chemical bonding mapped by energy-resolved 4D electron microscopy, Fabrizio Carbone, et al., Science, Vol. 325, Jul. 10, 2009, p. 181. Atomic-scale imaging in real and energy space developed in ultrafast electron microscopy, Hyun Soon Park, et al., Nanoletters, Vol. 7, No. 9, September 2007, p. 2545. It is also understood that the examples and embodiments described herein are for illustrative purposes only and that various modifications or changes in light thereof will be suggested to persons skilled in the art and are to be included within the spirit and purview of this application and scope of the appended claims.

059498374

claims

1. A nuclear reactor having a core including a plurality of seed-blanket units, each said seed-blanket unit comprising: a) a central seed region, said seed region containing plutonium seed fuel elements; b) a blanket region surrounding said seed region and containing blanket fuel elements comprising predominantly thorium oxide; c) moderator in said seed region in the volume ratio of moderator to fuel in the range of approximately 2.5 to 3.5; and d) moderator in said blanket region in the volume ratio of moderator to fuel of approximately 1.5 and 2.0. a) a central seed region, said seed region containing plutonium seed fuel elements, each of said seed fuel elements being comprised of plutonium-zirconium alloy; b) a blanket region surrounding said seed region and containing blanket fuel elements comprising predominantly thorium oxide with approximately 1% or less plutonium oxide, and approximately 2-5% by volume uranium tailings; c) moderator in said seed region in the volume ratio of moderator to fuel in the range of approximately 2.5 to 3.5; and d) moderator in said blanket region in the volume ratio of moderator to fuel of between approximately 1.5 and 2.0. 2. The nuclear reactor of claim 1, wherein each of said seed fuel elements is comprised of plutonium-zirconium alloy. 3. The nuclear reactor of claim 1, wherein said seed region comprises between approximately 45 and 55% of the total volume of each said seed-blanket unit. 4. The nuclear reactor of claim 1, wherein said blanket fuel elements further include plutonium oxide in the amount of no more than approximately 1%. 5. The nuclear reactor of claim 1, wherein said blanket fuel elements comprise approximately 2-5% by volume uranium tailings. 6. The nuclear reactor of claim 1, wherein the volume ratio of moderator to fuel in said seed region is in the range of approximately 2.5 to 3.0. 7. The nuclear reactor of claim 1, wherein said central seed region further contains a plurality of burnable poison containing rods. 8. The nuclear reactor of claim 7, wherein said plurality of burnable poison containing rods includes WABA poison rods and gadolinium containing fuel rods. 9. A nuclear reactor having a core including a plurality of seed-blanket units, each said seed-blanket unit comprising: 10. The nuclear reactor of claim 9, wherein said seed region comprises between approximately 45 and 55% of the total volume of each said seed-blanket unit. 11. The nuclear reactor of claim 10, wherein the volume ratio of moderator to fuel in said seed region is in the range of approximately 2.5 to 3.0. 12. The nuclear reactor of claim 11, wherein said central seed region further contains a plurality of burnable poison containing rods. 13. The nuclear reactor of claim 12, wherein said plurality of burnable poison containing rods includes WABA poison rods and gadolinium containing fuel rods.

055770819

summary

BACKGROUND OF THE INVENTION 1. Technical Field of the Invention The present invention relates to a method of forming grids for nuclear fuel assemblies, as well as to the grids formed by the application of the same method. 2. Background Art In the conventional method of manufacturing nuclear fuel assembly grids, straps 1, which are formed, for example, of nickel alloy so as to have slits therein, are, as shown in FIGS. 7A to 7C, assembled into a grid form, and the intersections 2 of the straps 1 are then brazed. In this method, nickel is usually plated on the surfaces of the straps 1 in advance in order to ensure high-quality brazing. More specifically, FIG. 7A depicts a part of the assembled straps 1, showing a brazing filler metal (hereinafter referred to as "filler metal") being adherently placed on top of the intersections 2 of the straps 1. When the straps 1 are heated in a vacuum type brazing furnace (hereinafter referred to as "vacuum furnace"), the filler metal melts and flows down along the intersections 2, so that the intersections 2 are presumed to be brazed uniformly over their entire lengths. FIG. 7B depicts the result of brazing in the case where the brazing is effected on the straps having nickel-plated surfaces, whereas FIGS. 7C and 7D depict the result of brazing in the cases where the brazing is carried out on the non-Ni plated straps. In either of the straps shown in FIGS. 7C and 7D, good brazing results have not been obtained due to insufficient or ununiform flow of the filler metal flowing down from the top of the intersections 2 therealong. In FIG. 7C, unbrazed portions are shown remaining, whereas in FIG. 7D, the width and thickness of the brazed parts have become excessive. Thus, it has hitherto been conventional to carry out nickel plating on the straps 1 in order to ensure excellent brazing quality. However, such a plating process is unavoidably associated with an increased cost and environmental pollution. Therefore, there has been the need for the development of a novel brazing technique which requires no plating treatment but achieves excellent brazing quality. SUMMARY OF THE INVENTION It is therefore the primary object of the present invention to provide a method of forming a nuclear fuel assembly grid which requires no plating treatment but ensures improved brazing quality. Another object of the invention is to provide a nuclear fuel assembly grid which is obtained by the aforesaid method. According to a first aspect of the invention, there is provided a method of forming a nuclear fuel assembly grid, which includes the steps of (a) preparing a plurality of formed alloy straps each having slits, (b) arranging the straps into a grid form by intersecting the straps with each other through the slits, and (c) brazing intersections of the associated straps, the method further comprising the step of: (d) subjecting those portions to be brazed to a pretreatment prior to the arranging step (b), the pretreatment including applying a paste, comprising a mixture of a filler metal and a vehicle, to the portions to be brazed to form a thin film thereon. In the foregoing, the pretreatment step (d) may further include drying the paste film, heating the straps in a vacuum furnace to melt the filler metal in the paste, and cooling the straps; and the brazing step (c) may include placing a filler metal daub on top of the intersections of the straps, and heating the straps in a vacuum furnace to effect the brazing of the straps. Alternatively, the method may further comprise the steps of drying the paste film, heating the straps in a vacuum furnace to melt the filler metal in the paste, and cooling the straps between the arranging step (b) and the brazing step (c); and the brazing step (c) may include placing a filler metal daub on top of the intersections of the straps, and heating the straps in a vacuum furnace to effect the brazing of the straps. Furthermore, the brazing step (c) may include placing a filler metal daub on top of the intersections of the straps, and heating the straps in a vacuum furnace to effect the brazing of the straps; and the method may further comprise the steps of drying the paste film after the pretreatment step (d), subsequently effecting the brazing step (c), and heating the straps in a vacuum furnace to effect the brazing of the straps. In this modification, the step of drying the paste film may be omitted. Moreover, the filler metal may contain Ni powder, whereas the vehicle may contain a synthetic resin and an organic solvent. In addition, the paste may further contain an additional substance selected from the group consisting of water, an organic solvent such as methyl alcohol and a liquid surface active agent such as polyethylene glycol fatty acid ester. According to another aspect of the invention, there is provided a nuclear fuel assembly grid formed using the aforesaid method. In the method of the present invention, since the pretreatment is carried out on the surfaces of the straps, excellent solderability can be ensured even though the plating is omitted. Therefore, the nuclear fuel assembly grids of excellent quality can be obtained at reduced cost without causing any environmental problems.

051679086

summary

BACKGROUND The invention relates to a device for recombination of hydrogen and oxygen. A device of this kind, to be described later in greater detail, is known from U.S. Pat. No. 4,911,879 (Heck et al.). An apparatus of that nature is discussed in German Patent No. DE-A-36 04 416 (corresponding to the Klatt et al U.S. Pat. No. 4,755,359). As set forth in detail in the Klatt et al. patent, the problem of eliminating hydrogen from a gas mixture arises in particular in nuclear reactor accidents, in which hydrogen escapes into the oxygen-containing atmosphere of the containment vessel or a pressure suppression system of the nuclear reactor, thus creating the risk of an explosion. To avoid this explosion danger, known methods are employed to eliminate the hydrogen through catalytically supported recombination with oxygen to form steam. Especially suitable catalyst materials for this purpose and hence also within the scope of the present invention are described in German Patent No. DE-A-37 25 290. Since a catalyst of this kind forms part of the safety equipment, which is only supposed to operate in the event of a malfunction, care must be taken to ensure that the catalyst retains its functional ability over very many years of storage. For this purpose, methods are known in which the catalyst is stored in an airtight sealed housing, within the vessel or space in which the hydrogen is to be eliminated in the event of an accident, said housing opening automatically when the accident occurs as a result of the influence of pressure and/or temperature, thus exposing the catalyst to the atmosphere-containing hydrogen and oxygen. During a core meltdown in a reactor pressure vessel (RPV), a temperature rise in the melt of up to 2400.degree. C. is reached, with large quantities of fission products and structural materials being released into the atmosphere of the containment. This results in a mixture of steam and gases in which aerosol particles with a weight concentration of up to 20 g/m.sup.3 can be suspended. The term "aerosol" is used herein in a broad sense to mean a suspension of liquid or solid particles in a gas. Thus for example in the low-pressure path at the beginning of the interaction between the melt and the concrete, 1 to 3 tons of dispersed material can be suspended in the air inside the containment vessel. By far the largest component, more than 95%, is non-radioactive. However, most of the radioactive substances are bound to the aerosol particles. The release of hydrogen during reactor accidents, mentioned at the outset, coincides in time with the above release of aerosols. Model tests have shown that the release of steam occurs practically simultaneously with the beginning of a core meltdown accident, while the release of hydrogen and simultaneously therewith, the release of aerosols, take place only after a certain delay. In the presence of large quantities of steam and a strong flow, the catalytic reaction to remove hydrogen proceeds more slowly. The reaction rate increases exponentially with temperature. It is only when a sufficiently high temperature has been reached on the surface of the catalyst system that a sufficient convection flow develops which is adequate to prevent the aerosol particles contained in the gas mixture from being deposited on the surface of the catalyst. This prevention is aided by the constant generation of reaction steam at the surface of the catalyst system, which becomes constant at a correspondingly high temperature and conversion rate. However, as long as the temperature of the catalyst system is still not sufficiently high during the initial phase, aerosol particles and grease particles contained in the steam can settle on the surface of the catalyst, thus reducing the effective catalyst surface and having a highly negative effect on catalytic reaction. Heck et al. mentioned at the outset, contains a catalyst system inside a cylindrical tube whose two ends are closed off by seals which open automatically in the event of an accident. The tube is mounted vertically in the area to be protected and has a filter system between its lower end and the catalyst system for chemically neutralizing catalyst poisons. The filter system can be a porous ceramic body or a molded fiber structure containing silver nitrate. When the seals at the two ends of the tube open, the atmosphere containing hydrogen penetrates the tube and passes through the filter into the catalyst system, which heats up because of the exothermic reaction, thus generating a gas flow through the tube. Examples cited in Heck et al. of seals which open automatically as a function of temperature are diaphragms made of a plastic which melt at high temperatures, as well as bimetallic sheet metal. The bimetallic sheet metal has no gas-tight seal. On the other hand, plastic diaphragms do not provide reliable long-term gas-tight seals. In addition, in the event of ignition, they can burn and impose a burden on the environment through the release of gases. The steam released initially in the event of an accident, in accordance with the above statements, passes through the rooms of the installation in which circulating pumps, slide bearings, electric motors, etc. are located, thereby carrying with it certain amounts of lubricating and sealing grease. Grease particles that reach the catalyst system can settle out on the catalyst surface, provided their temperature is below the vaporization point of the grease. It has been found that grease deposits of this kind have a highly disadvantageous effect on the action of the catalyst. Even a small amount of grease, only 0.05 g of grease per liter of steam, can prevent the catalytic reaction. To avoid the problems created by the grease, German Patent application P 40 03 833.5, not published previously, describes a protective device for the catalyst system. This protective device essentially consists of filters which are permeable to gas but have a high separation efficiency for aerosols and grease particles. The filters are so-called HEPA (High Efficiency Particulate Air) filters. These filters are made of glass wool and a binder which are highly temperature-resistant (up to about 900.degree. C.). The filters surround the catalyst system in such a way that aerosols and grease particles are kept away from the catalyst surface, while still permitting hydrogen and oxygen to reach this surface. As a result of inclusion by the filter and a correspondingly low heat loss, the temperature of the catalyst surface quickly rises because of the exothermic recombination reaction. As soon as the temperature has reached a value at which grease particles and aerosols can no longer settle on the catalyst surface, the filters open, thus exposing the catalyst system to unimpeded access by the atmosphere of the room to be protected, so that the catalyst system can then produce its total effect. The filters described in that patent application protect the catalyst system in the initial phase of an accident before aerosols and grease particles are deposited, however they cannot prevent the long-term deterioration of the catalyst as a result of catalyst poisons contained in the ambient atmosphere of the vessel, during the storage period prior to an accidental meltdown. The operating time of a reactor is up to forty years. During this long period of time, the devices for recombination of hydrogen and oxygen must maintain total functional ability in a state of readiness. It is known that palladium and platinum as catalyst materials are sensitive to surface contamination and lose their effectiveness. The alloys described in DE-A-37 25 290 are less sensitive, but no results are available on long-term tests on the effects of impurities such as chlorine, sulfur, and the like. SUMMARY OF THE INVENTION The goal of the invention is to design a device of the type described at the outset such that it does not lose its effectiveness either 1) because of a long-term state of readiness or 2) when an accident occurs, as the result of deposition of aerosols and grease particles on the catalyst surface. The solution to the stated goals provides that the catalyst system is located during the readiness state in a housing which is sealed gas-tight, preventing surface contamination of the catalyst surface. Preferably the housing is filled with an inert gas such as argon, nitrogen, hydrogen, or helium under pressure (on the order of 10.sup.5 Pa). On the basis of the design of the device according to the invention, three operating states can be distinguished, namely the readiness state before an accident occurs, a preliminary operating state following the occurrence of an accident, and the final operating state after a temperature is reached on the surface of the catalyst which guarantees effective recombination and at which a negative effect on the catalyst action produced by aerosol or grease deposits need no longer be feared. The occurrence of an accident is linked to a temperature increase to which the first seals, which open as a function of temperature, respond and expose openings in the housing, sealed gas-tight previously, so that the ambient atmosphere can penetrate the housing. The device thus shifts from its readiness state to the preliminary operating state. The response temperature of these first seals in the preferred application of the device is in the range of about 100.degree. C. The position of the catalyst system, the filter system in the housing, as well as the position and size of the openings, are selected so that sufficient hydrogen and oxygen for recombination reach the catalyst system, but an overly strong flow is not produced and grease and aerosol particles are kept away from the filter system, so that they cannot settle on the catalyst surface. The flow, which is relatively weak in this operating state, results in a rapid temperature rise in the catalyst system due to the exothermic reaction of the hydrogen, so that after a relatively short time a temperature above approximately 160.degree. C. is reached. at which a so-called self-sustaining accelerated catalytic reaction takes place. Upon this temperature rise, the response temperature of a second seal which opens as a function of temperature is reached, which then exposes another opening in the housing, thus bringing the device to its final operating state. In this final operating state, the catalyst system is fully exposed to the surrounding gas mixture from which the hydrogen is to be removed without the interposition of the filter system. The seals which open as a function of temperature are preferably soldered to the housing so that a reliable permanently gas-tight connection is produced. By choosing a solder which melts at a given temperature, preferably 100.degree. C. for the first seals and 160.degree. C. for the second seals, the seals can be welded to the housing such that at the melting point of the solder used, the seals are opened. Two embodiments of the invention will now be described in greater detail with reference to the schematic diagrams.

abstract

A crystal thin film is adopted as a specimen for measurement. A change in the contrast of crystal lattice fringes is measured under a condition that a diffracted wave and other wave are caused to interfere with each other. Thus, an information transfer limit of a transmission electron microscope can be measured quantitatively. Since the measurement is performed with a condition for interference restricted, the information transfer limit of the transmission electron microscope can be quantitatively assessed.

claims

1. A method comprising:maintaining a containment region at a below atmospheric pressure prior to a high pressure event, wherein the below atmospheric pressure is less than 300 mmHG absolute;identifying the high pressure event for a reactor vessel;releasing coolant into the containment region located between a containment vessel and the reactor vessel to remove decay heat from the reactor vessel, wherein the reactor vessel is substantially surrounded by the containment region;increasing a pressure within the containment region in response to releasing the coolant until the pressure reaches an upper pressure limit; anddecreasing the pressure through condensation until the pressure reaches a lower pressure limit, wherein the pressure is cyclically increased and decreased by alternatively releasing and prohibiting the release of coolant into the containment region. 2. The method according to claim 1, further comprising:condensing the coolant on an inner wall of the containment vessel during an over-pressurization or over-heating event. 3. The method according to claim 1, wherein the below atmospheric pressure prohibits substantially all convective heat transfer between the reactor vessel and the containment vessel prior to releasing the coolant. 4. The method according to claim 1, wherein the containment region remains substantially evacuated of all non-condensable gases both prior to and after releasing the coolant. 5. The method according to claim 1, wherein the containment region is substantially dry prior to the high pressure event. 6. The method of claim 1, wherein an outer surface of the reactor vessel is substantially surrounded by the below atmospheric pressure prior to releasing the coolant. 7. The method of claim 1, wherein the containment region remains substantially evacuated of air and hydrogen gases during normal operation of the reactor module to substantially eliminate all convective heat transfer between the reactor vessel and the containment vessel. 8. The method of claim 1, wherein a release valve mounted to the reactor vessel releases the coolant into the containment region during an emergency condition, and wherein a mixture of hydrogen and oxygen in the containment region is maintained at below combustible limits during the emergency condition without the use of a hydrogen recombiner. 9. An apparatus, comprising:means for maintaining a containment region at a below atmospheric pressure prior to a high pressure event, wherein the below atmospheric pressure is less than 300 mmHG absolute;means for identifying the high pressure event for a reactor vessel; andmeans for releasing coolant from the reactor vessel into the containment region located between a containment vessel and the reactor vessel to remove decay heat from the reactor vessel, wherein the reactor vessel is substantially surrounded by the containment region, wherein a reactor core is submerged in the coolant, and wherein the means for releasing comprises means for controllably releasing the coolant as steam into the containment region when the reactor core becomes over-heated or over-pressurized. 10. The apparatus according to claim 9, wherein a condensation of the steam on an interior wall of the containment vessel reduces pressure in the containment region at approximately the same rate that the released steam adds pressure to the containment region. 11. The apparatus according to claim 9, wherein the steam is released into the containment region to remove a decay heat of the reactor core primarily through condensation of the steam on an inner surface of the containment vessel. 12. The apparatus according to claim 9, wherein the containment region remains substantially evacuated of all non-condensable gases prior to releasing the coolant into the containment region. 13. The apparatus according to claim 9, wherein any hydrogen that is released together with the steam is released at a level that maintains an oxygen-hydrogen mixture within the containment region at a non-combustible level without using a hydrogen recombiner. 14. The apparatus according to claim 9, wherein an inner surface of the containment vessel substantially surrounds the reactor vessel, and wherein the inner surface of the containment vessel is substantially dry prior to releasing the coolant. 15. The apparatus of claim 9, wherein controllably releasing the coolant comprises increasing a pressure in the containment region, wherein the pressure in the containment region is decreased through condensation of the steam in the containment region, and wherein the pressure in the containment region is cyclically increased to an upper pressure limit and decreased to a lower pressure limit by alternatively releasing and prohibiting the release of the steam into the containment region. 16. A method, comprising:maintaining a containment region at a below atmospheric pressure prior to a high pressure event, wherein the below atmospheric pressure prohibits substantially all convective heat transfer between a reactor vessel and a containment vessel which substantially surrounds the reactor vessel;monitoring a pressure associated with the reactor vessel to identify the high pressure event; andin response to identifying the high pressure event, controllably releasing coolant as steam into the containment region located between the containment vessel and the reactor vessel, wherein a reactor core is submerged in the coolant, and wherein the coolant is controllably released as steam into the containment region when the reactor core becomes over-heated or over-pressurized. 17. The method of claim 16, wherein maintaining the containment region at a below atmospheric pressure comprises maintaining the containment region at a pressure that is less than 300 mmHG absolute. 18. The method of claim 16, wherein the steam is released from the reactor vessel into the containment region to remove a decay heat of the reactor core primarily through condensation of the steam on an inner surface of the containment vessel. 19. The method of claim 16, wherein controllably releasing the coolant comprises increasing a pressure in the containment region, wherein the pressure in the containment region is decreased through condensation of the steam in the containment vessel, and wherein the pressure in the containment region is cyclically increased to an upper pressure limit and decreased to a lower pressure limit by alternatively releasing and prohibiting the release of the steam into the containment region. 20. The method of claim 16, wherein maintaining the containment region at a below atmospheric pressure comprises evacuating substantially all non-condensable gases from the containment region prior to identifying the high pressure event. 21. An apparatus, comprising:means for maintaining a containment region at a below atmospheric pressure prior to a high pressure event, wherein the below atmospheric pressure prohibits substantially all convective heat transfer between a reactor vessel and a containment vessel which substantially surrounds the reactor vessel; andin response to identifying the high pressure event, means for controllably releasing coolant as steam into the containment region located between the containment vessel and the reactor vessel to remove decay heat from the reactor vessel, wherein the means for controllably releasing the coolant comprises means for increasing a pressure within the containment region, wherein the pressure is decreased through condensation of the steam in the containment region, and wherein the pressure in the containment region is cyclically increased to an upper pressure limit and decreased to a lower pressure limit by alternatively releasing and prohibiting the release of the steam into the containment region. 22. The apparatus of claim 21, wherein the means for maintaining comprises means for maintaining the containment region at a pressure that is less than 300 mmHG absolute. 23. The apparatus of claim 21, wherein the means for maintaining comprises means for evacuating substantially all air and hydrogen gases from the containment region prior to releasing the coolant.

053612884

claims

1. In a spacer having a matrix of individual cells, each cell for surrounding a fuel rod in a corresponding matrix of fuel rods, said spacer comprising: a plurality of spacer cells; said cells each including stop means for centering said fuel rods with respect to said cells and spring means for biasing said fuel rods into said stop means of said cells; each said spacer cell including upper and lower octagonal crowns, said octagonal crowns panel heights adjoining adjacent cells including means for adjoining like panels from adjacent panel cells in a single thickness along horizontal edges such that said like panels are in substantially vertical, co-planar alignment. said crowns at opposite ends of each octagonal spacer cell having inverted edge means; wherein respective cells surrounding a central cell are inverted with respect to said central cell whereby said crowns form a single thickness in forming upper and lower crown matrices holding adjoining cells of the spacer together. said stop means includes cell legs extending between the crowns with upper and lower stops immediately adjacent the crowns; and, said spring means includes cell legs extending between the crowns defining the required cell springs with spring contact points centrally of the legs with respect to the crowns. a full panel height adjoining the defined subchannel volume between fuel rods; and, half height walls adjoining adjacent cells. said cell legs extending between four full height sides; two adjacent legs define upper and lower stops; and two adjacent legs define springs and spring contact points. half wall heights at one crown panel are defined towards adjoining spacer cells and half wall heights at the other crown end are defined away from said spacer cell. a plurality of spacer cells; said cells each including stop means for centering said fuel rods with respect to said cells and spring means for biasing said fuel rods into said stop means of said cells; each said spacer cell including upper and lower octagonal crowns, said octagonal crown panel heights adjoining adjacent cells including edge means for adjoining like panels in single thickness from adjacent panel cells including a full panel height adjoining the defined sub-channel volume between fuel rods and vertically aligned substantially co-planar half height walls adjoining adjacent cells; and said crowns at opposite ends of each octagonal spacer cell having inverted edge means; and wherein respective cells surrounding a central cell are inverted with respect to said central cell whereby said crowns form a single thickness in forming upper and lower crown matrices holding adjoining cells of the spacer together. said stop means includes cell legs extending between the crowns with upper and lower stops immediately adjacent the crowns; and, said spring means includes cell legs extending between the crowns defining the required cell springs with spring contact points centrally of the legs with respect to the crowns. outer band means surrounding said spacer for abutting a channel at said band means; and, a defined interior aperture of said matrix of spacer cells for receiving a water rod; and, inner band means lining said interior aperture. a plurality of spacer cells; said cells each including stop means for centering said fuel rods with respect to said cells and spring means for biasing said fuel rods into said stop means of said cells; each said spacer cell including upper and lower octagonal crowns, said octagonal crowns panel heights adjoining adjacent cells including edge means for adjoining like panels in single thickness form adjacent panel cells including a full panel height adjoining the defined sub-channel volume between fuel rods and vertically aligned substantially co-planar half height walls adjoining adjacent cells; said crowns at opposite ends of each octagonal spacer cell having inverted edge means; respective cells surrounding a central cell being inverted with respect to said central cell whereby said crowns form a single thickness in forming upper and lower crown matrices holding adjoining cells of the spacer together; wherein said stop means includes cell legs extending between the crowns with upper and lower stops immediately adjacent the crowns; and further wherein said spring means includes cell legs extending between the crowns defining the required cell springs with spring contact points centrally of the legs with respect to the crowns. 2. In a spacer having a matrix of individual cells according to claim 1 and further including: 3. In a spacer having a matrix of individual cells according to claim 1 and further including: 4. In a spacer having a matrix of individual cells according to claim 1 and further including: 5. In a spacer having a matrix of individual cells according to claim 4 and further including: 6. In a spacer having a matrix of individual cells according to claim 4 and further including: 7. In a spacer having a matrix of individual cells, each cell for surrounding a fuel rod in a corresponding matrix of fuel rods, said spacer comprising: 8. In a spacer having a matrix of individual cells according to claim 7 and further including: 9. In a spacer having a matrix of individual cells according to claim 7 and further including: 10. In a spacer having a matrix of individual cells, each cell for surrounding a fuel rod in a corresponding matrix of fuel rods, said spacer comprising:

claims

1. A method for inspecting an annulus region of a reactor pressure vessel in a nuclear power plant, comprising:positioning a partial track on an annular rim of a core shroud in the reactor pressure vessel such that the track is horizontally movable along the rim;positioning a frame assembly on the partial track, the frame assembly comprising:a frame movably connected to the partial track such that the frame is horizontally movable along the partial track;connecting at least one mast assembly to the frame assembly;connecting at least one mast positioning assembly to the frame assembly;connecting at least one inspection device to the frame assembly;connecting a braking system to the partial track and the frame assembly; andmoving horizontally at least one of the partial track and the frame assembly along the rim, which comprises:activating the braking system to horizontally move the frame assembly along the partial track with the partial track being stationary; anddeactivating the braking system to horizontally move the partial track along the rim of the annular rim of the core shroud and the frame assembly being stationary; andinspecting a component in a limited access area. 2. The method of claim 1, further comprising assessing the inspection results and determining if modification or repair of the component is needed. 3. The method of claim 1, wherein the at least one mast assembly comprises a mast that is capable of becoming rigidly stable in an extended tube form and a retracted rolled form. 4. The method of claim 1, wherein the connecting at least one mast assembly to the frame assembly comprises positioning a first mast assembly on one side of the frame and a second mast assembly on an opposite side of the frame. 5. The method of claim 1, wherein the connecting at least one mast positioning device to the frame assembly comprises positioning a first mast positioning device on one side of the frame and a second mast positioning device on an opposite side of the frame. 6. The method of claim 1, wherein the connecting at least one mast positioning device to the frame assembly comprises positioning a first pan and tilt assembly on one side of the frame and a second pan and tilt assembly on an opposite side of the frame. 7. The method of claim 1, wherein moving the frame assembly along the partial track comprises connecting to the frame assembly a positioning motor and gear combination. 8. The method of claim 1, wherein the inspection device is a camera. 9. A method for inspecting a component in a nuclear power plant, comprising:positioning a partial track on an annular rim of a core shroud in the reactor pressure vessel such that the track is horizontally movable along the rim;positioning a frame assembly on the partial track, the frame assembly comprising:a frame movably connected to the partial track such that the frame is horizontally movable along the partial track;connecting at least one mast assembly to the frame assembly;connecting at least one mast positioning assembly to the frame assembly;connecting at least one inspection device to the frame assembly;connecting a braking system to the partial track and the frame assembly;moving horizontally at least one of the partial track and the frame assembly along the rim, which comprises:activating the braking system to horizontally move the frame assembly along the partial track with the partial track being stationary; anddeactivating the braking system to horizontally move the partial track along the rim of the annular rim of the core shroud and the frame assembly being stationary; andinspecting a component in a limited access area selected from a core annulus, core spray region and feedwater sparger region. 10. The method of claim 9, further comprising lowering the inspection device into an annulus formed between the reactor pressure vessel and the core shroud; and inspecting the core shroud.

description

One or more embodiments of the present invention relate to thermal interface materials made from graphite sheets under high vacuum condition having no risk of outgassing under ultrahigh vacuum. The boron neutron capture therapy (BNCT) in which neutrons are used has been attracting attention (Non-Patent Document 1), since it can remove a tumor at a deep part for which there is no cure by a routine surgical operation with regard to encephaloma, hepar, melanoma and the like. Examples of a method for generating neutrons used in this therapy include a method using a nuclear reactor and a method using an accelerator. As a simple and safe neutron-generating method, at present, a method using an accelerator has been attracting attention. In the apparatus, neutrons are generated by a method in which protons are gradually accelerated to be made into a proton beam and thereafter a neutron is made by a method in which the proton beam impinge on a metal-made or graphite-made lump called a target (Non-Patent Document 2). Moreover, such an accelerator-type neutron generator is expected to be utilized as an apparatus for nondestructively inspecting the soundness of steel frames in a bridge, and is expected to be utilized in the automobile industry, aircraft industry and space industry (Non-Patent Document 3). In order to generate neutrons with such an accelerator, it is necessary to make the beam have a high intensity. When this high-intensity beam passes through a target, the target results in high temperature and the target is tend to deform by heat. A heat sink for cooling is assembled behind the target and a cooling water circulates in the heat sink for cooling to protect the target from heat generated by the beam. However, a limited portion of the target is periodically intensely heated by the beam, and it follows that the heating is repeated for a long time. As such, there is a fear that not only a target but also a heat sink for cooling are broken by a heat shock. As a metal usually used for the heat sink is radioactivated and obstructs beam, only specific ones can be used. For example, titanium (22 W/mK), vanadium (31 W/mK), palladium (72 W/mK), niobium (54 W/mK), tantalum (58 W/mK) and the like are usable, but these are low in thermal conductivity. As such the heat from a target does not conduct to the whole heat sink and the cooling efficiency is poor. In reducing the thermal resistance, an thermal interface material (TIM: Thermal Interface Material) plays an important role. However, since the interior of an accelerator is kept in an ultra-high vacuum state (10−6 to 10−7 Pa), in the case where heat release grease or a phase change sheet, which is generally used, is adopted, contamination of the interior of the apparatus is caused by outgassing. Moreover, when a TIM containing a metal and inorganic filler is adopted, there is a fear that filler scatters and contaminates the inside of a beam line. Patent document 1: JP-B-4299261 Patent document 2: JP-B-4684354 Non-Patent Document 1: Association for Nuclear Technology in Medicine “Karada Ni Yasashii Kyuukyoku No Gantiryou (Ultimate Cancer Therapy Gentle To The Body) Boron Neutron Capture Therapy”, May, 2011 Non-patent Document 2: YAMAGATA, Y. et al, The 27th World Conference of the International Nuclear Target Development Society State-of-the-art Technologies for Nuclear Target and Charge Stripper Japan, Tokyo, September, 2014 Non-Patent Document 3: Yutaka Yamagata, “RIKEN Accelerator-driven compact Neutron Source RANS” Non-patent Document 4: Y. Hishiyama, A. Yoshida, Y. Kaburagi, Carbon 254, 176(2012) Non-patent Document 5: P. G. Klemens and D. F. Pedraza, Carbon 32 735(1994) Non-patent Document 6: P. G. Klemens, J. W. Bandgap, Materials, 7(4), 332(2000) One or more embodiments of the present invention have been made in view of the above-mentioned circumstances, and one or more embodiments provide a material which is excellent in a characteristic of thermal conductivity as an thermal interface material and has no risk of outgassing or contaminating the interior of an apparatus even under high-vacuum and high-temperature conditions. As a result of diligent researches, the present inventors have found that a graphite sheet eliminates the risk of outgassing even under ultrahigh vacuum and is a promising material as an thermal interface material (TIM). Moreover, the present inventors have found that, even in the case where a graphite sheet is used in an accelerator-type neutron generator, there is no fear of radioactivation or a beam obstruction, and moreover, the graphite sheet can withstand irradiation conditions in which a high-intensity beam is used at a high temperature for a long period of time and is promising especially in such applications. Incidentally, as a kind of graphite sheet, natural graphite has been known (Patent Document 1), and the use of such a material as the TIM is also conceivable. However, the thermal conductivity in the surface direction of a natural graphite sheet is 200 to 500 W/mK or so, and the natural graphite sheet is characterized as being light in weight but weak in sheet strength because powdery or scale-like natural graphite is used as the raw material, and in the case of being broken, there has been a risk that graphite flakes are scattered inside a housing body. A method of directly thermally treating a special polymer film to be graphitized has been developed (hereinafter, described as a polymer-annealing method). The graphite sheet preparation by this method is simple as compared with a preparation method of a conventional natural graphite sheet, and also, the resulting sheet is characterized as being excellent in mechanical properties, and furthermore, characterized in that extremely excellent thermal conductivity is attained (Patent Document 2). Since a graphite sheet prepared by the polymer-annealing method has a high thermal conductivity in the surface direction of 600 to 1600 W/mK, and furthermore, is resistant to bending, impacts or the like, at present, the sheet has been adopted in many mobile terminals. However, as described above, a graphite sheet exhibiting higher thermal conductivity than that of conventional ones under an ultrahigh-vacuum condition has been desired, and especially, a thermal interface material made from graphite sheet under high vacuum condition capable of withstanding irradiation with a high-intensity proton beam under ultrahigh-vacuum and high-temperature conditions has been eagerly desired. On that account, as a result of further studies, by using an aromatic polymer (especially, an aromatic polyimide) as a polymer, making the thickness of the finally resultant graphite sheet lie within the range of 9.6 μm to 50 nm, making the density of the graphite sheet become not less than 1.8 g/cm3 and performing the graphitization at an ultrahigh temperature of not less than 2900° C., a thermal interface material made from graphite sheet under high vacuum condition with a thermal conductivity of not less than 1000 W/mK is prepared. This sheet is a high thermal conducting material at the highest level as a film with a large area which can be easily practically handled, has no risk of outgassing even under ultrahigh vacuum and high temperature, and is greatly high in chemical stability and heat resistance. Accordingly, it is thought that the range of application thereof is extremely wide. A thermal interface material made from graphite sheet under high vacuum condition is characterized in having a thickness of not more than 9.6 μm and not less than 50 nm and a thermal conductivity in the a-b surface direction at 25° C. of not less than 1000 W/mK. It is preferred that a density be not less than 1.8 g/cm3. The graphite sheet of one or more embodiments of the present invention is preferably obtained by thermally treating a polymer film at a temperature of not less than 2900° C. The polymer film is preferably at least one kind selected from among polyamides, polyimides, polyquinoxalines, polyoxadiazoles, polybenzimidazoles, polybenzoxazoles, polybenzthiazoles, polyquinazolinediones, polybenzoxazinones, polyquinazolones, benzimidazobenzophenanthroline ladder polymers and derivatives thereof. The polymer film is preferably an aromatic polyimide. The aromatic polyimide is preferably a polyimide obtained by using either or both of pyromellitic acid anhydride and 3,3′,4,4′-biphenyltetracarboxylic acid dianhydride as the raw material, or by using either or both of 4,4′-diaminodiphenyl ether and p-phenylenediamine as the raw material. One or more embodiments of the present invention also include a graphite substrate material under high vacuum condition and a target substrate material under high vacuum condition, which are prepared from any one of the above-mentioned thermal interface material made from graphite sheet under high vacuum condition. One or more embodiments of the present invention also include a layered type target material for generating neutrons, comprising a neutron-producing metal member and a proton-absorbing metal substrate which are layered, wherein any one of the above-mentioned thermal interface material made from graphite sheet under high vacuum condition is interposed between the neutron-producing metal member and the proton-absorbing metal substrate. Further, one or more embodiments of the present invention include a target module for generating neutrons, comprising a neutron-producing metal member, a proton-absorbing metal substrate and a heat sink member which are layered in this order, wherein any one of the above-mentioned thermal interface material made from graphite sheet under high vacuum condition is interposed between the neutron-producing metal member and the proton-absorbing metal substrate, and any one of the above-mentioned thermal interface material made from graphite sheet under high vacuum condition is interposed between the proton-absorbing metal substrate and the heat sink member. In the target module, it is preferred that the neutron-producing metal member be a beryllium target, the proton-absorbing metal substrate be formed of at least one kind of material selected from among vanadium, niobium and tantalum, and the heat sink member be formed of at least one kind of material selected from among aluminum and titanium. According to the graphite sheet according to one or more embodiments of the present invention, there is no fear of outgassing even under high vacuum and excellent heat release properties are attained because the sheet has an extremely high thermal conductivity in the a-b surface direction at 25° C. of not less than 1000 W/mK. Moreover, even in the case of being used in an accelerator-type neutron generator, there is no fear of radioactivation or a beam obstruction, and furthermore, the sheet can withstand irradiation conditions in which a high-intensity beam is used at a high temperature for a long period of time. Hereinafter, the details of one or more embodiments of the present invention will be described, but the present invention should not be limited to the details given below. <Graphite Sheet> One or more embodiments of the present invention are characterized firstly in the point that used is a graphite sheet with a higher thermal conductivity (not less than 1000 W/mK, preferably not less than 1800 W/mK) compared with the natural graphite sheet with a thermal conductivity of 200 to 500 W/mK or so or the graphite sheet prepared by a conventional polymer annealing method with a thermal conductivity of 600 to 1600 W/mK or so. Such a graphite sheet with a high thermal conductivity is produced by a method in which a polymer film obtained from an aromatic polymer (especially, an aromatic polyimide) is heated to be carbonized and graphitized, and especially, can be produced by making the thickness of the finally resultant graphite sheet lie within the range of 9.6 μm to 50 nm, making the density of the graphite sheet become not less than 1.8 g/cm3 and performing the graphitization at an ultrahigh temperature of not less than 2900° C. <Polymer Raw Material> First, a polymer film raw material used in the production of the graphite sheet according to one or more embodiments of the present invention will be described. The polymer raw material preferably used in the graphite preparation is an aromatic polymer, and the aromatic polymer is preferably at least one kind selected from among polyamides, polyimides, polyquinoxalines, polyoxadiazoles, polybenzimidazoles, polybenzoxazoles, polybenzthiazoles, polyquinazolinediones, polybenzoxazinones, polyquinazolones, benzimidazobenzophenanthroline ladder polymers and derivatives thereof. A film composed of these polymer raw materials may be produced by a known production method. Especially preferred examples of the polymer raw material can include an aromatic polyimide, polyparaphenylene vinylene, and polyparaphenylene oxadiazole. Of these, an aromatic polyimide prepared through a polyamic acid from an acid dianhydride (especially an aromatic acid dianhydride) and a diamine (especially an aromatic diamine) which are described below is especially preferred as the polymer raw material for the graphite preparation. Examples of the acid dianhydride that can be used for the synthesis of the aromatic polyimide include pyromellitic acid anhydride, 2,3,6,7-naphthalenetetracarboxylic acid dianhydride, 3,3′,4,4′-biphenyltetracarboxylic acid dianhydride, 1,2,5,6-naphthalenetetracarboxylic acid dianhydride, 2,2′,3,3′-biphenyltetracarboxylic acid dianhydride, 3,3′,4,4′-benzophenonetetracarboxylic acid dianhydride, 2,2-bis(3,4-dicarboxyphenyl)propane dianhydride, 3,4,9,10-perylenetetracarboxylic acid dianhydride, bis(3,4-dicarboxyphenyl)propane dianhydride, 1,1-bis(2,3-dicarboxyphenyl)ethane dianhydride, 1,1-bis(3,4-dicarboxyphenyl)ethane dianhydride, bis(2,3-dicarboxyphenyl)methane dianhydride, bis(3,4-dicarboxyphenyl)ethane dianhydride, oxydiphthalic acid dianhydride, bis(3,4-dicarboxyphenyl)sulfone dianhydride, p-phenylenebis(trimellitic acid monoester acid anhydride), ethylenebis(trimellitic acid monoester acid anhydride), bisphenol A bis(trimellitic acid monoester acid anhydride), and analogues thereof, and those can be used alone or in combination of two or more kinds thereof as an arbitrary ratio mixture. In particular, from the viewpoints of a tendency for the orientation property of a polyimide film to be heightened as the film is made to have a more rigid polymer structure and the availability, pyromellitic acid anhydride and 3,3′,4,4′-biphenyltetracarboxylic acid dianhydride are especially preferred. Examples of the diamine that can be used for the synthesis of the aromatic polyimide include 4,4′-diaminodiphenyl ether, p-phenylenediamine, 4,4′-diaminodiphenyl propane, 4,4′-diaminodiphenyl methane, benzidine, 3,3′-dichlorobenzidine, 4,4′-diaminodiphenyl sulfide, 3,3′-diaminodiphenyl sulfone, 4,4′-diaminodiphenyl sulfone, 4,4′-diaminodiphenyl ether, 3,3′-diaminodiphenyl ether, 3,4′-diaminodiphenyl ether, 1,5-diaminonaphthalene, 4,4′-diaminodiphenyl diethylsilane, 4,4′-diaminodiphenyl silane, 4,4′-diaminodiphenyl ethylphosphine oxide, 4,4′-diaminodiphenyl N-methylamine, 4,4′-diaminodiphenyl N-phenylamine, 1,4-diaminobenzene(p-phenylenediamine), 1,3-diaminobenzene, 1,2-diaminobenzene, and analogues thereof, and those can be used alone or in combination of two or more kinds thereof as an arbitrary ratio mixture. Furthermore, from the viewpoints of heightening the orientation property of a polyimide film and the availability, it is especially preferred that 4,4′-diaminodiphenyl ether or p-phenylenediamine be used as the raw material to synthesize the aromatic polyimide. For the preparation of a polyamic acid from an acid dianhydride and a diamine, any known method can be used, and usually, at least one kind of aromatic acid dianhydride and at least one kind of diamine are dissolved in an organic solvent, and the obtained organic solvent solution of a polyamic acid is stirred under a temperature-controlled condition until the polymerization of the acid dianhydride and the diamine is completed to produce the polyamic acid. The solution of the polyamic acid is usually obtained with a concentration of 5 to 35 wt %, preferably 10 to 30 wt %. In the case where the concentration lies within this range, suitable molecular weight and solution viscosity can be attained. It is preferred that substantially equimolar amounts of an acid dianhydride and a diamine be dissolved in the raw material solution, and for example, the mole ratio is 1.5:1 to 1:1.5, preferably 1.2:1 to 1:1.2 and more preferably 1.1:1 to 1:1.1. <Synthesis of Polyimide, Film Formation> As a production method of a polyimide, a heat-curing method in which a polyamic acid as a precursor is imide-converted by heating and a chemically curing method in which a polyamic acid is imide-converted using a dehydrating agent typified by an acid anhydride such as acetic anhydride and a kind of tertiary amine as an imidation accelerator such as picoline, quinoline, isoquinoline and pyridine can be exemplified, and either thereof may be used. The chemically curing method is preferred, in the point that the coefficient of linear thermal expansion of the resulting film is likely to be small, the elastic modulus thereof is likely to be high, the birefringence thereof is likely to be large, the film is not broken even when tension is applied thereto during annealing, and moreover, graphite of good quality can be obtained. Moreover, the chemically curing method is also excellent in an aspect of the enhancement in thermal conductivity of a graphite film. With regard to the high thermal conducting graphite sheet (with a thermal conductivity of not less than 1000 W/mK) used in one or more embodiments of the present invention, the thickness thereof lies within the range of 9.6 μm to 50 nm, and in order to obtain the graphite sheet with a thickness lying within such a range, it is preferred that the thickness of the raw material polymer film lie within the range of 18 μm to 120 nm. This is because there are many cases in which the thickness of the finally resultant graphite sheet generally becomes 60 to 30% or so of the thickness of a starting polymer film with a thickness of not less than 1 μm and becomes 50 to 20% or so of the thickness of a starting polymer film with a thickness of not more than 1 μm. Thus, finally, in order to obtain a graphite sheet with a thickness of 9.6 μm to 50 nm, it follows that the thickness of a starting polymer film preferably lies within the range of not more than 30 μm and not less than 100 nm. On the other hand, with regard to the length direction, there are many cases in which the dimension is reduced to 100 to 70% or so of the dimension of a starting polymer film. The polymer film can be produced from the polymer raw material or the synthetic raw material thereof by any of the known various methods. For example, an organic solvent solution of a polyamic acid as the polyimide precursor is cast on a support such as an endless belt and a stainless steel drum and dried and imidized to produce the polyimide film. Specifically, the method for producing a film by a chemically curing method is as follows. First, to the polyamic acid solution, a stoichiometric amount or more of a dehydrating agent and a catalytic amount of an imidation accelerator are added, the solution is cast or applied on a support plate or a support such as an organic film including PET, a drum or an endless belt to be formed into a film shape, and the organic solvent is made to evaporate to obtain a film having a self-supportability. Then, this film is imidized while further being heated and dried to obtain a polyimide film. It is preferred that the temperature at the time of heating lie within the range of 150° C. to 550° C. Furthermore, it is preferred that a process of fixing or stretching the film to prevent the shrinkage be included in the production process of the polyimide. This is because the conversion to graphite proceeds more easily by using a film in which the molecular structure and the higher order structure thereof are controlled. That is, for making the graphitization reaction proceed smoothly, it is necessary for carbon molecules in the carbon precursor to be rearrayed, and it is presumed that the conversion to graphite easily proceeds even at a low temperature since the number of carbon molecules to be rearrayed can be minimized in a polyimide having an excellent orientation property. <Carbonization and Graphitization> Next, a method for carbonization and graphitization of a polymer film typified by a polyimide will be described. In one or more embodiments of the present invention, a polymer film as a starting material is preheated in an inert gas to be carbonized. As the inert gas, nitrogen, argon or a mixed gas of argon and nitrogen is preferably used. The preheating is usually performed at 100° C. or so. The temperature increasing rate to the preheating temperature is not particularly limited, and for example, the rate can to 5 to 15° C./minute. At a stage of the preliminary treatment, effective is applying a pressure in the surface direction to the degree, which doesn't cause breakage of a film, so as not to make the film lose the orientation property of the starting polymer film. A film carbonized by the above-mentioned method is fitted to the inside of a high-temperature furnace to perform graphitization. It is preferred that a carbonized film be fitted in a state of being sandwiched between CIP materials or glassy carbon substrates. Graphitization is usually performed at a high temperature of not less than 2600° C., and in order to create such a high-temperature atmosphere, a current is usually allowed to flow directly through a graphite heater and the Joule heat is utilized to perform heating. Graphitization is performed in an inert gas, and as the inert gas, argon is the most suitable and the argon may be added with a small amount of helium. The higher the treatment temperature is, the better quality the graphite after being converted can have. There are many cases in which, by pyrolysis and carbonization, the area of the carbonized film is contracted by about 10 to 40% or so compared with its original polyimide film, and conversely, the area thereof is expanded by about 10% or so in the process of graphitization. Due to such contraction or expansion, an internal stress is generated in a graphite sheet to generate a strain inside the graphite sheet. Such a strain and an internal stress are relaxed by being treated at a temperature of not less than 2900° C., layers of graphite are arrayed with regularity, and furthermore, the thermal conductivity is heightened. In order to obtain the graphite according to one or more embodiments of the present invention, the temperature of 2600° C. is still insufficient, the treatment temperature is preferably not less than 2900° C., treatment at a temperature of not less than 3000° C. is more preferable, and treatment at not less than 3100° C. is most preferable. Of course, this treatment temperature may be the highest treatment temperature in the graphitization process, and the resultant graphite sheet may be subjected to a reheating treatment (may be thermally treated again) so as to be annealed. In this connection, for example, even when the treatment temperature is set to a temperature of not more than 3700° C. (especially not more than 3600° C., or not more than 3500° C.), an excellent graphite film is obtained. For example, the temperature increasing rate from the preheating temperature to the heat treatment temperature can be 15 to 25° C./minute. For example, the retention time at the treatment temperature is not less than 20 minutes and preferably not less than 30 minutes, and may be not less than 1 hour. Although the upper limit of the retention time is not particularly limited, the upper limit is usually not more than 5 hours, and especially, may be not more than 3 hours or so. In the case of being thermally treated at a temperature of not less than 3000° C. to be graphitized, it is preferred that the inner atmosphere of a high-temperature furnace be pressurized by the inert gas. When the heat treatment temperature is high, carbon begins to sublime from the sheet surface, and deterioration phenomena such as expansion of a hole or a crack on the graphite sheet surface and film thinning are caused, but such deterioration phenomena can be prevented by pressurizing and an excellent graphite sheet can be obtained. For example, the atmospheric pressure (gauge pressure) of a high-temperature furnace by an inert gas is not less than 0.10 MPa, preferably not less than 0.12 MPa and further preferably not less than 0.14 MPa. Although the upper limit of the atmospheric pressure is not particularly limited, for example, the upper limit is not more than 2 MPa, and especially, may be not more than 1.8 MPa or so. After the heat treatment, for example, the temperature needs only to be dropped at a rate of 30 to 50° C./minute. <Features of Graphite Sheet> From the viewpoint that the thinner the thickness of the graphite sheet used in one or more embodiments of the present invention is, the more the graphite sheet is excellent in high thermal conductivity, the thickness thereof is preferably not more than 9.6 μm. The reason is presumed to be as follows. That is, in the graphite sheet production by a polymer-annealing method, it is considered that, at the time of the graphitization reaction, the graphite structure is formed on the outermost surface layer of the polymeric carbonized sheet and grows toward the inside of the film. When the film thickness of the graphite sheet becomes thick, the graphite structure of the inside of the carbonized sheet is disturbed at the time of graphitization and a cavity or a deficit portion is easily formed. Conversely, when the sheet becomes thin, graphitization of the graphite layer structure in a well-ordered state proceeds from the sheet surface to the inside thereof, and as a result, a well-ordered graphite structure is easily formed in the whole sheet. It is considered that a graphite sheet exhibiting high thermal conductivity is formed because the graphite layer structure is well-ordered as described above. On the other hand, in the preparation method of one or more embodiments of the present invention, when the thickness of a graphite sheet is not more than 50 nm, it is difficult to exhibit high thermal conductivity. The reason for this has not been necessarily elucidated yet, and when the thickness of a graphite sheet prepared by the method disclosed herein is not more than 50 nm, the sheet is made rich in flexibility but made poor in elasticity. Since it has been known that most of the thermal conduction of a graphite sheet is caused by a lattice vibration (phonon), it is presumed that this is because the reduction in elasticity of a film inhibits the expression of high thermal conductivity. It is difficult to prepare a graphite sheet which has a thickness of not more than 50 nm and is rich in elasticity. As described above, the thickness of the graphite sheet ranges from 9.6 μm to 50 nm, and is preferably 7.5 μm to 50 nm, more preferably 6.5 μm to 100 nm, further preferably 5.0 μm to 100 nm and most preferably 3.0 μm to 200 nm. A sheet thinned in thickness sticks to the substrate surface along the irregularity of the substrate, and once the sheet has stuck thereto, the sheet cannot be removed without using a tape or the like. When the thickness of a graphite sheet is more than 9.6 μm, the sheet is not preferred because there are cases where the graphite structure of the inside of the carbonized sheet is disturbed at the time of graphitization and a cavity or a deficit portion is easily formed. Moreover, when the thickness of a graphite sheet is less than 50 nm, the sheet is made rich in flexibility but made poor in elasticity, and is not preferred because there are cases where the expression of high thermal conductivity is inhibited. It is preferred that the density of the graphite sheet not be less than 1.8 g/cm3. In general, a high thermal conducting graphite sheet has a very dense structure in which a deficit portion or a cavity does not exist. When a deficit portion or a cavity exists in a graphite sheet, the density is decreased and there is also a tendency for thermal conductivity to be lowered. From this, it is preferred that the graphite be large in density, and the density is not less than 1.8 g/cm3, more preferably not less than 2.0 g/cm3 and most preferably not less than 2.1 g/cm3. The upper limit of the density is not more than 2.26 g/cm3, and may be not more than 2.20 g/cm3. As compared with highly oriented pyrolytic graphite (HOPG) prepared by further treating pyrolytic graphite (thermal decomposition graphite), which is obtained by supplying an organic gas such as methane onto a heated substrate and making the resultant grow out in a vapor phase therefrom, at a high temperature, a graphite sheet obtained by carbonizing and graphitizing such a polymer film used in one or more embodiments of the present invention also has a feature that no trace of the pyrolytic graphite exists. The pyrolytic graphite has a columnar structure, and even if this is subjected to a high-temperature treatment to prepare HOPG, this columnar grain boundary structure does not disappear completely. The average crystal grain diameter (domain size) of the graphite used in one or more embodiments of the present invention may be not more than 10 μm, may be not more than 7 μm and may be not more than 5 μm. Although it is advantageous for the achievement of high thermal conductivity to make the crystal grain diameter large, the graphite sheet used exhibits excellent thermal conductivity even when the average crystal grain diameter is not more than 10 μm. It is presumed that this is because the graphite sheet used is a high-quality graphite having no columnar grain boundary structure as described above. In the first place, the reason why the thermal conductivity is affected by the crystal grain diameter is because phonons, which contribute to thermal conductivity, are scattered at the crystal grain boundary. However, in the high-quality graphite, scatter of phonons becomes less dependent on a crystal grain diameter of small size. It is interpreted that this is because only a kind of scatter called the umklapp process becomes dominant in the high-quality graphite (Non-Patent Document 4). In this connection, for example, the average crystal grain diameter of a graphite sheet used is not less than 2 μm, preferably not less than 3 μm and more preferably not less than 4 μm. Moreover, for example, the average crystal grain diameter (domain size) is not less than 0.1 times the thickness of the graphite sheet, preferably not less than 1 time the thickness thereof and further preferably not less than 2 times the thickness thereof. Although the graphite sheet used in one or more embodiments of the present invention has a thermal conductivity in the a-b surface direction at a temperature of 25° C. of not less than 1000 W/mK, the thermal conductivity is preferably not less than 1800 W/mK, more preferably not less than 1960 W/mK, further preferably not less than 2000 W/mK, especially preferably not less than 2050 W/mK and most preferably not less than 2100 W/mK. There has been reported a theoretical limit value of the thermal conductivity in the graphite a-b surface direction of 1910 W/mK (Non-Patent Documents 5 and 6), and the thermal conductivity of not less than 1960 W/mK largely exceeds this limit value and is a result which had not been expected before. In this connection, for example, the thermal conductivity may be not more than 2400 W/mK and may be not more than 2300 W/mK. <Graphite Substrate Material Under High Vacuum Condition> The graphite sheet is recommended to be used for a thermal interface material (TIM) under high vacuum (not more than 10−4 Pa, for example, 10−6 to 10−7 Pa or so or not more than 10−7 Pa), and the graphite sheet itself can be used as a graphite substrate, and furthermore, can be used as a substrate prepared by being layered together with another base material. The graphite sheet does not contain impurities other than blacklead and is of high quality because the graphite sheet has already been subjected to graphitization at a temperature of not less than 2900° C. As such, even under high vacuum, and furthermore, even if being locally heated, outgassed components are not generated. In this connection, the graphite sheet is chemically stable, and as necessary, the graphite sheet may be used for applications other than the application under a high vacuum atmosphere. Examples of the atmosphere other than the high vacuum atmosphere include nitrogen, argon, neon, helium, hydrogen and the like. <Target Substrate Material Under High Vacuum Condition> Moreover, examples of the new application of the graphite sheet according to one or more embodiments of the present invention other than the TIM include a target substrate material under high vacuum condition which can be used under a high vacuum and highly reactive atmosphere by taking advantage of the property of being of high purity and being chemically stable. The target substrate material under high vacuum condition means a material prepared by bonding a target and a heat sink together using a graphite sheet by means of heat, pressurization, a laser or the like or a layered material prepared by mounting a target on a graphite sheet by a vapor deposition method, a sputtering method or an electrodeposition method, and the target can be irradiated with various kinds of beams to take out a reaction product between the target and the beam. The graphite sheet can be suitably used for such an application under a high vacuum and highly reactive atmosphere. As the beam, protons, neutrons, ions (heavy atoms, light atoms) and the like can be used. The graphite sheet does not affect the reaction product between any of these beams and the target, and contributes to the heat dissipation from the target. The source material for the target and the peripheral material thereof (heat sink material, casing material and the like) is not particularly limited, examples thereof include lithium, beryllium, boron, carbon, calcium, gold, silver, copper, aluminum, titanium, palladium, vanadium, tantalum, niobium, stainless steel, brass, molybdenum, and technetium, and moreover, examples thereof may include a doped product prepared with one kind thereof and a doped product prepared with combined two or more kinds thereof. Furthermore, an airtight container which is made of one kind of the element or combined two or more kinds thereof and allows the inside thereof to be filled with a gas such as hydrogen, helium, argon and nitrogen may be adopted. <Target Module for Generating Neutrons> The graphite sheet can also be used as a material for a target supporting substrate, an accelerator, an apparatus for generating neutrons, a sensor for a nuclear reactor, a beam sensor or the like, in addition to the graphite substrate material and target substrate material described above. Hereinbelow, as an example of such application technologies, an accelerator-type neutron generator will be given as an example to be explained. FIG. 1 is a schematic perspective view showing an example of the target module for generating neutrons constituting the center of a neutron generator. The target module 70 for generating neutrons is provided with a substrate 1 for fixing a target, and a layered type target material 60 for generating neutrons composed of a neutron-producing metal member (target) 10 and a proton-absorbing metal substrate 30 which is layered at the back side of this neutron-producing metal member 10 and has an outer circumference being a size larger than that of the neutron-producing metal member 10. The substrate 1 and the layered type target material 60 are objects to be irradiated with a beam, and at the back side of this layered type target material 60, a heat sink member 40 for cooling the layered type target material 60 is connected. And then, to the rear side of this heat sink member 10, a moderator 50 for making protons decelerate is fixed. The neutron generator is provided with an accelerator (not illustrated) for generating accelerated protons and a neutron flight unit (not illustrated), in addition to such a target module 70 for generating neutrons, and protons from the accelerator are made to collide with the neutron-producing metal member 10 under high vacuum (not more than 10−4 Pa) to produce neutrons. And then, the protons produced are made to pass through the proton-absorbing metal substrate 30, the heat sink member 40 and the moderator 50, which exist at the back side of the neutron-producing metal member 10, and made to reach the neutron flight unit (not illustrated) to be used for various kinds of applications such as the boron neutron capture therapy and the nondestructive inspection. In such a target module 70 for generating neutrons, the layered type target material 60 for generating neutrons becomes high in temperature by the reaction with high-energy protons. In order to cool the layered type target material 60, the heat sink member 40 is attached thereto, and the heat sink member as the illustrated example is a water-cooled one. Specifically, the heat sink member 40 as the illustrated example is provided with a chamber (jacket) 42 into which cooling water is introduced and two water flow pipes 41 for supplying/draining water to/from this jacket 42, and water in the jacket 42 can be brought into contact with the layered type target material 60 to cool the layered type target material 60. However, in the target module 70, a limited portion of the neutron-producing metal member 10 is periodically intensely heated (subjected to ultraheating) by the proton beam, and it follows that the heating is repeated for a long period of time. As such, just by simply being cooled with water, there is a fear that both of the layered type target material 60 and the heat sink member 40 are broken by a heat shock. On that account, in the module according to one or more embodiments of the present invention, a graphite sheet is used as a thermal interface material (TIM). In the illustrated example, the graphite sheet-made thermal interface materials 20 and 25 are interposed between the neutron-producing metal member (target) 10 and the proton-absorbing metal substrate 30 and between the proton-absorbing metal substrate 30 and the heat sink member 40, respectively. At least one (preferably both) of such graphite-made thermal interface materials 20 and 25 can be incorporated into the target module 70 to heighten the heat-release properties of the layered type target material 60, and the breakage thereof can be prevented. Moreover, since such a graphite-made TIM is a highly heat-resistant material, the material itself is not broken under a high temperature condition. In this connection, in the illustrated example, the graphite-made thermal interface material 20 between the neutron-producing metal member (target) 10 and the proton-absorbing metal substrate 30 has a circular shape equal to that of the neutron-producing metal member 10, and the graphite-made thermal interface material 25 between the proton-absorbing metal substrate 30 and the heat sink member 40 has a hollow disk-type (doughnut-type) shape, but the planar shape of the thermal interface material is not particularly limited as long as respective members between which the thermal interface material is interposed can be thermally bonded together and the thermal interface material may exist so as to overlap with the locus of a proton beam or a neutron beam. The graphite sheet is chemically stable, and even if the graphite sheet overlaps with the locus of a proton beam or a neutron beam, the graphite sheet does not adversely affect these beams, and moreover, the graphite sheet is not radioactivated. In the target module 70, as the source material for the neutron-producing metal member 10, beryllium can be adopted. As the source material for the proton-absorbing metal substrate 30, one kind or two or more kinds of metal such as vanadium, niobium and tantalum can be adopted. As the source material for the heat sink member 40, one kind or two or more kinds of metal such as aluminum and titanium can be adopted. The present application claims the profit of the right of priority to Japanese Patent application No. 2014-246129 filed on Dec. 4, 2014. The entire contents of the specification of the Japanese Patent application No. 2014-246129 filed on Dec. 4, 2014, are incorporated by reference herein. Hereinafter, the embodiment according to one or more embodiments of the present invention will be described in more detail with reference to examples. Of course, the present invention should not be limited to these examples, not to mention that various embodiments are possible with regard to the small details. (Evaluation Methods for Physical Properties) <Film Thickness> Each of the thicknesses of a polymer film as the raw material and a graphite sheet has an error of plus/minus 5 to 10% or so. As such, the ten-point average thickness of the film or sheet obtained was defined as the thickness of the sample in one or more embodiments of the present invention. <Density> With regard to the density of the graphite prepared, a graphite sheet was measured for the volume by means of a helium gas replacement type density meter [AccuPyc II 1340 SHIMADZU CORPORATION] and separately measured for the mass to calculate the density from the equation of Density (g/cm3)=Mass (g)/Volume (cm3). In this connection, the density of a graphite sheet with a thickness of not more than 200 nm failed to be measured by this method because the magnitude of the error was too large. As such, in the case of calculating the thermal conductivity from the thermal diffusivity of a graphite sheet with a thickness of not more than 200 nm, the density thereof was assumed to be 2.1 to calculate the thermal conductivity thereof. <Thermal Conductivity> A graphite sheet was measured for the thermal diffusivity using a thermal diffusivity measuring apparatus (ADVANCE RIKO, Inc., the “LaserPit” apparatus) by a periodic heating method at a frequency of 10 Hz under vacuum (10−2 Pa or so) at 25° C. This was a method of attaching a thermocouple to a point apart by a certain distance from an irradiation point irradiated with a laser beam to be heated and measuring a change in temperature at the point. By this method, the thermal conductivity (W/mK) was calculated by multiplying the thermal diffusivity (m2/s) by the density (kg/m3) by the specific heat (798 kJ/(kg·K)). In this context, in the case of using this apparatus, a graphite sheet with a thickness of not less than 1 μm can be measured for the thermal diffusivity, but the thermal diffusivity of a graphite sheet with a thickness of not more than 1 μm failed to be accurately measured because the magnitude of the measurement error became too large. On that account, using a periodic heating radiant temperature measuring method (the Thermoanalyzer TA3 available from BETHEL Co., Ltd.) as the second measuring method, the measurement was performed. This was an apparatus in which periodic heating is performed by a laser and temperature measurement is performed by a radiation thermometer, and even a sample of a graphite sheet with a thickness of not more than 1 μm can be measured since the radiation thermometer and a graphite sheet are in a completely non-contact state at the time of measurement. In order to confirm the reliability of measured values of the two apparatuses, with regard to some samples, the sample was measured by the respective two apparatuses and it was confirmed that the two numerical values coincide with each other. In the apparatus of BETHEL Co., Ltd., the frequency of periodic heating can be made to vary within a range of at most 800 Hz. That is, this apparatus is characterized in the point that temperature measurement, which is usually performed in a contact manner by a thermocouple, is performed by a radiation thermometer and the measurement frequency can be made to vary. In principle, a constant thermal diffusivity as a measured value should be attained even when the frequency is made to vary, and thus, in the measurement using this apparatus, the frequency was made to vary and the measurement of a thermal diffusivity was performed. In the case where a sample with a thickness of not more than 1 μm was measured, there were many cases in which the measured value fluctuates when measured at a frequency of 10 Hz or 20 Hz, but the measured value became almost constant when measured at each of frequencies ranging from 70 Hz to 800 Hz. On that account, a measured value (a numerical value measured at frequency ranging from 70 Hz to 800 Hz) obtained as a constant value irrespective of the frequency was defined as the thermal diffusivity. A hardener comprising 20 g of acetic anhydride and 10 g of isoquinoline was mixed to 100 g of an 18 wt % DMF solution of a polyamic acid synthesized from pyromellitic acid anhydride and 4,4′-diaminodiphenyl ether in a proportion of 1/1 in terms of the mole ratio to be stirred, and after being centrifuged to be degassed, the liquid was cast and applied on a sheet of aluminum foil. The liquid was stirred and then centrifuged to be degassed while being cooled to 0° C. The layered product of the sheet of aluminum foil and the polyamic acid solution was heated at 120° C. for 150 seconds and at 300° C., 400° C. and 500° C. for 30 seconds respectively, and thereafter the sheet of aluminum foil was removed to prepare a polyimide film (Polymer sample A) with a different thickness. Moreover, as in the case of the sample A, pyromellitic acid anhydride and p-phenylenediamine were used as the raw material to prepare a polyimide film (Polymer sample B), and 3,3′,4,4′-biphenyltetracarboxylic acid dianhydride and p-phenylenediamine were used as the raw material to prepare a polyimide film (Polymer sample C). With regard to the thickness of the polyimide film, by adjusting the casting speed and the like, several kinds of films differing in thickness within the range of 18 μm to 100 nm were prepared. Eight kinds of polyimide films (Polymer sample A) with respective thicknesses ranging from 18 μm to 100 nm, three kinds of polyimide films (Polymer sample B) with respective thicknesses ranging from 9.2 to 1.1 μm and three kinds of polyimide films (Polymer sample C) with respective thicknesses ranging from 7.5 to 1.0 μm were placed in an electric furnace, and the internal temperature thereof was elevated to 1000° C. at a rate of 10° C./minute in a nitrogen gas atmosphere and the temperature was kept at 1000° C. for 1 hour to perform a preliminary treatment. Next, the carbonized sheet obtained was fitted to the inside of a cylindrical graphite heater, and the internal temperature thereof was elevated to a treatment temperature (maximum temperature) of 2900° C., 3000° C., 3100° C. or 3200° C. at a temperature increasing rate of 20° C./minute. The sheet was held in place for 30 minutes or 120 minutes (treatment time) at this temperature, and afterward, the internal temperature was dropped at a rate of 40° C./minute to prepare a graphite sheet. The treatment was performed under a positive pressure of 0.15 MPa in an argon atmosphere. Values of the thickness (μm), density (g/cm3) and thermal conductivity (W/mK) of the graphite sheet obtained were shown in Table 1. It has been found that, when the film has a thickness lying within the range shown in this table, all of the samples exhibit excellent thermal conductivity of not less than 1000 W/mK, preferably not less than 1800 W/mK, after being subjected to a heat treatment at 2900° C. or higher for 30 minutes or more. TABLE 1MaximumThermalProductionPolymerTemperatureTreatmentThicknessDensityConductivityExampleSample(° C.)Time Minute )(μm)(g/cm3)(W/mK)1A3000309.62.0519602A3000304.72.0720103A3000302.12.1120804A3000301.22.2221005A3000300.722.2320806A3000300.312.221207A3000300.14—21208A3000300.06—19909A2900301.22.18180010A29001201.22.21188011A3100302.12.12215012A3200302.02.16223013B3000304.32.15202011B3000302.62.20210015B3000300.62.20198016C3000303.42.20204017C3000302.12.10200018C3000300.52.181980 Although only a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from embodiments disclosed herein. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims. 1: Substrate for fixing a target 10: Neutron-producing metal member 20, 25: Thermal interface material 30: Proton-absorbing metal substrate 40: Heat sink member 60: Layered type target material for generating neutrons 70: Target module for generating neutrons

description

With reference to the accompanying drawings, embodiments according to the present invention are explained. FIG. 1 is a block diagram showing a first embodiment of a radiation image taking apparatus according to the present invention. The radiation image taking apparatus of the first embodiment generally includes an X-ray source 10 for irradiating X-rays to a sample to be measured; a grid 20 for removing dispersion rays contained in the X-rays passing through the sample to be measured; a flat panel type X-ray sensor 30 for detecting the X-rays passing through the grid 20; an image correcting portion 40 for correcting a detected image outputted from the flat panel type X-ray sensor 30; an operation process portion 50 for carrying out an equalizing process of X-ray detection signals based on the X-ray detection signals outputted from the image correction portion 40; and an image displaying device 60 for outputting an image information outputted from the operation process portion 50 to display. Incidentally, the X-ray source 10 corresponds to the radiation irradiation device; the flat panel type X-ray sensor 30 corresponds to the radiation detecting device; the operation process portion 50 corresponds to the operation process device; and the image displaying device 60 corresponds to the image outputting device, of the present invention, respectively. Hereunder, structures and functions of the respective portions are explained. The X-ray source 10 irradiates cone-shape X-ray beams (hereinafter referred to as xe2x80x9cX-raysxe2x80x9d) to the sample to be measured. As shown in FIG. 2, when X-rays are ejected to detection pixel groups 31 of the flat panel type X-ray sensor 30 through the grid 20, the projection image is enlarged by a magnification determined by a distance L1 from the X-ray source 10 to the grid 20 and a distance L from the X-ray source 10 to the flat panel type X-ray sensor 30. In other words, a relationship between a pitch GP of the grid 20 and a pitch GPxe2x80x2 of the projection image can be expressed by the following equation (1): GPxe2x80x2=GPxc2x7L/L1xe2x80x83xe2x80x83(1) Also, as a characteristic structure of the present invention, the pitch or length GP of the slit of the grid 20 has a relationship such that the length obtained by multiplying odd-number to a half pitch of the projection image on the X-ray sensor 30 through the grid 20 is equal to a pitch SP of detection pixels of the flat panel type X-ray sensor 30. Namely, a relationship between the pitch GPxe2x80x2 of the projection image and the pitch SP of the detection pixel can be expressed by the following equation (2): (GPxe2x80x2/2)(2nxe2x88x921)=SPxe2x80x83xe2x80x83(2), wherein n represents a positive integer. More specifically, the pitch GP of the grid 20 has a relationship of the following equation (3) from the above equations (1) and (2): GP=2xc2x7SPxc2x7L1/Lxc2x7(2nxe2x88x921)xe2x80x83xe2x80x83(3) More specifically, in the first embodiment, the pitch GP of the grid 20 is structured such that when the X-rays are projected to the flat panel type X-ray sensor 30 through the grid 20, a length of a half of the pitch GPxe2x80x2 of the projection image is equal to the pitch SP of the detection pixels 31. Incidentally, the pitch GP of the grid 20 or slits is not limited to the above-mentioned relationship of the present embodiment, and there may be a relationship such that a length obtained by multiplying odd-number to the half pitch GPxe2x80x2 of the projection image, such as three times, five time, seven time . . . , is equal to the pitch SP of the detection pixels 31 of the flat panel type X-ray sensor 30. Also, in the grid 20, there are used flakes, such as Pb (lead), W (tungsten) of a high atomic number, U (uranium), through which X-rays do not relatively pass, and Al (aluminum) for a slit portion, through which X-rays pass. Also, a size of the grid 20 is changed according to a size of the flat panel type X-ray sensor 30. The flat panel type X-ray sensor 30, as shown in FIG. 3, includes X-ray detecting base plates 31; capacitors Cs for storing collection carriers through carrier collection electrodes of the X-ray detecting base plates 31; thin film transistors as switching elements 32, which are normally in an off state, for taking out charges stored in the capacitors Cs; a reading circuit 33 in an X-axis direction; and a reading circuit 34 in a Y-axis direction. Incidentally, although FIG. 3 shows a matrix structure consisting of only nine in total, i.e. 3 in a lengthwise direction and 3 in a widthwise direction for the sake of convenience, if necessary, for example, practically, a matrix has a structure of 1024 in a lengthwise direction and 1024 in a widthwise direction. The image correcting portion 40 carries out an operation process through filtration to remove artifacts and the like generated on a detection image. The operation process portion 50, as shown in FIG. 4, equalizes the irregularities of levels of X-ray detecting signals by carrying out the operation process through addition average or moving average with a two-pixel unit of the detection pixels, i.e. signs on an X-axis in the drawing, continuously lined up in a pitch direction of the grid based on the X-ray detection signals outputted from the image correction portion 40. Incidentally, the addition average and moving average are not limited to those of the two-pixel unit, and they may be carried out with a detection pixel group unit of even number continuously lined up in the pitch direction of the grid. The image displaying device 60 displays image information subjected to the operation process, such as various corrections. Incidentally, the image output device according to the present invention is not limited to the image displaying device 60, and it may be a light sensitive substance, such as a printer and a film. Next, operations of the radiation image taking apparatus of the present embodiment as described above are explained. As shown in FIG. 2, X-rays irradiated from the X-ray source 10 and passing through the sample to be measured pass through slits for the respective pitches GP provided on the grid 20 and are projected to the detection pixel groups 31 on the flat panel type X-ray sensor 30. The projected images detected at the detection pixel groups 31 are carrier-converted by the flat panel type X-ray sensor 30 and stored in the respective capacitors Cs. Then, the stored carriers are properly outputted to the image correction portion 40 for filtering, and the pixel information, artifacts of which are removed, is outputted to the operation process portion 50. The image information inputted into the operation process portion 50, for example, as shown in FIG. 4, is subjected to an addition average process or moving average process with two pixels, as a unit, of the detection image group 31 continuously lined up in the pitch direction of the grid 20 (in the drawing, X-axis plus direction). In other words, assuming that a level of the X-ray detection signal detected from each detection pixel is Sn (n represents a detection pixel number and is positive integer), the two-pixel addition average in an area A becomes an average of levels S1 and S2 of the X-ray detection signals of the first and second detection pixels. An average value obtained through the operation process is assigned to the first and second detection pixels. Also, in an area B, an average value of levels Sixe2x88x921 and Si of the X-ray detection signals from the detection pixels of the ixe2x88x921st and i-th is assigned to the respective detection pixels; and in an area C, an average value of levels Snxe2x88x921 and Sn of the X-ray detection signals from the detection pixels of the nxe2x88x921st and n-th is assigned to the respective pixels. As a result, the irregularities in levels of the X-ray detection signals caused by the grid 20 can be solved. Also, the two-pixel moving average is obtained such that, among levels Sn of the X-ray detection signals detected from the respective detection pixels, in the area A, an equalizing process of the levels S1 and S2 of the X-ray detection signals of the first and second detection pixels is carried out; the obtained average value is assigned to the first detection pixel; then, an equalizing process of the levels S2 and S3 of the X-ray detection signals of the second and third detection pixels is carried out; and the obtained average value is assigned to the second detection pixel. The two-pixel moving average as described above is carried out from area A to area C. As a result, irregularities of the levels of the X-ray detection signals can be solved. Further, by the two-pixel moving average, an output image having a higher resolution than that of the two-pixel addition average can be obtained. Incidentally, in the present embodiment, for the sake of explanatory convenience, although it is assumed that the X-ray detection signal levels are uniform, actually, the values obtained from the equalizing process are superposed on the detected X-ray detection signal levels of the sample to be measured. The image information, in which irregularities in the X-ray detection signal levels have been equalized at the operation process portion 50, is outputted to the image displaying device 60. At this time, as shown in FIG. 5, moires caused by the irregularities in the X-ray detection signal levels have been removed, and a clear image can be displayed. By the way, in the present embodiment, after the image correction is carried out at the image correction portion 40, the operation process is carried out at the operation process portion 50 to remove moires. However, after moires are removed, filtering of the structural images may be made at the image correction portion 40. FIG. 6 is a block diagram of a second embodiment of the radiation image taking apparatus according to the present invention. Characteristics of the present embodiment, as shown in FIG. 6, reside in that a driving portion 70 for swinging or moving the grid 20, and an operation portion 80 for operating the driving portion 70 are included. In case a stationary image is taken, the driving portion 70 horizontally swings the grid 20 while facing the flat panel type X-ray sensor 30 in the pitch direction. Thus, it is possible to prevent a resolution of the output image from being reduced by removing moires through the swinging of the grid 20. In other words, in case moires are removed through the equalizing process of a plurality of pixel units, since levels of the equalized X-ray detection signals are assigned to the respective detection pixels to be operated, the levels are slightly deteriorated when compared with the levels of the original X-ray detection signals detected from the respective detection pixels. In order to prevent such a resolution from being lowered, the grid 20 is swung or moved. In case of the stationary picture, since it is not necessary to swing or move the grid 20 at a high speed as in a moving image, it is not required to enlarge a structure of the device so much. Also, in case the moving image is taken, the grid 20 is not swung, and is fixed as in the first embodiment described above. Thus, since it is not required to forcibly swing the grid 20 at a high speed, a good moving image without moires can be taken. Incidentally, the driving portion 70 corresponds to the swinging device of the present invention. The operation portion 80 makes a switching operation in accordance with the stationary image or moving image taking condition. By the way, the operation portion 80 corresponds to the switching device of the grid 20. Since the other structures are the same as those of the first embodiment, explanations of the same are omitted. While the grid 20 in the present embodiment is used for taking images of both stationary image and moving image, in case the grids are provided separately, it is not necessary to use the grid 20 of the invention for the stationary image, and the pitch on the grid can be suitably set. The present invention is not limited to the above-described embodiments and can be modified as described below. An X-ray source 10 for outputting fan beams, a grid 20 and an X-ray detecting device having a one-dimensional matrix arrangement disposed to face the X-ray source 10 with respect to a sample to be measured therebetween may scan the sample to be measured. By using an X-ray source 10 for outputting cone beams, a grid 20 and an X-ray detecting device having a one-dimensional matrix arrangement may scan an area of a sample to be measured to which the cone beams are irradiated. The radiation detecting device is not limited to the flat panel type X-ray sensor 30. It may be a solid state image-taking element, such as a charge-coupled device (CCD). As apparent from the above description, according to the radiation image taking apparatus of the first aspect of the invention, when radiations are projected to the radiation detecting device through the grid, the radiation image is taken by using the grid having such a relationship that a length obtained by multiplying odd-number to a half pitch of a projection image on the radiation detecting device through the grid is equal to a pitch of detection pixels of the radiation detecting device. Then, the radiation detection signals detected from the detection pixels of the radiation detecting device through the grid are subjected to an equalizing process for every pixel groups, each having an even number of detection pixels, continuously lined up in a pitch direction of the grid to thereby remove moires from the output image outputted from the output image device. Even if the positions of the pitches of the slits on the grid and pitches of the detection pixels are slightly displaced, since the equalizing process is carried out with a combination, as a unit, of a high level radiation detection signal and a low level radiation detection signal from the respective even-number detection pixels lined up in the pitch direction of the grid, irregularities of the radiation detection signals can be reduced to a sufficiently practical level. As a result, it is not necessary to keep the pitches of the grid accurately, so that the radiation image taking apparatus can be made economical. Further, since the grid can be fixedly disposed without swing, the apparatus can be miniaturized. According to the radiation image taking apparatus of the second aspect of the invention, the grid used in the radiation image taking apparatus of the first aspect is set to have such a relationship that when radiations are projected to the radiation detecting device through the grid, a length of a half pitch of a projection image is equal to a pitch of a detection pixel of the radiation detecting device. Then, the radiation detection signals detected by the radiation detecting device through the grid are inputted into the operation device, and the equalizing process is carried out for every two detection pixel groups continuously lined up in the pitch direction of the grid to thereby keep reduction in a resolution of the output image outputted from the image output device to a minimum. According to the radiation image taking apparatus of the third aspect of the invention, when a stationary image is taken, since it is not necessary to swing the swinging device at a high speed as in case of taking a moving image, the grid is swung in its pitch direction with respect to the radiation detecting device. In other words, with use of the swinging device, it is not necessary to make corrections by the operation device to thereby prevent a resolution of the output image from being lowered. Also, when a moving image is taken, since it is not required that the grid is forcibly swung at a high speed by stop swinging of the grid with a switching device, a good moving image can be taken and moires can be removed from the output image outputted from the output device. While the invention has been explained with reference to the specific embodiments of the invention, the explanation is illustrative and the invention is limited only by the appended claims.

summary

039379710

summary

This invention relates to a shield of the kind employed in connection with radiation therapy machines to limit the area of exposure of a patient to cobalt rays or the like such that the radiation rays only strike at the very exact spot intended on the human body. In order that the rays strike only the intended spots, lead shields are positioned between the source of the cobalt rays and the patient's body such that the shields serve to protect those areas of the body that are not to be treated. Conventionally, focused shields are custom-made for each individual and contain an aperture therein having a configuration corresponding to the area of the body that is to be treated so that any cobalt rays directed to an area laterally of the aperture are blocked by the lead shield. Inasmuch as the patients normally require more than one treatment the shields must be very exact in order that the very same spot is uniformly and consistently exposed to the rays each time the patient is treated. The lead shields, which are approximately 2 inches thick, are disposed to intersect a radiation beam and thus block off all rays except those which are in a position to pass through the aperture in the shield. However, because of the thickness of the shields, as conventionally known, all of the rays entering the aperture do not necessarily exit the same because their angular disposition relative to the shield and the aperture sidewalls is such that they strike a sidewall before they have a chance to exit the aperture. Also, because of this aforementioned angularity of the rays relative to the focused shield, which is normally disposed perpendicular to the central, longitudinal axis of the radiation beam, there is also a "dead" spot below that portion of the aperture where the upper or entry edge of the aperture intersects the radiation rays proximal thereto. It is, therefore, a very important object of this invention to provide a method of fabricating a focused shield for use in connection with a radiation therapy machine or the like which the focused shield has a field of radiation aperture configured to permit precise exposure of a predetermined area of a patient's body and in which all of the radiation rays in alignment with the aperture pass therethrough to expose an area of the patient corresponding to the full area and configuration of the aperture. Another very important object of the invention is to provide a focused shield having an aperture therein through which any rays entering the aperture also exit the aperture in an unimpeded manner. It is another very important object of our invention to provide a method and apparatus for use in connection therewith for making a focused shield having an aperture therein that permits all radiation rays entering the aperture to exit therefrom in an unimpeded manner. Yet another important object of the instant invention is to provide a focused shield, as well as a method and apparatus for making the same, in which the focused shield has an aperture in which the sidewalls thereof are disposed to permit all radiation rays in alignment with the aperture to pass therethrough. A still further object of the instant invention is to provide a focused shield having a bevel-walled field of radiation aperture in which the sidewalls thereof are in substantial parallelism with the radiation rays passing through the aperture and proximal a sidewall thereof. A still further object of our invention is to provide a focused shield blank holding fixture adapted especially for use with a band saw or the like to permit cutting an aperture having the desired radiation field outline in which the sidewalls of the aperture are automatically beveled in order that the sidewalls will be substantially parallel with the radiation rays passing thereby and proximal thereto when the focused shield is inserted in a radiation therapy machine.

claims

1. A linkage mechanism of a scattered ray inhibition apparatus and a radiation field control apparatus, said linkage mechanism comprising:a first timing belt;a second timing belt; anda transmission mechanism between said first timing belt and said second timing belt, wherein said scattered ray inhibition apparatus is mounted on said first timing belt, said radiation field control apparatus is mounted on said second timing belt, the transmission ratio of said transmission mechanism is equal to the ratio of the moving speed of said scattered ray inhibition apparatus to the moving speed of said radiation field control apparatus. 2. The linkage mechanism according to claim 1, wherein said transmission mechanism comprises at least two gears. 3. The linkage mechanism according to claim 2, wherein said transmission mechanism further comprises:a third timing belt connected to said first timing belt; anda fourth timing belt connected to said second timing belt, wherein said at least two gears are disposed between said third timing belt and said fourth timing belt. 4. The linkage mechanism according to claim 1 further comprising a first linear guideway, said scattered ray inhibition apparatus connected to said first timing belt through said first linear guideway. 5. The linkage mechanism according to claim 4 further comprising a second linear guideway, said radiation field control apparatus connected to said second timing belt through said second linear guideway. 6. The linkage mechanism according to claim 5 further comprising an electrical motor configured to supply power to said transmission mechanism. 7. The linkage mechanism according to claim 1 further comprising a second linear guideway, said radiation field control apparatus connected to said second timing belt through said second linear guideway. 8. The linkage mechanism according to claim 7 further comprising an electrical motor configured to supply power to said transmission mechanism. 9. A collimator comprising a linkage mechanism of a scattered ray inhibition apparatus and a radiation field control apparatus, wherein said linkage mechanism comprises:a first timing belt;a second timing belt; anda transmission mechanism between said first timing belt and said second timing belt, wherein said scattered ray inhibition apparatus is mounted on said first timing belt, said radiation field control apparatus is mounted on said second timing belt, the transmission ratio of said transmission mechanism is equal to the ratio of the moving speed of said scattered ray inhibition apparatus to the moving speed of said radiation field control apparatus. 10. The collimator according to claim 9, wherein said transmission mechanism comprises at least two gears. 11. The collimator according to claim 10, wherein said transmission mechanism further comprises:a third timing belt connected to said first timing belt; anda fourth timing belt connected to said second timing belt, wherein said at least two gears are disposed between said third timing belt and said fourth timing belt. 12. The collimator according to claim 9 further comprising a first linear guideway, said scattered ray inhibition apparatus being connected to said first timing belt through said first linear guideway. 13. The collimator according to claim 12 further comprising a second linear guideway, said radiation field control apparatus being connected to said second timing belt through said second linear guideway. 14. The collimator according to claim 9 further comprising a second linear guideway, said radiation field control apparatus being connected to said second timing belt through said second linear guideway. 15. An X-ray machine comprising a linkage mechanism of a scattered ray inhibition apparatus and a radiation field control apparatus, said linkage mechanism comprising:a first timing belt;a second timing belt; anda transmission mechanism between said first timing belt and said second timing belt, wherein said scattered ray inhibition apparatus is mounted on said first timing belt, said radiation field control apparatus is mounted on said second timing belt, the transmission ratio of said transmission mechanism is equal to the ratio of the moving speed of said scattered ray inhibition apparatus to the moving speed of said radiation field control apparatus. 16. The X-ray machine according to claim 15, wherein said transmission mechanism comprises at least two gears. 17. The X-ray machine according to claim 16, wherein said transmission mechanism further comprises:a third timing belt connected to said first timing belt; anda fourth timing belt connected to said second timing belt, wherein said at least two gears are disposed between said third timing belt and said fourth timing belt. 18. The X-ray machine according to claim 15 further comprising a first linear guideway, said scattered ray inhibition apparatus being connected to said first timing belt through said first linear guideway. 19. The X-ray machine according to claim 18 further comprising a second linear guideway, said radiation field control apparatus being connected to said second timing belt through said second linear guideway. 20. The X-ray machine according to claim 15 further comprising a second linear guideway, said radiation field control apparatus being connected to said second timing belt through said second linear guideway.

summary

050930729

abstract

Process for the radioactive decontamination of metal surfaces, particularly portions of the primary circuits of water-cooled nuclear reactors, characterized in that it comprises subjecting said surfaces to the successive stages of an oxidizing pretreatment with the aid of a solution of potassium permanganate KMnO.sub.4 and nitric acid, rinsing with demineralized water and then reducing treatment in a basic medium with the aid of a solution of alkali metal gluconate of formula HOH.sub.2 C--CHOH--CHOH--CHOH--CHOH--COOM, in which M is an alkali metal chosen from among Na and K, as well as soda NaOH.

039390390

abstract

A nuclear reactor with a reactor core having a plurality of individual core elements is provided with a clamping device for at least some of the core elements, which clamping device includes a plurality of pawls pivotally mounted to the interior of each wall of the hexagonal outer wrapping tube for movement between a position within the wrapper tube and a position extending through an adjacent hole in the side wall of the wrapper tube, and an operating tube axially slidably mounted within the wrapper tube for moving the pawls between their two positions. When the pawls are extended by the operating tube, they will move outwardly a predetermined distance transversely of the core element to cooperatively engage other core elements and clamp the assembly. A lock mechanism is provided to lock the operating tube and wrapper tube in one position of the pawls, preferably the withdrawn position, to assist in inserting and removing the core element.

051204878

description

DETAILED DESCRIPTION OF THE INVENTION When superthermal electrons are heated briefly in a tokamak plasma, the change in the electron distribution function, particularly at high energy, is manifest in a change, or increment in the synchrotron emission. Since the excitation is brief, the changes incurred in both the electron distribution function and the synchrotron emission are transient. Thus, the incremental synchrotron radiation is a two-dimensional pattern in frequency-time space. The details of this pattern are governed by plasma parameters; for example, the higher the plasma density, the faster the decay of the incremental radiation. As is well known in the prior art, high-velocity, superthermal electrons radiate most copiously, but lose energy slowly, so that there can be independent time points in the radiation pattern R (.omega.,t). Dominated by Coulomb collisions and the dc electric field, these electrons mainly flow along the magnetic field, largely immune to temperature fluctuations and other turbulence in the bulk of the ion or electron distributions. Because relatively few parameters govern this response, given powerful analytic tools and the method of this invention, it is possible to determine the parameters from the radiation response. A relatively modest diagnostic embodiment of the current invention relies upon a brief, probing rf signal that leads to the incremental synchrotron signal, and an array of frequency detectors with submillisecond time resolution. FIGS. 1a and 1b numerically simulate the incremental synchrotron radiation response to a deliberate, brief heating of the plasma (e.g., by lower-hydrid waves) to produce radiation directly attributable to this probe. Both FIGS. 1a and 1b exhibit radiation at several harmonics from electrons initially with about 700 keV parallel energy, or tail electrons in a 20-keV reactor plasma. In FIG. 1a the parallel dc electric field corresponds to 0.02 V/m at density 10.sup.14 /cm.sup.3 ; in FIG. 1b it is -0.0067 V/m. The incremental or transient radiation response is defined as R(.omega.,t;.zeta.).XI.R.sub.tot (.omega.,t;.zeta.)-R.sub.back (.omega.,t;.zeta.), where R.sub.back is the background radiation associated with a relatively constant distribution function and R is the incremental radiation specifically due to the externally imposed impulsive momentum-space flux .GAMMA.(p,t). We can then write the distribution function f as f=.function..sub.m (1+.phi..sub.B +.phi., where .function..sub.m is a Maxwellian distribution, .phi..sub.B describes the relatively constant deviation from Maxwellian of the background distribution, and .phi. describes the time-dependent distribution specifically associated with the source .GAMMA.. For problems of interest, in terms of contributing to the collision integral, both .phi..sub.B and .phi. may be treated as small, so that f obeys the linearized Fokker-Planck equation. The evolution of .phi. is then governed, after the brief excitation, by Coulomb collisions and the dc electric field, EQU .function..sub.M .differential..phi./.differential.t+qE.multidot..gradient..sub.p .differential..sub.M .phi.-C(.phi.)=0 (1) with initial condition .function..sub.M .phi.(p,t=0)=Q(p), which is the result of the impulse .GAMMA.. The incremental or transient radiation response, viewed at angle .zeta. with respect to the magnetic field is then EQU R(.omega.,t;.zeta.)=.intg.d.sup.3 p.function..sub.M .phi.(p,t)I(.omega.,p;.zeta.), (2) where the radiation intensity I can be of ordinary or extraordinary polarization; for the latter, I=I.sup.x, we have ##EQU1## where n is the cyclotron harmonic, J.sub.n is the derivative of the nth Bessel function of the first kind, .omega..sub.c =e.sup.B /mc is the cyclotron frequency of nonrelativistic electrons, .mu.=p/mc, .gamma..sup.2 (u).XI.1+u.sup.2, .mu..XI.p.sub.11 /p, and .lambda.=1-u Sin .zeta./.gamma. is the extent of the Doppler shift through viewing the radiation signal at angle .zeta.. Very fast algorithms have been developed for solving for the radiation response R(.omega.,t). The fast algorithms make feasible a statistical analysis which would otherwise be unthinkable, and exploit several properties of Eqs. (1)-(3). First, note that Eqs. (1)-(3) admit several scale invariant transformations of the radiation response R(.omega.,t). Having solved for R(.omega.,t;.theta.), where .theta. is a set of parametric dependences which includes the magnetic field amplitude B, the electric field E, the density n, the viewing angle I and the perturbation amplitude Q, we also have for any constants .alpha..sub.1, .alpha..sub.2, and .alpha..sub.3, EQU R(.omega.,t;.alpha..sub.1 B,.alpha..sub.2 Q,.alpha..sub.3 n,E)=.alpha..sub.1 .alpha..sub.2 R(.omega./.alpha..sub.1,t/.alpha..sub.3 ;B,Q,n,E/ .alpha..sub.3). (4) The impulsive heating can be arranged to affect only nonrunaway electrons, so that Eq. (4) simplifies further through the linearization R=R.sub.0 +ER.sub.1. Second, since Eq. (1) is linear in .phi., a Green's function, .psi., can be defined for the radiation response. We write the radiation response as an integral over initial condition Q(p), EQU R(.omega.,t;.zeta.)=.intg.d.sup.3 u .psi.(.omega.,p,t;.zeta.)Q(p).(5) The Green's function makes efficient the simultaneous consideration of many perturbations Q(p). Third, choosing to perturb electrons on the tail of the distribution function (i.e. superthermal electrons but not runaways) makes possible an analytic solution for .psi.. For these electrons, energy diffusion by collisions is ignorable compared to energy loss. The Green's function for the radiation response, .psi., solves the relativistic Fokker-Planck adjoint equation, which we write as ##EQU2## written for superthermal excitation in the high-velocity limit and in terms of the normalized variables .tau.=v.sub.c t, v.sub.c =nq.sup.4 ln.LAMBDA./4.pi.m.sup.2 .epsilon..sub.0.sup.2 c.sup.3, and E=q E/mcv.sub.c, and to be solved with the following initial condition .psi.(.omega.,u;.zeta.,.tau.=0)=I(.omega.,u;.zeta.). An analytic solution is available as follows: separate .psi. and the initial conditions into Legendre harmonics [.psi.(u,.mu., .tau.)=.SIGMA..sub.k P.sub.k (.mu.).sub..psi.k (u, .tau.)], expand in the electric field [.psi..sub.k (u, .tau.)=.psi..sub.k.sup.(o) +E.psi..sub.k.sup.(1) +. . . , and then integrate the equation for .psi..sub.k.sup.(0) along characteristics to obtain ##EQU3## where .alpha..sub.k .XI.k(k+1) (Z.sub.eff + 1)/2, and the characteristic function X(.tau., u) can be written as x=g.sup.-1 [g(u)-.tau.], with g(u).XI.u-tan.sup.-1 u; g.sup.-1 is defined such that g.sup.-1 [ g(u)]=1. . The equation governing .psi..sub.k.sup.(1) to be solved with homogeneous initial conditions, is driven by the kth Legendre harmonic of .differential..psi..sup.(0) /.differential..mu..sub.11 ; fortunately, this inhomogeneous term can be simplified enormously so that .psi..sub.k.sup.(1) can be put into an efficient closed form. These fast algorithms enable consideration of essentially all competing parameter sets that might possibly explain obtained data. More than that, the worth of data can be estimated prior to obtaining it. Suppose that experimental measurements are of the following form R.sub.x (.omega.,t)=R(.omega.,t)+R(.omega.,t), where the extraneous signal R(.omega.,t) is Gaussian noise, uncorrelated in both frequency and time, with (R)=0 and (R.sup.2)=.sigma..sup.2. Given this model for data generation, and given a set of plasma parameters {.theta.}, we can express the probability P(R.sub.x .vertline..theta.;.sigma.) of generating a specific data set R.sub.x in the presence of noise characterized by .sigma. Given an a priori distribution P(.theta.) for the parameter set {.theta.}, by Bayes's theorem we can write P(.theta..vertline.R.sub.x ;.sigma.)=P(R.sub.x .vertline..theta.;.sigma.)P(.theta.)/P(R.sub.x). The probability distribution of the plasma parameter set {.theta.}, given that the data were obtained in the presence of noise .sigma. and generated with the specific plasma parameter set {.theta..sub.P }, can now be written as ##EQU4## where, in the first equality, the summation over all possible data sets {R.sub.x } is both unfeasible and, in practice, unnecessary; the second equality obtains, since, by construction, P(.theta..vertline.R.sub.x ;.sigma.) is sampled with probability P(R.sub.x .vertline..theta..sub.p ;.sigma.). Generally N.sub.R .about.80 suffices to approximate P(.theta..vertline..theta..sub.p ;.sigma.). Of course, the fast algorithms for generating R(.omega.,t) are indispensable, since R must be obtained for each competitive data set. Carrying out a program of examining P(.theta..vertline..theta..sub.p ;.sigma.) with various sets of plasma and heating parameters unknown, we find that the a priori probabilities P(.theta.) can be improved upon meaningfully. To take an example of particular interest, consider the simultaneous viewing of radiation from the core periphery of a tokamak, where in a coarse model, the two regimes have, respectively, densities n.sub.c and n.sub.p, and electric fields E.sub.c and E.sub.p. In other relevant respects, such as viewing angle or ion charge state, the two regimes are presumed identical. One detector then sums EQU R(.omega.,t)=Q.sub.c R(.omega.,t;n.sub.c,.epsilon..sub.c)+Q.sub.p R(.omega.,t;n.sub.p .epsilon..sub.p), where Q.sub.c, Q.sub.p, .epsilon..sub.c, and .epsilon..sub.p are assumed unknown, but n.sub.c and n.sub.p are known from other measurements. Of course, where n.sub.c =n.sub.p. there would be no distinguishing the radiation source. However, even a 10% variation in density is exploitable. In FIG. 2, data were simulated on a 40.times.40 grid in frequency-time space, with noise .sigma. of 10% of the maximum signal R(.omega.,t). In practice, purely experimental noise can be kept much lower and a larger differential in density makes this discrimination much easier. As shown in FIG. 2, the marginal probability distribution P(.epsilon..sub.c, .epsilon..sub.p) (the joint probability summed over all {Q.sub.c, Q.sub.p }) reveals the true parameters E.sub.c =0.08, E.sub.p 0, i.e., a loop voltage on axis not yet relaxed via magnetic diffusion. The model employed can be improved upon in several ways, particularly in accounting for cross-field transport due to imperfect magnetic surfaces. Accounting for losses of the fast electrons can probably be done analytically by introducing only a few new parameters; the fast algorithms should remain useful and the inference problem should remain tractable. Of course, in many instances the model as presented may suffice. The foregoing description of a preferred embodiment of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The embodiments described explain the principles of the invention and practical applications and should enable others skilled in the art to utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto.

description

FIG. 2 shows a preferred embodiment of a canister for the containment of a radioactive item according to the invention. Canister 101 comprises substantially tubular body 124, interior 128, a first, preferably closed, end 125, and second end 140. Interior 128 is adapted by size and geometric configuration to receive a radioactive item such as an nuclear reactor pressure vessel for storage, transportation, and disposal. Preferably interior 128 is large enough for such radioactive item to be disposed within the canister without difficulty, and to allow the addition of a stabilizer, as described herein, yet simultaneously as small as practicable, in order to reduce the size and weight of the completed package and to ease transportation and handling. Thus length width 134 and length 135 of the canister and in particular the canister interior are large enough to accommodate the item to be contained, but not larger than necessary for the purposes described herein. The selection of suitable dimensions and geometry will not trouble the designer of ordinary skill once he or she has been made familiar with disclosure. For most RPVs substantially circular cross sections will serve satisfactorily, and facilitate easy and inexpensive fabrication and employment of the canister. Body 124 of canister 101 further comprises integral sacrificial fenders 126 located adjacent each end of the canister. Sacrificial fenders 126 are comprised of extensions of body 124 of the canister beyond the end caps or closures of the canister, that is, beyond those portions of the canister actually used for containing the radioactive item, and are adapted to absorb or dissipate shocks administered to the completed containment package by deforming under contact loads. The mechanics of such fenders and their role in attenuating or absorbing shocks are well understood and will be plain to those of skill in the art, given the disclosure herein. The canister 101 shown in FIG. 2 further comprises lid or other closure means 108, which is adapted for attachment of a portion of the item to be contained. Lid or closure 108 can comprise a simple end plate, as shown, or might take the form of a cap-type enclosure sized to encompass the entire end of the canister, or any other suitable means for closing the canister. In the embodiment depicted in FIG. 2 closure 108 is adapted for the attachment of a portion of the contained device by means of holes 141, which are sized and positioned to accept attachment fittings present on the item to be contained, for example, the head attachment posts in a PWR pressure vessel. Preferably any portions of items to be attached to the exterior of the canister are not highly radioactive, or are sealable in their own right. Lid or top plate 108 further comprises optional fill and vent ports 160 and 161. Central ports 160 are provided for optional filling of the interior of the RPV body with grout or other sealant; peripheral ports 161 for filling the gap between the canister interior and the RPV exterior. Canister 101 in FIG. 2 further comprises optional secondary circumferential shield 130. Secondary shields are advantageously employed to provide additional containment of relatively highly radioactive portions of any contained items, such as some of the internal structures in a PWR pressure vessel. Preferably circumferential shields are employed in conjunction with cap or lid-type shields such as shields 122 and 142 shown in FIG. 4. A particular advantage of using substantially cylindrical canisters of the type shown in FIG. 2 is that secondary shields are relatively simple to fabricate and install, and provide substantial structural reinforcement as well. In the case of circumferential shields, open-ended cylinders of nearly the same size as the canister body may be employed, and may be disposed around the inner or outer surfaces of the canister, at any axial position along the canister that may be desired. Cap or lid type shields may be fabricated from flat plate material merely by trimming them to size, and may be placed at any axial location within the canister or covering one or both ends of the canister. In either case it is often suitable, as will be understood by those having ordinary familiarity with the art of radiation shielding, that the same materials as those employed in fabricating the canister body may be used in fabricating secondary shield structures, with substantial savings in cost. Cap or lid shields are particularly useful for providing ALARA (As Low As Reasonably Achievable) shields during stacking of internal parts, external fittings, and/or insulation inside an RPV as described herein, as an added shield against radiation for workers. Canisters or containment vessels according to the invention and as shown in FIG. 2 are substantially easier and less expensive to fabricate than prior art containment vessels. This is in large part due to their simplified construction, as described. They are also economical to use, especially during the containment and removal of decommissioned RPV""s, because they may easily be separated into sections, moved into place for containment of the RPV or other item, and reassembled easily. For example, the containment canister shown in FIG. 2 may be cut anywhere along the length of its body into two or more sections merely by cutting the container, as for example by means of any conventional metal cutting methods, along a circumference such as that shown by reference numeral 138 in FIG. 2, the location of which may be varied anywhere along the body of the canister, such that two sections 136 and 137 result. In such cases reassembly is accomplished merely by replacing second section 137 back in place adjacent to first section 136 and reattaching, as for example by welding. The use of secondary radiation shield 130 also facilitates the use of the canister in this fashion, as it can be used as a doubler or structural reinforcement as well as an additional radiation shield. Canister 101 may be fabricated economically and easily by rolling or otherwise forming tubular body 124 by conventional means from sheet or plate metal, and welding or otherwise attaching a bottom plate at closed end 125 and lid or closure plate 108. Integral fenders 126 are easily formed in such processes by placing the end closures at a suitable distance from the ends of the body structure, leaving the fenders protruding or extending from the body. Provision of optional fillet 143, which is also readily formed by rolling or other conventional means, is particularly beneficial, as it permits provision of integral fenders 126 as described, in such fashion that fenders 126 are able to perform their function with full efficiency, while optionally permitting the canister weight and the weight of any of its contents to be transferred directly to the floor or other surface on which canister 101 and any contents are placed, without passing through and possibly harming the fenders or reducing their capacity to absorb or dissipate shocks. Optionally fenders 126 are of sufficient depth to allow them to provide protection not only to the containment package as a whole, and in particular to the packaged radioactive item, but also to any additional items, such as removed reactor vessel pressure head, which may be attached to the exterior of the canister. An early part of the process for containing a radioactive item according to the invention is preparing the radioactive item for packing. Generally this comprises removing at least one external fitting from the item, and optionally portions of the internals of the item as well. A process of preparing the item for packing is shown in FIGS. 3 and 4. FIG. 3 is a cutaway schematic elevation of an intact radioactive item, specifically a PWR pressure vessel, prior to being processed for containment according to the invention. Reactor pressure vessel (RPV) 102 comprises body 114 and head 115, internals 117, and a number of external fittings 103, including water nozzles 144 and control structures 145. Head 115 is joined to body 114 at flange 146 by means of attachments 132, and insulation 116 is in place around exterior 105 of the RPV. Internals 117 comprise upper internals 147 and lower internals 148. In FIG. 4 the RPV of FIG. 3 has been at least partially processed for containment according to the invention. External fittings 103 have been trimmed so that non-removed portions 104 of the fittings are substantially flush with external surface 105 of body 114. In particular, non-removed portions 104 of the external fittings do not protrude past the outer circumference of flange 146. Moreover, internals portions 148 (FIG. 3), including the central portion of the core barrel and the core baffle assembly, have been removed from interior 109 of the RPV, and upper internals 147 have been stacked on top of support plate 142, which preferably serves also as a secondary radiation shield. Portions 149 of core barrel 151 (FIG. 3) are also disposed within the RPV. Additional portions 119 of the upper internals and insulation 116 removed from the exterior of the RPV are also placed in otherwise vacant space within the RPV body. A secondary support structure and ALARA shield 122 is placed atop internals 117, 147, and removed portions of external fittings 103 are placed thereupon. Additional insulation 116 taken from the exterior of the RPV body is placed atop fittings 103. Penetrations 120 of RPV body 114 have been stopped by means of plugs 121. As described herein, it is beneficial during at least the first portions of this process to leave the reactor coolant fluid or other liquid in the RPV, to serve as a radiation shield for those working on the containment process. Preferably this is accomplished by leaving water or other liquid in the RPV body to at least the level of 123 in FIG. 4 until the more highly-radioactive components of the core have been removed and all penetrations 120, for example, have been plugged; at this point it is advantageous to drain the fluid, install secondary supports and shield structures such as 142 and 122, and proceed with packaging. FIG. 5 is a schematic view of a radioactive item being disposed within a canister in accordance with the invention. Presented is one scenario of placing RPV 102 within canister 101. This scenario can be altered to accommodate plant specific and unique conditions. Internal shields 130 are welded to lower section 136 and upper section 137 of the canister during manufacturing. Lower section 136 of canister 101 has been placed atop transfer cart 160 with a removal frame and trunnions 139. Transfer cart 160 with lower section 136 has initially been placed in position 161 near RPV installation point 152. Head 115 of RPV 102 has been removed and lifting device 163 attached to RPV body 114. RPV 102 has been disconnected from the remainder of the plant of which it formed part by disconnecting external fittings 103, including piping 144, and penetrations 120 in RPV body 114 have been sealed. RPV external surfaces 105 are sealed with paint or other suitable substance to immobilize surface contaminants. RPV body 114 has been removed from its prior position 114xe2x80x2 in RPV installation 152 and raised, whereupon transfer cart 160 with lower section 136 has been moved into loading position 169, and RPV body 114 has been disposed within section 136 of the canister. Canister 101 and RPV body 114 are ready for a stabilizer to be introduced in gap 106 between the RPV body 114 and the interior wall of canister 101. After gap 106 has been filled to a level sufficient to allow the stabilizer to support RPV body 114 and the stabilizer allowed time to set sufficiently, or RPV body 114 otherwise sufficiently supported, upper section 137 of canister 101 is placed over the RPV body and reattached to lower section 136 by welding or other suitable means. RPV studs 185 are installed through top plate 108 of upper section 137 into the flange of RPV body 114. Spray metalizing is used to seal openings between RPV studs 185 and attachment penetrations 141 (FIG. 2) through upper section 137. Head 115 is placed atop external surface 127 of the canister, and fixed thereto, preferably by means of head attachments 132 (FIG. 3) threaded onto RPV studs 185. If necessary, the completed containment package will be turned about its upright longitudinal axis by pivoting the package with trunnions 139 on the removable frame on lower section 136. The package may then be removed from the plant housing and made ready for shipment by removing the frame with trunnions 139. It may be seen that division of canister 101 into two or more sections provides a number of benefits, such as a reduction in clearance height requirements to place RPV body 102 within the canister. This is especially beneficial in the limited workspaces of most nuclear plant installations. FIG. 6 is a cutaway schematic view of a radioactive item packaged in accordance with the invention. In addition to elements shown in other Figures, stabilizer 107 is shown substantially filling gap 106 between canister 101 and RPV 102. RPV head 115 is in place atop lid 108 of the canister, and attached by means of RPV head-body attachments 132, which, together with stabilizer 107, further comprise the sole attachment between the RPV body 114 and the containment canister. Optionally the entire interior of the RPV body is filled with stabilizer 107, to further immobilize contaminants and stored components. A containment package for a PWR pressure vessel is described. This example corresponds to plans for disposal of the Connecticut Yankee PWR. A containment canister according to the invention and as shown generally in FIG. 2, including top and bottom plates and fillet, is fabricated from three-inch thick structural carbon steel. Secondary shielding of two-inch thick carbon steel is placed within the canister body so as to shield the most highly radioactive portions of the completed package. The canister is fabricated in two sections, with the weld seam located behind the secondary shielding on rejoining. Rejoining is accomplished by full penetration weld. The canister, including integral fenders, 35xe2x80x2 3xe2x80x3 feet in length, 17xe2x80x2 10xe2x80x3 diameter, and weighs 190 tons empty. The completed package, with stabilizing grout and externally-attached RPV head, weighs 800 tons. The height of the package, with head attached, is 39xe2x80x2 7xe2x80x3. The head and RPV body are attached to each other, and to the canister, by means of the approximately twelve (12) head closure studs present on the reactor in service, which pass through canister lid and into upper flange of the RPV body. The canister provides containment shielding equivalent to DOT Industrial Package type 2, analyzed to withstand a 1 foot horizontal drop and a 1 foot drop with 2 feet of slap-down at either end. Ninety-nine point eight (99.8) percent of the radioactive material present is intrinsically contained within RPV activated metals themselves; remaining 0.2% is affixed to metal surfaces and is immobilized by grout or epoxy. A method for placing and sealing a PWR pressure within a containment vessel is described. The RPV is disconnected from external piping, controls, and the like, and the head is removed, as described and as shown generally in FIGS. 2-6. Highly radioactive portions of the internals are removed for separate containment and storage. Segmented internals, including particularly upper internal components, are placed inside the RPV body as described. Nominal 30 pcf low-density cellular concrete (LDCC) is placed inside the RPV body to seal and immobilize remaining and relocated internals. The RPV body is lifted over and lowered into position within the canister lower section, with a gap between the RPV and the canister interior. Nominal 70 pcf LDCC is poured into the gap to a sufficient depth to support the RPV after curing, and is allowed to cure. The lifting rig used to position the RPV is removed. Removed portions of the RPV nozzles are placed inside the RPV, atop an ALARA plate. RPV head closure guide studs (ref. 132 in FIG. 6) are installed in some of the RPV head attachment stud holes. The canister upper section is lifted and lowered into place over the guide studs, so that it rests upon the RPV head flange. RPV hold down studs are installed using remaining RPV head attachment stud holes. The canister upper and lower sections are welded together. Openings between the canister top plate and the RPV hold down and guide studs are sealed with metalizing spray. Nominal 70 pcf LDCC is pumped into remaining voids between the canister and the RPV body through peripheral fill ports opened in the top of the canister. Nominal 30 pcf LDCC is pumped into remaining voids inside the RPV body through center fill ports opened in the canister top plate. Fill and vent ports in the canister top plate are plugged and sealed. The RPV head is placed on top of the canister and the guide studs already in place. The guide studs are cut flush with the top of the RPV head flange. All LDCC is allowed to complete curing. The package is rigged for removal from the assembly location by the attachment of lugs and/or other structures to the canister exterior. The package is lifted and turned to a substantially horizontal position, secured to transport conveyance, and transported to a disposal site. Preferred embodiments of the various structures disclosed herein are fabricated from any materials having sufficient strength, durability, corrosion resistance, and radioactive shielding qualities to serve the purposes described for such structures. Suitable materials are known, and have been identified herein where appropriate; but any materials having suitable qualities will serve. While the invention has been described and illustrated in connection with preferred embodiments, many variations and modifications as will be evident to those skilled in this art may be made without departing from the spirit and scope of the invention, and the invention is thus not to be limited to the precise details of methodology or construction set forth above as such variations and modification are intended to be included within the scope of the invention.

052672743

claims

1. A method of determining the geological evolution of apatite grains contained within rock samples comprising obtaining a sufficiently pure quantity of representative apatite grains from a rock sample; forming at least one epoxy wafer containing said representative apatite grains for examination and polishing said epoxy wafer containing said representative apatite grains in order to expose internal planar surfaces of the apatite grains; chemically etching naturally occurring fission tracks and other crystallographic imperfections that intersect the polished internal planar surfaces of the said apatite grains with an acidic solution; selecting a first-set of apatite grains from among suitable candidate apatite grains for fission track age measurement; determining the density of naturally occurring fission tracks of said first-set apatite grains; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each first-set apatite grain; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each first-set apatite grain; selecting a second-set of apatite grains from among suitable candidate apatite grains for measurement of perceived track lengths of confined fission tracks; measuring the perceived track lengths of confined naturally occurring fission tracks within the second-set apatite grains; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each second-set apatite grain; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each second-set apatite grain; determining the concentration of .sup.238 U for the first-set apatite grains; determining the fission track ages of the first-set apatite grains; determining the chemical composition of first-set and second-set apatite grains; calculating the pooled fission track age and pooled distribution of perceived track lengths of fluorine-rich first-set and fluorine-rich second-set apatite grains; and calculating the pooled fission track age and pooled distribution of perceived track lengths of relatively non-fluorine-rich first-set and relatively non-fluorine-rich second-set apatite grains. spreading the representative apatite grains on a non-stick surface within an area of approximately one square centimeter defined by a form which is 1.5 millimeters deep and in contact with the non-stick surface; pouring a mix of epoxy resin and epoxy hardener over the sampling of representative apatite grains contained within the form; placing a petrographic microscope slide on top of the epoxy resin and applying a slight downward force to ensure that said slide will be attached to the epoxy resin; allowing the epoxy resin mix to harden for twenty four hours at room temperature thereby forming an epoxy wafer; detaching the resulting epoxy wafer from the non-stick surface while allowing the epoxy wafer to remain attached to the petrographic microscope slide; and polishing the planar surface of the resulting epoxy wafer opposite that attached to the petrographic slide to an extremely smooth finish thereby removing a portion of the epoxy wafer and a similar thickness of the apatite grains aligned with the planar surface being polished thereby exposing internal surfaces of the apatite grains. immersing the epoxy wafer and attached petrographic slide in an acidic solution whereby all naturally occurring fission tracks and other crystallographic imperfections exposed to the acidic solution will be chemically etched; removing the epoxy wafer and attached petrographic slide from the solution; washing the epoxy wafer and attached petrographic slide with distilled water; and drying the epoxy wafer and attached petrographic slide sufficiently to remove all fluid from the resulting etch pits. observing the etched apatite grains contained within the polished and etched surface of the epoxy wafer and identifying suitable candidate apatite grains for fission track age measurement which have their crystallographic c-axes oriented parallel to the polished and etched planar surface of the epoxy wafer; and selecting apatite grains from among the suitable candidate apatite grains possessing a relatively high fraction of etch pits that represent etched naturally occurring fission tracks in combination with a relatively large available etched surface area. viewing the first-set apatite grains through a magnifying device possessing a graticule grid of known dimensions and which is imposed upon viewed images; counting the number of etch figures resulting from the intersection of etch pits that represent etched naturally occurring fission tracks with the etched planar surface within an area of known dimensions defined by the graticule grid; and calculating the spontaneous fission track density according to the formula: EQU P.sub.S =N.sub.S /AREA where N.sub.S, in units of tracks, is the number of etch figures created by the intersection of etch pits that represent etched naturally occurring fission tracks with the etched planar surface of the first-set apatite grain within the area outlined by a portion of the graticule grid; and where AREA, in units of length squared, is the area of the surface of the first-set grain outlined by the graticule grid. viewing the first-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.1,Y.sub.1, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.2,Y.sub.2, of the point; calculating the length of the maximum diameter parallel to the crystallographic c-axis of each etch figure using the formula: EQU DPAR.sub.i =C sqrt ((X.sub.2 -X.sub.1).sup.2 +(Y.sub.2 -Y.sub.1).sup.2) where DPAR.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter parallel to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the first-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters parallel to the crystallographic c-axis for each first-set apatite grain studied by summing all values of DPAR.sub.i measured for each first-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. viewing the first-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.3,Y.sub.3, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.4,Y.sub.4, of the point; calculating the length of the maximum diameter perpendicular to the crystallographic c-axis of each etch figure using the formula: EQU DPER.sub.i =C sqrt ((X.sub.4 -X.sub.3).sup.2 +(Y.sub.4 -Y.sub.3).sup.2) where DPER.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter perpendicular to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the first-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters perpendicular to the crystallographic c-axis for each first-set apatite grain studied by summing all values of DPER.sub.i measured for each first-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. observing the etched apatite grains contained within the polished and etched surface of the epoxy wafer and identifying suitable candidate apatite grains that contain etched confined fission tracks and which have their crystallographic c-axes oriented parallel to the polished and etched planar surface of the epoxy wafer; and identifying as many as 200 confined fission tracks which are etched to their ends and which lie within approximately 10 degrees of parallel to the polished and etched planar surface of the apatite grains. viewing the second-set apatite grains under a binocular optical microscope having multiple illuminating light sources, and a projection tube by which a point source of light from a cursor apparatus attached to a digitizing tablet can be visually observed while looking through the microscope; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of each linear etched confined fission track, wholly contained within a second-set apatite grain, and electronically recording the coordinates, X.sub.5,Y.sub.5, of the point; placing the point source of the light from the cursor apparatus at precisely the opposite extreme of each linear etched confined fission track, wholly contained within a second-set apatite grain, and electronically recording the coordinates, X.sub.6,Y.sub.6, of the point; and calculating the perceived track length of each linear etched confined fission track, wholly contained within the second-set apatite grains, according to the formula: EQU TL=C sqrt((X.sub.6 -X.sub.5).sup.2 +(Y.sub.6 -Y.sub.5).sup.2) where TL, in units of length, is the perceived track length of a confined fission track in a second-set apatite grain; and where C, in units of length, is a scaling factor that converts the units of the digitizing tablet into units of length. viewing the second-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.1,Y.sub.1, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.2,Y.sub.2, of the point; calculating the length of the maximum diameter parallel to the crystallographic c-axis of each etch figure using the formula: EQU DPAR.sub.i =C sqrt ((X.sub.2 -X.sub.1).sup.2 +(Y.sub.2 -Y.sub.1).sup.2) where DPAR.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter parallel to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the second-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters parallel to the crystallographic c-axis for each second-set apatite grain studied by summing all values of DPAR.sub.i measured for each second-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. viewing the second-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.3,Y.sub.3, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.4,Y.sub.4, of the point; calculating the length of the maximum diameter perpendicular to the crystallographic c-axis of each etch figure using the formula: EQU DPER.sub.i =C sqrt ((X.sub.4 -X.sub.3).sup.2 +(Y.sub.4 -Y.sub.3).sup.2) where DPER.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter perpendicular to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the second-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters perpendicular to the crystallographic c-axis for each second-set apatite grain studied by summing all values of DPERi measured for each second-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. placing a muscovite mica detector in intimate contact with the etched planar surface of the epoxy wafer containing the first-set apatite grains; placing the epoxy wafer and muscovite mica detector in close proximity to the core of a nuclear reactor; placing a portion of uranium-doped glass in intimate contact with a muscovite mica detector in close proximity to the core of a nuclear reactor; irradiating the epoxy wafer and the uranium-doped glass and their respective muscovite mica masks with thermal neutrons thereby inducing fission of .sup.235 U in the first-set apatite grains within the epoxy wafer and the uranium-doped glass; removing the epoxy wafer, uranium-doped glass, and muscovite mica detectors from close proximity to the core of a nuclear reactor; chemically etching the induced fission tracks within the muscovite mica detectors; calculating the concentration of .sup.238 U for each first-set apatite grain according to the formula: EQU [.sup.238 U]=137.88 [.sup.235 U.sub.g ] (R.sub.g /R.sub.a) (P.sub.ia /P.sub.ig) where [.sup.238 U], in units of nuclei per length cubed, is the concentration of the uranium isotope .sup.238 U in a first-set apatite grain within the apatite volume of interest; where 137.88, in units of nuclei per nuclei, is a constant for all first-set apatite grains which represents the naturally occurring concentration ratio of the uranium isotopes .sup.238 U to .sup.235 U; where [.sup.235 U.sub.g ],in units of nuclei per length cubed, is the concentration of the uranium isotope .sup.235 U in the uranium-doped glass; where R.sub.g, in units of length, is the average distance travelled by a single fission fragment nucleus in the uranium-doped glass; where R.sub.a, in units of length, is the average distance travelled by a single fission fragment nucleus in the first-set apatite grain; where P.sub.ia, in units of tracks per length squared, is the surface density of induced fission track etch pits that cross the etched planar surface of the detector within the area of the detector outlined by the graticule grid that was in intimate contact with the previously studied area of the first-set apatite grain; and where P.sub.ig, in units of tracks per length squared, is the surface density of induced fission track etch pits that cross the etched planar surface of the detector that was in intimate contact with the uranium-doped glass. calculating the fission track age for each first-set apatite grain using the formula: EQU T=(1/l.sub.D) ln((l.sub.D /l.sub.F)([FT]/[.sup.238 U])+1) where T, in units of millions of years, is the fission track age for the first-set apatite grain; where l.sub.D, in units of nuclei per million years, is the total decay constant for .sup.238 U; where l.sub.F, in units of nuclei per million years, is the fission decay constant for .sup.238 U; where [FT], in units of tracks per length cubed, is the number of naturally occurring fission tracks, resulting from the spontaneous fission decay of .sup.238 U, per unit volume in a volume of interest in the first-set apatite; and where [.sup.238 U], in units of nuclei per length cubed, is the concentration of the uranium isotope .sup.238 U in the first-set apatite grain within the apatite volume of interest. plotting the individual apatite grain ages of the first-set apatite grains as a function of the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis; plotting the individual track lengths of the second-set apatite grains as a function of the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis; grouping each of the first-set apatite grains and second-set apatite grains into either a group which is predominantly composed of fluorine-rich apatite or a group which is predominantly composed of relatively non-fluorine-rich apatite by determining whether the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis on the planar surface of the apatite grain is less than or equal to a length of 2 micrometers, in the case of fluorine-rich apatite, or greater than 2 micrometers, in the case of relatively non-fluorine-rich apatite. calculating the fluorine concentration or [F] for first-set and second-set apatite grains according to the following formula: EQU [F]=4.6748-1.3106 DPAR+0.041759 DPAR.sup.2 where [F], in units of weight percent, is the fluorine concentration in the first-set or second-set apatite grain being studied; and where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied. calculating the chlorine concentration or [Cl] for first-set and second-set apatite grains according to the following formula: EQU [Cl]=-0.31045-0.053515 DPAR+0.26067 DPAR.sup.2 where [Cl], in units of weight percent, is the chlorine concentration in the first-set or second-set apatite grain being studied; and where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied. calculating the water concentration or [H2O] for first-set and second-set apatite grains according to the following formula: EQU [H.sub.2 O]=-0.048074+0.28092 DPAR where [H2O], in units of weight percent, is the water concentration in the first-set or second-set apatite grain being studied; and where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied. obtaining a sufficiently pure quantity of representative apatite grains from a rock sample; forming at least one epoxy wafer containing said representative apatite grains for examination and polishing said epoxy wafer containing said representative apatite grains in order to expose internal planar surfaces of the apatite grains; chemically etching naturally occurring fission tracks and other crystallographic imperfections that intersect the polished internal planar surfaces of the said apatite grains with an acidic solution; selecting a first-set of apatite grains from among suitable candidate apatite grains; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each first-set apatite grain; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each first-set apatite grain; selecting a second-set of apatite grains from among suitable candidate apatite grains; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each second-set apatite grain; measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each second-set apatite grain; and determining the chemical composition of first-set and second-set apatite grains. spreading the representative apatite grains on a non-stick surface within an area of approximately one square centimeter defined by a form which is 1.5 millimeters deep and in contact with the non-stick surface; pouring a mix of epoxy resin and epoxy hardener over the sampling of representative apatite grains contained within the form; placing a petrographic microscope slide on top of the epoxy resin and applying a slight downward force to ensure that said slide will be attached to the epoxy resin; allowing the epoxy resin mix to harden for twenty four hours at room temperature thereby forming an epoxy wafer; detaching the resulting epoxy wafer from the non-stick surface while allowing the epoxy wafer to remain attached to the petrographic microscope slide; and polishing the planar surface of the resulting epoxy wafer opposite that attached to the petrographic slide to an extremely smooth finish thereby removing a portion of the epoxy wafer and a similar thickness of the apatite grains aligned with the planar surface being polished thereby exposing internal surfaces of the apatite grains. immersing the epoxy wafer and attached petrographic slide in an acidic solution whereby all naturally occurring fission tracks and other crystallographic imperfections exposed to the acidic solution will be chemically etched; removing the epoxy wafer and attached petrographic slide from the solution; washing the epoxy wafer and attached petrographic slide with distilled water; and drying the epoxy wafer and attached petrographic slide sufficiently to remove all fluid from the resulting etch pits. observing the etched apatite grains contained within the polished and etched surface of the epoxy wafer and identifying suitable candidate apatite grains which have their crystallographic c-axes oriented parallel to the polished and etched planar surface of the epoxy wafer; and selecting apatite grains from among the suitable candidate apatite grains possessing etch figures on their polished and etched planar surfaces. viewing the first-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.1,Y.sub.1, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.2,Y.sub.2, of the point; calculating the length of the maximum diameter parallel to the crystallographic c-axis of each etch figure using the formula: EQU DPAR.sub.i =C sqrt ((X.sub.2 -X.sub.1).sup.2 +(Y.sub.2 -Y.sub.1).sup.2) where DPAR.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter parallel to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the first-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters parallel to the crystallographic c-axis for each first-set apatite grain studied by summing all values of DPAR.sub.i measured for each first-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. viewing the first-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.3,Y.sub.3, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.4,Y.sub.4, of the point; calculating the length of the maximum diameter perpendicular to the crystallographic c-axis of each etch figure using the formula: EQU DPER.sub.i =C sqrt ((X.sub.4 -X.sub.3).sup.2 +(Y.sub.4 -Y.sub.3).sup.2) where DPER.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter perpendicular to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the first-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters perpendicular to the crystallographic c-axis for each first-set apatite grain studied by summing all values of DPER.sub.i measured for each first-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. observing the etched apatite grains contained within the polished and etched surface of the epoxy wafer and identifying suitable candidate apatite grains which have their crystallographic c-axes oriented parallel to the polished and etched planar surface of the epoxy wafer; and identifying suitable candidate apatite grains that contain confined fission tracks which are etched to their ends and which lie within approximately 10 degrees of parallel to the polished and etched planar surface of the apatite grains. viewing the second-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.1,Y.sub.1, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.2,Y.sub.2, of the point; calculating the length of the maximum diameter parallel to the crystallographic c-axis of each etch figure using the formula: EQU DPAR.sub.i =C sqrt ((X.sub.2 -X.sub.1).sup.2 +(Y.sub.2 -Y.sub.1).sup.2) where DPAR.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter parallel to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the second-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters parallel to the crystallographic c-axis for each second-set apatite grain studied by summing all values of DPAR.sub.i measured for each second-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. viewing the second-set apatite grains through a magnifying device; placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.3,Y.sub.3, of the point; placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.4,Y.sub.4, of the point; calculating the length of the maximum diameter perpendicular to the crystallographic c-axis of each etch figure using the formula: EQU DPER.sub.i =C sqrt ((X.sub.4 -X.sub.3).sup.2 +(Y.sub.4 -Y.sub.3).sup.2) where DPER.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter perpendicular to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the second-set apatite grain being studied; and where C is a scaling factor that converts the units of the digitizing tablet into units of length; and calculating the arithmetic mean of the etch figure diameters perpendicular to the crystallographic c-axis for each second-set apatite grain studied by summing all values of DPER.sub.i measured for each second-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured. grouping each of the first-set apatite grains and second-set apatite grains into either a group which is predominantly composed of fluorine-rich apatite or a group which is predominantly composed of relatively non-fluorine-rich apatite by determining whether the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis on the planar surface of the apatite grain is less than or equal to a length of 2 micrometers, in the case of fluorine-rich apatite, or greater than 2 micrometers, in the case of relatively non-fluorine-rich apatite. calculating the fluorine concentration or [F] for first-set and second-set apatite grains according to the following formula EQU [F]=4.6748-1.3106 DPAR+0.041759 DPAR.sup.2 where [F], in units of Weight percent, is the fluorine concentration in the first-set or second-set apatite grain being studied; and where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied. calculating the chlorine concentration or [Cl] for first-set and second-set apatite grains according to the following formula EQU [Cl]=-0.31045-0.053515 DPAR+0.26067 DPAR.sup.2 where [Cl], in units of weight percent, is the chlorine concentration in the first-set or second-set apatite grain being studied; and where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied. calculating the water concentration or [H2O] for first-set and second-set apatite grains according to the following formula EQU [H.sub.2 O]=-0.048074+0.28092 DPAR where [H2O], in units of weight percent, is the water concentration in the first-set or second-set apatite grain being studied; and where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied. 2. A method according to claim 1 including forming at least one epoxy wafer containing said representative apatite grains for examination and polishing said epoxy wafer containing said representative apatite grains in order to expose internal planar surfaces of the apatite grains comprises 3. A method according to claim 1 including chemically etching naturally occurring fission tracks and other crystallographic imperfections that intersect the polished internal planar surfaces of the said apatite grains with an acidic solution comprises 4. A method according to claim 3 including said epoxy wafer and attached petrographic slide are immersed in a nitric acid solution of 5.5 Molar strength at 21 degrees Celsius for 20 seconds while being swirled vigorously within the solution. 5. A method according to claim 1 including selecting a first-set of apatite grains from among suitable candidate apatite grains for fission track age measurement comprises 6. A method according to claim 1 including determining the density of naturally occurring fission tracks of said first-set apatite grains comprises 7. A method according to claim 1 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each first-set apatite grain comprises 8. A method according to claim 1 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each first-set apatite grain comprises 9. A method according to claim 1 including selecting a second-set of apatite grains from among suitable candidate apatite grains for measurement of perceived track lengths of confined fission tracks comprises 10. A method according to claim 1 including measuring the perceived track lengths of confined naturally occurring fission tracks within the second-set apatite grains comprises 11. A method according to claim 1 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each second-set apatite grain comprises 12. A method according to claim 1 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each second-set apatite grain comprises 13. A method according to claim 1 including the determination of the concentration of .sup.238 U for first-set apatite grains comprises 14. A method according to claim 1 including determining the fission track age of said first-set apatite grains comprises 15. A method according to claim 1 including determining the chemical composition of the first-set and second-set apatite grains comprises 16. A method according to claim 1 including determining the chemical composition of the first-set and second-set apatite grains comprises 17. A method according to claim 1 including determining the chemical composition of the first-set and second-set apatite grains comprises 18. A method according to claim 1 including determining the chemical composition of the first-set and second-set apatite grains comprises 19. A method of determining the chemical composition of apatite grains contained within rock samples comprising 20. A method according to claim 19 including forming at least one epoxy wafer containing said representative apatite grains for examination and polishing said epoxy wafer containing said representative apatite grains in order to expose internal planar surfaces of the apatite grains comprises 21. A method according to claim 19 including chemically etching naturally occurring fission tracks and other crystallographic imperfections that intersect the polished internal planar surfaces of the said apatite grains with an acidic solution comprises 22. A method according to claim 21 including said epoxy wafer and attached petrographic slide are immersed in a nitric acid solution of 5.5 Molar strength at 21 degrees Celsius for 20 seconds while being swirled vigorously within the solution. 23. A method according to claim 19 including selecting a first-set of apatite grains from among suitable candidate apatite grains comprises 24. A method according to claim 19 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each first-set apatite grain comprises 25. A method according to claim 19 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each first-set apatite grain comprises 26. A method according to claim 19 including selecting a second-set of apatite grains from among suitable candidate apatite grains comprises 27. A method according to claim 19 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each second-set apatite grain comprises 28. A method according to claim 19 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each second-set apatite grain comprises 29. A method according to claim 19 including determining the chemical composition of the first-set and second-set apatite grains comprises 30. A method according to claim 19 including determining the chemical composition of the first-set and second-set apatite grains comprises 31. A method according to claim 19 including determining the chemical composition of the first-set and second-set apatite grains comprises 32. A method according to claim 19 including determining the chemical composition of the first-set and second-set apatite grains comprises

abstract

A lens system for a plurality of charged particle beams comprises a lens body with a first pole piece, a second pole piece and a plurality of lens openings for the respective charged particle beams; a common excitation coil arranged around the plurality of lens openings for providing a respective first magnetic flux to the lens openings; and a compensation coil arranged between the lens openings for providing a respective second magnetic flux to at least some of the lens openings so as to compensate for an asymmetry of the first magnetic flux.

040627241

abstract

A nuclear reactor construction comprising a fast reactor core submerged in a pool of liquid sodium in a primary vessel. A collecting tray for core debris is submerged in the pool below the core. The collecting tray comprises a base plate constituting a plane tube sheet while the wall of the tray constitutes an annular tube sheet. Coolant conducting tubes are end received in the tube sheets. An internal skirt of the primary vessel overlaps the wall of the tray.

summary

abstract

A charged particle beam irradiation apparatus includes: an irradiation section configured to irradiate an irradiated body with a charged particle beam; a multi-leaf collimator configured to set an irradiation range of the charged particle beam which is irradiated from the irradiation section; an imaging section that is provided so as to be able to advance and retreat with respect to an irradiation axis of the charged particle beam which is irradiated from the irradiation section, between the irradiation section and the multi-leaf collimator, and directly images an opening portion of the multi-leaf collimator; and a drive section configured to move the imaging section between an imaging position corresponding to an irradiation area which includes the irradiation axis of the charged particle beam and a retreated position away from the irradiation area.

abstract

The kind of a particle is determined by pressing a hard atomic force microscope stylus having a spring constant equal to or larger than 300 N/m onto a particle to be removed and detecting bending quantity relative to a press force and a kind of a stylus used for removing the particle is changed in accordance with the kind of the particle.

claims

1. A method of controlling the criticality of a nuclear fuel cycle facility, comprising:producing a reactor fuel by adding from 305 to 915 ppm of gadolinia to a uranium dioxide powder with a uranium enrichment of greater than 5% and 10% or less by weight;controlling an effective neutron multiplication factor of a uranium dioxide system containing the uranium dioxide powder to which gadolina is added to be less than or equal to a maximum of an effective neutron multiplication factor of a uranium dioxide system with a uranium enrichment of 5% by weight;ensuring a control of a mass subcriticality by:not handling any fuel having a mass exceeding a predetermined value relating to criticality safety design;not handling any fuel having a size exceeding a size of a predetermined value relating to criticality safety design; andmaintaining the fuel under complete submergence conditions such that spaces between particles of the uranium dioxide powder with a uranium enrichment are filled with water and the particles are surrounded by water;whereinthe control of the effective neutron multiplication factor is obtained by adding an amount of gadolinia to the enriched uranium dioxide powder such that the maximum of the effective neutron multiplication factor of the enriched uranium dioxide powder is less than or equal to an effective neutron multiplication factor of uranium dioxide powder with a uranium enrichment of 5% by weight, andthe amount of gadolinia added to the uranium dioxide powder with a uranium enrichment of greater than 5% by weight is proportional to the uranium enrichment thereof that exceeds 5% and a constant of the proportion is determined by dividing the amount of gadolinia added to a uranium dioxide powder with a uranium enrichment of 10% by weight by five.

abstract

There are provided a control rod holding unit 16 for releasably holding a control rod 7 which is loaded in a reactor vessel 1, and fuel support/control rod guide tube holding unit 17 for releasably holding a fuel support 8 which supports a bottom end of a fuel assembly 10 and a control rod guide tube 6 on which the fuel support 8 is placed at top end. The control rod holding unit 16 and the fuel support/control rod guide tube holding unit 17 are fitted to a main body frame 26 which can be hoisted down inside the reactor vessel 1. Accordingly, there can be provided a reactor-internal equipment handling apparatus and method which are capable of reducing a term of work which is required for operations to load/unload the control rods, the fuel supports, and the control rod guide tubes.

abstract

Examples of a system for generating and compressing magnetized plasma are disclosed. The system comprises a plasma generator with a first closed end and an outlet, and a flux conserving chamber that is in tight fluid communication with the outlet of the plasma generator such that the generated plasma is injected into an inner cavity of the flux conserving chamber. An elongated central axial shaft is also provided such that the central shaft extends through the outlet of the plasma generator into the flux conserver. The end of the central shaft in connected to the flux conserver. A power source that comprises a formation power circuit and a shaft power circuit is provided to provide a formation power pulse to the plasma generator to generate magnetized plasma, and a shaft power pulse to the central axial shaft to generate a toroidal magnetic field into the plasma generator and the flux conserving chamber. The duration of the shaft power pulse is longer than the duration of the formation power pulse to maintain plasma q-profile at a pre-determined range. During plasma compression the shaft power pulse is increased to match the raise of the plasma poloidal field due to the compression and thus maintain the q-profile of the plasma.

051820510

description

DESCRIPTION OF THE PREFERRED EMBODIMENTS The particles which can be made radioactive of the present invention are particles which contain a target element which is embedded in a sintered ceramic matrix. The radioactive isotope particles of the present invention are ceramic particles that emit gamma rays to allow their detection by instruments. The particles are made of sintered ceramic components and an element which has been bombarded with neutrons to become a gamma ray-emitting isotope. The ceramic components are common oxides, normally silica or alumina, but other oxides used in the ceramic art may be used. In the mixtures comprising predominantly silica and alumina, a range of mixtures from pure alumina to predominantly silica can be used. Mixed crystalline materials of silica and alumina such as mullite may be used. The ceramic components are first finely divided or powdered and mixed with the target element. By this technique, the target element can be uniformly distributed through the particle. The structure of the powdered starting materials may still be present in the finished particles, but the particles will have an effective amount of strength resulting from bonding of the original powder of ceramic components which has occurred during the sintering process. Other components may be added to aid sintering and to substantially lower the sintering temperature, such components being well known in the ceramics art. The sintered matrix of the particles should have sufficient strength to resist breaking when the particles are pumped in a stream of fluid. The amount of strength needed will depend upon their application. If the particles are to be pumped at high flow rates in a slurry, such as in hydraulic fracturing treatments in wells, the particles should be strong enough to prevent breaking at high stress, substantially like the ceramic particles now provided as proppant for this application. For added strength, particles having an alumina content above 30 percent by weight are preferred. Also, sintered particles made from very finely divided powder are higher in strength. Powder less than 25 microns in size is preferred. If the radioactive particles are to be incorporated into a flow stream moving at a low speed and without abrasive conditions, much lower strength ceramic particles are acceptable, although high strength will not be a disadvantage. In addition to strength, density and size may be important properties of the ceramic particles to be considered in each application. The target element added to emit gamma rays is embedded in the matrix of the ceramic materials before sintering. The element is selected based upon several variables. One of the important characteristics is the half-life of the radioactive isotope produced by neutron bombardment. This property is selected based on the measurements to be made and does not limit this invention. Half-lives of from about two days to about 250 days are commonly used. The energies of the gamma rays emitted by the isotope are also an important factor in selecting the element. This is especially true when two or more radioactive isotopes are to be used in the same flow stream, when it is desirable that the energy spectra of the different isotopes not excessively overlap. It is preferred that the energy spectrum of the gamma rays of the different isotopes not overlap such that the intensity of the gamma rays from each element can be more accurately measured. Thereby, the concentration of each individual isotope can be measured by spectral analysis of the gamma rays. The cost and availability of the target element embedded in the ceramic particles is one consideration in the selection of which element to use in a particle. Target elements suitable for use in the particles of this invention include gold, iodine, iridium, scandium, antimony, silver, hafnium, zirconium, rubidium, chromium, iron, strontium, cobalt, and zinc. Preferred target elements are antimony, iridium, scandium, silver, and hafnium. Most preferred are iridium and scandium. The target element may be present in its elemental form or as a compound. Compounds of elements useful in this invention are commonly salts or oxides. Iridium oxide is available as a black powder known as "iridium black." Hafnium oxide is available in pure form. Antimony bromide is available is very pure form as crystals. Other compounds of the element may be used, but oxides and salts are readily available. The compound should be stable at the high temperature of processing of the ceramic particle, such that sublimation does not deplete the particles of the compound. The temperature of sintering the particles will normally be above the melting point of the compound of the element. The concentration of the element in the ceramic particle will depend on the application of the particles, but an effective amount will be less than 5 per cent of the weight of the particle, preferably less than 1 per cent and most preferably less than 0.5 per cent by weight. Sizes of the particles will normally range from about 8 mesh to about 400 mesh. Particles of a wide range of sizes can be separated into desired sizes by sieving or other particle size separation techniques. Specific gravity of the particles will range from about 0.5 gm/cc to about 3.9 gm/cc. Particles of different densities can be made and separated by density using well known particle separation techniques. Radioactive ceramic particles may be manufactured by methods known in the ceramic industry for manufacturing proppants for use in hydraulic fracturing of wells or for manufacturing synthetic gravel for use in gravel packing of wells. Such ceramic particles for proppants are manufactured and used for their strength, their density and their sphericity. U.S. Pat. 4,668,645 discloses a particle for use as a proppant and a method of manufacturing such particles. U.S. Pat. No. 4,068,718 discloses the use of high strength and high density bauxite-containing particles for use as a proppant in wells and describes the methods of manufacture of such particles. The two aforesaid U.S. patents are incorporated herein for all purposes. Other methods for manufacturing sintered ceramic particles from powder, employing a variety of grinding, mixing, pelletizing and sintering techniques can be used. Ceramic particles of various densities and strengths can be made by mixtures of the oxides of aluminum, silicon, iron, magnesium and other minerals. Ceramic particles made for use as proppants or in gravel packing are manufactured by grinding the ceramic components to fine particle sizes, preferably less than 25 micron particle size, forming a paste of the finely ground material, forming the paste into rounded particles with pelletizing equipment and then sintering the particles. Such particles are sold by Norton Alcoa Proppants of Dallas, TX and by Carbo Ceramics Company of Dallas, TX. We have discovered that the ceramic components of such particles can be mixed with an element which, when bombarded with neutrons, forms a gamma ray emitting isotope, to produce a radioactive particle which has essentially the properties of the ceramic particle not containing the element. Such particles have high strength and resistance to crushing, and can be pumped into a variety of fluid streams without loss of radioactive material to the fluid stream and the conduits for the stream. MACROLITE.RTM. ceramic spheres sold by 3M Company of St. Paul, MN are made from a ceramic powder to have void spaces and specific gravities as low as about 0.58 gm/cc. The particles of this invention can be manufactured by incorporating a target element into the ceramic materials of MACROLITE.RTM. ceramic spheres before they are formed. It is advantageous to use elements which are not radioactive during formation of the particles, so that health hazards from radioactive materials are avoided during manufacture of the particles. This is an important feature of our invention. After the particles to be made radioactive, i.e. the precursor radioactive particles, are formed and sintered, the particles may be injected into a flow system or the particles may be transported to a nuclear reactor and radiated with neutrons such that the element present forms a radioactive isotope of that element. The equation given below describes the level of activity resulting from neutron radiation: EQU A=N.sub.f * (g/M)* X.sub.sect * h * N.sub.L * (1-e.sup.-(0.693/t1/2)) * t/3.7.times.10.sup.7 where: A.times.Activity in millicuries PA1 N.sub.L .times.6.022.times.10.sup.23 PA1 h=Isotopio Abundanoe PA1 X.sub.sect =Neutron Capture Cross Section PA1 g=Target element mass in grams PA1 t.sub.1/2 =Half life of produced nuclide in seconds PA1 N.sub.f =Neutron flux (neutron cm sec PA1 M=Target nuclide atomic weight in grams PA1 t=Neutron bombardment time in seconds. Activity produced is directly proportional to neutron bombardment time, neutron flux and target element mass. Once an element has been selected for its half-life of radioactivity and its desirable gamma ray spectrum, the concentration of the element needed to seed the particles and the neutron bombardment time can be calculated for a certain location in a certain nuclear reactor having a known neutron flux rate at different locations. The costs of the element and the neutron irradiation are selected to minimize the total cost of producing particles having an effective level of radioactivity. The selected amount of the target element is added to a suitable amount of ceramic powder which is to be formed into particles, such that the amount of powder to be irradiated, stored and injected into a stream is convenient for the irradiation facility, storage facilities and pumping equipment available for injecting the radioactive powder. Twenty millicuries of radioactivity is a common amount of radioactivity to transport in one batch. Therefore, this amount of radioactivity will be used as an example. Other amounts, for example 40 millicuries, are often used and the same principles are applicable. The equation above shows, for example, that if 20 millicuries of radioactivity from iridium-192 is to be produced, and the nuclear reactor produces a flux in the cans to be used in the reactor of 5=10.sup.12 neutrons cm.sup.-2 sec.sup.-1, 11.5 milligrams of iridium is needed for a bombardment time of 96 hours. This amount of iridium in the form of iridium black is added to a measured amount of ceramic powder, thoroughly mixed and blended, and formed into particles which are then sintered in accord with known techniques for producing sintered particles. The equation shows that if the amount of target element is doubled the amount of bombardment time can be halved. Therefore, the cost of producing particles having differing amounts of target elements can readily be determined, depending on the cost of the element and the cost of irradiation time. For many elements to be made radioactive, the lowest cost of radioactivity will be obtained with the largest amount of the target element in the ceramic particles. Then the highest limiting concentration of the element is determined by that concentration which changes the physical properties of strength or specific gravity of the ceramic particles into an unacceptable range of the property. Tests should be performed to determine the maximum acceptable concentration of target element by mixing various concentrations of element and ceramic components, sintering the particles and measuring the desired property. Specific gravity of particles may be measured by well known methods. Strength may be measured by crush tests of packed beds of particles or by individual particles strength tests which are well known for testing proppant particles. For some applications, only a small amount of particles is needed to contain 20 millicuries of radioactivity. But, it is possible to vary the concentration of target element in the ceramic over a wide range of concentrations. The lowest practical level of concentration will normally be determined by the volume available in the reactor used for irradiation or by the pump used to meter the particles into the stream where they will be used. For particles to be used in hydraulic fracturing, 20 millicuries of activity will preferably be contained in a volume of particles in the range from about 5 milliliters to about 100 milliliters of particles. Much larger amounts of particles could be used to contain the radioactivity, but the minimum concentration of target element in the ceramic will usually be determined by the pumping apparatus used to add the particles to a stream and the volume limitations of the reactor used for irradiation of the particles. Small volumes of particles can be used when accurate means are available for metering small amounts of particles into a stream. Radioactivity levels in the range from about 0.02 to about 20.0 millicuries per milliliter of particles are suitable. Preferably, the radioactivity level is in the range from about 0.2 to about 4.0 millicuries per milliliter of particles. After the particles are radiated with neutrons, their manufacture is complete. The particles must then be handled as radioactive sources. Well known techniques are used for protecting personnel from exposure to gamma rays emitted from the particles. Radioactive particles are added to a fluid which is being pumped into a well or are added to a fluid passing through surface piping or equipment for other applications by first mixing the radioactive particles with fluid to form a concentrated slurry. The liquid of the slurry may be viscosified by polymers. The slurry of radioactive particles is stored in a small closed radioactive materials reservoir. The reservoir may contain an agitator to keep the radioactive particles in suspension. The slurry is pumped from the reservoir into the low-pressure section of the flow stream to be traced With a low pressure pump such as a peristaltic pump. A high-pressure positive displacement pump can be used when the particles are injected into a high-pressure stream. The concentration of radioactive particles in the concentrated slurry or radioactive particles is usually in the range of about 10 grams to about 1000 grams per gallon of slurry. For most applications in wells, the slurry of radioactive particles is pumped out of the reservoir and into the stream at a rate such that 20 millicuries is used to trace from about 10,000 to about 100,000 pounds of solid particles or about 10,000 to about 100,000 gallons of fluid The activity level may vary in the range from about 0.1 to about 10 millicuries per thousand gallons of fluid or thousand pounds of solids. This amount of radioactivity is preferably contained in a volume of particles from about 5 cc to about 100 cc, but much larger volumes of particles may be used with a suitable pump for pumping the slurry of radioactive particles. If this amount of radioactivity is contained in a larger volume of particles, the radioactive particles will either contain a proportionately lower concentration of target element or the particles will be irradiated with neutrons for a proportionately smaller time. Preferably, the radioactive particles have about the same size and specific gravity as the non-radioactive particles in the flow stream when applied to tracing the particles in hydraulic fracturing and gravel packing operations. The particles should be small enough to produce low settling rates when used in cement slurries. For other types of fluids, the size and specific gravity will be selected to accomplish the purpose of the tracing application. For example, particles less than a certain size may be sieved from a mixture of sizes and added to a flow stream to determine the size of constrictions in the flow stream. Other applications dependent on size and specific gravity will be obvious to users of the particles. Specific gravity of the particles can be varied to be compatible with the application. The ceramic particles produced for hydraulic fracturing of wells vary in specific gravity from about 2.6 gm/cc to about 3.8 gm/cc. The density of these particles will not be significantly changed when the element to be made radioactive is embedded into the particles. Preferably, radioactive particles will be made to have approximately the same density as the non-radioactive particles with which they are used. Particles sold by 3M Company under the trademark MACROLITE.RTM. may have a specific gravity as low as 0.58 gm/cc. Again, preferably the radioactive particles will be made to approximately match the density of the non-radioactive particles. Strength of the particles will also vary with specific gravity, but even the relatively low strength of these low specific gravity particles will be adequate for gravel packing applications. Other applications not requiring high-strength can also use the low specific gravity particles. To avoid breaking and abrasion of particles, which can lead to loss of radioactivity from the particles, strength is preferably as high as consistent with other properties of the particles. After the radioactive particles are pumped into a well and out of the casing of the well so that they are no longer in the wellbore, a logging instrument is lowered into the well which is capable of detecting the gamma rays emitted by the isotope of the element. The gamma rays are capable of penetrating at least several inches of the earth surrounding the well and of penetrating the casing in the well. The gamma rays specific to the isotope of the element may be detected by performing an analysis of the energy of the gamma rays detected by the logging tool. A spectrum of energy of gamma rays characteristic of each radioactive element present is obtained. Techniques are used for determining, based on differing attenuation by Compton scattering of gamma rays having differing energy levels, the amount of gamma radiation coming from inside the wellbore, which would result from radioactive material lost from the particles during flow down the wellbore. Ceramic particles containing different target elements may be used at the same time or at different times in the pumping operation, may have different specific gravity or may have different size. The locations of the particles having different target elements are then determined with the gamma ray detector. In gravel packing operations, the radioactive particles may be inside the casing and outside a screen or other type filter in the wellbore. In this application, also, the logging tool is surrounded by the radioactive particles. In a flow stream or other surface apparatus, the gamma ray detection instrument is located in the vicinity of the radioactive particles to detect the gamma rays. Particle location of particles containing different target elements, which may also have different sizes and specific gravities, can be determined by spectral analysis of the gamma rays. The applications described above assumed that the particles had been irradiated by neutrons before injection into the well or flow stream. It should be understood that the precursor particles, obtained after sintering and before irradiation with neutrons, can be used in all applications if a neutron source is applied to the particles after they are in the flow stream or well. The particles of this invention will be stable to their environment of use, and can be irradiated or re-irradiated long after the time they are injected into a flow stream or well. EXAMPLE Ceramic particles containing iridium were manufactured. The procedures normally used for manufacturing a ceramic proppant particle containing primarily alumina and silica and smaller amounts of other oxide minerals were used. The ceramic materials were finely ground. About 20 grams of iridium black, available from Aldrich Chemical Company, was thoroughly mixed with 30,418 grams of the ceramic powder. The powdered mixture was then formed into a paste containing chemical binders. The paste was formed into approximately spherical particles. The ceramic materials are said to be "green" at this stage. The green ceramic particles were then sintered by firing in an oven at a temperature in the range of about 1400.degree. to 1500.degree. C. The particles containing the iridium were essentially the same density and crush resistance as the particles of high strength ceramic material without the iridium. The size range of the particles was from about 20 mesh to about 40 mesh. A portion of the particles containing iridium was then placed in a nuclear reactor for a period of 42 hours. A volume of 15 milliliters of particles was irradiated at a neutron flus of 9=10.sup.12 neutrons cm.sup.-2 sec.sup.-1. At the end of irradiation, the activity of the particles was measured to be about 20 millicuries. The activity calculated form the above equation was 20.7 millicuries. The radioactive particles was transported to a well where hydraulic fracturing operations was performed. Fracturing fluid is pumped down the casing of the well and through perforations. Sand in the size range 20-40 mesh is used as proppant. Radioactive ceramic particles manufactured according to the methods described herein are added to the fluid along with the sand at an appropriate time. The ceramic radioactive particles have about the density of sand and are 20-40 mesh size. After these fracturing operations are complete, the well is logged with the TRACERSCAN system. Results of the log show that gamma ray radiation from iridium is present only near the perforations. The very low level of radioactivity in the wellbore above the perforations shows that loss of radioactive iridium material from the particles during the operations is negligible. The invention has been described with reference to its preferred embodiments. Those of ordinary skill in the art may, upon reading this disclosure, appreciate changes or modifications which do not depart from the scope and spirity of the invention as described above or claimed hereafter.

description

This application is a continuation of U.S. patent application Ser. No. 10/620,101, filed Jul. 14, 2003, now abandoned which is a continuation of application Ser. No. 10/012,193, filed Dec. 5, 2001, now abandoned which is a continuation-in-part of prior U.S. patent application Ser. No. 09/921,363, filed Aug. 2, 2001 (now U.S. Pat. No. 6,546,066), priority from the filing date of which is hereby claimed under 35 U.S.C. § 120. This application also claims the benefit of U.S. Provisional Patent Application No. 60/311,328 filed Aug. 9, 2001, under 35 U.S.C. § 119. This invention relates to reactor vessel closure head assemblies and, in particular, to an integrated head assembly for a pressurized light water reactor. In a typical pressurized water reactor (PWR) power plant, various mechanical components and systems are installed on the reactor vessel closure head. These mechanical components and systems include, for example, a control rod drive mechanism (CRDM) cooling system, a reactor vessel closure head lift rig, CRDM seismic restraints, and a CRDM missile shield. Each of these components is typically designed and installed as a permanent fixture to perform designated functions during plant operation. However, during refueling of the reactor these components have to be disassembled in order to remove the reactor vessel closure head from the reactor vessel. These components are stored in designated storage areas, generally inside the reactor containment. Typically, in a PWR plant, a series of steps are followed before the reactor vessel closure head is removed from the reactor vessel. The operational steps that are performed prior to detensioning the reactor vessel closure head studs include some or all of the following: Remove and store heavy concrete missile shields. Remove and store the CRDM cooling ducts. Remove the seismic restraints. Disconnect and store the CRDM power and rod position indicator cables. Install the reactor head lifting rig tripod. Remove cable trays and cables running from the reactor head to the operating deck or walls. Disconnect heated junction thermocouples, nuclear steam supply system instrumentation, monitoring system cables, and reactor head vent lines. Install temporary lead shield blankets around the vessel closure head area. The procedure also requires that the nuts and washers be removed from the reactor vessel closure head and placed in storage racks during preparation for refueling. The storage racks are then removed from the refueling cavity and stored at convenient locations inside containment prior to reactor vessel closure head removal and refueling cavity flooding. The above steps are then reversed while reinstalling the reactor vessel closure head and the related reactor systems. Each of these steps contributes significantly to the total cost associated with refueling the reactor. The total costs include costs associated with personnel man-hours required to perform the refueling, power plant down time and consequent loss of electricity production, radiation exposure to personnel, and potential human errors. In addition, the various components that must be removed for refueling activities require a large amount of the limited storage space available inside containment and raise the risk of inadvertent contamination of work and storage areas. Concepts and designs for integrating some of the reactor vessel closure head systems into a modular integrated head design have been proposed. For example, in U.S. Pat. No. 4,678,623 to Malandra et al., a modular head assembly is disclosed wherein vertical lift rods are attached to the reactor vessel lifting lugs, and a missile shield, seismic support platform, CRDM cooling system, and lift rig are supported by the lift rods above the reactor vessel closure head. Because most or all of the modular head assembly taught by Malandra et al. is supported by the lift rods, however, very large loads are concentrated at the clevis connection at the reactor vessel closure head lifting lugs, which may cause damage to the lifting lugs and/or the body of the reactor vessel closure head. In addition, very heavy components such as the missile shield and the fans are supported at the distal ends of three relatively long lift rods, resulting in an unstable structure that may subject the lift rods to undesirable compressive, bending and torsional stresses. Malandra et al. also does not provide a structure for putting a shroud around the CRDMs. In U.S. Pat. No. 4,830,814, Altman discloses an integrated head package having a missile shield that is slidably mounted near the distal end of three lift rods connecting to the reactor vessel closure head lifting lugs. A shroud is shown disposed about the CRDMs. Similar to the apparatus disclosed by Malandra et al., however, the heavy missile shield and lifting rig are installed at the distal end of three elongate lift rods that are connected at their proximal end to the reactor vessel closure head lifting lugs. The Altman apparatus, therefore, will also produce relatively high local loads in the reactor vessel lifting lugs and head. Altman also does not disclose any system for cooling the CRDMs. Some commercial light water reactors—for example, pressurized water reactors produced by Babcock & Wilcox (B&W)—have a reactor vessel closure head having inverted L-shaped flanges that extend upwardly from the reactor vessel closure head. Many B&W reactors also employ a control rod design wherein the lead screw from each control rod must be decoupled from the control rod and parked before the reactor vessel closure head is removed from the reactor vessel. In order to decouple and park the control rod lead screw, a 15-foot tool is typically inserted from above into the CRDM housing. For these types of commercial reactors, therefore, significant overhead space, or headroom, is required above the reactor vessel to accommodate the control rod tool, prior to removing the reactor vessel closure head. To provide the necessary head room, various components disposed above the reactor may need to be disassembled, removed, and stored before the control rod lead screws can be decoupled and parked and the closure head removed. There is a need, therefore, for an integrated head assembly for a pressurized water reactor that can be removed from the reactor vessel integrally with the reactor vessel closure head, and that does not introduce undue local stresses at the reactor vessel closure head and lifting lugs. The present invention is directed to an apparatus and method that satisfies this need. The apparatus includes an integrated head assembly for a pressurized light water nuclear reactor having a lift assembly that engages the lifting lugs on the reactor vessel closure head. A support structure is provided above the reactor vessel closure head with a shroud assembly and a baffle structure attached thereto. At least one upwardly extending duct for a CRDM cooling system is also provided. The apparatus includes a seismic support system and a missile shield attached to the support structure and disposed generally above the control rod drive mechanisms. At least one cooling air fan is fluidly connected to the duct. In an embodiment of the invention, the duct is cooperatively formed by the baffle and the shroud assemblies. In an embodiment of the invention, the support structure includes a ring beam with a number of saddle members that are disposed atop the reactor vessel closure head. The ring beam may be formed from three annular segments that are joined end to end. The support structure may also include a cylindrical support grid that extends upwardly from the ring beam. The shroud assembly may also comprise multiple axial segments and provide air inlet port(s) for the air cooling system. In a disclosed embodiment, the air cooling system includes an upper plenum interconnecting three cooling fans and two vertical ducts. An embodiment of a method for retrofitting a pressurized water nuclear reactor according to the present invention includes shutting down the nuclear reactor and removing the reactor vessel closure head from the reactor vessel and placing it on a reactor head stand. Lift rods are then attached to the lifting lugs on the reactor vessel closure head. An integrated head assembly module is then installed, the module including a ring beam that rests atop the reactor vessel closure head, a shroud assembly that sets atop the ring beam, and a baffle assembly attached to the shroud assembly. A seismic support system is then connected to the control rod drive mechanisms and a missile shield is installed above the CRDMs. A lifting assembly is then operatively attached to the lift rods above the missile shield, and the reactor vessel closure head is reinstalled on the reactor vessel. In yet another embodiment of the present invention, an integrated head assembly includes a lower ring beam that is disposed atop the reactor vessel closure head, lift rods that attach to the vessel head lifting lugs, a shroud assembly with cooling air ducts that is supported by the ring beam, a seismic support assembly and missile shield assembly installed above the reactor vessel closure head, and fans connected to the cooling air ducts. An upper ring beam and lifting tripod may be provided at the upper end of the lift rods, wherein the upper ring beam acts as a spreader for the lifting tripod. The upper ring beam is annular, providing access to the upper portion of the integrated head assembly. In a disclosed embodiment, the missile shield assembly includes an array of shield plates, each shield plate positioned above a control rod drive mechanism, the shield plates being removable such that individual control rod drive mechanisms can be accessed from above. The shield plates are slidably retained between grooved beams and a center shield plate in each row is removable, allowing adjacent shield plates to be slid to access the desired control rod drive mechanism. Referring now to the figures, an integrated head assembly 100 according to the present invention is shown atop a reactor vessel closure head 90 in FIG. 1. The reactor vessel closure head 90 is attachable to the top of a reactor vessel (not shown) and seals the reactor vessel, which contains the nuclear fuel (not shown). As seen more clearly in FIG. 2, the reactor vessel closure head 90 is a circular structure that typically includes a dome-shaped central portion 92 and an outer ring portion 94 having a plurality of stud mounting holes 95. The dome portion 92 supports a number of control rod drive mechanisms (CRDMs) 96 that extend vertically above the reactor vessel closure head 90 and pass through the head into the reactor vessel. The CRDMs 96 are electrically operated devices that control the vertical position of the control rods (not shown) inside the reactor vessel. CRDMs 96 are well known in the art and are therefore depicted in the figures in functional form, without showing the structural detail. For example, CRDMs generally include upwardly extending guide tubes that, for clarity, are not shown in FIG. 2. The reactor vessel closure head 90 includes three integral lifting lugs 98 that are used to facilitate lifting the head for removal and replacement. The preferred embodiment of the integrated head assembly 100 includes a lift assembly 150 that provides support structure for lifting the reactor vessel closure head 90, a cylindrical shroud assembly 200 that rests atop the reactor vessel closure head 90, a seismic support system 300 (see FIG. 12) that protects the CRDMs 96 and integrated head assembly 100 from seismically-induced loads, a missile shield 400 (see FIGS. 11A and 11B) that provides protection in certain accident scenarios wherein the CRDMs 96 and/or control rods are ejected, a baffle assembly 500 (see FIG. 8) for directing the flow of cooling air to the CRDMs 96, and a CRDM cooling system including cooling air ducts 600 connected through an upper air plenum 680 to cooling fans 190. The primary components of the lift assembly 150 are shown in FIG. 2. The lift assembly 150 includes a bottom ring beam 151 that sets atop the reactor vessel closure head 90. The ring beam 151 of the preferred embodiment has a short, cylindrical lower portion 152 and a flange portion 153 that extends outwardly from the top edge of the cylindrical portion 152. A plurality of saddle members 155 is disposed peripherally around the ring beam 151, the saddle members 155 having a lower surface that generally conforms with the shape of the reactor vessel closure head 90, thereby distributing the weight of the integrated head assembly 100 over a larger portion of the reactor vessel closure head 90. In the preferred embodiment, the ring beam 151 comprises three generally identical segments that are connected through the lift rod connecting members 162, as described below. Three lift rods 160 extend vertically upwardly from the ring beam 151. Each lift rod 160 includes a connecting member 162 at one end having a clevis-type connector 163 that slidably engages one of the head lifting lugs 98. The connecting member 162 is attached to the head-lifting lug 98 with a clevis pin 166. A detail of the connecting member 162 of the preferred embodiment is shown in FIG. 3. The connecting member 162 is positioned between ring beam 151 segments, and includes oppositely disposed horizontal flanges 164 that connect to the ring beam 151 with bolts 165, thereby interconnecting the ring beam segments and removably attaching the ring beam 151 to the reactor vessel closure head 90. Although the preferred embodiment utilizes three ring beam segments, it will be appreciated that other configurations are possible and contemplated by the present invention, including, for example, a unitary ring beam having cut out portions to accommodate connecting members. The upper end of the lift rods 160 are threaded and extend through orifices 182 in a circular fan support plate 180 (see FIG. 10), where they are attached to the fan support plate 180 with the tripod base brackets 172 and/or other suitable connecting hardware. A lift tripod 170 is disposed above the fan support plate 180 and includes three rods 171, each rod 171 pivotally connected at one end to a tripod base bracket 172, and pivotally connected at the opposite end to a lift shackle 174. It will be appreciated that the lift assembly 150 permits the integrated head assembly 100 and the reactor vessel closure head 90 to be lifted as a single unit by an appropriate lifting mechanism, such as a hoist (not shown), acting on the lift shackle 174. It will be appreciated that the fan support plate 180 also functions as a spreader for the lift tripod 170. The three large apertures 184 through the fan support plate 180 are the outlet air ports for the upper air plenum 680 fluidly connected to the cooling fans 190 as described below. As seen most clearly in FIG. 4, a generally cylindrical support column assembly 202 is provided on top of the ring beam 151. The support column assembly 202 includes six support columns 204 that extend upwardly from the ring beam 151, each support column 204 preferably being positioned above one of the saddle members 155. The support columns 204 are attached to the ring beam 151 with a clip angle bolted connection 206. Curved transverse members 208 interconnect the support columns 204 at three vertically spaced locations. The support column assembly 202 provides a cylindrical grid support structure over the reactor vessel closure head 90 that supports the integrated head assembly components, and transfers the weight and dynamic loads from the integrated head assembly 100 to the ring beam 151. Although the preferred support structure has been described, it will be apparent to one of skill in the art that many variations in the support structure may be made without departing from the present invention. For example, and not by way of limitation, more or fewer support columns 204 and/or transverse members 208 may be utilized, or the transverse members 208 may be replaced with hoop beams that encircle the support columns. The shroud assembly 200 of the preferred embodiment includes bottom shroud 220, a middle shroud 240 and an upper shroud 260 (see FIG. 1). The bottom shroud 220, shown in FIG. 5, is a cylindrical assembly that is installed at the lower end of the support column assembly 202, extending upwardly from the ring beam 151. The bottom shroud 220 includes an outer wall panel 222 that is preferably formed in multiple sections. The outer wall 222 includes access openings 224 that provide access to the interior of the shroud assembly 200—for example, to monitor and/or service the CRDMs 96. A plurality of doors 226 are attached at the access openings 224, whereby the access openings 224 can be closed, for example, during operation of the reactor and when access to the interior of the shroud assembly 200 is not otherwise required. It will be appreciated that although hinged attachments are shown, any other suitable closure system could be used—for example, removable panels, sliding panels, and the like. The bottom shroud outer wall 222 and doors 226 may be made from any suitable material such as, for example, ASTM-A36 carbon steel. The thickness of the panel 222 and doors 226 are selected depending on the required level of radiation shielding that is desired. For example, in the preferred embodiment, the panel 222 and doors 226 are ¼ inch thick if radiation shielding is not an issue, and 1½ inches thick if radiation shielding is desired. A lower baffle portion 520 extends through the bottom shroud 220, comprising a left panel 521, a right panel 522, a forward panel 523, and a rearward panel 524. The baffle panels 521, 522, 523, and 524 are oriented approximately parallel to and generally surround the CRDMs 96. The lower baffle portion 520 defines a central airflow path for cooling airflow. The left and right panels 521, 522, cooperatively with a portion of the outer wall panel 222, form a pair of longitudinal channels 620 near the periphery of the integrated head assembly 100. Referring now to FIG. 6, a middle shroud 240 is aligned with the bottom shroud 220 and extends upwardly from the bottom shroud 220. Similar to the bottom shroud, the middle shroud 240 includes a multisection outer wall panel 242 that attaches to the support column assembly 202. Air inlet ports 244 are provided on opposite sides of the middle shroud 240 that permit ambient air to enter the shroud assembly 200 for cooling the CRDMs 96. A middle baffle portion 540 of the baffle assembly 500 extends vertically through the middle shroud 240. The baffle middle portion 540 includes a left panel 541 and a right panel 542 that each attach to the shroud outer wall 242, forming a pair of peripheral longitudinal channels 640, aligned with and vertically continuing the channels 620 formed in the bottom shroud 220. The baffle assembly middle portion 540 is preferably open at the oppositely disposed forward and rearward regions between the baffle left and right panels 541, 542, which openings are generally aligned with the shroud air inlet ports 244. Horizontal plates 248 extend inwardly from the bottom of the middle shroud 240 from the air inlet ports 244, such that air entering the air inlet ports 244 is directed to the interior of the baffle assembly 500 towards the CRDMs 96. An upper shroud 260 is shown in FIG. 7. The upper shroud 260 extends upwardly from the middle shroud 240 and includes an outer wall 262 that attaches to the support column assembly 202. A baffle upper portion 560 of the baffle assembly 500 extends vertically through the upper shroud 260, including a left panel 561 and a right panel 562, aligned with the middle baffle portion 540. The baffle upper portion 560 and upper shroud outer wall 262 cooperatively form a pair of longitudinal channels 660 aligned with and continuing the middle section channels 640. The forward and rearward portions of the upper shroud 260 have apertures 264 to provide electric power and control access to the CRDMs 96 through a CRDM cable disconnect panel 120 (see FIG. 13). It will be appreciated that the shroud channels 620, 640, and 660 cooperatively form longitudinal cooling ducts 600 that extend from near the reactor vessel closure head 96 upwardly substantially through the length of the shroud assembly 200. A view of the baffle assembly 500 disposed within the support column assembly 202 is shown in FIG. 8, with the shroud outer walls 222, 242, 262 removed for clarity. The baffle structure 500 extends upwardly from near the reactor vessel closure head 90 and provides a flow path for cooling air to the CRDMs 96. A gap is provided between the reactor vessel closure head 90 and the baffle assembly 500 that functions as an air outlet port such that the cooling air flowing downwardly along the CRDMs 96 exits the baffle and flows outwardly toward the periphery of the integrated head assembly. An upper air plenum 680, shown in FIG. 9, is provided at the top of the integrated head assembly 100. The upper air plenum 680 is a generally circular plenum that includes the fan support plate 180 having outlet ports 184 to the cooling air fans 190. The fan support plate 180, with three cooling air fans 190 installed, is shown in FIG. 10. The plenum lower panel comprising the missile shield 400 discussed in more detail below and a vertical peripheral wall 682 are provided between the fan support plate 180 and the missile shield 400. The missile shield 400 includes left and right cutout portions 420 that are disposed over the cooling air ducts 600 and provide the inlet ports to the upper air plenum 680. In the preferred embodiment, the cooling air fans 190 draw air upwardly through the upper air plenum 680. In operation, therefore, the fans 190 draw air into the middle shroud inlet ports 244, downwardly along the CRDMs 96 in the baffle assembly 500, upwardly through the ducts 600 into the upper air plenum 680, and out of the integrated head assembly 100. Referring now to FIGS. 11A and 11B, the missile shield 400 is provided above the CRDMs 96 near the top of the baffle assembly 500. The primary purpose of the missile shield 400 is to protect against the possible ejection of the CRDMs 96 or fuel rods in certain accident scenarios. The missile shield 400 may be made from any suitably strong material and is preferably a steel panel having circular forward and rearward portions 410 and cutout left and right portions 420 that are shaped to accommodate the cooling air ducts 600 as discussed above. The missile shield 400 is supported by the support columns 204 and includes outwardly extending tab portions 430 to facilitate attachment to the support columns 204. FIG. 11B shows a plan view of the missile shield 400 installed in the integrated head assembly 100 (with some structural detail removed for clarity). A seismic support system 300 for the integrated head assembly 100 is shown in FIG. 12. The seismic support system 300 is designed to support the CRDMs 96 in a seismic event to ensure that the control rods are able to drop down into the reactor if it is necessary to shut the reactor down. The seismic support system 300 includes an array of seismic cap plates 310 of various shapes (310a, 310b, 310c, and 310d), each seismic cap plate attached to the upper end of a CRDM 96. The seismic cap plates 310 include a generally flat portion 311 with a notched-out section 312 to accommodate electrical power and control cables. A hat-shaped recess or cavity 313 is formed at an intermediate portion of the seismic cap plate 310, and sized to accommodate the end of a CRDM 96. The CRDM 96 extends into the cavity 313 and is attached to the respective seismic cap plate 310. As shown in FIG. 12, the flat portions 311 of the cap plates 310 are approximately adjacent neighboring cap plates 310, such that the cap plates 310 cooperatively form a lateral support panel across the CRDMs 96. A baffle stiffener ring beam 320 surrounds the seismic cap plate 310 array, and preferably a plurality of adjustable engagement mechanisms (not shown) are provided between the cap plate 310 array and the baffle stiffener ring beam 320, whereby only a slight gap is provided therebetween. A seismic ring beam 340, comprising a generally circular beam, surrounds the baffle stiffener ring beam 320 and is connected to the ring beam 320 with forward and rearward seismic stiffener plates 330 and left and right seismic stiffener beams 335. In the preferred embodiment, a bolt tensioner rail 350 is provided on the outer perimeter of the seismic ring beam 340 to accommodate a bolt tensioning/detensioning apparatus (not shown). A plurality of seismic restraints 360 connects the seismic ring beam 340 to a relatively stable anchor such as the reactor containment walls (not shown). FIG. 13 shows the CRDM cable disconnect panel 120 discussed above, which is preferably installed in the upper shroud 260. The cable disconnect panel 120 provides an array of electrical connectors 122 providing a central location to disconnect the CRDMs 96 from their electric power and control systems prior to removal of the reactor vessel closure head 90. More than one cable disconnect panel 120 may be provided. The integrated head assembly 100 of the present invention simplifies the removal and replacement of the reactor vessel closure head 90 for standard maintenance procedures, as well as for unscheduled outages, by integrating the lifting support, CRDM cooling system, missile shield, and seismic support into a single assembly that may be removed as a unit from the reactor vessel. In practice, to remove the integrated head assembly a polar crane hook or other appropriate lifting and moving mechanism is attached to the tripod assembly lift shackle 174, the CRDM cables are disconnected at the cable disconnect panel 120, the seismic restraints 360 are disconnected, and the reactor vessel closure head studs are loosened and removed. Additional site-specific steps well known in the art and not important to understanding of the present invention may also be required, such as moving one or more cable bridges away from the lift path of the head. The reactor vessel closure head can then be removed from the reactor vessel to permit the necessary maintenance procedures to be performed. Although the preferred embodiment has been described in some detail, it will be readily apparent to one of skill in the art that many variations in the present invention may be made without departing from the present invention. It will be appreciated that the present invention is amenable to retrofitting of existing nuclear power plants. No modifications to the reactor vessel closure head 90 would be required. In a preferred method of retrofitting an existing plant, it is contemplated that the design, fabrication, and installation effort for the integrated head assembly 100 of the present invention would be performed over a period of approximately 24 calendar months. The integrated head assembly 100 installation would preferably be performed during a refueling outage of the plant, such as are typically scheduled every 18 months. Accordingly, the design/fabrication/installation process needs to be scheduled based on the plant refueling schedule. The integrated head assembly shroud assembly 200 and associated components may be fabricated and shipped in three modules. The first module comprises the bottom ring beam 151, the bottom shroud 220, the baffle lower portion 520, and other appurtenances associated with the bottom shroud 220. The second module would comprise the middle shroud 240, the baffle middle portion 540, including the cooling air inlets, and other associated appurtenances. The third module would include the upper shroud 260, baffle upper portion 560, partial air inlet, partial assembly of the CRDM 96 seismic support system 300, and related head area cable support systems and wires in pre-routed condition, the cable disconnect panel(s) 120, the missile shield 400, the cooling fans 190, and other associated appurtenances. It is contemplated, although clearly not critical to the present invention, that the three lift rods 160 and the lift tripod 170 would be shipped as separate items. The assembly of these components would preferably be accomplished while the reactor vessel closure head 90 is resting on a reactor head stand inside the containment. In a typical installation, the existing rig assembly would first be disassembled from the reactor vessel closure head 90. The three lift rods 160 are then attached to the three lift lugs 98 on the reactor vessel closure head 90. Temporary supports are preferably provided at the top of the lift rods 160 to hold them in place. Assembly of integrated head assembly components is accomplished starting from the bottom of the integrated head assembly (i.e., near the reactor vessel closure head 90) and continuing on in upward direction. The first module is inserted through three lift rods 160 and the bottom ring beam 151 is attached to the connecting members 162 of the lift rods 160. Once the lower shroud 220 is in place, the second module is lowered through the lift rods 160 and bolted to the bottom shroud 220 at the transverse members (i.e., ring angles) 208 and at the support columns 204. For accessibility for bolted connections, some or all of the outer wall panel 242 of the middle shroud 240 may be removed from the shroud. It is possible that the elevation of the top of the second module is very close to the elevation of the CRDM seismic cap plates 310. In such cases, install all CRDM seismic cap plates 310 on all CRDMs 96 prior to lowering the third module over the lift rods 160. In the next step of this preferred method, lower the third module through three lift rods 160 and attach it to the top of the middle shroud 240 by bolts at the transverse members 208 as well as at the support columns 204. Again for accessibility for bolted connections, some or all of the outer wall panel 262 of the upper shroud 260 may be removed from the shroud. The installation of the CRDM seismic support system 300 may be completed at this time, excepting attachment of the seismic restraints 360. The seismic restraints 360 are preferably installed when the integrated head assembly is in place atop the reactor vessel. After the third module is assembled and installed, the missile shield 400 may be installed along with the cooling fan support plate 180 including the rest of the upper air plenum 680, the cooling fans 190, and the lift tripod 170. After the cooling fan base is installed, the refueling disconnect panels may be installed near the bottom surface of the cooling fan support plate 180. The retrofit is completed with the assembly of miscellaneous non-structural elements. After the assembly is complete, the whole integrated head assembly 100 with the reactor vessel closure head 90 is lifted and held in a lifted position for some time by the containment polar crane and then put back on the head stand. At this time all component connections are checked once again for their effectiveness. When it is ready to install the reactor vessel closure head 90 back on the reactor vessel, the entire integrated head assembly 100, with the reactor vessel closure head 90, is lifted from the head stand and moved over the reactor vessel and lowered slowly until the head is properly aligned and resting on the reactor vessel, and the assembly is attached to the reactor vessel. After the reactor vessel closure head studs are properly torqued, the seismic restraints 360 are attached to the integrated head assembly 100 on one side and to the refueling walls on the other side. After the integrated head assembly is installed it is contemplated that airflow test would be performed to ensure proper operation of the cooling fans 190 and the entire CRDM cooling system. It will be apparent to one of skill in the art that other assembly methods are possible although less preferred, including, for example, installing or partially installing the integrated head assembly to the reactor vessel closure head while it is attached to the reactor vessel, or installing the integrated head assembly to the reactor vessel closure head utilizing more smaller modules, or fewer larger modules. In particular, it is contemplated that the integrated head assembly 100 could be substantially completely assembled prior to installing it on the reactor vessel closure head. As discussed above, some commercial nuclear reactors require that the lead screw from each control rod be decoupled from the control rod and parked prior to removal of the reactor vessel closure head. Such reactors typically require significant headroom over the reactor vessel in order to decouple and park the control rod lead screws. A second embodiment of the present invention that provides substantial reactor vessel headroom, is shown in FIGS. 14 to 20. Referring now to FIG. 14, a perspective view of a second embodiment of an integrated head assembly 1100 according to the present invention is shown. The integrated head assembly 1100 includes three lift rods 160 that attach to lifting lugs 1098 on a reactor vessel closure head 1090—for example, in a manner similar to that shown in FIG. 3. Although it is not essential to the present invention, in the disclosed example the reactor vessel closure head 1090 includes an upwardly-extending flange 1093, generally in the shape of an inverted “L,” as seen most clearly in FIG. 15. Such flanges are a common feature of certain existing commercial light water reactor designs. The integrated head assembly 1100 includes a ring beam 1151 having an L-shaped lower portion 1152 that is adapted to rest atop the reactor vessel closure head flange 1093. It will be appreciated that this configuration distributes the weight of the integrated head assembly 1100 over a large portion of the reactor vessel closure head 1090. As on the first embodiment disclosed above, the ring beam 1151 also includes a ring-shaped horizontal flange portion 1153. The ring beam 1151 may further be attached to the reactor vessel closure head flange 1093—for example, with nuts and bolts or other clamps (not shown) as are well known in the art. In the preferred embodiment, the ring beam 1151 is formed in three approximately 120° segments, although more or fewer segments that cooperatively form a ring beam are also contemplated by the present invention. The integrated head assembly 1100 includes a lift assembly having three lift rods 160 (two shown in FIG. 14) that connect at the lower end to the lifting lugs 1098 on the reactor vessel closure head 1090 (for example, with clevis-type connecting members 162) and at the upper end to a lift tripod 170 (for example, with tripod base brackets 172). The lift assembly is generally the same as that shown in FIG. 2, except that an upper ring beam 1180 acts as a spreader for the lift tripod 170 (rather than the fan support plate 180). The upper ring beam 1180 is an annular beam, thereby providing access to the interior of the integrated head assembly 1100 from above. The upper end of the lift rods 160 are threaded and extend through orifices in the upper ring beam 1180, where they are attached to the upper ring beam 1180 with the tripod base brackets 172 and/or other suitable connecting hardware. The lift tripod 170 is disposed above the upper ring beam 1180, and includes three rods 171, each rod 171 pivotally connected at one end to one of the tripod base brackets 172 and pivotally connected at the opposite end to a lift shackle 174. It will be appreciated that the lift assembly 170 permits the integrated head assembly 1100 and the reactor vessel closure head 1090 to be lifted as a single unit by an appropriate lifting mechanism, such as a hoist (not shown), acting on the lift shackle 174. A generally cylindrical shroud assembly 1200 extends upwardly from the ring beam 1151, preferably including a bottom shroud 1220, a middle shroud 1240, and an upper shroud 1260. Access doors 226 are provided in the bottom shroud 1220 over access openings 224. A baffle assembly 1500 extends upwardly from the reactor vessel closure head 1090, the baffle assembly being attached to the shroud assembly 1200, and cooperatively with the shroud assembly 1200 forming a plurality of vertical cooling air ducts 1600 that extend upwardly for a substantial portion of the integrated head assembly height. In the preferred embodiment three cooling air ducts 1600 are provided, circumferentially spaced around the integrated head assembly 1100, as seen most clearly in FIG. 16. Referring again to FIG. 14, three cooling fans 190 are installed in the vertical wall of the upper shroud 1260. The cooling fans 190 are directed outwardly, and each fan 190 is fluidly connected to one of the vertical cooling air ducts 1600, to draw air upwardly through the air duct 1600. Inlet ports 1244 through the middle shroud 1240 and the baffle assembly 1500 provide a flow path for cooling air to enter the integrated head assembly 1100 for cooling the control rod drive mechanisms 96. Horizontal plates 1248 are provided at the inlet ports 1244 between the shroud wall and the baffle assembly 1500. It will now be appreciated that the cooling fans 190 operate to draw ambient air into the integrated head assembly 1100 through the inlet ports 1244. The air flows into the baffle assembly 1500 and downwardly over the CRDMs 96 convectively cooling the CRDMs 96, and into the inlet disposed at the bottom of the cooling air ducts 1600, where the air flows upwardly and out of the assembly 1100 through the cooling fans 190. Although the upper end of the cooling air ducts 1600 of the preferred embodiment are not fluidly interconnected at the top end, it is contemplated that an annular upper air plenum (not shown) could be provided to fluidly connect the cooling air ducts 1600. An upper air plenum would improve airflow over the control rods 96 if one or two of the fans 190 fail or are otherwise not operational. A seismic support system 1300 for the integrated head assembly 1100 is shown in FIG. 17. The seismic support system stabilizes the CRDMs 96 in a seismic event to ensure that the control rods are able to drop down into the reactor if it is necessary to shut the reactor down. In this embodiment, the seismic support system 1300 includes an array of seismic support plates 1310 having an aperture 1313 that is sized to slidably receive the end of a CRDM 96. The seismic support plates 1310 include a second aperture 1312, which may overlap the first aperture, to accommodate electrical power and control cables and piping for the CRDM stator cooling water. A seismic support plate 1310 is provided for each CRDM 96, forming an array of plates as shown in FIG. 17, and the seismic support plate 1310 clamps to the CRDM 96. As shown in FIGS. 17 and 18, the seismic support plates 1310 are approximately adjacent to neighboring seismic support plates 1310, such that the seismic support plates 1310 cooperatively form a lateral support panel across the CRDMs 96. Although the seismic support plates are shown fixedly attached to each CRDM 96, is it also contemplated that the seismic support plates 1310 may alternatively loosely engage the CRDMs 96 and be attached to a rectangular grid frame structure (not shown) that holds the seismic support plates 1310 in proper alignment. A baffle stiffener ring beam 1320 surrounds the seismic cap plate 1310 array. Adjustable engagement mechanisms (not shown) may be provided between the cap plate 1310 array and the baffle stiffener ring beam 1320, to adjustably maintain a slight gap therebetween. A seismic ring beam 1340, comprising a generally circular beam, surrounds the baffle stiffener ring beam 1320, and is connected to the ring beam 1320 with a plurality of seismic stiffener plates 1330. In the preferred embodiment, a bolt tensioner rail 1350 is provided on the outer perimeter of the seismic ring beam 1340 to accommodate a bolt tensioning/detensioning apparatus (not shown). In this embodiment the seismic support system does not include any seismic restrains for connection to the containment wall. The seismic forces are therefore transmitted to the reactor vessel closure head 1090 through the integrated head assembly 1100 structure. A missile shield assembly 1400 is disposed above the seismic support system 1300, as shown in more detail in FIG. 19. The missile shield assembly 1400 includes a support structure 1410 including three work platforms 1412 that are circumferentially spaced around the missile shield assembly. A sliding frame structure comprising a number of parallel slotted beams 1420 is disposed generally between the work platforms 1412. A plurality of missile shield plates 1422 are slidably inserted between adjacent slotted beams 1420, as shown in FIG. 19. The missile shield plates 1422 are arranged in an array between adjacent slotted beams 1420 substantially filling the area between the work platforms 1412 over the CRDMs 96. A central portion of each slotted beam 1420 is provided with a removable frame member 1424 that is secured to the slotted beam 1420, for example, with bolts 1426, such that removal of adjacent frame members 1424 will permit the missile shield plate 1422 disposed therebetween to be lifted out. It will be apparent from FIG. 19 that if a shield plate 1422 in any row of shield plates is removed, adjacent shield plates 1422 in the same row can be slidably moved to provide access therebelow. In the preferred embodiment, the missile shield plates 1422 are each provided with a pair of handles 1428 to facilitate sliding the shield plates 1422 within the slotted tracks. In the embodiment shown in FIG. 19, the shield plates 1422 are sized such that one shield plate 1422 is disposed directly above each one of the CRDMs 96. It is also preferred that the missile shield assembly 1400 be made from a suitable material to provide radiation shielding to workers above the missile shield assembly 1400, and that the assembly be sturdy enough to safely support such workers. It should now be appreciated that the missile shield assembly 1400 disclosed above provides a work platform directly over the CRDMs 96, whereby the 15-foot tool can be inserted into the CRDM casing to decouple and park the lead screw in each CRDM 96 so that the reactor vessel closure head 1090 can be removed. It will also be appreciated that by removing only a single shield plate 1422 at a time and sliding adjacent shield plates 1422 to access the desired CRDM 96, the workers' radiation exposure will be minimal when performing this task. As seen most clearly in FIGS. 14 and 20, in the disclosed embodiment the integrated head assembly 1100 is provided with a retractable cable bridge 1700. The retractable cable bridge 1700 provides a platform for supporting cables that provide electric power and control signals (i.e., rod position indicator cables) to the CRDMs 96. The cables are preferably removably connected to the CRDMs 96 through a CRDM cable disconnect panel 120 such as that described above and shown in FIG. 13. The cable bridge 1700 includes a support platform 1710 that is pivotally connected at an inner end 1720 to a work platform 1412 of the missile shield assembly 1400. A pair of cables 1724 pivotally connects an outer end 1722 of the support platform 1710 to the upper ring beam 1180 through an attachment bracket 1730. A pair of motorized pulleys 1732 is provided to retract and extend the cable bridge 1700, as desired. While the preferred embodiment of the invention has been illustrated and described, it will be appreciated that various changes can be made therein without departing from the spirit and scope of the invention.

054917301

abstract

Pipes are mounted horizontally on an outlet portion of a gas vent pipe in a condenser-type heat removal system, and have-openings which are formed only in a portion below a horizontal plane in which axes of these pipes lie, thereby enlarging a region where uncondensed steam is mixed with water in a suppression pool. With this arrangement, a surface portion of the water of the suppression pool is prevented from becoming hot, and the temperature of this pool water is uniformed. As a result, the temperature of the water surface of the suppression pool is lowered, thereby decreasing the pressure within a primary containment vessel. This enhances the reliability of the primary containment vessel, and reduces a design strength of the primary containment vessel.

claims

1. An apparatus for measuring film stack characteristics of a sample, the apparatus comprising: a beam generator configurable to direct an electron beam towards the sample such that the electron beam completely penetrates a plurality of desired layers of the film stack, the electron beam causing X-rays to emanate from the sample; at least a first and a second wavelength dispersive X-ray detector positioned above the sample wherein each detector detects X-rays about a different characteristic emission level, wherein the first detector is configured to detect X-rays having characteristic emission levels for a top layer of the film stack and the second detector is configured to detect X-rays having characteristic emission levels for an underlying layer that lies beneath the top layer, whereby material characteristics of the desired layers can be measured simultaneously; and an analysis unit that collects data resulting from the detected X-rays, wherein the data that is collected is raw data, the analysis unit also configured to compare predicted data derived from one or more equations that model the film stack against the raw data. 2. The apparatus as recited in claim 1 wherein the first X-ray detector is configured to detect X-rays of a specific energy level. claim 1 3. The apparatus as recited in claim 1 wherein the wavelength dispersive system contains a reflective surface and a sensor, the reflective surface configured to direct X-rays of a predetermined energy level to the sensor. claim 1 4. The apparatus as recited in claim 1 further comprising a processor linked to the beam generator and to the first X-ray detector. claim 1 5. The apparatus as recited in claim 4 wherein the processor is configured to control the first X-ray detector so that it detects X-rays of a specific energy level. claim 4 6. The apparatus as recited in claim 4 wherein the processor is configured to control the beam generator so that the electron beam directed to the sample penetrates at least a conductive film layer and a liner film layer of the sample. claim 4 7. An apparatus as recited in claim 1 wherein each of the characteristic emission levels correspond to a different layer of the film stack. claim 1 8. An apparatus as recited in claim 1 wherein the electron beam completely penetrates the top and the underlying layers of the film stack so that the thickness of the top and the underlying layers can be determined. claim 1 9. An apparatus as recited in claim 1 wherein the electron beam completely penetrates at least a conductive film layer and a liner film layer of the sample. claim 1 10. An apparatus as recited in claim 1 wherein the electron beam is set at a substantially constant voltage level. claim 1 11. The method of determining film stack characteristic values as recited in claim 10 further comprising recording the set of estimated film stack characteristic values when a difference between the predicted data and the raw data is equal to or smaller than the predetermined margin of error, wherein the estimated film stack characteristic values are an acceptable estimate of the film stack""s characteristic. claim 10 12. A method for measuring at least one characteristic of a film stack on a sample, the method comprising: directing a charged particle beam towards the sample such that the charged particle beam completely penetrates at least two layers of the film stack, the charged particle beam causing X-rays to emanate from the sample; detecting X-rays at a first characteristic emission level that represents an emission level for a top layer of the film stack using at least a first wavelength dispersive X-ray detector that is positioned above the sample; detecting X-rays at a second characteristic emission level that represents an emission level for an underlying layer of the film stack using at least a second wavlength dispersive X-ray detector that is positioned above the sample, the underlying layer being a layer of material underneath the top layer; collecting data resulting from the detected X-rays, wherein the data that is collected is raw data; and comparing predicted data derived from one or more equations that model the film stack against the raw data. 13. The method for measuring as recited in claim 12 , further comprising configuring the first X-ray detector to detect X-rays of a specific energy level. claim 12 14. The method for measuring as recited in claim 12 further comprising positioning a reflective surface contained within the wavelength dispersive system in an orientation to direct X-rays of a predetermined energy level to a sensor contained within the wavelength dispersive system. claim 12 15. The method for measuring as recited in claim 12 , the method further comprising selecting a charged particle beam energy and a charged particle beam current at which the charged particle beam will be produced. claim 12 16. The method for measuring as recited in claim 12 wherein a conductive film layer and a liner film layer are two of the at least two layers that are penetrated by the charged particle beam. claim 12 17. The method of determining film stack characteristic values as recited in claim 12 wherein the raw and predicted data represent a count value of X-rays having a specific energy level, the count value being the total number of X-rays received by each of the wavelength dispersive systems over a period of time. claim 12 18. A method as recited in claim 12 wherein each of the characteristic emission levels correspond to a different layer of the film stack. claim 12 19. A method as recited in claim 12 wherein the charged particle beam completely penetrates the thickness of the top and the underlying layers of the film stack so that the thickness of the top and the underlying layers are determined. claim 12 20. An apparatus for measuring the thickness of two or more layers within a film stack sample, the apparatus comprising: a beam generator configurable to direct an electron beam towards the sample such that the electron beam completely penetrates at least two layers of the film stack, the electron beam causing X-rays to emanate from the sample; at least a first and a second wavelength dispersive X-ray detector positioned above the sample wherein each detector is configured to detect a respective portion of the X-rays emanating from the sample, whereby material characteristics of the at least two layers can be measured simultaneously; and an analysis unit that collects data resulting from the detected X-rays, wherein the data that is collected is raw data, the analysis unit also configured to compare predicted data derived from one or more equations that model the film stack against the raw data. 21. An apparatus as recited in claim 20 wherein the first X-ray detector is configured to detect X-rays of a specific energy level. claim 20 22. An apparatus as recited in claim 20 wherein the first X-ray detector is a wavelength dispersive system. claim 20 23. An apparatus as recited in claim 22 wherein the wavelength dispersive system contains a reflective surface and a sensor, the reflective surface configured to direct X-rays of a predetermined energy level to the sensor. claim 22 24. An apparatus as recited in claim 20 further comprising a second X-ray detector, wherein the first and second X-ray detectors are wavelength dispersive systems. claim 20 25. A method for measuring as recited in claim 12 , further comprising: claim 12 selecting a set of estimated film stack characteristic values; and obtaining the predicted data by solving the one or more equations that model the film stack using the set of estimated film stack characteristic values. 26. A method for measuring as recited in claim 25 , further comprising: claim 25 selecting a new set of estimated film stack characteristic values when a difference between the predicted data and the raw data is larger than a predetermined margin of error; and obtaining a new set of predicted data by solving equations which model the film stack using the new set of estimated film stack characteristic values when the difference between the predicted data and the raw data is larger than the predetermined margin of error. 27. An apparatus as recited in claim 20 wherein the electron beam can be scanned over the film stack sample in a scan pattern. claim 20 28. An apparatus as recited in claim 27 further comprising: claim 27 an octupole for aligning the electron beam generated by the beam generator; and a lower quadrupole for further adjusting the alignment of the electron beam.

056595905

summary

TECHNICAL FIELD This invention relates to boiling water nuclear reactors and specifically, to a dew core shroud and pump deck design which allows for easy removal and/or replacement of these reactor structural components when damaged or otherwise in need of repair or replacement. BACKGROUND Typical boiling water nuclear reactors include a reactor assembly which consists of the reactor vessel and its internal components including the core, core shroud, top guide assembly, core plate assembly, steam separator and dryer assemblies, and jet pumps. Also included in the reactor assembly are the control rods, control rod drive housings and the control rod drives. The reactor vessel is a generally cylindrical pressure vessel (RPV) with a single full diameter removable head. The shroud is a cylindrical stainless steel structure located within the RPV and which surrounds the core, providing a barrier to separate the upward flow through the core from the downward flow in the annulus between the RPV wall and the core shroud. The conventional core shroud is welded to the bottom of the RPV and supports the weight of the top guide, core plate and shroud head along with attached steam separators. Recent discoveries of unexpected circumferential cracks propagating through the thickness of the shrouds in relatively young operating BWR's has prompted a re-design of the core shrouds for future BWR's. The primary cause of the observed cracking has been intergranular stress corrosion in the heat affected zones near many of the horizontal welds of the shroud and shroud supports. There have also been some cracks observed in the mid-belt regions of BWR shrouds, and these have been thought to be caused by irradiation assisted stress corrosion. The current advanced boiling water reactor (ABWR) shroud, like the conventional BWR shroud, is permanently welded to the bottom of the vessel and is not intended to be removed or replaced. The shroud in the ABWR has various horizontal welds similar to the BWR shrouds in current operating plants, and therefore may also be at risk of similar stress corrosion cracking problems. The conventional pump deck section is permanently welded in place between the shroud and the reactor pressure vessel, and it too is not intended to be removed or replaced. As with the shroud welds, the pump deck welds are also susceptible to stress corrosion cracking. SUMMARY OF THE INVENTION This invention relates to a new and improved shroud and pump deck design which allows for the relatively easy removal of both components. In accordance with the invention, both the shroud and pump deck are bolted to the top of the shroud support leg extending upwardly from the bottom of the RPV. Specifically, the shroud has a radially inwardly extending flange at its bottom end for bolting into the upper cylindrical section of the shroud support leg. The bolts restrain vertical loading on the shroud while horizontal loading is restrained by wedges mounted between the shroud and a plurality of wedge support blocks on the pump deck. Thus, the inner diameter portion of the pump deck is vertically sandwiched between the shroud flange and the upper edge of the cylindrical section of the shroud support leg. At the same time, the outer diameter of the pump deck is held in place within a radially inwardly facing groove on the inside wall of the reactor pressure vessel. The pump deck is formed in ten separate segments with a reactor internal pump diffuser adapted to extend vertically through an opening in the middle of each segment. In a further feature of the invention, a keyed pump deck segment locks the remaining nine deck segments of the pump deck in place. It is the last portion of the pump deck to be installed and the first portion of the pump deck to be removed. This keyed segment is very similar in construction to the other nine segments; however, it is bolted into a support ledge on the reactor pressure vessel wall as opposed simply to being held by the groove on the reactor pressure vessel wall as in the case of the other nine pump deck segments. From the above, it will be appreciated that after the shroud bolts have been removed, the shroud may be lifted vertically from the core. The keyed pump deck segment can then be removed, followed by the remaining pump deck segments. Thus, in accordance with one aspect of the subject invention, there is provided in a pressure vessel of a nuclear reactor containing a core assembly enclosed within a core shroud, the core shroud spaced radially inwardly of a side wall of the pressure vessel with an annular pump deck located between the core shroud and the side wall of the pressure vessel, the improvement wherein the shroud is removably secured to an annular support of the pressure vessel. In accordance with another aspect, the subject invention relates to a pressure vessel of a nuclear reactor containing a core assembly enclosed within a core shroud, the core shroud spaced radially inwardly of a side wall of the pressure vessel with an annular pump deck located between the core shroud and the side wall of the pressure vessel, the improvement wherein the annular pump deck is provided in the form of a plurality of removable segments. In accordance with still another aspect, the invention relates to a pressure vessel of a nuclear reactor containing a core assembly enclosed within a core shroud, the core shroud spaced radially inwardly of a side wall of the pressure vessel with an annular pump deck located in an annular radial space between the core shroud and the side wall of the pressure vessel, the improvement wherein the shroud is removably secured to an annular support leg extending upwardly from the bottom of the pressure vessel; and further wherein the annular pump deck is provided in the form of a plurality of removable segments. It will thus be appreciated that the invention provides a shroud and a pump deck capable of being easily removed and reused or replaced. The invention also provides a wedge mechanism to transfer the horizontal loads of a core shroud to the pump deck or other supporting member. The construction in accordance with this invention also results in most horizontal welds being located in otherwise removable elements, facilitating repair and/or replacement of faulty welds. Other objects and advantages of the subject invention will become apparent from the detailed description which follows.

description

This application is a national stage application of PCT/EP2011/060626, filed on Jun. 24, 2011, which claims priority to German Application 10 2010 025 033.3, filed on Jun. 23, 2010, herein incorporated by reference in its entirety. The present invention relates to the field of analyzing and/or repairing of an EUV mask defect. As a result of the shrinking sizes of integrated circuits, photolithographic masks have to project smaller and smaller structures onto a photosensitive layer i.e. a photoresist dispensed on a wafer. In order to enable the decrease of the critical dimension (CD) of the structure elements forming the integrated circuits (ICs), the exposure wavelength of photolithographic masks has been shifted from the near ultraviolet across the mean ultraviolet into the far ultraviolet region of the electromagnetic spectrum. Presently, a wavelength of 193 nm is typically used for the exposure of the photoresist on wafers. As a consequence, the manufacturing of photolithographic masks with increasing resolution is becoming more and more complex. In the future, photolithographic masks will use even smaller wavelengths in the extreme ultraviolet (EUV) wavelength range of the electromagnetic spectrum. The term EUV mask denotes in the following a photolithographic mask for the EUV wavelength range (preferably 10 nm to 15 nm). The optical elements for the EUV wavelength range will preferably be reflective optical elements. For the fabrication of an EUV optical element a multilayer structure or a multilayer film is deposited on a substrate having an ultralow thermal expansion (ULE). Fused silica is an example of a substrate used for EUV optical elements. The multilayer system typically comprises 80 to 120 alternating layers of molybdenum (Mo) and silicon (Si). A pair of a Mo—Si layer or a Mo—Si bilayer has a depth of approximately 7 nm. At the boundary of the Mo—Si layers a portion of the incident EUV radiation is reflected, so that a Mo—Si multilayer layer system ideally reflects more than 70% of the incident EUV radiation. In addition to the multilayer structure, an EUV mask comprises a pattern or an absorbing pattern structure on top of the multilayer. For example, the EUV radiation absorbing pattern can be formed of titanium nitride, tantalum nitride, or chromium. The interaction of the EUV radiation absorbing portions and EUV radiation reflecting portions of the EUV mask generates in case of an illumination with EUV radiation the pattern to be presented in the photoresist dispensed on a semiconductor wafer. Highest precision is required at the fabrication of EUV optical elements, in particular for EUV masks. Errors in the order of 1 nm can already cause errors in the image of the pattern structure on the wafer. Mask errors or defects which are apparent on the pattern of the wafer generated by the mask are called printing errors. Defects of different types can occur at various positions of the EUV mask leading to various effects. EUV inspection and review systems operating at the illumination wavelength are already known. The U.S. Pat. Nos. 6,954,266, or 5,808,312 describe EUV inspection and review systems or tools operating in combination with a mask repairing system. EUV review systems are also denoted as EUV mask inspection microscopes (EUVM). Further investigation methods for EUV masks are also known. The US 2009/0 286 166 discloses the use of an atomic force microscope (AFM) for the localization of concave defects on EUV masks. The U.S. Pat. No. 6,844,272 describes the determination of the height of the surface of EUV masks by the use of an interferometer. Defects of the absorbing pattern structure may occur if absorbing material is missing at positions which should be opaque, or when absorbing material is existent at positions which should be dear. Further, dirt particles may be attached to the surfaces of EUV optical elements. This type of error results predominantly in amplitude errors. It can be recognized by a surface analysis of the EUV optical element; for example by using a scanning electron microscope (SEM). Using a known mask repairing system, as for example the MeRiT® system of Carl Zeiss SMS excessive material can be removed. An electron beam in combination with a suitable etching gas can be used for this task. Missing absorber material can for example be added by locally depositing chromium with the aid of an electron beam together with a respective precursor gas. EUV optical elements can be washed or polished in order to dean their surfaces from disturbing particles or substances. On the other hand, so-called buried defects can occur in EUV optical elements, i.e. EUV mirrors and/or EUV masks. In the following, the term “buried defect” means a defect or an error which is located on the substrate and/or within the multilayer structure of the EUV optical element. Buried defects lead to both, amplitude and phase errors, i.e. buried defects comprise amplitude and phase error portions. Buried defects are also called topological errors. The U.S. Pat. No. 6,016,357 describes a method for correcting errors of the absorbing pattern structure by the measurement of focus stacks in phase shift masks (PSM) illuminated with deep ultraviolet (DUV) radiation. Further, this document describes a repairing method for removing excessive absorbing materials and for depositing missing absorbing material. This repairing method is denoted as compensational repair. The U.S. Pat. No. 6,235,434 describes the repair of amplitude and phase errors of EUV masks. Independent of the type of error, the repair is done by compensation, i.e. correcting of the absorbing pattern by removing excessive material from the absorbing pattern structure or depositing absorbing material to the absorbing pattern structure, respectively. Further, the US 2005/0 157 384 also discloses the removal of material, whereas the U.S. Pat. No. 6,849,859 describes the adjustment of a thickness of a layer by depositing an additionally layer and by adjusting the thickness of the additional layer. When excessive absorbing material is removed by an ion beam, ions are implanted in a buffer layer arranged between the multilayer film and the absorbing pattern structure. The implanted ions may vary the reflectivity of the corrected EUV mask portion. The JP 2008 085 223 A discloses a method to correct the reflectivity change induced by the implanted ions by respectively correcting the absorbing pattern structure. The article “Study of critical dimensions of printable phase defects using an extreme ultraviolet microscope” by Y. Kamaji et al., Jpn. J. of Appl. Phys. 48 (2009), pp. 06FA07-1-06FA07-4 explains why pits are more often defects in multilayer films of EUV masks than bumps. Further, the article reports on the fabrication of programmed phase defects and their analysis in order to determine the resolution limit of an EUV microscope (EUVM). The thesis of C. H. Clifford: “Simulation and compensation methods for EUV lithography masks with buried defects”, Electrical Engineering and Computer Sciences, University of California at Berkeley, Techn. Report No. UCB/EECS-2010-62 describes simulation methods which allow generating simulation configurations based on aerial images of defects. This document also reports on two methods for defect compensation by adjusting the absorber pattern of EUV masks. The article “Natural EUV mask blank defects: evidence, timely detection, analysis and outlook” by D. van den Heuvel et al., SPIE/BACUS Conf. Proc. 2010, describes a method to combine aerial images, marks and AFM measurement data in order to localise and to measure an EUV defect which cannot be recognized in a scanning electron microscope (SEM). Moreover, this paper describes that both, pits as shallow as 3 nm and bumps just 3 nm high at the surface can results in critical printing defects buried in the multilayer. The above mentioned documents do often not clearly distinguish between amplitude errors and phase errors of buried defects, i.e. of defects on substrates and/or multilayer films of EUV masks. The repair methods denoted as “compensational repair” addresses the amplitude error portions of buried defects, but ignores their phase error portions. FIG. 1 schematically illustrates the compensational repair of a multilayer defect by removing a portion of the absorbing pattern elements adjacent to the defect in order to compensate for the reduced reflectivity of the buried multilayer defect. The compensational repair has the drawback that it results in a diminution of the process window at the wafer illumination, since an EUV mask compensated with this approach has a focus dependency which deviates significantly from the ideal focus characteristics. Moreover, the compensational repair method cannot be applied to correct defects in EUV mirrors not having an absorbing pattern structure. It is therefore one object of the present invention to provide a method and an apparatus for analysing and/or repairing of a defect of an EUV mask, which at least partially overcome the above mentioned drawbacks of the prior art. According to a first aspect of the invention, a method according to claim 1 is provided. In an embodiment, a method for analyzing a defect of a photolithographic mask for an extreme ultraviolet (EUV) wavelength range (EUV mask) comprises (a) generating at least one focus stack relating to the defect using an EUV mask inspection tool, (b) determining a surface configuration of the EUV mask at the position of the defect, (c) providing model structures having the determined surface configuration which have different phase errors and generating the respective focus stacks, and (d) determining a three dimensional error structure of the EUV mask defect by comparing the at least one generated focus stack of the defect and the generated focus stacks of the model structures. The described method exploits that amplitude errors and phase errors become manifest in different focus characteristics. Therefore, the measured focus stack enables discriminating between amplitude errors and phase errors. Amplitude errors basically correspond to surface defects and phase errors basically corresponds to buried defects. Amplitude errors are corrected using a method known in the state of the art. The surface configuration of an identified buried defect which demonstrates in a phase error is analyzed. From the measured surface configuration model structures are calculated from which a three dimensional (3D) error structure of the defect is determined. Thus, the described methods define a procedure to reliably detect and discriminate defects of an EUV mask and to determine an individual 3D error structure of identified buried defects. The 3D error structure of the buried defect can be used to develop a repairing or a compensation policy individually designed for the analyzed buried defect. An EUV mask is preferably a reflective optical element. However, it is also possible to apply the method defined in the first paragraph of this section to transmissive optical elements. Furthermore, the described method is not restricted for analyzing defects of EUV masks. In fact, it can also be applied to analyze defects of photolithographic masks or more general of optical elements designed for a longer wavelength range as well as for a shorter wavelength range. In a further aspect determining the surface configuration comprises scanning the defect with an atomic force microscope, and/or with a scanning tunnelling microscope, and/or with a stylus profilometer, and/or with an interferometer. After a phase error has been identified and localised by analysing a focus stack measured with a mask inspection tool, the surface of the EUV mask above the buried defect causing the phase error is scanned in detail in order to determine the surface configuration. The surface configuration corresponds to the surface topology at the defective position of the EUV optical element. The exemplary combination of both measurement data allows the determination of a 3D error structure for the analyzed defect. Another aspect comprises the step of applying different repairing methods to the three dimensional error structure and simulating associated focus stacks in order to determine an optimal repairing method. After having determined a 3D error structure, the effect of various repairing methods on the resulting focus stack can be evaluated by simulation prior to the application of the respective repairing method. A repairing method is identified by simulation which is optimally adapted to the analyzed defect prior to the correction of the defect. In particular, the described repairing method is not restricted to a modification of the pattern structure arranged on the multilayer film of an EUV mask. Rather, the defined repairing method explicitly includes a modification of the substrate and/or of the multilayer film of the EUV mask in order to correct analyzed defects not only of EUV mask but also of EUV mirrors. Therefore, the defined method corrects buried defects instead of just compensating their amplitude error portion by a compensational repair. In a further aspect determining the optimal repairing method comprises selecting one of the different repairing methods as the optimal repairing method which generates a focus stack which maximizes a process window for the EUV optical element at the illumination of a wafer. The process window is maximized for the repairing method whose aerial images of the focus stack fulfill a predetermined critical dimension (CD) variation for the largest defocus range of the different repairing methods. The application of this optimization criterion maximizes the process window at the illumination of the corrected EUV optical element or which maximizes the depth of focus (DOF), which is of utmost interest for the application of the EUV optical element in a lithography system. Another aspect comprises applying the optimal repairing method to the defective position. The specific treatment of the defective position minimizes the influence of the defect on the image of the EUV pattern in the photoresist arranged on a wafer, so that the EUV optical element can again be utilized in the production process after the respective error handling. In still a further aspect, the model structures comprise an absorbing pattern structure on a surface of the EUV mask. The existence of an absorbing pattern structure facilitates the determination of model structures for a defective position, as the absorbing pattern structure can be used for the identification of the defect position on the surface of the EUV mask. Further, a modification of the pattern elements can also be part of the error correction process. On the other hand, it is not mandatory that the model structures of a buried defect comprise a pattern structure. Rather, the described method can also be applied to EUV mirrors which do not have an absorbing pattern. Another aspect comprises providing the absorbing pattern structure from EUV mask design data and/or from of a recording of at least one image. When the pattern data is available, it is used as input for the simulation process of the effects of the various repairing methods. On the other hand, if this information is not available, it can alternatively be obtained from the recording of an image of the pattern structure. A scanning electron microscope (SEM) can be used for recording an image of the pattern. It is also possible to use a combination of both methods in order to determine the pattern data of an EUV mask. A further aspect comprises using a repairing method correcting the three dimensional error structure so that a resulting multilayer structure is at least approximately corrected to an ideal multilayer structure. In contrast to a compensational repair which just modifies pattern elements when trying to compensate a buried defect, i.e. a multilayer and/or a substrate defect, the described method modifies the substrate and/or the multilayer in order to correct a buried error. Thus, the defined method allows correcting analyzed buried defects to a much higher amount than by a compensational repair, which just addresses the amplitude error portion of a buried defect. Consequently, the described method maximizes the process window of an EUV optical element at its use in a lithography system. Another aspect comprises applying the repairing method directly onto the defective position of the EUV mask. As already mentioned above, the described method analyzes the 3D error structure of a buried defect and corrects the defect by acting on the substrate and/or on the multilayer film instead of only partially compensating the defect by locally modifying pattern elements close to the buried defect. According to another aspect, the repairing method comprises at least partially removing the multilayer structure, in particular drilling at least one hole into the multilayer structure. By removing the portion of the multilayer structure which comprises the buried defect, the defect is also removed. Then a defect-free multilayer film can be newly deposited. Although, this procedure requires some efforts, it does not compensate the defect; rather it is removed by the repairing process. In still another aspect, the repairing method comprises locally compacting and/or expanding the multilayer structure and/or of a substrate of the EUV mask or generally of an EUV optical element by locally focusing femtosecond laser pulses into the EUV mask. The defined repairing method is an example of a repairing which directly corrects a buried defect by acting upon the substrate and/or the multi-layer film of the EUV optical element. In this context, a variation of the substrate is preferred, because the impact of the repair of the defect on the multilayer can be minimized. In another aspect, the femtosecond laser pulses are incident through the substrate of the EUV mask. When the femtosecond laser pulses are directed through the substrate to the defective position, the multilayer or at least the most important upper Mo—Si layers of the multilayer film are not or at least not significantly influenced by the correction of the buried defect. According to a further aspect, an inspection microscope for photolithographic masks in the extreme ultraviolet wavelength range performs a method of any of the aspects described above. According to a further aspect of the invention, a method according to patent claim 11 is provided. In an embodiment, a method for repairing a buried defect in an extreme ultraviolet (EUV) optical element comprises directing an ion beam onto the buried defect so that an ion dose is implanted in the EUV optical element suitable to locally change a volume of the EUV optical element. The EUV optical element comprises an EUV mirror having a substrate and a multilayer structure and/or an EUV mask having a substrate, a multilayer structure and an absorbing pattern structure. The inventive method corrects buried defects of EUV optical elements by directly modifying the substrate and/or the multilayer instead of just compensating the amplitude error portions of these defects by applying a compensational repair. Thus, the inventive method can not only be applied to EUV masks, but it can also be used to correct buried defects of EUV mirrors. EUV optical elements will probably be reflective optical elements. However, the inventive method is not restricted to reflective optical elements, but can also be applied to transmissive optical elements. Moreover, the defined method is also not limited for the correction of buried errors of EUV optical elements. Rather, it can be applied to compensate buried defects of optical elements designed for longer as well as for shorter wavelengths. In still a further aspect, the ion beam comprises inert gas ions, preferably noble gas ions, and most preferably helium ions. Inert gas ions have the advantage that they do not react with the material into which they are implanted. This means, the mechanical and/or the optical properties of the substrate and/or the multilayer film are not significantly modified as a consequence of implanting ions. Further, the noble gas characteristics of the inert gas ions also prevents that the EUV photons of the lithography system induce a reaction of the implanted inert gas with the surrounding material during the operation of the EUV optical element which could change its optical properties in the course of time. A further aspect comprises adapting an ion beam energy to a depth of the buried defect below a surface of the EUV optical element. In yet another aspect, the ion beam energy comprises a range of 1 keV to 200 keV, preferably 5 keV to 100 keV, and most preferably of 10 keV to 50 keV. Ions are implanted in the EUV optical element with a specific spatial distribution. The spatial distribution as well as the maximum of the distribution depend on the energy with which the ions hit on the EUV optical element. The distribution of the implanted ions in beam direction is in the following called depth distribution. The energy with which the ions impinge of the EUV optical element can be selected so that the maximum of the depth distribution of the implanted ions fits to the depth of the buried defect. In still another aspect, the EUV optical element comprises a multilayer structure and the energy of the ion beam is selected such that the ions are essentially implanted below layers of the multilayer structure of the EUV optical element which determine its reflective properties. The term “essentially” means here as well as at further positions within this specification that the maximum and/or the width of the depth distribution are adjusted to the respective Mo—Si layers so that these layers comprise the majority of the implanted ions. As already mentioned in the second section, ions implanted in the multi-layer structure may locally change the reflectivity of EUV photons and may such form an amplitude error. It is well known that a multilayer film shows an asymptotic reflectance characteristic. This means that the Mo—Si layers close to the surface of the EUV element account for the major portion of the reflected EUV radiation, whereas layers close to the substrate only insignificantly contribute to the reflectivity of the EUV optical element. Consequently, ions implanted in the lower Mo—Si layers (the Mo—Si layers dose to the substrate) can efficiently correct a buried defect without essentially influencing the reflective properties of the EUV optical element. In a further aspect, the EUV optical element comprises at least one capture layer arranged between the substrate and the multilayer structure, and wherein ion beam energy is adjusted so that the ions are essentially implanted in the at least one capture layer. By implanting the majority of the ions in the capture layer the reflective properties of the multilayer structure is not or at least not significantly changed. A defect located on the substrate surface in the Mo—Si layers close to the substrate may propagate through at multilayer and thus affecting its reflective characteristic. Therefore, by implanting the majority of the ions in a capture layer, a buried defect can efficiently be removed, so that the defect correction process does not significantly influence the reflective properties of the multilayer structure. Still a further aspect comprises arranging a local protection layer on a surface of the EUV optical element through which the ion beam is directed when repairing the defect prior to directing the ion beam onto the defect and removing the local protection layer at the end of the repairing. Ions impinging on an EUV optical element have a sputter effect on the surface of the EUV optical element, i.e. they have an energy to remove atoms from the surface of the EUV optical element. Hence, the impinging ions may damage the surface of the EUV optical element. This effect can be avoided by locally arranging of a protection layer on the multi-layer prior to the ion bombardment and by removing the protection layer at the end of the defect repairing process. In accordance with a further aspect, the ion beam is not perpendicularly directed through a surface of the EUV optical element onto the buried defect. As already mentioned, beside the sputter effect, ions may induce damages in the multilayer along their paths from the multilayer surface to their implanted position. By using an inclined incidence for the ion beam, a portion of the EUV optical element can be selected for the paths of the ions which has less impact on the imaging of the mask pattern on the wafer. In particular, an incidence angle can be chosen so that the ion beam incidents on an absorbing element. By this approach the multi-layer structure above a buried defect is not damaged during the repairing of the defect. In yet another aspect, the buried defect is a concave defect, in particular a pit and/or a scratch and the local volume change comprises a local volume increase, in particular a local height increase. According to another aspect, the buried defect is a convex defect, in particular a bump and the local volume change comprises a local volume decrease, in particular a local height decrease. Moreover, still a further aspect comprises the step of analyzing the buried defect with a method of any of the aspects described above. Finally, according to another aspect, a focused ion beam apparatus performs a method of any of the aspects described above. In the following, the present invention will be more fully described with reference to the accompanying figures, in which exemplary embodiments of the invention are illustrated. However, the present invention may be embodied in different forms and should not be construed as limited to the examples set forth herein. Rather, these examples are provided so that the disclosure will be thorough and will convey the scope of the invention to persons skilled in the art. FIG. 1 shows a top view of a cut-out of an EUV mask 100. The left diagram no comprises a multilayer structure 120 which has a multilayer defect 130 buried in the multilayer structure 120, which is called a buried defect. On the multilayer 120 two pattern elements 140 are arranged having a form of absorbing stripes. The right diagram 150 illustrates the absorber structure 160 of the left diagram no of the EUV mask 100 after the multilayer defect 130 of has been partially compensated by removing a portion of the absorbing material of the pattern elements 160 around the buried defect 130 in order to compensate the reduced reflectance of the area covered by the buried defect 130. As already mentioned in the third section, this approach of buried defect repairing is called “compensational repair”. FIG. 2 shows a schematic cross-sectional view of a photolithographic mask 200 for an exposure wavelength of 13.5 nm. Different from presently applied photolithographic masks, the EUV mask 200 is a reflective optical element based on a multilayer structure 205. The multilayer structure 205 acts as a mirror which selectively reflects incident EUV photons. The multilayer structure 205 of the EUV mask 200 is deposited on a front substrate surface 215 of a suitable substrate 210, such as a fused silica substrate. Other transparent dielectrics, glass materials or semiconducting materials may also be applied as substrates for photolithographic masks as for example ZERODUR®, ULE® or CLEARCERAM®. It is preferred that the material of the substrate 210 has a very low thermal expansion coefficient. The multilayer film or multilayer structure 205 comprises 40 to 60 pairs of alternating molybdenum (Mo) 220 and silicon (Si) layers 225 (referred to in the following as Mo—Si layers). The thickness of each Mo layer 220 is 4.15 nm and that of the Si layer 225 amounts to 2.80 nm. In order to protect the multilayer structure 205, a capping layer 230 of silicon with a native oxide of 7 nm depth is arranged on top of the multilayer structure 205. Other materials can also be used for forming a capping layer 230 as for example ruthenium. In the multilayer 205, the Mo layers 220 act as scattering layers, whereas the silicon layers 225 function as separation layers. For the scattering layers instead of Mo other elements with a high Z number may be utilized, such as cobalt (Co), nickel (Ni), tungsten (W), rhenium (Re) and iridium (Ir). As already mentioned, the multilayer structure 205 on the substrate 210 of the EUV mask 200 acts as a mirror for EUV electromagnetic radiation. In order to become an EUV mask 200, a buffer structure 235 and an absorbing pattern structure 240 are additionally deposited on the capping layer 230. The buffer layer 235 may be deposited to protect the multilayer structure 205 during processing, for example during etching and/or repairing of the absorbing pattern structure 240. Possible buffer structure materials are for example of fused silica (SiO2), silicon-oxygen-nitride (SiON), ruthenium (Ru), chromium (Cr), and/or chromium nitride (CrN). The absorbing structure 240 comprises a material having a large absorption constant for photons in the EUV wavelength range. Examples of these materials are chromium (Cr), titanium nitride (TiN) and/or tantalum nitride (TaN). An anti-reflective (AR) layer 245 can additionally be arranged on the absorbing pattern structure 240 in order to secure that no photons are reflected by the surface of the absorber pattern 240. A material for an AR layer is for example tantalum oxynitride (TaON). A thickness of about 50 nm is sufficient to absorb basically all EUV photons 250 incident on the absorbing structure 240. In contrast, the majority of the photons 250 incident on the capping layer 230 is reflected as photons 255. In this context as well as on further positions of this description the term “basically” means a numeric value of a quantity within its measurement limit. The substrate 210 of the EUV mask 200 has typical lateral dimensions of 152 mm×152 mm and a thickness or height of essentially 6.35 mm. The rear surface 270 of the substrate 210 or the rear substrate surface 270 has a thin metallic coating 275. Typically this coating 275 comprises chromium. The metallic coating 275 is used to fix the EUV mask 200 at the EUV scanner by the application of electrostatic forces. FIG. 3 represents the EUV mask 300 of FIG. 2 having various defects. In order to keep the following consideration simple, the capping layer 230, the buffer layer 235 as well as the AR layer 245 is omitted in FIG. 3. On the multilayer structure 305 an absorbing pattern 340 is deposited. The pattern element 350 of the absorbing pattern 340 has a portion which partially misses the absorbing material. Furthermore, a dirt particle 360 is attached on the surface 370 of the multilayer 305. The dirt particle 360 can be removed by a cleaning process, i.e. by washing and/or polishing the EUV mask 300. Both types of defect, absorber defects 350 and particle defects 360 on the surface 370 of the EUV mask 300 are in the following called surface defects 380. The surface defects 380 can be detected by a surface analysis of the EUV mask 300. An electron beam of a scanning electron microscope (SEM) can for example be applied for the surface analysis of the EUV mask 300. Furthermore, the surface defects 380 are accessible to a repair by a modification of the absorbing pattern 340. As already mentioned in the second section, this can be performed by using a mask inspection and repairing system, as for example the MeRiT® system of Carl Zeiss SMS. Such a tool allows adding absorber material to the defective pattern element 350 by using an electron beam in combination with a suitable precursor gas or a combination of precursor gases. Examples of precursor gases are metal carbonyls, in particular dicobalt octacarbonyl (Co2(CO)8). When the dirt particle 360 can not be removed by a cleaning process, the absorbing pattern 340 can be modified in order to compensate for the reduced reflectance in the area of multilayer 305 of the EUV mask 300 which comprises the dirt particle 360. This can be done by removing a portion the absorbing pattern 340 around the particle defect 360 as it is schematically indicated in FIG. 1 for the compensational repair of a buried defect 130. An electron beam together with an etching gas or a combination of etching gases can be applied in order to selectively remove a portion of the absorbing pattern 340. For example, xenon difluroride (XeF2) can be used as an etching gas. Further, the EUV mask 300 of FIG. 3 also shows a defect 320 in the substrate 310. In the example of FIG. 3, the substrate defect 320 is a pit or a scratch on the surface of the substrate 310. The substrate defect 320 propagates as defect 330 in the multilayer structure 305 of EUV mask 300. During its propagation through the multilayer structure 305, the multilayer defect 330 increases its lateral dimension, i.e. the distortion of the Mo—Si layers towards the multilayer surface extends on a larger area. At the same time, the variation of the height of the individual Mo—Si layers reduces during the propagation of the multilayer defect 330 through the multilayer structure 305. As indicated in FIG. 3, the substrate defect 320 of the substrate 310 is reflected in a shallow depression of the surface 370 of the multilayer 305 above the buried defect 320. The height variation of the depression at the surface 370 of the multilayer 305 may be as small as a few nanometers. As discussed above, FIG. 3 represents a buried defect 320 caused by a pit or a scratch on the substrate 310. It is also possible that there is for example a dust particle on the surface of the substrate 310 at the beginning of the deposition of the multilayer 305. Furthermore, the substrate 310 may have a small local raise of its surface 370. FIG. 4 schematically depicts a cross section of a cut-out of an EUV mask 400 wherein a substrate 410 has a bump defect 420. Similar to the pit defect 320 of FIG. 3, the bump defect 420 propagates as multilayer defect 430 through the multilayer 405. In addition to the substrate defects 320, 420, buried defects can also be localized in the multilayer 305, 405. For example, individual Mo and/or Si layers may have defective positions at which the width of one or several layers may deviate from its target value (not indicated in FIGS. 3 or 4). Moreover, it is conceivable that a dust particle on a specific Mo and/or Si layer may disturb the periodicity of successively deposited Mo—Si layers of the multilayer structure 305, 405. Similar to the substrate defects 320, 420, these local distortions of the periodicity of the multilayer structure 305, 405 can propagate towards the surface 370, 470 of the multilayer 305, 405. In the following, defects of a substrate 310, 410 and defects within a multilayer structure 305, 405 are summarized as buried defects 480. In contrast to surface defects 380 which lead to amplitude errors on a wafer, buried defects 480 primarily result in phase errors at wafer illumination. Although the substrate defects 320, 420 as well as the defects within the multilayer 305, 405 often become manifest only in a small local depression or a small local increase of the multilayer surface 370, these defects may cause printable errors on a wafer at its illumination. The detection of the substrate defects 320, 420 or generally of buried defects 480 is involved. An electron beam of a SEM can neither detect the substrate defects 320, 420 nor the shallow depression or increase at the surface 370, 470 of the multilayer 305, 405 induced by the defects 320, 420. For example, an atomic force microscope (AFM) can detect the shallow variation of the surface 370, 470 of the multilayer system 305, 405. However, the substrate defects 320, 420 or generally the buried defect 480 causing a small local increase or depression have already been identified and localized by another metrology tool. Time constraints prevent to scan the overall EUV mask 300, 400 which an AFM. Recording not only a single aerial image of the defective position of an EUV mask 300, 400 with a mask inspection tool, but recording of a set of aerial images through focus can reveal the buried defects 320, 420. For this purpose, an aerial image of the defective position is recorded in the best focus plane. Additionally, aerial images are recorded with a distance above and below to the focal plane, as for example ±15 nm, ±30 nm, ±45 nm, ±60 nm, and ±75 nm. In this example, the focus stack comprises 11 images. The number of images as well as the defocus distance can be adjusted to the analyzed defect. FIG. 5 shows a diagram 500 of a simulation of the critical dimension (CD) variation as a function of the offset which is the distance between the center 650 of an absorbing pattern element 640 and the location 660 of the center of the defect 630. FIG. 6 illustrates the configuration simulated in FIG. 5. FIG. 6 depicts a multilayer structure 605 having a buried defect 620 similar to the bump defect 420 of FIG. 4. The bump defect 620 propagates as defect 630 towards the multilayer surface 680. The multilayer surface 670 has an absorbing pattern element 640. The center 650 of the absorbing pattern element 640 is the reference point 650 of the offset of or the distance to the center 660 of the defect 630. A shift of the buried defect 620 in the left direction in FIG. 6 results in FIG. 5 in a positive offset and vice versa. In FIG. 5 the CD amounts to 22 nm as indicated by the vertical dashed line 510 at this CD numerical value. An upper dashed line 520 and the lower dashed line 530 represent boundary lines of a CD variation of ±10%. The curve 540 represents a simulation of the CD variation in focus as a function of the distance of the defect 620 from the center 650 of the pattern element 640. For an offset in the range between 60 nm and 80 nm the simulated CD variation is larger than 2.2 nm, i.e. the CD variation is larger than 10%. The curve 550 shows the simulated CD variation as a function of the offset for a defocus of +75 nm. For this defocus, the CD variation is within the ±10% CD variation bandwidth across the overall simulated offset. On the other hand, the curve 560 simulated with a defocus of −75 nm is for the larger portion of the simulated offset range beyond the tolerable CD variation of ±10%. The simulated curves 540, 550, 560 indicate a strong dependence of the CD variation of the focus position. Such a behaviour is expected for a phase error as is indicated by the buried defect 620 in FIG. 6. FIG. 5 demonstrates that the measurement of aerial images of a focus stack or through focus can be used to discriminate between amplitude errors of surface defects 380 and phase errors of buried defects 480 of EUV masks 300, 400, 600. The curves 540, 550 and 560 of FIG. 5 can be used for a compensational repair. An improvement of the in focus curve 540 can be obtained by modifying the pattern element 640 as schematically indicated in FIG. 1, so that the in focus curve 540 fulfils the ±10% variation criterion across the overall offset range. However, the CD variation of the defocus curves 550 and/or 560 may still be beyond the ±10% variation criterion. Thus, such a repairing diminishes the process window at the illumination of a wafer with the EUV mask 600. This situation is unsatisfactory; therefore a defect recognition method is necessary which analyzes a buried defect in detail. Further, a defect repairing method is required which repairs buried defects in such a way that the process window is as large as possible at the end of the repairing process. The surface configuration of the EUV mask 300, 400, 600 is measured around the identified buried defect 320, 420, 620 for example with an atomic force microscope (AFM). Further tools which can be applied to scan the defective position are for example a scanning tunnelling microscope, a stylus profilometer, and/or an interferometer. The measured surface configuration allows the determination of the deviation of the measured surface configuration from an ideal surface configuration for the EUV masks 300, 400, 600. In the next step, model structures are generated for various buried defects of an EUV mask. For the generation of the model structures, the data of the absorber pattern of the EUV mask at the defective position is required. This data is obtained from the design data of the mask, or it is obtained from the image recorded with an SEM. Although the defect analysis is in the following explained for an EUV mask, it is appreciated that the described method can also be applied for the defect analysis of EUV mirrors. Moreover, the defined method is not restricted to the EUV wavelength range, but can also be utilized for the defect analysis of transmissive optical elements. For each of the generated model structures aerial images for each focus position of a focus stack are simulated. In this simulation process, a plurality of the above discussed defects is considered for each surface configuration. Then the measured surface configuration and the measured aerial images of the focus stack at the defective position are compared with the simulated aerial images of the focus stacks of the generated model structures. The model structure whose aerial images provide the best agreement with the measured aerial images across the focus stack is taken as the three dimensional (3D) error structure of the identified defect. Finally, based on the determined 3D error structure, a repairing or compensation policy is developed which minimizes the impact of the 3D error structure of the EUV mask at the wafer illumination by a specific treatment of the defective position. The objective of the treatment is to again utilize the EUV mask in a production process for the wafer illumination at the end or the repairing process. Two alternative approaches for the determination of a 3D error structure are conceivable: (a) if the measured aerial images of the focus stack indicate that the identified error is an amplitude error, the surface defect 380 causing the amplitude error can directly be corrected by varying the pattern structure 340, 640. This alternative does not analyze the surface configuration of the EUV mask around the detected surface defect 380 by scanning with an AFM. (b) Irrespective of the identified error type, the surface configuration of the detected defect in scanned for example with an AFM in order to determine a surface configuration for a subsequent determination of a 3D error structure for each identified defect. For the correction of the determined 3D error structure various repairing methods can be applied. As already mentioned above, a portion of an absorbing pattern structure can be removed by using an electron beam and/or an ion beam and as appropriate in combination with an etching gas or a combination of etching gases. Absorbing material can be removed in the vertical as well as in the horizontal direction. Alternatively, absorber material, as for example chromium, may be added in both vertical and horizontal directions. The deposition can also be performed with an electron beam and/or with an ion beam and as appropriate together with a respective precursor gas or a combination of precursor gases. Both methods can be applied to correct surface defects 380 and may be employed for a compensational repair of buried defects 480 as schematically illustrated in FIG. 1. A further repairing method comprises at least partially removing of the multilayer structure 305, 405, 605, as for example by drilling a hole into the multilayer structure 305, 405, 605 having a suitable dimension. If the portion of the multilayer structure 305, 405, 605 which comprises the buried defect 480 is removed, the defect 480 is also removed. Then a defect-free multilayer structure 305, 405, 605 can newly be deposited on the removed multilayer portion. The effect of the repairing method described in the preceding paragraph is investigated by simulation prior to performing the replacement of a portion of the multilayer structure 305, 405, 605. This means, the intended correction is initially applied to the determined 3D error structure and a simulation of the resulting aerial images of the focus stack is performed. Only when the result confirms that the resulting aerial images of the corrected position have a sufficiently wide process window, the repairing method is really executed. If this is not the case, further simulations are performed with varied repairing methods or repairing parameters, respectively. The parameters of a repairing method can be optimized by an iterative method. For example, if a buried defect 480 in a multilayer structure 305, 405, 605 is to be repaired by drilling of a hole into the multilayer 305, 405, 605, simulations are performed for holes having various depths, different diameters and/or having various distances from the buried defect. For performing the above mentioned repairing methods an EUV mask inspection microscope is provided having an integrated repairing system. It is also possible to apply the defect analyzing and the defect repairing in separate systems. A further repairing method comprises a local compaction and/or a local expansion of the substrate 310, 410 and/or of the multilayer structure 305, 405, 605 by the impact of electromagnetic radiation. The substrate 310, 410 and/or the multilayer structure 305, 405, 605 can for example be compacted or expanded by the usage of femtosencond laser pulses. A compaction as well as an expansion of the various layers of an EUV optical element can also be achieved by implanting ions at a suitable position of an EUV optical element. In the example described in the following, the method is discussed in the context of a volume expansion. However, it is appreciated that the discussion of a volume expansion does not restrict the described method to volume expansion. Rather, it is also applicable to perform a respective volume compaction. FIG. 7 presents a curve which shows an induced change of the height of a photolithographic mask as a function of the implanted ion dose. In the example of FIG. 7, the mask was irradiated with a helium ion beam having a beam energy of 30 keV. As already mentioned, the helium beam or generally an ion beam has basically two effects: (a) a sputtering effect, i.e. (helium) ions collide with atoms of the sample and release atoms from the sample, (b) implantation, (helium) ions stay in the sample material. In the example of FIG. 7, the implantation of helium atoms does basically not lead to a volume change below a built in ion dose of approximately 2·1016 cm2. Above this value the implantation of helium ions results in a volume expansion of the mask material which goes steeply up with an increase of the implanted helium dose. FIG. 7 illustrates the interrelationship between a volume expansion of a photolithographic mask and the implanted ion dose for the example of helium ions. It is appreciated that similar curves also exist of other inert gas atoms, in particular for noble gas atoms. The focussed ion beam of an ion beam (FIB) apparatus can be used in order to implant an ion dose in an EUV mask with a defined depth distribution as well as with a defined lateral distribution of the implanted ions. Alternatively, the FIB source can be integrated in the mask inspection tool which is applied for the defect analysis as discussed above. Furthermore, an AFM can for example be utilized to determine the volume change induced by the implanted ions. It is also possible to use one of the scanning tools or a combination of them mentioned in the context of the determination of the surface configuration in order to detect the local height change caused by the implantation of ions into an EUV mask. FIG. 8 shows a simulation of the depth distribution of a helium ion beam into an EUV mask as a function of the ion energy. The helium beam hits the EUV mask at a position without an absorbing pattern element. The ordinate indicates the cumulated normalized sum of implanted ions. As can be seen from FIG. 2, the EUV mask has a thin capping layer 230 which is denoted with the reference numeral 830 in FIG. 8. The multilayer structure 805 has a width of approximately 280 nm. It is deposited on a substrate 810 having a width in the millimetre range of which only the upper relevant portion is indicated in FIG. 8. FIG. 9 presents a simulation of the depth distribution of a helium ion beam into an EUV mask as a function of the ion energy. The helium beam hits the EUV mask at a position of an absorbing pattern element. Similar to FIG. 8, the ordinate indicates again the cumulated normalized sum of implanted ions. As indicated in FIG. 2, the absorbing pattern 940 has a thin AR layer 945 of a few nanometers arranged on the absorbing pattern elements 940. The absorbing pattern structure 940 has a width of approximately 70 nm. As already mentioned in the context of the discussion of FIG. 2, depending of the absorber material, a thickness of approximately 50 nm is sufficient to basically absorb all incident EUV photons. The multilayer structure 905 and the substrate 910 of FIG. 9 are identical the multilayer 805 and the substrate 810 of FIG. 8. As can be seen from FIGS. 8 and 9, the depth at which the ions are implanted in the EUV mask depends on the energy with which the ions hit on the surface of the EUV mask. This means that the depth distribution of the implanted ions can be set by selected by the ion beam energy. Further, FIGS. 8 and 9 also reveal that the width of the depth distribution also varies with the energy of the helium beam. Even for ion beam energies of 90 keV the ions are implanted in a way so that more than 50% of the implanted ions are integrated in a depth range of 200 nm. For ion beam energies of 50 keV of less the majority of the build in ions is implanted in a depth range of 100 nm or less. A comparison of FIG. 8 and FIG. 9 shows that an absorbing pattern element does not significantly change the depth distribution of the implanted helium ions. The simulations of FIGS. 8 and 9 have been performed with the software program SRIM, which is described in the article “The Stopping and Range of Ions in Solids” by J. F. Ziegler, J. P. Biersack, and U. Littmark, Pergamon Press, New York, 1985. The implanted dose distribution within an EUV mask can for example be determined by preparing cross-section samples of an EUV mask and investigating the samples with transmission electron microscopy (TEM). The relationship between an exposition of the EUV mask for a predetermined time with predetermined ion beam parameters and the resulting implanted dose distribution within the EUV mask can also be obtained for example from TEM measurements of a series of prepared test samples. This means that the spatial distribution of the implanted ions can be controlled by the selection of the ion beam parameters. FIG. 10 schematically shows in the left partial image a pit defect 1020 in a substrate 1020 of an EUV mask 1000. Similar to the FIGS. 3, 4 and 6 the pit defect propagates as defect 1030 through the multilayer structure 1005. The right partial image schematically shows the multilayer structure 1005 after the implantation of ions as for example helium ions. The helium ions are preferably integrated in Si layers 1040 which causes a local increase of the volume of the Si layers 1040. It has been observed that the induced volume change varies as function of the ion species and ion absorbing material. Built-in helium ions in Mo—Si layers predominantly result in a volume expansion of the Si layers 1040. As a result, the local volume expansion of the Si layers 1040 corrects the effect of the pit defect 1020 at the surface 1070 of the multilayer structure 1005. In the example of FIG. 10, the correction of the pit defect 1020 is performed by a local volume increase of individual Mo layers 1040 of the multilayer structure 1005. This repairing method results in a local breach of the Bragg reflection condition. This problem can be avoided or at least reduced if the ions are preferably implanted in the lowest Mo—Si layers of the multilayer structure 1005 which are close to the substrate 1010. As already explained above, the multilayer structure 1005 shows an asymptotic reflective behaviour. The upper Mo—Si layers close to the surface 1070 of the EUV mask moo contribute the major portion to the reflected EUV radiation, whereas the contribution of the lowest Mo—Si layers is insignificant. Therefore, by correcting the pit defect 1020 of the EUV mask moo by implanting ions in the lowest Mo—Si layers of the multilayer structure 1005 the local breach of the Bragg reflection condition due to the repairing process has a minor effect on the reflectivity of the multilayer structure 1005. FIG. 11 schematically illustrates a further approach with allows the repairing of a defect buried in a multilayer without basically distort the reflectivity of the multilayer structure. In the EUV mask 1100 a so-called capture layer 1115 is inserted between the substrate 1210 and the multilayer structure 1105. The capture layer 1115 has a width of approximately several hundred nanometers. Suitable materials for a capture layer are for example silicon (Si) and/or molybdenum disilicide (MoSi2). It is the purpose of the capture layer 1115 to efficiently capture ions and to provide a large local volume change. The diagram of the right partial image of FIG. 11 schematically presents the depth distribution of the implanted ions. In the thin capture layer 1115 the majority of the ions impinging on the multilayer 1105 is captured and integrated. FIG. 7 depicts that there is a threshold for the ion dose below which a material does not show a volume expansion. Therefore, the depth distribution of the implanted ions (right partial image) indicates that the capture layer 1115 can provide a large local volume expansion which can be adjusted by controlling the beam parameters of the incident ion beam. On the other hand, the doses implanted in the substrate 1110 and in the multilayer structure 1105 are not high enough in order to induce a volume change in these layers. As already mentioned, the bombardment of a surface with an ion beam leads to a local removal of atoms from the material surface. This effect may be detrimental to a multilayer as the upper Mo—Si layers provide an important contribution to the overall reflectivity of the multilayer structure. FIG. 12 shows an EUV optical element 1200 which can comprise an EUV mask and/or an EUV mirror. The EUV optical element 1200 has as substrate 1210 which has a pit defect 1220 and a multilayer structure 1205. For simplicity reasons the propagation of the buried defect through the multilayer structure 1205 is suppressed. Before starting the defect repairing process by implanting of ions with an incident ion beam, a local protection layer 1230 is deposited on the multilayer structure 1205. As can be seen from a comparison of FIGS. 8 and 9, the use of a thin protection layer does not significantly distort the spatial distribution or depth distribution of the implanted ions. The protection layer 1230 has a width of at least the lateral dimension of the buried defect and a height of about 100 nm. Preferred materials for a protection layer 1230 are for example carbon (C) and/or tetraethyl orthosilicate (TEOS). The protection layer 1230 is locally deposited on the multilayer structure 1205 by using an electron bean and/or an ion beam in combination with a precursor gas. After the local deposition of the protection layer 1230, the buried defect 1220 is corrected by implanting an appropriate ion dose in the multilayer structure 1205 as discussed above. The correction of the buried defect 1320 is schematically depicted in the middle part of FIG. 12. The incident ions sputter a portion 1240 of the upper part of the protection layer 1230. Therefore, the protection layer 1230 efficiently protects the surface of the multilayer structure 1205 from the sputter action of the incident ions. At the end of the ion implantation process, the protection layer 1230 is again removed. This can for example be done by an etching process using an electron beam and/or an ion beam together with one etching gas or a combination of etching gases. Beside the sputter action at the surface, the interaction of the ions with the material along their path through the material may induce damages in the material along the ion path. Therefore, it can be beneficial to guide the incident ions through portions of a multilayer structure of an EUV optical element whose integrity is of less importance for the reflectivity of the multilayer film. FIG. 13 schematically illustrates an example how such an improvement can be realized for EUV mask 1300. Similar to the left partial image of FIG. 12, the left partial image of FIG. 13 presents again a substrate 1310 having a pit defect 1320. The propagation of the buried defect through the multilayer structure 1305 is again ignored. An absorbing pattern 1340 is deposited on the multilayer film 1305. The buried defect 1320 is not localised below an absorbing pattern element 1340, but below the surface 1370 of the multilayer structure 1305. If an ion beam perpendicularly incidents on the buried defect 1320, it has to pass through the surface 1370 of the multilayer 1305 and may damage the surface 1370 by sputtering atoms from the Mo—Si layers closest to the surface 1370. Furthermore, the ion beam might damage the multilayer structure 1305 along its path to the buried defect 1320 as explained in the preceding paragraph. FIG. 13 illustrates a configuration with which a possible damage of reflectivity critical portions of the multilayer can at least partially be avoided. The left partial image of FIG. 13 schematically shows the configuration at the beginning of the ion beam irradiation. The ion beam 1380 obliquely impacts on the pattern element 1340 and obliquely crosses the multilayer structure 1305 on its path to the buried defect 1320. The right partial image of FIG. 13 schematically shows the situation at the end of the repairing process. The local volume expansion caused by the implanted ions corrected the buried defect 1320. The surface 1360 of the pattern element 1340 is damaged by the sputter action of the ion beam 1380 during the repairing process. If necessary, the surface damage 1360 of the pattern element 1340 can be corrected by locally depositing absorber material on the damaged surface 1360 by using a method described above. The white area 1330 below the absorbing pattern element 1340 indicates the area with might be damaged by the interaction of the ions of the ion beam 1380 with the Mo and Si atoms of the multilayer structure 1305. It has a drop shaped form. The major portion of the potentially damaged area is located below the pattern element 1340. In particular, ions do not cross the Mo—Si layers closest to the surface 1370 of the multilayer structure 1305. Thus, by the selected path of the ion beam 1380, the impact of the ion beam 1380 on the reflectivity of the multilayer structure 1305 is minimized. An EUV mirror which does not have an absorber pattern can also be corrected with the discussed procedure if a protection layer 1230 of FIG. 12 in arranged on the EUV mirror instead of the pattern element 1340. Finally, the discussed repairing methods can also be applied on defects of a mask blank prior to the deposition of a multilayer structure. By correcting defects existent on the substrate already on the mask blank possible damages of the multilayer structure can be avoided. The defined method for defect analysis reliably discriminates between surface defects and buried defects of EUV optical elements. Instead of incompletely compensating the impact of buried defects of EUV masks by modifying of the absorbing pattern, the discussed repairing method corrects buried defects by a modification of the substrate and/or of the multilayer structure of EUV optical elements.

summary

claims

1. Goggles for receiving at least one radiation protection material which protects the eyes of a patient from radiation being harmful to the eyes, wherein the goggles comprise:two goggle frames each comprising a continuously circumferential side wall structure completely enclosing an area around the respective eye of the patient,a length-adjustable connection element between the two goggle frames in the area of the nose of the patient for changing the distance between the two goggle frames relative to one another, andat least one length-adjustable holding element for fixing the two goggle frames to the head of the patient,wherein the side wall structures are configured for receiving at least one radiation protection material substantially completely around its circumference,wherein each side wall structure comprises an inner and an outer side wall which are connected by means of a base wall at an end of the side wall structure, wherein the inner and the outer side wall have a predetermined distance in the cross direction to the viewing direction of the patient in order to form a space, the space being configured for receiving the at least one radiation protection material. 2. The goggles according to claim 1, wherein the at least one radiation protection material is configured so as to fill the space completely in the longitudinal direction. 3. The goggles according to claim 2, comprising a light transmissive element which is preferably arranged in the area of the distal end of each goggle frame, wherein preferably the inner side wall has a smaller height in the distal direction than the outer side wall, wherein the transmissive element is substantially flush with the outer side wall and/or rests against the distal end of the inner side wall. 4. The goggles according to claim 3, wherein the light transmissive element comprises a radiation protection material. 5. The goggles according to claim 4, wherein said radiation protection material is a low-Z material. 6. The goggles according to claim 5, wherein said low-Z material is acrylic glass or plastic materials loaded with high-Z materials. 7. The goggles according to claim 6, wherein said high-Z materials are bismuth or lead acrylic. 8. The goggles according to claim 3, wherein the shape and size of the light transmissive element are substantially adapted to the shape and size of the inner circumference of the outer side wall. 9. The goggles according to claim 1, wherein the at least one radiation protection material comprises a first material layer formed of a material having a low atomic number Z, and/or a second material layer formed of a material having a high atomic number Z, wherein the first material layer and the second material layer are provided as a compound layer, as a thin film or as a powder dispersed in a matrix material or as a liquid for casting or injection molding. 10. The goggles according to claim 9, wherein the first material layer is arranged in the space neighboring the outer side wall and the second material layer is arranged in the space neighboring the inner side wall. 11. The goggles according to claim 9, wherein said first material layer is Aluminum and said second material layer is lead or lead replacement materials such as bismuth, tungsten, tantalum or compounds of these metals. 12. The goggles according to claim 1, further comprising a first eye provided at the part of the respective side wall structure of a goggle frame facing the nose for attaching the connection element and/or further comprising a second eye provided at the part of the respective side wall structure of a goggle frame opposite the part facing the nose for attaching the holding element. 13. The goggles according to claim 1, wherein the proximal end of the side wall structure, has a shape and/or size being ergonomically adapted to the shape of the patient's head in the area around the eyes. 14. The goggles according to claim 1, wherein said goggles protects the eyes of a patient from β-radiation, x-ray radiation and/or gamma radiation.

047864605

description

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The right-hand part of FIG. 1 shows a portion of the main vessel 10 of a fast neutron nuclear reactor. In known manner the vessel 10 is filled with sodium 12 and contains the reactor core 14, only a small portion of which is shown in FIG. 1. The core is formed by a large number of fissile, fertile assemblies, one 16 of which is shown. In reactors of integrated type the main vessel 10 also contains all the components of the primary circuit, more particularly the pumps and heat exchangers. In loop-type reactors at least a proportion of these components is situated outside the vessel 10. The main reactor vessel 10 is received in a vessel well formed by a concrete structure a portion 18 of which is shown in FIG. 1. A metal skin 20 lining the vessel well 18 forms a safety vessel. The main vessel 10 is suspended by its top end from a horizontal floor 22 covering the peripheral edge of the vessel well. At its top end the main vesssel 10 is closed by a caisson-type closure slab 24 bearing at its centre, generally via a system of two over-lapping rotary plugs (not shown), an assembly-handling apparatus 16, such as a stirring rod 26. The rod 26 enables an assembly 16 to be introduced into a handling or transporting pot 28 forming one of the elements of the handling installation according to the invention. To this end the assembly 16 can be taken either from the reactor core 14, or from a storage zone (not shown) provided inside the main reactor vessel 10. Of course, the rod 26 permits the converse handling operation consisting in taking a new assembly from the pot 28 to introduce it into the reactor core 14. In addition to the pot 28, the handling installation according to the invention comprises a primary ramp 30, a secondary ramp 34 and a transfer hood 32. The ramps 30 and 34 are inclined in opposite directions by an angle of about 20.degree. to the vertical. More precisely, their axes lie in the same plane, forming an inverted V. The primary ramp 30 extends through the slab 24 and opens at its bottom end inside the vessel 10 in a zone close to the core 14 and generally called the loading-unloading station of the reactor, referred to hereinafter as the primary station to simplify matters. The secondary ramp 34 extends through the top end of the vessel well 18 and then the wall 35 of a structure adjacent such well, to enter an adjoining vessel 36 via a tube 36a. The vessels 10 and 36 are situated at approximately the same level one alongside the other. As a variant, the wall 35 and the wall of the vessel well 18 might be formed by one single wall. The diameter of the adjoining vessel 36 differs in dependence on whether the assemblies placed in the vessel have or have not previously been stored inside the reactor vessel itself. In the embodiment illustrated in FIG. 1, it is supposed that the assemblies have been stored in the primary vessel. The diameter of the vessel 36 is therefore small, since the assemblies can be evacuated directly. To this end a handling system (not shown) can be placed in a cell disposed above the vessel 36. Like the main reactor vessel 10, the adjoining vessel 36 is filled with liquid sodium 12, as well as the bottom portion of the secondary ramp 34 disposed in the tube 36a. The zone defined by the bottom end of the vessel 36 into which the secondary ramp 34 opens is generally called the secondary loading-unloading station, but to simplify matters will be hereinafter referred to as the secondary zone. The transfer hood 32 rests on the slab 24 and on the floor 22 and is so mounted as to pivot around a vertical axis (arrow F1) in a manner which will be disclosed in greater detail hereinafter. It should be noted that the axis of rotation of the hood 32 coincides with the axis of symmetry of the ramps 30 and 34. The hood 32 is mainly formed by a thick cylindrical tube 32b whose geometrical axis is inclined by an angle identical with the angle of inclination of the primary ramp 32 and the secondary ramp 34. By rotating the hood 32 through 180.degree., therefore, the open bottom end of the hood can be successively moved into the prolongation of the open top end of the primary ramp 30 and into the prolongation of the open bottom end of the secondary ramp 34. The hood 32 is closed at its top end and its internal diameter is approximately the same as that of the ramps 30 and 34. Due to this configuration the biological screening is situated as close as possible to the assembly during transfer. Although the thickness of the screening is compulsory, in this way its mass and therefore cost are reduced. The simplicity of shape of the biological screening also enables it to be hermeticized. It therefore ensures the containment of the covering gas above the sodium 12 in the period of handling during the power-generating operation of the reactor. The thick tube 32b is lined on the outside by a heat insulation 32c allowing an ascending circulation of air or gas by natural convection in an annular space bounded between the heat insulation 32c and the wall of the tube 32b. To this end inlet and outlet windows, whose opening is controlled by closure members 32d, are formed at the bottom and top of the heat insulation 32c respectively. The circulation of air by the natural convection of the air enables the residual power of the fissile assemblies to be evacuated when they are unloaded. Moreover, the thermal inertia of the thick walls of the tube 32b make a number of hours available to take action in case of an incident. The hood 32 thus forms a "hot" biological screening ensuring by conduction the thermal regulation of the pot which it contains, without the necessity to use forced ventilation. To prevent the solidification of the liquid metal contained in the pot during the handling period, a heating system 32 is disposed around the thick tube 32b and in contact therewith. The handling installation according to the invention comprises a single pot 28 which is moved from the secondary station to the primary station and conversely, passing successively via the secondary ramp 34, the rotary hood 32 and the primary ramp 30 (arrows F2 in FIG. 1). To this end the pot 28 is attached to lifting means which will be disclosed in greater detail hereunder. It will simply be pointed out here that the lifting means comrise two cables 40 whose bottom ends are attached to the pot 28 or, more precisely, to the top end of a rocking rod 28b whose bottom end is articulated at a place 28c to the body 28d of the pot, substantially halfway up such body. To ensure its guidance when it moves inside the ramps 30 and 34 and the hood 32, the pot has two pairs of wheels 28a guided by rails 30a, 32a and 34a disposed in the ramp 30, the hood 32 and the ramp 34 respectively. One of the pairs of wheels 28a is mounted at the top end of the rockig rod 28b, while the other pair of wheels is mounted on the body 28d, below the articulation 28c. As shown in FIG. 1, due to the structure of the pot 28 just described and the attachment of the pot to the cables 40 by the top end of the rocking rod 28b, the pot is inclined to follow the rails disposed inside the ramps and the hood and resumes its vertical position when it arrives at the primary or secondary loading-unloading station (arrow F3). As a result of limiting the number of wheels 28a to two pairs, the pot 28 is guided isostatically inside the ramps and the hood. This eliminates any risk of the pot being blocked during its movement, even if there should be angular offsetting between the hood and one or other of the ramps. Referring to FIG. 2, it can be seen that the isostatic nature of the guiding of the pot is made possible by the fact that there is practically no break between the rails 32a of the hood and the rails 30a or 34a of the ramp with which the hood is aligned. There is therefore no longer any need to give the pot extra pairs of guide wheels, as was the case with the handling installation of the Super Phenix reactor. According to the invention this result is made possible by eliminating the sluice-like operation of the transfer hood during handling. It should be noted that such elimination is perfectly possible, since the sodium 12 contained in the lower portion of the secondary ramp 34 disposed in the tube 36a (FIG. 1) then ensures that the internal atmosphere of the main reactor vessel 10 is contained in relation to the outside. Thus, according to the invention the open top ends of the primary ramp 30 and the secondary ramp 34 are closed only during the power operation of the reactor. Such closure is performed by means of two flaps 46 (FIG. 3b) mounted on a rotary horizontal platform 48 to which the hood 32 is also attached (preferably demountably). The platform 48 takes the form of a disc whose geometrical axis coincides with the vertical axis of rotation of the platform. The flaps 46 are disposed symmetrically in relation to the vertical axis of rotation of the hood 32 and the platform 48, for example at 90.degree. on either side of the hood. Each of the flaps 46 is formed by a solid disc of vertical axis bearing at its periphery two toric sealing joints. The platform 48 is disposed immediately above a fixed base plate 50 which ensures that the platform is supported and rotated. As shown in FIG. 3a, the plate 50 is a horizontal disc-shaped plate which has a diameter slightly larger than that of the platform 48 and whose geometrical axis coincides with the axis of rotation of the platform 48. The top ends of the ramps 30 and 34 open into the plate at diametrically opposite locations. More precisely, the rails 30a ad 34a of the ramps 30 and 34 project upwards beyond the upper face of the plate 50, the rails 32a of the hood 32 projecting downwards beyond the lower face of the platform 48, so that a very small clearance (a few millimetres) is left between the ends of the rails when the hood is placed above one of the ramps (FIG. 2). A larger space is formed between the plate 50 and the platform 48, so that the latter can rotate when a flap closes one of the ramps. Thus, at the end of a handling period and before the reactor power rises, the effect of a rotaton of the plate 48 through 90.degree. is to move the diametrically opposite flaps 46 to face the top ends of the ramps 30 and 34. The control mechanisms of the flaps 46 will be disclosed in greater detail hereinafter with reference to FIG. 5. Here it will merely be stated that during handling, the flaps 46 occupy a raised position in which they are retracted into recesses 48b (FIGS. 2 and 5) formed inside the rotary platform 48, so as not to impede the rotation of the platform. In contrast, when the reactor is operating, the flaps are lowered to hermetically seal the top ends of the ramps. In that position the flaps 46 are completely released from the recesses 48b, so that the platform 48 can similarly be rotated. In addition to the two flaps 46 disposed at diametrically opposite locations on the platform 48, the installation according to the invention advantageously comprises another flap 46' forming a spare flap. The third flap 46' is mounted on the platform 48 at a location diametrically opposite that occupied by the hood 32 (FIG. 3b). When the hood 32 is disposed in the prolongation of one or other of the primary 30 and secondary 34 ramps, therefore, the spare flap 46' is situated opposite the top end of the other ramp. The spare flap 46' is identical with the two other flaps. Similarly, the spare flap control mechanism is identical with the control mechanisms of each of the two other flaps 46. The presence of the spare flap 46' on the rotary platform 48 has the advantage of enabling either of the two other flaps 46 to be very rapidly interchanged, for example, when the sealing joints of the flaps have become damaged. To allow such interchange, the base plate 50 comprises, at a location angularly offset, for example, by 90.degree. in relation to the top ends of the ramps, a recess 60 opening on to the upper face of the plate 50 (FIGS. 3a and 4). The recess 60 forms a withdrawal station for the flaps as a result of which one of the two "active" flaps 46 can be replaced by the spare flap 46'. The replacement can be performed very simply in the following manner. In a first stage, with the spare flap 46' and the hood 32 facing the ramps 30 and 34, the operator actuates the control mechanism of the flap 46 to be replaced, which is disposed above the recess 60, to introduce such plate into the recess and disconnect it from its control mechanism. By a rotation of the platform 48 through half a turn, the second flap 46 is in turn moved above the recess 60. The spare flap 46' is then opposite the top end of one of the ramps 30 or 34. The operator lowers such flap inside the base plate 50 and disconnects the flap from its control mechanism, to close the end of the corresponding ramp. By rotating the platform 48 through a quarter of a turn in the opposite direction, the second flap 46 is moved above the other ramp, then introduced into the base plate by the actuation of its control mechanism. The installation is then in a position to operate, the worn flap 46 having been replaced by the spare flap 46'. These operations for replacing the flap 46 are so performed that the hood 32 is never opposite a ramp closed by a flap. In this way the cutting of the rails 30a, 32a and 34a is reduced to the minimum compatible with the mechanical constructional tolerances. In practice it is a few millimetres. Moreover, these operations are performed without infringing the hermeticity of the assembly. To enable the worn flap 46 to be evacuated and a fresh, spare flap 46' to be introduced in its place, the control mechanism of the spare flap 46' is mounted in the rotary platform 48 via a demountable plug 62, as shown more particulary in FIG. 5. The plug 62 is mounted and demounted, for example, by unscrewing three shoes 64 screwed on to the top horizontal surface of the rotating platform 48 and bearing against the upper surface of the plug 62. To maintain the containment of the space formed between the rotary platform 48 and the base plate 50, two sealing joints are mounted on the periphery of the plug 62 and an argon-circulating system is provided between the joints. It should be noted that a similar system is used for all the joints ensuring containment. Referring to FIGS. 3a, 3b and 4, it can be seen that a hood closure member 140 can also be received in the recess 60 formed in the base plate 50. In that case the upper surface of the closure member 140 is formed with a circular recess 140a whose dimensions enable it to receive the spare flap 46' or one of the flaps 46. The closure member 140 also comprises two diametrically opposite lugs which are formed with tapped holes 142b. When the bottom end of the hood 32 is to be closed, the flaps 46 and 46' are retracted into the rotary platform 48 by actuating the control means associated with them. By rotating the rotary platform 48 the operator moves the bottom end of the hood 32 above the recess 60 receiving the hood closure member 140. Screws 142 permanently received in the wall of the hood 32 are then screwed into the tapped holes 140b. The hood closure member is then attached to the hood 32 to hermetically close its open bottom end. The hood 32 thus closed can then be demounted from the rotary platform to which it is attached, for example, by screws or pins (not shown). This feature can be used more particularly to take action on the transporting pot 28, which is then moved back into the hood 32. The feature also enables fuel to be handled on a number of reactors situated on the same site, using a single hood 32. A description will now be given, with reference to FIG. 2, of the means for supporting and rotatably entraining the rotary platform 48 from the base plate 50. These functions are moved upwards, due to coaxial tubes 48a and 50a prolonging the peripheral edges of the platform 48 and the plate 50 respectively upwards, so as to prevent the heat at the level of the plate 50 from breaking down the hermeticity of the rotary joints. The platform 48 is supported by a rolling bearing 52 with three sets of rollers which is disposed between the top end of the flanges 48a and 50a. The entrained rotation of the platform 48 is performed by a step-down motor 54 supported by the top end of the tube 48a. The output shaft of the step-down motor 52 bears a pinion 56 meshing with a toothed rim 58 with which the top end of the external surface of the tube 50a is formed. Preferably the step-down motor 54 provides a fast rotary speed and a slow speed, the latter being used at the end of the movement. To maintain the containment of the space bounded between the rotary platform 48 and the base plate 50, rotary sealing joints (not shown) are associated with the rolling bearing 52. Moreover, an argon circulation is provided between these joints to enable a leakage of one of them to be detected immediately. FIG. 5 shows to an enlarged scale the mechanism 66 controlling the movement of the spare flap 46' between its bottom closure position, shown in solid lines, and its raised retracted position inside a recess 48b formed in the platform 48 below the plug 62 (this position being shown in chain-dot lines). The mechanism also enables the gripping of the flap to be controlled and its presence to be checked. As already mentioned, the control mechanisms associated with each of the flaps 46 are identical with the control mechanism 66 associated with the spare flat 46a. The following description of the mechanism 66 therefore also applies to the mechanisms used for controlling the two flaps 46, the only difference being that the latter mechanisms are placed directly in the platform, and not in a plug 62. The control mechanism 66 comprises a supporting member 68 whose lower portion 68a, taking the form of a sheath, is attached hermetically, for example, by screws 69, in a bore extending through the centre of the plug 62. The member 68 is prolonged upwards beyond the flat upper surface of the platform 48, in the form of a vertical portion 68b having a U-shaped horizontal section. At its top end the portion 68b of the member 68 terminates in a horizontal plate 68c. The member 68 supports a member 70 which can move vertically along the vertical axis shared by the plug 62 and the flap 46'. The lower portion 70a of the member 70 takes the form of a cylindrical sleeve tube slidably received in the lower sheath-shaped portion 68a of the member 68. The member 70 is prolonged above the upper surface of the rotary platform 48 by a vertical portion 70b having a U-shaped section and disposed inside the portion 68b of the member 68. At its top end the portion 70b terminates in a horizontal plate 70c disposed below the plate 68c. A screwthreaded rod 70d projects vertically upwards along the axis of the plug 62 and the flap 46a, passing freely through the plate 68c. The plate 68c supports an endless screw jack 72 which is actuated manually, for example, by means of a flywheel shown diagrammatically at a place 74 in FIG. 4. By taking action of the jack 72 using the wheel 74, the raising or lowering of the member 70 inside the member 68 can be controlled as required. The square flap 46' (or one of the flaps 46) is connected to the bottom end of the member 70 via a hollow vertical rod 76 extending through the lower portion 70a of the member 70. At its bottom end the rod 76 has a screwthreading and projects beyond the bottom end of the portion 70a, so that it can be screwed into a nut 46a borne at the centre of the upper surface of the flap 46. At its top end projecting above the portion 70a of the member 70, the rod 76 has a hexagonal head 76a enabling the rod of the nut 64a to be tightened or unscrewed using a suitable spanner. The portion of the rod 76 adjacent the head 76a is also screwthreaded to receive a counternut 78 adapted to bear against the upper surface of the portion 70a, to immobilize the rod 76 in the member 70 when the rod is screwed into the nut 46a. In that position a nose 70e in the form of a collar formed at the bottom end of the portion 70a of the member 70 is fitted into the flap 46 around the nut 46a. The hollow rod 76 has a central bore in which a central rod 80 forming a finger checking for the presence of the flap 46 moves freely. A compression spring 82 interposed between the top end of the finger 80 and the plate 70c of the member 70 always exerts a downward thrust on the finger 80. Sealing bellows 84 are interposed between the bottom end of the member 68 and the bottom end of the member 70. Similarly, sealing bellows 86 are interposed between the top end of the hollow rod 76 and the top end of the finger 80. Two annular sealing joints are also provided between the portion 68a of the member 68 and the plug 62, an intermediate argon circulation being provided between such joints. Contactors 88 and 90 are mounted on the plug 62 and the portion 68b of the member 68 respectively to detect the bottom and top positions of the member 70. These two positions of the member 70 correspond to the closure of the corresponding ramp by the flap 46 or the retraction of such flap inside the rotary platform 48 respectively. In the embodiment shown in FIG. 5, a visual check is made on the gripping of the flap 48 by the hollow rod 76 and the presence of the flap opposite such rod. For this purpose the top end of the hollow rod 76 is surmounted by a drum 94 bearing a visual reference mark. Similarly, the top end of the rod 80 is surmounted by a drum 94 bearing a visual reference mark. The drums 92 and 94 are disposed inside the portion 70b of the member 70. Corresponding reference marks made on the fixed member 68 enable the gripping of the flap 46 and its presence to be checked. Thus, when the hollow rod 76 is screwed into the nut 46a, the reference mark formed on the drum 92 is normally opposite a first reference mark on the member 68. When the rod 76 is completely unscrewed from the nut 46a, the reference mark on the drum 92 is opposed a second reference mark on the fixed member. By taking action on the wheel 74, the member 70 is then moved upwards to disengage the nose 70e formed at the bottom end of this member 70 from the flap 46'. When this operation is completed, the reference mark on the drum 92 is opposite a third reference mark formed on the fixed member 68. In parallel, when the nose 70e of the member 70 is fitted into the flap 46', the reference marker formed on the drum 94 always remains opposite a corresponding reference mark formed on the fixed member 68, since in that case the bottom end of the finger 80 bears against the flap 46. In contrast, when the rod 76 is unscrewed from the nut 46a and the member 70 moves away from the flap 46', the finger 80 is forced down by the compression spring 82. The reference mark formed on the drum 94 then moves downwards in relation to the corresponding reference marked formed on the fixed member 68. A visual check can therefore be made that the member 70 is properly separated from the flap 46. FIG. 6 shows diagrammatically the principle of the supporting of the base plate 50 by the slab 24 closing the reactor vessel and by the floor 22 disposed on the peripheral wall of the vessel well. A tube 96 encloses the primary ramp 30 in the portion thereof which extends through the slab 24 and is situated thereabove. The tube 96 is welded to the top flange 24a of the slab 24 and comprises at its top end a spherical bearing area 96a received in a cylindrical passage 50a in the plate 50, as illustrated in FIGS. 6 and 7. The base plate 50 rests on the top end of the tube 96 via a shoulder 50b disposed in the passage 50a above the cylindrical portion thereof in which the spherical bearing surface 96a is received. So as not to block the swivel link formed by the cooperation between the surface 96a and the bore 50a, the plate 50 is attached to the end of the tube 96 only in that portion of the shoulder 50b which is furthest away from the vertical axis of the base plate 50. Such attachment is obtained by means of pins 98 or the like, a bearing wedge 100 being interposed between the shoulder 50b and the tube 96. Hermeticity is produced between the base plate 50 and the top end of the tube 96 by a resilient diaphragm 102 (FIG. 7) in the form of washer, whose external and internal peripheries are welded to the upper surface of the plate 50 and the end of the tube 96 respectively. To prevent any differential expansion between the base plate 50, the upper flange 24a of the slab and the floor 22 from affecting the mechanical behaviour of these members, the swivel link just described, between the tube 96 borne by the slab and the base plate 50, is completed by two shoes 104 disposed at about 120.degree. in relation to such swivel link. The shoes 104 are sliding shoes with which the lower surface of the base plate 50 is formed and which rest on the floor 22. To prevent the plate 50 from rotating horizontally around the swivel link 96a-50a, a key-type guide system 106 is provided at a location diametrically opposite from the swivel link. The guide system 106 is oriented radially in relation to the vertical axis of the plate 50 and disposed between the lower surface of the plate 50 and the upper surface of the floor 22. As was already shown, one of the main advantages of the invention is the small clearance between the guide rails 30a and 34a formed inside the ramps and the guide rails 32a formed in the hood 32. To keep such spacing substantially constant at all temperatures, the ramps 30 and 34 are suspended from the base plate 50 in a manner which will now be disclosed in greater detail with reference to FIGS. 7 and 8. As shown by FIG. 7, the primary ramp 30 is supported by a spherical bearing surface 30b bearing swivelably against a conical bearing 96b formed inside the tube 96 adjacent the base plate 50. In a comparable manner (FIG. 8), the secondary ramp 34 has adjacent its top end a spherical bearing surface 34b which bears swivelably against a frustoconical bearing surface 108a formed on a member 108 attached to the lower surface of the base plate 50. Hermeticity between the top end of the ramp 34 and the base plate 50 is provided by a resilient diaphragm 110 in the form of a washer, whose external and internal peripheral edges are welded to the upper surface of the plate 50 and the lower surface of the secondary ramp 34 respectively. Of course, means are provided in association with the swivel links just described with reference to FIGS. 7 and 8, to prevent the ramps from rotating in relation to the members supporting the ramps. As shown in FIG. 8 in the case of ramp 34, the means can more particularly be formed by a finger 112 connected in this case to the member 108 and entering a suitably shaped recess in the ramp 34. To complete the supporting performed by these swivel links without producing mechanical stress in the primary and secondary ramps, their bottom ends are guided by guide members 114 and 116 (FIG. 1) attached to the internal structures of the main vessel 10 and the adjoining vessel 36 respectively. As already stated, the means for lifting the pot 28 comprise two cables 40. FIG. 1 shows how the cables pass over two return pulleys 42 of common horizontal axis disposed above the hood 32, before being wound on two drums 44 also having a common horizontal axis. FIGS. 9 and 9a show the motorization system for simultaneously driving the two drums 44 on which the lifting cables 40 are wound (the system is shown in section in the right-hand half of FIG. 9). FIG. 9 clearly shows that the motorization system is symmetrical in relation to the vertical plane containing the axis of the hood 32. The drums 44 are therefore disposed on either side of such plane of symmetry on two coaxial driving shafts 118 separately supported rotatably by a single casing 120 attached to the outside of the hood 32. The shafts 118 project outside the casing 120, where each of them is rotated by an irreversible step-down motor 126 whose casing is not connected to the casing 120. The input of each of the step-down motors 126 is connected to the output shaft of a single asynchronous motor assembly via an angle gear 122 and two universal joint mechanisms 124. More precisely, the geometrical axis shared by the motor 122 at its output shaft and at the angle gear 122 lies in the plane of symmetry of the motorization system, the mechanism 124 being oriented normally in a direction perpendicular to such plane and lying on either side thereof. The motor assembly 121 preferably enables the movment of the pot to be controlled at high and low speed, the latter being used only at the end of movement of the pot, or on its arrival in the hood, or on its arrival at the primary and secondary loading-unloading stations. To this end the assembly 121 in that case has two asynchronous motors with incorporated brakes, whose common output shaft also comprises a torque limiter. Preferably an optical encoder 128 is disposed at the end of each of the shafts 118, if necessary behind a reducing gear 129, so that the position of the pot in the installation can be detected at any moment. A bolt 150 is mounted on the casing 120 opposite a toothed rim 152 rotated by one of the shafts 111, to block the drum 44 if action must be taken on the corresponding reducing gear 126. Although this is not shown in FIG. 9, a similar arrangement is provided on the other shaft 118. The motorization system just described comprises two kinematic chains which are perfectly symmetrical in relation to the vertical plane of symmetry defined hereinbefore. In this system, due to the floatable mounting of the casings 126 of the step-down units and the presence of universal joint mechanisms 124, any imbalance occurring between the torques exerted on each of the shafts 118 results in the pivoting in the opposite direction of the casings of the step-donwn units around such shafts. By detecting such pivoting, it is therefore possible to immediately detect such an imbalance and therefore the start of rupture of one of the cables 40. To this end the casing 120 also supports the pivot 130 of an imbalance-detecting level or rocker 132. The pivot 130 coincides with the axis of the motor assembly 121 and the lever 132 extends symmetrically on either side of such pivot 130. At each of its ends the lever 132 is attached to the end of a shock-absorber 134 whose axis is oriented in a direction at right angles to both the geometrical axes of the motor 121 and of each of the shafts 128. Each of the shock-absorbers 134 comprises a weighing cell 135 (FIG. 9a) and is articulated by its opposite end to a lever 136 connected to the casing of each of the step-down units 126 and oriented radially in relation to the corresponding shaft 128. When the torques exerted on the shafts 128 are equal, the levers 136 are perfectly symmetrical in relation to the plane of symmetry of the system. In contrast, if an imbalance appears between the torques exerted on each of the shafts 128, for example, because of the start of rupture of one of the cables 40, the casings 126 of the step-down units tend to rotate in the opposite direction around the axis shared by the two shafts 128. The relative rotation is transmitted to the lever 130 via the shock-absorbers 134 and is immediately detected by electric contacts 138 (FIG. 9a) mounted on the casing 120 and sensitive to any offsetting of the level 132 in relation to its equilibrium position. It should be noted that the lever 132 also allows the incorrect winding of one of the cables 40 on to the corresponding drums 44. From this aspect the structure of the drums 44 and the casing 120 is such that the cables can never escape from the drums. Advantageously sight holes can be provided, more particularly in the casing 120, to enable the condition of the cables 40 to be checked visually. Moreover, the casing 120 (which also contains the return pullies 42) and the hood 32 are heated to about 150.degree. C. to avoid hooping on the drums due to cable. Preferably the installation is also designed in such a way that the portion of the cables 40 wetted by the sodium 12 is never wound on to the drums 44. Lastly, a manual control (not shown) enables the movable equipment to be returned to a safe position in all cases. As a result of all these features of the pot-lifting system, safety is such that the pot parachute of the existing installations is no longer needed. The elimination of the parachute enables another possible cause of the jamming of the pot in the ramps to eliminated. It also results in an appreciable reduction in the cost of the installation. Finally, the installation according to the invention leads to considerable progress in comparison with existing installations. In the first place, it practically eliminates any risk of the pot getting jammed, and all the difficulties arising therefrom. Secondly, it reduces the mass, space occupied and more particularly the cost of the installation (more particularly the hood) to a very important extent. Lastly, it allows a global doubling of the rate of handling, despite the simplification of the system (one single pot). Of course, the installation disclosed can be modified in various ways without exceeding the scope of the invention. Thus, merely by way of example, the flaps and the hood can be differently positioned on the rotary platform from the way shown in FIG. 3a. More particularly, if the vertical pivoting axis of the platform is offset in relation to the vertical plane containing the axes of the ramps, the flaps will not be situated at diametrically opposite locations on the platform. The ramps can also be located in two parallel planes, so as to deal with two pots associated with two hoods identical with the hood 32 described, but offset on the platform 48 in relation to the vertical pivoting axis of the platform. This arrangement enables the handling rate to be substantially improved.

summary

claims

1. A structure for suppressing flow induced vibration in a nuclear reactor vessel comprising:a guide tube provided inside a hollow upper core support column interposed between an upper core support plate and an upper core plate in a reactor vessel;a head nozzle provided at a lower end of the upper core support column; andan instrumentation tube disposed inside the guide tube, whereina lower hole is provided at a lower portion of a side surface of the guide tube, andthe instrumentation tube is disposed to contact with an inner circumferential surface of the side surface of the guide tube on which the lower hole is provided, such that the instrumentation tube is pressed against the side surface by a differential pressure between coolant inside and outside the lower hole. 2. The structure for suppressing flow induced vibration according to claim 1, whereina pressure adjustment hole is provided at a side surface of the upper core support columnfor allowing coolant flowing into the guide tube from a lower end of the guide tube to flow out to outside from inside the guide tube through a gap between the instrumentation tube and the lower hole, and then to flow out to outside from inside the upper core support column through the pressure adjustment hole. 3. A structure for suppressing flow induced vibration in a nuclear reactor vessel comprising:a guide tube provided inside a hollow upper core support column interposed between an upper core support plate and an upper core plate in a reactor vessel;a head nozzle provided at a lower end of the upper core support column; andan instrumentation tube disposed inside the guide tube, whereinan upper hole and a lower hole are provided at two portions, namely an upper portion and a lower portion, of a side surface of the guide tube, andthe instrumentation tube is disposed to contact with an inner circumferential surface of the side surface of the guide tube on which the upper hole and the lower hole are provided, such that the instrumentation tube is pressed against the side surface by a differential pressure between coolant inside and outside the upper hole and the lower hole. 4. The structure for suppressing flow induced vibration according to claim 3, whereinan upper pressure adjustment hole and a lower pressure adjustment hole are provided at two positions, namely, an upper portion and a lower portion, of a side surface of the upper core support columnfor allowing the coolant flowing into the guide tube from an upper end of the guide tube to flow out to outside from inside the guide tube through a gap between the instrumentation tube and the upper hole, and also to flow out to outside from inside the upper core support column through the upper pressure adjustment hole, andfor allowing coolant flowing into the guide tube from a lower end of the guide tube to flow out to outside from the inside of the guide tube through a gap between the instrumentation tube and the lower hole, and also to flow out to outside from inside the upper core support column through the lower pressure adjustment hole. 5. The structure for suppressing flow induced vibration according to claim 3, whereinthe upper hole and the lower hole are formed in slits extending in an axis direction of the guide tube, and includes expanded portions expanded in oval shapes at middle portions of the slits.

claims

1. A beam line system of an ion implanter, the beam line system comprising:a hollow tube having an inlet and an outlet, wherein the hollow tube is a collimator tube, an ion beam emitted by the ion implanter is introduced into the hollow tube through the inlet and exited from the hollow tube through the outlet; anda plurality of protruding structures formed on an inner wall of the hollow tube, wherein each of the protruding structures has a reflective surface for reflecting a portion of the ion beam. 2. The beam line system according to claim 1, wherein the hollow tube is made of graphite. 3. The beam line system according to claim 1, wherein the protruding structures are contiguous wedge-shaped structures on the inner wall of the hollow tube. 4. The beam line system according to claim 1, wherein the reflective surface of the protruding structure is substantially vertical to a traveling direction of the ion beam. 5. The beam line system according to claim 1, wherein a ratio of a height of the reflective surface of the protruding structure to a length of the protruding structure along a traveling direction of the ion beam is about 1:5. 6. The beam line system according to claim 1, wherein the portion of the ion beam which is not reflected by the protruding structures is exited from the outlet of the hollow tube. 7. The beam line system according to claim 6, wherein an end analyzer is positioned at a terminal of the beam line system to detect the portion of the ion beam which is exited from the outlet of the hollow tube. 8. The beam line system according to claim 7, wherein the end analyzer is a Faraday cup detector. 9. An ion implantation process, which is implemented by the beam line system according to claim 1. 10. An ion implanter, comprising:an ion source for producing ions;an analyzing magnet for producing an ion beam by selecting desired types of ions; anda beam line system for transmitting the ion beam, wherein the beam line system comprises a hollow tube with an inlet and an outlet and a plurality of protruding structures formed on an inner wall of the hollow tube, wherein the hollow tube is a collimator tube, the ion beam is introduced into the hollow tube through the inlet and exited from the hollow tube through the outlet, wherein each of the protruding structures has a reflective surface for reflecting a portion of the ion beam. 11. The ion implanter according to claim 10, further comprising:an accelerating system for accelerating the ion beam;a focusing system for focusing the accelerated ion beam; anda target chamber for receiving the ion beam from the focusing system. 12. The ion implanter according to claim 10, wherein the hollow tube is made of graphite. 13. The ion implanter according to claim 10, wherein the protruding structures are contiguous wedge-shaped structures on the inner wall of the hollow tube. 14. The ion implanter according to claim 10, wherein the reflective surface of the protruding structure is substantially vertical to a traveling direction of the ion beam. 15. The ion implanter according to claim 10, wherein a ratio of a height of the reflective surface of the protruding structure to a length of the protruding structure along a traveling direction of the ion beam is about 1:5. 16. The ion implanter according to claim 10, wherein the portion of the ion beam which is not reflected by the protruding structures is exited from the outlet of the hollow tube. 17. The ion implanter according to claim 16, wherein an end analyzer is positioned at a terminal of the beam line system to detect the portion of the ion beam which is exited from the outlet of the hollow tube. 18. The ion implanter according to claim 17, wherein the end analyzer is a Faraday cup detector.