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https://optimization-online.org/2017/04/5982/ | # Outer-Product-Free Sets for Polynomial Optimization and Oracle-Based Cuts
Cutting planes are derived from specific problem structures, such as a single linear constraint from an integer program. This paper introduces cuts that involve minimal structural assumptions, enabling the generation of strong polyhedral relaxations for a broad class of problems. We consider valid inequalities for the set $S\cap P$, where $S$ is a closed set, and $P$ is a polyhedron. Given an oracle that provides the distance from a point to $S$ we construct a pure cutting plane algorithm; if the initial relaxation is a polytope, the algorithm is shown to converge. Cuts are generated from convex forbidden zones, or $S$-free sets derived from the oracle. We also consider the special case of polynomial optimization. Polynomial optimization may be represented using a symmetric matrix of variables, and in this lifted representation we can let $S$ be the set of matrices that are real, symmetric outer products. Accordingly we develop a theory of \emph{outer-product-free} sets. All maximal outer-product-free sets of full dimension are shown to be convex cones and we identify two families of such sets. These families can be used to generate intersection cuts that can separate any infeasible extreme point of a linear programming relaxation in polynomial time. Moreover, in the special case of polynomial optimization we derive strengthened oracle-based intersection cuts that can also ensure separation in polynomial time.
## Citation
Manuscript, Columbia University, 04/2017. Submitted to Mathematical Programming A. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9081764221191406, "perplexity": 360.6191735114231}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500017.27/warc/CC-MAIN-20230202101933-20230202131933-00027.warc.gz"} |
https://eprint.iacr.org/2017/590 | ## Cryptology ePrint Archive: Report 2017/590
Constant bandwidth ORAM with small block size using PIR operations
Linru Zhang and Gongxian Zeng and Yuechen Chen and Siu-Ming Yiu and Nairen Cao and Zheli Liu
Abstract: Recently, server-with-computation model has been applied in Oblivious RAM scheme to achieve constant communication (constant number of blocks). However, existing works either result in large block size O(log^6N), or have some security flaws. Furthermore, a lower bound of sub-logarithmic bandwidth was given if we do not use expensive fully homomorphic operations. The question of \whether constant bandwidth with smaller block size without fully homomorphic operations is achievable" remains open. In this paper, we provide an armative answer. We propose a constant bandwidth ORAM scheme with block size O(log^3N) using only additive homomorphic operations. Our scheme is secure under the standard model. Technically, we design a non-trivial oblivious clear algorithm with very small bandwidth to improve the eviction algorithm in ORAM for which the lower bound proof does not apply. As an additional bene t, we are able to reduce the server storage due to the reduction in bucket size.
Category / Keywords: cryptographic protocols / ORAM, constant communication overhead, oblivious clear algorithm | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9486712217330933, "perplexity": 3785.3102088406495}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267161098.75/warc/CC-MAIN-20180925044032-20180925064432-00365.warc.gz"} |
https://www.physicsforums.com/threads/magnetic-force.118040/ | # Magnetic force
1. Apr 19, 2006
### spoonthrower
In a television set, electrons are accelerated from rest through a potential difference of 19 kV. The electrons then pass through a 0.29 T magnetic field that deflects them to the appropriate spot on the screen. Find the magnitude of the maximum magnetic force that an electron can experience.
Here are my thoughts so far.... this is all i know....
B=F/(qv)
B=.29
19kV=19000 V
I need to find the velocity of the electron to solve for F, the only problem is.....
2. Apr 19, 2006
### neutrino
Electrons gain energy when the are accelerated. Once they escape the influence which was accelarates them, the energy is purely kinetic.
3. Apr 19, 2006
### spoonthrower
i dont understand still....do i have to use the kinetic energy theorom??? and if i do what do i plug into it??? thanks
4. Apr 19, 2006
### EbolaPox
We know that the maximum magnetic force occurs when velocity is maximum.
The electron is being accelerated through a potential difference. By the Work-Energy Theorem
$$1/2 mv^2 = qV$$
When all the energy the electron gains from the potential difference goes to kinetic energy, its velocity is maximized.
Solve for velocity. Does that help?
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https://www.physicsforums.com/threads/quantum-mechanics-matrices.672363/ | # Quantum Mechanics: Matrices
1. Feb 17, 2013
1. The problem statement, all variables and given/known data
The problem is I am unable to understand the proof. I understand how it is done but I do not know how it is related to the theorem. It is probably because I am unable to understand the notation of matrices, the one involving k.
It is given that
I=δ_ij
= 1 0 0...0
0 1 0...0
...........0
...........1
So now how do I relate k with it?
So before you explain to me whats going on, please elaborate on the notation.
Thank you.
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
#### Attached Files:
• ###### question.png
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2. Feb 17, 2013
### Fredrik
Staff Emeritus
If you mean that you don't understand how to go from the first line to the second, all they've done is to insert the identity operator in the form $1=\sum_k|k\rangle\langle k|$. If you mean that you don't understand how to go from the second row to the third, then you need to learn about the relationship between linear operators and matrices.
Let U and V be vector spaces. Let $T:U\to V$ be linear. Let $A=(u_1,\dots,u_n)$ and $B=(v_1,\dots,v_m)$ be ordered bases for U and V respectively. The matrix [T] of the linear operator T with respect to the pair (A,B) of ordered bases is defined by
$$[T]_{ij}=(Tu_j)_i.$$ The right-hand side is interpreted as "the ith component of the vector $Tu_j$ in the ordered basis B".
You should find it very easy to verify that if B is an orthonormal ordered basis, we have $[T]_{ij}=\langle v_i,Tu_j\rangle$.
The reason for the definition of [T] can be seen by doing a simple calculation. Suppose that Tx=y. I won't write any summation sigmas, since we can remember to do a sum over each index that appears twice.
\begin{align}y &=y_i v_i\\ Tx &= T(x_j u_j)=x_jT(u_j)=x_j(Tu_j)_i v_i.\end{align} Since the v_i are linearly independent, this implies that $y_i=(Tu_j)_i x_j$. This can be interpreted as a matrix equation [y]=[T][x], if we define [y] and [x] in the obvious ways, and [T] as above. (Recall that the definition of matrix multiplication is $(AB)_{ij}=A_{ik}B_{kj}$).
When U=V, it's convenient to choose A=B, and we can talk about the matrix of a linear operator with respect to an ordered basis, instead of with respect to a pair of ordered bases.
Notations like [T] are typically only used in explanations like this. I think most books would use T both for the linear operator and the corresponding matrix with respect to a pair of ordered bases.
Edit: It would be a good exercise for you to prove that if $T:U\to V$ and $S:V\to W$ are linear, then $[S\circ T]=[T]$. This result is the main reason why matrix multiplication is defined the way it is.
Last edited: Feb 17, 2013
Similar Discussions: Quantum Mechanics: Matrices | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9840443134307861, "perplexity": 222.82505383239197}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187825900.44/warc/CC-MAIN-20171023111450-20171023131450-00524.warc.gz"} |
https://arxiv.org/abs/0712.3323 | Full-text links:
math.PR
(what is this?)
# Title: Analysis of the optimal exercise boundary of American options for jump diffusions
Abstract: In this paper we show that the optimal exercise boundary / free boundary of the American put option pricing problem for jump diffusions is continuously differentiable (except at the maturity). This differentiability result has been established by Yang et al. (European Journal of Applied Mathematics, 17(1):95-127, 2006) in the case where the condition $r\geq q+ \lambda \int_{\R_+} (e^z-1) \nu(dz)$ is satisfied. We extend the result to the case where the condition fails using a unified approach that treats both cases simultaneously. We also show that the boundary is infinitely differentiable under a regularity assumption on the jump distribution.
Comments: Key Words: American put option, jump diffusions, smoothness of the early exercise boundary, integro-differential equations, parabolic differential equations Subjects: Probability (math.PR); Analysis of PDEs (math.AP) Cite as: arXiv:0712.3323 [math.PR] (or arXiv:0712.3323v6 [math.PR] for this version)
## Submission history
From: Erhan Bayraktar [view email]
[v1] Thu, 20 Dec 2007 04:07:34 GMT (47kb)
[v2] Thu, 3 Jan 2008 21:47:24 GMT (47kb)
[v3] Mon, 18 Feb 2008 03:10:56 GMT (48kb)
[v4] Tue, 19 Feb 2008 02:27:29 GMT (49kb)
[v5] Tue, 26 Aug 2008 17:49:33 GMT (56kb)
[v6] Wed, 26 Nov 2008 23:26:26 GMT (57kb) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8354379534721375, "perplexity": 2874.0950557411293}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583510749.55/warc/CC-MAIN-20181016113811-20181016135311-00261.warc.gz"} |
https://zbmath.org/?q=an:1307.81062 | ×
# zbMATH — the first resource for mathematics
Precanonical quantization and the Schrödinger wave functional revisited. (English) Zbl 1307.81062
Summary: We address the issue of the relation between the canonical functional Schrödinger representation in quantum field theory and the approach of precanonical field quantization proposed by the author, which requires neither a distinguished time variable nor infinite-dimensional spaces of field configurations. We argue that the standard functional derivative Schrödinger equation can be derived from the precanonical Dirac-like covariant generalization of the Schrödinger equation under the formal limiting transition $$\gamma^0 \varkappa \to \delta(0)$$, where the constant $$\varkappa$$ naturally appears within precanonical quantization as the inverse of a small “elementary volume” of space. We obtain a formal explicit expression of the Schrödinger wave functional as a continuous product of the Dirac algebra valued precanonical wave functions, which are defined on the finite-dimensional covariant configuration space of the field variables and space-time variables.
##### MSC:
81T70 Quantization in field theory; cohomological methods 81S05 Commutation relations and statistics as related to quantum mechanics (general) 81S10 Geometry and quantization, symplectic methods
Full Text: | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8552622199058533, "perplexity": 1043.2121891536406}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305052.56/warc/CC-MAIN-20220127012750-20220127042750-00201.warc.gz"} |
https://math.stackexchange.com/questions/2993010/finding-integers-satisfying-the-equations | # Finding Integers Satisfying The Equations
Okay, so I have these equations:
$$x = 1^p + 2^p + 3^p +... m^p$$ $$x = 1^q + 2^q + 3^q +... n^q$$
How many possible values of positive integers $$(m, n, p, q)$$ are there, if any, such that the equations hold with $$p,q,m, n> 1$$ where $$p \ne q$$?
I tried approaching the problem by first considering the smaller values of $$p$$ and $$q$$ like $$2,3$$. and found no solution over the positive integers. I have no idea how to proceed with it. Any help will be appreciated.
• For $p=2,\ q=3$ you need to find solutions (if they exist) to $\frac{m(m+1)(2m+1)}{6}=\frac{n^2(n+1)^2}{4}$ – Keith Backman Nov 11 '18 at 16:58
• @KeithBackman They do not exist, except for $n=m=1$. – Dietrich Burde Nov 11 '18 at 17:14
The question is not known in general, I think, but is known for special cases like $$p=2$$, $$q=3$$, see the comments:
By the Cannonball problem, $$1^2+2^2+3^2+\cdots +m^2=\frac{m(m+1)(2m+1)}{6}=N^2$$ is only solvable for $$m=1$$ and $$m=24$$ with $$N=1$$, and $$N=70$$. In order to equal a sum of cubes, $$1^3+2^3+\cdots +n^3=\left(\frac{n(n+1)}{2}\right)^2=70^2,$$ we obtain $$70=n(n+1)/2$$, a contradiction. The trivial solution $$m=n=1$$ is excluded.
• The question asks for the impossible. I don't think this is known in general (as usual for such problems). But, as you wrote in your question, "considering the smaller values of $p$ and $q$ like $2,3$" is already interesting and can be solved. – Dietrich Burde Nov 12 '18 at 15:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 18, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9632452726364136, "perplexity": 144.87611084379827}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573444.87/warc/CC-MAIN-20190919060532-20190919082532-00039.warc.gz"} |
http://www.ck12.org/physical-science/Kinetic-Theory-of-Matter-in-Physical-Science/lesson/user:c2Vob292ZXJAaW50ZXJhY3QuY2NzZC5uZXQ./Kinetic-Theory-of-Matter/r4/ | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Kinetic Theory of Matter
## Introduces the theory that all matter consists of constantly moving particles.
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Kinetic Theory of Matter
These neat rows of cola bottles represent matter in three different states—solid, liquid, and gas. The bottles and caps are solids, the cola is a liquid, and carbon dioxide dissolved in the cola is a gas. CO2 gives cola its fizz. Solids, liquids, and gases such as these have different properties. Solids have a definite shape and volume. Liquids also have a definite volume but can change their shape with the shape of the container they are in. Gases have neither a definite shape or volume. What explains these differences in states of matter? The answer has to do with energy.
### Moving Matter
Energy is the ability to cause changes in matter. For example, your body uses chemical energy when you lift your arm or take a step. In both cases, energy is used to move matter—you. Any matter that is moving has energy just because it’s moving. The energy of moving matter is called kinetic energy. Scientists think that the particles of all matter are in constant motion. In other words, the particles of matter have kinetic energy. The theory that all matter consists of constantly moving particles is called the kinetic theory of matter.
There are three parts to the theory:
1. All matter is composed of tiny particles (atoms, molecules, ions, etc...)
2. Thes particles are in constant and random motion.
3. These particles collide with each other and their walls of their container without loosing energy in the collisions (elastic collisions).
### Kinetic Energy and States of Matter
Differences in kinetic energy explain why matter exists in different states. Particles of matter are attracted to each other, so they tend to pull together. The particles can move apart only if they have enough kinetic energy to overcome this force of attraction. It’s like a tug of war between opposing sides, with the force of attraction between particles on one side and the kinetic energy of individual particles on the other side. The outcome of the “war” determines the state of matter.
• If particles do not have enough kinetic energy to overcome the force of attraction between them, matter exists as a solid. The particles are packed closely together and held rigidly in place. All they can do is vibrate. This explains why solids have a definite volume and shape.
• If particles have enough kinetic energy to partly overcome the force of attraction between them, matter exists as a liquid. The particles can slide past one another but not pull apart completely. This explains why liquids can change shape but still have a definite mass.
• If particles have enough kinetic energy to completely overcome the force of attraction between them, matter exists as a gas. The particles can pull apart and spread out. This explains why gases have neither a definite volume or shape. Becasue the gases can spread out this also means that they can be compressed into smaller volumes or can expand into larger volumes.
Look at the Figure below. It sums up visually the relationship between kinetic energy and state of matter. You can see an animated diagram at this URL:
• The final state of matter is plasma. Plasma (from Greek πλάσμα, "anything formed"). It comprises the major component of the Sun. Heating a gas may ionizeits molecules or atoms (reducing or increasing the number of electrons in them), thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions. Other than in the sun, plasma is found in lightening, can be created in neon lights with high-energy devices (like a plasma torch).
### Summary
• According to the kinetic theory, particles of matter are in constant motion. The energy of motion is called kinetic energy.
• The kinetic energy of particles of matter determines the state of matter. Particles of solids have the least kinetic energy and particles of gases have the most.
• There are four states of matter: solid, liquid, gas and plasma.
### Review:
1. Create a six to nine pannel cartoon that explains the kinetic model and the four states of matter.
1. The cartoon strip must have information about the different energy levels of each state and the basic properties of the state (like liquids taking on the shape of the container).
2. The carton must be neat.
3. Color is good but it is optional.
### Notes/Highlights Having trouble? Report an issue.
Color Highlighted Text Notes | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8454544544219971, "perplexity": 737.6755341411817}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982295103.11/warc/CC-MAIN-20160823195815-00290-ip-10-153-172-175.ec2.internal.warc.gz"} |
http://eventos.cmm.uchile.cl/dmmp2015/program/abstracts/ | # Abstracts and Slides
D. AHLBERG Quenched Voronoi percolation
Slides
In a seminal work from 1999, Benjamini, Kalai and Schramm introduced a
framework for studying sensitivity of Boolean functions with respect
to small portions of noise. They moreover made a series of conjectures
that have been highly influential for the development since. We will discuss
this development in some detail, and look more closely at the recent
solution to one of these conjectures, concerning Voronoi percolation:
Position a large number of points in the unit square and consider their
Voronoi tessellation. Next, colour each cell either red or blue. The question
is whether observing the tessellation, but not the colouring, will help us in
guessing whether the colouring will produce a horizontal red crossing or
not? We establish that this is not the case.
E. AÏDÉKON Scaling limit of the recurrent biased random walk on a Galton-Watson tree
We consider a biased random walk on a Galton-Watson tree. This Markov chain is null recurrent for a critical value of the bias. In that case, Peres and Zeitouni proved that the height of the Markov chain properly rescaled converges in law to a reflected Brownian motion $B$. We show here that the trace of this Markov chain converges in law to the Brownian forest encoded by $B$. Joint work with Loïc de Raphélis.
L.-P. ARGUIN Fluctuation bounds for interface free energies in spin glasses
Slides
One way to understand the structure of the Gibbs states of disordered systems is to get good bounds on the fluctuations of the free energy difference between two states. This approach has led to the proof of the absence of phase transition in the 2D Random Field Ising Model (RFIM) at the end of the 1980’s. We will explain a method to obtain lower bounds for the variance of the free energy difference of the Edwards-Anderson (EA) spin glass model on Z^d between certain incongruent states (if they exist…). Unlike the RFIM, there is no dominance of the (+) and (-) states in the EA model. One interesting point of the method is to overcome this lack of monotonicity. The lower bound is also used to rule out particular structures of the Gibbs states in d=2. This is joint work with D. Stein, C. Newman and J. Wehr.
A. AUFFINGER Recent results on mean field spin glass model
I will survey recent and ongoing progress on mean field spin glasses. I will primarily discuss the behavior and role of the Parisi measure in the SK model, and its connections to ultrametricity and chaos.
Based on joint works with Wei-Kuo Chen (U. Minnesota).
Y. BAKHTIN Ergodic theory of Burgers equation with random forcing
Slides
I will talk about extending the ergodic theory of randomly forced Burgers equation (a basic nonlinear evolution PDE related to hydrodynamics and growth models) to the noncompact setting. In the inviscid case, a variational principle holds, so an essential part of the program is constructing one-sided infinite minimizers of random action and studying their properties. The corresponding results are joint with Eric Cator and Kostya Khanin for Poissonian forcing and due to myself in the kicked forcing case. I will also report on the progress for the viscous case (joint with Liying Li). Here the variational characterization is replaced by the Feynman-Kac formula, so a natural approach is to construct and study infinite-volume polymer measures.
P. BOURGADE The eigenvector moment flow and applications
Slides
For generalized Wigner matrices, I will explain a probabilistic version of quantum unique ergodicity at any scale, and gaussianity of the eigenvectors entries. The proof relies on analyzing the effect of the Dyson Brownian motion on eigenstates. Relaxation to equilibrium of the eigenvectors is related to a new multi-particle random walk in a random environment, the eigenvector moment flow. Applications of this local quantum unique ergodicity to universality will be mentioned. This is joint work with H.-T. Yau.
A. BOVIER Extremes of Gaussian Processes on Trees
Slides
Gaussian processes indexed by trees form an interesting class of correlated random fields where the structure of extremal processes can be studied.
One popular example is Branching Brownian motion, which has received a lot of attention over the last decades, non the least because of its connection to the KPP equation.
In this talk I review the construction of the extremal process of standard and variable speed BBM (with Arguin, Hartung, and Kistler).
N. CURIEN First passage percolation on random planar maps
Slides
Random planar maps are a model of random two dimensional discrete geometry studied a lot in recent years and motivated by two dimensional quantum gravity. We prove a general principle showing that perturbing locally the graph distance in a random planar map does not change the large scale geometric structure up to multiplying it by a deterministic constant. This applies in particular to perturbations of the metric obtained by first-passage percolation or by taking the dual of the map. The dilation constant is given by a subtle subadditive lemma taking place in a half-planar version of these maps. In certain cases such as first-passage percolation with exponential edge weights on the dual (known as Eden model in the literature), or Tutte’s classical bijection between quadrangulations and general maps we are even able to compute explicitly the dilation constant. Based on joint works with J.F. Le Gall.
P. DEY Longest increasing path within the critical strip
Consider a Poisson Point Process of intensity one in the two-dimensional square $[0,n]^2$. In Baik-Deift-Johansson (1999), it was shown that the length $L_n$ of a longest increasing path (an increasing path that contains the most number of points) when properly centered and scaled converges to the Tracy-Widom distribution. Later Johansson (2000) showed that all maximal paths lie within the strip of width $n^{2/3+\epsilon}$ around the diagonal with probability tending to $1$ as $n\to \infty$. We consider the length $L_n^{(\gamma)}$ of maximal increasing paths restricted to lie within a strip of width $n^{\gamma}, \gamma<2/3$ around the diagonal and show that when properly centered and scaled it converges to a Gaussian distribution. We also obtain tight bounds on the expectation and variance of $L_n^{(\gamma)}$. Joint work with Matthew Joseph and Ron Peled.
P. FERRARI Phase transition for the diluted clock model
Slides
We prove that phase transition occurs in the dilute ferromagnetic nearest-neighbour q-state clock model in Z^d, for every q≥2 and d≥2. This follows from the fact that the Edwards-Sokal random-cluster representation of the clock model stochastically dominates a supercritical Bernoulli bond percolation probability, a technique that has been applied to show phase transition for the low-temperature Potts model. The domination involves a combinatorial lemma which has interest by itself. Joint work with Inés Armendariz and Nahuel Soprano-Loto.
M. GUBINELLI Regularisation by noise in some PDEs
Slides
We discuss some examples of the “good” effects of “very bad”, “irregular” functions. In particular we will look at non-linear differential (partial or ordinary) equations perturbed by noise. By defining a suitable notion of “irregular” noise we are able to show, in a quantitative way, that the more the noise is irregular the more the properties of the equation are better. Some examples includes: ODE perturbed by additive noise, linear stochastic transport equations and non-linear modulated dispersive PDEs. It is possible to show that the sample paths of Brownian motion or fractional Brownian motion and related processes have almost surely this kind of irregularity. (Joint work with R. Catellier and K. Chouk).
L. KORALOV Averaging, homogenization, and large deviation results for the study of randomly perturbed dynamical systems
Slides
In this talk we’ll discuss several asymptotic problems that can be formulated in terms of PDEs and solved using probabilistic methods. The first set of problems concerns the asymptotic behavior of solutions to quasi-linear parabolic equations with a small parameter at the second order term. Here we employ an extension of the large-deviation theory of Freidlin and Wentzell. Another set of problems concerns equations with a small diffusion term, where the first-order term corresponds to an incompressible flow, possibly with a complicated structure of flow lines. Here we use an extension of the averaging principle. Finally, we’ll consider equations with a small diffusion term with periodic coefficients in a large domain. Depending on the relation between the parameters, either averaging or homogenization need to be applied in order to describe the behavior of solutions. We’ll discuss the transition regime. Different parts of the talk are based on joint results with D. Dolgopyat, M. Freidlin, M. Hairer, and Z. Pajor-Guylai.
B. RIDER Spiking the random matrix hard edge
Slides
The largest eigenvalues of a finite rank perturbation of a random hermitian matrix are known to exhibit a phase transition. If the perturbation is “small” one sees Tracy-Widom behavior, while a “large” perturbation results in Gaussian effects (with a scaling window about the critical value leading to a separate interpolating family of limit laws). This basic discovery is due to Baik, Ben Arous, and Peche at “beta=2”, with Bloemendal and Virag later showing the picture persists in the context of the general beta ensembles. Yet another route, explained here, is to go through the random matrix hard edge, perturbing the smallest eigenvalues in the sample covariance set-up. A limiting procedure then recovers all the alluded to distributions. (Joint work with Jose Ramirez.)
L. ROLLA Absorbing-State Phase Transitions
Modern statistical mechanics offers a large class of driven-dissipative stochastic systems that naturally evolve to a critical state, of which activated random walks is perhaps the best example. The main pursuit in this field is to describe the critical behavior, the scaling relations and critical exponents of such systems, and whether the critical density in the infinite system is the same as the equilibrium density in their driven-dissipative finite-volume version. These questions are however far beyond the reach of existing techniques. In this talk we will report on the progress obtained in recent years, and discuss some of the open problems.
A. SEN Double Roots of Random Littlewood Polynomials
Slides
We consider random polynomials whose coefficients are independent and uniform on {-1,1}. We will show that the probability that such a polynomial of degree n has a double root is o(n^{-2}) when n+1 is not divisible by 4 and is of the order n^{-2} otherwise. We will also discuss extensions to random polynomials with more general coefficient distributions.
This is joint work with Ohad Feldheim, Ron Peled and Ofer Zeitouni.
A. STAUFFER Random walk on dynamical percolation
Slides
We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph G are either open or closed, and refresh their status at rate \mu. At the same time a random walker moves on G at rate 1 but only along edges which are open. The regime of interest here is when \mu goes to zero as the number of vertices of G goes to infinity, since this creates long-range dependencies on the model. When G is the d-dimensional torus of side length n, we prove that in the subcritical regime, the mixing times is of order n^2/\mu. We also obtain results concerning mean squared displacement and hitting times. This is a joint work with Yuval Peres and Jeff Steif.
L. TOURNIER Activated random walks with bias
Slides
The Activated Random Walk model is a conservative particle system in which particles move independently except that, when alone at a vertex, particles may switch to a passive state and then stay still until the visit of another particle. The competition between local deactivation and global spread of activity by diffusion is believed to lead, in wide generality, to a nontrivial phase transition as the initial density increases: at low density, local configurations eventually stabilize, while at higher density activity persists locally forever. The case when the particle motion is biased was first specifically considered by Taggi. In this talk, we will present an extension of this result. This is joint work with Leonardo Rolla.
M. E. VARES Layered systems at the mean field critical temperature
Slides
In this talk, I will report on a recent work in collaboration with L.R. Fontes, D. Marchetti, I. Merola, and E. Presutti. We consider the Ising model on $\mathbb Z\times \mathbb Z$ where on each horizontal line $\{(x,i), x\in \mathbb Z\}$, the interaction is given by a ferromagnetic Kac potential with coupling strength $J_\ga(x,y)\sim\gamma J(\gamma (x-y))$ at the mean field critical temperature. We then add a nearest neighbor ferromagnetic vertical interaction of strength $\epsilon$ and prove that for every $\epsilon >0$ the systems exhibits phase transition provided $\gamma>0$ is small enough.
J. YIN Comparison method in random matrix theory
Slides
Comparison method has been used in the proofs of many theorems in random matrix theory, e.g., bulk universality, edge universality of Wigner matrix, local circular law. In previous work, most comparison work is based on Lindeberg strategy. In this talk, we will introduce a new comparison method: continuous self consistent comparison method, and discuss its applications on random matrix theory.
O. ZEITOUNI Large deviations, random matrices and random surfaces
Slides
I will describe recent progress in the study of random Gaussian functions in high dimensions. Special emphasis will be on the study of the extremal process of maxima. A key tool is the study of certain determinants involving random matrices.
Based on work of E. Subag and on ongoing work with him and with G. Ben Arous. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8937841057777405, "perplexity": 606.7328996762747}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592579.77/warc/CC-MAIN-20180721125703-20180721145703-00286.warc.gz"} |
http://mathhelpforum.com/trigonometry/102402-graphing-trigonometric-functions.html | 1. ## Graphing trigonometric functions
Okay, so my book spends a whole lot of paper and ink talking about these, but it never goes and explicitly breaks down what's going on.
What would help my understanding immensely is if someone took the following functions and broke down what each variable did on the graph.
$Y= c + a sin 2\pi/b (x - d)$
$Y= C + a tan \pi/b (x-d)$
and the equivelents for the secant and cosecant functions. (cos and cot behave the same way as sin and tangent if I'm getting anything at all from the book) I'm having a lot of trouble because my book and the online video lectures split the sections up differently and emphasize different parts.
2. Hello Wolvenmoon
Originally Posted by Wolvenmoon
Okay, so my book spends a whole lot of paper and ink talking about these, but it never goes and explicitly breaks down what's going on.
What would help my understanding immensely is if someone took the following functions and broke down what each variable did on the graph.
$Y= c + a sin 2\pi/b (x - d)$
$Y= C + a tan \pi/b (x-d)$
and the equivelents for the secant and cosecant functions. (cos and cot behave the same way as sin and tangent if I'm getting anything at all from the book) I'm having a lot of trouble because my book and the online video lectures split the sections up differently and emphasize different parts.
I'll show you how the first one works, and leave you to sort out the second for yourself - it's basically similar.
In the attachments, I've built up the function step by step.
The first shows $y=\sin(2\pi x)$. This is a single cycle of a sine wave for values of $x$ from $0$ to $1$. Note that $y$ has values between $\pm1$.
The second shows $y=\sin\Big(\frac{2\pi}{4}\, x\Big)$; in other words $y=\sin\Big(\frac{2\pi}{b}\, x\Big)$, with $b =4$. You'll see that the difference is that $x$ now needs to take values from 0 to 4 to give one complete cycle. So $b$ gives the wavelength of the sine wave.
The third graph shows $y=\sin\Big(\frac{2\pi}{4} (x-.05)\Big)$. So I've given $d$ the value $0.5$ in your formula $y=c+a\sin\Big(\frac{2\pi}{b} (x-d)\Big)$. If you look closely, you'll see that the graph has been shifted $0.5$ units to the right. So $d$ gives the phase-shift.
Graph #4 is $y=3\sin\Big(\frac{2\pi}{4} (x-0.5)\Big)$. So I've put $a=3$. You'll notice that $y$ now takes values between $\pm3$. So $a$ is the amplitude of the sine wave.
Finally, I've shown you the graph of $y=1+3\sin\Big(\frac{2\pi}{4} (x-.05)\Big)$. So I've put $c=1$. You'll see that $y$ now takes values between $-2$ and $+4$, the graph having been shifted upwards by $1$ unit. $c$, then, is the vertical shift. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 33, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8857974410057068, "perplexity": 326.8287410321463}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368701806508/warc/CC-MAIN-20130516105646-00033-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/1-population-certain-planet-believed-growing-according-logistic-equation-maximum-populatio-q4068867 | 1. The population of a certain planet is believed to be growing according to the logistic equation. The maximum population the planet can hold is 10^10. In year zero the population is 50% of this maximum, and the rate of increase of the population is 10^9 per year. (a) What is the logistic equation satised by the population, y(t)? (b) How many years until the population reaches 90% of the maximum? (c) Sketch this solution curve in the ty-plane, as well as the steady-state solutions y(t) =0 and y(t) = 10^10. 2. Consider two tanks, labeled tank A and tank B for reference. Tank A contains 100 gal of solution in which is dissolved 20 lb of salt. Tank B contains 200 gal of solution in which is dissolved 40 lb of salt. Pure water flows into tank A at a rate of 5 gal/sec. There is a drain at the bottom of tank A, and the solution leaves tank A via this drain at a rate of 5 gal/sec and flows immediately into tank B at the same rate. A drain at the bottom of tank B allows the solution to leave tank B at a rate of 2.5 gal/sec. What is the salt content in tank B at the precise moment that tank B contains 250 gal of solution. 5. In this problem, we will nd all solutions to the boundary value problem (BVP) y''= y, y(0) = y(pi) = 0, where is a constant. This equation will turn up later when we study PDEs. (a) First, suppose that lambda = 0. That is, solve y''= 0, y(0) = y(pi) = 0. (b) Next, suppose lambda= w^2 >= 0. (i) Solve the boundary value problem y''=w^2y,y(0) = y(pi) = 0. (ii) Let u_1(t) = cosh wt =(e^wt+e^-wt)/2 and u_2(t) = sinh wt =(e^wt-e^-wt)/2. Show that u_1(t) and u_2(t) both solve y''= (w^2)y, and use this to write the general solution of this differential equation. (iii) Solve the boundary value problem from part (i) again, but this time, start by using the general solution you found in Part (ii) (instead of exponentials). (c) Finally, suppose lambda=-w^2 < 0. That is, solve y''= -w^2y, y(0) = y(pi) = 0. (d) Using your results from parts (a)-(c), describe all solutions to the boundary value problem y'' = y, y(0) = y(pi) = 0. What are the possibile values for ?
Best answer: | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.962380051612854, "perplexity": 919.358948131905}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657123284.86/warc/CC-MAIN-20140914011203-00041-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://www.physicsforums.com/threads/can-the-electromagnetic-vector-potential-be-written-in-terms-of-a-complex-field.653164/ | # Can the electromagnetic vector potential be written in terms of a complex field?
1. Nov 18, 2012
### Spinnor
Is there a complex field that when properly interpreted yields the four components of electromagnetic vector potential, A_0, A_1, A_2, and A_3?
Somewhat along the lines of the complex field ψ yielding information about a particles energy, momentum, and position probability.
Thanks for any help!
2. Nov 18, 2012
### andrien
faraday tensor does describe in a single way the fields.it is an antisymmetric tensor having six independent components.However one can write maxwell eqn in a form similar to dirac eqn in which E and B are used in some form like E+iB. Although those potentials can be combined to called four potentials but it is just a way of simplification and covariance. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9015587568283081, "perplexity": 1033.7674453509192}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257828010.15/warc/CC-MAIN-20160723071028-00279-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://socratic.org/questions/how-do-i-make-a-hashtag-character-appear-as-a-hashtag-character-in-a-comment-or-#534447 | Socratic Meta
Topics
# How do I make a hashtag character appear as a hashtag character in a Comment (or anywhere else I assume)?
## Enclosing the hashtag in quotation marks did not seem to work.
Jan 12, 2018
Use a line break to separate the hashtags.
#### Explanation:
To add the symbol in answers and in comments, include a line break in between any two hashtags symbols. This will prevent the editor from converting everything written in between the two hashtags symbols to math text.
So, for example, I used a symbol in the previous paragraph and I can use one in this paragraph because I inserted a line break--newline, or simply an EOL character--to separate the paragraphs.
For illustration purposes--I'm pretty sure you've seen this happen before--I'll use two symbols in the same line.
If you use one $s y m b o l \in a p a r a g r a p h \mathmr{and} f \mathmr{and} \ge t \to \mathrm{do} a l \in e b r e a k , t h e e \mathrm{di} \to r w i l l s i m p l y u s e t h e \sec o n d$ symbol to convert everything written after the first hashtag and before the second one to math text.
So as long as you have one symbol per line, you should be in good shape.
Now, writing a hashtag symbol in between hashtags, i.e. getting the editor to format a hashtag symbol as math text, is a little more tedious mainly because I don't remember how to do it :D
I'll try to see if I can find a reference somewhere and come back to edit this answer.
Jul 27, 2018
Is this what is wanted?
Some text. Now math: ${a}^{2} + {b}^{2} = {c}^{2}$. Hashtag: . Now math: ${e}^{\pi i} + 1 = 0$. Some text. Hashtag: ... some more text. Now math: $2 + 3$.
A new paragraph with two hashtags: and .
The effect is achieved by three consecutive hashtags in a row (though it shows up improperly in the preview), which as seen above, is not affected even if math is added into the same paragraph.
By the way, it seems that it is possible to format a hashtag as math using a hashtag, two backslashes, and two hash tags. However, this only works in preview and does not, sadly, appear properly in the answer, as I learned the hard way.
##### Impact of this question
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http://pdglive.lbl.gov/DataBlock.action?node=Q008BPP | # ${{\boldsymbol b}^{\,'}}(-1$/3)-quark/hadron mass limits in ${{\boldsymbol p}}{{\overline{\boldsymbol p}}}$ and ${{\boldsymbol p}}{{\boldsymbol p}}$ collisions INSPIRE search
VALUE (GeV) CL% DOCUMENT ID TECN COMMENT
$> 730$ 95 1
2017 AU
CMS
$\bf{>880}$ 95 2
2016 AN
CMS B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) = 1
$> 620$ 95 3
2015 BY
ATLS ${{\mathit W}}{{\mathit t}}$ , ${{\mathit Z}}{{\mathit b}}$ , ${{\mathit h}}{{\mathit b}}$ modes
$> 730$ 95 4
2015 BY
ATLS B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) = 1
$> 810$ 95 5
2015 Z
ATLS
$\bf{> 755}$ 95 6
2014 AZ
ATLS
$> 675$ 95 7
2013 I
CMS B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) = 1
$\bf{> 190}$ 95 8
2008 X
D0 c = 200mm
$\bf{>190}$ 95 9
2003
CDF quasi-stable ${{\mathit b}^{\,'}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$\text{<350, 580 - 635, >700}$ 95 10
2015 AR
ATLS B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit H}}{{\mathit b}}$ ) = 1
$> 690$ 95 11
2015 CN
ATLS B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit q}}$ ) = 1 (${{\mathit q}}={{\mathit u}}$)
$> 480$ 95 12
2012 AT
ATLS B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) = 1
$> 400$ 95 13
2012 AU
ATLS B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit b}}$ ) = 1
$> 350$ 95 14
2012 BC
ATLS B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit q}}$ ) = 1 (${{\mathit q}}={{\mathit u}},{{\mathit c}}$)
$> 450$ 95 15
2012 BE
ATLS B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) = 1
$> 685$ 95 16
2012 BH
CMS ${\mathit m}_{{{\mathit t}^{\,'}}}$ = ${\mathit m}_{{{\mathit b}^{\,'}}}$
$> 611$ 95 17
2012 X
CMS B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) = 1
$> 372$ 95 18
2011 J
CDF ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$
$> 361$ 95 19
2011 L
CMS Repl. by CHATRCHYAN 2012X
$> 338$ 95 20
2010 H
CDF ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$
$\text{>380 - 430}$ 95 21
2010
RVUE ${\mathit m}_{{{\mathit b}^{\,'}}}>$ ${\mathit m}_{{{\mathit t}^{\,'}}}$
$> 268$ 95 22, 23
2007 C
CDF B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ) = 1
$>199$ 95 24
2000
CDF NC: ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit b}}$
$>148$ 95 25
1998 N
CDF NC: ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit b}}$ + vertex
$>96$ 95 26
1997 D
D0 NC: ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit b}}{{\mathit \gamma}}$
$>128$ 95 27
1995 F
D0 ${{\mathit \ell}}{{\mathit \ell}}$ $+$ jets, ${{\mathit \ell}}$ $+$ jets
$>75$ 95 28
1993
RVUE NC: ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit b}}{{\mathit \ell}}{{\mathit \ell}}$
$>85$ 95 29
1992
CDF CC: ${{\mathit \ell}}{{\mathit \ell}}$
$>72$ 95 30
1990 B
CDF CC: ${{\mathit e}}$ $+$ ${{\mathit \mu}}$
$>54$ 95 31
1990
UA2 CC: ${{\mathit e}}$ $+$ jets + $\not E_T$
$>43$ 95 32
1990 B
UA1 CC: ${{\mathit \mu}}$ $+$ jets
$>34$ 95 33
1988
UA1 CC: ${{\mathit e}}$ or ${{\mathit \mu}}$ + jets
1 SIRUNYAN 2017AU based on $2.3 - 2.6$ fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 13 TeV. Limit on pair-produced singlet vector-like ${{\mathit b}^{\,'}}$ using one lepton and several jets. The mass bound is given for a ${{\mathit b}^{\,'}}$ transforming as a singlet under the electroweak symmetry group, assumed to decay through ${{\mathit W}}$, ${{\mathit Z}}$ or Higgs boson (which decays to jets) and to a third generation quark.
2 KHACHATRYAN 2016AN based on 19.7 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV. Limit on pair-produced vector-like ${{\mathit b}^{\,'}}$ using 1, 2, and $>$2 leptons as well as fully hadronic final states. Other limits depending on the branching fractions to ${{\mathit t}}{{\mathit W}}$ , ${{\mathit b}}{{\mathit Z}}$ , and ${{\mathit b}}{{\mathit H}}$ are given in Table IX.
3 AAD 2015BY based on 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV. Limit on pair-produced vector-like ${{\mathit b}^{\,'}}$ assuming the branching fractions to ${{\mathit W}}$, ${{\mathit Z}}$, and ${{\mathit h}}$ modes of the singlet model. Used events containing ${}\geq{}2{{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$2j (${}\geq{}$1 ${{\mathit b}}$) and including a same-sign lepton pair.
4 AAD 2015BY based on 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV. Limit on pair-produced chiral ${{\mathit b}^{\,'}}$-quark. Used events containing ${}\geq{}2{{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$2j (${}\geq{}$1 ${{\mathit b}}$) and including a same-sign lepton pair.
5 AAD 2015Z based on 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV. Used events with ${{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$6j (${}\geq{}$1 ${{\mathit b}}$) and at least one pair of jets from weak boson decay, primarily designed to select the signature ${{\mathit b}^{\,'}}$ ${{\overline{\mathit b}}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}}{{\mathit t}}{{\overline{\mathit t}}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}}{{\mathit W}}{{\mathit W}}{{\mathit b}}{{\overline{\mathit b}}}$ . This is a limit on pair-produced vector-like ${{\mathit b}^{\,'}}$. The lower mass limit is 640 GeV for a vector-like singlet ${{\mathit b}^{\,'}}$.
6 Based on 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV. No significant excess over SM expectation is found in the search for pair production or single production of ${{\mathit b}^{\,'}}$ in the events with dilepton from a high $p_T$ ${{\mathit Z}}$ and additional jets (${}\geq{}$ 1 ${{\mathit b}}$-tag). If instead of B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) = 1 an electroweak singlet with B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) $\sim{}$ 0.45 is assumed, the limit reduces to 685 GeV.
7 Based on 5.0 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. CHATRCHYAN 2013I looked for events with one isolated electron or muon, large $\not E_T$, and at least four jets with large transverse momenta, where one jet is likely to originate from the decay of a bottom quark.
8 Result is based on 1.1 fb${}^{-1}$ of data. No signal is found for the search of long-lived particles which decay into final states with two electrons or photons, and upper bound on the cross section times branching fraction is obtained for 2 $<$ c $<$ 7000 mm; see Fig. 3. 95$\%$ CL excluded region of ${{\mathit b}^{\,'}}$ lifetime and mass is shown in Fig. 4.
9 ACOSTA 2003 looked for long-lived fourth generation quarks in the data sample of 90 pb${}^{-1}$ of $\sqrt {\mathit s }$=1.8 TeV ${{\mathit p}}{{\overline{\mathit p}}}$ collisions by using the muon-like penetration and anomalously high ionization energy loss signature. The corresponding lower mass bound for the charge (2/3)e quark (${{\mathit t}^{\,'}}$) is 220 GeV. The ${{\mathit t}^{\,'}}$ bound is higher than the ${{\mathit b}^{\,'}}$ bound because ${{\mathit t}^{\,'}}$ is more likely to produce charged hadrons than ${{\mathit b}^{\,'}}$. The 95$\%$ CL upper bounds for the production cross sections are given in their Fig.$~$3.
10 AAD 2015AR based on 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV. Used lepton-plus-jets final state. See Fig. 24 for mass limits in the plane of B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) vs. B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit H}}{{\mathit b}}$ ) from ${{\mathit b}^{\,'}}$ ${{\overline{\mathit b}}^{\,'}}$ $\rightarrow$ ${{\mathit H}}{{\mathit b}}{+}$ ${{\mathit X}}$ searches.
11 AAD 2015CN based on 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV. Limit on pair-production of chiral ${{\mathit b}^{\,'}}$-quark. Used events with ${{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$4j (non-${{\mathit b}}$-tagged). Limits on a heavy vector-like quark, which decays into ${{\mathit W}}$ ${{\mathit q}}$ , ${{\mathit Z}}{{\mathit q}}$ , ${{\mathit h}}{{\mathit q}}$ , are presented in the plane B( ${{\mathit Q}}$ $\rightarrow$ ${{\mathit W}}{{\mathit q}}$ ) vs. B( ${{\mathit Q}}$ $\rightarrow$ ${{\mathit h}}{{\mathit q}}$ ) in Fig. 12.
12 Based on 1.04 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. No signal is found for the search of heavy quark pair production that decay into ${{\mathit W}}$ and a ${{\mathit t}}$ quark in the events with a high $p_T$ isolated lepton, large $\not E_T$, and at least 6 jets in which one, two or more dijets are from ${{\mathit W}}$.
13 Based on 2.0 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. No ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit b}}$ invariant mass peak is found in the search of heavy quark pair production that decay into ${{\mathit Z}}$ and a ${{\mathit b}}$ quark in events with ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ and at least one ${{\mathit b}}$-jet. The lower mass limit is 358 GeV for a vector-like singlet ${{\mathit b}^{\,'}}$ mixing solely with the third SM generation.
14 Based on 1.04 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. No signal is found for the search of heavy quark pair production that decay into ${{\mathit W}}$ and a quark in the events with dileptons, large $\not E_T$, and ${}\geq{}$2 jets.
15 Based on 1.04 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. AAD 2012BE looked for events with two isolated like-sign leptons and at least 2 jets, large $\not E_T$ and H$_{T}$ $>$ 350 GeV.
16 Based on 5 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. CHATRCHYAN 2012BH searched for QCD and EW production of single and pair of degenerate 4'th generation quarks that decay to ${{\mathit b}}{{\mathit W}}$ or ${{\mathit t}}{{\mathit W}}$ . Absence of signal in events with one lepton, same-sign dileptons or tri-leptons gives the bound. With a mass difference of 25 GeV/c${}^{2}$ between ${\mathit m}_{{{\mathit t}^{\,'}}}$ and ${\mathit m}_{{{\mathit b}^{\,'}}}$, the corresponding limit shifts by about $\pm20$ GeV/c${}^{2}$.
17 Based on 4.9 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. CHATRCHYAN 2012X looked for events with trileptons or same-sign dileptons and at least one ${{\mathit b}}$ jet.
18 Based on 4.8 fb${}^{-1}$ of data in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at 1.96 TeV. AALTONEN 2011J looked for events with ${{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$5j (${}\geq{}$1 ${{\mathit b}}$ or ${{\mathit c}}$). No signal is observed and the bound ${\mathit \sigma (}$ ${{\mathit b}^{\,'}}{{\overline{\mathit b}}^{\,'}}{)}$ $<$ 30 fb for ${\mathit m}_{{{\mathit b}^{\,'}}}$ $>$ 375 GeV is found for B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) = 1.
19 Based on 34 pb${}^{-1}$ of data in ${{\mathit p}}{{\mathit p}}$ collisions at 7 TeV. CHATRCHYAN 2011L looked for multi-jet events with trileptons or same-sign dileptons. No excess above the SM background excludes ${\mathit m}_{{{\mathit b}^{\,'}}}$ between 255 and 361 GeV at 95$\%$ CL for B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) = 1.
20 Based on 2.7 fb${}^{-1}$ of data in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV. AALTONEN 2010H looked for pair production of heavy quarks which decay into ${{\mathit t}}{{\mathit W}^{-}}$ or ${{\mathit t}}{{\mathit W}^{+}}$ , in events with same sign dileptons (${{\mathit e}}$ or ${{\mathit \mu}}$), several jets and large missing $\mathit E_{T}$. The result is obtained for ${{\mathit b}^{\,'}}$ which decays into ${{\mathit t}}{{\mathit W}^{-}}$ . For the charge 5/3 quark (${{\mathit T}_{{5/3}}}$) which decays into ${{\mathit t}}{{\mathit W}^{+}}$ , ${\mathit m}_{{{\mathit T}_{{5/3}}}}$ $>$ 365 GeV (95$\%$ CL) is found when it has the charge $-1$/3 partner B of the same mass.
21 FLACCO 2010 result is obtained from AALTONEN 2010H result of ${\mathit m}_{{{\mathit b}^{\,'}}}>$ 338 GeV, by relaxing the condition B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) = 100$\%$ when ${\mathit m}_{{{\mathit b}^{\,'}}}>$ ${\mathit m}_{{{\mathit t}^{\,'}}}$.
22 Result is based on 1.06 fb${}^{-1}$ of data. No excess from the SM ${{\mathit Z}}$+jet events is found when ${{\mathit Z}}$ decays into ${{\mathit e}}{{\mathit e}}$ or ${{\mathit \mu}}{{\mathit \mu}}$ . The ${\mathit m}_{{{\mathit b}^{\,'}}}$ bound is found by comparing the resulting upper bound on ${\mathit \sigma (}$ ${{\mathit b}^{\,'}}{{\overline{\mathit b}}^{\,'}}{)}$ [1-(1-B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit b}}$ ))${}^{2}$] and the LO estimate of the ${{\mathit b}^{\,'}}$ pair production cross section shown in Fig. 38 of the article.
23 HUANG 2008 reexamined the ${{\mathit b}^{\,'}}$ mass lower bound of 268 GeV obtained in AALTONEN 2007C that assumes B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit b}}$ ) = 1, which does not hold for ${\mathit m}_{{{\mathit b}^{\,'}}}$ $>$ 255 GeV. The lower mass bound is given in the plane of sin$^2(\theta _{ {{\mathit t}} {{\mathit b}^{\,'}} })$ and ${\mathit m}_{{{\mathit b}^{\,'}}}$.
24 AFFOLDER 2000 looked for ${{\mathit b}^{\,'}}$ that decays in to ${{\mathit b}}+{{\mathit Z}}$. The signal searched for is ${{\mathit b}}{{\mathit b}}{{\mathit Z}}{{\mathit Z}}$ events where one ${{\mathit Z}}$ decays into ${{\mathit e}^{+}}{{\mathit e}^{-}}$ or ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ and the other ${{\mathit Z}}$ decays hadronically. The bound assumes B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit b}}$ )= 100$\%$. Between 100 GeV and 199 GeV, the 95$\%$CL upper bound on $\sigma\mathrm {( {{\mathit b}^{\,'}} \rightarrow {{\overline{\mathit b}}^{\,'}} )}{\times }B{}^{2}$( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit b}}$ ) is also given (see their Fig.$~$2).
25 ABE 1998N looked for ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ decays with displaced vertices. Quoted limit assumes B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit b}}$ )=1 and ${{\mathit c}}{{\mathit \tau}_{{\mathit ^{'}}}}$ =1$~$cm. The limit is lower than ${\mathit m}_{{{\mathit Z}}}+{\mathit m}_{{{\mathit b}}}$ ($\sim{}$96 GeV) if ${{\mathit c}}{{\mathit \tau}}$ $>22~$cm or ${{\mathit c}}{{\mathit \tau}}$ $<0.009~$cm. See their Fig.$~$4.
26 ABACHI 1997D searched for ${{\mathit b}^{\,'}}$ that decays mainly via FCNC. They obtained 95$\%$CL upper bounds on B( ${{\mathit b}^{\,'}}$ ${{\overline{\mathit b}}^{\,'}}$ $\rightarrow$ ${{\mathit \gamma}}$ + 3 jets) and B( ${{\mathit b}^{\,'}}$ ${{\overline{\mathit b}}^{\,'}}$ $\rightarrow$ 2 ${{\mathit \gamma}}$ + 2 jets), which can be interpreted as the lower mass bound ${\mathit m}_{{{\mathit b}^{\,'}}}>{\mathit m}_{{{\mathit Z}}}+{\mathit m}_{{{\mathit b}}}$.
27 ABACHI 1995F bound on the top-quark also applies to ${{\mathit b}^{\,'}}$ and ${{\mathit t}^{\,'}}$ quarks that decay predominantly into ${{\mathit W}}$. See FROGGATT 1997 .
28 MUKHOPADHYAYA 1993 analyze CDF dilepton data of ABE 1992G in terms of a new quark decaying via flavor-changing neutral current. The above limit assumes B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit b}}{{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ )=1$\%$. For an exotic quark decaying only via virtual ${{\mathit Z}}$ [B( ${{\mathit b}}{{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ ) = 3$\%$], the limit is 85 GeV.
29 ABE 1992 dilepton analysis limit of $>$85 GeV at CL=95$\%$ also applies to ${{\mathit b}^{\,'}}$ quarks, as discussed in ABE 1990B.
30 ABE 1990B exclude the region 28$-$72 GeV.
31 AKESSON 1990 searched for events having an electron with $\mathit p_{\mathit T}$ $>$ 12 GeV, missing momentum $>$ 15 GeV, and a jet with $\mathit E_{\mathit T}$ $>$ 10 GeV, $\vert \eta \vert$ $<$ $2.2$, and excluded ${\mathit m}_{{{\mathit b}^{\,'}}}$ between 30 and 69 GeV.
32 For the reduction of the limit due to non-charged-current decay modes, see Fig.$~$19 of ALBAJAR 1990B.
33 ALBAJAR 1988 study events at $\mathit E_{{\mathrm {cm}}}$ = 546 and 630 GeV with a muon or isolated electron, accompanied by one or more jets and find agreement with Monte Carlo predictions for the production of charm and bottom, without the need for a new quark. The lower mass limit is obtained by using a conservative estimate for the ${{\mathit b}^{\,'}}{{\overline{\mathit b}}^{\,'}}$ production cross section and by assuming that it cannot be produced in ${{\mathit W}}$ decays. The value quoted here is revised using the full $\mathit O(\alpha {}^{3}_{\mathit s}$) cross section of ALTARELLI 1988 .
References:
SIRUNYAN 2017AU
JHEP 1711 085 Search for Pair Production of Vector-Like and Quarks in Single-Lepton Final States using Boosted Jet Substructure in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV
KHACHATRYAN 2016AN
PR D93 112009 Search for Pair-Produced Vectorlike Quarks in Proton-Proton Collisions at $\sqrt {s }$ = 8 TeV
PR D92 112007 Search for Pair Production of a New heavy Quark that Decays into a ${{\mathit W}}$ Boson and a Light Quark in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
JHEP 1510 150 Analysis of Events with ${\mathit {\mathit b}}$-Jets and a Pair of Leptons of the Same Charge in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
JHEP 1508 105 Search for Production of Vector-Like Quark Pairs and of Four Top Quarks in the Lepton-plus-Jets Final State in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
PR D91 112011 Search for Vector-Like Quarks in Events with One Isolated Lepton, Missing Transverse Momentum and Jets at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
JHEP 1411 104 Search for Pair and Single Production of New Heavy Quarks that Decay to a ${{\mathit Z}}$ Boson and a Third-Generation Quark in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
CHATRCHYAN 2013I
JHEP 1301 154 Search for Heavy Quarks Decaying into a Top Quark and a ${{\mathit W}}$ or ${{\mathit Z}}$ Boson using Lepton + Jets Events in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
PRL 109 032001 Search for Down-Type Fourth Generation Quarks with the ATLAS Detector in Events with One Lepton and Hadronically Decaying ${{\mathit W}}$ Bosons
PRL 109 071801 Search for Pair Production of a New ${\mathit {\mathit b ^{\prime}}}$ Quark that Decays into a ${{\mathit Z}}$ Boson and a Bottom Quark with the ATLAS Detector
JHEP 1204 069 Search for Same-Sign Top-Quark Production and Fourth-Generation Down-Type Quarks in ${{\mathit p}}{{\mathit p}}$ Collisions at with the ATLAS Detector
PR D86 012007 Search for Pair-Produced Heavy Quarks Decaying to ${{\mathit W}}{\mathit {\mathit q}}$ in the Two-Lepton Channel at $\sqrt {s }$ = 7 TeV with the ATLAS Detector
CHATRCHYAN 2012BH
PR D86 112003 Combined Search for the Quarks of a Sequential Fourth Generation
CHATRCHYAN 2012X
JHEP 1205 123 Search for Heavy Bottom-Like Quarks in 4.9 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
AALTONEN 2011J
PRL 106 141803 Search for Heavy Bottomlike Quarks Decaying to an Electron or Muon and Jets in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
CHATRCHYAN 2011L
PL B701 204 Search for a Heavy Bottom-Like Quark in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
AALTONEN 2010H
PRL 104 091801 Search for New Bottomlike Quark Pair Decays ${{\mathit Q}}$ ${{\overline{\mathit Q}}}$ $\rightarrow$ ( ${{\mathit t}}{{\mathit W}^{\mp}}$) ( ${{\overline{\mathit t}}}{{\mathit W}^{\pm}}$) in Same-Charge Dilepton Events
FLACCO 2010
PRL 105 111801 Direct Mass Limits for Chiral Fourth-Generation Quarks in All Mixing Scenarios
ABAZOV 2008X
PRL 101 111802 Search for Long-Lived Particles Decaying into Electron or Photon Pairs with the ${D0}$ Detector
AALTONEN 2007C
PR D76 072006 Search for New Particles Leading to ${{\mathit Z}}$ +jets Final States in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
ACOSTA 2003
PRL 90 131801 Search for Long Lived Charged Massive Particles in ${{\overline{\mathit p}}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 1.8 TeV
AFFOLDER 2000
PRL 84 835 Search for a Fourth Generation Quark More Massive than the ${{\mathit Z}}$ Boson in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.8 TeV
ABE 1998N
PR D58 051102 Search for Longlived Parents of ${{\mathit Z}}$ Bosons in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.8 TeV
ABACHI 1997D
PRL 78 3818 Search for a Fourth Generation Charge -1/3 Quark via Flavor Changing Neutral Current Decay
ABACHI 1995F
PR D52 4877 Top Quark Search with the ${D0}$ $1992 - 1993$ Data Sample
PR D48 2105 Tevatron Mass Limits for Heavy Quarks Decaying via Flavor Changing Neutral Current
ABE 1992
PRL 68 447 A Lower Limit on the Top Quark Mass from Events with Two Leptons in ${{\overline{\mathit p}}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 1.8 TeV
ABE 1990B
PRL 64 147 Search for New Heavy Quarks in Electron Muon Events at the Fermilab Tevatron Collider
AKESSON 1990
ZPHY C46 179 Search for Top Quark Production at the CERN ${{\overline{\mathit p}}}{{\mathit p}}$ Collider
ALBAJAR 1990B
ZPHY C48 1 Search for New Heavy Quarks in Proton Antiproton Collisions at $\sqrt {s }$ = 0.63 TeV
ALBAJAR 1988
ZPHY C37 505 Search for New Heavy Quarks at CERN Proton-Antiproton Collider
ABE 1992L
PRL 69 3439 Search for Squarks and Gluinos from ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$=1.8 TeV
FROGGATT 1997
ZPHY C73 333 Could there be a Fourth Generation of Quarks without More Leptons?
ALTARELLI 1988
NP B308 724 Total Cross Sections for Heavy Flavor Production in Hadronic Collisions and QCD
ABE 1992G
PR D45 3921 A Limit on the Top Quark Mass from Proton Antiproton Collisions at $\sqrt {s }$ = 1.8 TeV
HUANG 2008
PR D77 037302 Experimental Constraints on Fourth Generation Quark Masses | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9831409454345703, "perplexity": 2224.4498772953043}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583763839.28/warc/CC-MAIN-20190121070334-20190121092334-00357.warc.gz"} |
http://tex.stackexchange.com/questions/139824/disabling-the-select-reference-format-menu-in-reftex | Disabling the “select reference format” menu in reftex
I'm not sure if this is the right place to ask this question, so if not, please let me know where it would be more appropriate.
Since upgrading to Ubuntu 13.10, something seems to have gone wonky with RefTeX. It seems that Emacs was "upgraded" to 24.3.1, and I think this may be the culprit.
The problem: when I type C-c ) to insert a label, instead of just going to my list of references as usual, the frame splits in half and the following appears in the bottom half:
SELECT A REFERENCE FORMAT
[^M] \ref
[p] \pageref
If I hit C-m then it goes to my reference list and I can choose the reference as I normally would. I really don't want to have this extra step there, any idea how to disable that and restore the previous behavior?
In case it matters, I'm also using the solution from this answer to make RefTeX work with cleverref.
-
To skip the selection of the reference style you have to set the variable reftex-ref-macro-prompt to nil, see the RefTeX manual. To do this you can customize that variable or add the following code to your init file:
(setq reftex-ref-macro-prompt nil)
It has been reported that this solution to use RefTeX with the cleverref package no longer works with Emacs 24.3.1 and AUCTeX 11.87, look at this instead. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8086835145950317, "perplexity": 1061.186874215523}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049276415.60/warc/CC-MAIN-20160524002116-00061-ip-10-185-217-139.ec2.internal.warc.gz"} |
http://math.stackexchange.com/users/774/neil-g?tab=activity&sort=all&page=8 | # Neil G
less info
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# 183 Actions
Nov3 answered Chinese remainder theorem Nov3 comment Chinese remainder theorem Yes, I will add it as a solution. Nov3 accepted Chinese remainder theorem Nov3 revised Chinese remainder theorem Forgot a condition Nov3 comment Chinese remainder theorem I will update the question. (This problem is a part of a larger problem and I forgot the conditions that I'd used.) Nov3 asked Chinese remainder theorem Oct28 accepted What is an example of a lambda-system that is not a sigma algebra? Oct28 comment What is an example of a lambda-system that is not a sigma algebra? Even though both answers are correct, I'm going to mark this answer because it gives me a bit of intuition about what's going. The other answer would have been a better solution to an exam question. Oct28 comment What is an example of a lambda-system that is not a sigma algebra? I think you only need relative complement of included sets? I.e., $A \subseteq B \Rightarrow B \setminus A \in L$. Oct28 asked What is an example of a lambda-system that is not a sigma algebra? Sep21 comment Example where union of increasing sigma algebras is not a sigma algebra Not to me :) But, even if I were one of your students, I don't think this question goes beyond what students would discuss between themselves. Sep21 accepted Why are the sets of rational and irrational numbers Borel sets (over the reals)? Sep21 awarded Commentator Sep21 comment Why are the sets of rational and irrational numbers Borel sets (over the reals)? Thank you very much; I see it now. Sep21 comment Why are the sets of rational and irrational numbers Borel sets (over the reals)? @Qiaochu, I see it now. Sep21 asked Why are the sets of rational and irrational numbers Borel sets (over the reals)? Sep21 accepted Example where union of increasing sigma algebras is not a sigma algebra Sep21 asked Example where union of increasing sigma algebras is not a sigma algebra Sep15 accepted Why do lambda and pi go together? Sep14 revised Sufficient statistics vs. Bayesian sufficient statistics added 20 characters in body; added 9 characters in body; added 27 characters in body | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8486133813858032, "perplexity": 719.4286648886448}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500823598.56/warc/CC-MAIN-20140820021343-00310-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/questions/36060/proper-spacing-using-minipages-dealing-with-margins-and-succeding-text | # Proper spacing using minipages, dealing with margins and succeding text
So I have this user defined function below. This gives me near optimal results. The code is supposed to make numbered subsections. Where the rest of the text is aligned below. Since these subsections usually only span over 1-3 lines, this looks good.
\documentclass[10pt,a4paper]{article}
\usepackage[hmargin=3.5cm,vmargin=2cm]{geometry}
\usepackage{lipsum}
\newcounter{problem}
\setcounter{problem}{0}
\newcounter{navn}[problem]
\renewcommand{\thenavn}{\alph{navn}}
\newcommand{\navn}{ \stepcounter{navn} \hspace{ -0.12cm} \bfseries \thenavn) }
\setcounter{navn}{0}
\newcommand{\NR}[1]
{ \vspace{5mm} \begin{minipage}[t]{0.051 \textwidth}
\navn \hspace{0pt}
\end{minipage}
\begin{minipage}[t]{0.949\textwidth}
#1
\end{minipage}
\vspace{-0.3cm}
}
\newcommand{\UR}[1]
{ \begin{minipage}[t]{0.051 \textwidth}
\hspace{0pt}
\end{minipage}
\begin{minipage}[t]{0.949\textwidth}
#1
\end{minipage}\vspace*{-0.4cm}
}
\setlength{\parindent}{0in}
\begin{document}
\NR{\lipsum[1]}
{\lipsum[5]}
\UR{\lipsum[2]}
\NR{Hello}
$x^2 + 3x + 4$
\NR{Problems}
\NR{Problems}
\lipsum[3]
\end{document}
Now, after compiling this code. One can clearly see that the text beneath the \NR command is coming to close to the actual text. Of course this is caused by the negative spacing inside the command. However this code is needed otherwise the spacing between the \NR command, and following images are far to large. Also the spacing regarding functions increases too much.
One can also see in the code, that the length of the command is set by default.
The spacing in my MWE between c) and e) Is perfect. I know I can use \\ to increase the spacing, but this gets tedious and is against the spirit of Latex.
My question now is how do I properly define the spacing? More specifically:
• How do I define that the minipages, should always start at the width of the page, with a default indent?
• How do I properly define the horizontal space before and after the command? (So that it is the same as in the MWE but also fixes the normal text problem)
-
Is there a reason why a standard enumerate environment does not work for you? If you want to consider that I would use the enumitem package. See what are the differences between using paralist vs enumitem – Peter Grill Nov 24 '11 at 15:46
I also need text between the parts, that is not indented. – N3buchadnezzar Nov 24 '11 at 15:50
For that you could just end the enumerate and resume it after. Is there something other than indentation that you are trying to accomplish with these minipages? – Peter Grill Nov 24 '11 at 16:04
If you don't want to use enumitem, here is an improved version of your macros:
\newcounter{navn}[problem]
\renewcommand{\thenavn}{\alph{navn}}
\newcommand{\navn}{\stepcounter{navn}\bfseries\thenavn)}
\setcounter{navn}{0}
\newcommand{\NR}[1]{%
\begin{minipage}[t]{0.95\textwidth}
#1\par\xdef\tpd{\the\prevdepth}
\end{minipage}\par\prevdepth\tpd
}
\newcommand{\UR}[1]{%
\noindent\makebox[0.05\textwidth][l]{}%
\begin{minipage}[t]{0.95\textwidth}
#1\par\xdef\tpd{\the\prevdepth}
\end{minipage}\par\prevdepth\tpd
}
Uncomment the two lines if you want to ensure a minimum spacing after the minipages. For the \prevdepth trick, see How to keep a constant baselineskip when using minipages (or \parboxes)?
-
I would recommend that you use enumerate from the enumitem package. For text that is not to be indented you can end the enumerate and simply use the resume option when you start it up again:
## Basic Solution:
\documentclass[10pt,a4paper]{article}
\usepackage[hmargin=3.5cm,vmargin=2cm]{geometry}
\usepackage{enumitem}
\usepackage{lipsum}
\setlength{\parindent}{0in}
\begin{document}
\begin{enumerate}[label=\textbf{\alph*}),labelsep=1.5em]
\item \lipsum[1]
\end{enumerate}
\lipsum[5]
\lipsum[2]
\begin{enumerate}[resume,label=\textbf{\alph*}),labelsep=1.5em]
\item Hello
$x^2 + 3x + 4$
\item Problems
\item Problems
\end{enumerate}
\lipsum[3]
\end{document}
## Updated Solution:
If there is often a need to exit/resume the enumerate environment you could just wrap that into a macro:
\documentclass[10pt,a4paper]{article}
\usepackage[hmargin=3.5cm,vmargin=2cm]{geometry}
\usepackage{enumitem}
\usepackage{lipsum}
\setlength{\parindent}{0in}
\newcommand{\PauseList}[1]{%
\end{enumerate}
#1
\begin{enumerate}[resume,label=\textbf{\alph*}),labelsep=1.5em]
}%
\begin{document}
\begin{enumerate}[label=\textbf{\alph*}),labelsep=1.5em]
\item \lipsum[1]
\PauseList{
\lipsum[5]
}
\item Hello
$x^2 + 3x + 4$
\item Problems
\item Problems
\end{enumerate}
\lipsum[3]
\end{document}
-
Only problem is that there is alot of space not needed to indent. So using the enumerate package would be more tedious... In my eyes. – N3buchadnezzar Nov 24 '11 at 16:09
Ok, then you could simply wrap a macro around that. See updated solution. – Peter Grill Nov 24 '11 at 16:19
Thanks for your comment. Here is an example file of what I am making. This is made using the command above 2shared.com/document/ZMtCAlq2/T1_H10.html. I just feel the minipages are far more flexible. Now could one have sublists like itemize, tables, figures, reseting the list, inside one enumerate list? Otherwise this once again seems tedious. Thanks a ton for your comments though =) – N3buchadnezzar Nov 24 '11 at 16:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9583886861801147, "perplexity": 1470.790506837527}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701148402.62/warc/CC-MAIN-20160205193908-00127-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://www.gradesaver.com/textbooks/science/physics/conceptual-physics-12th-edition/chapter-7-think-and-solve-page-128/50 | ## Conceptual Physics (12th Edition)
The total energy stays the same, as discussed on page 118. In other words, at the beginning, the banana's mechanical energy is all in the form of PE = $mgh$, where h = 0 at the surface of the river. This energy is transformed into KE as the banana falls. When the banana is about to hit the water, h = 0 and the energy is all in the form of KE, $\frac{1}{2}mv^{2}$. This expresses conservation of energy. $$mgh=\frac{1}{2}mv^{2}$$ Solve for the speed just before hitting the water. $$2mgh=mv^{2}$$ $$2gh=v^{2}$$ $$\sqrt{2gh}=v$$ We have proven the desired result. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.953265905380249, "perplexity": 244.81553126903214}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218191986.44/warc/CC-MAIN-20170322212951-00005-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/calculus-of-variations.683355/ | # Calculus of variations
1. Apr 5, 2013
### V0ODO0CH1LD
My first question is with regards to the "status" of calculus of variations. Because I read in wolfram alpha that it was a generalization of calculus? Is that right?
Anyway; my main question has to do with the process of getting the answer you're looking for. Is every problem in calculus of variations possible to be set as a solvable differential equation? And by solvable I don't mean keep guessing the answer until you eventually get it and then prove it was the right one using some method. Which to me looks like a general trend in calculus of variations.
If you can set at least most problems of calculus of variations as differential equations, how do you go about doing it? Should I look deeper into functional analysis, banach spaces, metric spaces and so on?
Could anyone show me an "algorithmic" way to find, for instance, the solution to the problem of finding the shortest path between two point in the xy plane? Without assuming you already know the answer and is just trying to prove it's the right one?
2. Apr 5, 2013
### SteamKing
Staff Emeritus
3. Apr 5, 2013
### Omega0
If you have around 15 bucks or so I recommend: "Mathematics of Classical and Quantum Physics" from Byron and Fuller, Dover Publishing. Forget about deeper functional analysis for a first understanding (<- my opinion).
What do you mean with "guessing"?
I cite the book: "One of the oldest problems in mathematical physics is that of trying to minimize expressions which do not depend on some simple continuous variable, but rather on a function".
That's it. Why should this be something different than "analysis"? Where does "analysis" end? Is "vector analysis" a new one? Or "theory of functions"?
You simply set up an expression (or a couple of them) like
ds = sqrt(1 + y'(x)^2) dx
which you would like to minimize. Here you simply describe the length of the little path pieces. And now you think: Fine, I would like to minimize the path. So you are writing down on a piece of paper the integral. Now you realize: Nice, I have an integral I can't integrate because I don't know the function y(x). Now you think hmmm if I want to have the minimum then the function y(x,epsilon) can only be the minimum if epsilon is zero, meaning you are adding simply something which has to be gone in the end.
Example: Integral from 0 to 1. y(x) unknown. So y(x) + epsilon * sin(x / PI) is an idea. But the test function is not important.
So the brilliant idea is to think about a test function which disappears in the minimum and that function has nothing to do but fulfilling some conditions.
Doing that you will get the Euler-Lagrange equation(s). This means that you have a (set of) differential equation(s) to be solved.
You have a deep lack in understanding if you think that the test functions are the problem. I would say: Have fun with solving the system of differential equations you will get! ;)
4. Apr 5, 2013
### jambaugh
For the optimization problem you essentially follow the same steps as in single and multivariable calculus.
In single variable calculus you express the quantity to be optimized as a function of the variable and solve for where the derivative is zero. After taking the derivative this is a single variable algebra problem.
In multi-variable calculus you express the quantity to be optimized as a function of the many variables (which you can call a single vector variable). The derivative generalizes to the "gradient" here i.e. the vector of partial derivatives. You then solve the vector equation you get setting this general derivative to (the) zero (vector). The vector equation is then a system of equations.
In functional analysis a function can be thought of as a vector (infinite dimensional) and you do the same as above except now the "function" of your vector is a functional, i.e. a mapping from the function to a number. This functional has a derivative in the generalized setting and setting it to (the) zero (functional) gives you a continuum system of equations typically expressed as a differential equation on the function at which optimization occurs.
As an example of shortest path. You would express an arbitrary path by giving position as a function of some parameter, i.e. x(t), y(t), and z(t) for 0<t<1. You then need to express how to get the thing to be optimized form the functions, e.g. for distance you have to do a path integral to get arclength...
$$s[x,y,z] = \int_{0}^1 \sqrt{\dot{x}^2 + \dot{y}^2 + \dot{z}^2}dt$$
Note here that the arclength s is not a function of the values of x,y, and z but rather a functional of x,y,z as functions of t. (We'd be better off using different names for the variables x,y,z and their functional dependence on t... something like:
$$x=f(t), y=g(t), z=h(t)$$
and similarly arclength s as some functional, say Lambda of these functions (I use Lambda to stand for the "L"ength functional.)
$$s=\Lambda[f,g,h] = \int_{0}^1 \sqrt{\dot{f}(t)^2 + \dot{g}(t)^2 + \dot{h}(t)^2}dt$$
)
Now we have this mapping from functions to a number s. We take its generalized derivative which is a linear functional depending on the function (including its derivatives). So setting it to the zero function gives you typically a differential equation.
---------------
In summary you in all cases express the quantity to be optimized as a mapping from the variable entity to a number, you in some sense take the derivative of this mapping and set that to the zero object for its type and solve. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8859460949897766, "perplexity": 395.34212447151924}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948513784.2/warc/CC-MAIN-20171211164220-20171211184220-00066.warc.gz"} |
http://adam.chlipala.net/cpdt/repo/rev/3b21f4395178 | changeset 514:3b21f4395178
Fix a word that was only included in LaTeX version
author Adam Chlipala Thu, 26 Sep 2013 15:26:12 -0400 a4b3386ae140 ffe99c02fa18 src/GeneralRec.v 1 files changed, 1 insertions(+), 1 deletions(-) [+]
line wrap: on
line diff
--- a/src/GeneralRec.v Thu Sep 19 17:28:32 2013 -0400
+++ b/src/GeneralRec.v Thu Sep 26 15:26:12 2013 -0400
@@ -169,7 +169,7 @@
red; intro; eapply lengthOrder_wf'; eauto.
Defined.
- (** Notice that we end these proofs with %\index{Vernacular commands!Defined}%[Defined], not [Qed]. Recall that [Defined] marks the theorems as %\emph{transparent}%, so that the details of their proofs may be used during program execution. Why could such details possibly matter for computation? It turns out that [Fix] satisfies the primitive recursion restriction by declaring itself as _recursive in the structure of [Acc] proofs_. This is possible because [Acc] proofs follow a predictable inductive structure. We must do work, as in the last theorem's proof, to establish that all elements of a type belong to [Acc], but the automatic unwinding of those proofs during recursion is straightforward. If we ended the proof with [Qed], the proof details would be hidden from computation, in which case the unwinding process would get stuck.
+ (** Notice that we end these proofs with %\index{Vernacular commands!Defined}%[Defined], not [Qed]. Recall that [Defined] marks the theorems as %\emph{%#<i>#transparent#</i>#%}%, so that the details of their proofs may be used during program execution. Why could such details possibly matter for computation? It turns out that [Fix] satisfies the primitive recursion restriction by declaring itself as _recursive in the structure of [Acc] proofs_. This is possible because [Acc] proofs follow a predictable inductive structure. We must do work, as in the last theorem's proof, to establish that all elements of a type belong to [Acc], but the automatic unwinding of those proofs during recursion is straightforward. If we ended the proof with [Qed], the proof details would be hidden from computation, in which case the unwinding process would get stuck.
To justify our two recursive [mergeSort] calls, we will also need to prove that [split] respects the [lengthOrder] relation. These proofs, too, must be kept transparent, to avoid stuckness of [Fix] evaluation. We use the syntax [@foo] to reference identifier [foo] with its implicit argument behavior turned off. (The proof details below use Ltac features not introduced yet, and they are safe to skip for now.) *) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.823072612285614, "perplexity": 4537.895679393658}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813883.34/warc/CC-MAIN-20180222022059-20180222042059-00000.warc.gz"} |
http://paperity.org/search/?q=authors%3A%22Wojciech+Jarmo%C5%82owski%22 | # Search: authors:"Wojciech Jarmołowski"
2 papers found.
Use AND, OR, NOT, +word, -word, "long phrase", (parentheses) to fine-tune your search.
#### Fast Estimation of Covariance Parameters in Least-Squares Collocation by Fisher Scoring with Levenberg–Marquardt Optimization
Maximum likelihood (ML) and restricted maximum likelihood (REML) are nowadays very popular in geophysics, geodesy and many other fields. There is also a growing number of investigations into how to calculate covariance parameters by ML/REML accurately and fast, and assure the convergence of the iteration steps in derivative-based approaches. The latter condition is not satisfied in ...
#### Least squares collocation with uncorrelated heterogeneous noise estimated by restricted maximum likelihood
The article describes the estimation of a priori error associated with heterogeneous, non-correlated noise within one dataset. The errors are estimated by restricted maximum likelihood (REML). The solution is composed of a cross-validation technique named leave-one-out (LOO) and REML estimation of a priori noise for different groups obtained by LOO. A numerical test is the main ... | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8078135251998901, "perplexity": 3092.0806111897828}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187826114.69/warc/CC-MAIN-20171023145244-20171023165244-00624.warc.gz"} |
http://lists.gnu.org/archive/html/lilypond-user/2012-02/msg00511.html | lilypond-user
[Top][All Lists]
## Re: polychords: a working solution
From: Thomas Morley Subject: Re: polychords: a working solution Date: Thu, 16 Feb 2012 23:05:10 +0100
```Hi Jean-Alexis,
>
>> as remarked here:
>> lists.gnu.org/archive/html/lilypond-user/2012-02/msg00177.html
>> there are some problems with "polychord-column".
>> I changed it to the new "dir-column-line".
>>
>> But in both cases the chords are aligned with their root. Depending
>> whether an accidental is added or not the horizontal line is more or
>> less raised (especially when you add \override ChordNames.ChordName
>> #'font-size = #6 or sth like that to enlarge the ChordNames).
>> I'm not sure how it _should_ look, what do you think?
>>
>> Regards,
>> Harm
>> <polychordsDemo-rev-01.ly><polychordsDemo-rev-01.png>_______________________________________________
>> lilypond-user mailing list
>> https://lists.gnu.org/mailman/listinfo/lilypond-user
>
> It sure does look even better!
>
> To be perfect, we should add some thickness to the line. I could look into
> that next time I'm doing a score with polychords.
> Anyway, I think your code should be in the snippets and it has more uses that
> just polychords ! :)
>
> Thanks!
>
> Jean-Alexis
on purpose to add it to the LSR I tried to downgrade the functions to
"2.12.12", but I failed. :(
Do you think it makes sense to add them anyway, using the [needs LSR
upgrade]-feature? They will not be approved or listed until the LSR is | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8142653107643127, "perplexity": 4808.935718786441}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131297281.13/warc/CC-MAIN-20150323172137-00178-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://fr.mathworks.com/help/signal/ref/tf2zp.html | # tf2zp
Convert transfer function filter parameters to zero-pole-gain form
## Syntax
``[z,p,k] = tf2zp(b,a)``
## Description
example
````[z,p,k] = tf2zp(b,a)` finds the matrix of zeros `z`, the vector of poles `p`, and the associated vector of gains `k` from the transfer function parameters `b` and `a`. The function converts a polynomial transfer-function representation $H\left(s\right)=\frac{B\left(s\right)}{A\left(s\right)}=\frac{{b}_{1}{s}^{n-1}+\cdots +{b}_{n-1}s+{b}_{n}}{{a}_{1}{s}^{m-1}+\cdots +{a}_{m-1}s+{a}_{m}}$of a single-input/multi-output (SIMO) continuous-time system to a factored transfer function form $H\left(s\right)=\frac{Z\left(s\right)}{P\left(s\right)}=k\frac{\left(s-{z}_{1}\right)\left(s-{z}_{2}\right)\cdots \left(s-{z}_{m}\right)}{\left(s-{p}_{1}\right)\left(s-{p}_{2}\right)\cdots \left(s-{p}_{n}\right)}.$ NoteUse `tf2zp` when working with positive powers (s2 + s + 1), such as in continuous-time transfer functions. A similar function, `tf2zpk`, is more useful when working with transfer functions expressed in inverse powers (1 + z–1 + z–2). ```
## Examples
collapse all
Generate a system with the following transfer function.
`$H\left(s\right)=\frac{2{s}^{2}+3s}{{s}^{2}+\frac{1}{\sqrt{2}}s+\frac{1}{4}}=\frac{2\phantom{\rule{0.16666666666666666em}{0ex}}\left(s-0\right)\phantom{\rule{0.16666666666666666em}{0ex}}\left(s-\left(-\frac{3}{2}\right)\right)}{\left(s-\frac{-1}{2\sqrt{2}}\left(1-j\right)\right)\phantom{\rule{0.16666666666666666em}{0ex}}\left(s-\frac{-1}{2\sqrt{2}}\left(1+j\right)\right)}$`
Find the zeros, poles, and gain of the system. Use `eqtflength` to ensure the numerator and denominator have the same length.
```b = [2 3]; a = [1 1/sqrt(2) 1/4]; [b,a] = eqtflength(b,a); [z,p,k] = tf2zp(b,a)```
```z = 2×1 0 -1.5000 ```
```p = 2×1 complex -0.3536 + 0.3536i -0.3536 - 0.3536i ```
```k = 2 ```
Plot the poles and zeros to verify that they are in the expected locations.
`fvtool(b,a,'polezero')`
```text(real(z)+.1,imag(z),'Zero') text(real(p)+.1,imag(p),'Pole')```
## Input Arguments
collapse all
Transfer function numerator coefficients, specified as a vector or matrix. If `b` is a matrix, then each row of `b` corresponds to an output of the system. `b` contains the coefficients in descending powers of s. The number of columns of `b` must be less than or equal to the length of `a`.
Data Types: `single` | `double`
Transfer function denominator coefficients, specified as a vector. `a` contains the coefficients in descending powers of s.
Data Types: `single` | `double`
## Output Arguments
collapse all
Zeros of the system, returned as a matrix. `z` contains the numerator zeros in its columns. `z` has as many columns as there are outputs.
Poles of the system, returned as a column vector. `p` contains the pole locations of the denominator coefficients of the transfer function.
Gains of the system, returned as a column vector. `k` contains the gains for each numerator transfer function.
## Version History
Introduced before R2006a | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9430566430091858, "perplexity": 1482.0103374056762}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103945490.54/warc/CC-MAIN-20220701185955-20220701215955-00012.warc.gz"} |
http://www.physicsforums.com/showthread.php?p=1939682 | # Curve ball problem, the spin axis will change?
by zyh
Tags: axis, ball, curve, spin
P: 134 HI, I encountered a problem about the curve ball (table tennis ball) flying in the air. See the pictures below. A ball with an initial velocity V along X axis, and has a spin along Z axis. As far As I know ( see my previous post in The air drag problem... ) . F1 is the air drag. F2 is the gravity. F3 is the magnus force( sometimes we call it lift force). So, the ball will not travel directly through X axis, it will curve to left. My question is : What about the spin axis? Will it shift from A1 to A2? ( A1 is the axis parallel to Z axis as the initial state )? If Yes, How can I estimate the angle between A1 and A2? Any suggestion is appreciated. Thank you very much. Attached Thumbnails
P: 134 I'm sorry that the attachment image is destroyed(I upload the jpg file as an attachment, but it doesn't appeared). I will upload it soon! Image added!
P: 4,513 The way you have it drawn, the ball will curve to the right, and also lift from gravitational effects.
P: 134 Curve ball problem, the spin axis will change? Thanks Phark. To my knowledge, I think the revolution axis(or spin axis) will remain its original direction( in the picture, it is A1), because, the drag, life and gravity force all have no effects on the spin Torque.
P: 4,513 My mistake about the directions of deflection. I got everything inverted. The question is, what happens when the spin axis is at some accute angle to the velocity, like when the ball starts dropping, right? The lift and the induced drag, for instance, will act somewhere toward the 'leading edge'. But where is the profile drag--the viscous and eddy current drag?
P: 134 Hi, Phrak, I received your message. In my case: the revolution axis is transverse with Velocity, which is more simple than your question" spin axis is some accute angle to the velocity". I think the lift force ( magnus force ) is defined by: $$\overrightarrow{F_{lifg}}=k1\overrightarrow{\omega}\times\overrightarro w{V}$$ Through I'm not sure this formula is right. The profile drag(Let me guess its meaning) is defined by: $$\overrightarrow{F_{drag}}=-k2\parallel\overrightarrow{V}\parallel\overrightarrow{V}$$ where K1 and k2 are all drag coefficients.
P: 4,513 Let me make sure I have this right. You want to know if the spin axis will precess, right? For something with little angular mass, such as a ping pong ball, it seems, it precession could be substancial at the right angle of attack. What's required for it to precess is force couple whos axis isn't parallel with the spin axis. I'd have to get out my crayons to see how the distributed forces would do this. It's probably more intuitive to draw the spin axis as horizontal, where the axis is oriented in the airflow like the span of a wing, then give it a little yaw.
P: 134 Thanks, Yes, I'm try to find whether the spin axis will precess. Do you mean "Angular mass" is the same as "Angular momentum" ? see in http://en.wikipedia.org/wiki/Angular_momentum I'm my picture, I think the torque given by "distributed forces" is symmetric on the spin axis. So, the precess may not happen.
Sci Advisor P: 2,510 First of all, let me say that your direction of curve in the original illustration is correct. The ball will curve in the same direction it is spinning. The curve in the opposite direction would be true on Mars (or maybe at extremely high altitudes), but not on Earth. Secondly, I can see no force that would cause the axis to tilt. As I understand it, precession is a phenominon that takes place when the axis of rotation is already tilted. Maybe I'm not using the right frame of reference?
P: 134 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8634569644927979, "perplexity": 858.444164435025}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510258086.28/warc/CC-MAIN-20140728011738-00288-ip-10-146-231-18.ec2.internal.warc.gz"} |
http://physics.bgu.ac.il/COURSES/PHYSICS_ExercisesPool/CONTRIBUTIONS/e_10_1_022_s_1.html | ### Inertial and noninertial reference frames
see Fig.1.
If we define the axis and $\theta$ as in Fig. 1, then we can write the velocity vector of the river as:
$\vec{v}=v\sin{\theta}\hat{y}-v\cos{\theta}\hat{z}$
since $\vec{\omega}=\omega\hat{z}$, we have that the coriolis correction to the acceleration vector is
$\vec{a_c}=-2\vec{\omega}\times\vec{v}=2\omega v \sin{\theta}\hat{x}$
Now observe at Fig. 2.
it shows a cross-section of the river, as it flows towards you. convince yourself that the new x' axis, which is pointing towards the left bank of the river, is the same as the previous x axis, so the river feels coriolis' acceleration
$a_{x'}=2\omega v \sin{\theta}$
also, it feels an acceleration downwards, we'll naturally call it g, which is comprised of the gravity acceleration and a small, insignificant, centrifugal correction. so we have
$a_{y'}=g$
and now we'll argue that
$h/L=a_x/a_y=\frac{2\omega v\sin{\theta}}{g}$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 7, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9201714992523193, "perplexity": 657.4308009746379}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818686169.5/warc/CC-MAIN-20170920033426-20170920053426-00558.warc.gz"} |
https://experts.mcmaster.ca/display/publication227300 | On Gaugino Condensation with Field-Dependent Gauge Couplings Academic Article
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abstract
• We study in detail gaugino condensation in globally and locally supersymmetric Yang-Mills theories. We focus on models for which gauge-neutral matter couples to the gauge bosons only through nonminimal gauge kinetic terms, for the cases of one and several condensing gauge groups. Using only symmetry arguments, the low-energy expansion, and general properties of supersymmetry, we compute the low energy Wilson action, as well as the (2PI) effective action for the composite {\it classical} superfield $U\equiv\langle \Tr\WW \rangle$, with $W_\alpha$ the supersymmetric gauge field strength. The 2PI effective action provides a firmer foundation for the approach of Veneziano and Yankielowicz, who treated the composite superfield, $U$, as a quantum degree of freedom. We show how to rederive the Wilson action by minimizing the 2PI action with respect to $U$. We determine, in both formulations and for global and local supersymmetry, the effective superpotential, $W$, the non-perturbative contributions to the low-energy K\"ahler potential $K$, and the leading higher supercovariant derivative terms in an expansion in inverse powers of the condensation scale. As an application of our results we include the string moduli dependence of the super- and K\"ahler potentials for simple orbifold models.
• August 1996 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9322137832641602, "perplexity": 1107.9589736253133}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989814.35/warc/CC-MAIN-20210513142421-20210513172421-00139.warc.gz"} |
https://arxiv.org/abs/2003.11989 | # Title:Superdeterministic hidden-variables models I: nonequilibrium and signalling
Abstract: This is the first of two papers which attempt to comprehensively analyse superdeterministic hidden-variables models of Bell correlations. We first give an overview of superdeterminism and discuss various criticisms of it raised in the literature. We argue that the most common criticism, the violation of free-will', is incorrect. We take up Bell's intuitive criticism that these models are conspiratorial'. To develop this further, we introduce nonequilibrium extensions of superdeterministic models. We show that the measurement statistics of these extended models depend on the physical system used to determine the measurement settings. This suggests a fine-tuning in order to eliminate this dependence from experimental observation. We also study the signalling properties of these extended models. We show that although they generally violate the formal no-signalling constraints, this violation cannot be equated to physical signalling, in the sense of information transfer between the wings. We therefore suggest that the so-called no-signalling constraints be more appropriately named the marginal-independence constraints. We discuss the mechanism by which marginal-independence is violated in superdeterministic models. We use this to delineate the superdeterministic contribution to the net change in marginals for a hybrid nonlocal superdeterministic model (in nonequilibrium). Lastly, we consider a hypothetical scenario where two experimenters use the apparent-signalling of a superdeterministic model to communicate with each other. This scenario suggests another conspiratorial feature peculiar to superdeterminism. These suggestions are quantitatively developed in the second paper.
Comments: 14 pages, 5 figures Subjects: Quantum Physics (quant-ph); History and Philosophy of Physics (physics.hist-ph) Cite as: arXiv:2003.11989 [quant-ph] (or arXiv:2003.11989v1 [quant-ph] for this version)
## Submission history
From: Indrajit Sen [view email]
[v1] Thu, 26 Mar 2020 15:49:34 UTC (115 KB) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8797315955162048, "perplexity": 2074.314963978076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370493121.36/warc/CC-MAIN-20200328225036-20200329015036-00415.warc.gz"} |
https://math.stackexchange.com/questions/1705772/how-to-prove-that-the-area-of-the-parallelogram-is-half-of-that-of-the-quadrilat | # How to prove that the area of the parallelogram is half of that of the quadrilateral in diagram?
In the given figure,ABCD is a quadrilateral and E,F G and H are respectively the mid-points of its sides. Prove that the area of the parallelogram EFGH formed by joining the mid-points of the sides of the quadrilateral is half the area of the quadrilateral.
The question can be easily proved if the ABCD is a parallelogram but as the ABCD is a quadrilateral it is being difficult. How to go about it?
$EF$ is the basis media of triangle $ABC$, and then $A(BEF)=1/4A(ABC)$. Idem $A(GHD)=1/4A(ACD)$.
Now, note that $A(ACD)+A(ABC)=A(ABCD)\to A(BEF)+A(GHD)=1/4A(ABCD)[*_1]$.
Idem, $A(HEA)+A(GFC)=1/4A(ABCD)[*_2]$.
Adding $[*_1] +[*_2]$ the problem is solved
• Excellent !! @vvnitram – Vinay5forPrime Mar 20 '16 at 15:03
HINT.-The shortest way could be, I think, the vector viewpoint.
Let $A,B,C,D$ the vertices of the quadrilateral; $A',B',C',D'$ the midpoints of segments $AB,BC,CD,DA$ respectively. We have
Area $\triangle ABD=\frac 12||\vec{CB}\text{x}\vec{CD}||$ and Area $\triangle DBC=\frac 12||\vec{AB}\text{x}\vec{AD}||$ Hence the area of the quadrilateral is the sum of these two areas.
Similarly, area $\triangle D'A'C'=\frac 12||\vec{D'A'}\text{x}\vec{D'C'}||$ and Area $\triangle C'A'B'=\frac 12||\vec{B'C'}\text{x}\vec{B'A'}||$
Now it is clear because $\vec{OA'}=\frac{\vec{OA}+\vec{OB}}{2}$ et cetera.
• Rather good and abstract approach! Never thought of it in this manner.@Piquito – Vinay5forPrime Mar 22 '16 at 7:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9013491272926331, "perplexity": 257.88775093850774}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986703625.46/warc/CC-MAIN-20191020053545-20191020081045-00291.warc.gz"} |
https://cassandrahunt.com/topics/LaTeX | # LaTeX Tools and Hacks
Since I began fighting the good fight for my thesis, I've been exposed to several of the vagaries and idiosyncrasies of LaTeX. I decided to collect together some of the most useful things I've learned, for my own future reference and to help any other desperate soul battling the same demon.
LaTeX.
LaTeX is the demon.
If you have your own tricks you'd like to share, please send them my way and I'll include them here.
You can personalize how links are formatted with hypersetup. (Make sure to include the hyperref package!)
Here's a list of some of the important options below. (This is how my thesis is set up. The commented out lines are options I decided against, but someone else might like.)
\hypersetup{
% if needed
colorlinks =true, % Font in color, otherwise in
% frame (yuck)
hypertexnames=false, % Needed for correct links to
% figures
plainpages =true, % Do page number anchors as plain
% Arabic
% on TOC
citecolor=MyGreen, % Color of links to bibliography
urlcolor =MyRed, % Color of external url links
filecolor=blue, % Color of file links
% of each item in the
% bibliography, as a list of page
% numbers.
[...]
A complete list of options is available here (pdf).
To personalize the colors of your links, include the color package, "\usepackage{color}". Then specify your colors (using rgb), like so:
\definecolor{MyRed}{rgb}{0.5,0,0}
\definecolor{MyGreen}{rgb}{0,0.5,0}
\definecolor{MyBlue}{rgb}{0,0,0.5}
[top]
##### Modify PDF Meta Data with hyperref
The hypersetup options are just crawling with goodies. You can specify meta information, how the pdf looks when it's opened, how links are formatted, etc. A complete list of options is available here (pdf).
Here are some of the settings I use,
\hypersetup{
[...]
pdfstartview=FitH, % Set by page width
pdfborder={0 0 0}, % document border
pdfauthor={Cassandra R. Hunt},
pdftitle ={My Title},
pdfsubject = {Ph.D. Thesis},
pdfkeywords = {My,Keywords,Separated,by,Commas},
pdfcreator = {LaTeX with hyperref package},
pdfproducer = {pdflatex}
}
(When using hypersetup, make sure to include the hyperref package!)
[top]
##### Format the Bibliography
How difficult should it be to have a bibliography that has these basic features:
• Numbered references. (Who in their right mind thinks monstrosities like [GBlahman2001] scattered throughout their text are helpful?)
• User set-able number of authors before using et al.
• Shows the title, without weird formatting. (There is nothing more eye-bleeding than reading a chemical formula in all lower case.)
• Includes links to the articles.
This is pretty basic stuff people. And yet I could not find such a .bst file anywhere. My husband had gone part of the way with his thesis, modifying the APS standard apsrev4-1.bst to allow you to set the number of entries before using et al. as well as the number of authors to include when et al. is used. I started from his version and we modified it further to by default include article titles in quotes, without additional formatting. This required a bit of fiddling, because LaTeX programming consists mostly of archaic runes and secret enchantments, all but lost to the ages.
But it is done. And only a few minor demons were accidentally summoned in the process. I present our bastard progeny:
apsrev4-1-etal.bst
Here's how the citations look:
How to use this file
You're going to need the same packages as the standard apsrev4-1.bst file requires. You can find a list on the APS website. Hope there is no pain getting it working, but if there is, you are on your own. Don't ask me. I'm not a LaTeX guru, just another lost soul.
If you're wondering where to put these files, well that depends on how your LaTeX libraries are organized and how your interpreter knows how to search for the files it needs. I'm using Kile, which is a bit of a magic program that comes batteries included. For me it's just been plug and play. Including the .bst file in the appropriate directory (the same one as my .tex file) was all I needed to do. The style files and packages were already downloaded.
Include natbib like so: "\usepackage[numbers]{natbib}" if you want to have numbered entries. And don't forget to include the hyperref package to have linked references. For the LaTeX newbies, include packages at the top of your file (after \documentclass{...} and before \begin{document}). Then, before \end{document}, include the bibliography as follows:
Make sure the link to your .bib file doesn't actually include the .bib extension. (How to write a .bib file.)
Author settings
To set the number of authors, the solution is inelegant. I did say this was a bastard child. Search for the text %%%MODIFIED-ETAL-START in apsrev4-1-etal.bst. The text should look as follows:
The default number of authors to show when using et al. is set to 4 and the maximum number of authors to display without using et al. is set to 7. Change these numbers to whatever you like.
If someone who actually knows how to set variables in LaTeX wants to improve on this, please let me know.
What if I don't want titles?
It is infuriating isn't it, not finding exactly what you're looking for? Especially when it's something so straightforward. If you like the et al. feature but don't want titles, you can easily comment out this part of the code. Search for the text %%%MODIFIED-ATITLE-START in apsrev4-1-etal.bst. It'll look like this:
Comment out the code between %%%MODIFIED-ATITLE-START and %%%MODIFIED-ATITLE-END to suppress titles.
[top]
##### Force an image into a section
There's no silver bullet for getting your images where you want them with LaTeX. But this is something that's help me keep a little sanity when my figures want to wander too far afield: placeins. Use the command \FloatBarrier throughout your text to specify boundaries that figures may not cross. I like to do this at the end of subsections.
Import the package as "\usepackage[sections]{placeins}" to keep figures within sections. Use the keyword "below", "\usepackage[below]{placeins}", to allow images in the following section, assuming that at least part of the previous section is on the same page.
[top]
Is a little structure too much to ask?
If you want to LaTeX to search sub-directories to find images, you can use \graphicspath{} to do it. In the part of your tex file where you include packages, add the sub-directories that need to be searched as follows:
\graphicspath{{subdirectory/one/}
{subdirectory/two/}}
These paths need to be located in subfolders of the one housing your tex file. (Sorry, I haven't found a way around that constraint yet. The standard unix "../" doesn't do the trick.)
[top] | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8278468251228333, "perplexity": 2585.4753972191716}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337680.35/warc/CC-MAIN-20221005234659-20221006024659-00248.warc.gz"} |
https://link.springer.com/article/10.1007%2Fs13253-015-0243-0 | # Using Species Proportions to Quantify Turnover in Biodiversity
• Yuan Yuan
• Stephen T. Buckland
• Phil J. Harrison
• Sergey Foss
• Alison Johnston
Open Access
Article
## Abstract
Quantifying species turnover is an important aspect of biodiversity monitoring. Turnover measures are usually based on species presence/absence data, reflecting the rate at which species are replaced. However, measures that reflect the rate at which individuals of a species are replaced by individuals of another species are far more sensitive to change. In this paper, we propose families of turnover measures that reflect changes in species proportions. We study the properties of our measures, and use simulation to assess their success in detecting turnover. Using data on the British farmland bird community from the breeding bird survey, we evaluate our measures to quantify temporal turnover and how it varies across the British mainland.
## Keywords
Biodiversity Breeding bird survey Species abundance distribution Turnover measures
## 1 Introduction
Perhaps appropriately, there is a great diversity of measures for quantifying biodiversity (Pielou 1975; Krebs 1989; Magurran 2004). Choice of measure depends both on the type of data available and on the questions being asked. Maurer and McGill (2010) reviewed a large number of indices to measure species diversity, and gave a list of indices to measure different aspects of diversity, such as richness, evenness, dominance and rarity. This paper concentrates on temporal turnover, which we define as the change in species proportions over time, taking into account species identity. Thus, if a community is to exhibit zero turnover, then each species should represent a constant proportion of the community. We propose families of turnover measures in this paper, and link some of them to the metrics summarized by Martín-Fernández et al. (1998). We further study their properties in the context of measuring turnover, and provide transformation and modification for general applications. Although we focus on temporal turnover, these measures can also be used for quantifying spatial turnover between two neighbouring locations.
Spatial turnover is closely related to the concept of beta diversity. If we consider total diversity of a region (termed gamma diversity), we can partition it into alpha diversity, which measures average diversity at locations within the region, and beta diversity, which reflects spatial heterogeneity in diversity (Lande 1996). Thus, a region with high beta diversity has a diverse range of communities, perhaps reflecting a wide variety of habitats, while a region with low beta diversity has a relatively homogeneous community of species across the region. We refer to spatial turnover as the dissimilarity between pairs of locations that are neighbours, whereas beta diversity does not require this, and can be used to compare multiple assemblages. Beta diversity covers a broader range of objectives than the spatial turnover we discuss here. Jøst et al. (2010) reviewed a number of indices used for measuring similarities between assemblages in the context of beta diversity. Here, we concentrate on the dissimilarity of species composition. Measuring turnover, whether spatial or temporal, is about assessing the changes between two species compositions, and such change is measured by dissimilarity, which is also referred to as differentiation, divergence or distance in different scientific fields, such as probability theory, mathematical geology and cluster analysis. Given species proportions, we propose four different families of turnover measure, all of which can be used to quantify either spatial or temporal change in diversity.
There is no simple relationship between species turnover and other measures of diversity such as richness and evenness. For example, one assemblage can have complete turnover (no species in common between two time points), but its evenness might stay the same (the species proportions might remain the same, even though they relate to different species for the two time points). The relationship between richness and turnover is more complicated; both negative and positive relationships between spatial turnover and richness have been observed in studies on spatial turnover using species–area relationships (Clarke and Lidgard 2000; Stevens and Willig 2002; Koleff et al. 2003; Lennon et al. 2001; Lyons and Willig 2002). Quantifying changes in species diversity over time or space provide valuable insights into understanding biodiversity trends.
Traditionally, turnover usually refers to spatial turnover, and is usually measured from species presence–absence data (Rodrigues et al. 2000; La Sorte and Boecklen 2005). However, if available, it is more informative to use species abundance distributions to measure the compositional change over time (Magurran 2010). Measures based on the species abundance distribution or on species proportions are more informative and sensitive to biodiversity changes than measures based on presence/absence data. When we use species abundance distributions to measure turnover, turnover is evaluated by quantifying the rate at which individuals of one species are being replaced by individuals of another species.
The U.K. Breeding Bird Survey (BBS, Risely et al. 2013) has been conducted annually since 1994 on a stratified random sample of 1 km squares. Sites are surveyed twice a year by volunteers walking along two parallel 1 km transect lines, and recording any adult birds detected. Harrison et al. (2014) fitted models to these data to allow estimation of abundance in any 1 km square on the British mainland for any species with adequate data. We use those estimates for farmland species to estimate temporal turnover in the British farmland bird community, and study how it varies spatially. The BBS is undertaken by the British Trust for Ornithology (BTO) and jointly funded by the BTO, the Joint Nature Conservation Committee and the Royal Society for the Protection of Birds. The BBS data are available through the British Trust for Ornithology’s standard data request procedure (see http://www.bto.org/research-data-services/data-services/data-and-informationpolicy).
## 2 Background
Before introducing families of turnover measures, we briefly review indices that have been used for, or are related to, measuring turnover. Most have been used for measuring beta diversity, i.e. assessing compositional similarity between assemblages. Jøst et al. (2010) gave a list of distance-based similarity measures, some of which can be expressed by the $$L^p$$ distance-based measures proposed in Sect. 4.1. Some of the entropy-based similarity measures proposed by Jøst et al. (2010) have forms similar to the one introduced in Sect. 4.4. All of the indices that we propose can be used to measure either spatial or temporal turnover. However, spatial and temporal turnover measures have different interpretations. As pointed out by Magurran (2010), spatial heterogeneity (beta diversity) typically corresponds to different subsets of individuals, whereas in temporal studies, we follow a single community of individuals over time.
There are essentially three different methods to study turnover (Chao et al. 2006; Jøst et al. 2010). First, incidence-based and abundance-based similarity measures are widely used, and they usually share similar forms. Most studies that use them are in the context of beta diversity. When there is only one assemblage and a time series of observations on it, these indices can also be used to measure temporal change in diversity. Incidence-based indices use presence–absence data, while abundance-based indices use counts or abundances. These counts or abundances are often scaled to give species proportions.
Second, spatial turnover can also be evaluated by studying the species–area relationship, which is the relationship between species richness (i.e. the number of species in an assemblage) and the size of the area that the assemblage occupies. Power and logarithmic functions have been used to estimate how the number of species increases as the size of the sampled area increases (Conner and McCoy 1979; Lennon et al. 2001; Rosenzweig 1995). The species–time relationship, a temporal analogue of the species–area relationship, is used to evaluate the dependence of species richness on temporal scale (Grinnell 1922; Preston 1960; Rosenzweig 1995). Power functions (Adler and Lauenroth 2003; Hadly and Maurer 2001) and logarithmic functions (Rosenzweig 1995; White 2004) have been used to estimate the species–time relationship and hence the temporal turnover of species.
Third, the species range shifts, i.e. changes in species’ ranges over time, are estimated to quantify species turnover. As for incidence-based indices, presence–absence data are typically used, and turnover is measured by modelling species ranges, thus allowing the species extinctions and colonizations in the survey area to be estimated (Nenzén and Araújo 2011; Thuiller et al. 2005; Lawler et al. 2009). In the study of Island Biogeography theory, MacArthur and Wilson (1967) defined species turnover as the number of species eliminated and replaced per unit time, and focus on equilibrium state in terms of immigration and extinction in an island population. In applications, we often take the predicted future range of each species based on modelling climate or land use changes, and the consequent impact on the species.
Both incidence-based and species–area relationship methods use presence–absence data. However, ‘absence’ typically equates to ‘not recorded’, which may be a consequence of failure to detect the species when it is present, rather than genuine absence. In addition, rare species are more difficult to detect and may be under-represented relative to more abundant species. For the method based on species range shifts, change in species’ ranges tends to be slow and difficult to detect, as species are typically sparsely distributed at the edge of their range, so that the problem of undetected presence is greater. However, species proportions change almost continuously. Methods based on species proportions are more sensitive to changes in the community than those based on changing ranges. We therefore concentrate on turnover measures that use the species proportion vector, derived from the estimated species abundance distributions over time or space. We introduce notation in Sect. 3.1 and some key transformations in Sect. 3.2. We give a list of criteria and discuss their importance in measuring turnover in Sects. 3.3 and 3.4. We then introduce four families of turnover measure (Sect. 4). We summarize the proposed turnover measures in tables (Web Appendix A) and compare them through a simulation study (Web Appendix B). In Sect. 5, we apply our measures to quantify turnover in the farmland breeding bird community of the British mainland for the period 1994 to 2011. Finally, we summarize our findings from the simulation study (Sect. 6) and discuss the choice of different turnover measures (Sect. 7).
## 3 Preliminary Information
### 3.1 Notation
We use $$\varvec{p}=(p_1, \ldots , p_K)$$ to denote the vector of species proportions, where $$p_k \ge 0$$, $$\sum _{k=1}^K p_k =1$$, and K is the number of species. Note that some $$p_k$$ may be zero. However, zero values are problematic for measures involving the ratio of $$p_k$$’s, which includes several of our indices. In practice, therefore, K might be taken to be the number of species for which $$p_k>0$$. For regional surveys, we may be interested in quantifying temporal turnover by location, so that spatial variation in temporal turnover can be assessed. In this case, even common species are likely to have observed species proportions of zero at some locations. In this circumstance, spatio-temporal models can be fitted to the data for each species, and species proportions calculated from the predicted abundances at each location (Harrison et al. 2014). Temporal turnover can then be evaluated at each location using all those species with a predicted abundance exceeding zero at that location (Harrison et al. 2015; Yuan et al. n.d.), even though some of those species may not have been recorded at that location. The spatio-temporal modelling also reduces the sampling error in estimated species proportions.
For simplicity, we assume $$p_k>0$$ for any species k, so that all families of turnover measures proposed here are well defined. Therefore, $$\varvec{p}$$ is considered in an open simplex, denoted by $$\mathbb {P}_+^{K-1}=\left\{ p_1, \ldots , p_K \left| \,\sum _{k=1}^K p_k =1 \text{ and } \forall k \, \,p_k>0\right. \right\}$$. We assume that $$\varvec{p}$$ is a known probability distribution vector, although to evaluate turnover measures in practice, we would need to replace it by an estimate $$\widehat{\varvec{p}}$$ . Turnover measures assess the difference between two probability distribution vectors, which we denote by $$\varvec{p}_1$$ and $$\varvec{p}_2$$ at two different time points. Thus $$\varvec{p}_i$$ is the species proportion vector at time point i, $$\varvec{p}_i = (p_{i1}, \ldots , p_{iK})$$, for $$i=1,2$$. Measures can also be defined that are not a function of the species proportion vectors. For example, we might use the species density vector. In such cases, we use $$\varvec{p}^*$$ to denote the vector, which is no longer a probability distribution vector: $$p^*_k>0,\, \forall k$$ as before, but $$\sum _{k=1}^K p^*_i \in (0, \infty )$$.
### 3.2 Some Useful Transformations
We list three transformations on the open simplex $$\mathbb {P}_+^{K-1}$$, and all of them are one-to-one.
1. 1.
Transform into a positive sphere In order to use the distributional theory that has been established for the sphere (Stephens 1982; Stanley 1990), the simplex $$\mathbb {P}_+^{K-1}$$ needs to be transformed to a sphere, and such a transformation is denoted by $$\mathcal {S}(\varvec{p})$$,
\begin{aligned} \mathcal {S}(\varvec{p}): = (\sqrt{p_1}, \ldots , \sqrt{p_K}). \end{aligned}
(1)
Using this transformation, $$\mathbb {P}_+^{K-1}$$ is transformed into a positive sphere, denoted by $$\mathbb {S}_+^{K-1} = \left\{ \left( \sqrt{p_1}, \ldots , \sqrt{p_K}\right) \, \left| \, p_k>0,\sum _{k=1}^K p_k=1 \right. \right\} .$$ The transformed species proportion vector is no longer a probability distribution vector after transformation $$\mathbb {S}_+^{K-1}$$, because $$\sum _{k=1}^K \sqrt{p_k} \ne 1$$.
2. 2.
Transform using a weight vector We may wish to assign different levels of importance to different species. Such importance can be related to, for example, the commercial value of different species in the fishing industry, different functional roles in the ecosystem, or genetic distance of a species from others in the community. The importance of each species is represented by a weight. Let $$\varvec{w}$$ denote the weight vector, where $$\varvec{w} \, \in \,\mathbb {P}_+^{K-1}$$ with $$\sum _{k=1}^K w_k = 1$$. For any $$\varvec{w}$$, the weight transformation, $$\displaystyle {F_{\varvec{w}}}(\varvec{p})$$, is a simplex operation (a transformation from $$\mathbb {P}_+^{K-1}$$ to $$\mathbb {P}_+^{K-1}$$),
\begin{aligned} F_{\varvec{w}}(\varvec{p}):= \left( \frac{p_1w_1}{\langle \varvec{p}, \varvec{w}\rangle } , \ldots , \frac{p_K w_K}{\langle \varvec{p}, \varvec{w}\rangle } \right) \end{aligned}
(2)
where $$\langle \varvec{p}, \varvec{w}\rangle =\sum _{k=1}^K p_k w_k$$ is the scalar product of $$\varvec{p}$$ and $$\varvec{w}$$.
Note that when combining the above two transformations $$\mathcal {S}$$ given by (1) and $$F_{\varvec{w}}$$ given by (2), we get a transformation from a simplex to a weighted positive sphere. Let $$\mathcal {S}_{\varvec{w}}$$ denote the resulting transformation from $$\mathbb {P}_+^{K-1}$$ to $$\mathbb {S}_+^{K-1}$$ using the weight vector $$\varvec{w}$$:
\begin{aligned} \mathcal {S}_{\varvec{w}}(\varvec{p}) := \left( \sqrt{\frac{p_1 w_1}{\langle \varvec{p}, \varvec{w}\rangle }},\ldots , \sqrt{\frac{p_K w_K}{\langle \varvec{p}, \varvec{w}\rangle }}\right) . \end{aligned}
(3)
After transformation $$F_{\varvec{w}}(\varvec{p})$$ as defined in (2), the species proportion vector is still a probability distribution vector. However, this is not the case for $$\mathcal {S}_{\varvec{w}}(\varvec{p})$$ defined in (3).
3. 3.
Centred log-ratio (clr) transformation It can be useful to transform proportions to the real line. The log-ratio transformation, $$\log (p_k/p_K)$$, $$k =1,\ldots , K-1$$, is used to transform $$\varvec{p}$$ in the simplex $$\mathbb {P}_+^{K-1}$$ into data in $$\mathbb {R}^{K-1}$$. However, this log-ratio transformation affects each element of $$\varvec{p}$$ differently because of its dependence on the (arbitrary) ordering of the specie in $$\varvec{p}$$. In order to obtain a one-to-one transformation and a symmetric operation for all K components in $$\varvec{p}$$, Aitchison (1982, page 79) proposed the clr transformation which uses the geometric mean as the divisor. Let $$g(\varvec{p})$$ denote the geometric mean of $$\varvec{p}$$, i.e. $$g(\varvec{p})= \left( \prod _{k=1}^K p_{k}\right) ^{1/K}$$. The clr transformation is defined as $$\text{ clr }(\varvec{p}):=\left( \log \frac{p_1}{g(\varvec{p})}, \ldots , \log \frac{p_K}{g(\varvec{p})}\right)$$. The species proportions after applying $$\text{ clr }(\varvec{p})$$ lie in $$\mathbb {R}$$. Therefore, the transformed vector is not a distribution vector.
### 3.3 Properties of Turnover Measures
A turnover measure, $$d(\varvec{p}_1, \varvec{p}_2)$$, is considered as a function from $$\mathbb {P}_+^{K-1}\times \mathbb {P}_+^{K-1} \rightarrow \mathbb {R}$$. Such a function can be used to measure either temporal or spatial turnover. The form of the function stays the same but the arguments are different: for temporal turnover, $$\varvec{p}_i$$, $$i=1, 2$$, is the species proportion vector at time i (in a given location or region), while for spatial turnover, $$\varvec{p}_i$$, $$i=1, 2$$, is the species proportion vector at location i (at a given time point). Whether spatial or temporal, $$d(\varvec{p}_1, \varvec{p}_2)$$ is a metric if it satisfies the following three properties, but the relative importance of the properties differs for the two cases.
1. 1.
Positive definiteness $$d(\varvec{p}_{1}, \varvec{p}_{2})>0$$ for any $$\varvec{p}_1\ne \varvec{p}_2$$, and $$d(\varvec{p}_{1}, \varvec{p}_{2})=0$$ if and only if $$\varvec{p}_1 = \varvec{p}_2$$. For turnover measures, the positive definiteness means that the minimum value of a turnover measure is zero, and a turnover measure equals zero if and only if there is no change in species composition.
2. 2.
Symmetry $$d(\varvec{p}_{1}, \varvec{p}_{2})=d(\varvec{p}_{2}, \varvec{p}_{1})$$, for any $$\varvec{p}_1\ne \varvec{p}_2$$. Symmetry is necessary when two assemblages or communities are compared for turnover. However, symmetry is not necessarily required for measuring temporal turnover, for which it is natural to follow the temporal order.
3. 3.
Triangle inequality $$d(\varvec{p}_1, \varvec{p}_3) \le d(\varvec{p}_1, \varvec{p}_2)+d(\varvec{p}_2, \varvec{p}_3).$$ For both spatial and temporal turnover measures, it is preferred to have the triangle inequality. In the case of temporal turnover, for example, when comparing the turnover for three consecutive time points, the turnover between time point 1 and time point 3 should be no larger than the sum of turnover of time point 1 versus time point 2 and of time point 2 versus time point 3.
In addition to the above three properties, we note that permutation invariance is another property that is important for turnover measures. For a turnover measure, permutation invariance means that changing the sequence of the species in $$\varvec{p}$$ does not change the result. As all the measures discussed in this paper are permutation invariant, we do not list it above. It is also important to consider the above three properties for a turnover measure that is not defined on probability distribution vectors. The species proportion vector is obtained simply by scaling a density or abundance vector. For a vector $$\varvec{p^*}$$, if we can find a constant $$c>0$$ such that $$\varvec{p}^*= c \,\varvec{p}$$, we say that $$\varvec{p}^*$$ is equivalent to $$\varvec{p}$$. Given this definition, the species density vector, $$\varvec{\lambda }=(\lambda _1, \lambda _2, \ldots , \lambda _K)$$, is equivalent to a species proportion vector, $$\varvec{p}$$, because $$\varvec{p}=\varvec{\lambda }/\sum _{k=1}^K\lambda _k$$. Some measures have the above three properties not only for $$\varvec{p}$$, but also for any of its equivalent vectors. When a measure is equivalently defined on $$\varvec{p}$$ and all its equivalent vectors $$\varvec{p^*}$$, we use $$d(\varvec{p}^*_1, \varvec{p}^*_2)$$ to denote the turnover measure.
### 3.4 Further Properties of Turnover Measures
It is important to examine the properties of turnover measures and understand the advantage of having these properties in applications. Jøst et al. (2010) suggested three basic properties for any ecologically useful measure of similarity and discussed these properties in the context of measuring beta diversity. Aitchison (1992) gave a list of criteria for measures to assess compositional difference in geological applications. Although concerned with a different application, their summary sheds light on the properties of turnover measures, which we discuss here. In this section, we discuss the properties of turnover measures in the context of measuring turnover as a ‘distance’ or ‘divergence’ between two probability distributions of frequencies specified by two different species proportion vectors $$\varvec{p}_1$$ and $$\varvec{p}_2$$. In Sect. 3.3, we listed three basic properties for a turnover measure to be a metric. The following lists another two useful properties:
1. 4.
Scale invariance $$d(a\,\varvec{p}_{1}, b\,\varvec{p}_{2}) = d(\varvec{p}_{1}, \varvec{p}_{2})$$, for any constants $$a>0$$ and $$b>0$$. If a turnover measure is scale invariant, then $$\varvec{p}_1$$ and $$\varvec{p}_2$$ do not have to be probability distribution vectors, i.e. $$\sum _{k=1}^K p_{1k}$$ and $$\sum _{k=1}^K p_{2k}$$ do not necessarily have to be one. A scale invariant turnover measure remains unchanged as long as the species compositional vectors are proportional to the species probability vector, as is the case for species density and abundance vectors.
2. 5.
Insensitivity to coordinate scaling $$d(\varvec{p}_1, \varvec{p}_2)=d(\varvec{\mathcal {C}}\circ \varvec{p}_1, \varvec{\mathcal {C}}\circ \varvec{p}_2)$$, for any coordinate scaling function $$\varvec{\mathcal {C}}$$, which is an operation defined on vector $$\varvec{x}$$. Let $$\varvec{y}$$ denote the vector after applying $$\varvec{\mathcal {C}}$$ to $$\varvec{x}$$, then $$\varvec{y} = \varvec{\mathcal {C}}\circ \varvec{x} = (\mathcal {C}_1 x_1, \ldots , \mathcal {C}_K x_K)$$, and for each $$k, y_k=\mathcal {C}_k \,x_{k}$$. Note that for a turnover measure, if the difference between each component in $$\varvec{p}_1$$ and $$\varvec{p}_2$$ is measured in the form of ratios, i.e. $$p_{1k}/p_{2k}$$ for any species k, then this turnover measure is insensitive to any coordinate scaling.
Scale invariance is a special case of insensitivity to coordinate scaling, as it is the same scaling factor applied to each coordinate, i.e. $$\mathcal {C}_k$$ in the coordinate scaling function is constant for any k. We consider properties 1 to 3 of Sect. 3.3 together with these two further properties in the context of the proposed turnover measures (see Web Appendix A for details).
### 3.5 The Advantage of Being Insensitive to Coordinate Scaling for Turnover Measures
It is rare to have perfect detection in wildlife abundance surveys. Therefore, we need to apply detection probabilities to the survey data to estimate abundance. Such a process can be considered as scaling each element in the species proportion vector $$\varvec{p}$$ by the inverse of the detection probability for the given species.
The coordinate scaling function is expressed as $$\varvec{\mathcal {C}}^{-1}= \big (\mathcal {C}_1^{-1}, \ldots , \mathcal {C}_K^{-1}\big )$$, where $$\mathcal {C}_k$$ is the detection probability for species k with $$0<\mathcal {C}_k\le 1$$. The following proves that if a turnover measure is insensitive to coordinate scaling (which implies scale invariant), and if the detection probability for a given species is constant, then the measure is independent of the detection probability vector $$\varvec{\mathcal {C}}^{-1}$$. Using insensitivity to coordinate scaling and scale invariance in the following three steps, we have $$d(\varvec{p}_1, \varvec{p}_2) = d(\varvec{\lambda }_1, \varvec{\lambda }_2)= d(\varvec{\mathcal {C}}^{-1}\circ \varvec{\lambda }_1, \, \varvec{\mathcal {C}}^{-1}\circ \varvec{\lambda }_2)= d\left( \varvec{p}^{(c)}_1, \varvec{p}^{(c)}_2\right)$$, where $$\varvec{p}^{(c)}$$, $$i=1,2$$, is the species proportion vector after applying the capture probabilities. This means that for species k, we have $$p_k^{(c)} = \frac{\lambda _k/{\mathcal {C}}_k}{\sum _{s=1}^K\left( \lambda _s/{\mathcal {C}}_s\right) }$$. Therefore, provided that for any given species, the detection probability does not change over time, so that $$\varvec{\mathcal {C}}$$ is constant, we do not need to be able to estimate detection probability for a turnover measure that is scale invariant and insensitive to coordinate scaling. For surveys with standardized field procedures, such as national breeding bird surveys or long-term bottom trawl fish surveys using standard gear, it may not be unreasonable to assume that the detection probability does not change over time.
## 4 Different Families of Turnover Measures
### 4.1 The $$L^{q}$$-Distance Turnover Measure and Its Generalizations
It is natural to use distance to measure the difference between two vectors in $$\mathbb {P}_+^{K-1}$$. There are different forms of distance-based similarity/dissimilarity indices, and the $$L^1$$ and $$L^2$$ distances are most common in biodiversity applications. Ludwig and Reynolds (1988) listed a group of indices based on Euclidean distance for assessing similarity/dissimilarity between two objects, and discussed their applications in measuring difference in abundance between different sampling locations. Foster and Bills (2004) reviewed a similar group of distance-based dissimilarity indices in measuring biodiversity of fungi. Champely and Chessel (2002) generated the Euclidean dissimilarity coefficient as a function of Euclidean distance, and combined it together with principal component analysis to compare communities. Jøst et al. (2010) reviewed different distance-based similarity measures in the context of measuring beta diversity, and these measures are related to either $$L^1$$ or $$L^2$$ distance.
In contrast with the frequent use of $$L^1$$ and $$L^2$$ distances in measuring similarity or dissimilarity between communities/assemblages, we find that the $$L^q$$ distance with $$0<q<1$$ is rarely used in the biodiversity literature. Most of the distance-based measures can be unified into a class of distance-based indices using the $$L^q$$ norm, where q is a positive real number. In this section, we introduce a family of measures based on the $$L^q$$ distance together with a generalization when $$q=2$$. We use $$|| \,.\,||_q$$ to denote the $$L^q$$-norm of $$\varvec{p}$$, $$||\varvec{p}||_q=\left( \sum _{k=1}^K |p_k|^q\right) ^{\frac{1}{q}}$$, and for simplicity, $$||\varvec{p}||=||\varvec{p}||_2$$. Given the $$L^q$$-norm, we define the $$L^{q}$$-distance measure, $$d_{q}(\varvec{p}_{1}, \varvec{p}_{2})$$, as
\begin{aligned} d_{q}(\varvec{p}_{1}, \varvec{p}_{2}) = \frac{||\varvec{p}_1-\varvec{p}_2||_q}{||\varvec{p}_1||_q + ||\varvec{p}_2||_q}. \end{aligned}
(4)
1. 1.
When $$q\ge 1$$, (4) is based on the Minkowski distance. The numerator itself, $$||\varvec{p}_1-\varvec{p}_2||_q$$, is a metric when $$q\ge 1$$ (Minkowski 1896). However, (4), with the normalising denominator to ensure $$d_{q}(\varvec{p}_{1}, \varvec{p}_{2})\in [0,1]$$, only obeys the triangular inequality (and hence is only a metric) when $$q=1$$. When $$q=1$$, we have
\begin{aligned} d_1(\varvec{p}_{1}, \varvec{p}_{2})= \frac{1}{2} \sum _{k=1}^{K} |p_{1k}- p_{2k}|=1 - \sum _{k=1}^{K}\min \{p_{1k}, p_{2k}\}. \end{aligned}
(5)
The distance measure given by (5) is known as the total variation distance between probability measures in probability theory, and it is also known as the Manhattan distance, city-block distance, the $$L^{1}$$-norm or the taxicab distance when constructing non-Euclidean geometries (Krause 1975). When $$q=2$$, the numerator of (4) is the Euclidean distance between $$\varvec{p}_1$$ and $$\varvec{p}_2$$, and
\begin{aligned} d_2(\varvec{p}_{1}, \varvec{p}_{2})= \frac{\sqrt{\sum _{k=1}^K (p_{1k} - p_{2k})^2}}{ \sqrt{\sum _{k=1} ^K p_{1k}^2} + \sqrt{\sum _{k=1}^K p_{2k}^2}}. \end{aligned}
(6)
This Euclidean-distance-based index can also be applied to presence–absence data to assess turnover. La Sorte and Boecklen (2005) used the Euclidean distance between expected and observed presence–absence vectors to evaluate the level of compositional similarity for common species in avian assemblages in North America. When $$q \rightarrow + \infty$$, only the largest changes in species proportions contribute to the $$L^q$$ distance turnover measure. Clearly, $$\displaystyle {\lim _{q \rightarrow +\infty } } \left( p_1^q + \cdots + p_K^q\right) ^{1/q} = \underset{k}{\max } \,\,p_k$$.
2. 2.
Clearly, $$p_k^q \rightarrow 1$$ as $$q\rightarrow 0$$, so $$\displaystyle {\lim _{q \rightarrow 0 } }\left( p_1^q + \cdots + p_K^q \right) ^{1/q} = \infty$$ if $$K\ge 0$$ and at least two of the $$p_k$$’s are strictly positive. Instead, we may consider $$\displaystyle {\lim _{q \rightarrow 0 } \left( \frac{p_1^q + \cdots + p_K^q}{ K} \right) ^{1/q} }$$ to shed some light on the properties of the $$L^q$$ distance when $$q\in (0,1)$$. By l’Hôpital’s rule,
\begin{aligned} \displaystyle {\lim _{q\rightarrow 0}} \left( \frac{p_1^q+\ldots +p_K^q}{K} \right) ^{1/q}&=\exp \left( \lim _{q\rightarrow 0} \frac{1}{q} \log \left( \frac{ p_1^q+\ldots +p_K^q}{K} \right) \right) \\ {}&=\exp \left( \lim _{q\rightarrow 0} \frac{K}{\sum _{k=1}^K p_k^q} \sum _{k=1}^K \frac{p_k^q \log p_k}{K}\right) = \prod _{k=1}^K p_k^{1/K}. \end{aligned}
This means that if we use $$\left( \sum _{k=1}^K |p_k|^q\big /K\right) ^{1/q}$$ as the $$L^q$$ norm when $$0<q<1$$, then when $$q\rightarrow 0$$, for any species k, change in $$p_k$$ contributes to the turnover measure through the Kth root of the absolute difference in species proportions, $$|p_{1k} -p_{2k}|^{1/K}$$. After taking the Kth root of the absolute change, the difference between abundant and rare species is much less severe compared with the limiting case when $$q \rightarrow + \infty$$. Royden (1968) pointed out that the $$L^q$$ distance with $$0<q<1$$ is less affected by extreme differences than the Euclidean distance and can therefore be more robust to outliers. In the context of measuring turnover, the outliers can be thought of as species that contribute most to the turnover, i.e. the species that have the greatest change in their proportion. The absolute change in proportions will tend to be larger for abundant species than for rare species.
3. 3.
We consider a generalization of the $$L^2$$-distance measure to include similarity among species. We write (6) in a quadratic form as $$\sqrt{(\varvec{p}_{1} - \varvec{p}_{2})^T \varvec{H}(\varvec{p}_{1} - \varvec{p}_{2})}\big /\left( \Vert \varvec{p}_{1}\Vert + \Vert \varvec{p}_{2}\Vert \right)$$, where the matrix $$\varvec{H}$$ is an identity matrix, i.e. $$h_{ks} = 1$$ if $$k=s$$, and $$h_{ks}=0$$ if $$k\ne s$$. Motivated by this quadratic form of (6), we incorporate the similarity among species into (6) by using a similarity matrix $$\varvec{Z}$$ instead of $$\varvec{H}$$, $$d_{2S}(\varvec{p}_{1}, \varvec{p}_{2}) = \frac{\sqrt{(\varvec{p}_{1} - \varvec{p}_{2})^T \varvec{Z}(\varvec{p}_{1} - \varvec{p}_{2})}}{\sqrt{\varvec{p}_{1}^T \varvec{Z} \varvec{p}_1} \, +\, \sqrt{\varvec{p}_{2}^T \varvec{Z}\varvec{p}_2}}$$, where the similarity matrix, $$\varvec{Z}$$, is a $$K \times K$$ matrix. $$\varvec{Z}$$ is a symmetric positive-definite matrix. The element in the kth row and sth column, $$Z_{ks}$$, quantifies the similarity between the kth and sth species, and $$Z_{ks}=Z_{sk}$$ for any k, s $$\in \{ 1, \ldots , K\}$$. We define $$0\le Z_{ks}\le 1$$ with $$Z_{ks} = 0$$ meaning complete dissimilarity and $$Z_{ks}=1$$ meaning that two species are identical. Unlike the asymmetric similarity matrix used by Leinster and Cobbold (2012), we take $$\varvec{Z}$$ as symmetric positive-definite so that the product under the square root in the numerator of $$d_{2S}(\varvec{p}_{1}, \varvec{p}_{2})$$ is always positive as long as $$\varvec{p}_{1}\ne \varvec{p}_{2}$$. When including the similarity information in the numerator, we change the denominator accordingly by incorporating $$\varvec{Z}$$ in the $$L^2$$-norm of the species proportion vector: $$\sqrt{\varvec{p}_{1}^T \varvec{Z}\varvec{p}_1}$$ is considered as an $$L^2$$-norm of $$\varvec{p}_1$$ weighted by the similarity matrix.
### 4.2 The Angular Turnover Measure
In addition to the family of distance-based measures proposed in Sect. 4.1, we can also use the angle between $$\varvec{p}_{1}$$ and $$\varvec{p}_{2}$$ to evaluate the species turnover. In this section, we propose two different groups of angular turnover measures on the basis of the space in which the angle is considered: one group is based on the angle between $$\varvec{p}_{1}$$ and $$\varvec{p}_{2}$$ in the $$\mathbb {P}_+^{K-1}$$, and the other is based on the angle in $$\mathbb {S}_+^{K-1}$$ after applying the transformation (1) to $$\varvec{p}_{1}$$ and $$\varvec{p}_{2}$$ .
1. 1.
The angle in $$\mathbb {P}_+^{K-1}$$ Let $$\theta$$ denote the angle between $$\varvec{p}_1$$ and $$\varvec{p}_2$$ in $$\mathbb {P}_+^{K-1}$$; see Sect. 3.1 for the definition of $$\mathbb {P}_+^{K-1}$$. The cosine of $$\theta$$ is calculated as $$\cos \theta = \langle \varvec{p}_1, \varvec{p}_2\rangle \big /\left( \Vert \varvec{p}_{1}\Vert \,\Vert \varvec{p}_{2}\Vert \right)$$. To obtain a turnover measure as a monotonically increasing function about $$\theta$$, we use $$1-\cos \theta$$ as an angular turnover measure, denoted by $$d_{\cos }(\varvec{p}_{1} , \varvec{p}_{2})$$, where
\begin{aligned} d_{\cos }(\varvec{p}_{1} , \varvec{p}_{2}) = 1- \displaystyle {\frac{\sum _{k=1}^K p_{1k} p_{2k}}{\sqrt{\sum _{k=1}^ K p_{1k}^2 } \sqrt{\sum _{k=1}^K p_{2k}^2}} }. \end{aligned}
(7)
It follows that $$d_{\cos }(\varvec{p}_{1} , \varvec{p}_{2})=0$$ if and only if there is no turnover, and the greater the turnover, the closer $$d_{\cos }(\varvec{p}_{1} , \varvec{p}_{2})$$ is to 1. Given that the angle is considered in an open simplex (i.e. for any k, $$p_k>0$$), $$d_{\cos }(\varvec{p}_{1} , \varvec{p}_{2})<1$$. As mentioned in Sect. 3.2, sometimes it is necessary to incorporate different weights for different species in measuring turnover, and this can be done by using the weight transformation (2). Given the weight vector $$\varvec{w}$$, we obtain $$d_{\cos }^{\varvec{w}}(\varvec{p}_{1} , \varvec{p}_{2}) = 1- \displaystyle {\frac{\sum _{k=1}^K( p_{1k} p_{2k}w_k^2)}{\sqrt{\sum _{k=1}^ K (p_{1k}w_k)^2 } \sqrt{\sum _{k=1}^K( p_{2k} w_k)^2}} }$$. It follows that (7) is a special case of $$d_{\cos }^{\varvec{w}}(\varvec{p}_{1} , \varvec{p}_{2})$$ when each species has equal weight, i.e. $$w_k=1/K$$ for all k.
2. 2.
The angle in $$\mathbb {S}_+^{K-1}$$ The transformation given by (1) is to transform $$\varvec{p}$$ from the simplex $$\mathbb {P}_+^{K-1}$$ to the positive sphere $$\mathbb {S}_+^{K-1}$$, so that we can use the distribution theory that has already been established for the sphere (Stephens 1982; Stanley 1990). This section introduces the idea of using the angle in $$\mathbb {S}_+^{K-1}$$ because of its connection to the Bhattacharyya divergence measure (Bhattacharyya 1943). Although the Bhattacharyya divergence measure is usually referred to as a similarity measure of two probability distributions, we find that it can be derived as the angle in the positive sphere $$\mathbb {S}_+^{K-1}$$ between transformed species proportion vectors.
The idea is to transform $$\varvec{p}$$ using (1), and then use the cosine of the angle in $$\mathbb {S}_+^{K-1}$$ to measure turnover. Further, we incorporate weights for each species using the weight transformation given in (2). The weighting and transformation process combines (1) and (2) as $$(p_1, \ldots , p_K): \rightarrow \left( \sqrt{\displaystyle {\frac{p_1w_1}{\langle \varvec{p}, \varvec{w}\rangle }}},\ldots , \sqrt{\displaystyle {\frac{p_K w_K}{\langle \varvec{p}, \varvec{w}\rangle }}}\right)$$. The cosine of the angle in $$\mathbb {S}_+^{K-1}$$ is then evaluated by $$\sum _{k=1}^K \sqrt{\displaystyle {\frac{p_{1k} w_k}{\langle \varvec{p}_{1}, \varvec{w}\rangle }}}\sqrt{\displaystyle {\frac{p_{2k}w_k}{\langle \varvec{p}_{2}, \varvec{w}\rangle }}}$$, where $$\langle \varvec{p}, \varvec{w}\rangle =\sum _{k=1}^K p_k w_k$$ with a weight vector $$\varvec{w}$$. In application, $$\varvec{w}$$ is usually defined in the simplex $$\mathbb {P}_+^{K-1}$$, i.e. for any species k, $$w_k>0$$ and $$\sum _{k=1}^K w_k=1$$. However, as suggested by Aitchison (1982), it is difficult to interpret $$\varvec{w}$$ on the positive sphere after being transformed from $$\mathbb {P}_+^{K-1}$$. Similar to (7), we use $$1- \sum _{k=1}^K \sqrt{\displaystyle {\frac{p_{1k} w_k}{\langle \varvec{p}_{1}, \varvec{w}\rangle }}}\sqrt{\displaystyle {\frac{p_{2k}w_k}{\langle \varvec{p}_{2}, \varvec{w}\rangle }}}$$ as a turnover measure. When using equal weights, i.e. $$w_k = 1/K$$, $$\forall k$$, we have
\begin{aligned} d_{\cos }^*(\varvec{p}_{1}, \varvec{p}_{2}) =1- \sum _{k=1}^K \sqrt{p_{1k}\,p_{2k}}. \end{aligned}
(8)
Neither (7) nor (8) is a metric as the triangle inequality can fail. If these angular measures are considered as metrics, then they must be considered as directions on the positive sphere $$\mathbb {S}_+^{K-1}$$, in which case $$\theta$$ (rather than $$1-\cos \theta$$) should be used for measuring turnover; the geodesic distance on a unit sphere is $$2\theta$$. Therefore, $$\theta$$, used as a turnover measure, is a metric. We instead use $$1-\cos \theta$$ because 0 then corresponds to no turnover, and 1 to complete turnover, as for the distance-based measures introduced in Sect. 4.1.
### 4.3 Pairwise Turnover Measures
By using pairwise comparisons, we obtain indices that are more sensitive to changes in less abundant species. We introduce two pairwise measures in this section: pairwise angular and pairwise centred log-ratio.
The pairwise angular measure uses angles between each of the $$K(K-1)/2$$ pairs of species to measure the spatial or temporal changes in species composition. Let k and s denote any two species ($$k, s \in \{1,\dots ,K$$}; $$k\ne s$$). Consider their species proportions $$(p_{k}, p_{s})$$ in an x-y plot, with the x-axis corresponding to species k and the y-axis to species s. Let $$\theta _1^{(ks)}$$ and $$\theta _2^{(ks)}$$ denote the angle between species k and s in time point 1 and 2, respectively. The sine and cosine of $$\theta _1^{(ks)}$$ and $$\theta _2^{(ks)}$$ are evaluated by $$\sin \theta _1^{(ks)} =\displaystyle {\frac{p_{1s}}{\sqrt{p_{1k}^2 + p_{1s}^2}}}$$, $$\sin \theta _2^{(ks)} =\displaystyle {\frac{p_{2s}}{\sqrt{p_{2k}^2 + p_{2s}^2}}}$$, $$\cos \theta _1^{(ks)} =\displaystyle {\frac{p_{1k}}{\sqrt{p_{1k}^2 + p_{1s}^2}}}$$, and $$\cos \theta _2^{(ks)} =\displaystyle {\frac{p_{2k}}{\sqrt{p_{2k}^2 + p_{2s}^2}}}$$. We then evaluate $$\sin \left( \theta _1^{(ks)}-\theta _2^{(ks)}\right) =\sin \theta _1^{(ks)} \cos \theta _2^{(ks)} - \cos \theta _1^{(ks)} \sin \theta _2^{(ks)}$$. If there is no turnover between species k and s from time point 1 to time point 2, then there is no difference between $$\theta _1^{(ks)}$$ and $$\theta _2^{(ks)}$$, and it follows that $$\sin (\theta _1^{(ks)}-\theta _2^{(ks)})=0$$. We use the number of pairs of species, $$K(K-1)/2$$, to scale the sum of absolute values over all unique pairs, i.e. $$\frac{1}{2}\sum _{k=1}^K\sum _{s=1}^K\left| \sin \left( \theta _1^{(ks)}-\theta _2^{(ks)}\right) \right|$$. As a result, the measure does not depend on K, and has range [0, 1]. The pairwise angular measure $$d_{\sin }$$ is defined as
\begin{aligned} d_{\sin }(\varvec{p}_1, \varvec{p}_2)= & {} \frac{1}{K(K-1)}\sum _{k=1}^K\sum _{s=1}^K\frac{|p_{1k} p_{2s} - p_{1s} p_{2k}|}{\sqrt{p_{1k} ^2 + p_{1s}^2} \sqrt{p_{2k} ^2 + p_{2s}^2}}. \end{aligned}
(9)
Note that we can also use tangent to replace sine in (9), i.e. $$\tan \left( \theta _1^{(ks)}-\theta _2^{(ks)}\right)$$ instead of $$\sin \left( \theta _1^{(ks)}-\theta _2^{(ks)}\right)$$; we just need the trigonometric function to be monotonically increasing between $$-\pi /2$$ to $$\pi /2$$. Whichever trigonometric function we use, it is not possible to have the insensitivity to coordinate scaling described in Sect. 3.4. However, $$d_{\sin }$$ given by (9) does satisfy the first two properties of a metric. Given the inequality $$|\sin (\alpha + \beta )| \le |\sin \alpha | +|\sin \beta |$$ for any $$\alpha$$ and $$\beta$$, it is easy to prove that $$d_{\sin }$$ also satisfies the triangular inequality and therefore $$d_{\sin }$$ is a metric.
The pairwise centred-log-ratio measure is based on the following metric introduced by Aitchison et al. (2000) in statistical analysis of compositional data in geology,
\begin{aligned} d_2^{clr}(\varvec{p}_1, \varvec{p}_2)= & {} \left\{ \sum _{k=1}^K \left[ \log \frac{p_{1k}}{g(\varvec{p}_1)} - \log \frac{p_{2k}}{g(\varvec{p}_2)} \right] ^2\right\} ^{1/2} \end{aligned}
(10)
\begin{aligned}= & {} \left\{ \frac{1}{K} \sum _{k<s} \left[ \log \frac{p_{1k}}{p_{1s}} - \log \frac{p_{2k}}{p_{2s}} \right] ^2\right\} ^{1/2}. \end{aligned}
(11)
$$d_2^{clr}$$ can be thought of as a pairwise measure based on (11), and thus shares the sensitivity to rare species of all pairwise measures. Based on (10), the pairwise centred-log-ratio measure is based on the Euclidean distance between species proportions transformed by the centred log-ratio function given in Sect. 3.2. It follows that the pairwise centred-log-ratio measure is a metric as well. We note that K in (11) can be considered as a scalar, and $$d_2^{clr}$$ can also be written as $$\left\{ \frac{1}{2K} \sum _{k=1}^K\sum _{s=1}^K\left[ \log \frac{p_{1k}}{p_{2k}} - \log \frac{p_{1s}}{p_{2s}} \right] ^2\right\} ^{1/2}$$. Similar to $$d_\mathrm{sin}$$ given by (9), instead of K, we suggest using the number of pairs of species, $$K(K-1)/2$$, as the divisor. An alternative form of $$d_2^{clr}$$ is defined as
\begin{aligned} d_2^{clr\varvec{S}}(\varvec{p}_1, \varvec{p}_2)= & {} \left\{ \frac{1}{K(K-1)} \sum _{k=1}^K\sum _{s=1}^K\left[ \log \frac{p_{1k}}{p_{2k}} - \log \frac{p_{1s}}{p_{2s}} \right] ^2\right\} ^{1/2}. \end{aligned}
(12)
Using the number of pairs as divisor in both (9) and (12) can be thought of as taking the average across all pairs of species. This ensures comparability when K varies across regions, allowing us to compare temporal turnover at different locations. As the turnover measures are defined for species proportion vectors of the same dimension, K is constant in (12). Therefore, (12) still has all the properties that hold for (10).
### 4.4 Divergence-Based Turnover Measure
Pearson’s $$\chi ^2$$ and the log-likelihood ratio test are commonly used for testing the goodness-of-fit of multinomial models. Cressie and Read (1984) considered these two tests as special cases of power divergence statistics. Studeny et al. (2011) used the family of divergence measures to evaluate the degree of departure from the perfectly even abundance distribution, which serves as a null model. In this section, we derive a turnover measure based on one case of the power divergence statistics, the Kullback–Leibler (KL) divergence measure. We show that it has the same form as the J-divergence measure studied by Martín-Fernández et al. (1998), which is used for hierarchical classification. The link between our measures and those studied by Martín-Fernández et al. (1998) is given in Web Appendix A. Suppose we wish to test whether the observed species distribution is significantly different from the species distribution specified by a null hypothesis, denoted by $$\varvec{\pi }_0=(\pi _{01}, \ldots , \pi _{0K})$$, with K species in total. Let $$\varvec{p}_t=({p}_{t1}, \ldots , {p}_{tK})$$ denote the proportion vector at t. The null hypothesis is $$H_0: \varvec{p}_t= \varvec{\pi _0}$$ versus the alternative, $$H_1: \varvec{p}_t\ne \varvec{\pi }_0$$. The family of power divergence statistics to quantify the divergence of $$\varvec{p}_t$$ from $$\varvec{\pi }_0$$ is defined as $$I_{\nu }(\varvec{p}_{t}; \varvec{\pi }_0) = \frac{1}{\nu (\nu +1)} \sum _{k=1}^K p_{tk}\left\{ \left( \frac{p_{tk}}{\pi _{0k}}\right) ^{\nu }-1\right\}$$, where $$\nu \in \mathbb {R}$$. One advantage of using the parametric family of divergence measures is to have a parameter $$\nu$$ that controls the relative weighting given to common and rare species (Studeny et al. 2011). $$\nu$$ specifies different members of the test statistic in the family. When $$\nu \rightarrow -1$$, $$I_{\nu }(\varvec{p}_{t}; \varvec{\pi }_0)$$ is known as the KL divergence measure.
For the case of species distribution vectors, we concentrate on the divergence between two discrete distributions. Let $$KL(\varvec{p}_t ;\, \varvec{\pi }_0)$$ denote the KL divergence of $$\varvec{p}_t$$ from $$\varvec{\pi }_0$$, $$KL(\varvec{p}_t ;\,\varvec{\pi }_0)= \displaystyle {\lim _{\nu \rightarrow -1 }} I_{\nu }(\varvec{p}_{t}; \, \varvec{\pi }_0) = \sum _{k=1}^K \pi _{0k} \log \left( \frac{\pi _{0k}}{p_{tk}} \right)$$. We think of measuring turnover as measuring the degree of departure between two species proportion vectors, $$\varvec{p}_1$$ and $$\varvec{p}_2$$. We use $$KL(\varvec{p}_2;\, \varvec{p}_1 )$$ to quantify the divergence of $$\varvec{p}_2$$ from $$\varvec{p}_1$$, $$KL(\varvec{p}_2;\, \varvec{p}_1 ) = \displaystyle {\sum _{k=1}^K} p_{1k} \log \left( \frac{p_{1k}}{p_{2k}}\right)$$, which is also known as the Kullback–Leibler information number when being used as a divergence measure between two multinomial probability distributions. Given the inequality $$p_{1k} \log \left( \frac{p_{1k}}{p_{2k}}\right) \ge \frac{1}{2} p_{1k}(p_{1k} -p_{2k})^2 ~~\forall k$$ (Rao 1973, p. 58), it follows that $$KL(\varvec{p}_2 ; \, \varvec{p}_1 )$$ is non-negative and $$p_{1k} \log \left( \frac{p_{1k}}{p_{2k}}\right) = \frac{1}{2} p_{1k}(p_{1k} -p_{2k})^2$$ if and only if $$p_{1k}=p_{2k}$$ $$\forall k \in \{1, 2, \ldots , K\}$$. In other words, $$KL(\varvec{p}_2 ; \, \varvec{p}_1 )=0$$ if and only if the proportion of each species stays the same, i.e. no turnover. The upper bound for $$p_{1k} \log \left( \frac{p_{1k}}{p_{2k}}\right)$$ in certain cases can be found in Sayyareh (2011). Clearly, $$KL(\varvec{p}_2;\,\varvec{p}_1 )$$ is not symmetric, i.e. $$KL(\varvec{p}_2;\, \varvec{p}_1 ) \ne KL(\varvec{p}_1;\, \varvec{p}_2)$$. Symmetry is a desirable property for a turnover measure. Therefore, we propose the following measure:
\begin{aligned} d_{KL}(\varvec{p}_1, \varvec{p}_2 ) =\frac{1}{2} \displaystyle {\sum _{k=1}^K}(p_{1k} - p_{2k}) \log \left( \frac{p_{1k}}{p_{2k}}\right) . \end{aligned}
(13)
$$d_{KL}(\varvec{p}_1 \, , \, \varvec{p}_2)$$ does not satisfy the triangular inequality in general, and so it is not a metric. We note that the divergence-based index $$d_{KL}$$ has the same form as the J-divergence measure (Jeffreys 1946) apart from the constant 1 / 2.
## 5 Application to the BBS Data
The BBS is conducted annually on a stratified random sample of 1 km squares (see Web Appendix C for data accessibility). Line transect surveys are carried out along two parallel 1 km lines, and detected birds are assigned to one of four categories: 0–25m from the line, 25–100m, $$>$$100m, or flying over. We use a preference index to determine which species form the farmland community (Newson et al. 2008; Renwick et al. 2012; Johnston et al. 2014).
For each species, Harrison et al. (2014) analysed the abundance data using a generalized additive model with time point, easting, northing, elevation and habitat of each 1 km square as covariates. The models incorporate a space-time smoother using eastings, northings and time point, along with a separate smooth term for altitude and each habitat covariate (Harrison et al. 2014). We use abundance estimates of each species in each 1 km square within its assumed range (see Harrison et al. (2014)) for each time point to evaluate the measures proposed in Sects. 4.14.24.3 and 4.4. The results are plotted in Fig. 1. For a more direct comparison of the measures shown in Fig. 1, each of the nine estimated measures is represented by a different colour in each 100 km square in Fig. 2.
All measures indicate relatively high turnover in the west of Scotland and in the south-east of England. Harrison et al. (2015) analyse BBS data in greater depth, using three measures ($$L^1$$-distance, $$d_\mathrm{cos}$$ and $$d_2^{clr\varvec{S}}$$), and include 94 species in their analyses.
## 6 Simulation Study
We provide details of a simulation study to assess the power of each measure for detecting turnover in Web Appendix B. Our study shows that all measures but the $$L^q$$-distance measures with $$q<1$$ perform well in detecting turnover when there are large changes in the community. Over-dispersion has little effect on the conclusions. The mathematical form of the measures means that $$d_2^{clr\varvec{S}}$$, $$d_\mathrm{sin}$$ and $$d_\mathrm{cos}^*$$ should be more sensitive to changes among the scarce species than are $$d_1$$, $$d_2$$ and $$d_\mathrm{cos}$$. Close inspection of the simulation results confirms this, although the differences are small. This greater sensitivity is likely to be offset at least to some degree by lower precision for these measures (as greater weight is given to scarce species with smaller sample sizes), and their inability to accommodate zero species proportions.
## 7 Discussion
If a measure sensitive to changes in the scarce species is required, we recommend $$d_2^{clr\varvec{S}}$$, which is the only measure that satisfies all five of the desirable properties of Sects. 3.3 and 3.4. If a measure that has good precision is required, and sensitivity to changes in scarce species is not of primary interest, then we recommend $$d_1$$, which satisfies four of the properties, and is simple, being half the sum of absolute differences in species proportions. If greater discrimination is needed between communities showing high turnover from those showing rather lower turnover, then measure $$d_2$$ or $$d_\mathrm{cos}$$ might be preferred. In practice, given the multivariate nature of biodiversity data, we recommend applying several turnover measures, to gain a better understanding of changes in the scarce and dominant species of the community. When the measures are applied to the BBS data, they identify high turnover in the west of Scotland and in the south-east of England. The measure $$d_2^{clr\varvec{S}}$$ differs from the rest by also indicating high turnover in Wales.
Figure 1 shows that precision of our turnover measures is relatively poor in the west of Scotland, reflecting poor survey coverage. Nevertheless, the lower confidence limits for some of our measures in this area exceed the upper confidence limits for most of Britain, supporting our conclusion that turnover is high here. Harrison et al. (2015), in a more extensive analysis of 94 species, also reached this conclusion, and speculated that this reflects an increase in species that benefit from climate change. They attributed the high turnover in the south-east of England at least in part to a decline in scarcer specialist species.
## Notes
### Acknowledgments
We are very grateful to all the volunteers who have contributed to the BBS. Yuan was funded by EPSRC/NERC grant EP/1000917/1. Harrison was funded by the Scottish Government’s Centre of Expertise ClimateXChange (www.climatexchange.org.uk).
## Supplementary material
13253_2015_243_MOESM1_ESM.pdf (168 kb)
Supplementary material 1 (pdf 167 KB)
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## Authors and Affiliations
• Yuan Yuan
• 1
• Stephen T. Buckland
• 1
• Phil J. Harrison
• 2
• Sergey Foss
• 3
• Alison Johnston
• 4
1. 1.School of Mathematical and StatisticsUniversity of St AndrewsSt AndrewsUK
2. 2.School of Mathematical and StatisticsArtDatabankenUppsalaSweden
3. 3.School of Mathematical and Computer SciencesHeriot-Watt UniversityEdinburghUK
4. 4.British Trust for OrnithologyNorfolkUK | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9504818916320801, "perplexity": 1500.2903377284938}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039747369.90/warc/CC-MAIN-20181121072501-20181121094501-00484.warc.gz"} |
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[1] Xianghong Chen. A Fourier restriction theorem based on convolution powers. Proc. Amer. Math. Soc. Abstract, references, and article information View Article: PDF [2] D. J. Daley and E. Porcu. Dimension walks and Schoenberg spectral measures. Proc. Amer. Math. Soc. 142 (2014) 1813-1824. Abstract, references, and article information View Article: PDF [3] William Beckner. Multilinear embedding -- convolution estimates on smooth submanifolds. Proc. Amer. Math. Soc. 142 (2014) 1217-1228. Abstract, references, and article information View Article: PDF [4] Michael Christ and René Quilodrán. Gaussians rarely extremize adjoint Fourier restriction inequalities for paraboloids. Proc. Amer. Math. Soc. 142 (2014) 887-896. Abstract, references, and article information View Article: PDF [5] Daniel Blasi Babot. Heisenberg uniqueness pairs in the plane. Three parallel lines. Proc. Amer. Math. Soc. 141 (2013) 3899-3904. Abstract, references, and article information View Article: PDF [6] Allison Lewko and Mark Lewko. Endpoint restriction estimates for the paraboloid over finite fields. Proc. Amer. Math. Soc. 140 (2012) 2013-2028. Abstract, references, and article information View Article: PDF [7] Daniel M. Oberlin. A uniform Fourier restriction theorem for surfaces in $\mathbb{R}^{d}$. Proc. Amer. Math. Soc. 140 (2012) 263-265. MR 2833538. Abstract, references, and article information View Article: PDF [8] Heping Liu and Yingzhan Wang. A restriction theorem for the H-type groups. Proc. Amer. Math. Soc. 139 (2011) 2713-2720. MR 2801610. Abstract, references, and article information View Article: PDF [9] Philip T. Gressman. On multilinear determinant functionals. Proc. Amer. Math. Soc. 139 (2011) 2473-2484. MR 2784813. Abstract, references, and article information View Article: PDF [10] E. K. Narayanan and P. K. Ratnakumar. Benedicks' theorem for the Heisenberg group. Proc. Amer. Math. Soc. 138 (2010) 2135-2140. MR 2596052. Abstract, references, and article information View Article: PDF [11] Daniel M. Oberlin. A uniform estimate for Fourier restriction to simple curves. Proc. Amer. Math. Soc. 137 (2009) 4227-4242. MR 2538584. Abstract, references, and article information View Article: PDF [12] Ákos Magyar. On Fourier restriction and the Newton polygon. Proc. Amer. Math. Soc. 137 (2009) 615-625. MR 2448583. Abstract, references, and article information View Article: PDF [13] Shuanglin Shao. A note on the cone restriction conjecture in the cylindrically symmetric case. Proc. Amer. Math. Soc. 137 (2009) 135-143. MR 2439434. Abstract, references, and article information View Article: PDF [14] Andrzej Makagon and Agnieszka Wylomanska. On the support of the spectral measure of a harmonizable sequence. Proc. Amer. Math. Soc. 136 (2008) 2609-2613. MR 2390533. Abstract, references, and article information View Article: PDF This article is available free of charge [15] William Beckner. Pitt's inequality with sharp convolution estimates. Proc. Amer. Math. Soc. 136 (2008) 1871-1885. MR 2373619. Abstract, references, and article information View Article: PDF This article is available free of charge [16] Z. Adwan and G. Hoepfner. On the $C^{\infty }$ wave-front set of traces of CR functions on maximally real submanifolds. Proc. Amer. Math. Soc. 136 (2008) 999-1008. MR 2361874. Abstract, references, and article information View Article: PDF This article is available free of charge [17] Daniel M. Oberlin. Convolution and restriction estimates for measures on curves in $\mathbb R^2$. Proc. Amer. Math. Soc. 136 (2008) 213-217. MR 2350406. Abstract, references, and article information View Article: PDF This article is available free of charge [18] Bassam Shayya. An affine restriction estimate in $\mathbb{R}^3$. Proc. Amer. Math. Soc. 135 (2007) 1107-1113. MR 2262912. Abstract, references, and article information View Article: PDF This article is available free of charge [19] Leonardo Colzani, Christopher Meaney and Elena Prestini. Almost everywhere convergence of inverse Fourier transforms. Proc. Amer. Math. Soc. 134 (2006) 1651-1660. MR 2204276. Abstract, references, and article information View Article: PDF This article is available free of charge [20] S. Hofmann and A. Iosevich. Circular averages and Falconer/Erdös distance conjecture in the plane for random metrics. Proc. Amer. Math. Soc. 133 (2005) 133-143. MR 2085162. Abstract, references, and article information View Article: PDF This article is available free of charge [21] Jong-Guk Bak and Sanghyuk Lee. Estimates for an oscillatory integral operator related to restriction to space curves. Proc. Amer. Math. Soc. 132 (2004) 1393-1401. MR 2053345. Abstract, references, and article information View Article: PDF This article is available free of charge [22] Daniel M. Oberlin. A uniform Fourier restriction theorem for surfaces in $\mathbb{R}^{3}$. Proc. Amer. Math. Soc. 132 (2004) 1195-1199. MR 2045437. Abstract, references, and article information View Article: PDF This article is available free of charge [23] Bassam Shayya. Adjoint restriction estimates and scaling on spheres. Proc. Amer. Math. Soc. 132 (2004) 1517-1524. MR 2053360. Abstract, references, and article information View Article: PDF This article is available free of charge [24] Kathryn E. Hare and Maria Roginskaya. The energy of signed measures. Proc. Amer. Math. Soc. 132 (2004) 397-406. MR 2022362. Abstract, references, and article information View Article: PDF This article is available free of charge [25] Mihail N. Kolountzakis and Szilárd Gy. Révész. On a problem of Turán about positive definite functions. Proc. Amer. Math. Soc. 131 (2003) 3423-3430. MR 1990631. Abstract, references, and article information View Article: PDF This article is available free of charge [26] Jonathan M. Bennett and Ana Vargas. Randomised circular means of Fourier transforms of measures. Proc. Amer. Math. Soc. 131 (2003) 117-127. MR 1929031. Abstract, references, and article information View Article: PDF This article is available free of charge [27] Tian-You Hu, Ka-Sing Lau and Xiang-Yang Wang. On the absolute continuity of a class of invariant measures. Proc. Amer. Math. Soc. 130 (2002) 759-767. MR 1866031. Abstract, references, and article information View Article: PDF This article is available free of charge [28] Daniel M. Oberlin. Fourier restriction for affine arclength measures in the plane. Proc. Amer. Math. Soc. 129 (2001) 3303-3305. MR 1845006. Abstract, references, and article information View Article: PDF This article is available free of charge [29] Tilmann Gneiting. Criteria of Pólya type for radial positive definite functions. Proc. Amer. Math. Soc. 129 (2001) 2309-2318. MR 1823914. Abstract, references, and article information View Article: PDF This article is available free of charge [30] Fulvio Ricci and Giancarlo Travaglini. Convex curves, Radon transforms and convolution operators defined by singular measures. Proc. Amer. Math. Soc. 129 (2001) 1739-1744. MR 1814105. Abstract, references, and article information View Article: PDF This article is available free of charge
Results: 1 to 30 of 43 found Go to page: 1 2 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9827766418457031, "perplexity": 2299.0968826016097}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500812662.69/warc/CC-MAIN-20140820021332-00085-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/152684/yn-x-n-causal-or-not-memory-or-memoryless/152733 | # $y(n) = x(-n)$ , causal or not , memory or memoryless?
$y(n) = x(-n)$ , causal or not , memory or memory-less ?
it's a question in digital signal processing course .
My guess it's memory less , causal because $x(-n)$ is only the inverse of the function ?
Memoryless System A system is memoryless if the output y[n] at every value of n depends only on the input x[n] at the same value of n
Causality A system is causal it’s output is a function of only the current and previous samples
-
It helps (you and the others) that the problem statement has a subject and a predicate. Eg: Is the filter/system defined by the relation $y[n]=x[-n]$ causal or not... ? ($x[n]$ is the input and $y[n]$ the output? Do you know the definition of a memory-less filter? What is the output at time, say $n=5$? – leonbloy Jun 1 '12 at 23:39
I got it in the sheet like , tell whether the system is memory or memory less, causal or non – xsari3x Jun 1 '12 at 23:56
well, a system is memoriles if output y[n] for every value of n (say, for n=5, y[5]) depends only of the input at the same instant (x[5]) But y[5] does depend rather on x[-5], so... – leonbloy Jun 2 '12 at 1:02
• It is not causal. Consider $n=-1$. The output $y(-1)$ depends on the input at $n=1$, which is only available in future.
• It is not memoryless. Consider any $n > 0$. The output $y$ depends on the input at $-n$ which was applied in the past. Thus the system has memory. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8679980635643005, "perplexity": 1087.505970670952}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997883466.67/warc/CC-MAIN-20140722025803-00229-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/does-an-analogous-idea-of-energy-exist-and-satisfy-conservation.117152/ | # Does an analogous idea of energy exist and satisfy conservation?
1. Apr 10, 2006
### 0rthodontist
Under what general formal mathematical conditions does an analogous idea of energy exist and satisfy conservation? In a gradient vector field, energy as force times distance exists and is conserved in some sense. What is a more general idea? What, conceptually, makes energy "energy"? Is energy just any conserved quantity or is there another essential characteristic?
2. Apr 11, 2006
### Nimz
There are other physical quantities that are conserved for the same mathematical reasons as energy, like total angular momentum. However, angular momentum isn't energy - it doesn't even have the same units. As I recall, the difference between energy and angular momentum is in the choice of coordinates when using the lagrangian. Energy comes from using rectangular coordinates, angular momentum comes from using spherical coordinates. If your generalized space has units other than distance, you can come up with other conserved quantities when using the lagrangian.
So energy isn't just any conserved quantity. It is a specific conserved quantity. You might want to ask the question of what the other essential characteristics are in the physics section.
3. Apr 11, 2006
### Staff: Mentor
Well first of all energy is a scalar quantity and momentum (like velocity) is a vector quantity.
In physics, energy is considered the 'ability to do work', and it can be kinetic (motion) or potential. See - http://hyperphysics.phy-astr.gsu.edu/hbase/enecon.html
Momentum - tp://hyperphysics.phy-astr.gsu.edu/hbase/mom.html#mom
Conservation laws - http://hyperphysics.phy-astr.gsu.edu/hbase/conser.html#cons
Mathematics is simply a systematic method of describing the relationships observed in physics - mathematics is more or less the language of physics.
4. Apr 11, 2006
### Curious3141
I think the concept of "energy" has a specific physical meaning. But if you're looking for mathematical formalism surrounding the concept, I'd suggest Lagrangian and Hamiltonian Mechanics.
5. Apr 13, 2006
### 0rthodontist
I'm not looking for specific physics. Energy is a very broad concept even in physics that includes not only Newtonian mechanics as you linked to, but also every other physical formulation. In Newtonian mechanics, if my understanding is correct, energy is conserved because all force fields involved are gradients. Is there a similarly simple generalized reason in modern physics?
My interest is that energy is a useful tool for analyzing physical systems. So a generalization of energy might be a useful tool for analyzing some mathematical or computational systems. Entropy has been generalized via math to apply to algorithms and such, and energy is somewhat related to entropy, so perhaps there is a like generalization.
If a system is given as a set of objects and states for those objects, together with a next-state function, I think a quantity called energy would have to have the following characteristics. It would have to be defined for a given next-state function and computed from any group of objects and states under that function. It would have to be invariant for all groups of objects and states under applications of the function. And it would have to depend sensitively on the objects and states of the system, in the sense that for any object of the system, removing the object, adding a new object, or changing the state of the object in an appropriate manner will change the energy of the system.
I think may be something to be said in this context about conversion of energy from one form to another, but I am unsure.
This is not intended as a philosophical discussion, but I take the opposite view: physics is an instance of mathematics.
Last edited: Apr 13, 2006
6. Apr 13, 2006
### HallsofIvy
Staff Emeritus
"Energy" is NOT a mathematical concept- "conservation" of a quantity is. One can argue that the history of the concept of energy is a continuing struggle to HAVE a conserved quantity! It was relatively late that it was recognized that heat is a form of energy- and that "definition" of heat as energy was precisely to maintain conservation of energy. And, of course, with the recognition, in relativity, that mass itself could be converted to energy, we had to accept mass as a type of energy, simply to maintain "conservation of energy".
7. Apr 13, 2006
### 0rthodontist
The fact that physicists have been so successful at maintaining conservation of energy suggests that energy is fairly fundamental. This is in contrast to, for example, conservation of mass. Maybe energy has no analogue in systems that differ much from the universe, but why assume that? Energy absolutely can be formulated mathematically in our particular universe. What I'm looking for is not energy per se--that's just a casual use of the word. I am looking for energy-like quantities.
8. Apr 13, 2006
### Nimz
Would you be interested in something like knot energies, then? Knot energy isn't energy in the physical sense, but would seem to have some of the properties you are looking for. I don't know much about the subject of knot energy (yet), so I can't help you with any details.
9. Apr 13, 2006
### matt grime
But is not *defined* mathematically. You are asking this in completely the wrong (sub)forum. It is just, mathematically, some number, that is invariant under some conditions. There are literally hundreds of numerical invariants in mathematics, which is thankfully far richer than Astronuc's descriptions of it would have people believe. (I'm equally sure he'd not like me describing physics as merely one small application of mathematics, which is neither true nor accurate.) | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9054691195487976, "perplexity": 507.81912558972346}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170609.0/warc/CC-MAIN-20170219104610-00478-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://www.thespectrumofriemannium.com/tag/pulley/ | ## LOG#042. Pulley with variable mass.
This interesting problem was recently found in certain public examination. I will solve it here since I found it fascinating and useful, since it is a problem with “variable mass”. A pulley with negligible mass is given (see the figures … Continue reading | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8805080652236938, "perplexity": 1202.931466580877}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304859.70/warc/CC-MAIN-20220125160159-20220125190159-00421.warc.gz"} |
https://www.arxiv-vanity.com/papers/1307.8024/ | \textwidth
480pt \textheight665pt \oddsidemargin5pt \evensidemargin5pt \topmargin-10pt
Bose Einstein condensation of the classical axion field in cosmology?
IPNL, Université de Lyon, Université Lyon 1, CNRS/IN2P3, 4 rue E. Fermi 69622 Villeurbanne cedex, France
Abstract
The axion is a motivated cold dark matter candidate, which it would be interesting to distinguish from weakly interacting massive particles. Sikivie has suggested that axions could behave differently during non-linear galaxy evolution, if they form a Bose-Einstein condensate, and argues that “gravitational thermalisation” drives them to a Bose-Einstein condensate during the radiation dominated era. Using classical equations of motion during linear structure formation, we explore whether the gravitational interactions of axions can generate enough entropy. At linear order in , we interpret that the principle activities of gravity are to expand the Universe and grow density fluctuations. To quantify the rate of entropy creation we use the anisotropic stress to estimate a short dissipation scale for axions, which does not confirm previous estimates of their gravitational thermalisation rate.
## 1 Introduction
Axions [1, 2, 3] are hypothetical light pseudoscalar bosons, with phenomenological and theoretical attractions. They could constitute a quarter of the mass density of the Universe today, being the cold dark matter(CDM) responsible for the growth of galaxies and large scale structure. The axion constitutes a minimal and theoretically attractive candidate, because it arises in models which solve the “strong CP problem” of QCD, and is accompanied by no other new particles at accessible energies [4, 5].
An interesting question is whether axions can be distinguished from more massive CDM candidates, such as weakly interacting massive particles(WIMPs) [6]. The axion is the Goldstone boson of the Peccei-Quinn symmetry [2] that breaks at a high scale GeV. It acquires a small mass eV by mixing with the pion. The very light axion can nonetheless constitute CDM if it is non-relativistic, which requires a non-thermal production mechanism. For instance, an oscillating classical axion field can be produced at the QCD phase transition. It is well-known that the energy density of a homogeneous and isotropic scalar field redshifts [7, 8] like CDM, and that the linear growth of density fluctuations is the same for axions and WIMPs [9, 10, 11, 12]111The doubts in the appendix of [13] are addressed in [14] and [11, 15].. Sikivie and collaborators [16, 17, 18] have extensively explored the differences between axions and WIMPs, in search of distinguishing observables. In an extended study [17], Erken, Sikivie, Tam and Yang (hereafter ESTY; see also the formalised analysis of [19]) argue that axion-CDM forms a Bose-Einstein (BE) condensate due to gravitational scattering at photon temperatures keV, and since the BE condensate can support vortices, this allows caustics in the dark matter distribution of our galaxy today. They conclude that axions behave differently from WIMPs during non-linear structure formation.
The results of [17, 19] are obtained using Quantum Field Theory and Newtonian gravity, and have various curious features, which are mentioned at the end of section 2. The aim of this paper is to study axion evolution in an alternative formalism. We use classical equations of motion for axions in an expanding Universe with metric perturbations222The beautiful quantum analysis in a perturbed expanding Universe of Nambu and Sasaki [12] is helpful for making contact between the quantum and classical studies.. A classical analysis should give the lowest order solution, and gravity is a classical theory. We study axion evolution in the early Universe, after the QCD phase transition and in the regime where departures from the homogeneous and isotropic solutions can be treated in linear perturbation theory. (The Appendix recalls that the effect of the homogeneous and isotropic gravitational interactions is to redshift the axion momenta.) Even during this period, the equations of motion for the axion field are non-linear, so we study instead the fluctuations of the axion stress-energy tensor. This is the current to which gravity couples, so we anticipate that its components are appropriate variables for describing gravitational interactions of axions.
Section 2 contains a review of axion cosmology, and some basics of Bose-Einstein condensation. We wish to know if the gravitational interactions of axions generate entropy during linear structure formation, so we are looking for a dissipative process. In section 3, we focus on physics inside the horizon, and equate the axion stress-energy tensor of the perturbed Universe, with the stress-energy tensor of an imperfect fluid. This gives an estimate of the viscosity of the axion fluid due to metric/density fluctuations, and viscosity, in fluid dynamics, wipes out short distance modes. The damping scale this gives is very short, and does not indicate that the axion field forms a BE condensate. Section 4 discusses our result and its relation to the literature, and section 5 is a summary.
## 2 Review
After a brief introduction of the theory of axions, section 2.1 tells the story of their cosmological evolution before and after the epochs of interest in this paper. In section 2.2 we briefly recall what is Bose-Einstein condensation in equilibrium and non-equilibrium field theory.
### 2.1 Axions and their cosmology
The strong CP problem of QCD is that instantons should generate an term in the Lagrangian, with coefficient . However, the non-observation of the neutron electric dipole moment [20] implies [21]. This discrepancy can be explained by making a massive dynamical field — the axion [2]. Axion models can be constructed by extending the particle content of the Standard Model Lagrangian to allow a global chiral U(1) symmetry, referred to as a Peccei-Quinn [2] symmetry, which is broken by colour anomalies [22]. The is also spontaneously broken at a high scale, which ensures that the Goldstone boson is the only new particle at low energies, and that it has tiny interactions with the SM [4, 5]. The couplings to photons and gluons, are suppressed by ; other interactions of axions can be found in [23]. The colour anomalies give this axion a small mass from mixing with the pion:
ma≃mπfπfPQ√mumdmu+md≃6×10−6eV1012GeVfPQ . (1)
Axions are searched for in various experiments [25, 26], and can be constrained by astrophysical observations [3]. The most stringent lower bound is GeV, to ensure that axions do not carry to much energy out of stars [3, 24].
Due to the high scale , it is unclear whether the Peccei Quinn (PQ) phase transition occurs before or after inflation. Both scenarios have been extensively studied (for reviews and references, see, e.g. [27, 28, 29]), with emphasis on large scale density fluctuations relevant to the CMB and galaxy formation. The axion fluctuations we will study in this paper are on distances at least a million times shorter.
If the PQ phase transition occurs sufficiently before inflation, a coherent patch of axion field will be inflated beyond the size of the visible Universe. During inflation, the axion field, like the inflaton, will develop fluctuations on scales relevant to the CMB and large scale structure: [27]. Provided that , these will be small fluctuations on a homogeneous and isotropic axion field (see [28] for the case ). When the axion acquires a potential at the QCD phase transition, it inherits the adiabatic density perturbations that the inflaton imprinted on the plasma, and in addition, its own fluctuations become isocurvature density perturbations [30]333For a pedagogical introduction to adiabatic and isocurvature fluctuations, see e.g. [31]. The non-observation in CMB data of isocurvature perturbations allows to constrain this axion scenario where the PQ transition is before inflation [28].
When the PQ phase transition occurs after inflation, which is the scenario of interest in this paper, the axion field will have random different values in different causally connected volumes of the Universe. The coherence scale of the field grows with the horizon 444This follows from the equations of motion for a massless field in the Friedman Roberson Walker Universe. until the QCD phase transition, and a network of cosmic strings develops. The strings disappear after the QCD phase transition [32, 33], radiating axions with momentum of order the Hubble expansion rate. This population of non-relativistic axions is difficult to calculate reliably [32, 33]; a recent estimate of their contribution to the CDM density today [32] is:
Ωa∼0.2×(fPQ1011 GeV)6/5 (from strings). (2)
In this paper, for simplicity, we neglect this bath of cold axion particles. We also restrict to axion models which do not generate domain walls.
Until shortly before the QCD Phase Transition, the potential for the axion field was flat. Afterwards, massive pions appear, and the axion field develops a potential(we follow here [1])
V(a)≈f2PQm2a[1−cos(a/fPQ)]≃12m2aa2−14!m2af2PQa4 . (3)
The QCD phase transition is a cross-over in lattice simulations [35], suggesting that the turn-on of the axion mass is a smooth and homogeneous process. A few Hubble times later, the mass will have settled to its value today, and the axion field will oscillate around the minimum with a frequency . The axions making up this field are non-relativistic, because their momenta , where
HQCD=12tQCD=1.66√g∗T2QCDmpl≃2×10−20GeVT2QCD(200MeV)2 (4)
and km is the age of the Universe, or the horizon scale at the QCD Phase Transition. This comoving scale corresponds to parsec today (recall the distance to the galactic centre is kpc).
The energy density in these coherent oscillations redshifts like matter, as where is the scale factor of the Universe, and contributes to the dark matter density today[36]:
Ωa∼0.7×(fPQ1012 GeV)7/6(a(tQCD)πfPQ)2 (coherent oscillations), (5)
where is the value of the axion field averaged over the Universe at the QCD phase transition. Recall that corresponds to the phase of a complex scalar field, so could have any value between and in a causally connected volume. In the case of interest here, when the PQ phase transition is after inflation, if one supposes that all phases are equally probable with linear measure, then the value of the axion field, averaged over the Universe is
a(tQCD)≃πfPQ/√3 . (6)
Requiring that the axions from topological defects (2) and the condensate (5) not over-contribute to gives GeV [32] in this case of the PQ transition after inflation. On the other hand, if the PQ transition is before inflation, can be tuned to be much smaller than . This is referred to as the anthropic region of axion parameter space [37], and allows values of at the GUT scale.
Axions also have quartic interactions, as seen in eqn (3). The coupling is very small, but for , the contributions to the potential from the quartic and quadratic terms can be comparable. We will neglect the quartic terms, because we are interested in axion evolution after the QCD, so the quartic term is suppressed by with respect to the quadratic term (where is the scale factor, see eqn (11)).
We review in section 3.2 some results of density fluctuation growth in a Universe whose CDM is axions.
Galactic halos made of BE condensed scalars, of diverse masses and self-interaction strengths (but not axions), have been studied in [38], who confirm the presence of vortices. Galaxy formation with axion-CDM has recently been studied by Banik and Sikivie [39].
### 2.2 Bose-Einstein condensation
This section discusses what is a BE condensate, and some approaches to calculating how to get there.
The notion of a BE condensate, in equilibrium, is familiar from the statistical mechanics of particles: in a thermal bath with a sufficiently large conserved charge density, the free energy is minimised if charge-carrying bosons migrate to the zero-momentum state.
Equilibrium BE condensation is also a familiar notion for scalar fields in cosmology. The classic papers of Kapusta [41] and Haber and Weldon [42], evaluate the partition function for an interacting complex scalar field at finite temperature, in the presence of a net charge density. They show that the chemical potential associated to the conserved charge contributes a negative mass-squared to the effective potential. So a sufficient charge density can drive a phase transition, to a scalar vacuum expectation value, which carries the excess charge not stored in the equilibrium bath of particles:
nQ=m⟨Φ⟩2+∫d3k(2π)3(1e(E−μ)/T−1−1e(E+μ)/T−1) (7)
where is the charge density of the plasma.
If these equilibrium estimates are applied to axions, after the QCD phase transition, it is clear that an axion number density , if in thermal equilibrium, must be in a BE condensate. However, axions are not thermally produced, and interact very feebly. ESTY [17] propose that they “thermalise gravitationally”. However [17, 19] do not show that the axion distribution approaches an equilibrium distribution, or a migration of axion modes towards the infrared.
The particle and scalar field descriptions of BE condensation make contact in coherent state notation [63], in second quantised field theory, where a coherent state is denfined so that the expectation value of the field operator gives the classical field (see eqn (36)). This illustrates the observation of Bogoliubov [40], that BE condensation in non-relativistic systems can be described as a phase transition. In the coherent state perspective, the above two descriptions of BE condensation have two features:
1. a classical field is born from a state containing particles. This requires , because should be distributed differently in the Lagrangian to obtain particles or fields in the classical limit [58] (the mass has dimension length for fields).
2. the particles move to a homogeneous and isotropic configuration where they are in their lowest energy state
It is unclear to the authors which features define a BE condensate, or, more precisely, what are the characteristics required of the axion dark matter to allow caustic formation as envisaged by Sikivie and collaborators. Is it coherence — that is, a classical scalar field? Or is it a large population in the zero momentum lowest energy state?
If the crucial feature is coherence, then any (non-relativistic) classical field would be a BE condensate. For instance, the axion field made via the misalignment mechanism, which can be decomposed on fourier modes, could correspond to a superposition of BE condensates (one for each three-momentum)555 In the approximation of this paper where we neglect quartic axion self-interactions, these BE condensates have only gravitational interactions with each other.. This would be consistent with the detection of BE condensation in alkali gases [43], demonstrated by coherent collective behaviour of the atoms ( the BE condensate is allowed velocity). Maybe the two simple equilibrium examples of BE condensates, introduced above, are homogeneous and isotropic because equilibrium is homogeneous and isotropic. If the classical axion field is by nature a BE condensate, then the “gravitational thermalisation” of misalignment axions is unneccessary and this paper is beside the point.
Experimentally, BE condensation occurs far from equilibrium [43, 44, 45]. Theoretically, a Closed-Time-Path [46] implementation of the 2 Particle Irreducible effective action [47] (see e.g. the chapter on this subject in [46]), allows to compute the out-of-equilibrum generation of a BE condensate. The 2PI effective action is a function of both the classical field and of the two point function (and the two point function in closed time path represents the number density and propagator). Analytic calculations have been performed in self-interacting scalar field theories [48], and show [49] that at NLO, an overpopulation of low momentum modes in the number density can institute an inverse cascade towards the infrared, without first establishing an equilibrium distribution. Recall, however, that a high density of low momentum modes is not a classical field (or a BE condensate); it lacks the required coherence.
In summary, we focus on the gravitational interactions of the misalignment axions, which are already a classical field. We look for dissipation in these interactions, because this increases entropy. In 2PI formalism, thermalisation does not occur at leading order in the coupling in models; extrapolating naively, this suggests that gravitational thermalisation, or entropy generation, does not occur at leading order in . Instead of including , we look for dissipation/thermalisation at order . This could be relevant to BE condensation, if the axion field produced by the misalignment mechanism is not already a BE condensate. (This assumption is consistent with [19]. References [16, 17] envisage, that in this case, the “gravitational thermalisation” of axions will drive them to a BE condensate.)
### 2.3 Axion Bose-Einstein condensation in cosmology
This project was motivated by the scenario envisaged in [16, 17], where axions form a Bose-Enstein condensate in the early Universe at photon temperatures keV, due to gravitational scattering among the axions. The gravitational interaction rate of [16, 17] was confirmed by Saikawa and Yamaguchi (SY) [19], who calculate in Quantum Field Theory, the rate of change of the axion number operator . SY describe the axions as a coherent state (see eqn (36)) in Minkowski space-time, interacting via Newtonian gravity. This significant calculation has various curious features: the Newtonian analysis is applied in the early Universe, without a distinction between the homogeneous energy density which drives expansion, and the fluctuations. Also, intuition and the equations of linear structure growth say that gravity grows inhomogeneities, which appears naively at odds with gravitational interactions driving axions to Bose-Einstein condense in the zero mode. Another curious feature is that, although gravity should be universal, the axions are found to “gravitationally thermalise” with themselves, but not with other particles. We discuss the interpretation of our estimates and these earlier calculations in section 4.
Finally, we raise one more confusing issue. A BE condensate in statistical mechanics is a large number of particles in a -function at zero kinetic energy. In the coherent state notation of eqn (36), these particles make up the first term of eqn(7). However, in cosmology, it is unclear how narrow is the energy range for the axions making up the “zero mode”, or BE condensate. At the QCD phase transition, the axions of mass and momentum , have kinetic energy . During radiation domination, the ratio
EKH≃HQCD2ma≪1 (8)
remains constant; between matter-radiation equality and today, it increases by a factor , but does not attain one. Therefore, the Heisenberg uncertainty principle could imply that the age of the Universe is not long enough to distinguish that the axions are not in the zero mode. Does this imply that they are in a BE condensate? Notice that their three-momentum can be distinguished from zero, so if the condensate was defined as the zero-momentum state, then the axions are not in it.
## 3 Estimating axion viscosity
This section aims to address whether classical gravitational interactions among axions can dissipate fluctuations and generate entropy. The Appendix suggests that in a homogeneous and isotropic Universe, the answer is “no” (gravity merely redshifts the axion momenta, in a Friedman-Robertson-Walker Universe). So we study a cosmological scenario with density fluctuations, whose gravitational effects can be treated in the linear approximation. The question would be more difficult, in the case where gravity is non-linear.
We take an initial condensate made of axions with comoving momenta of order . We compute their stress-energy tensor in an almost homogeneous and isotropic Universe, including scalar metric perturbations in Newtonian gauge [27, 50]. In particular, the metric perturbations will give spatial off-diagonal components , for . We equate the term involving the gravitational potential with the off-diagonal of an imperfect fluid in a homogeneous and isotropic Universe. In an imperfect fluid, the elements, for , are proportional to the viscosity, which damps short-scale fluctuations. The only interactions of the axions are gravitational, so implicitly, the “bath” responsible for dissipation in the fluid contains metric and density fluctuations. Equation (31) is an estimate of the damping scale of density fluctuations, due to the gravitational self-interactions of axions.
### 3.1 Axion initial conditions after the QCD phase transition
We take our initial conditions a few Hubble times after the QCD phase transition, when the axion mass is settled to its value today. We focus on the classical axion field produced by misalignment, this does not include the axions from strings. Classical field means in principle the variable in the 1PI action, and in practise the expectation value of the field operator in the ground state. It can be expressed as a coherent state, see eqn (36). We suppose that at the QCD phase transition, the axion field was approximately constant within a horizon volume, and randomly distributed between and from one horizon volume to another. So the initial axion field oscillates rapidly in time with frequency , and more slowly in space with co-moving momentum . It can be expanded on Fourier modes of a homogeneous and isotropic Universe:
a(→x,t)=1√2mVR3(t)∑p[˜a(→p,t)exp{i(→p⋅→x−ωt)}+˜a∗(→p,t)exp{−i(→p⋅→x−ωt)}] (9)
where is the comoving three-momentum, and the field is normalised in a comoving box of volume . Recall that has mass dimension one, so the are dimensionless, and is the number of axions of momentum in the volume (see eqn (15)). The fast time dependence , which we approximate as can be averaged [8, 9, 11] on the longer evolution timescale of the spatial variations666It can be removed more elegantly by studying the non-relativistic field [12].. can evolve in time on this longer timescale. The axion is a real field, so the Fourier coefficients satisfy . Fourier transforms are performed in a comoving box , and defined to be “dimensionless” to simplify dimensional analysis; we write
d3xV , and ∑p=V∫d3p(2π)3 .
Notice that the density fluctuations are of order one on the comoving scale : the field can be zero in one horizon volume, and in the next. We are interested in comoving distances longer than a few , so we take for and expect that it is flat for , because the Fourier transform of a random distribution in is a constant 777This means that fluctuations get smaller on larger distances : ..
Equation (9) appears different from the usual treatment of axion CDM, where (most of) the axions are taken to be in the zero-momentum mode(see e.g. [10]):
a(→x,t)=1√2mVR3(t)(˜a0(tQCD)cos(mt)+∑p[δ˜a(→p,t)ei(→p⋅→x−mt)+δ˜a∗(→p,t)e−i(→p⋅→x−mt)]) (10)
where is the averaged-over-the-Universe value of the field at the QCD phase transition, and the small fluctuations considered are on large scale structure scales. As discussed in [28], the difference between these two forms for the growth of linear density perturbations is negligible: the kinetic energy density in the horizon-scale fluctuations is negligible (compared to the potential and the time oscillations), and on structure formation scales, .
### 3.2 The stress-energy tensor with perturbed metric
This section reviews the stress-energy tensor and equations of motion for scalar perturbations in an almost homogeneous and isotropic Universe.
The metric in Newtonian gauge can be written
ds2 = (1+2ψ)dt2−R2(t)(1−2ϕ)δijdxidxj (11)
where will be the Newtonian potential inside the horizon, and we take the scale factor dimensionless and equal to 1 at the QCD phase transition.
The stress-energy tensor for a homogeneous and isotropic Universe is , where and are the (homogeneous and isotropic) energy density and pressure. In the presence of scalar fluctuations, can be described with four additional parameters, written in Fourier space as [50]
¯¯¯ρ(t)→¯¯¯ρ(t)+δ~ρ(→k,t) , ¯¯¯¯P(t)→¯¯¯¯P(t)+~δP(→k,t) ikjδT0j=(¯¯¯ρ+¯¯¯¯P)θ(→k,t) , (^ki^kj−13δij)δTij=−(¯¯¯ρ+¯¯¯¯P)σ(→k,t) (12)
where parametrises a fluid velocity, and is the anisotropic stress.
For a massive non-interacting real scalar field, such as the axion, the stress-energy tensor has the form
Tμν=a;μa;ν−12(a;αa;α−m2a2)δμν . (13)
Equating (13) and (12) allows to determine the density fluctuations and other fluid parameters of the classical axion field.
For axions of the form given in eqn (9), is the Fourier mode of the density :
¯¯¯ρa(t) = ∫Vd3xVT00(→x,t) (14) = m2[R(t)]3∑q|˜a(→q,t)|2mV(1+q2m2R(t)2)+...
where the contains subdominant terms involving , and , and the term will be neglected. The (volume-averaged) number density of axions in the classical field can similarly be expressed as
na(t) = m[R(t)]3∑q|˜a(→q,t)|2mV+... . (15)
If , and is approximately constant for , then .
The Fourier transform of the density fluctuations in the classical axion field is
δ˜ρa(→k,t) = ∫d3xVe−i→k⋅→x[ρa(→x,t)−¯¯¯ρa(t)] (16) = m2mV[R(t)]3∑q˜a(→q+→k/2,t)˜a∗(→q−→k/2,t) k≠0
where we have dropped terms proportional to , and , and . Notice that this formula is different (less intuitive) from the case usually studied in structure formation, where most axions are in a zero-momentum condensate. If most axions are in the zero mode, the density fluctuations on scale are linear in the field fluctuations, so are made up of axions of momentum (in the coherent state formalism of eqn (36)).
The dynamics is controlled by , and by Einstein’s Equations . In the absence of perturbations, these give the Hubble expansion rate
where is the Universe-averaged density in the axion field, in the axions from strings, and in radiation.
The equations for the scalar metric and density fluctuations can be found in [27, 50, 13]. For the stress-energy tensor of the axion field, eqn (12), the condition , gives the scalar equation of motion in the perturbed Universe. Whereas for a perturbed fluid, eqn (13), , gives two equations for the four parameters. If the speed of sound can be calculated, and neglected, then to determine the dynamics of the fluid (like those of the field), requires only one additional equation from Einsteins Equations. We will be interested in fluctuations inside the horizon, so neglecting terms of order , the Einsteins Equations give, in Fourier space, the Poisson equation for :
−|→p|2R2(t)˜ϕ(→p,t)≃4πGNδ˜ρ(→p,t) (18)
where is the Fourier transform of the density fluctuation (in radiation and axions). Notice that this can be interpreted as the potential due to single graviton exchange [51], which we will allude to in the discussion.
Combining the various equations gives the well-known equation [9, 11, 10] for the evolution of adiabatic scalar density fluctuations :
¨δ+2H˙δ−4πGN¯¯¯ρδ+c2sk2R2(t)δ=0 (19)
The equations for isocurvature fluctuations are different [52], but they share with this equation the property that density fluctuations are frozen within the horizon during radiation domination[52], and can grow during matter domination. For a homogeneous axion field with small fluctuations, as would arise if the PQ phase transition was before inflation (see eqn (10)), the equation (19) is elegantly obtained in [10]. In this case, it is shown that and . The (physical) axion Jeans length is therefore
λJ(t)≃2π[16πGN¯¯¯ρ(t)m2]1/4∼6√H(t)m ; (20)
on shorter distances, the fluctuations oscillate due to axion pressure, on larger distances, they can grow in a matter-dominated Universe. It can be checked that , suggesting that axions behave like dust on the comoving distance of the QCD horizon.
A caveat is that and may be different for the axion field configuration arising when the PQ transition is after inflation (see eqn (9)). However, by dimensional analysis, and , so they naively appear insignificant to fluctuation evolution on the comoving scale .
Recall that the fluctuations in the density of the axion field on the scale are of . After matter-radiation equality, these short-distance isocurvature fluctuations can grow and promptly decouple from the Hubble flow, to form gravitationally bound axion configurations called “miniclusters” [53]. The miniclusters can further cool and contract due to gravitational interactions [54]. The position-space perspective on these inhomogeneities is instructive. One can estimate that an axion (particle?) with comoving momentum cannot escape from a fluctuation of comoving size prior to matter-radiation equality. That is, the fluctuations are not damped by free-streaming. If an axion BE condensate should be approximately homogeneous, then it is unclear to the authors how the axions making up density fluctuations on scales can migrate to the zero-momentum mode, because they do not seem to move fast enough to homogenise in position space.
### 3.3 Anisotropic stress
The previous section showed that the small elements of the stress energy tensor of the classical axion field where unimportant for fluctuation growth. This section calculates these off-diagonal elements, with the aim of identifying in them some gravitational dissipation.
The off-diagonal spatial elements are interesting for two reasons: they are gauge invariant, and in the fluid approximation, they are proportional to the viscosity. Viscosity damps fluctuations on small scales [55], so we hope that an estimate of the viscosity will give some notion of gravity’s ability to generate entropy. The first step is to compute , for :
Ti j(→x,t)=−(1+2ϕ)R2(t)∂ia∂ja (21)
so in Fourier space:
Ti j(→k,t) = −1mVR5(t)[∑q(q+k/2)i(q−k/2)j˜a(→q+→k/2,t)˜a∗(→q−→k/2,t) (22) +2∑p,q(q+k/2)i(q+p−k/2)j˜ϕ(→p,t)˜a(→q+→k/2,t)˜a∗(→q+→p−→k/2,t)] .
We drop the first term (not involving the metric fluctuation) in this expression, which arises because the condensate of axions with finite momentum is not perfectly homogeneous and isotropic. This term is naively of order the axion pressure , which we also neglect. This first term in principle contributes to distinguishing from (see the metric of eqn(11)) in the perturbed Eintein Equations :
kikj(˜ϕ(→k,t)−˜ψ(→k,t))=12πGNTij (i≠j) . (23)
However, we neglect this effect and take , because the axions constitute initially a tiny fraction of the energy density, and this contribution to decreases as compared to the total density (second order radiation perturbations could be more significant). The second term of eqn (22), which contains the gravitational potential of density perturbations, is the piece from which we wish to extract axion viscosity.
### 3.4 Matching to an imperfect fluid
We aim to obtain a viscosity coefficient for our axion fluid, despite that we do a classical field analysis with coherent initial conditions. We need fluctuations and dissipation, and since we approximate the axions to have only gravitational interactions, these must involve gravity. We therefore map the stress tensor of the Universe with metric fluctuations, onto the imperfect fluid stress tensor of a homogeneous and isotropic Universe. One can imagine that the density/metric fluctuations generate the viscosity.
The stress-energy tensor for an imperfect fluid in a homogeneous and isotropic expanding Universe is given in [55]. For :
Tij(→x,t) = −η(t)(∂jUi(→x,t)+∂iUj(→x,t)) (24)
where is the fluid four-velocity, which Weinberg defines from the conserved number current (). Since axions are a real field, it is convenient to use an alternative definition, so we define from the energy flux: . This has the added interest of giving a term in eqn(26). As discussed with care in Weinberg’s paper [55], it is important to use a self-consistent formalism, so we anticipate that our estimate will not have the correct constant factors. We hope that the dependence on physical parameters will nonetheless be correct. For non-relativistic axions, eqn(13) in a homogeneous and isotropic Universe gives
U0Ui(→x,t)≃−1R2(t)¯¯¯ρ(t)∂ta(→x,t)∂ia(→x,t) (25)
which gives
Tij(→k,t) = −η(t)mVR5(t)na(t)∑q[qikj+kiqj−kikj]˜a(→q+→k/2,t)˜a∗(→q−→k/2,t) (26)
with from eqn (15).
Equating the coefficients of in eqns (26) and the second line of eqn(22), gives
η(t)na(t)∼−2πGN∑pδ˜ρ(p,t)R2(t)|→p|2 (27)
where we suppose the in the sum on of makes little difference.
This estimate used a description of imperfect fluids [55] which can suffer from non-causal information propagation. Such difficulties are avoided with the causal thermodynamics of [56], which adds approximately a factor to the right side of (27), where is the gravitational interaction rate of axions (see eqn 32). The correction factor exceeds 2 for (for fixed) and grows linearly with . However, we neglect this effect, because it never allows the time or length scale of dissipation to reach the horizon, and because axions gravitationally thermalise after keV in the scenario of Sikivie and collaborators.
There are two simple limits for the estimate of eqn (27). First, if the dominant density fluctuations are the no-scale adiabatic fluctuations in the radiation, then the sum is infrared divergent and dominated by horizon-scale fluctuations888If is the comoving scale at the horizon, we can write , to obtain a no-scale power spectrum such that . Then :
∣∣∣η(t)na(t)∣∣∣∼2πGN∣∣ ∣ ∣∣δ˜ρ(H(t)TQCDT,t)H2(t)∣∣ ∣ ∣∣≃34∣∣ ∣ ∣∣δ˜ρ(H(t)TQCDT,t)ρ(t)∣∣ ∣ ∣∣ (28)
Before and during linear fluctuation growth, this gives .
The second case is when the dominant density fluctuations are the axion inhomogeneities on the co-moving scale . Then the sum in eqn (27) is dominated by , giving
∣∣∣η(t)na(t)∣∣∣∼2πGN∣∣ ∣∣δ˜ρ(HQCD,t)R2(t)H2QCD∣∣ ∣∣\vbox<\nointerlineskip∼8πGNρa(tQCD)3H2QCD(TTQCD) = ρa(tQCD)ρrad(tQCD)(TTQCD) (29) = TeqTT2QCD
where is the photon temperature at matter-radiation equality.
Weinberg gives [55] that modes of comoving wavenumber decay at a rate
Γ∼η(t)|→p|2R2(t)¯¯¯ρ(t) (30)
So the physical distance on which fluctuations could disappear grows as the square root of the time available. This makes intuitive sense when fluctuations are damped by particles random-walking out999 Recall, however, that this picture corresponds to perturbation theory in the mean free path . So weakly interacting particles diffuse more easily out of perturbations, and the interpretation is unclear for particles whose mean free path is the size of the perturbation.. In the axion case studied here, in the lifetime of the Universe , fluctuations on physical distances less than could dissipate, where
ℓ2damp(t=1/H)∼1H(t)maη(t)na(t)ρa(t)ρ(t) (31)
It is clear that these estimates give a damping distance much shorter than the comoving scale . The Jeans distance for axions is [9]; at shorter distances, density fluctuations in axions oscillate due to pressure, and at larger distances the fluctuations can grow (during matter domination). It is reassuring that the damping distance due to viscosity (31) is shorter than the Jeans length.
## 4 Discussion and comparison to previous results
The estimated damping scale (31) for axion density fluctuations prior to the period of non-linear structure formation, is always shorter than the QCD horizon scale . It does not confirm that “gravitational thermalisation” erases axion fluctuations on the QCD horizon scale at keV. We first comment on our estimate, then compare to the calculation of Saikawa and Yamaguchi [19].
### 4.1 Our estimate
A first simplifying approximation made in this paper, is that we only work to linear order in . This could appear curious compared to thermalisation rates associated to Boltzmann Equations, where the rates are proportional to couplings-squared. But classical fields, expressed as coherent states, correspond to the coherent superposition of amplitudes, so classical gravitational effects appear at linear order in (as is well known).
We focus on the axion energy density, and fluctuations therein, rather than on the axion field. It is clear that in general, the field carries more information than the energy density, since it allows to compute a wider variety of correlation functions. However, at the classical level used in this paper, the equations of motion for both the axion field and the density fluctuations are obtained from and the Poisson Equation (18), which suggests that it is merely two different parametrisations of the same physics 101010Whether this formulations are equivalent is important, because BE condensation corresponds to suppressing the field fluctuations. One can wonder if gravitational interactions could homogenize the field configuration without changing the stress-energy tensor. The linearised Einsteins Equations might suggest not: the stress-energy fluctuations induce the Newtonian potential. . The equations for the density fluctuations have the advantage that they are linear and can be solved. They say that gravity grows inhomogeneities in axions. Whereas the equations for the field are non-linear; a gravitational interaction rate for axions can be calculated without solving the equations, but that does not say what gravity does with the axions. So we do not disagree with the gravitational interaction rate of axions obtained by [17, 19] (we can reproduce it, see eqn (32)); however, we disagree with its interpretation as a thermalisation rate. We suspect that it is the rate associated with the gravitational growth of density fluctuations (which is compensated by the expansion of the universe during radiation domination).
We supposed that BE condensation requires dissipation, and furthermore, that leading order solutions of classical equations of motion do not exhibit dissipation or thermalisation. This is a usual perspective in non-equilibrium field theory — to obtain dissipation from time-reversal invariant equations requires summing over a bath of fluctuations. We are unclear on how to separate gravitational interactions in the early Universe into a leading order solution plus fluctuations that we can integrate. Therefore, we hesitate to discuss a “gravitational thermalisation” rate, because its definition seems to require this separation of gravitational interactions into “leading order” and “dissipative”. It may be unwise to identify the homogeneous and isotropic component of the Universe as the leading order solution, and the fluctuations as the bath, because density fluctuation growth is an important part of the classical solution. However, the terms are usually neglected in these equations, so we attempt to associate dissipation with them: in the perturbed, expanding Universe, the off-diagonal spatial elements of the stress-energy tensor are gauge invariant, of , and unimportant for fluctuation growth. We identify them with the off-diagonal elements of the stress energy tensor of an imperfect fluid. An imperfect fluid can grow density fluctuations, but contains dissipation, so we hope, by this identification, to be summing over the gravitational fluctuations that are not an important part of the classical solution. Fortunately, the damping scale we obtain is irrelevantly short, so whether this trick is credible is of minor importance.
It can be useful to compare to classical thermalisation studies in models [57], using the 2PI action [47] in closed time path formalism. In this formalism, the dynamical variables are the classical field and the two point function (which describes the density of incoherent modes and the propagator). Intuitively, one could anticipate that the classical field could dissipate by interacting with the bath of incoherent fluctuations. In this paper, we neglected the cold axion particles produced by strings, which could be the bath thermalising the axion field (because at linear order in , they should just constitute an additional contribution to density fluctuations, with which the fluctuations in the density of the axion field could interact). Studies of thermalisation in find that the incoherent modes thermalise at NLO [48]. So perhaps it would be interesting to study the evolution of axions from strings and misalignment using the 2PI effective action, in the Closed Time Path formalism used by Saikawa and Yamaguchi.
### 4.2 Making contact with previous calculations
We now address the differences between our estimate and the calculation of Saikawa and Yamaguchi (SY) [19]. We focus on this impressive analytic calculation, because they introduce very clearly the used formalism and obtain the same result as [17]. SY calculate the time evolution of the axion number operator, using a closed time path formalism of Quantum Field Theory, in flat space-time with Newtonian gravity. They evaluate (which is the rate of change of the number density of axions of momentum due to gravitational interactions), in a coherent state representing highly populated low-momentum axion states. This rate is interpreted as an axion thermalisation rate, and it is larger than for photon temperatures 1 keV.
An unimportant difference is that the redshifting due to Universe expansion does not appear in the SY calculation. The gravitational effect of the homogeneous and isotropic axion density is to drive expansion, but since SY calculate with Newtonian gravity in a non-expanding space-time, all the gravitational effects of the axions are included in the “thermalisation” process. This is a relatively minor issue; scale factors can be judiciously distributed in their formulae, and within the horizon, density fluctuations can be described by Newtonian gravity. If the density in the SY formulae is replaced by the density fluctuation , then their equations are consistent with the classical linearised Einsteins Equations in Newtonian gauge.
An obvious difference from our classical discussion is that SY calculate in quantum field theory. This seems also to be unimportant, because using classical equations of motion we can obtain a similar 111111From eqn (15), is the fractional number density of axions of momentum . This equation can be obtained from the equations of motion for the fourier-transformed field, multiplied by . The equations of motion for the field, like those for , are obtained from eqn (18) and . result:
i∂∂t|˜a(→q,t)|2≃4πmGN∑kR2(t)|→k|2δρ(→k,t){˜a∗(→q+→k,t)˜a(→q,t)−˜a∗(→q,t)˜a(→q−→k,t)} . (32)
SY describe the axions as a coherent state, so it is unsurprising that their calculation gives the same result as the classical field equations, because coherent states are constructed for that purpose. In the understanding of the authors, the quantum aspect of the SY result is to identify as a number density of axion particles121212 This is because the distribution of s in the Lagrangian is different, depending on whether the classical limit should be fields or particles [58]. So to define the particle number of a classical field configuration requires ..
An important difference is that the axion number density studied by SY is labelled by the axion momentum, whereas density fluctuations are labelled by the momentum of the graviton which they exchange. Notice that the same dynamics should be included in of SY and the equation of fluctuation growth (eqn 19), because they are both the result of and the Poisson equation. To the understanding of the authors, the SY calculation shows that the rate for an axion to emit a graviton of any wavelength is large (compared to ). However, what the gravitons then do is unknown. Whereas the solution of the equations of motion for density fluctuations say that the gravitons cause the density fluctuations to grow.
Finally, SY show that axions do not have coherent gravitational interactions with other particles, such as photons, in the early Universe plasma. This is good, because it means that axions are not heated to the photon temperature. However, the classical Einsteins Equations say that gravity is universal, so that density fluctuations in the axions are subject to the gravitational attraction of other fluids (at linear order in ). Indeed, our estimate of the gravitational damping scale involves the density fluctuation, irrespective of whether it is made of axions or other particles. How can these two perspectives be consistent? At order , the axions should have gravitational interactions with the fluctuations in the density of other particles, rather than with the individual particles. That is, to find the universal gravitational attraction between hot other particles and the cold axions, one should describe the other particles with an “effective Lagrangian” at the scale of the graviton momentum. For instance, in the Closed Time Path formalism of SY, the radiation plasma in the early Universe can be described (in 2PI formalism) by its two-point function. Averaged over short distances , the two point function becomes a Wigner function, which can be approximated as a Boltzmann phase space distribution on the scale of axion momenta. The density fluctuations encoded in the temperature variations of this Boltzmann distribution are the density fluctuations which interact gravitationally with the axions at order . We interpret that the axions do not interact with individual hot photons, which could destroy the axion condensate, but rather, that the axion interactions with the long range density fluctuations in other particles will grow density perturbations, and could contribute to the axion dissipation.
## 5 Summary
The question of interest for this paper is whether gravitational interactions can “thermalise” the axions produced via the misalignment mechanism. We reproduce earlier estimates of the gravitational interaction rate of these axions, but do not confirm that it is a thermalisation rate.
We discuss this issue in cosmology, prior to the epoch of non-linear structure formation, because gravitational interactions can be treated in the linear approximation. We suppose that the Peccei-Quinn phase transition occurred after inflation, so when the axion mass turns on at the QCD phase transition and the axion field starts to oscillate, the coherence length of the field is of order the horizon. Equivalently, the comoving momentum of the field (or of the axion particles in the coherent state that makes it up) is of order the expansion rate . The axions should form CDM, therefore the gravitational interactions of the homogeneous component must drive expansion, and the gravitational interactions of density fluctuations should cause them to grow. The question is whether, in addition, gravity can “thermalise” these axions, and cause them to form a Bose Einstein condensate as anticipated by Sikivie and collaborators [16, 17]. This question is only relevant, if the misalignment axions are not already a Bose Einstein condensate, as discussed in section 2.2.
The field theory literature indicates that Bose Einstein condensation can arise in non-equilibrium situations, as well as in thermal equilibrium – but that entropy is not generated in the leading order classical solution of time-reversal-invariant equations. Instead, some fluctuations must be resummed to obtain a Bose Einstein condensate in a calculation. So in this paper, we attempt to identify and “resum” some gravitational interactions which are not those driving the expansion or growing density perturbations. In section 3.3, we estimate the contribution of metric fluctuations to the off-diagonal elements of the stress-energy tensor . These elements are commonly neglected in calculating the evolution of axion density perturbations, so we imagine that we can resum these fluctuations. We do this in section 3.4, by equating the of section 3.3 to the of an imperfect fluid in a homogeneous and isotropic Universe. This gives an estimate for the “gravitational viscosity” of the axion fluid. We find that this viscosity damps fluctuations on distances smaller than the axion Jeans length . The damping scale is given in eqn (31). In particular, fluctuations on the comoving scale are not damped during the cosmological periods we consider. So we do not confirm the interpretation of [17, 19] that axions migrate to the zero mode (form a Bose Einstein condensate) at a photon temperature keV, due to “gravitational thermalisation”. We can reproduce the gravitational interaction rate obtained by [17, 19], but it is unclear to us that this is a thermalisation rate: some of the gravitons should be contributing to the growth of density fluctuations. Section 4 discusses our estimates and compares to the calculation of [19].
## Acknowledgements
We thank J. Gascon, A. Strumia, P Sikivie, S. Theissen and C. Wetterich for useful conversations. We are very grateful to T. Noumi, K. Saikawa, R. Sato, and M. Yamaguchi, for discussions and for allowing us to see their work in progress [59]. And we especially thank Georg Raffelt, for uncountable discussions, suggestions and comments, as well as for careful reading of the manuscript. The project was performed in the context of the Lyon Institute of Origins, grant ANR-10-LABX-66, and acknowledges partial support from the EU FP7 ITN invisibles (MC Actions, PITN-GA-2011-289442).
Note added: When this paper was nearing completion, appeared an interesting discussion [60] of the connection between the field theory and fluid descriptions of a BE condensate.
## 6 Appendix
In this Appendix, we study whether gravity can redistribute the momenta of CDM axions in a homogeneous and isotropic Universe described by Einsteins Equations. We consider a classical free scalar field, that is, a coherent state, evolving in a Friedman-Robertson-Walker universe. We suppose this to be an adequate description of dark matter axions after the QCD phase transition, during linear structure formation. So from an S-matrix perspective, we take the “in” states to be axion modes shortly after the QCD phase transition, and the “out” states prior to . We describe the CDM axions as a coherent state of “in-particles”. We then evaluate, in that state, the expectation value of the number operator of “out-particles”, thereby obtaining their momentum distribution. As expected, the physical momentum of the modes redshifts, and the comoving momentum distribution does not change at leading order.
### 6.1 The Calculation
We take the starting time for our study to be a few Hubble times after the QCD phase transition, when the axion dark matter can be described as a real free scalar field in a Friedmann-Robertson-Walker background, with metric
ds2=gμνdxμdxν=dt2−R2(t)[dx2+dy2+dz2] (33)
We follow the evolution of axion dark matter until this description breaks down, when structure formation becomes non-linear. We approximate this time as . During this period, the axion field satisfies the equations of motion:
¨a+3H˙a−1R2(t)∂i∂ia+m2a=0 (34)
where . Following [61, 62], the field can be expanded on a complete set of orthogonal eigenmodes , which are solutions of eqn (34), and which correspond to axion particles at . We follow the conventions of [62], but with the metric of eqn (33). It is convenient to normalise the eigenmodes in a box of physical volume :
uin→k(t,→x)=1[R(t)L]3/2χin(t)ei→k⋅→x (35)
Notice that solutions of the Klein Gordon equation (34) are separable, due to the homogeneity of FRW spacetime.
In a second-quantised formalism, the axion field operator can be expanded in the usual way on (time-dependant) annihilation and creation operators which satisfy [61], and which multiply the modes . These annihilation operators define the “in” vacuum. The classical axion field can therefore be written as a coherent state [63] of (non-relativistic) axion particles:
|a(→x,t)⟩ = 1Nexp⎧⎨⎩∑→pa(→p,t)^b†→p⎫⎬⎭|0in⟩ . (36)
where is a normalisation factor to ensure . This state describes the classical axion field: .
We wish to know the spectrum of axions that this state describes at . It is well-known that gravity can change momenta and create particles. Canonical examples are momentum red-shifting in FRW cosmologies, and black hole radiation: in a the curved space-time outside a black hole, the state with no particles at will contain particles at . This can be described [62] by writing the in- vacuum creation operators (or equivalently, eigenmodes) in terms of the out-vacuum operators using Bogolibov coefficients:
uout→k=∑→qα→k→quin→q+β→k→quin,∗→q . (37)
Recall that the coefficients, which parametrise the overlap between positive and negative frequency modes, describe particle creation by gravity. In the axion case, we wish to know the momentum distribution of “out-state” axions — that is, axion particles at the end of linear structure formation —in the coherent state of eqn (36). This can be evaluated if we know the Bogoliubov transformation between the “in” and “out” creation and annihilation operators, or equivalently, if one can express the “out” eigenmodes in terms of the “in” eigenmodes, as in eqn (37).
The out eigenmodes can be written
uout→k(t,→x)=1[R(t)L]3/2χout(t)ei→k⋅→x (38)
where is a solution of
∂2∂t2χout+|→k|2R2(t)χout+m2χout=0
and chosen to describe axion particles at ( is a solution of the same equation). The homogeneity of FRW spacetimes means that co-moving momentum is conserved, or equivalently, the Bogoliubov coefficients are diagonal in momentum space [62]:
α→k,→q=(uout→k,uin→q)∝δ→k,→q , β→k,→q=−(uout→k,uin,∗→q)∝δ→k,−→q (39)
so the number operator for axion particles at is
^bout†→k^bout→k=(α→k,→k^bin†→k−β→k,−→k^bin−→k)(α∗→k,→k^bin→k−β∗→k,−→k^bin†−→k) . (40)
This shows that the effect of gravity on axions, in an expanding FRW Universe, is to redshift their momenta (and possibly create particles). There is no indication, from this calculation, that gravity modifies the co-moving momentum distribution of the axions.
The axion creation by gravity, encoded in the coefficients , is expected to be negligible because . It can be estimated, following [61], by taking the lowest order adiabatic approximation
χ(t)=1√2ωei∫tωdt′ (41)
with . For , we obtain 131313Specifically, by substituting (41) into eqn (22) of [61], then integrating eqn (26) of [61] neglecting | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9582833647727966, "perplexity": 854.8725594427235}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948673.1/warc/CC-MAIN-20230327154814-20230327184814-00679.warc.gz"} |
http://galileo.phys.virginia.edu/classes/752.mf1i.spring03/Time_Dep_PT.htm | # Time-Dependent Perturbation Theory
Michael Fowler
### Introduction: General Formalism
We look at a Hamiltonian $H={H}^{0}+V\left(t\right)$, with $V\left(t\right)$ some time-dependent perturbation, so now the wave function will have perturbation-induced time dependence.
Our starting point is the set of eigenstates $|n〉$ of the unperturbed Hamiltonian ${H}^{0}|n〉={E}_{n}|n〉$, notice we are not labeling with a zero, no ${E}_{n}^{0}$, because with a time-dependent Hamiltonian, energy will not be conserved, so it is pointless to look for energy corrections. What happens instead, provided the perturbation is not too large, is that the system makes transitions between the eigenstates $|n〉$ of ${H}^{0}$.
Of course, even for $V=0,$ the wave functions have the usual time dependence,
$|\psi \left(t\right)〉=\sum _{n}{c}_{n}{e}^{-i{E}_{n}t/\hslash }|n〉$
with the ${c}_{n}$ ’s constant. What happens on introducing $V\left(t\right)$ is that the ${c}_{n}$ ’s themselves acquire time dependence,
$|\psi \left(t\right)〉=\sum _{n}{c}_{n}\left(t\right){e}^{-i{E}_{n}t/\hslash }|n〉$
and this time dependence is determined by Schrödinger’s equation with $H={H}^{0}+V\left(t\right)$:
$i\hslash \frac{\partial }{\partial t}\sum _{n}{c}_{n}\left(t\right){e}^{-i{E}_{n}t/\hslash }|n〉=\left({H}^{0}+V\left(t\right)\right)\sum _{n}{c}_{n}\left(t\right){e}^{-i{E}_{n}t/\hslash }|n〉$
so
$i\hslash \sum _{n}{\stackrel{˙}{c}}_{n}\left(t\right){e}^{-i{E}_{n}t/\hslash }|n〉=V\left(t\right)\sum _{n}{c}_{n}\left(t\right){e}^{-i{E}_{n}t/\hslash }|n〉$
Taking the inner product with the bra $〈m|{e}^{i{E}_{m}t/\hslash }$, and introducing ${\omega }_{mn}=\frac{{E}_{m}-{E}_{n}}{\hslash }$,
$i\hslash {\stackrel{˙}{c}}_{m}=\sum _{n}〈m|V\left(t\right)|n〉{c}_{n}{e}^{i{\omega }_{mn}t}=\sum _{n}{V}_{mn}{e}^{i{\omega }_{mn}t}{c}_{n}$
This is a matrix differential equation for the ${c}_{n}$ ’s :
$i\hslash \left(\begin{array}{c}{\stackrel{˙}{c}}_{1}\\ {\stackrel{˙}{c}}_{2}\\ {\stackrel{˙}{c}}_{3}\\ .\\ .\end{array}\right)=\left(\begin{array}{ccccc}{V}_{11}& {V}_{12}{e}^{i{\omega }_{12}t}& .& .& .\\ {V}_{21}{e}^{i{\omega }_{21}t}& {V}_{22}& .& .& .\\ .& .& {V}_{33}& .& .\\ .& .& .& .& .\\ .& .& .& .& .\end{array}\right)\left(\begin{array}{c}{c}_{1}\\ {c}_{2}\\ {c}_{3}\\ .\\ .\end{array}\right)$
and solving this set of coupled equations will give us the ${c}_{n}\left(t\right)$ ’s, and hence the probability of finding the system in any particular state at any later time.
If the system is in initial state $|i〉$ at $t=0,$ the probability amplitude for it being in state $|f〉$ at time $t$ is to leading order in the perturbation
${c}_{f}\left(t\right)={\delta }_{fi}-\frac{i}{\hslash }\underset{0}{\overset{t}{\int }}{V}_{fi}\left({t}^{\prime }\right){e}^{i{\omega }_{fi}{t}^{\prime }}d{t}^{\prime }.$
The probability that the system is in fact in state $|f〉$ at time $t$ is therefore
${|{c}_{f}\left(t\right)|}^{2}=\frac{1}{{\hslash }^{2}}{|\underset{0}{\overset{t}{\int }}{V}_{fi}\left({t}^{\prime }\right){e}^{i{\omega }_{fi}{t}^{\prime }}d{t}^{\prime }|}^{2}.$
Obviously, this is only going to be a good approximation if it predicts that the probability of transition is small$—$otherwise we need to go to higher order, using the Interaction Representation (or an exact solution like that in the next section).
Example: kicking an oscillator.
Suppose a simple harmonic oscillator is in its ground state $|0〉$ at $t=-\infty .$ It is perturbed by a small time-dependent potential $V\left(t\right)=-eEx{e}^{-{t}^{2}/{\tau }^{2}}.$ What is the probability of finding it in the first excited state $|1〉$ at $t=+\infty$?
Here ${V}_{fi}\left({t}^{\prime }\right)=-eE〈1|x|0〉{e}^{-{{t}^{\prime }}^{2}/{\tau }^{2}}$, and $x=\sqrt{\hslash /2m\omega }\left(a+{a}^{†}\right)$, from which the probability can be evaluated. It is $\left({e}^{2}{E}^{2}/{\hslash }^{2}\right)\left(\hslash /2m\omega \right)\pi {\tau }^{2}{e}^{-{\omega }^{2}{\tau }^{2}/2}.$
It’s worth thinking through the physical interpretations for very long and for very short times, and explaining the significance of the time for which the probability is a maximum.
### The Two-State System: an Exact Solution
For the particular case of a two-state system perturbed by a periodic external field, the matrix equation above can be solved exactly. Of course, real physical systems have more than two states, but in fact for some important cases two of the states may be strongly coupled to each other, but only weakly coupled to other states, and the analysis then becomes relevant. A famous example, the ammonia maser, is discussed at the end of the section.
For a two-state system, then, the most general wave function is
$|\psi \left(t\right)〉={c}_{1}\left(t\right){e}^{-i{E}_{1}t/\hslash }|1〉+{c}_{2}\left(t\right){e}^{-i{E}_{2}t/\hslash }|2〉$
and the differential equation for the ${c}_{n}\left(t\right)$ ’s is:
$i\hslash \left(\begin{array}{c}{\stackrel{˙}{c}}_{1}\\ {\stackrel{˙}{c}}_{2}\end{array}\right)=\left(\begin{array}{cc}0& V{e}^{i\omega t}{e}^{i{\omega }_{12}t}\\ V{e}^{-i\omega t}{e}^{-i{\omega }_{12}t}& 0\end{array}\right)\left(\begin{array}{c}{c}_{1}\\ {c}_{2}\end{array}\right).$
Writing $\omega +{\omega }_{12}=\alpha$ for convenience, the coupled equations are:
$\begin{array}{l}i\hslash {\stackrel{˙}{c}}_{1}=V{e}^{i\alpha t}{c}_{2}\\ i\hslash {\stackrel{˙}{c}}_{2}=V{e}^{-i\alpha t}{c}_{1}.\end{array}$
These two first-order equations can be transformed into a single second-order equation by differentiating the second one, then substituting ${\stackrel{˙}{c}}_{1}$ from the first one and ${c}_{1}$ from the second one to give
${\stackrel{¨}{c}}_{2}=-i\alpha \text{ }{\stackrel{˙}{c}}_{2}-\frac{{V}^{2}}{{\hslash }^{2}}{c}_{2}.$
This is a standard second-order differential equation, solved by putting in a trial solution ${c}_{2}\left(t\right)={c}_{2}\left(0\right){e}^{i\Omega t}$ . This satisfies the equation if
$\Omega =-\frac{\alpha }{2}±\sqrt{\frac{{\alpha }^{2}}{4}+\frac{{V}^{2}}{{\hslash }^{2}}}$,
so, reverting to the original $\omega +{\omega }_{12}=\alpha$, the general solution is:
${c}_{2}\left(t\right)={e}^{-i\frac{\left(\omega -{\omega }_{21}\right)}{2}t}\left(A{e}^{i\sqrt{{\left(\frac{\omega -{\omega }_{21}}{2}\right)}^{2}+\frac{{V}^{2}}{{\hslash }^{2}}}\text{\hspace{0.17em}}t}+B{e}^{-i\sqrt{{\left(\frac{\omega -{\omega }_{21}}{2}\right)}^{2}+\frac{{V}^{2}}{{\hslash }^{2}}}\text{\hspace{0.17em}}t}\right)$.
Taking the initial state to be ${c}_{1}\left(0\right)=1,\text{\hspace{0.17em}}\text{\hspace{0.17em}}{c}_{2}\left(0\right)=0$ gives $A=-B.$
To fix the overall constant, note that at t = 0,
${\stackrel{˙}{c}}_{2}\left(0\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{V}{i\hslash }{c}_{1}\left(0\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{V}{i\hslash }.$
Therefore
${|{c}_{2}\left(t\right)|}^{2}=\frac{\frac{{V}^{2}}{{\hslash }^{2}}}{{\left(\frac{\omega -{\omega }_{21}}{2}\right)}^{2}+\frac{{V}^{2}}{{\hslash }^{2}}}{\mathrm{sin}}^{2}\left(\sqrt{{\left(\frac{\omega -{\omega }_{21}}{2}\right)}^{2}+\frac{{V}^{2}}{{\hslash }^{2}}}\text{\hspace{0.17em}}t\right).$
Note in particular the result if $\omega ={\omega }_{12}:$
${|{c}_{2}\left(t\right)|}^{2}={\mathrm{sin}}^{2}\left(\frac{Vt}{\hslash }\right)$.
Assuming ${E}_{2}>{E}_{1},$ and the two-state system to be initially in the ground state $|1〉$, this means that after a time $h/4V$ the system will certainly be in state $|2〉$, and will oscillate back and forth between the two states with period $h/2V$
That is to say, a precisely timed period spent in an oscillating field can drive a collection of molecules all in the ground state to be all in an excited state. The ammonia maser works by sending a stream of ammonia molecules, traveling at known velocity, down a tube having an oscillating field for a definite length, so the molecules emerging at the other end are all (or almost all, depending on the precision of ingoing velocity, etc.) in the first excited state. Application of a small amount of electromagnetic radiation of the same frequency to the outgoing molecules will cause some to decay, generating intense radiation and therefore a much shorter period for all to decay, emitting coherent radiation.
### A “Sudden” Perturbation
A sudden perturbation is defined here as a sudden switch from one time-independent Hamiltonian ${H}_{0}$ to another one ${{H}^{\prime }}_{0}$, the time of switching being much shorter than any natural period of the system. In this case, perturbation theory is irrelevant: if the system is initially in an eigenstate $|n〉$ of ${H}_{0}$, one simply has to write it as a sum over the eigenstates of ${{H}^{\prime }}_{0}$, $|n〉=\sum _{{n}^{\prime }}|{n}^{\prime }〉〈{n}^{\prime }|n〉$. The nontrivial part of the problem is in establishing that the change is sudden enough, by estimating the actual time taken for the Hamiltonian to change, and the periods of motion associated with the state $|n〉$ and with its transitions to neighboring states.
(We discussed one example last semester$—$an electron in the ground state in a one-dimensional box that suddenly doubles in size. Other favorite examples include an atom with spin-orbit coupling in a magnetic field that suddenly reverses (Messiah p 743), and the reaction of orbiting electrons to nuclear $\alpha$ - or $\beta$ -decay.)
### Harmonic Perturbations: Fermi’s Golden Rule
Let us consider a system in an initial state $|i〉$ perturbed by a periodic potential $V\left(t\right)=V{e}^{-i\omega t}$ switched on at $t=0.$ For example, this could be an atom perturbed by an external oscillating electric field, such as an incident light wave.
What is the probability that at a later time $t$ the system be in state $|f〉$?
Recall the matrix differential equation for the ${c}_{n}$ ’s :
$i\hslash \left(\begin{array}{c}{\stackrel{˙}{c}}_{1}\\ {\stackrel{˙}{c}}_{2}\\ {\stackrel{˙}{c}}_{3}\\ .\\ .\end{array}\right)=\left(\begin{array}{ccccc}{V}_{11}& {V}_{12}{e}^{i{\omega }_{12}t}& .& .& .\\ {V}_{21}{e}^{i{\omega }_{21}t}& {V}_{22}& .& .& .\\ .& .& {V}_{33}& .& .\\ .& .& .& .& .\\ .& .& .& .& .\end{array}\right)\left(\begin{array}{c}{c}_{1}\\ {c}_{2}\\ {c}_{3}\\ .\\ .\end{array}\right)$
Since the system is definitely in state $|i〉$ at $t=0,$ the ket vector on the right is initially ${c}_{i}=1,\text{\hspace{0.17em}}{c}_{j\ne i}=0.$
The first-order approximation to keep the vector ${c}_{i}=1,\text{\hspace{0.17em}}{c}_{j\ne i}=0$ on the right, that is, to solve the equations
$i\hslash {\stackrel{˙}{c}}_{f}\left(t\right)={V}_{fi}{e}^{i{\omega }_{fi}t}.$
Integrating this equation, the probability amplitude for an atom in initial state $|i〉$ to be in state $|f〉$ after time $t$ is, to first order:
$\begin{array}{c}{c}_{f}\left(t\right)=-\frac{i}{\hslash }\underset{0}{\overset{t}{\int }}〈f|\text{\hspace{0.17em}}V|i〉{e}^{i\left({\omega }_{fi}-\omega \right){t}^{\prime }}d{t}^{\prime }\\ =-\frac{i}{\hslash }〈f|V|i〉\frac{{e}^{i\left({\omega }_{fi}-\omega \right)t}-1}{i\left({\omega }_{fi}-\omega \right)}.\end{array}$
The probability of transition is therefore
${P}_{i\to f}\left(t\right)={|{c}_{f}|}^{2}=\frac{1}{{\hslash }^{2}}{|〈f|V|i〉|}^{2}{\left(\frac{\mathrm{sin}\left(\left({\omega }_{fi}-\omega \right)t/2\right)}{\left({\omega }_{fi}-\omega \right)/2}\right)}^{2}$
and we’re interested in the large $t$ limit.
Writing $\alpha =\left({\omega }_{fi}-\omega \right)/2$, our function has the form $\frac{{\mathrm{sin}}^{2}\alpha t}{{\alpha }^{2}}$. This function has a peak at $\alpha =0,$ with maximum value ${t}^{2},$ and width of order $1/t,$ so a total weight of order $t.$ The function has more peaks at $\alpha t=\left(n+1/2\right)\pi$. These are bounded by the denominator at $1/{\alpha }^{2}$. For large $t$ their contribution comes from a range of order $1/t$ also, and as $t\to \infty$ the function tends to a $\delta$ function at the origin, but multiplied by $t.$
This divergence is telling us that there is a finite probability rate for the transition, so the likelihood of transition is proportional to time elapsed. Therefore, we should divide by $t$ to get the transition rate.
To get the quantitative result, we need to evaluate the weight of the $\delta$ function term. We use the standard result ${\underset{-\infty }{\overset{\infty }{\int }}\left(\frac{\mathrm{sin}\xi }{\xi }\right)}^{2}d\xi =\pi$ to find ${\underset{-\infty }{\overset{\infty }{\int }}\left(\frac{\mathrm{sin}\alpha t}{\alpha }\right)}^{2}d\alpha =\pi t$, and therefore
$\underset{t\to \infty }{\mathrm{lim}}\frac{1}{t}{\left(\frac{\mathrm{sin}\alpha t}{\alpha }\right)}^{2}=\pi \delta \left(\alpha \right).$
Now, the transition rate is the probability of transition divided by $t$ in the large $t$ limit, that is,
$\begin{array}{l}{R}_{i\to f}\left(t\right)=\underset{t\to \infty }{\mathrm{lim}}\frac{{P}_{i\to f}\left(t\right)}{t}=\underset{t\to \infty }{\mathrm{lim}}\frac{1}{t}\frac{1}{{\hslash }^{2}}{|〈f|V|i〉|}^{2}\left[\frac{\mathrm{sin}\left(\left({\omega }_{fi}-\omega \right)t/2\right)}{\left({\omega }_{fi}-\omega \right)/2}\right]\\ =\frac{1}{{\hslash }^{2}}{|〈f|V|i〉|}^{2}\pi \delta \left(\frac{1}{2}\left({\omega }_{fi}-\omega \right)\right)\\ =\frac{2\pi }{{\hslash }^{2}}{|〈f|V|i〉|}^{2}\delta \left({\omega }_{fi}-\omega \right)\end{array}$
This last line is Fermi’s Golden Rule: we shall be using it a lot. You might worry that in the long time limit we have taken the probability of transition is in fact diverging, so how can we use first order perturbation theory? The point is that for a transition with ${\omega }_{fi}\ne \omega$, “long time” means $\left({\omega }_{fi}-\omega \right)t\gg 1$, this can still be a very short time compared with the mean transition time, which depends on the matrix element. In fact, Fermi’s Rule agrees extremely well with experiment when applied to atomic systems.
### Another Derivation of the Golden Rule
Actually, when light falls on an atom, the full periodic potential is not suddenly switched on, on an atomic time scale, but builds up over many cycles (of the atom and of the light). Baym re-derives the Golden Rule assuming the limit of a very slow switch on,
$V\left(t\right)={e}^{\epsilon t}V{e}^{-i\omega t}$
with $\epsilon$ very small, so $V$ switched on very gradually in the past, and we are looking at times much smaller than $1/\epsilon$. We can then take the initial time to be $-\infty$, that is,
${c}_{f}\left(t\right)=-\frac{i}{\hslash }\underset{-\infty }{\overset{t}{\int }}〈f|\text{\hspace{0.17em}}V|i〉{e}^{i\left({\omega }_{fi}-\omega -i\epsilon \right){t}^{\prime }}d{t}^{\prime }=-\frac{1}{\hslash }\frac{{e}^{i\left({\omega }_{fi}-\omega -i\epsilon \right)t}}{{\omega }_{fi}-\omega -i\epsilon }〈f|V|i〉$
so
${|{c}_{f}\left(t\right)|}^{2}=\frac{1}{{\hslash }^{2}}\frac{{e}^{2\epsilon t}}{{\left({\omega }_{fi}-\omega \right)}^{2}+{\epsilon }^{2}}{|〈f|V|i〉|}^{2}$
and the time rate of change
$\frac{d}{dt}{|{c}_{f}\left(t\right)|}^{2}=\frac{1}{{\hslash }^{2}}\frac{2\epsilon {e}^{2\epsilon t}}{{\left({\omega }_{fi}-\omega \right)}^{2}+{\epsilon }^{2}}{|〈f|V|i〉|}^{2}$.
In the limit $\epsilon \to 0$, the function
$\frac{2\epsilon }{{\left({\omega }_{fi}-\omega \right)}^{2}+{\epsilon }^{2}}\to 2\pi \delta \left({\omega }_{fi}-\omega \right)$
giving the Golden Rule again.
### Harmonic Perturbations: Second-Order Transitions
Sometimes the first order matrix element $〈f|V|i〉$ is identically zero (parity, Wigner-Eckart, etc.) but other matrix elements are nonzero$—$and the transition can be accomplished by an indirect route. In the notes on the interaction representation, we derived the probability amplitude for the second-order process,
${c}_{n}^{\left(2\right)}\left(t\right)={\left(\frac{1}{i\hslash }\right)}^{2}\sum _{n}\underset{0}{\overset{t}{\int }}\underset{0}{\overset{{t}^{\prime }}{\int }}d{t}^{\prime }d{{t}^{\prime }}^{\prime }{e}^{-i{\omega }_{f}\left(t-{t}^{\prime }\right)}〈f|{V}_{S}\left({t}^{\prime }\right)|n〉{e}^{-i{\omega }_{n}\left({t}^{\prime }-{{t}^{\prime }}^{\prime }\right)}〈n|{V}_{S}\left({{t}^{\prime }}^{\prime }\right)|i〉{e}^{-i{\omega }_{i}{t}^{″}}$,
Taking the gradually switched-on harmonic perturbation ${V}_{S}\left(t\right)={e}^{\epsilon t}V{e}^{-i\omega t}$, and the initial time $-\infty$, as above,
${c}_{n}^{\left(2\right)}\left(t\right)={\left(\frac{1}{i\hslash }\right)}^{2}\sum _{n}〈f|V|n〉〈n|V|i〉{e}^{-i{\omega }_{f}t}\underset{-\infty }{\overset{t}{\int }}d{t}^{\prime }\underset{-\infty }{\overset{{t}^{\prime }}{\int }}d{{t}^{\prime }}^{\prime }{e}^{i\left({\omega }_{f}-{\omega }_{n}-\omega -i\epsilon \right){t}^{\prime }}{e}^{i\left({\omega }_{n}-{\omega }_{i}-\omega -i\epsilon \right){{t}^{\prime }}^{\prime }}.$
Exactly as in the section above on the first-order Golden Rule, we can find the transition rate:
$\frac{d}{dt}{|{c}_{n}^{\left(2\right)}\left(t\right)|}^{2}=\frac{2\pi }{{\hslash }^{4}}{|\sum _{n}\frac{〈f|V|n〉〈n|V|i〉}{{\omega }_{n}-{\omega }_{i}-\omega -i\epsilon }|}^{2}\delta \left({\omega }_{f}-{\omega }_{i}-2\omega \right).$
(The ${\hslash }^{4}$ in the denominator goes to $\hslash$ on replacing the frequencies $\omega$ with energies $E,$ both in the denominator and the delta function, remember that if $E=\hslash \omega$, $\delta \left(\omega \right)=\hslash \delta \left(E\right).$ )
This is a transition in which the system gains energy $2\hslash \omega$ from the beam, in other words two photons are absorbed, the first taking the system to the intermediate energy ${\omega }_{n}$, which is short-lived and therefore not well defined in energy$—$there is no energy conservation requirement into this state, only between initial and final states.
Of course, if an atom in an arbitrary state is exposed to monochromatic light, other second order processes in which two photons are emitted, or one is absorbed and one emitted (in either order) are also possible. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 139, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.975575864315033, "perplexity": 513.7590095083004}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720737.84/warc/CC-MAIN-20161020183840-00363-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://astronomy.stackexchange.com/questions/38819/can-concentration-of-gas-in-exoplanet-atmosphere-be-found-out-from-wavelength-an | # Can concentration of gas in exoplanet atmosphere be found out from wavelength and absorbing radius from spectral data?
I was working on exoplanet spectral data from which I need to infer the concentration of gases. However, the exoplanet spectroscopy data contains only absorption wavelength and absorption radius. Is there any way with which I can derive the concentration of the elements in the exoplanet's atmosphere? | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9003762006759644, "perplexity": 1232.3649091387078}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488286726.71/warc/CC-MAIN-20210621151134-20210621181134-00270.warc.gz"} |
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## mathsucksalot123 4 years ago Rock music accounted for 30.5% of the total sales of recorded music in 1999 , and 20.4% of the total sales of recorded music in 2009 . Find the average rate of change of the percentage of sales of rock music from 1999 to 2009 . Round to the nearest hundredth of a percent. Note that the percentage sign is already given in the answer, so you do not need to enter it. The average rate of change is . Delete Cancel Submit
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1. helpingtutors
• 4 years ago
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(30.5 - 20.4)/10 = 10.1/10 = 1.01
2. mathsucksalot123
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i tried that. it says its wrong :(
3. satellite73
• 4 years ago
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that is because your answer should be negative. sales declined over the ten year period
4. satellite73
• 4 years ago
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$\frac{30.5-20.4}{1999-2009}=\frac{10.1}{-10}$
5. mathsucksalot123
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thanks
6. satellite73
• 4 years ago
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yw
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9972937107086182, "perplexity": 4589.260094324698}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448399455473.15/warc/CC-MAIN-20151124211055-00293-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/almost-black-holes.612796/ | # Almost black holes
1. Jun 9, 2012
### mrspeedybob
If there were a star which was almost, but not quite massive enough to become a black hole it seems as though gravitational time dilation should make it appear very dim. If time dilation resulted in 1/1000 of the time passing within the star as passes for us, we should see a star emitting 1/1000 the energy that it's mass would otherwise suggest. Do we see such stars in the universe?
2. Jun 9, 2012
### Bobbywhy
Just an off-the-wall question from a non-astronomer: Would these "almost black holes" exhibit an intrinsic red-shift? I think I remember that Halton C. Arp proposed that for explaining the red-shift of quasars.
3. Jun 9, 2012
### Staff: Mentor
No, such objects can only be Neutron Stars, which are extremely tiny in size, yet comparable to the mass of the Sun. There are no stars that are still fusing elements in their cores that are anywhere close to being a black hole.
Your question should apply to a neutron star though. I would expect to see significant redshift on radiation coming from a neutron star.
4. Jun 10, 2012
### ImaLooser
A star that is not quite a black hole is a neutron star. The energy that comes off of a neutron star is red shifted, but I don't know how much.
Last I looked only one neutron star had been directly observed. (Usually we see the glow of the surrounding matter.) But that should enough to get a real figure.
5. Jun 10, 2012
### stevebd1
The smallest a neutron star can get before run away collapse occurs is r0=9M/4 or 2.25M in order to have positive tangential pressures (according to the Schwarzschild interior metric, this is the point that the time dilation at the very interior of the star becomes zero). If we consider the gravitational redshift-
$$z=\frac{1}{\sqrt{1-\frac{2M}{r}}}-1=\frac{\lambda_o-\lambda_e}{\lambda_e}$$
where z is the redshift, $\lambda_o$ is the wavelength observed and $\lambda_e$ is the wavelength emitted. The above can be rewritten-
$$\lambda_o=(z\cdot\lambda_e)+\lambda_e$$
if we consider a 3 sol mass as an absolute maximum, then M=4430.55, then you can pretty much work out what z would be and what the emitted wavelength of light would be shifted to.
Regarding gravitational time dilation, this would be expressed as-
$$d\tau=dt\sqrt{1-\frac{2M}{r}}$$
so the greatest time dilation due to gravity at the surface of a stable neutron star at the very boundary of collapse would be 0.333 or ~1/3.
Last edited: Jun 10, 2012
6. Jun 10, 2012
### Chronos
7. Jun 11, 2012
### ImaLooser
Duh.
What's M? What's z?
8. Jun 11, 2012
### Staff: Mentor
I believe M = mass, and Z = the measure of redshift.
9. Jun 12, 2012
### Chronos
Yes, but, just to clarify, M is expressed in units of solar mass.
10. Jun 12, 2012
### Rorkster2
I don't think it would appear dim to us. Light would travel very slowly away from it when released because of massive gravity pulling backwards, but as soon as the light moves far enough away it would resume its 'speed of light' pase. And reach us just like a normal star. Unless gravity pulled back some photons and not others it would have the same luminosity
11. Jun 12, 2012
### Bobbywhy
It appears you have a mistaken view of "gravitational redshift". It is true when we say photons "climb out of the gravitational potential" of a massive object. But this does not mean their velocity is changed...they still travel at c. What happens is just what's been mentioned above: redshift. This term comes from the optical part of the EM spectrum where red is a longer wavelength than, say, blue. This means the WAVELENGTH of the light has been stretched out and its "color" will be different (redder). Light never "slows down" or "resumes its pace", at least in this kind of example.
12. Jun 12, 2012
### Algr
Does this mean that one second passes on the nutron star for every 3 seconds outside of it? If so, then I'd think that that would indeed dim the star by a factor of 3. Regardless of red shift, the star would produce one third the number of photons in 1 second that it would in 3. And an observer on the neuron star would see the rest of the universe as sped up, and three times as bright.
13. Jun 12, 2012
### Rorkster2
Sorry to say but i believe your wrong. First off, light can indeed change its speed. For example, in near absolute zero it is possible to slow photons to a crawl, and also 'speed of light' refers to its speed when traveling threw a vaccuum, not its constant speed. Next, you are right in saying that the redshift and blueshift waves are a derived from its frequnecy, however in this example you also have to include the fact that light DOES slow down, because black holes change light momentum from going 'forward' to 'backwards', and a near blackhole object would be in the very close inbetween where it slows down but does not quite go 'backward'
14. Jun 12, 2012
### Staff: Mentor
It is a well known fact that light does indeed change speeds in a material, but when anyone says that the speed of light doesn't change or is invariant they are referring to the velocity in a vacuum, which is c always.
This is incorrect. The change in momentum in no way affects the speed of light. As for the forward and backward stuff, I'm not sure what you are getting at.
15. Jun 12, 2012
### Chronos
The time dilation factor goes by (1 + z), so a neutron star with a gravitational redshift of .33 would be time dilated by 1/1.33, or basically it would take 1.33 seconds to emit the same amount radiation as it would radiate in 1 second if not redshifted.
16. Jun 12, 2012
### ImaLooser
Aha. Well, I'm duh again because I don't know what it means to express radius of an object in units of mass.
17. Jun 13, 2012
### Staff: Mentor
The radius isn't being expressed in units of mass. You are dividing the mass by the radius because more mass packed into a smaller radius means more gravity and more time dilation.
18. Jun 14, 2012
### stevebd1
In the paper posted by Chronos, M refers to mass, in the post I made, M is the geometric unit of mass, sometimes referred to as the gravitational radius where M=Gm/c2 where G is the gravitational constant, m is the mass in SI units (i.e. kg) and c is the speed of light in m/s.
19. Jun 18, 2012
### grantwilliams
If a photon is considered to be without mass how can light have momentum?
note: my only exposure to physics has been in an AP mechanics class and in the books i've read over this summer. (i won't begin more formal study until i begin college next fall)
20. Jun 18, 2012
### Staff: Mentor
The momentum and energy of a photon is determined by the frequency. Higher frequency photons have more momentum and energy. You can read a bit more here: http://en.wikipedia.org/wiki/Photon#Physical_properties
If that isn't detailed enough or doesn't answer your question just say so. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8265753984451294, "perplexity": 915.2850277115546}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589222.18/warc/CC-MAIN-20180716060836-20180716080836-00154.warc.gz"} |
https://latex.org/forum/viewtopic.php?f=59&t=31393 | ## LaTeX forum ⇒ Theses, Books, Title pages ⇒ Bibliography In Separate Chapters
Classicthesis, Bachelor and Master thesis, PhD, Doctoral degree
BrilPoets
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### Bibliography In Separate Chapters
Dear All,
I am writing my PhD thesis, making use of the template as provided in this link http://www.latextemplates.com/template/ ... ral-thesis. In the original template, the all bibliography is supposed to go in the end of the manuscript. But I would like, instead, to put the bibliography in the end of each single chapter, and to have an automatic update of the citations when adding/subtracting a reference, and subsequently to "import" it every time I need through the "\include{}" command.
Is this possible? Can you kindly suggest me how to solve this issue? I tried several approaches as suggested in different websites, but none of them worked properly, and i think it is because it is also a "class"-dependent problem.
Many thanks in advance for the help!!!
All the Best,
Tommy
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The smart way: Calm down and take a deep breath, read posts and provided links attentively, try to understand and ask if necessary.
reyaz
Posts: 12
Joined: Sun Apr 22, 2018 6:05 am
BrilPoets wrote:Dear All,
I am writing my PhD thesis, making use of the template as provided in this link http://www.latextemplates.com/template/ ... ral-thesis. In the original template, the all bibliography is supposed to go in the end of the manuscript. But I would like, instead, to put the bibliography in the end of each single chapter, and to have an automatic update of the citations when adding/subtracting a reference, and subsequently to "import" it every time I need through the "\include{}" command.
Is this possible? Can you kindly suggest me how to solve this issue? I tried several approaches as suggested in different websites, but none of them worked properly, and i think it is because it is also a "class"-dependent problem.
Many thanks in advance for the help!!!
All the Best,
Tommy
Hi If You have found any solution then please forward me I am also facing same problem. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8439540863037109, "perplexity": 1111.1608051051567}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202450.64/warc/CC-MAIN-20190320170159-20190320192031-00011.warc.gz"} |
https://repozytorium.bg.ug.edu.pl/info/article/UOG8acbf47c64c54bbfbd3b559f27599279/ | ## Classical simulation of photonic linear optics with lost particles
### Michał Oszmaniec , Daniel J. Brod
#### Abstract
Weexplore the possibility of efficient classical simulation of linear optics experiments under the effect of particle losses. Specifically, we investigate the canonical boson sampling scenario in which an nparticle Fock input state propagates through a linear-optical network and is subsequently measured by particle-number detectors in themoutput modes.Weexamine two models of losses. In the first model a fixed number of particles is lost.Weprove that in this scenario the output statistics can be well approximated by an efficient classical simulation, provided that the number of photons that is left grows slower than n. In the second loss model, every time a photon passes through a beamsplitter in the network, it has some probability of being lost. For this model the relevant parameter is s, the smallest number of beamsplitters that any photon traverses as it propagates through the network.We prove that it is possible to approximately simulate the output statistics already if s grows logarithmically withm, regardless of the geometry of the network. The latter result is obtained by proving that it is always possible to commute s layers of uniform losses to the input of the network regardless of its geometry, which could be a result of independent interest.Webelieve that our findings put strong limitations on future experimental realizations of quantum computational supremacy proposals based on boson sampling.
Author Michał Oszmaniec (FMPI / ITPA) Michał Oszmaniec,, - Institute of Theoretical Physics and Astrophysics , Daniel J. Brod Daniel J. Brod,, - Journal series New Journal of Physics, ISSN , e-ISSN 1367-2630, (A 40 pkt) Issue year 2018 Vol 20 No 9 Pages 1-27 Publication size in sheets 1.3 Keywords in English boson sampling, quantum computing, quantum optics, linear optics, classical simulation DOI DOI:10.1088/1367-2630/aadfa8 URL https://doi.org/10.1088/1367-2630/aadfa8 Language en angielski License Journal (articles only); published final; Uznanie Autorstwa (CC-BY); with publication Score (nominal) 40 Score Ministerial score = 40.0, 10-10-2018, ArticleFromJournalMinisterial score (2013-2016) = 40.0, 10-10-2018, ArticleFromJournal Publication indicators WoS Impact Factor: 2016 = 3.786 (2) - 2016=3.637 (5) Citation count*
Cite | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.855979859828949, "perplexity": 2962.720537547057}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039747024.85/warc/CC-MAIN-20181121032129-20181121054129-00289.warc.gz"} |
http://mathhelpforum.com/discrete-math/273649-probability.html | 1. ## probability
We choose a point (x,y) from analytic plane. What is the probability
that x>y?
2. ## Re: probability
"Analytic plane"? Do you mean that (x, y) is a Cartesian coordinate system? Since this problem is symmetric in x and y, and the line y= x has measure 0, the probability that y> x is 1/2.
3. ## Re: probability
Many Thanks.Yes it is 1/2. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9870197772979736, "perplexity": 1622.0023894584913}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945660.53/warc/CC-MAIN-20180422212935-20180422232935-00476.warc.gz"} |
http://nrich.maths.org/6411 | ### Understanding Hypotheses
This article explores the process of making and testing hypotheses.
# What's Your Mean?
##### Stage: 5 Challenge Level:
The probability density functions for two related, but unknown, distributions are given in the following accurately plotted chart.
It is known that the means of the distributions are whole numbers, and that the two pdfs only have a single turning point.
By numerically estimating the required integrals, what can you deduce with certainty about the two means? | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8366683125495911, "perplexity": 1363.7156362033006}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049278244.7/warc/CC-MAIN-20160524002118-00058-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/weak-form-of-the-poisson-problem.745171/ | # Weak Form of the Poisson Problem
1. Mar 25, 2014
### Morberticus
Hi,
I know the weak form of the Poisson problem
$\nabla^2 \phi = -f$
looks like
$\int \nabla \phi \cdot \nabla v = \int f v$
for all suitable $v$. Is there a similarly well-known form for the slightly more complicated poisson problem?
$\nabla (\psi \nabla \phi ) = -f$
I am writing some finite element code and variational/weak forms are very handy.
Last edited: Mar 25, 2014
2. Mar 25, 2014
### pasmith
By the product rule
$$\int_V v\nabla \cdot(\psi \nabla \phi)\,dV = \int_V\nabla\cdot(v\psi \nabla \phi) - \psi (\nabla \phi) \cdot (\nabla v)\,dV = \int_{\partial V} v\psi \nabla \phi \cdot dS - \int_V\psi (\nabla \phi) \cdot (\nabla v)\,dV$$
and hence the weak form of $\nabla \cdot(\psi\nabla\phi) = - f$ is
$$\int_V \psi (\nabla \phi) \cdot (\nabla v)\,dV = \int_V fv\,dV$$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9955335855484009, "perplexity": 2726.5470502136827}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886104172.67/warc/CC-MAIN-20170817225858-20170818005858-00395.warc.gz"} |
http://mymathforum.com/calculus/341185-second-derivative-test-conclusions.html | My Math Forum Second derivative test conclusions
Calculus Calculus Math Forum
July 15th, 2017, 11:02 AM #1 Senior Member Joined: Nov 2015 From: United States of America Posts: 167 Thanks: 21 Math Focus: Calculus and Physics Second derivative test conclusions Hello forum, In multivariable calculus, when finding critical points and utilizing the second derivative test, if you are trying to determine if a critical point is a max, min, or saddle, you find D = D(a,b) = $\dfrac{\partial^2 f}{\partial x^2}$ $\dfrac{\partial^2 f}{\partial y^2}$ - $(\dfrac{\partial^2 f}{\partial xy})^2$ If D is any real value between negative and positive infinity, but $\dfrac{\partial^2 f}{\partial x^2}$ = 0, what could I conclude about the second derivative test here? My book only gives me cases for when $\dfrac{\partial^2 f}{\partial x^2}$ > 0 or $\dfrac{\partial^2 f}{\partial x^2}$ < 0. Thank you for taking the time to read my post and help me out. Jacob
July 15th, 2017, 11:29 AM #2 Senior Member Joined: Oct 2009 Posts: 428 Thanks: 144 The test in inconclusive. Compare with a real valued function $f:\mathbb{R}\rightarrow \mathbb{R}$ with $f'(a) = f''(a) = 0$, then it is also inconclusive. For example, take $f(x) = x^3$, then we have a saddle at $0$. While if $f(x) = x^4$, then we have a maximum at $0$. Note that in both cases, $f'(0) = f''(0) = 0$. To conclude whether you have a saddle, minimum or maximum, you'll need to check higher derivatives. Thanks from SenatorArmstrong
July 15th, 2017, 11:33 AM #3 Senior Member Joined: Oct 2009 Posts: 428 Thanks: 144 Note that if $H:= f_{xx}f_{yy} - (f_{xy})^2 > 0$, then $f_{xx}$ has to be nonzero. If $f_{xx} = 0$, then $H = -(f_{xy})^2 < 0$. Thanks from SenatorArmstrong
July 15th, 2017, 01:12 PM #4
Senior Member
Joined: Nov 2015
From: United States of America
Posts: 167
Thanks: 21
Math Focus: Calculus and Physics
Quote:
Originally Posted by Micrm@ss The test in inconclusive. Compare with a real valued function $f:\mathbb{R}\rightarrow \mathbb{R}$ with $f'(a) = f''(a) = 0$, then it is also inconclusive. For example, take $f(x) = x^3$, then we have a saddle at $0$. While if $f(x) = x^4$, then we have a maximum at $0$. Note that in both cases, $f'(0) = f''(0) = 0$. To conclude whether you have a saddle, minimum or maximum, you'll need to check higher derivatives.
Thanks a lot for helping me out.
What could I conclude from say $\dfrac{\partial^3 f}{\partial x^3}$ or $\dfrac{\partial^3 f}{\partial y^3}$ ?
For example... $f(x,y) = xy^2 + x^2 y + 8xy$
Graphically, I see there is a critical point at $f(x,y) = f(0,0)$
Also algebraically, $\dfrac{\partial f}{\partial x} = y^2 + 2xy+ 8y$
By factoring the $y$ out, I noticed that $\dfrac{\partial f}{\partial x} =y^2 + 2xy+ 8y = 0$ , when $y=0$
The same can be said about $\dfrac{\partial f}{\partial y}$ except this time $x$ will be factored out.
$\dfrac{\partial f}{\partial y} = x^2 + 2xy + 8x = 0$ when $x=0$.
$\dfrac{\partial f^2}{\partial y^2} = 2x$ and $\dfrac{\partial f^2}{\partial x^2}=2y$
So when $f(x,y) = f(0,0)$ the second derivative test is inconclusive for those values. Additionally, $\dfrac{\partial^3 f}{\partial x^3}$ and $\dfrac{\partial^3 f}{\partial y^3} = 0$
What would be an advisable approach at this point in the problem to help drive the point home that $(0,0)$ is a critical point on $f(x,y)$. Unless it is not a critical point and I made a mistake?
Thanks a ton,
Jacob
July 15th, 2017, 01:29 PM #5
Senior Member
Joined: Oct 2009
Posts: 428
Thanks: 144
Quote:
Originally Posted by SenatorArmstrong Thanks a lot for helping me out. What could I conclude from say $\dfrac{\partial^3 f}{\partial x^3}$ or $\dfrac{\partial^3 f}{\partial y^3}$ ? For example... $f(x,y) = xy^2 + x^2 y + 8xy$ Graphically, I see there is a critical point at $f(x,y) = f(0,0)$ Also algebraically, $\dfrac{\partial f}{\partial x} = y^2 + 2xy+ 8y$ By factoring the $y$ out, I noticed that $\dfrac{\partial f}{\partial x} =y^2 + 2xy+ 8y = 0$ , when $y=0$ The same can be said about $\dfrac{\partial f}{\partial y}$ except this time $x$ will be factored out. $\dfrac{\partial f}{\partial y} = x^2 + 2xy + 8x = 0$ when $x=0$. $\dfrac{\partial f^2}{\partial y^2} = 2x$ and $\dfrac{\partial f^2}{\partial x^2}=2y$ So when $f(x,y) = f(0,0)$ the second derivative test is inconclusive for those values. Additionally, $\dfrac{\partial^3 f}{\partial x^3}$ and $\dfrac{\partial^3 f}{\partial y^3} = 0$ What would be an advisable approach at this point in the problem to help drive the point home that $(0,0)$ is a critical point on $f(x,y)$. Unless it is not a critical point and I made a mistake? Thanks a ton, Jacob
But $f_{xy}\neq 0$, so $H = f_{xx} f_{yy} - (f_{xy})^2 < 0$. So the second derivative test works. It only doesn't work when $H=0$.
July 15th, 2017, 01:53 PM #6
Senior Member
Joined: Nov 2015
From: United States of America
Posts: 167
Thanks: 21
Math Focus: Calculus and Physics
Quote:
Originally Posted by Micrm@ss But $f_{xy}\neq 0$, so $H = f_{xx} f_{yy} - (f_{xy})^2 < 0$. So the second derivative test works. It only doesn't work when $H=0$.
Okay thank you. And since in my case $H<0$ it is not a local maximum or minimum. That is strange though, since wolfram does consider it a critical point.
July 15th, 2017, 01:54 PM #7
Senior Member
Joined: Oct 2009
Posts: 428
Thanks: 144
Quote:
Originally Posted by SenatorArmstrong Okay thank you. And since in my case $H<0$ it is not a local maximum or minimum. That is strange though, since wolfram does consider it a critical point.
It's a saddle point. That's counted as a critical point.
July 15th, 2017, 02:22 PM #8
Senior Member
Joined: Nov 2015
From: United States of America
Posts: 167
Thanks: 21
Math Focus: Calculus and Physics
Quote:
Originally Posted by Micrm@ss It's a saddle point. That's counted as a critical point.
Thanks for all the help
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https://kar.kent.ac.uk/53658/ | # Forecasting with the Standardized Self-Perturbed Kalman Filter
Grassi, Stefano, Nonejad, Nima, Santucci de Magistris, Paolo (2016) Forecasting with the Standardized Self-Perturbed Kalman Filter. Journal of Applied Econometrics, 32 (2). pp. 318-341. ISSN 0883-7252. E-ISSN 1099-1255. (doi:10.1002/jae.2522) (KAR id:53658)
PDF Author's Accepted Manuscript
Language: English
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Official URL
http://dx.doi.org/10.1002/jae.2522
## Abstract
We propose and study the finite-sample properties of a modified version of the self-perturbed Kalman filter of Park and Jun (1992) for the on-line estimation of models subject to parameter instability. The perturbation term in the updating equation of the state covariance matrix is now weighted by the estimate of the measurement error variance. This avoids the calibration of a design parameter as the perturbation term is scaled by the level of uncertainty in the data. It is shown by Monte Carlo simulations that this perturbation method is associated with a good tracking of the dynamics of the parameters compared to other on-line, classical and Bayesian methods. The standardized self-perturbed Kalman filter is adopted to forecast the equity premium on the S&P 500 index under several model specifications, and determine the extent to which realized volatility
can be used to predict excess returns.
Item Type: Article 10.1002/jae.2522 TVP models, Self-Perturbed Kalman Filter, Forecasting, Equity Premium, Realized Variance H Social Sciences > H Social Sciences (General) Faculties > Social Sciences > School of Economics Stefano Grassi 09 Jan 2016 22:28 UTC 10 Feb 2020 12:14 UTC https://kar.kent.ac.uk/id/eprint/53658 (The current URI for this page, for reference purposes)
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http://en.wikipedia.org/wiki/Closure_(topology) | # Closure (topology)
For other uses, see Closure (disambiguation).
In mathematics, the closure of a subset S in a topological space consists of all points in S plus the limit points of S. The closure of S is also defined as the union of S and its boundary. Intuitively, these are all the points in S and "near" S. A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior.
## Definitions
### Point of closure
For S a subset of a Euclidean space, x is a point of closure of S if every open ball centered at x contains a point of S (this point may be x itself).
This definition generalises to any subset S of a metric space X. Fully expressed, for X a metric space with metric d, x is a point of closure of S if for every r > 0, there is a y in S such that the distance d(x, y) < r. (Again, we may have x = y.) Another way to express this is to say that x is a point of closure of S if the distance d(x, S) := inf{d(x, s) : s in S} = 0.
This definition generalises to topological spaces by replacing "open ball" or "ball" with "neighbourhood". Let S be a subset of a topological space X. Then x is a point of closure (or adherent point) of S if every neighbourhood of x contains a point of S.[1] Note that this definition does not depend upon whether neighbourhoods are required to be open.
### Limit point
The definition of a point of closure is closely related to the definition of a limit point. The difference between the two definitions is subtle but important — namely, in the definition of limit point, every neighborhood of the point x in question must contain a point of the set other than x itself.
Thus, every limit point is a point of closure, but not every point of closure is a limit point. A point of closure which is not a limit point is an isolated point. In other words, a point x is an isolated point of S if it is an element of S and if there is a neighbourhood of x which contains no other points of S other than x itself.[2]
For a given set S and point x, x is a point of closure of S if and only if x is an element of S or x is a limit point of S (or both).
### Closure of a set
The closure of a set S is the set of all points of closure of S, that is, the set S together with all of its limit points.[3] The closure of S is denoted cl(S), Cl(S), $\scriptstyle\bar{S}$ or $\scriptstyle S^-$. The closure of a set has the following properties.[4]
• cl(S) is a closed superset of S.
• cl(S) is the intersection of all closed sets containing S.
• cl(S) is the smallest closed set containing S.
• cl(S) is the union of S and its boundary ∂(S).
• A set S is closed if and only if S = cl(S).
• If S is a subset of T, then cl(S) is a subset of cl(T).
• If A is a closed set, then A contains S if and only if A contains cl(S).
Sometimes the second or third property above is taken as the definition of the topological closure, which still make sense when applied to other types of closures (see below).[5]
In a first-countable space (such as a metric space), cl(S) is the set of all limits of all convergent sequences of points in S. For a general topological space, this statement remains true if one replaces "sequence" by "net" or "filter".
Note that these properties are also satisfied if "closure", "superset", "intersection", "contains/containing", "smallest" and "closed" are replaced by "interior", "subset", "union", "contained in", "largest", and "open". For more on this matter, see closure operator below.
## Examples
Consider a sphere in 3 dimensions. Implicitly there are two regions of interest created by this sphere; the sphere itself and its interior (which is called an open 3-ball). It is useful to be able to distinguish between the interior of 3-ball and the surface, so we distinguish between the open 3-ball, and the closed 3-ball - the closure of the 3-ball. The closure of the open 3-ball is the open 3-ball plus the surface.
• In any space, $\varnothing=\mathrm{cl}(\varnothing)$.
• In any space X, X = cl(X).
Giving R and C the standard (metric) topology:
• If X is the Euclidean space R of real numbers, then cl((0, 1)) = [0, 1].
• If X is the Euclidean space R, then the closure of the set Q of rational numbers is the whole space R. We say that Q is dense in R.
• If X is the complex plane C = R2, then cl({z in C : |z| > 1}) = {z in C : |z| ≥ 1}.
• If S is a finite subset of a Euclidean space, then cl(S) = S. (For a general topological space, this property is equivalent to the T1 axiom.)
On the set of real numbers one can put other topologies rather than the standard one.
• If X = R, where R has the lower limit topology, then cl((0, 1)) = [0, 1).
• If one considers on R the discrete topology in which every set is closed (open), then cl((0, 1)) = (0, 1).
• If one considers on R the trivial topology in which the only closed (open) sets are the empty set and R itself, then cl((0, 1)) = R.
These examples show that the closure of a set depends upon the topology of the underlying space. The last two examples are special cases of the following.
• In any discrete space, since every set is closed (and also open), every set is equal to its closure.
• In any indiscrete space X, since the only closed sets are the empty set and X itself, we have that the closure of the empty set is the empty set, and for every non-empty subset A of X, cl(A) = X. In other words, every non-empty subset of an indiscrete space is dense.
The closure of a set also depends upon in which space we are taking the closure. For example, if X is the set of rational numbers, with the usual relative topology induced by the Euclidean space R, and if S = {q in Q : q2 > 2, q > 0}, then S is closed in Q, and the closure of S in Q is S; however, the closure of S in the Euclidean space R is the set of all real numbers greater than or equal to $\sqrt2.$
## Closure operator
A closure operator on a set X is a mapping of the power set of X, $\mathcal{P}(X)$, into itself which satisfies the Kuratowski closure axioms.
Given a topological space $(X, \mathcal{T})$, the mapping : SS for all SX is a closure operator on X. Conversely, if c is a closure operator on a set X, a topological space is obtained by defining the sets S with c(S) = S as closed sets (so their complements are the open sets of the topology).[6]
The closure operator is dual to the interior operator o, in the sense that
S = X \ (X \ S)o
and also
So = X \ (X \ S)
where X denotes the underlying set of the topological space containing S, and the backslash refers to the set-theoretic difference.
Therefore, the abstract theory of closure operators and the Kuratowski closure axioms can be easily translated into the language of interior operators, by replacing sets with their complements.
The set $S$ is closed if and only if $Cl(S)=S$. In particular, the closure of the empty set is the empty set, and the closure of $X$ itself is $X$. The closure of an intersection of sets is always a subset of (but need not be equal to) the intersection of the closures of the sets. In a union of finitely many sets, the closure of the union and the union of the closures are equal; the union of zero sets is the empty set, and so this statement contains the earlier statement about the closure of the empty set as a special case. The closure of the union of infinitely many sets need not equal the union of the closures, but it is always a superset of the union of the closures.
If $A$ is a subspace of $X$ containing $S$, then the closure of $S$ computed in $A$ is equal to the intersection of $A$ and the closure of $S$ computed in $X$: $Cl_A(S) = A\cap Cl_X(S)$. In particular, $S$ is dense in $A$ if and only if $A$ is a subset of $Cl_X(S)$.
## Categorical interpretation
One may elegantly define the closure operator in terms of universal arrows, as follows.
The powerset of a set X may be realized as a partial order category P in which the objects are subsets and the morphisms are inclusions $A \to B$ whenever A is a subset of B. Furthermore, a topology T on X is a subcategory of P with inclusion functor $I: T \to P$. The set of closed subsets containing a fixed subset $A \subseteq X$ can be identified with the comma category $(A \downarrow I)$. This category — also a partial order — then has initial object Cl(A). Thus there is a universal arrow from A to I, given by the inclusion $A \to Cl(A)$.
Similarly, since every closed set containing X \ A corresponds with an open set contained in A we can interpret the category $(I \downarrow X \setminus A)$ as the set of open subsets contained in A, with terminal object $int(A)$, the interior of A.
All properties of the closure can be derived from this definition and a few properties of the above categories. Moreover, this definition makes precise the analogy between the topological closure and other types of closures (for example algebraic), since all are examples of universal arrows.
## Notes
1. ^ Schubert, p. 20
2. ^ Kuratowski, p. 75
3. ^ Hocking Young, p. 4
4. ^ Croom, p. 104
5. ^ Gemignani, p. 55, Pervin, p. 40 and Baker, p. 38 use the second property as the definition.
6. ^ Pervin, p. 41
## References
• Baker, Crump W. (1991), Introduction to Topology, Wm. C. Brown Publisher, ISBN 0-697-05972-3
• Croom, Fred H. (1989), Principles of Topology, Saunders College Publishing, ISBN 0-03-012813-7
• Gemignani, Michael C. (1990) [1967], Elementary Topology (2nd ed.), Dover, ISBN 0-486-66522-4
• Hocking, John G.; Young, Gail S. (1988) [1961], Topology, Dover, ISBN 0-486-65676-4
• Kuratowski, K. (1966), Topology I, Academic Press
• Pervin, William J. (1965), Foundations of General Topology, Academic Press
• Schubert, Horst (1968), Topology, Allyn and Bacon | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 30, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9505622386932373, "perplexity": 259.83714467375006}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657140890.97/warc/CC-MAIN-20140914011220-00330-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://portlandpress.com/biochemj/article-abstract/153/2/191/10799/Mobility-of-sodium-dodecyl-sulphate-protein | Reduced and unreduced lysozyme aggregates formed by formaldehyde cross-linking comprise a set of model compounds for studying the effects of protein conformation on the electrophoretic mobilities of sodium dodecyl sulphate-protein complexes. The reduced aggregates were indistinguisable from normal proteins, but the unreduced aggregates migrated anomalously fast by about 14%. Contrary to expectations, plots of logarithm Rf versus Kr (retardation coefficient) failed to reveal an unusual conformation for the unreduced aggregates. Thus the anomalous mobility caused by several intramolecular disulphide bonds escaped detection by the above two diagnostic plots. Also included in this paper is a discussion of the implications of these results with regard to current models for sodium dodecyl sulphate-protein complexes.
This content is only available as a PDF.
You do not currently have access to this content. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8618865609169006, "perplexity": 4163.329219923873}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668539.45/warc/CC-MAIN-20191114205415-20191114233415-00078.warc.gz"} |
https://ru.scribd.com/document/371114997/6ffc8cf65c32f101c8ed97374635df25-c34abad318bdb9df77011169a21da5a7 | Вы находитесь на странице: 1из 2
1.
A translational mechanical system is shown below: mass M 1 , mass M 2 , spring with stiffness K and damper with damping constant B. A force f(t) is applied to M1 as shown below. The spring is not deflected when x 1 =0.
x
1
B
M 1
f(t)
x
2
K
M
2
(1) Draw the free body diagram for M 1 and M 2 . Write the equations of motion for this system. (2) Write the input output form model with f(t) as the input and x 1 as the output.
1
2. A rotational mechanical system is shown below: inertia J 1 and J 2 , a gear set with ratio N (
2
N
), a
damper with damping constant B, the connections between the inertia and gear set are rigid. There is no inertia for the gear itself. A torque T(t) is applied to J 1 as shown below.
T(t)
1
2
J 1
Gear
J 2
B
2
.
(1) Write the state variable form model using variable
(2) Draw the block diagram for the above state variable form model.
3. An electrical circuit is shown below: voltage source E ( t ) , resistor R, inductor L and capacitor C.
I L
I c
R
E
( t )
L
V
C
C
(1) Write the state variable form model using variables I L , V C .
I
(2) Write the input output form model with E ( t ) as the input and
L as the output.
1.
2.
3.
Given a second-order system y6 y8 y u (t ) , where y (0) y(0) 0 and the input u (t ) is a unit step function.
a) Calculate the natural frequency and damping ratio.
b) Solve the output y ( t ) for the above dynamic system.
c) What is the steady state response of the above system?
Given a transfer function
the output.
(
H s
)
(
Y s
)
s 5
X ( s ) s
2
7
s
12
, where X ( s ) is the input and Y ( s ) is
a) Calculate the poles and zeros of the transfer function. Draw the pole zero plot.
b) Calculate the frequency response function
angle () input x (t ) ?
H
( y j ) (t ) sin t
, the magnitude
M ()
and the phase
. If the desired steady state output
, what is the appropriate
Given a nonlinear system
2
yy
sin
y
0
, where y (0) 1, y(0) 0 .
a) Let the operating point y 0 . Develop a linear model for the above nonlinear system at the operating point. Also indicate the initial conditions of the linear model.
b) Is the linear system obtained in (a) stable? Justify your answer. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9627620577812195, "perplexity": 1656.9864073090628}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107891228.40/warc/CC-MAIN-20201026115814-20201026145814-00097.warc.gz"} |
https://www.coursehero.com/file/73466915/Orgo-2-Lab-Report-12docx/ | # Orgo 2 Lab Report 12.docx - Experiment 33 B Oxidation of an...
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Experiment 33 B: Oxidation of an Alcohol: 9-Fluorenone Objective The lab works to explain the basic techniques of an oxidation reaction. This reaction involves the oxidation of a secondary alcohol to a ketone through the use of an oxidizing agent. The oxidizing reagent in this lab was sodium hypochlorite. It has an available chlorine with the same oxidizing capacity relative to molecular chlorine. The reaction occurs by removal of hydrogens and forming a second carbon to oxygen bond. So that the carbon is now at an oxidation level of two. This reaction was done on a 1.5x scale Stirring was necessary for the reaction to occur. The reaction progress was monitored by TLC. There are three spots on the TLC plate a 9-fluoronol standard, a co-spot and a crude reaction mixture. TLC is done to ensure the reaction is completed and there is none of the starting material present. UV light was used to assess the TLC plates. 9- fluorenol is more polar than 9-fluorenone because of hydrogen bonding. The difference in polarity contributes to the different Rf values. The more polar the lower the Rf so 9-fluorenol will have a lower Rf than 9-fluoreone. The stronger a compound is bound, the slower it moves up the TLC plate. So polar compounds move slower. This reaction occurred under a gentle reflux and was and stirred. Hexane was the solvent used for the extraction procedure. The organic layer was extracted and a pastur filter pipette and drying procedures were used. The product was then | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8180322051048279, "perplexity": 3008.113644921323}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300343.4/warc/CC-MAIN-20220117061125-20220117091125-00315.warc.gz"} |
https://www.physicsforums.com/threads/left-righthanded-fermions.225050/ | # Left-/righthanded fermions
263
70
## Main Question or Discussion Point
Hey
I have a basic question about the Standard Model. In this forum and on other places the expression left-/righthanded fermions. Can someone explain the difference between these two types of fermions.
Related High Energy, Nuclear, Particle Physics News on Phys.org
neu
220
1
nrqed
Homework Helper
Gold Member
3,540
181
Hey
I have a basic question about the Standard Model. In this forum and on other places the expression left-/righthanded fermions. Can someone explain the difference between these two types of fermions.
It's a bit confusing at first because there are two concepts involved and people use the term right and left handed in two different contexts.
There is something called "chirality" and something called "helicity". Unfortunately, left and right handed is used to refer to eigenstates of chirality sometimes and of helicity sometimes.
The chirality operator is $$\gamma_5$$. You can define define positive and negative chirality fermions as the ones that are eigenstates of the chirality operator (it turns out that the eigenvalues are plus or minus 1)
$$\gamma_5 \Psi= \pm \Psi$$.
Those eigenstates are called left and right handed fermions unfortunately (because it has nothing to do with another concept of left and right associated to helicity..see below).
In general, a Dirac fermion is not a chirality eigenstate.
So, why should we care? We have to cae because the weak interaction couples the weak gauge bosons to chiral states! So we can't couple the weak gauge bosons directly to Dirac fermions.
However, one can always construct chiral eigenstates out of an arbitrary Dirac fermion by using what we call the projectors
$$P_\pm = (1 \pm \gamma_5)/2$$ .
Then, for any Dirac fermion $$\Psi$$,
the projection $$P_+ \Psi$$ is automatically an eigenstate of the chirality operator with eigenvalue +1 ( check it! It's obvious if you use the fact that $$\gamma_5^2 = \gamma_5$$). And people call this a right-handed state so they write
$$\Psi_R = P_+ \Psi$$
Likewise, we can get a left-handed state using
$$\Psi_L = P_- \Psi$$
Helcity is a totally different concept. There is something called a helicity operator that measures the projection of the spin along the motion of the particle. The only states which are helicity eigenstates are massless states. It turns out that for a massless particle, the eigenstates of the helicity operator are the same as the eigenstates of the chirality operator which is probably why people use right-handed and left-handed in the two contexts.
263
70
Okay. Thank you for the explanation and the link!
441
2
Is there an operator that measures the spin component not along the momentum of the fermion but say perpendicular to it?
In the usual non-relativistic QM, you have Sz but also Sx, and Sy operators. Why something similar is not considered for the solutions of Dirac's equation?
Hans de Vries
Gold Member
1,085
21
Is there an operator that measures the spin component not along the momentum of the fermion but say perpendicular to it?
In the usual non-relativistic QM, you have Sz but also Sx, and Sy operators. Why something similar is not considered for the solutions of Dirac's equation?
Yes, this is simply done with the Pauli matrices.
The reason that people generally talk about the spin being along the momentum
direction is because in high energy physics the particles move very close to c.
The spin-component along the momentum increases the closer the particle gets to
the speed of light. The spin-components perpendicular to the momentum however
stay constant. This is true for any object, also for a rotating rock for example.
Regards, Hans
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2K | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9186322093009949, "perplexity": 649.2752214599541}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540511946.30/warc/CC-MAIN-20191208150734-20191208174734-00329.warc.gz"} |
http://tex.stackexchange.com/questions/148572/cant-compile-anymore-after-trying-to-install-dsfont-in-miktex-2-8 | # Can't compile anymore after trying to install dsfont in MiKTeX 2.8 [closed]
I'm currently writing my master thesis with MiKTeX 2.8. Now I wanted to install `dsfont`. But since 2.8 seems not to be supported anymore, I tried to install the package manually. I downloaded the `doublestroke` package, which contains `dsfont`, here and followed these instructions:
• I already created the folder `C:\localtexmf` a few months ago
• I created a new folder `dsfont` in `C:\localtexmf\tex\latex`
• I put the `dsfont.sty` file into that folder
• In MiKTeX settings, I pressed the `refresh FNDB` and the `Update formats` buttons
• I loaded the package via `\usepackage{dsfont}` in my main file
That did not work. I got no error messages, but 81 warnings. Since I did not know why it didn't work, I also followed these instructions:
• I executed `initexmf --edit-config-file=updmap.cfg`
• then I entered ```# <font name> or <package name> or what fits better for you Map dsfont.map``` into the file
• I executed `initexmf -u` as well as `initexmf --mkmaps`
• again, I pressed the `refresh FNDB` and the `Update formats` buttons
Still didn't work. Even worse, even if I don't try to load `dsfont` in my main file, the document is not compiled. That means that I can't keep working on my thesis even without using dsfont. The problem seems to be with BibTeX, because I get error messages from BibTeX:
I found no `\citation` commands
I found no `\bibdata`
Note that there is a folder for `biblatex` in the `localtexmf` folder: `C:\localtexmf\tex\latex\biblatex`. But I'm not sure that I really needed that one for bibtex to work. Furthermore, since I got these problems, there is also a new file called `Masterarbeit.synctex(busy)` in my main folder (`Masterarbeit.tex` is my main document).
So, does anybody know how to make it work again? This is pretty important, because I don't have much time left and I don't want to risk to mess everything up with a new installation of MiKTeX. What did I do wrong during my installation of `dsfont`? Please help me!
EDIT: uploaded the log file from Latex and also bibtex
UPDATE: Installed MikTeX 2.9 on a different PC, still the same errors/warnings. Something is wrong in the way I'm creating my Bib, but I don't know what since I did not change anything concerning my Bib.
-
## closed as off-topic by Speravir, Martin Schröder, mafp, Guido, cmhughesFeb 7 at 0:54
• This question does not fall within the scope of TeX, LaTeX or related typesetting systems as defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.
Looks like everything is already messed up. It'll probably be quicker and easier to remove miktex 2.8 and do a clean install of miktex 2.9 and/or TeX Live 2013 (including `dsfont`). Perhaps somebody has a swift solution, but maybe you'd start the download in the meantime... – DG' Dec 5 '13 at 20:07
The bibtex messages are warnings not errors. Without more informations egg log-files, it is not possible to say what wrong – Ulrike Fischer Dec 5 '13 at 20:24
If you have internet, download MiKTeX version 2.9 and install it and update. This would be the easy way out. Did you run `updmap`? – azetina Dec 5 '13 at 20:45
You need someone which can look at your system and sort it out. – Ulrike Fischer Dec 6 '13 at 12:47
This question appears to be off-topic because according to comments it seems to be caused by a fundamental problem of OP's operating system. – Speravir Feb 6 at 23:39 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8533399701118469, "perplexity": 1967.2148672159715}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931008105.47/warc/CC-MAIN-20141125155648-00206-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/1544782/if-f-in-lp-1e-is-bounded-then-f-in-lp-2-for-any-p-2p-1?noredirect=1 | If $f \in L^{p_1}(E)$ is bounded then $f\in L^{p_2}$ for any $p_2>p_1$
Show that if $f$ is a bounded function on $E$ that belongs to $L^{p_1}(E)$ then it belongs to $L^{p_2}(E)$ for any $p_2>p_1$
How can I insert argument about the boundedness of $f$? I can prove $L^{p_2} \subset L^{p_1}$ but I am stuck here. Please help.
• i am thinking define E1={x: f(x)≤ 1} and E2={{x: f(x) ≥1} – Biswa Nov 24 '15 at 19:06
• There's no inclusion between the two spaces unless the measure of $E$ is finite. – Silvia Ghinassi Nov 24 '15 at 19:10
• its a problem of royden fitzpatrick sec7.2 problem 13. the only condition is f is a bounded function – Biswa Nov 24 '15 at 19:13
Let $f \in L^{p_1}(E)$ bounded. Then there exists $M\geq 0$ such that $\sup_{x \in E} |f(x)| \leq M$ and $\|f\|_{p_1}^{p_1}=\int_E |f(x)|^{p_1}\,dx < \infty$.
Case 1: $p_2<\infty$
For $p_2 > p_1$, we have \begin{align} \|f\|_{p_2}^{p_2}& =\int_E |f(x)|^{p_2}\,dx \\ &= \int_E |f(x)|^{p_2-p_1}|f(x)|^{p_1}\,dx \\ & \leq \left(\sup_{x \in E} |f(x)|^{p_2-p_1}\right)\int_E |f(x)|^{p_1}\,dx \\ & \leq \left(\sup_{x \in E} |f(x)|\right)^{p_2-p_1}\int_E |f(x)|^{p_1}\,dx \\ & \leq M^{p_2-p_1} \|f\|_{p_1}^{p_1} < \infty \end{align}
so that $\|f\|_{p_2}^{p_2} < \infty$ and hence $f \in L^{p_2}(E)$.
Note that we have used the fact that $p_2-p_1>0$ to claim $\sup_{x \in E} |f(x)|^{p_2-p_1}\leq \left(\sup_{x \in E} |f(x)|\right)^{p_2-p_1}$.
Case 2: $p_2=\infty$
Since $f$ is bounded, $\|f\|_{\infty}=\operatorname{ess sup}_{x \in E} |f(x)| \leq \sup_{x \in E} |f(x)| \leq M< \infty$ by hypothesis, so $f \in L^{\infty}(E)$.
• thanks so much.such a nice proof it is.that looks alright.but what about if P2=∞? there is no restriction on P2 – Biswa Nov 24 '15 at 19:33
• See my edit. – Silvia Ghinassi Nov 24 '15 at 19:38
• thank you so much.My confusion has gone – Biswa Nov 24 '15 at 19:41
• You're welcome, @Biswa. Since you are a new user, I thought I should let you know about accepting and/or upvoting answers, see here. – Silvia Ghinassi Nov 24 '15 at 19:58
Hint: If $|f|\le 1,$ then $|f|^{p_2} \le |f|^{p_1}.$
• The size of $E$ can be unbounded. You probably cannot use that. – user398843 Oct 31 '18 at 21:55
• @user398843 We know $f\in L^{p_1}$ and $f$ is bounded. The result follows easily – zhw. Oct 31 '18 at 22:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999034404754639, "perplexity": 646.5045134817169}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027317037.24/warc/CC-MAIN-20190822084513-20190822110513-00448.warc.gz"} |
https://www.arxiv-vanity.com/papers/0709.0197/ | # Convective and non-convective mixing in AGB stars
Falk Herwig\altaffilmark1,2, Bernd Freytag\altaffilmark1,3, Tyler Fuchs\altaffilmark4, James P. Hansen\altaffilmark4, Robert M. Hueckstaedt\altaffilmark1, David H. Porter\altaffilmark4, Francis X. Timmes\altaffilmark1, Paul R. Woodward\altaffilmark4
###### Abstract
We review the current state of modeling convective mixing in AGB stars. The focus is on results obtained through multi-dimensional hydrodynamic simulations of AGB convection, both in the envelope and the unstable He-shell. Using two different codes and a wide range of resolutions and modeling assumptions we find that mixing across convective boundaries is significant for He-shell flash convection. We present a preliminary quantitative analysis of this convectively induced extra mixing, based on a sub-set of our simulations. Other non-standard mixing will be discussed briefly.
\altaffiltext
1Los Alamos National Laboratory, Los Alamos, NM, USA \altaffiltext2Keele Astrophysics Group, School of Physical and Geographical Sciences, Keele University, UK \altaffiltext3Centre de Recherche Astronomique de Lyon, Lyon, France \altaffiltext4Laboratory for Computational Science & Engineering, University of Minnesota, USA
## 1 Introduction
Our understanding of the physics of mixing in stars especially AGB stars (Iben & Renzini, 1983; Herwig, 2005), is not in a satisfying state. We do get many global properties right, but the list of things that models can not accurately account for is getting longer as the observations are becoming more detailed and numerous. The lack of predictive models for mixing and consequent stellar properties and nuclear yields is severely inhibiting the usefulness of this field for helping to address some general questions in astronomy; for example in the emerging field of near-field cosmology. With better simulations we could use detailed abundance observations to precisely characterize extra-galactic populations. Thus, there is a real need for improving our understanding of convective and non-convective mixing in AGB stars.
The most important physical process for mixing in stars is convection. In 1D stellar evolution models we use the mixing-length theory (Böhm-Vitense, 1958) or some variant. The mixing-length parameter determines the geometric scale of convective eddies and is calibrated by using a solar model. However, we know for certain that the mixing length parameter is not constant throughout all phases and conditions in stellar evolution. Figure 5 in the important paper by Ludwig et al. (1999) shows the mixing-length parameter from their set of 2D radiation-hydrodynamic simulations of the outer convection layer in stars similar to the sun. These simulations show that the mixing-length parameter is very sensitive to the temperature (and thus to the depth of the convection zone), and that just within the small parameter range covered here, say within the mixing-length parameter changes by . Such a variation would change many important features in AGB simulations, most notably dredge-up and the hot-bottom burning efficiency. This has been known since first shown by Boothroyd & Sackmann (1988) and should be kept in mind when comparing dredge-up efficiency-dependent model predictions and observations. The hot-bottom burning dependence on the mixing-length parameter has implications in particular for super-AGB stars and massive low-metallicity AGB stars.
How can this situation be improved? Canuto & Mazzitelli (1991) and collaborators have suggested the Full-spectrum turbulence convection model as an alternative. This theory overcomes one important simplification of MLT: convection does not only consist of one blob size, but rather contains a spectrum of scales. Unfortunately, so far it seems that no convincing validation case for AGB envelope convection has been identified. Other uncertain input physics such us mass loss, other sources of mixing (rotation and gravity waves), and in some cases nuclear reaction rates have a similar, independent effect on the same astrophysical observable (e.g. certain abundances, like the / ratio). In addition the variability of a convection parameter studied by Ludwig et al. (1999, see above) applies here as well (see their Fig. 6).
A resolution to these problems can only come from simulations. Several years ago Porter & Woodward (2000) presented highly resolved simulations with simplyfied input physics (Fig. 1). One of their important results was that convection settles into a dominant global dipole mode, a finding that is now confirmed for fully convective spheres in core-carbon burning WDs that are about to ignite a SN Ia (Kuhlen et al., 2006). Another finding was that convection itself without any other physical mechanism leads to pulsations. These may match observed pulsations of AGB stars, but a more detailed comparison needs to be done. Other AGB envelope models in 3D were developed by Freytag (see Freytag, 2003; Höfner et al., 2005bf for more details). These models feature a more realistic outer boundary condition but are not as highly resolved as the Porter & Woodward simulations.
Porter & Woodward derived a mixing-length parameter equivalent to the velocity field from the simulations. They find . These simulations, both by Freytag and by Porter & Woodward, did not resolve the inner parts of the envelope convection, which is so crucial for nucleosynthesis. We anticipate that significant improvements of the treatment of convection properties in stellar evolution modeling can be made through hydrodynamic models with available and coming resources.
## 2 Multi-D hydrodynamic simulations of He-shell flash convection
### Motivation, codes and setup
In order to understand better nucleosyntheis in AGB stars, we have performed multi-dimensional He-shell flash convection simulations. This work has several goals. First of all, the hydrodynamics of He-shell flash convection has never been simulated before. So, we want to investigate the hydrodynamical properties and the topology of He-shell flash convection. For example, how well does MLT describe the vertical velocity profile of the convection zone? What are the dominating scales? What is the dependence on resolution and on the nuclear energy generation? Obtaining a resolved velocity distribution from hydrodynamic simulations can give a new framework to study short-lived, temperature-dependent s-process branchings fueled by the neutron source. And, most importantly, we want to study convection induced mixing across the convective boundaries. Several 1D stellar evolution studies using a parameterized recipe for convective overshooting (e.g. Herwig, 2000; Lugaro et al., 2003) have shown that overshooting at the bottom of the He-shell flash convection zone strongly affects the pulse strength, and thus the dredge-up efficiency, as well as the intershell abundance and the temperature for the s-process. Some of the predictions of stellar evolution models with convective extra mixing at the bottom of the He-shell flash convection zone have been confirmed by observations of H-deficient post-AGB stars (Werner & Herwig, 2006).
We have performed simulations using two codes. One set of simulations (see Herwig et al., 2006, for initial results) was done with the RAGE code, an explicit, compressible, Eulerian grid code. The other code (scPPM) is a PPM (Eularian, compressible grid as well) code for stellar convection that solves for perturbations to a base state defined in the problem setup. This later approach takes advantage of the fact that buoyancy driving the convection in these stellar interior environments is very small and that Mach numbers of the flow are small (). We will give more details on the scPPM code in a forthcoming paper.
For the initial setup we construct a piecewise polytropic stratification with gravity that resembles closely the actual conditions in a detailed thermal pulse stellar evolution model just before the He-shell flash peak luminosity. The driving of the convection results from a constant volume heating at the bottom of the convectively unstable region that injects the same amount of energy as the corresponding stellar model.
The stratification comprises approximately 11 pressure scale heights, half of which represent the convectively unstable region. This gives enough simulation space for stable layers both above and below the convection zone to avoid artifacts in the convection boundary simulation from simulation box boundary effects.
### Morphology and gravity waves
In Fig. 2 we show a snapshot from a 2D RAGE run on a grid. The same heating rate as in the stellar evolution model was applied. At the snapshot time the simulation has lasted for approximately 5 convective turn-over times and has thus reached convective steady-state. The initially imposed convective boundaries are well maintained, sharp and clearly visible in this snapshot. The convective flow is dominated by three to four large systems, which vertically span the entire unstable layer and are centered in the lower half of the unstable region. In the stable layers above and below the convection zone oscillations due to internal gravity waves can be seen. Through a systematic resolution study we find that the total number of large convective systems does not change over a wide range of grid sizes, down to a grid.
Gravity waves can be identified in the top and bottom stable layers. Movies of these simulations show that the g-modes in the stable layer above the convection zone are excited even before the convective motions have reached the top boundary of the unstable layer. In contrast to shallow surface convection, for example in A-type stars (Freytag et al., 1996), coherent convective systems do not cross the convective boundaries in a fashion visible in this representation. This is not surprising, because the relative stability of convective boundaries in the stellar interior is much larger than in stellar near-surface convection.
We have performed 3D simulations with both the RAGE and scPPM code. The vertical velocities in one snapshot of the 3D RAGE run are shown in Fig. 3. In the He-shell flash convection zone, convection originates through heating at the bottom, contrary to surface or envelope convection which is driven by cooling from the surface. It is interesting to note that here we see near the bottom of the convection zone (panel 2.23Mm) structures that resemble the inverse of solar granulation: cool granules with hot intergranular lanes.
Even outside the convection zone dynamic fluid motions exist, and their patterns again depend on the distance to the convective boundary. Panel 1.51Mm shows a very granular appearance with a lot of detail on small scales whereas both the panels above and below show fluctuations on larger scales. The layers most distant from the convection zone, both above and below, show a rather diffuse pattern of large-scale fluctuations.
Although the coherent convective systems do not cross the convective boundary on a scale that is any significant fraction, of the horizontal scale, this does not mean that there is no oscillation exitation and mixing across the boundary. Looking at the vertical velocity reveals how motions and oscillations in the stable and unstable layer do in fact correlate, and therefore communicate. Features in one slice have corresponding features in neighboring slices above and below inside the convection zone, even if the dominating scales are different in different layers of the convection zone. This is consistent with the observation in the 2D snapshots that convective system traverse the entire convection zone vertically. However, patterns in the vertical velocity images also show correlations between the boundary planes just inside the convection zone and the neighboring planes several hundred km out in the stable layer. Thus, while convective systems do not cross the convective boundaries, they do imprint their signature on the oscillation properties of the stable layers.
But how do properties like the vertical velocities depend on numerical resolution and numerical scheme? To address this question we compare in Fig. 4 a snapshot of the velocity field in the upper layers of the convection zone from the RAGE and scPPM simulations. While the scPPM simulation shows much more small scale structure, there are similarities in the overall pattern. Downflows are ordered in lanes surounding larger areas with upwelling flows. The more highly resolved grid of the scPPM simulation is only partly responsible for the difference. The main reason for the difference in scale distribution is the higher order of the PPM numerical scheme compared the modified Van Leer method implemented in the RAGE version used here.
The correspondence between different layers, including nearby convective and non-convective layers, can be further analysed in a series of k- diagrams of several vertical planes in the 3D RAGE run (Fig. 5). These diagrams show the distribution of power as a function of wavelength and frequency. In these diagrams the signature of convective motions shows up as an unstructured blob in the lower left part of the diagram. It is most prominent in the panels showing planes in the unstable region. However, even in the panels representing the stable layer a significant convective signature is evident. In addition, the stable layers show the characteristic signature of gravity waves, and all panels show the signature of p-modes.
We conclude that our simulations show that convection does influence the fluid flows in the neighboring stable layers, both through exciting g-mode oscillations and by forcing motions with convective wavelengths and frequencies. We now need to look at how these correspondences between fluid flows on both sides of the convective boundary translate into actual mixing.
### Mixing for He-shell flash convection
The scPPM simulation has been performed with multiple fluids representing the different abundance compositions in the three layers of our sandwich setup. In Fig. 6 we show the result of material from the top stable layer above the convection zone being entrained into the convection zone. Conceptually, such a situation may occur in He-shell flashes of extremely metal-poor stars when the convection zone reaches into the H-rich envelope, or in the very-late thermal pulse flash associated with the born-again evolution. In this simplified simulation, the effect of -gradients has been neglected as all fluids have the same molecular weight. Therefore the entrainment seen in this case is probably an upper limit. However, we do see that the distribution of the fluid from the upper stable layer in the convection zone is rather isotropic. If the fluid from above would react with the material in the convection zone we would likely be in a distributed burning regime, rather than in a flame propagation situation. Using the multi-fluid scPPM code we will in the future be able to quantify mixing across the convective boundary. In this way we can take full advantage of the high-order advection scheme implemented here (Woodward et al., 2006).
With the RAGE simulations we performed a mixing analysis based on the tracer particle technique of Freytag et al. (1996). We determined diffusion coefficients at different horizontal positions, in particular near the convective boundaries. An example for this approach (full details will be given in Freytag etal. 2006, in prep) is shown Fig. 7. The final solution of the diffusion coefficient as a function of vertical position is a composite of two approaches. Diffusion coefficients derived from the spread evolution of the entropy are more suitable for the stable layer. The evolution of the vertical coordinate is more appropriate in the convection zone. In the transition layer, both approaches give the same result. The fall-off of the diffusion coefficient has been fitted with an exponential. This approach has before been used by Freytag et al. (1996) and applied to stellar evolution calculations, first by Herwig et al. (1997). Within this framework, the convection induced mixing across the bottom convective boundary can be described by a succession of two exponential decay laws of the form where is the distance from the location at which a baseline has been determined, and is the pressure scale height (Freytag et al., 1996; Herwig, 2000). The first decay starts already somewhat inside the convection zone with , while just outside the convection zone (when D has fallen to ) the decay of mixing efficiency flattens and can be represented by . At the top boundary our initial analysis gives a single exponential decay with .
The f-value determination varies as a function of resolution within a factor of a few. However, we could not find any apparent trend, indicating that resolution may be a limiting aspect within the chosen range of simulations. Also we did not find a systematic difference between simulations with the realistic heating rate compared to those with 30 times larger heating rate. This indicates that within a range of driving energies, mixing properties will depend predominantly on the background stratification. This means that the f-value for mixing across the convective boundary remains the same for a given convective boundary until the conditions change drastically.
From the few 3D results we have, we find that the 2D/3D difference is of the same order as the dependence on resolution. Overall the 3D runs confirm the results we found in 2D.
Initial stellar evolution test calculations over a couple of thermal pulses implementing these hydrodynamic convective mixing results indicate that we recover the increased O and C intershell abundance that we found in earlier calculations using the f-overshoot for this convection zone. The simulated C and O abundances in the intershell are consistent with observations of H-deficient PG1159 and [WC]-CSPN stars (Werner & Herwig, 2006).
## 3 Non-convective mixing
Rotation has an important effect on the production of elements in AGB stars but is unfortunately not yet studied very well. Models of rotating AGB stars (Langer et al., 1999) show that with the present physics model rotation induced mixing at the convective boundary is insufficient for the formation of the -pocket for the process. Even worse, Herwig et al. (2003) showed that rotationally induced mixing may be even harmful to the -process nucleosynthsis. In models in which a pocket was introduced using the convective overshooting paradigm, rotation induced mixing of into the -pocket during the interpulse phase. The neutron exposure is well below which is far too low to reproduce well established s-process observables. acts as a neutron poison due to its large cross section. Overall, there are indications that angular momentum transport from the core to the envelope is underestimated in current models of rotating AGB stars. Therefore angular velocity gradients at the core-envelope interface, and consequently rotation induced mixing at this interface are overestimated. The -pocket is located exactly at this interface. Another indication for missing angular momentum transport is that core rotation rates of rotating AGB models are too large compared to observed rotation rates from white dwarf pulsations (Kawaler, 2003).
Magnetic fields could add angular momentum transport and reduce angular velocity gradients that cause shear mixing. However, there is another likely possibility, in particular in light of what we see in our hydrodynamic simulations. Internal gravity waves could have a similar desired effect of angular momentum transport (Talon & Charbonnel, this volume). We see them plentifully in the hydrodynamic simulations, and their effect on mixing in AGB stars has not yet been studied in sufficient detail. The only work on gravity waves in AGB stars besides the new results by Talon & Charbonnel is that by Denissenkov & Tout (2003) who show that mixing induced by these waves may provide the conditions needed for the formation of a -pocket. However, more detailed studies in this area are needed.
## 4 Conclusions
Hydrodynamic simulations of convection in AGB stars which give meaningful insight for stellar evolution models, both in the envelope and in the intershell are feasible and offer an exciting tool to study mixing. We can obtain a detailed picture of flow structures both within the unstable zone as well as in the neighboring layers. We will study in greater detail the variation of the averaged mixing efficiency for AGB envelopes that determines important evolutionary properties, such as the dredge-up efficiency as well as the hot-bottom burning efficiency. Our initial results on He-shell flash convection allow a first quantitative glimpse at mixing at and across the convective boundaries. The simulations emphasize the need to study the role of gravity waves in much greater detail. The issue of rotationally induced mixing is much more difficult to approach with multi-dimensional simultions, mainly because the flow velocities are significantly smaller than in convection. This is especially unfortunate as rotating models currently do not reproduce observables of AGB stars although these stars obviously rotate, at least their cores.
\acknowledgements
This work was carried out in part under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9099218249320984, "perplexity": 1363.3414948515094}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703514423.60/warc/CC-MAIN-20210118061434-20210118091434-00233.warc.gz"} |
https://accesspharmacy.mhmedical.com/content.aspx?bookid=2733§ionid=226711355 | ## CHAPTER OBJECTIVES
• Define and differentiate point estimation and interval estimation
• Describe important statistical distributions
• Explain the role of the central limit theorem in statistical analysis
• Explain the basic mechanics of hypothesis testing
• Explain how confidence intervals can be used to test hypotheses
• Differentiate among various types of hypothesis tests
• Explain the difference between the frequentist and Bayesian approaches to statistical inference
• Describe the basic principles of Bayesian statistical analysis
• Define and differentiate statistical significance and clinical significance
## KEY TERMINOLOGY
• Alternate hypothesis
• Bayes’ theorem
• Bayesian statistics
• Central limit theorem
• Clinical significance
• Confidence intervals
• Degrees of freedom
• Directional tests
• Empirical distribution
• Hypotheses
• Hypothesis testing
• Nondirectional tests
• Normal distribution
• Null hypothesis
• Parameters
• Point estimate
• Population
• Posterior distribution
• Power
• Prior distribution
• p-value
• Sample
• Statistic
• Statistical distribution
• Statistical estimation
• Statistical inference
• Statistical significance
• Test of difference
• Test of equivalence
• Test of noninferiority
• Test of superiority
• Type I error, or α error
• Type II error, or β error
## INTRODUCTION
Descriptive statistics provide a useful tool for presenting basic information, such as the central tendency (mean, median, or mode) and spread (standard deviation or interquartile range), of a given sample. While these are useful, the focus is often on taking the findings from a sample used for research and applying them to a target population of interest. For example, in a sample of 200 individuals, half of whom received a new medication to reduce LDL cholesterol and the other half received a placebo, the new medication reduced LDL cholesterol by 30 mg/dL. Initially, this finding may seem exciting, but subsequent steps would determine whether the observed reduction was indeed statistically significant (i.e., hypothesis testing) and provide an idea of how large the actual reduction might be in the target population of individuals with high LDL cholesterol (i.e., statistical estimation). Inferential statistics provide the tools to answer these questions.
This chapter begins with a brief discussion of statistical distributions and statistical theory supporting statistical inference. Information about basic principles of point and interval estimation is then presented followed by a discussion of hypothesis testing. A brief discussion of the Bayesian approach to statistical inference is then provided. This chapter finishes with a discussion of the importance of statistical and clinical significance in biomedical research.
## STATISTICAL DISTRIBUTIONS AND THE CENTRAL LIMIT THEOREM
A variable’s distribution is made up of all the possible values and their relative frequency of occurrence. When the values are taken from actual data and the relative frequencies of occurrence are calculated (e.g., the observed lengths of stay for patients in a hospital), this observed distribution is referred to as an empirical distribution. A statistical distribution is a type of distribution that is defined by some theoretical probability distribution.1 These statistical distributions are important since they describe the way in which random variables are expected to behave.2 They also form the ...
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https://www.physicsforums.com/threads/physics-electric-fields-can-someone-please-explain-this-to-me.472513/ | # Physics-Electric Fields: Can someone please explain this to me?
• Start date
• #1
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My professor didn't explain this well.
Question: http://i324.photobucket.com/albums/k327/ProtoGirlEXE/q1.jpg [Broken]
(part 2) http://i324.photobucket.com/albums/k327/ProtoGirlEXE/q3.jpg [Broken]
I'm completely lost on this one. I don't understand how this problem was solved.
So I'm guessing q4 is the point where you measure the forces from the other 3 points. But I thought that q3 won't have a y value and q1 won't have an x value.
So q2 is only measured by the diagonal right? So it would just be F= k Q^2/(2L^2)---I understand this
why wouldn't q1 and q3 just be F=k Q^2/L^2?
I would like it if someone would explain this whole problem because I feel like I'm completely lost on it.
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• #2
tiny-tim
Homework Helper
25,832
251
Hi MitsuShai!
(try using the X2 and X2 icons just above the Reply box )
… But I thought that q3 won't have a y value and q1 won't have an x value.
So q2 is only measured by the diagonal right? So it would just be F= k Q^2/(2L^2)---I understand this
why wouldn't q1 and q3 just be F=k Q^2/L^2?
They are.
I think you're confused about what the x and y coordinates are.
Your professor has looked at the diagram, and decided that it's obvious that the total force will be along the diagonal …
and so he's decided to make his x coordinate in that direction (instead of along the bottom of the square, as you'd expect).
Does his work make sense now?
• #3
159
0
Hi MitsuShai!
(try using the X2 and X2 icons just above the Reply box )
They are.
I think you're confused about what the x and y coordinates are.
Your professor has looked at the diagram, and decided that it's obvious that the total force will be along the diagonal …
and so he's decided to make his x coordinate in that direction (instead of along the bottom of the square, as you'd expect).
Does his work make sense now?
Oh ok I think I know what you mean. The forces are the diagonal [F= k Q[SUP]2[/SUP]/(2L2)] and the x and y components of the diagonal, which are F=k Q2/L2 each.
And to get the total forces, you have to add up these forces, but the answer is suppose to be [Q2/(8pi*epsilon_0*L2)] (1+2sqrt(2)) and you don't get that with these forces....
• #4
tiny-tim
Homework Helper
25,832
251
Hi MitsuShai!
(have a square-root: √ and an epsilon: √ and a pi: π )
And to get the total forces, you have to add up these forces, but the answer is suppose to be [Q2/(8pi*epsilon_0*L2)] (1+2sqrt(2)) and you don't get that with these forces....
Show us what you get.
(btw, i've just noticed i should have said "y" not "x" in my last post )
• #5
159
0
Hi MitsuShai!
(have a square-root: √ and an epsilon: √ and a pi: π )
Show us what you get.
(btw, i've just noticed i should have said "y" not "x" in my last post )
F(total)= [ k Q2/(2L2)] + [ k Q2/(L2)] + [ k Q2/(L2)] = [ k Q2/(2L2)] + [2k Q2/(L2)]= [ k Q2/(2L2)] + [4k Q2/(2L2)]= 5k Q2/(2L2)= 3k Q2/(L2)
• #6
tiny-tim
Homework Helper
25,832
251
Hi MitsuShai!
(just got up :zzz: …)
F(total)= [ k Q2/(2L2)] + [ k Q2/(L2)] + [ k Q2/(L2)] = [ k Q2/(2L2)] + [2k Q2/(L2)]= [ k Q2/(2L2)] + [4k Q2/(2L2)]= 5k Q2/(2L2)= 3k Q2/(L2)
ah I see …
no, you need to use the component of F1 and F3 along the diagonal, not the whole of F1 and F3
try again!
• #7
159
0
Hi MitsuShai!
(just got up :zzz: …)
ah I see …
no, you need to use the component of F1 and F3 along the diagonal, not the whole of F1 and F3
try again!
Oh right, I forgot about that part, so
F(total)= [ k Q^2/(2L^2)] + [ k Q^2/(L^2)]sin(45) + [ k Q^2/(L^2)]cos(45)= 2[ k Q^2/(L^2)](1/sqrt(2)) + [ k Q^2/(2L^2)]= [ k Q^2/(2L^2)](1/sqrt(2)) + 4k Q^2/(2L^2)][1/sqrt(2)/(1/sqrt(2)] I'm doing this wrong, somehow..... :/
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• #8
tiny-tim
Homework Helper
25,832
251
Hi MitsuShai!
2[ k Q^2/(L^2)](1/sqrt(2)) + [ k Q^2/(2L^2)]
that's correct …
i can't see where you've gone wrong after that
• #9
159
0
Hi MitsuShai!
that's correct …
i can't see where you've gone wrong after that
Where do I go from there? I was thinking of adding them and to do that I would need to have common denominators, so I would have to get common denominators and I just noticed that I typed that in wrong.... ._.
2[ k Q^2/(L^2)](1/sqrt(2)) + [ k Q^2/(2L^2)]= [ k Q^2/(2L^2)](1/sqrt(2)) + 4k Q^2/(2L^2)](1/sqrt(2))= 5k Q^2/(4L^2), which isn't right
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732 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8548817038536072, "perplexity": 2712.3198480440974}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487586465.3/warc/CC-MAIN-20210612222407-20210613012407-00539.warc.gz"} |
https://epja.epj.org/articles/epja/abs/1999/10/epja105/epja105.html | 2018 Impact factor 2.481
Eur. Phys. J. A 6, 203-210
Nucleon form factors in a relativistic quark model
Y.B. Dong - A. Faessler - K. Shimizu
Institüt für Theoretische Physik, Universität of Tübingen, 72076 Tübingen, Germany
Received: 10 March 1999 / Revised version: 14 June 1999 Communicated by F. Lenz
Abstract
Electromagnetic form factors of protons and neutrons are investigated based on a relativistic quark model with the inclusion of a pion cloud. Pseudo-scalar -quark interaction is employed to study the coupling between the nucleon and the . The results show the important role of the pion cloud for the neutron charge form factor. Moreover, our numerical analysis indicates a difference between the relativistic and the nonrelativistic treatments.
PACS
12.39.Jh Nonrelativistic quark model - 12.39.Ki Relativistic quark model - 12.39.Pn Potential models - 12.40.Vv Vector-meson dominance - 12.40.Yx Hadron mass models and calculations - 13.40.Em Electric and magnetic moments - 13.40.Gp Electromagnetic form factors - 13.40.Hq Electromagnetic decays | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8642234802246094, "perplexity": 3108.5203221224524}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195524522.18/warc/CC-MAIN-20190716095720-20190716121720-00247.warc.gz"} |
https://hal.archives-ouvertes.fr/hal-00332745/fr/ | # Scaling approach to existence of long cycles in Casimir boxes
Abstract : We analyse the concept of generalized Bose-Einstein condensation (g-BEC), known since 1982 for the perfect Bose gas (PBG) in the Casimir (or anisotropic) boxes. Our aim is to establish a relation between this phenomenon and two concepts: the concept of long cycles and the Off-Diagonal-Long-Range-Order (ODLRO), which are usually considered as some adequate way to describe the standard BEC on the ground state for the cubic boxes. First we show that these three criterions are equivalent in this latter case. Then, basing on a scaling approach, we revise formu- lation of these concepts to prove that the classification of the g-BEC into three types I,II,III, implies a hierarchy of long cycles (depending on their size scale) as well as a hierarchy of ODLRO which depends on the coherence length of the condensate.
Keywords :
Type de document :
Article dans une revue
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2009, 43 (23), pp.235204
Domaine :
Liste complète des métadonnées
https://hal.archives-ouvertes.fr/hal-00332745
Contributeur : Mathieu Beau <>
Soumis le : lundi 27 avril 2009 - 16:29:00
Dernière modification le : mercredi 29 novembre 2017 - 10:28:30
Document(s) archivé(s) le : jeudi 23 septembre 2010 - 17:25:18
### Fichiers
ScalingApproachVersion3.pdf
Fichiers produits par l'(les) auteur(s)
### Identifiants
• HAL Id : hal-00332745, version 3
• ARXIV : 0810.4001
### Citation
Mathieu Beau. Scaling approach to existence of long cycles in Casimir boxes. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2009, 43 (23), pp.235204. 〈hal-00332745v3〉
### Métriques
Consultations de la notice
## 291
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http://cpb.iphy.ac.cn/article/2015/cpb_24_5_054501.html | Bifurcation for the generalized Birkhoffian system*
Mei Feng-Xiang, Wu Hui-Bin†
School of Mathematics, Beijing Institute of Technology, Beijing 100081, China
Corresponding author. E-mail: [email protected]
*Project supported by the National Natural Science Foundation of China (Grant No. 11272050).
Abstract
The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper, the condition under which the generalized Birkhoffian system can be a gradient system is given. The stability of equilibrium of the generalized Birkhoffian system is discussed by using the properties of the gradient system. When there is a parameter in the equations, its influences on the stability and the bifurcation problem of the system are considered.
Keyword: 45.20.Jj; 46.40.Ff; generalized Birkhoffian system; gradient system; stability; bifurcation
1. Introduction
The Birkhoffian mechanics is a generalization of the Hamiltonian mechanics. Great progress has been made on its research.[13] Reference [4] derived the generalized Birkhoff equations when discussing the generalized quasi-symmetric transformation of the Pfaffian action. The system whose motion is described by the generalized Birkhoff equations is called a generalized Birkhoffian system. This kind of system is a general enough constrained mechanical system. The gradient system is a kind of mathematical system with very good properties. Particularly, it is suitable for studying the problem of stability.[5] Under certain conditions, a generalized Birkhoffian system can become a gradient system. Then the stability of equilibrium and the static bifurcation of the system can be discussed by using properties of the gradient system.
2. The generalized Birkhoffian system
The equations of the generalized Birkhoffian system have the form[6]
where and in the following, the same index in a term indicates to take the sum with it. In Eq. (1), B = B(t, a) is the Birkhoffian, Rμ = Rμ (t, a) are Birkhoff’ s functions, and Λ μ = Λ μ (t, a) are the added terms. We have
For a constant generalized Birkhoffian system, there are
Then equation (1) becomes
In order to discuss the equilibrium and the bifurcation problem of the system, suppose that a parameter u appears in Λ ν , namely,
The differential equations of the gradient system have the form[5]
where V = V(x) is called a potential function. The gradient system has the following important properties: (i) V can be a Lyapunov function of the gradient system, and = 0 if and only if x = (x1, x2, … , xm) is an equilibrium point of the system. (ii) For the gradient system (5), the linearized system at any equilibrium point only has real characteristic roots.
The above two properties can be applied to discuss the stability of equilibrium of the generalized Birkhoffian system which has been transformed into a gradient system.
Generally speaking, the equations of a generalized Birkhoffian system cannot become a gradient system. If the following conditions:
are satisfied, then the system can be transformed into a gradient system whose potential function V satisfies
5. The stability of equilibrium
When a generalized Birkhoffian system is transformed into a gradient system, its stability of equilibrium and bifurcation problem can be studied by using the properties of the gradient system. Since the linearized system at any equilibrium point only has real characteristic roots, the stability of the zero solution can be stable, asymptotically stable, or unstable. According to Lyapunov’ s first degree approximation theory, if the roots of the first degree approximation characteristic equation are all real and negative, then the zero solution is asymptotically stable; if there is a positive real root, then it is unstable; if there is a simple zero root, and the others are not positive real roots, then it is stable, but not asymptotically stable; if there is a multiple zero root, then it is unstable.
When the added terms Λ ν have the form of expression (4), the characteristic equation will contain the parameter u. It has a great influence on the stability of equilibrium. Under certain values of the parameter, the stability of the system can take a catastrophe, namely, bifurcation.
6. Illustrative examples
Example 1 A generalized Birkhoffian system of the second order is
where u is a parameter. We study the relation between the stability of the zero solution and the parameter u.
The equations of the system are
This is a gradient system whose first degree approximation equations have the following characteristic equation:
When u > 1/4, the two roots of the above equation are both negative, the equilibrium position is asymptotically stable; when u = 1/4, one root of the above equation is zero and the other is negative, the equilibrium position is stable; when u < 1/4, one root of the above equation is positive, the equilibrium position is unstable. So, when u = 1/4, the bifurcation will appear.
Example 2 A generalized Birkhoffian system is
where u is a parameter. We study the stability of equilibrium of the system.
The differential equations of the system are
This is a gradient system. When u = 0, there is an equilibrium position (0, 0); one of the roots of the first degree approximation characteristic equation is zero, the other is negative, then the equilibrium position is stable. When u ≠ 0, there are three equilibrium positions (0, 0), (u/2, 0), and (u, 0), which are sink, saddle point, and sink, also stable, unstable, and stable respectively. So, u = 0 is a bifurcation value. When u changes from zero to non-zero, the number of equilibrium positions will increase from one to three.
7. Conclusion
The gradient system has the essential significance for studying the stability of equilibrium and the bifurcation problem. A generalized Birkhoffian system under certain conditions can be transformed into a gradient system. After that, its stability of equilibrium and bifurcation problem can be discussed by using the properties of the gradient system. The bifurcation point of example 1 shows that the equilibrium of the system changes from unstable to stable, and then to asymptotically stable. The bifurcation point of example 2 indicates that the number of equilibrium points of the system takes catastrophe. The bifurcation discussed here is not the Hopf bifurcation in the general sense.
Reference
1 Santilli R M 1983 Foundations of Theoretical Mechanics II New York Springer-Verlag 30 67 [Cited within:1] 2 Mei F X, Shi R C, Zhang Y F and Wu H B 1996 Dynamics of Birkhoffian System Beijing Beijing Institute of Technology Press 37 226(in Chinese) [Cited within:1] 3 Galiullin A S, Gafarov G G, Malaishka R P and Khwan A M 1997 Analytical Dynamics of Helmholtz, Birkhoff, Nambu systems Moskow UFN 118 220(in Russian) [Cited within:1] 4 Mei F X 1993 Science in China, Ser. A 36 1456 [Cited within:1] 5 Hirsch M W, Smale S and Devaney R L 2008 Differential Equations, Dynamical Systems, and an Introduction to Chaos Singapore Elsevier 165 168 [Cited within:2] 6 Mei F X 2013 Dynamics of Generalized Birkhoffian System Beijing Science Press 202 203(in Chinese) [Cited within:1] | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9272329211235046, "perplexity": 726.8348740448286}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738982.70/warc/CC-MAIN-20200813103121-20200813133121-00437.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/171057-determine-effect-following-transformations.html | # Math Help - Determine the effect of the following transformations
1. ## Determine the effect of the following transformations
Determine the effect of the following transformations
a) Rotation through pi/2, followed by projection on the Y axis, followed by reflection in the lines y=x.
b) Projection on the X axis followed by reflection in the line y=x.
2. It is easy to find the matrix of the rotation $R$ and the reflection $S$ :
$R \equiv \begin{bmatrix}{0}&{-1}\\{1}&{\;\;0}\end{bmatrix},\quad S \equiv \begin{bmatrix}{0}&{1}\\{1}&{0}\end{bmatrix}$
So,
$S\circ R\equiv \begin{bmatrix}{1}&{\;\;0}\\{0}&{-1}\end{bmatrix}$
that is, $S\circ R$ is the reflection in the $x$ axis.
Try b) .
Fernando Revilla | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9027900695800781, "perplexity": 556.1724657261451}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394021378450/warc/CC-MAIN-20140305120938-00048-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://qchu.wordpress.com/tag/group-actions/ | Feeds:
Posts
Projective representations give categorical representations
Today we’ll resolve half the puzzle of why the cohomology group $H^2(BG, k^{\times})$ appears both when classifying projective representations of a group $G$ over a field $k$ and when classifying $k$-linear actions of $G$ on the category $\text{Mod}(k)$ of $k$-vector spaces by describing a functor from the former to the latter.
(There is a second half that goes in the other direction.)
Hecke operators are also relative positions
Continuing yesterday’s story about relative positions, let $G$ be a finite group and let $X$ and $Y$ be finite $G$-sets. Yesterday we showed that $G$-orbits on $X \times Y$ can be thought of as “atomic relative positions” of “$X$-figures” and “$Y$-figures” in some geometry with symmetry group $G$, and further that if $X \cong G/H$ and $Y \cong G/K$ are transitive $G$-sets then these can be identified with double cosets $H \backslash G / K$.
Representation theory provides another interpretation of $G$-orbits on $X \times Y$ as follows. First, if $\mathbb{C}[X]$ is any permutation representation, then the $G$-fixed points $\mathbb{C}[X]^G$ have a natural basis given by summing over $G$-orbits. (This is a mild categorification of Burnside’s lemma.) Next, consider the representations $\mathbb{C}[X], \mathbb{C}[Y]$. Because $\mathbb{C}[X]$ is self-dual, we have
$\displaystyle \text{Hom}_G(\mathbb{C}[X], \mathbb{C}[Y]) \cong (\mathbb{C}[X] \otimes \mathbb{C}[Y])^G \cong \mathbb{C}[X \times Y]^G$
and hence $\text{Hom}_G(\mathbb{C}[X], \mathbb{C}[Y])$ has a natural basis given by summing over $G$-orbits of the action on $X \times Y$.
Definition: The $G$-morphism $\mathbb{C}[X] \to \mathbb{C}[Y]$ associated to a $G$-orbit of $X \times Y$ via the above isomorphisms is the Hecke operator associated to the $G$-orbit (relative position, double coset).
Below the fold we’ll write down some details about how this works and see how we can use the idea that $G$-morphisms between permutations have a basis given by Hecke operators to work out, quickly and cleanly, how some permutation representations decompose into irreducibles. At the end we’ll state another puzzle.
The p-group fixed point theorem
The goal of this post is to collect a list of applications of the following theorem, which is perhaps the simplest example of a fixed point theorem.
Theorem: Let $G$ be a finite $p$-group acting on a finite set $X$. Let $X^G$ denote the subset of $X$ consisting of those elements fixed by $G$. Then $|X^G| \equiv |X| \bmod p$; in particular, if $p \nmid |X|$ then $G$ has a fixed point.
Although this theorem is an elementary exercise, it has a surprising number of fundamental corollaries.
Connected objects and a reconstruction theorem
A common theme in mathematics is to replace the study of an object with the study of some category that can be built from that object. For example, we can
• replace the study of a group $G$ with the study of its category $G\text{-Rep}$ of linear representations,
• replace the study of a ring $R$ with the study of its category $R\text{-Mod}$ of $R$-modules,
• replace the study of a topological space $X$ with the study of its category $\text{Sh}(X)$ of sheaves,
and so forth. A general question to ask about this setup is whether or to what extent we can recover the original object from the category. For example, if $G$ is a finite group, then as a category, the only data that can be recovered from $G\text{-Rep}$ is the number of conjugacy classes of $G$, which is not much information about $G$. We get considerably more data if we also have the monoidal structure on $G\text{-Rep}$, which gives us the character table of $G$ (but contains a little more data than that, e.g. in the associators), but this is still not a complete invariant of $G$. It turns out that to recover $G$ we need the symmetric monoidal structure on $G\text{-Rep}$; this is a simple form of Tannaka reconstruction.
Today we will prove an even simpler reconstruction theorem.
Theorem: A group $G$ can be recovered from its category $G\text{-Set}$ of $G$-sets.
Groupoid cardinality
Suitably nice groupoids have a numerical invariant attached to them called groupoid cardinality. Groupoid cardinality is closely related to Euler characteristic and can be thought of as providing a notion of integration on groupoids.
There are various situations in mathematics where computing the size of a set is difficult but where that set has a natural groupoid structure and computing its groupoid cardinality turns out to be easier and give a nicer answer. In such situations the groupoid cardinality is also known as “mass,” e.g. in the Smith-Minkowski-Siegel mass formula for lattices. There are related situations in mathematics where one needs to describe a reasonable probability distribution on some class of objects and groupoid cardinality turns out to give the correct such distribution, e.g. the Cohen-Lenstra heuristics for class groups. We will not discuss these situations, but they should be strong evidence that groupoid cardinality is a natural invariant to consider.
Groupoids
My current top candidate for a mathematical concept that should be and is not (as far as I can tell) consistently taught at the advanced undergraduate / beginning graduate level is the notion of a groupoid. Today’s post is a very brief introduction to groupoids together with some suggestions for further reading. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 66, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9598557353019714, "perplexity": 175.19065406064357}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738663010.9/warc/CC-MAIN-20160924173743-00155-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://export.arxiv.org/abs/1509.00008v1 | Full-text links:
hep-th
(what is this?)
# Title: Conformal Invariance in the Long-Range Ising Model
Abstract: We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.
Comments: 52pp Subjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech) Report number: CERN PH-TH/2015-200 Cite as: arXiv:1509.00008 [hep-th] (or arXiv:1509.00008v1 [hep-th] for this version)
## Submission history
From: Slava Rychkov [view email]
[v1] Mon, 31 Aug 2015 20:08:47 GMT (666kb,D)
[v2] Tue, 15 Sep 2015 19:14:36 GMT (667kb,D)
[v3] Wed, 9 Dec 2015 15:06:50 GMT (667kb,D)
Link back to: arXiv, form interface, contact. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.812344491481781, "perplexity": 1588.12155200034}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499634.11/warc/CC-MAIN-20230128121809-20230128151809-00062.warc.gz"} |
https://arithmos.wordpress.com/2011/03/08/main-proof-part-3/ | ## Main Proof (part 3)
We will now define certain increasing sequences ${\langle \alpha_n:n<\omega\rangle}$ and ${\langle i_n:n<\omega\rangle}$ as in the last post, along with another sequence ${\langle \epsilon_n:n<\omega\rangle}$.
Start by setting ${\alpha_0=\min({\rm nacc}(C_\delta))}$ and ${i_0=0}$. Given ${\alpha_n}$ and ${i_n}$, we let ${\alpha_{n+1}}$ be the least element of ${{\rm nacc}(C_\delta)}$ above ${\alpha_n}$ with the property that
$\displaystyle \gamma(\alpha_n)<\sup(C_{\alpha_{n+1}}), \ \ \ \ \ (1)$
and define
$\displaystyle \epsilon_n = \min(C_{\alpha_{n+1}}\setminus\gamma(\alpha_n). \ \ \ \ \ (2)$
What is the point? Note that this arrangement ensures that
$\displaystyle f_{\epsilon_n}\in \mathcal{N}(\alpha_{n+1}, i) \ \ \ \ \ (3)$
for any ${i<\kappa}$. Since ${\gamma(\alpha_n)\leq\epsilon}$, it follows that we can choose ${i_{n+1}\geq i_n}$ such that “${f_{\epsilon_n}}$ majorizes ${g(\alpha_n, i_n)}$ beyond ${\mu_{i_{n+1}}}$”, i.e.,
$\displaystyle \sup(\mathcal{N}^+(\alpha_n, i_n)\cap\theta)
whenever ${\theta\in \mathfrak{a}_{\alpha_n, i_n}\setminus \mu_{i_{n+1}}}$.
Now define
$\displaystyle N=\bigcup_{n<\omega}\mathcal{N}(\alpha_n, i_n), \ \ \ \ \ (5)$
and
$\displaystyle N^+=\bigcup_{n<\omega}\mathcal{N}^+(\alpha_n, i_n). \ \ \ \ \ (6)$
We know the following facts from previous posts:
• ${N\in M^*\cap [\mu]^{<\mu}=\mathcal{P}}$,
• ${N\subseteq N^+}$, and
• ${a\subseteq N^+}$.
Thus, the theorem will be done provided we establish
$\displaystyle N\cap\mu = N^+\cap \mu. \ \ \ \ \ (7)$
Here we use the “Elementary submodel argument” from February 12, which tells us that we have what we want provided
$\displaystyle \theta\in N\cap\mu\cap{\sf Reg}\Longrightarrow \sup(N^+\cap\theta)=\sup(N\cap\theta). \ \ \ \ \ (8)$
The above is satisfied trivially for ${\theta\leq\mu_{i^*}}$ as ${\mu_{i^*}\subseteq N}$; thus, we need only verify things for ${\theta\in N\cap\mu\cap{\sf Reg}}$ which are greater than ${\mu_{i^*}}$. Furthermore, we know ${N\subseteq N^+}$, so
$\displaystyle \sup(N\cap\theta)\leq\sup(N^+\cap\theta) \ \ \ \ \ (9)$
in any case.
Assume now by way of contradiction that we have ${\theta}$ such that
• ${\theta\in N\cap\mu\cap{\sf Reg}}$,
• ${\mu_{i^*}<\theta}$, and
• ${\sup(N\cap\theta)<\sup(N^+\cap\theta)}$.
Choose ${n<\omega}$ so large that
• ${\sup(N\cap\theta)<\sup(\mathcal{N}^+(\alpha_n, i_n)\cap\theta)}$, and
• ${\theta\in \mathcal{N}(\alpha_n, i_n)}$.
Since ${\mu_{i_{n+1}}<\mu_{i^*}}$ and ${\theta\in\mathfrak{a}_{\alpha_n, i_n}}$, it follows from the definition of ${\epsilon_n}$ that
$\displaystyle \sup(\mathcal{N}^+(\alpha_n, i_n)\cap\theta)
But
$\displaystyle f_{\epsilon_n}(\theta)\leq \sup(\mathcal{N}(\alpha_{n+1}, i_{n+1})\cap\theta) \ \ \ \ \ (11)$
as both ${\mathfrak{a}_{\alpha_n, i_n}}$ and ${f_{\epsilon_n}}$ are in the latter model. Thus, on the one hand we have
$\displaystyle \sup(N\cap\theta)\leq \sup(\mathcal{N}^+(\alpha_n, i_n)\cap\theta)
and on the other,
$\displaystyle f_{\epsilon_n}(\theta)\leq \sup(\mathcal{N}(\alpha_{n+1}, i_{n+1})\cap\theta)\leq \sup(N\cap\theta). \ \ \ \ \ (13)$
Clearly, this is absurd. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 50, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.99825119972229, "perplexity": 1837.8167623112681}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934809746.91/warc/CC-MAIN-20171125090503-20171125110503-00393.warc.gz"} |
https://dsp.stackexchange.com/users/26549/soumee?tab=summary | Soumee
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2 homework × 3 0 modulation × 2 2 fourier-transform × 3 0 linear-systems × 2 2 sampling 0 impulse-response 0 signal-analysis × 4 0 z-transform 0 demodulation × 2 0 continuous-signals | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8151823282241821, "perplexity": 4501.772563133898}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572879.28/warc/CC-MAIN-20190916155946-20190916181946-00033.warc.gz"} |
http://engineersphere.com/ohms-law | Ohm’s Law
What is Ohm’s Law?
Ohm’s law defines the relationship between voltage, current, and resistance by the equation below. The second equation better represents voltage as the difference between two electric potentials.
$V = IR$ $V_{1} - V_{2} = IR$
Note that V1 and V2 are voltages measured with respect to ground and V is the voltage potential measured between them.
The equation derived from Ohm’s law is incredibly useful for an electrical engineer. Ohm’s law allows many circuits to be fully analyzed with the aid of just a few measurements. Many circuit analysis techniques you will learn involve some combination of KCL, KVL, and/or Ohm’s law.
Ohm’s law states that there must be a voltage drop (or voltage difference) across a resistor in order for any current to flow. If V1 and V2 are the same, no current flows through the resistor. In terms of currents, a current produces a voltage drop across a resistor; if there is no current, there is no voltage drop across the resistor.
A circuit component that follows Ohm’s law has a constant resistance. Increasing the current through the component will produce a proportional increase in the voltage drop across it. The plot of the current through the component versus the voltage drop across it will be linear, with the slope of the line determining the resistance of the component.
I-V Plot to describe Ohm’s Law
Figure 2 shows I-V plot of a 1 Ω and a 2 Ω resistor, both of which follow Ohm’s law. Figure 3 shows the I-V curve of a component not following Ohm’s law. You will learn about two components that don’t follow Ohm’s law later in the course (diodes and MOSFETs).
Written by Ryan Eatinger ([email protected]). Thank you! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 2, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8200539350509644, "perplexity": 706.5177728849042}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320270.12/warc/CC-MAIN-20170624170517-20170624190517-00291.warc.gz"} |
https://fpqc.wordpress.com/2010/09/04/86/ | ## Nobuo
In the previous post we started with ${\mathsf{C}}$ (the category of open subsets of ${\mathbb{R}^n}$‘s), embedded it inside ${\mathsf{Top}}$ and formed topological manifolds via gluing. (not much of a surprise there…)
We mentioned that there is another way to enlarge ${\mathsf{C}}$ using the Yoneda lemma. Let’s (briefly) see how.
Let’s start from the easiest case: take ${X}$ to be a set. Pick any set with one element ${\bullet}$, in other words a final object in ${\mathsf{Set}}$.
We usually care more about when two objects, in a given category, are isomorphic than when they are actually equal. In ${\mathsf{Set}}$ two objects are isomorphic if and only if they have the same cardinality. As the set
$\displaystyle h_X(\bullet) := Hom_{\mathsf{Set}}(\bullet,X),$
of maps from the singleton ${\bullet}$ to ${X,}$ has the same cardinality of ${X,}$ we can recover (up to isomorphism) ${X}$ by considering the set ${h_X(\bullet).}$ (the definition of ${h_X}$ depends of course on the underlying category; being in this case ${\mathsf{Set}}$)
Of course the same idea does not work for a general category. For example if we take a topological space ${X \in \mathsf{Top},}$ then the set
$\displaystyle h_X(\bullet) = Hom_{\mathsf{Top}}(\bullet,X)$
only recovers the underlying set of ${X}$, but completely forgets about its topology.
The incredibly brilliant idea is that, in order to recover ${X}$ (as an object of ${\mathsf{Top}}$), one should consider all the sets
$\displaystyle h_X(Y) = Hom_{\mathsf{Top}}(Y,X)$
at once, where ${Y}$ varies over all topological spaces.
More precisely: start from a category ${\mathsf{C}}$, then any object ${X \in \mathsf{C}}$ determines a functor
$\displaystyle h_X : \mathsf{C}^\circ \rightarrow \mathsf{Set}$
(where ${\circ}$ stands for opposite category), ${h_X(Y) := Hom_{\mathsf{C}}(Y,X).}$
Actually one can check that the assignment ${X \mapsto h_X}$ determines a functor
$\displaystyle h : \mathsf{C} \rightarrow Fun(\mathsf{C}^\circ,\mathsf{Set}).$
(where ${Fun}$ stands for the category of functors)
• Theorem (The Yoneda Lemma) The functor ${h}$ above is fully faithful.
Actually we have a sharper result.
• Theorem Let ${P}$ be any object of ${Fun(\mathsf{C}^\circ,\mathsf{Set}),}$ and let ${X}$ be any object in ${\mathsf{C}.}$ Then
$\displaystyle Hom(h_X,P) \simeq P(X).$
We therefore have our desired result: any category ${\mathsf{C}}$ can be embedded into ${Fun(\mathsf{C}^\circ,\mathsf{Set}).}$
From now on we shall adopt the following notation
$\displaystyle PSh\mathsf{C}:= Fun(\mathsf{C}^\circ,\mathsf{Set})$
(presheaves on ${\mathsf{C}}$), which shall be explained in the next post.
Our next task is to come up with a gluing operation inside ${PSh\mathsf{C},}$ which will lead to the definition of a subcategory ${Sh\mathsf{C}}$ (sheaves on ${\mathsf{C}}$). But for that we need to know what a site is. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 44, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9420642852783203, "perplexity": 208.46136375461657}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549428300.23/warc/CC-MAIN-20170727142514-20170727162514-00607.warc.gz"} |
https://www.siyavula.com/read/science/grade-12/doppler-effect/06-doppler-effect-03 | We think you are located in United States. Is this correct?
# 6.3 The Doppler effect with light
## 6.3 The Doppler effect with light (ESCMS)
Light is a wave and earlier you learnt how you can study the properties of one wave and apply the same ideas to another wave. The same applies to sound and light. We know the Doppler effect is relevant in the context of sound waves when the source is moving. Therefore, in the context of light (EM waves), the frequency of observed light should be different to the emitted frequency when the source of the light is moving relative to the observer.
A frequency shift of light in the visible spectrum could result in a change of colour which could be observable with the naked eye. There will still be a frequency shift for frequencies of EM radiation we cannot see.
We can apply all the ideas that we learnt about the Doppler effect to light. When talking about light we use slightly different terminology to describe what happens. If you look at the colour spectrum (more details in Chapter 12) then you will see that blue light has a shorter wavelength than red light. Since for light, $$c=f\lambda$$, shorter wavelength equals higher frequency. Relative to the middle of the visible spectrum (approximately green light) longer wavelengths (or lower frequencies) are redder and shorter wavelengths (or higher frequencies) are bluer. So we call shifts towards longer wavelengths "redshifts" and shifts towards shorter wavelengths "blueshifts".
A shift in wavelength implies that there is also a shift in frequency. Longer wavelengths of light have lower frequencies and shorter wavelengths have higher frequencies. From the Doppler effect we know that when the source moves towards the observer any waves they emit that you measure are shifted to shorter wavelengths (blueshifted). If the source moves away from the observer, the shift is to longer wavelengths (redshifted).
temp text
### The expanding universe (ESCMT)
Stars emit light, which is why we can see them at night. Galaxies are huge collections of stars. An example is our own Galaxy, the Milky Way, of which our sun is only one of the billions of stars!
Using large telescopes like the Southern African Large Telescope (SALT) in the Karoo, astronomers can measure the light from distant galaxies. The spectrum of light can tell us what elements are in the stars in the galaxies because each element has unique energy levels and therefore emits or absorbs light at particular wavelengths. These characteristic wavelengths are called spectral lines because the lines show up as discrete frequencies in the spectrum of light from the star.
If these lines are observed to be shifted from their usual wavelengths to shorter wavelengths, then the light from the galaxy is said to be blueshifted. If the spectral lines are shifted to longer wavelengths, then the light from the galaxy is said to be redshifted. If we think of the blueshift and redshift in Doppler effect terms, then a blueshifted galaxy would appear to be moving towards us (the observers) and a redshifted galaxy would appear to be moving away from us.
1. If the light source is moving away from the observer (positive velocity) then the observed frequency is lower and the observed wavelength is greater (redshifted).
2. If the source is moving towards the observer (negative velocity), the observed frequency is higher and the wavelength is shorter (blueshifted).
Edwin Hubble (20 November 1889 - 28 September 1953) measured the Doppler shift of a large sample of galaxies. He found that the light from distant galaxies is redshifted and he discovered that there is a proportionality relationship between the redshift and the distance to the galaxy. Galaxies that are further away always appear more redshifted than nearby galaxies. Remember that a redshift in Doppler terms means a velocity of the light source directed away from the observer. So why do all distant galaxies appear to be moving away from our Galaxy? None of them seem to be moving towards us.
The reason is that the universe is expanding! Some of the galaxies will be moving in our direction but more slowly than the space between us and them is expanding. The expansion is so large that it is the primary effect that we observe. The primary reason the light is redshifted isn't actually because all of the Doppler effect, it is redshifted because the space is expanding, the waves are being stretched out. If the Doppler effect were a larger effect then some of the galaxies would still be blueshifted (just less than if space were not expanding).
You might think that this means we are at the centre of the universe. This isn't correct, the situation will look the same from every galaxy because space is expanding in all directions.
Hubble's Law is:
$\boxed{v = H_0\times d}$
where latest value of $$H_0$$ is $$\text{67,15}$$ $$\text{km.s^{-1}.Mpc^{-1}}$$ (rate of expansion of the Universe). Latest value from Planck mission, 2013.
There are two things you can do to help you visualise this a little better. One thing to try is to get a balloon and draw some dots on it with a marker. As you blow the balloon up all the dots get further away from all the other dots. The dots represent galaxies in a two-dimensional, expanding universe (the balloon surface). Another thing to imagine is baking raisin bread. As the bread rises, the distance between all the raisins gets larger. Every raisin thinks that all the other raisins are moving away from it.
In this picture the bottom vertex represents the beginning of time, the flat surface represents space. As you move up through the panels you are moving later in time and the expansion of the the flat surface shows the expansion of the universe. The galaxies shown on the surface get further away from each other just because of the expansion of space.
Cool exercise that can be done with Sloan Digital Sky Survey data: Sloan Digital Sky Survey | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8043091297149658, "perplexity": 323.70213641296}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710978.15/warc/CC-MAIN-20221204172438-20221204202438-00545.warc.gz"} |
https://www.physicsforums.com/threads/projectile-motion-of-tabletop-ball.903805/ | # Projectile motion of tabletop ball?
1. Feb 13, 2017
### Sagrebella
Hello,
Could someone please check my answers to this physics problem? All my work and equations are clearly shown in the pictures below. If I got the problem wrong, please provide me with some suggestions as to how I can get it right . I'm not expecting anyone to just give me the answers :)
Thanks!
Problem 6
You flick a ball from a tabletop, so that the ball lands on the floor 1.50 m below. The ball's initial speed is 2.10 m/s. Use g = 9.80 m/s2.
(a) f the ball is launched off the table horizontally, what is the horizontal distance between the launch point and the point where the ball hits the floor?
(b) If the ball is launched off the table at a 30° angle above the horizontal, what is the horizontal distance between the launch point and the point where the ball hits the floor?
2. Feb 13, 2017
### BvU
My compliments for your neat style of working !
Don't you think it's strange the ball should travel so far in part a) ? Check your math for 2.10 * 0.31 = ....
And if you find a flight time of 0.31 s in part a), wouldn't you expect it to be in the air a little longer in part b) ?
The mistake here is that you let it land with a $v_{f, y}=0$. Just before impact that is definitely not true !.
You want to use one of the other SUVAT equations; can you determine which one you need ?
3. Feb 13, 2017
### BvU
A few more suggestions: In a), $v_{\rm f, x} = 0 \$ is not right: there is no force in the x-direction (you yourself write $a=0$ too), so the motion is uniform with constant speed in that direction: $v_{\rm f, x} = v_{\rm i, x} = 2.10 \;$m/s.
In b) you confuse yourself using $v_{\rm f,x}$ for $v_{\rm f,y}$. And itis not zero.
I have to admit to a too hasty response: I now see you split up the trip in two parts. One to the highest point and one from there to ground. Let me re-read and hopefully stand corrected ...
4. Feb 13, 2017
### BvU
Alas, I can follow the 2nd part of the trip to the point $x_f = 1.5056$ m (rounding off is not such a good idea here, I think... --- and I would use a notation that has only $y$ in the y direction, but never mind...).
Then I see $0 = ...$ where you mix the initial $y$ at time t= 0.107 s and the initial $v_{\rm i, y}$ at time t = 0. That's where things are going wrong. Fortunately, it's easy to fix: take both at t = 0 and solve the quadratic equation (you have to do that anyway) -- saves you half a page of extra work too !
5. Feb 13, 2017
### Sagrebella
Hi BvU,
thank you for your thorough explanation, and thanks for the compliment . Hopefully I interpreted your suggestions correctly when revising my work.
For part a) I rechecked my multiplication and got and got 0.65 meters. Hopefully thats correct
and I redid my work for part b) too (work posted below in the pictures). Would please mind checking again? Thanks
6. Feb 13, 2017
### Staff: Mentor
For part (a) you wrote:
Check the calculation you did for the last line.
7. Feb 13, 2017
### BvU
Thanks @gneill , I sure missed that one !
@Sagrebella:
For part b) you now find the right answer, again in two steps: from 1.5 m to $y_{\rm max}$ and then from $y_{\rm max}$ to 0.
Do you realize you can do it in one step by solving $$y(t) = 0 = y_0 + v_0\cos\left ({\pi\over 6}\right ) t - {1\over 2} g t^2 \quad \rm ?$$
8. Feb 13, 2017
### Sagrebella
thank you for catching that error. There are so many equations and numbers its hard to keep track sometimes :P
9. Feb 13, 2017
### Sagrebella
Thanks for checking my answer. And actually I was going to ask you about solving it in one step; I still don't quite understand. Would you mind elaborating a little more please?
10. Feb 13, 2017
### cnh1995
I believe there should be sin(π/6) instead of cos in BvU's equation for y(t).
The y displacement of the ball is -1.5m when it hits the floor. Instead of writing it in two parts, you can write it in a single equation that BvU wrote. Take v=2.10sin30, a=-9.81 m/s2 and y= -1.5m.
11. Feb 14, 2017
### BvU
You bet there should ! Sorry for possible confusion !
12. Feb 19, 2017
### Sagrebella
Hello,
I know I asked this question a while ago, but I'm looking over my latest threads in order to review for a physics exam i'll be taking soon. I think I understand this problem, but would you mind explaining part b.) again please. How is it that I can solve for the total flight time of the ball using this one equation instead of breaking up the trip into two steps in the y-direction? Doesn't one have to consider the fact that the ball initially travels above the horizontal before landing on the ground?
13. Feb 19, 2017
### cnh1995
You have already considered that when you use vsin30° as the initial velocity and -g as the acceleration.
Draft saved Draft deleted
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http://libros.duhnnae.com/2017/jun9/149855087778-Kernel-estimation-of-Greek-weights-by-parameter-randomization-Mathematics-Probability.php | # Kernel estimation of Greek weights by parameter randomization - Mathematics > Probability
Kernel estimation of Greek weights by parameter randomization - Mathematics > Probability - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.
Abstract: A Greek weight associated to a parameterized random variable $Z\lambda$ isa random variable $\pi$ such that$abla {\lambda}E\phiZ\lambda=E\phiZ\lambda\pi$ for any function$\phi$. The importance of the set of Greek weights for the purpose of MonteCarlo simulations has been highlighted in the recent literature. Our mainconcern in this paper is to devise methods which produce the optimal weight,which is well known to be given by the score, in a general context where thedensity of $Z\lambda$ is not explicitly known. To do this, we randomize theparameter $\lambda$ by introducing an a priori distribution, and we useclassical kernel estimation techniques in order to estimate the score function.By an integration by parts argument on the limit of this first kernelestimator, we define an alternative simpler kernel-based estimator which turnsout to be closely related to the partial gradient of the kernel-based estimatorof $\mathbb{E}\phiZ\lambda$. Similarly to the finite differencestechnique, and unlike the so-called Malliavin method, our estimators arebiased, but their implementation does not require any advanced mathematicalcalculation. We provide an asymptotic analysis of the mean squared error ofthese estimators, as well as their asymptotic distributions. For adiscontinuous payoff function, the kernel estimator outperforms the classicalfinite differences one in terms of the asymptotic rate of convergence. Thisresult is confirmed by our numerical experiments.
Autor: Romuald Elie, Jean-David Fermanian, Nizar Touzi
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https://worldwidescience.org/topicpages/r/radioactive+ion+accelerator.html | #### Sample records for radioactive ion accelerator
International Nuclear Information System (INIS)
Laxdal, R.E.
2003-01-01
There is an intense interest world-wide in the use of radioactive ion beams (RIBs) for experiment. In many existing or proposed facilities ions are produced or collected at source potential, ionized and re-accelerated. Within the past year three new ISOL based facilities have added dedicated post-accelerators to deliver accelerated RIBs to experiment. The paper gives an overview of RIB accelerators present and future, and explores the inherent features in the various acceleration methods with an emphasis on heavy ion linacs. The ISAC-I and ISAC-II post-accelerators are discussed as examples. Commissioning results and initial operating experience with ISAC-I will be presented
2. Accelerator complex for a radioactive ion beam facility at ATLAS
International Nuclear Information System (INIS)
Nolen, J.A.
1995-01-01
Since the superconducting heavy ion linac ATLAS is an ideal post-accelerator for radioactive beams, plans are being developed for expansion of the facility with the addition of a driver accelerator, a production target/ion source combination, and a low q/m pre-accelerator for radioactive ions. A working group including staff from the ANL Physics Division and current ATLAS users are preparing a radioactive beam facility proposal. The present paper reviews the specifications of the accelerators required for the facility
3. The production of accelerated radioactive ion beams
International Nuclear Information System (INIS)
Olsen, D.K.
1993-01-01
During the last few years, substantial work has been done and interest developed in the scientific opportunities available with accelerated radioactive ion beams (RIBs) for nuclear physics, astrophysics, and applied research. This interest has led to the construction, development, and proposed development of both first- and second-generation RIB facilities in Asia, North America, and Europe; international conferences on RIBs at Berkeley and Louvain-la-Neuve; and many workshops on specific aspects of RIB production and science. This paper provides a discussion of both the projectile fragmentation, PF, and isotope separator on-line, ISOL, approach to RIB production with particular emphasis on the latter approach, which employs a postaccelerator and is most suitable for nuclear structure physics. The existing, under construction, and proposed facilities worldwide are discussed. The paper draws heavily from the CERN ISOLDE work, the North American IsoSpin Laboratory (ISL) study, and the operating first-generation RIB facility at Louvain-la-Neuve, and the first-generation RIB project currently being constructed at ORNL
4. Techniques to produce and accelerate radioactive ion beams
CERN Document Server
Penescu, Liviu Constantin; Lettry, Jacques; Cata-Danil, Gheorghe
The production and acceleration of the Radioactive Ion Beams (RIB) continues the long line of nuclear investigations started in the XIXth century by Pierre and Marie Curie, Henri Becquerel and Ernest Rutherford. The contemporary applications of the RIBs span a wide range of physics fields: nuclear and atomic physics, solid-state physics, life sciences and material science. ISOLDE is a world-leading Isotope mass-Separation On-Line (ISOL) facility hosted at CERN in Geneva for more than 40 years, offering the largest variety of radioactive ion beams with, until now, more than 1000 isotopes of more than 72 elements (with Z ranging from 2 to 88), with half-lives down to milliseconds and intensities up to 1011 ions/s. The post acceleration of the full variety of beams allows reaching final energies between 0.8 and 3.0 MeV/u. This thesis describes the development of a new series of FEBIAD (“Forced Electron Beam Induced Arc Discharge”) ion sources at CERN-ISOLDE. The VADIS (“Versatile Arc Discharge Ion Source�...
5. Positron emission medical measurements with accelerated radioactive ion beams
International Nuclear Information System (INIS)
Llacer, J.
1988-01-01
This paper reviews in some detail the process by which a heavy ion accelerator can be used to inject positron emitting radioactive particles into a human body for a range of possible medical measurements. The process of radioactive beam generation and injection is described, followed by a study of the relationship between activity that can be injected versus dose to the patient as a function of which of the positron emitting ions is used. It is found that 6 C 10 and 10 Ne 19 are the two isotopes that appear more promising for injection into humans. The design considerations for a non-tomographic instrument to obtain images from beam injections are outlined and the results of 10 Ne 19 preliminary measurements with human phantoms and actual patients for the determination of end-of-range of cancer therapy ion beams is reported. Accuracies in the order of ±1 mm in the measurements of stopping point of a therapy beam with safe doses to the patient are reported. The paper concludes with a simple analysis of requirements to extend the technique to on-line verification of cancer treatment and to nuclear medicine research and diagnostics measurements. 17 refs.; 16 figs.; 3 tabs
6. The 1+ → n+ transformation for the radioactive ion acceleration
International Nuclear Information System (INIS)
Chauvin, N.; Lamy, T.; Bruandet, J.F.; Bouly, J.L.; Curdy, J.C.; Geller, R.; Sole, P.; Sortais, P.; Vieux-Rochaz, J.L.
1999-01-01
The radioactive ions are produced as single-charge ions either starting from nuclear reactions induced by a high energy primary beam, or by neutron bombarding of a target. However, in order to obtain beams of several MeV per nucleon, il will be convenient of transforming the mono-charged ions issued from the production source, in multicharged ions. Consequently, an operation should be implemented to transform the 1+ charge state into n+ state, with a double requirement of maximal yield and minimal response time. The objectives are a particle yield of several percents and a response time below 1 second, taking into account the low lifetimes of certain radioactive nuclei. The conjoint achievement of both high charged states and maximal beam intensity forced us to make a choice for an ECR (Electron Cyclotron Resonance) type source to realize the transformation 1+ → n+
7. Proceedings of the workshop on prospects for research with radioactive beams from heavy ion accelerators
International Nuclear Information System (INIS)
Nitschke, J.M.
1984-04-01
The SuperHILAC Users Executive Committee organized a workshop on Prospects for Research with Radioactive Beams from Heavy Ion Accelerators. The main purpose of the workshop was to bring together a diverse group of scientists who had already done experients with radioactive beams or were interested in their use in the future. The topics of the talks ranged from general nuclear physics, astrophysics, production of radioactive beams and high energy projectile fragmentation to biomedical applications. This publication contains the abstracts of the talks given at the workshop and copies of the viewgraphs as they were supplied to the editor
8. A singly charged ion source for radioactive 11C ion acceleration
Science.gov (United States)
Katagiri, K.; Noda, A.; Nagatsu, K.; Nakao, M.; Hojo, S.; Muramatsu, M.; Suzuki, K.; Wakui, T.; Noda, K.
2016-02-01
A new singly charged ion source using electron impact ionization has been developed to realize an isotope separation on-line system for simultaneous positron emission tomography imaging and heavy-ion cancer therapy using radioactive 11C ion beams. Low-energy electron beams are used in the electron impact ion source to produce singly charged ions. Ionization efficiency was calculated in order to decide the geometric parameters of the ion source and to determine the required electron emission current for obtaining high ionization efficiency. Based on these considerations, the singly charged ion source was designed and fabricated. In testing, the fabricated ion source was found to have favorable performance as a singly charged ion source.
9. First radioactive ions charge bred in REXEBIS at the REX-ISOLDE accelerator
CERN Document Server
Wolf, B H; Fostner, O; Wenander, F; Ames, F; Reisinger, K; Liljeby, L; Skeppstedt, Ö; Jonson, B; Nyman, G H
2003-01-01
REXEBIS is the charge breeder of the REX-ISOLDE post accelerator. The radioactive 1$^{+}$ ions produced at ISOLDE are accumulated, phase-space cooled and bunched in the REXTRAP, and thereafter injected into the EBIS with an energy up to 60 keV. The REXEBIS produced the first charge bred ions in August 2001 and has been running nearly non-stop during September to December 2001. It has delivered stable $^{39}$K$^{10+}$ and $^{23}$Na$^{6+}$ beams generated in the ion source in front of REXTRAP with a Na$^{7+}$ current exceeding 70 pA (6x10$^{7}$ p/s). Stable $^{27}$Al$^{7+}$ and $^{23}$Na$^{6+}$ from ISOLDE and also the first radioactive $^{26}$Na$^{7+}$ and $^{24}$Na$^{7+}$ beams (just 5x10$^{5}$ p/s) have been charge bred and accelerated for tests of the experimental setup. Despite some problems with the electron gun, which had one breakdown after about 1500 hours of operation and displays slow changes of the emission conditions, the EBIS is working remarkably stable (24 hours / 7 days a week). We will report ...
10. Nuclear structure and astrophysics with accelerated beams of radioactive ions: A new multidisciplinary research tool
International Nuclear Information System (INIS)
Garrett, J.D.
1995-01-01
After a brief discussion of the techniques for producing accelerated radioactive ion beams (RIBs), several recent scientific applications are mentioned. Three general nuclear structure topics, which can be addressed using RIBs, are discussed in some detail: possible modifications of the nuclear shell structure near the particle drip lines; various possibilities for decoupling the proton and neutron mass distributions for weakly bound nuclei; and tests of fundamental nuclear symmetries for self-conjugate and nearly self-conjugate nuclei. The use of RIBs to study r- and rp-process nucleosynthesis also is discussed
11. Beam Dynamics Design Studies of a Superconducting Radioactive Ion Beam Post-accelerator
CERN Document Server
Fraser, MA; Pasini, M
2011-01-01
The HIE-ISOLDE project at CERN proposes a superconducting upgrade to increase the energy range and quality of the radioactive ion beams produced at ISOLDE, which are currently post- accelerated by the normal conducting REX linac. The specification and design choices for the HIE-ISOLDE linac are outlined along with a comprehensive beam dynamics study undertaken to understand and mitigate the sources of beam emittance dilution. The dominant cause of transverse emittance growth was attributed to the coupling between the transverse and longitudinal motions through the phase dependence of the rf defocusing force in the accelerating cavities. A parametric resonance induced by the coupling was observed and its excitation surveyed as a function of trans- verse phase advance using numerical simulations and analytic models to understand and avoid the regions of transverse beam instability. Other sources of emittance growth were studied and where necessary ameliorated, including the beam steering force in the quarter-wa...
12. High current pulsed ion inductor accelerator for destruction of radioactive wastes
Energy Technology Data Exchange (ETDEWEB)
Korenev, S.A.; Puzynin, I.V.; Samoilov, V.N.; Sissakian, A.N. [Joint Inst. for Nuclear Research, Dubna (Russian Federation)
1997-09-01
The project of a high current pulsed linear ion accelerator is described in this paper. The accelerator consists of an ion injector, a system of charge and energy separation, an inductor accelerator and an output system. The ion source with explosive ion emission can produce all kinds of ions. The separation system includes a pulsed magnetic system. The inductors are based on amorphous iron with inside magnetic elements. 3 refs., 3 figs.
13. High current pulsed ion inductor accelerator for destruction of radioactive wastes
International Nuclear Information System (INIS)
Korenev, S.A.; Puzynin, I.V.; Samoilov, V.N.; Sissakian, A.N.
1997-01-01
The project of a high current pulsed linear ion accelerator is described in this paper. The accelerator consists of an ion injector, a system of charge and energy separation, an inductor accelerator and an output system. The ion source with explosive ion emission can produce all kinds of ions. The separation system includes a pulsed magnetic system. The inductors are based on amorphous iron with inside magnetic elements. 3 refs., 3 figs
14. High current pulsed ion inductor accelerator for destruction of radioactive wastes
Energy Technology Data Exchange (ETDEWEB)
Korenev, S A; Puzynin, I V; Samojlov, V N; Sissakyan, A N [Joint Institute for Nuclear Research, Dubna (Russian Federation)
1997-12-31
A new high-current pulsed linear induction accelerator proposed for application in beam-driven transmutation technologies is described. The accelerator consists of an ion injector, of ion separation and induction accelerating systems, and of an output system for extracting an ion beam into open air. An ion source with explosive ion emission, capable of producing various kinds of ions, is used as an injector. The ion separator exploits a pulsed magnetic system. The induction acceleration structure includes inductors with amorphous iron cores. Imbedded magnetic elements assure the ion beam transport. Main parameters of the accelerator are given in the paper and the design of an ion injector is discussed in more detail. (J.U.). 3 figs., 3 refs.
15. High current pulsed ion inductor accelerator for destruction of radioactive wastes
International Nuclear Information System (INIS)
Korenev, S.A.; Puzynin, I.V.; Samojlov, V.N.; Sissakyan, A.N.
1996-01-01
A new high-current pulsed linear induction accelerator proposed for application in beam-driven transmutation technologies is described. The accelerator consists of an ion injector, of ion separation and induction accelerating systems, and of an output system for extracting an ion beam into open air. An ion source with explosive ion emission, capable of producing various kinds of ions, is used as an injector. The ion separator exploits a pulsed magnetic system. The induction acceleration structure includes inductors with amorphous iron cores. Imbedded magnetic elements assure the ion beam transport. Main parameters of the accelerator are given in the paper and the design of an ion injector is discussed in more detail. (J.U.). 3 figs., 3 refs
CERN Document Server
Kluge, Heinz-Jürgen
2004-01-01
International Nuclear Information System (INIS)
Kluge, H.-J.; Blaum, K.
2004-01-01
18. Problems raised by radioactive ion acceleration in the SPIRAL project. Accelerator tuning and stabilisation; Problemes poses par lacceleration dions radioactifs dans le project SPIRAL. Reglage et stabilisation de laccelerateur
Energy Technology Data Exchange (ETDEWEB)
Boy, L. [Paris-6 Univ., 75 (France)
1997-12-31
This study is related to the SPIRAL project. This facility uses a cyclotron to accelerate radioactive ion beams produced in a thick target by the Grant Accelerateur National dIons Lourds primary beam. The low intensity of radioactive beams and the mixing of several species imply special tuning methods and associated diagnostics. Also, a cyclotron and the beam line will be used to switch from this tuning beam to the radioactive one. We present a theoretical study and a numerical simulation of the tuning of five radioactive beams using three different methods. the beam dynamic is performed through the injection beam line and the cyclotron up to the electrostatic deflector. Within the frame of these methods we have described all the SPIRAL beam diagnostics. Construction and test of a new low intensity diagnosis based on a plastic scintillator for phase measurement inside the cyclotron is described in details. (author). 63 refs.
19. The use of aluminum nitride to improve Aluminum-26 Accelerator Mass Spectrometry measurements and production of Radioactive Ion Beams
Science.gov (United States)
Janzen, Meghan S.; Galindo-Uribarri, Alfredo; Liu, Yuan; Mills, Gerald D.; Romero-Romero, Elisa; Stracener, Daniel W.
2015-10-01
We present results and discuss the use of aluminum nitride as a promising source material for Accelerator Mass Spectrometry (AMS) and Radioactive Ion Beams (RIBs) science applications of 26Al isotopes. The measurement of 26Al in geological samples by AMS is typically conducted on Al2O3 targets. However, Al2O3 is not an ideal source material because it does not form a prolific beam of Al- required for measuring low-levels of 26Al. Multiple samples of aluminum oxide (Al2O3), aluminum nitride (AlN), mixed Al2O3-AlN as well as aluminum fluoride (AlF3) were tested and compared using the ion source test facility and the stable ion beam (SIB) injector platform at the 25-MV tandem electrostatic accelerator at Oak Ridge National Laboratory. Negative ion currents of atomic and molecular aluminum were examined for each source material. It was found that pure AlN targets produced substantially higher beam currents than the other materials and that there was some dependence on the exposure of AlN to air. The applicability of using AlN as a source material for geological samples was explored by preparing quartz samples as Al2O3 and converting them to AlN using a carbothermal reduction technique, which involved reducing the Al2O3 with graphite powder at 1600 °C within a nitrogen atmosphere. The quartz material was successfully converted to AlN. Thus far, AlN proves to be a promising source material and could lead towards increasing the sensitivity of low-level 26Al AMS measurements. The potential of using AlN as a source material for nuclear physics is also very promising by placing 26AlN directly into a source to produce more intense radioactive beams of 26Al.
20. Heavy ion accelerators
International Nuclear Information System (INIS)
Schmelzer, C.
1974-01-01
This review of the present state of work on heavy-ion accelerators pays particular attention to the requirements for nuclear research. It is divided into the following sections: single-particle versus collective acceleration, heavy-ion accelerators, beam quality, and a status report on the UNILAC facility. Among the topics considered are the recycling cyclotron, linacs with superconducting resonators, and acceleration to the GeV/nucleon range. (8 figures, 2 tables) (U.S.)
1. HEAVY ION LINEAR ACCELERATOR
Science.gov (United States)
Van Atta, C.M.; Beringer, R.; Smith, L.
1959-01-01
A linear accelerator of heavy ions is described. The basic contributions of the invention consist of a method and apparatus for obtaining high energy particles of an element with an increased charge-to-mass ratio. The method comprises the steps of ionizing the atoms of an element, accelerating the resultant ions to an energy substantially equal to one Mev per nucleon, stripping orbital electrons from the accelerated ions by passing the ions through a curtain of elemental vapor disposed transversely of the path of the ions to provide a second charge-to-mass ratio, and finally accelerating the resultant stripped ions to a final energy of at least ten Mev per nucleon.
2. Ion sources for accelerators
International Nuclear Information System (INIS)
Alton, G.D.
1974-01-01
A limited review of low charge sate positive and negative ion sources suitable for accelerator use is given. A brief discussion is also given of the concepts underlying the formation and extraction of ion beams. Particular emphasis is placed on the technology of ion sources which use solid elemental or molecular compounds to produce vapor for the ionization process
3. Recent radioactive ion beam program at RIKEN and related topics
Keywords. RIKEN; radioactive ion beams; magic numbers. PACS No. 21.10.-k. 1. Introduction. In RIKEN, there are several heavy ion accelerators. Main accelerator is the RIKEN ring cyclotron (RRC) with K = 540, that has been operated from 1986. The RRC has two injectors; one is heavy ion linear accelerator that has been ...
4. Radioactive ion beam facilities at INFN LNS
International Nuclear Information System (INIS)
Rifuggiato, D; Calabretta, L; Celona, L; Chines, F; Cosentino, L; Cuttone, G; Finocchiaro, P; Pappalardo, A; Re, M; Rovelli, A
2011-01-01
Radioactive ion beams are produced at INFN- Laboratori Nazionali del Sud (LNS) by means of the two operating accelerators, the Tandem and the Superconducting Cyclotron (CS), originally designed to accelerate stable beams. Both the ISOL (Isotope Separation On Line) and the IFF (In-Flight Fragmentation) methods are exploited to produce RIBs in two different ways at different energies: in the first case, the Cyclotron is the primary accelerator and the Tandem accelerates the secondary beams, while in the second case radioactive fragments are produced by the Cyclotron beam in a thin target with energies comparable to the primary beam energy. The ISOL facility is named EXCYT (Exotics at the Cyclotron and Tandem) and was commissioned in 2006, when the first radioactive beam ( 8 Li) has been produced. The IFF installation is named FRIBs (in Flight Radioactive Ion Beams), and it has started to produce radioactive beams in 2001, placing a thin target in the extraction beam line of the Cyclotron. The development of both facilities to produce and accelerate radioactive ion beams at LNS, is briefly described, with some details on the future prospects that are presently under consideration or realization.
5. Collective ion acceleration
International Nuclear Information System (INIS)
Godfrey, B.B.; Faehl, R.J.; Newberger, B.S.; Shanahan, W.R.; Thode, L.E.
1977-01-01
Progress achieved in the understanding and development of collective ion acceleration is presented. Extensive analytic and computational studies of slow cyclotron wave growth on an electron beam in a helix amplifier were performed. Research included precise determination of linear coupling between beam and helix, suppression of undesired transients and end effects, and two-dimensional simulations of wave growth in physically realizable systems. Electrostatic well depths produced exceed requirements for the Autoresonant Ion Acceleration feasibility experiment. Acceleration of test ions to modest energies in the troughs of such waves was also demonstrated. Smaller efforts were devoted to alternative acceleration mechanisms. Langmuir wave phase velocity in Converging Guide Acceleration was calculated as a function of the ratio of electron beam current to space-charge limiting current. A new collective acceleration approach, in which cyclotron wave phase velocity is varied by modulation of electron beam voltage, is proposed. Acceleration by traveling Virtual Cathode or Localized Pinch was considered, but appears less promising. In support of this research, fundamental investigations of beam propagation in evacuated waveguides, of nonneutral beam linear eigenmodes, and of beam stability were carried out. Several computer programs were developed or enhanced. Plans for future work are discussed
6. First Results with TIGRESS and Accelerated Radioactive Ion Beams from ISAC: Coulomb Excitation of 20,21,29Na
Science.gov (United States)
Schumaker, M. A.; Hurst, A. M.; Svensson, C. E.; Wu, C. Y.; Becker, J. A.; Cline, D.; Hackman, G.; Pearson, C. J.; Stoyer, M. A.; Andreyev, A.; Austin, R. A. E.; Ball, G. C.; Bandyopadhyay, D.; Barton, C. J.; Boston, A. J.; Boston, H. C.; Buchmann, L.; Churchman, R.; Cifarelli, F.; Colosimo, S. J.; Cooper, R. J.; Cross, D. S.; Dashdorj, D.; Demand, G. A.; Dimmock, M. R.; Djongolov, M.; Drake, T. E.; Finlay, P.; Gallant, A. T.; Garrett, P. E.; Gray-Jones, C.; Green, K. L.; Grint, A. N.; Grinyer, G. F.; Harkness, L. J.; Hayes, A. B.; Kanungo, R.; Leach, K. G.; Kulp, W. D.; Lisetskiy, A. F.; Lee, G.; Lloyd, S.; Maharaj, R.; Martin, J.-P.; Millar, B. A.; Moisan, F.; Morton, A. C.; Mythili, S.; Nelson, L.; Newman, O.; Nolan, P. J.; Orce, J. N.; Oxley, D. C.; Padilla-Rodal, E.; Phillips, A. A.; Porter-Peden, M.; Ressler, J. J.; Rigby, S. V.; Roy, R.; Ruiz, C.; Sarazin, F.; Scraggs, D. P.; Sumithrarachchi, C. S.; Triambak, S.; Waddington, J. C.; Walker, P. M.; Wan, J.; Whitbeck, A.; Williams, S. J.; Wong, J.; Wood, J. L.
2009-03-01
The TRIUMF-ISAC Gamma-Ray Escape Suppressed Spectrometer (TIGRESS) is a state-of-the-art γ-ray spectrometer being constructed at the ISAC-II radioactive ion beam facility at TRIUMF. TIGRESS will be comprised of twelve 32-fold segmented high-purity germanium (HPGe) clover-type γ-ray detectors, with BGO/CsI(Tl) Compton-suppression shields, and is currently operational at ISAC-II in an early-implementation configuration of six detectors. Results have been obtained for the first experiments performed using TIGRESS, which examined the A = 20, 21, and 29 isotopes of Na by Coulomb excitation.
7. Ion optics for accelerators
International Nuclear Information System (INIS)
Enge, H.A.
1974-01-01
A review is given of ion-optic devices used in particle accelerators, including electrostatic lenses, magnetic quadrupoles, and deflecting magnets. Tube focusing in dc accelerators is also treated, and a novel scheme for shaping the electrodes to produce strong focusing is described. The concepts of emittance (phase space) and emittance conservation are briefly discussed. Chromatic and spatial aberrations are introduced, and it is shown how they can be calculated and sometimes substantially reduced. Some examples are given
8. Collective focusing ion accelerator
International Nuclear Information System (INIS)
Goldin, F.J.
1986-01-01
The principal subject of this dissertation is the trapping confinement of pure electron plasmas in bumpy toroidal magnetic fields, with particular attention given to the trapping procedure and the behavior of the plasma during the final equilibrium. The most important aspects of the equilibrium studied were the qualitative nature of the plasma configuration and motion and its density, distribution and stability. The motivation for this study was that an unneutralized cloud of electrons contained in a toroidal system, sufficiently dense and stable, may serve to electrostatically focus ions (against centrifugal and self space charge forces) in a cyclic ion accelerator. Such an accelerator, known as a Collective Focusing Ion Accelerator (CFIA) could be far smaller than conventional designs (which use external magnetic fields directly to focus the ions) due to the smaller gyro-radium of an electron in a magnetic field of given strength. The electron cloud generally drifted poloidally at a finite radius from the toroidal minor axis. As this would preclude focusing ions with such clouds, damping this motion was investigated. Finite resistance in the normally perfectly conductive vessel wall did this. In further preparation for a working CFIA, additional experiments studied the effect of ions on the stability of the electron cloud
9. Heavy ion accelerator GANIL
International Nuclear Information System (INIS)
1975-04-01
This article presents GANIL, a large national heavy ion accelerator. The broad problems of nuclear physics, atomic physics, astrophysics and physics of condensed media which can be approached and studied with this machine are discussed first, after which the final construction project is described. The project comprises a circular injector, a separated sector cyclotron up beam stripper, and a second separated cyclotron downstream [fr
10. Post-acceleration of sup 7 Be at the Louvain-la-Neuve radioactive ion beam facility
CERN Document Server
Gaelens, M; Loiselet, M; Ryckewaert, G
2003-01-01
The development of an intense and pure post-accelerated sup 7 Be beam at Louvain-la-Neuve will be discussed. Given its properties (metallic nature, long half-life (53 days)) and the special beam parameters required (multi-charge ions, high purity), a range of special techniques had to be investigated. At Louvain-la-Neuve, sup 7 Be is produced by irradiating a lithium target with 30 mu A of 27 MeV protons and is extracted using offline chemical separation techniques. Because of the large amounts of activity required, the chemistry has to be adapted for use in hotcells. The ionization is performed with an Electron Cyclotron Resonance ion source with the sup 7 Be injected in the source by means of sputtering. Special techniques have to be used to prevent the beryllium atoms from being lost on the plasma chamber walls. A dedicated heated plasma chamber for the ion source was developed. The ionization efficiency was increased by studying the chemistry involved in the ion source. The atoms are ionized to the 1+ or ...
11. Ion accelerators for space
International Nuclear Information System (INIS)
Slobodrian, R.J.; Potvin, L.
1991-01-01
The main purpose of the accelerators is to allow ion implantation in space stations and their neighborhoods. There are several applications of interest immediately useful in such environment: as ion engines and thrusters, as implanters for material science and for hardening of surfaces (relevant to improve resistance to micrometeorite bombardment of exposed external components), production of man made alloys, etc. The microgravity environment of space stations allows the production of substances (crystalline and amorphous) under conditions unknown on earth, leading to special materials. Ion implantation in situ of those materials would thus lead uninterruptedly to new substances. Accelerators for space require special design. On the one hand it is possible to forego vacuum systems simplifying the design and operation but, on the other hand, it is necessary to pay special attention to heat dissipation. Hence it is necessary to construct a simulator in vacuum to properly test prototypes under conditions prevailing in space
12. Medical heavy ion accelerator proposals
International Nuclear Information System (INIS)
Gough, R.A.
1985-05-01
For several decades, accelerators designed primarily for research in nuclear and high energy physics have been adapted for biomedical research including radiotherapeutic treatment of human diseases such as pituitary disorders, cancer, and more recently, arteriovascular malformations. The particles used in these treatments include pions, protons and heavier ions such as carbon, neon, silicon and argon. Maximum beam energies must be available to penetrate into an equivalent of about 30 cm of water, requiring treatment beams of 250 to 1000 MeV/nucleon. Certain special treatments of superficial melanoma, however, require that beam energies as low as 70 MeV/nucleon also be available. Intensities must be adequate to complete a 100 rad treatment fraction in about 1 minute. For most heavy ion treatments, this corresponds to 10 7 -10 9 ions/second at the patient. Because this research is best conducted in a dedicated, hospital-based facility, and because of the clinical need for ultra-high reliability, the construction of new and dedicated facilities has been proposed. Heavy ion accelerators can provide a variety of ions and energies, permitting treatment plans that exploit the properties of the ion best suited to each individual treatment, and that employ radioactive beams (such as 11 C and 19 Ne) to precisely confirm the dose localization. The favored technical approach in these proposals utilizes a conventional, strong-focusing synchrotron capable of fast switching between ions and energies, and servicing multiple treatment rooms. Specialized techniques for shaping the dose to conform to irregularly-shaped target volumes, while simultaneously sparing surrounding, healthy tissue and critical structures, are employed in each treatment room, together with the sophisticated dosimetry necessary for verification, monitoring, and patient safety. 3 refs., 8 figs
13. Accelerator development for a radioactive beam facility based on ATLAS
International Nuclear Information System (INIS)
Shepard, K. W.
1998-01-01
The existing superconducting linac ATLAS is in many respects an ideal secondary beam accelerator for an ISOL (Isotope separator on-line) type radioactive beam facility. Such a facility would require the addition of two major accelerator elements: a low charge state injector for the existing heavy ion linac, and a primary beam accelerator providing 220 MV of acceleration for protons and light ions. Development work for both of these elements, including the option of superconducting cavities for the primary beam accelerator is discussed
14. Accelerator development for a radioactive beam facility based on ATLAS.
Energy Technology Data Exchange (ETDEWEB)
Shepard, K. W.
1998-01-08
The existing superconducting linac ATLAS is in many respects an ideal secondary beam accelerator for an ISOL (Isotope separator on-line) type radioactive beam facility. Such a facility would require the addition of two major accelerator elements: a low charge state injector for the existing heavy ion linac, and a primary beam accelerator providing 220 MV of acceleration for protons and light ions. Development work for both of these elements, including the option of superconducting cavities for the primary beam accelerator is discussed.
15. Heavy ion accelerating structure
International Nuclear Information System (INIS)
Pottier, Jacques.
1977-01-01
The heavy ion accelerating structure concerned in this invention is of the kind that have a resonance cavity inside which are located at least two longitudinal conducting supports electrically connected to the cavity by one of their ends in such a way that they are in quarter-wavelength resonance and in phase opposition. Slide tubes are electrically connected alternatively to one or the other of the two supports, they being electrically connected respectively to one or the other end of the side wall of the cavity. The feature of the structure is that it includes two pairs of supports symmetrically placed with respect to the centre line of the cavity, the supports of one pair fitted overhanging being placed symmetrically with respect to the centre line of the cavity, each slide tube being connected to the two supports of one pair. These support are connected to the slide wall of the cavity by an insulator located at their electrically free end. The accelerator structure composed of several structures placed end to end, the last one of which is fed by a high frequency field of adjustable amplitude and phase, enables a heavy ion linear accelerator to be built [fr
16. Development of the Holifield Radioactive Ion Beam Facility
International Nuclear Information System (INIS)
Tatum, B.A.
1997-01-01
The Holifield Radioactive Ion Beam Facility (HRIBF) construction project has been completed and the first radioactive ion beam has been successfully accelerated. The project, which began in 1992, has involved numerous facility modifications. The Oak Ridge Isochronous Cyclotron has been converted from an energy booster for heavy ion beams to a light ion accelerator with internal ion source. A target-ion source and mass analysis system have been commissioned as key components of the facility's radioactive ion beam injector to the 25MV tandem electrostatic accelerator. Beam transport lines have been completed, and new diagnostics for very low intensity beams have been developed. Work continues on a unified control system. Development of research quality radioactive beams for the nuclear structure and nuclear astrophysics communities continues. This paper details facility development to date
17. Proceedings of national seminar on physics with radioactive ion beams
International Nuclear Information System (INIS)
Chintalapudi, S.N.; Shyam, R.
1991-01-01
This volume containing the proceedings of the national seminar on physics with radioactive ion beams gives a broad overview of the developments taking place in the area of nuclear physics and accelerator physics with special emphasis on the utilization of radioactive ion beams for various studies. Topics covered include studies on nuclear structure and nuclear astrophysics and the wide ranging applications of radioactive ion beams in these and other areas of nuclear sciences. Papers relevant to INIS are indexed separately
18. Review of ion accelerators
International Nuclear Information System (INIS)
Alonso, J.
1990-06-01
The field of ion acceleration to higher energies has grown rapidly in the last years. Many new facilities as well as substantial upgrades of existing facilities have extended the mass and energy range of available beams. Perhaps more significant for the long-term development of the field has been the expansion in the applications of these beams, and the building of facilities dedicated to areas outside of nuclear physics. This review will cover many of these new developments. Emphasis will be placed on accelerators with final energies above 50 MeV/amu. Facilities such as superconducting cyclotrons and storage rings are adequately covered in other review papers, and so will not be covered here
19. BEARS: Radioactive ion beams at LBNL
International Nuclear Information System (INIS)
Powell, J.; Guo, F.Q.; Haustein, P.E.
1998-01-01
BEARS (Berkeley Experiments with Accelerated Radioactive Species) is an initiative to develop a radioactive ion-beam capability at Lawrence Berkeley National Laboratory. The aim is to produce isotopes at an existing medical cyclotron and to accelerate them at the 88 inch Cyclotron. To overcome the 300-meter physical separation of these two accelerators, a carrier-gas transport system will be used. At the terminus of the capillary, the carrier gas will be separated and the isotopes will be injected into the 88 inch Cyclotron's Electron Cyclotron Resonance (ECR) ion source. The first radioactive beams to be developed will include 20-min 11 C and 70-sec 14 O, produced by (p,n) and (p,α) reactions on low-Z targets. A test program is currently being conducted at the 88 inch Cyclotron to develop the parts of the BEARS system. Preliminary results of these tests lead to projections of initial 11 C beams of up to 2.5 x 10 7 ions/sec and 14 O beams of 3 x 10 5 ions/sec
20. Experiments with SIRA - the radioactive ion separator
International Nuclear Information System (INIS)
Angelique, J.C.; Orr, N.A.
1998-01-01
There are two main techniques to obtain radioactive ion beams. One, consisting in the fragmentation of projectile in a thin target followed by a separation carried out with LISE or SISSI type spectrometers or by an alpha spectrometer is used currently at GANIL. The second one, the ISOL (Isotope Separator One-Line) is presently under study on the SIRa benchmark, as part of the SPIRaL (Source de Production d'Ions Radioactifs en Ligne). A high energy light ion beam is stopped by a thick target to produce radioactive nuclei by various reactions in the target. The target, usually of carbon, is heated at around 1800 deg. C in order to accelerate the migration of the atoms produced at the target surface. These atoms are then diffused by a transfer tube up to plasma region where they are ionized and then accelerated. As projectiles the GANIL project makes use of a large variety of heavy ions. A table containing the radioactive ion beam characteristics (charge state and lifetime), the primary beams, the yields and the expected intensities to be obtained with SPIRaL is presented. Also, data concerning the production rates of rare gases obtained during 1993 to 1994 are given
1. Electron string ion sources for carbon ion cancer therapy accelerators
Science.gov (United States)
Boytsov, A. Yu.; Donets, D. E.; Donets, E. D.; Donets, E. E.; Katagiri, K.; Noda, K.; Ponkin, D. O.; Ramzdorf, A. Yu.; Salnikov, V. V.; Shutov, V. B.
2015-08-01
The type of the Electron String Ion Sources (ESIS) is considered to be the appropriate one to produce pulsed C4+ and C6+ ion beams for cancer therapy accelerators. In fact, the new test ESIS Krion-6T already now provides more than 1010 C4+ ions per pulse and about 5 × 109 C6+ ions per pulse. Such ion sources could be suitable to apply at synchrotrons. It has also been found that Krion-6T can provide more than 1011 C6+ ions per second at the 100 Hz repetition rate, and the repetition rate can be increased at the same or larger ion output per second. This makes ESIS applicable at cyclotrons as well. ESIS can be also a suitable type of ion source to produce the 11C radioactive ion beams. A specialized cryogenic cell was experimentally tested at the Krion-2M ESIS for pulse injection of gaseous species into the electron string. It has been shown in experiments with stable methane that the total conversion efficiency of methane molecules to C4+ ions reached 5%÷10%. For cancer therapy with simultaneous irradiation and precise dose control (positron emission tomography) by means of 11C, transporting to the tumor with the primary accelerated 11C4+ beam, this efficiency is preliminarily considered to be large enough to produce the 11C4+ beam from radioactive methane and to inject this beam into synchrotrons.
2. Ion sources for electrostatic accelerators
International Nuclear Information System (INIS)
Hellborg, R.
1998-01-01
Maybe the most important part of an electrostatic accelerator system, and also often the most tricky part is the ion source. There has been a rapid growth in activity in ion-source research and development during the last two to three decades. Some of these developments have also been of benefit to electrostatic accelerator users. In this report some of the different types of ion sources used in electrostatic accelerators are described. The list is not complete but more an overview of some of the more commonly used sources. The description is divided into two groups; positive ion sources for single stage electrostatic accelerators and negative ion sources for two stages (i.e. tandem) accelerators
3. Ion sources for medical accelerators
Science.gov (United States)
Barletta, W. A.; Chu, W. T.; Leung, K. N.
1998-02-01
Advanced injector systems for proton synchrotrons and accelerator-based boron neutron capture therapy systems are being developed at the Lawrence Berkeley National Laboratory. Multicusp ion sources, particularly those driven by radio frequency, have been tested for these applications. The use of a radio frequency induction discharge provides clean, reliable, and long-life source operation. It has been demonstrated that the multicusp ion source can provide good-quality positive hydrogen ion beams with a monatomic ion fraction higher than 90%. The extractable ion current densities from this type of source can meet the injector requirements for both proton synchrotron and accelerator-based boron neutron capture therapy projects.
4. Molecular ion acceleration using tandem accelerator
Energy Technology Data Exchange (ETDEWEB)
Saito, Yuichi; Mizuhashi, Kiyoshi; Tajima, Satoshi [Japan Atomic Energy Research Inst., Takasaki, Gunma (Japan). Takasaki Radiation Chemistry Research Establishment
1996-12-01
In TIARA compound beam radiation system, cluster beams have been produced using 3 MV tandem accelerator (9SDH-2) to supply them to various radiation on injection experiments. Till now, productions of C{sub 2-8}, Si{sub 2-4} and O{sub 2} and their accelerations up to 6 MeV have been succeeded. This study aimed at production and acceleration of B{sub 2-4} and LiF. Anion clusters were produced using the conventional ion source of cesium sputter type. The proportions of atoms, molecules and clusters elicited from the ion source were varied depending on the materials properties and the operating conditions of ion source such as sample temperature, sputter voltage and the shape of sample. The anion clusters were accelerated toward the high voltage terminal in the center of tandem accelerator, leading to cations through losing their electrons by the collision to N{sub 2} gas in a charge conversion cell at the terminal. Positively charged cluster ions could be obtained by modulating the pressure of N{sub 2} gas. Thus, B{sub 2} (64 nA), B{sub 3} (4.4 nA) and B{sub 4} (2.7 nA) have been produced and their maximum survival probabilities were higher than those of carbon or silicon clusters. In addition, the relationship between beam current and gas pressure was investigated for Bn (n = 2-4) and LiF. (M.N.)
5. Heavy ion accelerators at GSI
International Nuclear Information System (INIS)
Angert, N.
1984-01-01
The status of the Unilac heavy ion linear accelerator at GSI, Darmstadt is given. A schematic overall plan view of the Unilac is shown and its systems are described. List of isotopes and intensities accelerated at the Unilac is presented. The experimental possibilities at GSI should be considerably extended by a heavy ion synchrotron (SIS 18) in combination with an experimental storage ring (ESR). A prototype of the rf-accelerating system of the synchrotron has been built and tested. Prototypes for the quadrupole and dipole magnets for the ring are being constructed. The SIS 18 is desigmed for a maximum magnetic rigidity of 18Tm so that neon can be accelerated to 2 GeV/W and uranium to 1 GeV/u. The design allows also the acceleration of protons up to 4.5 GeV. The ESR permits to storage fully stripped uranium ions up to an energy of approximately R50 MeV/u
6. Heavy ion medical accelerator, HIMAC
International Nuclear Information System (INIS)
1993-01-01
The heavy ion beam is undoutedly suitable for the cancer treatment. The supriority of the heavy ions over the conventional radiations including protons and neutrons comes mainly from physical characteristics of a heavy particle with multiple charges. A straggling angle due to a multiple Coulomb scattering process in a human body is small for heavy ions, and the small scattering angle results in a good dose localization in a transverse direction. An ionization ratio of the heavy ion beam makes a very sharp peak at the ends of their range. The height of the peak is higher for the heavier ions and shows excellent biomedical effects around Ne ions. In order to apply heavy ion beams to cancer treatment, Heavy Ion Medical Accelerator in Chiba (HIMAC) has been constructed at National Institute of Radiological Sciences. The accelerator complex consists of two ion sources, two successive linac tanks, a pair of synchrotron rings, a beam transport system and an irradiation system. An operation frequency is 100 MHz for two linacs, and the ion energy is 6.0 MeV/u at the output end of the linac. The other four experimental rooms are prepared for basic experiments. The synchrotron accelerates ions up to 800 MeV/u for a charge to mass ratio of 1/2. The long beam transport line provides two vertical beams in addition with two horizontal beams for the treatment. The three treatment rooms are prepared one of which is equipped with both horizontal and vertical beam lines. The whole facility will be open for all scientists who have interests in the heavy ion science as well as the biophysics. The conceptual design study of HIMAC started in 1984, and the construction of the accelerator complex was begun in March 1988. The beam acceleration tests of the injector system was successfully completed in March of this year, and tests of the whole system will be finished throughout this fyscal year. (author)
International Nuclear Information System (INIS)
Pokonova, Yu.P.; Ivshina, O.A.; Il'ina, O.V.
1993-01-01
Properties of some binding agents for fixing radioactive cationites and anionites, namels cement, bitumen, carbamide and polyether resins are analyzed. It is shown that localization of ionites in carbamide resin is not very effective, the same is true of cementing process owing to considerable washing out of cesium-137 (∼ 1.1 x 10 -1 cm) and low water resistance (the samples are destructed when, storage conditions vary). Products of ionite localization in polyether feature a lower washing out (3x10 -2 - 4x10 -2 cm) and a better water resistance (water absorption rate is approximattely 1.5 x 10 -4 cm/day)/ Polyethers despite their high cost, are preferable for processing and transportation of small amounts of the ionites (up to 100 m 3 /year)
8. Detection systems for radioactive ion beams
International Nuclear Information System (INIS)
Savajols, H.
2002-01-01
Two main methods are used to produce radioactive ion beams: -) the ISOL method (isotope separation on-line) in which the stable beam interacts with a thick target, the reaction products diffuse outside the target and are transferred to a source where they are ionized, a mass separator and a post-accelerator drive the selected radioactive ions to the right energy; -) the in-flight fragmentation method in which the stable beam interacts with a thin target, the reaction products are emitted from the target with a restricted angular distribution and a velocity close to that of the incident beam, the experimenter has to take advantage from the reaction kinetics to get the right particle beam. Characteristic time is far longer with the ISOL method but the beam intensity is much better because of the use of a post-accelerator. In both cases, the beam intensity is lower by several orders of magnitude than in the case of a stable beam. This article presents all the constraints imposed by radioactive beams to the detection systems of the reaction products and gives new technical solutions according to the type of nuclear reaction studied. (A.C.)
9. Electron string ion sources for carbon ion cancer therapy accelerators
Energy Technology Data Exchange (ETDEWEB)
Boytsov, A. Yu.; Donets, D. E.; Donets, E. D.; Donets, E. E.; Ponkin, D. O.; Ramzdorf, A. Yu.; Salnikov, V. V.; Shutov, V. B. [Joint Institute for Nuclear Research, Dubna 141980 (Russian Federation); Katagiri, K.; Noda, K. [National Institute of Radiological Science, 4-9-1 Anagawa, Inage-ku, Chiba 263-8555 (Japan)
2015-08-15
The type of the Electron String Ion Sources (ESIS) is considered to be the appropriate one to produce pulsed C{sup 4+} and C{sup 6+} ion beams for cancer therapy accelerators. In fact, the new test ESIS Krion-6T already now provides more than 10{sup 10} C{sup 4+} ions per pulse and about 5 × 10{sup 9} C{sup 6+} ions per pulse. Such ion sources could be suitable to apply at synchrotrons. It has also been found that Krion-6T can provide more than 10{sup 11} C{sup 6+} ions per second at the 100 Hz repetition rate, and the repetition rate can be increased at the same or larger ion output per second. This makes ESIS applicable at cyclotrons as well. ESIS can be also a suitable type of ion source to produce the {sup 11}C radioactive ion beams. A specialized cryogenic cell was experimentally tested at the Krion-2M ESIS for pulse injection of gaseous species into the electron string. It has been shown in experiments with stable methane that the total conversion efficiency of methane molecules to C{sup 4+} ions reached 5%÷10%. For cancer therapy with simultaneous irradiation and precise dose control (positron emission tomography) by means of {sup 11}C, transporting to the tumor with the primary accelerated {sup 11}C{sup 4+} beam, this efficiency is preliminarily considered to be large enough to produce the {sup 11}C{sup 4+} beam from radioactive methane and to inject this beam into synchrotrons.
10. Compact ion accelerator source
Science.gov (United States)
Schenkel, Thomas; Persaud, Arun; Kapadia, Rehan; Javey, Ali
2014-04-29
An ion source includes a conductive substrate, the substrate including a plurality of conductive nanostructures with free-standing tips formed on the substrate. A conductive catalytic coating is formed on the nanostructures and substrate for dissociation of a molecular species into an atomic species, the molecular species being brought in contact with the catalytic coating. A target electrode placed apart from the substrate, the target electrode being biased relative to the substrate with a first bias voltage to ionize the atomic species in proximity to the free-standing tips and attract the ionized atomic species from the substrate in the direction of the target electrode.
11. Predicting Induced Radioactivity at High Energy Accelerators
Energy Technology Data Exchange (ETDEWEB)
Fasso, Alberto
1999-08-27
Radioactive nuclides are produced at high-energy electron accelerators by different kinds of particle interactions with accelerator components and shielding structures. Radioactivity can also be induced in air, cooling fluids, soil and groundwater. The physical reactions involved include spallations due to the hadronic component of electromagnetic showers, photonuclear reactions by intermediate energy photons and low-energy neutron capture. Although the amount of induced radioactivity is less important than that of proton accelerators by about two orders of magnitude, reliable methods to predict induced radioactivity distributions are essential in order to assess the environmental impact of a facility and to plan its decommissioning. Conventional techniques used so far are reviewed, and a new integrated approach is presented, based on an extension of methods used at proton accelerators and on the unique capability of the FLUKA Monte Carlo code to handle the whole joint electromagnetic and hadronic cascade, scoring residual nuclei produced by all relevant particles. The radiation aspects related to the operation of superconducting RF cavities are also addressed.
12. ISOL science at the Holifield Radioactive Ion Beam Facility
Energy Technology Data Exchange (ETDEWEB)
Beene, James R [ORNL; Bardayan, Daniel W [ORNL; Galindo-Uribarri, Alfredo {nmn} [ORNL; Gross, Carl J [ORNL; Jones, K. L. [University of Tennessee, Knoxville (UTK); Liang, J Felix [ORNL; Nazarewicz, Witold [ORNL; Stracener, Daniel W [ORNL; Tatum, B Alan [ORNL; Varner Jr, Robert L [ORNL
2011-01-01
The Holi eld Radioactive Ion Beam Facility, located in Oak Ridge, Tennessee, is operated as a National User Facility for the U.S. Department of Energy, producing high quality ISOL beams of short-lived, radioactive nuclei for studies of exotic nuclei, astrophysics research, and various societal applications. The primary driver, the Oak Ridge Isochronous Cyclotron, produces rare isotopes by bombarding highly refractory targets with light ions. The radioactive isotopes are ionized, formed into a beam, mass selected, injected into the 25-MV Tandem, accelerated, and used in experiments. This article reviews HRIBF and its science.
13. Ion sources for initial use at the Holifield radioactive ion beam facility
International Nuclear Information System (INIS)
Alton, G.D.
1994-01-01
The Holifield Radioactive Ion Beam Facility (HRIBF) now under construction at the Oak Ridge National Laboratory will use the 25-MV tandem accelerator for the acceleration of radioactive ion beams to energies appropriate for research in nuclear physics; negative ion beams are, therefore, required for injection into the tandem accelerator. Because charge exchange is an efficient means for converting initially positive ion beams to negative ion beams, both positive and negative ion sources are viable options for use at the facility; the choice of the type of ion source will depend on the overall efficiency for generating the radioactive species of interest. A high-temperature version of the CERN-ISOLDE positive ion source has been selected and a modified version of the source designed and fabricated for initial use at the HRIBF because of its low emittance, relatively high ionization efficiencies and species versatility, and because it has been engineered for remote installation, removal and servicing as required for safe handling in a high-radiation-level ISOL facility. Prototype plasma-sputter negative ion sources and negative surfaceionization sources are also under design consideration for generating negative radioactive ion beams from high electron-affinity elements. A brief review of the HRIBF will be presented, followed by a detailed description of the design features, operational characteristics, ionization efficiencies, and beam qualities (emittances) of these sources
14. Optimization of negative ion accelerators
International Nuclear Information System (INIS)
Pamela, J.
1991-01-01
We have started to study negative ion extraction and acceleration systems in view of designing a 1 MeV D - accelerator. This study is being made with a two-Dimensional code that has been specifically developed in our laboratory and validated by comparison to three sets of experimental data. We believe that the criteria for negative ion accelerator design optimization should be: (i) to provide the best optics; (ii) to reduce the power load on the extraction grid; (iii) to allow operation with low electric fields in order to reduce the problem of breakdowns. We show some results of optics calculations performed for two systems that will be operational in the next months: the CEA-JAERI collaboration at Cadarache and the european DRAGON experiment at Culham. Extrapolations to higher energies of 500 to 1100 keV have also been conducted. All results indicate that the overall accelerator length, whatever be the number of gaps, is constrained by space charge effects (Child-Langmuir). We have combined this constraint with high-voltage hold-off empirical laws. As a result, it appears that accelerating 10 mA/cm 2 of D - at 1 MeV with good optics, as required for NET or ITER, is close to the expected limit of high-voltage hold-off
15. Development of heavy ion linear accelerators
International Nuclear Information System (INIS)
Bomko, V.A.; Khizhnyak, N.A.
1981-01-01
A review of the known heavy ion accelerators is given. It is stated that cyclic and linear accelerators are the most perspective ones in the energy range up to 10 MeV/nucleon according to universality in respect with the possibility of ion acceleration of the wide mass range. However, according to the accelerated beam intensity of the heavier ions the linear accelerators have considerable advantages over any other types of accelerators. The review of the known heavy ion linac structures permits to make the conclusion that a new modification of an accelerating structure of opposite pins excited on a H-wave is the most perspective one [ru
16. Accelerators for heavy ion fusion
International Nuclear Information System (INIS)
Bangerter, R.O.
1985-10-01
Large fusion devices will almost certainly produce net energy. However, a successful commercial fusion energy system must also satisfy important engineering and economic constraints. Inertial confinement fusion power plants driven by multi-stage, heavy-ion accelerators appear capable of meeting these constraints. The reasons behind this promising outlook for heavy-ion fusion are given in this report. This report is based on the transcript of a talk presented at the Symposium on Lasers and Particle Beams for Fusion and Strategic Defense at the University of Rochester on April 17-19, 1985
17. Study of the on line radioactive multicharged ion production
International Nuclear Information System (INIS)
Lecesne, N.
1997-01-01
This work is directly related to the SPIRAL project (Systeme de Production d'Ions Radioactifs Acceleres en Ligne) which will start at GANIL at the end of 1998. The aim of the thesis was to study the on line radioactive multicharged ion beam production stages, i.e. the production and diffusion of the radioactive nuclei in a thick target, their possible transfer up to an ECR ion source and their ionisation. Production cross sections of radioactive neutron rich nuclei, formed by fragmentation of a heavy ion beam in a thick target, were measured. An external target-ECR source system, dedicated to the radioactive noble gases production, and two internal target-ECR source systems, dedicated to the radioactive condensable element production, were built and tested on the SIRa tests bench (Separateur d'Ions Radioactifs). Different detection configurations were elaborated in order to identify the radioactive nuclei and estimate their production yields. Finally, a new method for measuring the overall efficiency of the separator was developed and allowed to study the diffusion properties of radioactive noble gases in various targets. (author)
18. Status of radioactive ion beams at the HRIBF
CERN Document Server
Stracener, D W
2003-01-01
Radioactive Ion Beams (RIBs) at the Holifield Radioactive Ion Beam Facility (HRIBF) are produced using the isotope separation on-line technique and are subsequently accelerated up to a few MeV per nucleon for use in nuclear physics experiments. The first RIB experiments at the HRIBF were completed at the end of 1998 using sup 1 sup 7 F beams. Since then other proton-rich ion beams have been developed and a large number of neutron-rich ion beams are now available. The neutron-rich radioactive nuclei are produced via proton-induced fission of uranium in a low-density matrix of uranium carbide. Recently developed RIBs include sup 2 sup 5 Al from a silicon carbide target and isobarically pure beams of neutron-rich Ge, Sn, Br and I isotopes from a uranium carbide target.
19. Unlimited ion acceleration by radiation pressure.
Science.gov (United States)
Bulanov, S V; Echkina, E Yu; Esirkepov, T Zh; Inovenkov, I N; Kando, M; Pegoraro, F; Korn, G
2010-04-02
The energy of ions accelerated by an intense electromagnetic wave in the radiation pressure dominated regime can be greatly enhanced due to a transverse expansion of a thin target. The expansion decreases the number of accelerated ions in the irradiated region resulting in an increase in the ion energy and in the ion longitudinal velocity. In the relativistic limit, the ions become phase locked with respect to the electromagnetic wave resulting in unlimited ion energy gain.
20. Construction of ion accelerator for ion-surface interaction research
International Nuclear Information System (INIS)
Obara, Kenziro; Ohtsuka, Hidewo; Yamada, Rayji; Abe, Tetsuya; Sone, Kazuho
1977-09-01
A Cockcroft-Walton type ion accelerator for ion-surface interaction research was installed at Plasma Engineering Laboratory, Division of Thermonuclear Fusion Research, JAERI, in March 1977. Its maximum accelerating voltage is 400 kV. The accelerator has some outstanding features compared with the conventional type. Described are setup of the accelerator specification of the major components, safety system and performance. (auth.)
1. A radioactive ion beam facility using photofission
CERN Document Server
Diamond, W T
1999-01-01
Use of a high-power electron linac as the driver accelerator for a Radioactive Ion Beam (RIB) facility is proposed. An electron beam of 30 MeV and 100 kW can produce nearly 5x10 sup 1 sup 3 fissions/s from an optimized sup 2 sup 3 sup 5 U target and about 60% of this from a natural uranium target. An electron beam can be readily transmitted through a thin window at the exit of the accelerator vacuum system and transported a short distance through air to a water-cooled Bremsstrahlung-production target. The Bremsstrahlung radiation can, in turn, be transported through air to the isotope-production target. This separates the accelerator vacuum system, the Bremsstrahlung target and the isotope-production target, reducing remote handling problems. The electron beam can be scanned over a large target area to reduce the power density on both the Bremsstrahlung and isotope-production targets. These features address one of the most pressing technological challenges of a high-power RIB facility, namely the production o...
2. Negative ion sources for tandem accelerator
International Nuclear Information System (INIS)
Minehara, Eisuke
1980-08-01
Four kinds of negative ion sources (direct extraction Duoplasmatron ion source, radial extraction Penniing ion source, lithium charge exchange ion source and Middleton-type sputter ion source) have been installed in the JAERI tandem accelerator. The ion sources can generate many negative ions ranging from Hydrogen to Uranium with the exception of Ne, Ar, Kr, Xe and Rn. Discussions presented in this report include mechanisms of negative ion formation, electron affinity and stability of negative ions, performance of the ion sources and materials used for negative ion production. Finally, the author will discuss difficult problems to be overcome in order to get any negative ion sufficiently. (author)
3. Selection and design of ion sources for use at the Holifield radioactive ion beam facility
International Nuclear Information System (INIS)
Alton, G.D.; Haynes, D.L.; Mills, G.D.; Olsen, D.K.
1994-01-01
The Holifield Radioactive Ion Beam Facility now under construction at the Oak Ridge National Laboratory will use the 25 MV tandem accelerator for the acceleration of radioactive ion beams to energies appropriate for research in nuclear physics; negative ion beams are, therefore, required for injection into the tandem accelerator. Because charge exchange is an efficient means for converting initially positive ion beams to negative ion beams, both positive and negative ion sources are viable options for use at the facility. The choice of the type of ion source will depend on the overall efficiency for generating the radioactive species of interest. Although direct-extraction negative ion sources are clearly desirable, the ion formation efficiencies are often too low for practical consideration; for this situation, positive ion sources, in combination with charge exchange, are the logical choice. The high-temperature version of the CERN-ISOLDE positive ion source has been selected and a modified version of the source designed and fabricated for initial use at the facility because of its low emittance, relatively high ionization efficiencies, and species versatility, and because it has been engineered for remote installation, removal, and servicing as required for safe handling in a high-radiation-level ISOL facility. The source will be primarily used to generate ion beams from elements with intermediate to low electron affinities. Prototype plasma-sputter negative ion sources and negative surface-ionization sources are under design consideration for generating radioactive ion beams from high-electron-affinity elements. The design features of these sources and expected efficiencies and beam qualities (emittances) will be described in this report
Energy Technology Data Exchange (ETDEWEB)
Paul, A.; Keyser, U. [Physikalisch-Technische Bundesanstalt, Braunschweig (Germany)
1998-08-01
A new method based on parallel aerosol size spectrometry and {gamma}-spectrometry is introduced for the measurement of short-lived radioactive ions, fission products or super-heavy elements produced at accelerators. Furthermore a new aerosol generator is presented.The possibility of controlling and changing the aerosol size distribution in the helium aerosol jet produced by the aerosol generator allows the process of the adsorption and transport of radioactive ions on aerosols to be examined for the first time. This is due to the fact that the distribution is surveyed on-line using a negligible part of its total volume and parallel to the transporting flow. The radioactivity of the transported ions is measured by a germanium detector in offline position. In principle, both an on- or offline position with narrow multi-detector geometry (e.g. {beta}{gamma}{gamma}) is possible. (orig.) With 8 figs., 14 refs.
5. Accelerator development for heavy ion fusion
International Nuclear Information System (INIS)
Talbert, W.L. Jr.; Sawyer, G.A.
1980-01-01
Accelerator technology development is presented for heavy ion drivers used in inertial confinement fusion. The program includes construction of low-velocity ''test bed'' accelerator facilities, development of analytical and experimental techniques to characterize ion beam behavior, and the study of ion beam energy deposition
6. Compact RF ion source for industrial electrostatic ion accelerator
Energy Technology Data Exchange (ETDEWEB)
Kwon, Hyeok-Jung, E-mail: [email protected]; Park, Sae-Hoon; Kim, Dae-Il; Cho, Yong-Sub [Korea Multi-purpose Accelerator Complex, Korea Atomic Energy Research Institute, Gyeongsangbukdo 38180 (Korea, Republic of)
2016-02-15
Korea Multi-purpose Accelerator Complex is developing a single-ended electrostatic ion accelerator to irradiate gaseous ions, such as hydrogen and nitrogen, on materials for industrial applications. ELV type high voltage power supply has been selected. Because of the limited space, electrical power, and robust operation, a 200 MHz RF ion source has been developed. In this paper, the accelerator system, test stand of the ion source, and its test results are described.
7. Compact RF ion source for industrial electrostatic ion accelerator
Science.gov (United States)
Kwon, Hyeok-Jung; Park, Sae-Hoon; Kim, Dae-Il; Cho, Yong-Sub
2016-02-01
Korea Multi-purpose Accelerator Complex is developing a single-ended electrostatic ion accelerator to irradiate gaseous ions, such as hydrogen and nitrogen, on materials for industrial applications. ELV type high voltage power supply has been selected. Because of the limited space, electrical power, and robust operation, a 200 MHz RF ion source has been developed. In this paper, the accelerator system, test stand of the ion source, and its test results are described.
8. Radioactive ion beam production by the ISOL method for SPIRAL
International Nuclear Information System (INIS)
Landre-Pellemoine, Frederique
2001-01-01
This work is directly related to the SPIRAL project (Systeme de Production d'Ions Radioactifs Acceleres en Lignes) of which the start up will begin in September 2001 at GANIL (Grand Accelerateur National d'Ions Lourds) in Caen. This thesis primarily concerns the development of radioactive ion production systems (target/ion source) by the thorough study of each production stage of the ISOL (Isotopic Separation On Line) method: target and/or projectile fragmentation production, diffusion out of target material, effusion into the ion source and finally the ionization of the radioactive atoms. A bibliographical research and thermal simulations allowed us to optimize materials and the shape of the production and diffusion targets. A first target was optimized and made reliable for the radioactive noble gases production (argon, neon...). A second target dedicated to the radioactive helium production was entirely designed and realised (from the specifications to the 'off line' and 'on line' tests). Finally, a third target source system was defined for singly-charged radioactive alkaline production. The intensities of secondary beams planned for SPIRAL are presented here. A detailed study of the diffusion effusion efficiency for these various targets showed that the use of a fine microstructure carbon (grain size of 1 μm) improved the diffusion and showed the importance of thickness of the lamella for the short lived isotope effusion. (author) [fr
9. Radioactive ion beams and techniques for solid state research
International Nuclear Information System (INIS)
Correia, J.G.
1998-01-01
In this paper we review the most recent and new applications of solid state characterization techniques using radioactive ion beams. For such type ofresearch, high yields of chemically clean ion beams of radioactive isotopesare needed which are provided by the on-line coupling of high resolution isotope separators to particle accelerators, such as the isotope separator on-line (ISOLDE) facility at CERN. These new experiments are performed by an increasing number of solid state groups. They combine nuclear spectroscopic techniques such as Moessbauer, perturbed angular correlations (PAC) and emission channeling with the traditional non-radioactive techniques liked deep level transient spectroscopy (DLTS) and Hall effect measurements. Recently isotopes of elements, not available before, were successfully used in new PAC experiments, and the first photoluminescence (PL) measurements, where the element transmutation plays the essential role on the PL peak identification, have been performed. The scope of applications of radioactive ion beams for research in solid state physics will be enlarged in the near future, with the installation at ISOLDE of a post-accelerator device providing radioactive beams with energies ranging from a few keV up to a few MeV. (orig.)
10. National Centre for Radioactive Ion Beams (NCRIB)
International Nuclear Information System (INIS)
Chintalapudi, S.N.
1999-01-01
A dedicated National Centre for RIB (NCRIB) proposed discussed at several forums is presented. The production of (RIB) radioactive ion beams and applications of beams leading to competitive studies in nuclear structure, nuclear reactions, condensed matter, bio-science and radioactive isotope production etc. are mentioned
11. Ion accelerator based on plasma vircator
CERN Document Server
Onishchenko, I N
2001-01-01
The conception of a collective ion accelerator is proposed to be developed in the frameworks of STCU project 1569 (NSC KIPT, Ukraine) in coordination with the ISTC project 1629 (VNIEF, Russia). The main processes of acceleration are supposed to be consisted of two stages.First one is the plasma assistance virtual cathode (VC) in which plasma ions are accelerated in a potential well of VC. Along with ion acceleration the relaxation oscillations, caused by diminishing the potential well due to ion compensation, arise that provides the low-frequency (inverse ion transit time) temporal modulation of an intense relativistic electron beam (IREB) current. At the second stage temporally modulated IREB is injected into the spatially periodic magnetic field. The further ion acceleration is realized by the slow space charge wave that arises in IREB due to its simultaneous temporal and spatial modulation.
12. Bunching and cooling of radioactive ions with REXTRAP
CERN Document Server
Schmidt, P; Bollen, G; Forstner, O; Huber, G; Oinonen, M; Zimmer, J
2002-01-01
The post-accelerator REX-ISOLDE at ISOLDE/CERN will deliver radioactive ion beams with energies up to 2.2 MeV/u. For this purpose, a Penning trap and an electron-beam ion source are combined with a linear accelerator. REXTRAP—a large gas-filled Penning trap—has started its commissioning phase. First tests have shown that REXTRAP is able to accumulate, cool and bunch stable ISOLDE ion beams covering a large mass range. Fulfilling the REX-ISOLDE demands, it can handle beam intensities from a few hundred up to 1×10 6 ions per pulse at repetition rates up to 50 Hz.
13. Radioactive ions and atoms in superfluid helium
NARCIS (Netherlands)
Dendooven, P.G.; Purushothaman, S.; Gloos, K.; Aysto, J.; Takahashi, N.; Huang, W.; Harissopulos, S; Demetriou, P; Julin, R
2006-01-01
We are investigating the use of superfluid helium as a medium to handle and manipulate radioactive ions and atoms. Preliminary results on the extraction of positive ions from superfluid helium at temperatures close to 1 K are described. Increasing the electric field up to 1.2 kV/cm did not improve
14. Heavy-ion fusion accelerator research, 1989
International Nuclear Information System (INIS)
1990-06-01
This report discusses the following topics on heavy-ion fusion accelerator research: MBE-4: the induction-linac approach; transverse beam dynamics and current amplification; scaling up the results; through ILSE to a driver; ion-source and injector development; and accelerator component research and development
15. The Pulse Line Ion Accelerator Concept
Energy Technology Data Exchange (ETDEWEB)
Briggs, Richard J.
2006-02-15
The Pulse Line Ion Accelerator concept was motivated by the desire for an inexpensive way to accelerate intense short pulse heavy ion beams to regimes of interest for studies of High Energy Density Physics and Warm Dense Matter. A pulse power driver applied at one end of a helical pulse line creates a traveling wave pulse that accelerates and axially confines the heavy ion beam pulse. Acceleration scenarios with constant parameter helical lines are described which result in output energies of a single stage much larger than the several hundred kilovolt peak voltages on the line, with a goal of 3-5 MeV/meter acceleration gradients. The concept might be described crudely as an ''air core'' induction linac where the PFN is integrated into the beam line so the accelerating voltage pulse can move along with the ions to get voltage multiplication.
16. Ion acceleration in modulated electron beams
International Nuclear Information System (INIS)
Bonch-Osmolovskij, A.G.; Dolya, S.N.
1977-01-01
A method of ion acceleration in modulated electron beams is considered. Electron density and energy of their rotational motion are relatively low. However the effective ion-accelerating field is not less than 10 MeV/m. The electron and ion numbers in an individual bunch are also relatively small, although the number of produced bunches per time unit is great. Some aspects of realization of the method are considered. Possible parameters of the accelerator are given. At 50 keV electron energy and 1 kA beam current a modulation is realized at a wave length of 30 cm. The ion-accelerating field is 12 MeV/m. The bunch number is 2x10 3 in one pulse at a gun pulse duration of 2 μs. With a pulse repetition frequency of 10 2 Hz the number of accelerated ions can reach 10 13 -10 14 per second
17. Heavy Ion Fusion Accelerator Research (HIFAR)
International Nuclear Information System (INIS)
1991-04-01
This report discusses the following topics: emittance variations in current-amplifying ion induction lina; transverse emittance studies of an induction accelerator of heavy ions; drift compression experiments on MBE-4 and related emittance; low emittance uniform- density C s + sources for heavy ion fusion accelerator studies; survey of alignment of MBE-4; time-of-flight dependence on the MBE-4 quadrupole voltage; high order calculation of the multiple content of three dimensional electrostatic geometries; an induction linac injector for scaled experiments; induction accelerator test module for HIF; longitudinal instability in HIF beams; and analysis of resonant longitudinal instability in a heavy ion induction linac
18. Ion acceleration in the plasma source sheath
International Nuclear Information System (INIS)
Birdsall, C.K.
1986-01-01
This note is a calculation of the potential drop for a planar plasma source, across the source sheath, into a uniform plasma region defined by vector E = 0 and/or perhaps ∂ 2 PHI/∂ x 2 = 0. The calculation complements that of Bohm who obtained the potential drop at the other end of a plasma, at a planar collector sheath. The result is a relation between the source ion flux and the source sheath potential drop and the accompanying ion acceleration. This planar source sheath ion acceleration mechanism (or that from a distributed source) can provide the pre-collector-sheath ion acceleration as found necessary by Bohm. 3 refs
19. Evaluation and analysis of the residual radioactivity for the 15UD Pelletron accelerator facility
International Nuclear Information System (INIS)
2007-01-01
For the assessment of radiological impact of the accelerators, it will be better to have the documented information on activation of metal parts of the accelerator components. It is very much essential to get reliable data on these subjects. During acceleration of light ion, the residual radioactivity in the accelerator facility was found near the Analyzing Magnet, single slit, Beam Profile Monitors (BPM), Faraday Cups (FC), bellows, beginning of switching magnet bellows, at the target and the ladder. Study with HPGE detector gives an insight of the formation of the short or long lived radionuclides. The different targets used in the light ion experiment were also monitored and proper decommissioning and decontamination steps were followed. This paper presents the data of residual radioactivity in the 15UD Pelletron accelerator infrastructure. (author)
20. Ion exchange currents in vacuum accelerator tubes
International Nuclear Information System (INIS)
Eastham, D.A.; Thorn, R.
1978-01-01
Ion exchange currents (microdischarges) have been observed in short lengths of accelerator tube. The occurrence of these discharges can be related to the trajectories of ions in the tube. High-resolution mass spectra of the negative and positive ion components have been obtained. (author)
1. Radioactive heavy ion secondary beams
International Nuclear Information System (INIS)
Bimbot, R.
1987-01-01
The production of secondary radioactive beams at GANIL using the LISE spectrometer is reviewed. The experimental devices, and secondary beam characteristics are summarized. Production of neutron rich secondary beams was studied for the systems Ar40 + Be at 44 MeV/u, and 018 + Be at 45 and 65 MeV/u. Partial results were also obtained for the system Ne22 + Ta at 45 MeV/u. Experiments using secondary beams are classified into two categories: those which correspond to fast transfer of nuclei from the production target to a well shielded observation point; and those in which the radioactive beam interacts with a secondary target
2. Neutron and proton transmutation-activation cross section libraries to 150 MeV for application in accelerator-driven systems and radioactive ion beam target-design studies
International Nuclear Information System (INIS)
Koning, A.J.; Chadwick, M.B.; MacFarlane, R.E.; Mashnik, S.; Wilson, W.B.
1998-05-01
New transmutation-activation nuclear data libraries for neutrons and protons up to 150 MeV have been created. These data are important for simulation calculations of radioactivity, and transmutation, in accelerator-driven systems such as the production of tritium (APT) and the transmutation of waste (ATW). They can also be used to obtain cross section predictions for the production of proton-rich isotopes in (p,xn) reactions, for radioactive ion beam (RIB) target-design studies. The nuclear data in these libraries stem from two sources: for neutrons below 20 MeV, we use data from the European activation and transmutation file, EAF97; For neutrons above 20 MeV and for protons at all energies we have isotope production cross sections with the nuclear model code HMS-ALICE. This code applies the Monte Carlo Hybrid Simulation theory, and the Weisskopf-Ewing theory, to calculate cross sections. In a few cases, the HMS-ALICE results were replaced by those calculated using the GNASH code for the Los Alamos LA150 transport library. The resulting two libraries, AF150.N and AF150.P, consist of 766 nuclides each and are represented in the ENDF6-format. An outline is given of the new representation of the data. The libraries have been checked with ENDF6 preprocessing tools and have been processed with NJOY into libraries for the Los Alamos transmutation/radioactivity code CINDER. Numerous benchmark figures are presented for proton-induced excitation functions of various isotopes compared with measurements. Such comparisons are useful for validation purposes, and for assessing the accuracy of the evaluated data. These evaluated libraries are available on the WWW at: http://t2.lanl.gov/. 21 refs
3. Radioactive ion implantation as a tool for wear measurements
International Nuclear Information System (INIS)
Bagger, C.; Soerensen, G.
1979-01-01
The present paper deals with ion implantation of radioactive krypton ions in surfaces with aim of measuring wear of different magnetic materials in sound-heads. The technique is especially suited for a relatively fast comparison of wear-characteristics of materials of varying composition in small inaccessible areas. In the present case utilisation of a 60 KeV accelerator allows determination of a total wear as small as 0.05 μm with an accuracy of 10%. Further the technique yields information of the time dependence of the wear process with an accuracy less than 0.001 μm. (author)
4. Folded tandem ion accelerator facility at BARC
International Nuclear Information System (INIS)
Agarwal, Arun; Padmakumar, Sapna; Subrahmanyam, N.B.V.; Singh, V.P.; Bhatt, J.P.; Ware, Shailaja V.; Pol, S.S; Basu, A.; Singh, S.K.; Krishnagopal, S.; Bhagwat, P.V.
2017-01-01
The 5.5 MV single stage Van de Graaff (VDG) accelerator was in continuous operation at Nuclear Physics Division (NPD), Bhabha Atomic Research Centre (BARC) since its inception in 1962. During 1993-96, VDG accelerator was converted to a Folded Tandem Ion Accelerator (FOTIA). The scientists and engineers of NPD, IADD (then a part of NPD) along with several other divisions of BARC joined hands together in designing, fabrication, installation and commissioning of the FOTIA for the maximum terminal voltage of 6 MV. After experiencing the first accelerated ion beam on the target from FOTIA during April 2000, different ion species were accelerated and tested. Now this accelerator FOTIA is in continuous use for different kind of experiments
5. Cyclotron method for heavy ion acceleration
International Nuclear Information System (INIS)
Gikal, B.N.; Gul'bekyan, G.G.; Kutner, V.B.; Oganesyan, R.Ts.
1984-01-01
Studies on heavy ion beams in a wide range of masses (up to uranium) and energies disclose essential potential opportunities for solution of both fundamental scientific and significant economical problems. A cyclotron method for heavy ion acceleration is considered. Development of low and medium energy heavy ion accelerators is revealed. The design of a complex comprising two isochronous cyclotrons which is planned to be constrdcted 1n the JINR is described. The cyclotron complex includes the U-400 and the U-400 M cyclotrons and it is intended for acceleration of both 35-20 MeV/nucleon superheavy ions such as Xe-U and 120 MeV/nucleon light ions. Certain systems of the accelerators are described. Prospects of the U-400 and the U-400 M development are displayed
6. Experimental studies with radioactive ion beams
International Nuclear Information System (INIS)
Sastry, D.L.; Sree Krishna Murty, G.; Chandrasekhar Rao, M.V.S.
1991-01-01
The sources of information presented are essentially taken from the papers reported at several international seminars and those appeared in the Journal of Nuclear Instruments and Methods in Physics Research. Production and usage of radioactive ion beams (RIB) in research have received the attention of scientists all over the world during the past six years. The first radioactive ion beams ( 19 Ne) were produced at Bevalac for the purpose of medical research using a primary beam of energy 800 MeV/a.m.u. (author). 19 refs., 2 figs., 3 tabs
7. Studies of pear-shaped nuclei using accelerated radioactive beams
CERN Document Server
Gaffney, L P; Scheck, M; Hayes, A B; Wenander, F; Albers, M; Bastin, B; Bauer, C; Blazhev, A; Bonig, S; Bree, N; Cederkall, J; Chupp, T; Cline, D; Cocolios, T E; Davinson, T; DeWitte, H; Diriken, J; Grahn, T; Herzan, A; Huyse, M; Jenkins, D G; Joss, D T; Kesteloot, N; Konki, J; Kowalczyk, M; Kroll, Th; Kwan, E; Lutter, R; Moschner, K; Napiorkowski, P; Pakarinen, J; Pfeiffer, M; Radeck, D; Reiter, P; Reynders, K; Rigby, S V; Robledo, L M; Rudigier, M; Sambi, S; Seidlitz, M; Siebeck, B; Stora, T; Thoele, P; Van Duppen, P; Vermeulen, M J; von Schmid, M; Voulot, D; Warr, N; Wimmer, K; Wrzosek-Lipska, K; Wu, C Y; Zielinska, M
2013-01-01
There is strong circumstantial evidence that certain heavy, unstable atomic nuclei are ‘octupole deformed’, that is, distorted into a pear shape. This contrasts with the more prevalent rugby-ball shape of nuclei with reflection-symmetric, quadrupole deformations. The elusive octupole deformed nuclei are of importance for nuclear structure theory, and also in searches for physics beyond the standard model; any measurable electric-dipole moment (a signature of the latter) is expected to be amplified in such nuclei. Here we determine electric octupole transition strengths (a direct measure of octupole correlations) for short-lived isotopes of radon and radium. Coulomb excitation experiments were performed using accelerated beams of heavy, radioactive ions. Our data on and $^{224}$Ra show clear evidence for stronger octupole deformation in the latter. The results enable discrimination between differing theoretical approaches to octupole correlations, and help to constrain suitable candidates for experimental...
8. Radioactive ion beam production challenges at the Holifield Heavy Ion Research Facility
International Nuclear Information System (INIS)
Meigs, M.J.; Alton, G.D.; Dowling, D.T.; Haynes, D.L.; Jones, C.M.; Juras, R.C.; Lane, S.N.; Mills, G.D.; Mosko, S.W.; Olsen, D.K.; Tatum, B.A.
1992-01-01
The radioactive ion beam (RIB) project at the Holifield Heavy Ion Research Facility (HHIRF) will provide for reconfiguration of the HHIRF accelerator system to enable provision of low-intensity RIBs for nuclear and astrophysics research. As we have progressed with the design of the reconfiguration, we have encountered several challenges that were not immediately obvious when first contemplating the project. The challenges do not seem insurmountable but should keep life interesting for those of us doing the work. A brief review of the project will allow a better understanding of the challenges in RIB production. Radioactive ion beams will be produced with the Isotope Separator On-Line (ISOL) postacceleration technique. In particular, radioactive atoms will be produced by reactions in the thick stopping target of an ISOL-type target-ion source assembly using intense beams from the Oak Ridge Isochronous Cyclotron equipped with a light-ion internal source. This ISOL target-ion source assembly will be mounted on a high-voltage platform with a mass separator. The target ion source will operate at potentials up to 50 kV with respect to the high voltage platform. The radioactive atoms produced by nuclear reactions in the target diffuse to the surface of the heated target material, desorb from this surface, and effuse through a heated transfer tube into an ion source where ionization and extraction take place. Two types of ion sources will be initially considered. A Forced Electron Beam Induced Arc Discharge source, similar to those used by the ISOLDE facility at CERN and by the UNISOR facility at ORNL, will be built to produce positive ions. These positive ions will be focused through an alkali vapor charge-exchange canal to produce negative ions for tandem injection. In addition, a direct negative surface ionization addition or modification to the above source will be built and investigated
9. Accelerated ion beam research at ATOMKI
International Nuclear Information System (INIS)
Kiss, A.Z.
2009-01-01
The paper summarizes the studies on accelerated ion beams at ATOMKI and their technical background, their use from chemical analysis to biological, medical, geological, archaeological applications, their advance from material science to micromachining. (TRA)
10. Heavy-Ion Fusion Accelerator Research, 1991
International Nuclear Information System (INIS)
1992-03-01
This report discusses the following topics: research with multiple- beam experiment MBE-4; induction linac systems experiments; and long- range research and development of heavy-ion fusion accelerators
11. Ion acceleration in the plasma focus
International Nuclear Information System (INIS)
Deutsch, R.
1982-09-01
Experimental informations are used to estimate the time dependence of the current density in the plasma focus and the electromagnetic field is determined from the Maxwell equations. The acceleration of the ions in these fields is studied. A detailed analysis of the acceleration in the compression phase, in the expansion phase and during the evolution of the m=O instability is made. It is shown, that the appearance of fast selffocused quasineutral electron beams, as a result of the betatron acceleration, has a decisive importance in the ion acceleration during the m=O constriction. Models for electromagnetic ion acceleration are described for each phase. A concordance with many experimental results can be observed. (orig.)
12. Nuclear astrophysics at the Holifield Radioactive Ion Beam Facility
International Nuclear Information System (INIS)
Smith, M.S.
1994-01-01
The potential for understanding spectacular stellar explosions such as novae, supernovae, and X-ray bursts will be greatly enhanced by the availability of the low-energy, high-intensity, accelerated beams of proton-rich radioactive nuclei currently being developed at the Holifield Radioactive Ion Beam Facility (HRIBF) at Oak Ridge National Laboratory. These beams will be utilized in absolute cross section measurements of crucial (p, γ) capture reactions in efforts to resolve the substantial qualitative uncertainties in current models of explosive stellar hydrogen burning outbursts. Details of the nuclear astrophysics research program with the unique HRIBF radioactive beams and a dedicated experimental endstation--centered on the Daresbury Recoil Separator--will be presented
13. National Centre for Radioactive Ion Beams (NCRIB)
International Nuclear Information System (INIS)
Chintalapudi, S.N.
1999-01-01
Radioactive Ion (nuclear) Beams have become prolific recently. Nuclear physics and associated subjects have staged a comeback to almost the beginning with the advent of RIB. A dedicated National Centre for RIB (NCRIB) proposed, discussed at several forums and under serious consideration is described
14. Impulsive ion acceleration in earth's outer magnetosphere
International Nuclear Information System (INIS)
Baker, D.N.; Belian, R.D.
1985-01-01
Considerable observational evidence is found that ions are accelerated to high energies in the outer magnetosphere during geomagnetic disturbances. The acceleration often appears to be quite impulsive causing temporally brief (10's of seconds), very intense bursts of ions in the distant plasma sheet as well as in the near-tail region. These ion bursts extend in energy from 10's of keV to over 1 MeV and are closely associated with substorm expansive phase onsets. Although the very energetic ions are not of dominant importance for magnetotail plasma dynamics, they serve as an important tracer population. Their absolute intensity and brief temporal appearance bespeaks a strong and rapid acceleration process in the near-tail, very probably involving large induced electric fields substantially greater than those associated with cross-tail potential drops. Subsequent to their impulsive acceleration, these ions are injected into the outer trapping regions forming ion ''drift echo'' events, as well as streaming tailward away from their acceleration site in the near-earth plasma sheet. Most auroral ion acceleration processes occur (or are greatly enhanced) during the time that these global magnetospheric events are occurring in the magnetotail. A qualitative model relating energetic ion populations to near-tail magnetic reconnection at substorm onset followed by global redistribution is quite successful in explaining the primary observational features. Recent measurements of the elemental composition and charge-states have proven valuable for showing the source (solar wind or ionosphere) of the original plasma population from which the ions were accelerated
15. Apparatus for neutralization of accelerated ions
International Nuclear Information System (INIS)
Fink, J.H.; Frank, A.M.
1979-01-01
Apparatus is described for neutralization of a beam of accelerated ions, such as hydrogen negative ions (H - ), using relatively efficient strip diode lasers which emit monochromatically at an appropriate wavelength (lambda = 8000 A for H - ions) to strip the excess electrons by photodetachment. A cavity, formed by two or more reflectors spaced apart, causes the laser beams to undergo multiple reflections within the cavity, thus increasing the efficiency and reducing the illumination required to obtain an acceptable percentage (approx. 85%) of neutralization
16. Heavy ion medical accelerator in chiba
International Nuclear Information System (INIS)
Hirao, Y.; Ogawa, H.; Yamada, S.
1992-12-01
The HIMAC (Heavy Ion Medical Accelerator in Chiba) construction project has been promoted by NIRS (National Institute of Radiological Sciences) as one of the projects of 'Comprehensive 10 year Strategy for Cancer Control' HIMAC is the first heavy-ion accelerator dedicated to medicine in the world, and its design parameters are based on the radiological requirements. It consists of two types of ion sources, an RFQ and an Alvarez linacs, dual synchrotron rings, high energy beam transport lines, and irradiation facilities for treatment and experiments. This report mainly describes the outline of the structure and performance of each HIMAC subsystem. (J.P.N.)
17. Radioactive Ions for Surface Characterization
CERN Multimedia
2002-01-01
The collaboration has completed a set of pilot experiments with the aim to develop techniques for using radioactive nuclei in surface physics. The first result was a method for thermal deposition of isolated atoms (Cd, In, Rb) on clean metallic surfaces. \\\\ \\\\ Then the diffusion history of deposited Cd and In atoms on two model surfaces, Mo(110) and Pd(111), was followed through the electric field gradients (efg) acting at the probe nuclei as measured with the Perturbed Angular Correlation technique. For Mo(110) a rather simple history of the adatoms was inferred from the experiments: Atoms initially landing at terrace sites diffuse from there to ledges and then to kinks, defects always present at real surfaces. The next stage is desorption from the surface. For Pd a scenario that goes still further was found. Following the kink stage the adatoms get incorporated into ledges and finally into the top surface layer. For all these five sites the efg's could be measured.\\\\ \\\\ In preparation for a further series o...
18. Overview of The Pulse Line Ion Accelerator
International Nuclear Information System (INIS)
Briggs, R.J.; Bieniosek, F.M.; Coleman, J.E.; Eylon, S.; Henestroza, E.; Leitner, M.; Logan, B.G.; Reginato, L.L.; Roy, P.K.; Seidl, P.A.; Waldron, W.L.; Yu, S.S.; Barnard, J.J.; Caporaso, G.J.; Friedman, A.; Grote, D.P.; Nelson, S.D.
2006-01-01
An overview of the Pulse Line Ion Accelerator (PLIA) concept and its development is presented. In the PLIA concept a pulse power driver applied to one end of a helical pulse line creates a traveling wave pulse that accelerates and axially confines a heavy ion beam pulse The motivation for its development at the IFE-VNL is the acceleration of intense, short pulse, heavy ion beams to regimes of interest for studies of High Energy Density Physics and Warm Dense Matter. Acceleration scenarios with constant parameter helical lines are described which result in output energies of a single stage much larger than the several hundred kilovolt peak voltages on the line, with a goal of 3-5 MeV/meter acceleration gradients. The main attraction of the concept is the very low cost it promises. It might be described crudely as an ''air core'' induction linac where the pulse-forming network is integrated into the beam line so the accelerating voltage pulse can move along with the ions to get voltage multiplication
19. Heavy ion acceleration at the AGS
International Nuclear Information System (INIS)
Lee, Y.Y.
1989-01-01
The Brookhaven AGS is alternating gradient synchrotron, 807 meters in circumference, which was originally designed for only protons. Using the 15 MV Brookhaven Tandem Van de Graaff as an injector, the AGS started to accelerate heavy ions of mass lighter than sulfur. Because of the relatively poor vacuum (∼10 -8 Torr), the AGS is not able to accelerate heavier ions which could not be fully stripped of electrons at the Tandem energy. When the AGS Booster, which is under construction, is completed the operation will be extended to all species of heavy ions including gold and uranium. Because ultra-high vacuum (∼10 -11 Torr) is planned, the Booster can accelerate partially stripped elements. The operational experience, the parameters, and scheme of heavy ion acceleration will be presented in detail from injection to extraction, as well as future injection into the new Relativistic Heavy Ion Collider (RHIC). A future plan to improve intensity of the accelerator will also be presented. 5 figs., 4 tabs
20. Condensed matter physics with radioactive ion beams
International Nuclear Information System (INIS)
Haas, H.
1996-01-01
An overview of the present uses of radioactive ion beams from ISOLDE for condensed matter research is presented. As simple examples of such work, tracer studies of diffusion processes with radioisotopes and blocking/channeling measurements of emitted particles for lattice location are discussed. Especially the application of nuclear hyperfine interaction techniques such as PAC or Moessbauer spectroscopy has become a powerful tool to study local electronic and structural properties at impurities. Recently, interesting information on impurity properties in semiconductors has been obtained using all these methods. The extreme sensitivity of nuclear techniques makes them also well suited for investigations of surfaces, interfaces, and biomolecules. Some ideas for future uses of high energy radioactive ion beams beyond the scope of the present projects are outlined: the study of diffusion in highly immiscible systems by deep implantation, nuclear polarization with the tilted-foil technique, and transmutation doping of wide-bandgap semiconductors. (orig.)
1. The future of the accelerator mass spectrometry of rare long-lived radioactive isotopes
International Nuclear Information System (INIS)
Litherland, A.E.
1990-01-01
Accelerators, originally designed for nuclear physics, can be added to mass spectrometric apparatus to increase the sensitivity so that isotope ratios in the range 10 -12 to 10 -15 can be measured routinely. This significant improvement of high-sensitivity mass spectrometry has been called Accelerator Mass Spectrometry. The present article addresses the basic principles of accelerator mass spectrometry and some recent applications which show its versatility. In particular, it is noted that accelerator mass spectrometry could play an increasing role in the measurement of the levels of long lived radioactivities in the environment, including the actinides, which result from human activities such as the use of nuclear power. To fulfill this promise, continued research and development is necessary to provide ion sources, various types of heavy ion accelerators and peripheral magnetic and electric analysers. (N.K.)
2. Heavy-ion accelerator mass spectrometry with a 'small' accelerator
International Nuclear Information System (INIS)
Steier, P.; Golser, R.; Priller, A.; Vockenhuber, C.; Irlweck, K.; Kutschera, W.; Lichtenstein, V.
2001-01-01
Full text: VERA, the Vienna environmental research accelerator, is based on a 3-MV pelletron tandem accelerator and is designed to allow the transport of ions of all elements, from the lightest to the heaviest. The VERA heavy ion program tries to establish measurement methods which work for the long-lived radionuclides where suppression of isobars is not required. Among these are 129 I, 210 Pb, 236 U and all heavier ions where no stable isobars exist. To suppress neighboring masses, the resolution of VERA was increased, both by improving the ion optics of existing elements and by installing a new electrostatic separator after the analyzing magnet. Interfering ions which pass all beam filters are identified with a high-resolution time-of-flight system, using a 0.5 μg/cm 2 DLC (diamond-like carbon) foil in the start detector, which substantially reduces beam straggling. Compared to heavy ion AMS at large tandem accelerators (TV ≥ 8 MV) and for cases where stable isobar interference is absent, it is possible to offset the disadvantage of lower ion energy. Moreover, the more compact facilities like VERA achieve higher stability and reliability and provide advanced computer control. This promises even higher precision and sensitivity for a larger number of samples, which is a prerequisite for research on natural-occurring heavy radioisotopes at environmental levels. First results on the measurement of 210 Pb (half-life 22 a) and 236 U (23 Ma) encourages us to push towards even heavier radionuclides (e.g. 224 Pu, 81 Ma). (author)
3. Linear induction accelerator for heavy ions
International Nuclear Information System (INIS)
Keefe, D.
1976-01-01
There is considerable recent interest in the use of high energy heavy ions to irradiate deuterium-tritium pellets in a reactor vessel to constitute a power source at the level of 1 GW or more. Various accelerator configurations involving storage rings have been suggested. This paper discusses how the technology of linear induction accelerators - well known to be matched to high current and short pulse length - may offer significant advantages for this application. (author)
4. Next generation of relativistic heavy ion accelerators
International Nuclear Information System (INIS)
Grunder, H.; Leemann, C.; Selph, F.
1978-06-01
Results are presented of exploratory and preliminary studies of a next generation of heavy ion accelerators. The conclusion is reached that useful luminosities are feasible in a colliding beam facility for relativistic heavy ions. Such an accelerator complex may be laid out in such a way as to provide extractebeams for fixed target operation, therefore allowing experimentation in an energy region overlapping with that presently available. These dual goals seem achievable without undue complications, or penalties with respect to cost and/or performance
5. Heavy-ion-linac post-accelerators
International Nuclear Information System (INIS)
Bollinger, L.M.
1979-01-01
The main features of the tandem-linac system for heavy-ion acceleration are reviewed and illustrated in terms of the technology and performance of the superconducting heavy-ion energy booster at Argonne. This technology is compared briefly with the corresponding technologies of the superconducting linac at Stony Brook and the room-temperature linac at Heidelberg. The performance possibilities for the near-term future are illustrated in terms of the proposed extension of the Argonne booster to form ATLAS
6. Relativistic ion acceleration by ultraintense laser interactions
International Nuclear Information System (INIS)
Nakajima, K.; Koga, J.K.; Nakagawa, K.
2001-01-01
There has been a great interest in relativistic particle generation by ultraintense laser interactions with matter. We propose the use of relativistically self-focused laser pulses for the acceleration of ions. Two dimensional PIC simulations are performed, which show the formation of a large positive electrostatic field near the front of a relativistically self-focused laser pulse. Several factors contribute to the acceleration including self-focusing distance, pulse depletion, and plasma density. Ultraintense laser-plasma interactions are capable of generating enormous electrostatic fields of ∼3 TV/m for acceleration of protons with relativistic energies exceeding 1 GeV
7. Targets for ion sources for RIB generation at the Holifield Radioactive Ion Beam Facility
International Nuclear Information System (INIS)
Alton, G.D.
1995-01-01
The Holifield Radioactive Ion Beam Facility (HRIBF), now under construction at the Oak Ridge National Laboratory, is based on the use of the well-known on-line isotope separator (ISOL) technique in which radioactive nuclei are produced by fusion type reactions in selectively chosen target materials by high-energy proton, deuteron, or He ion beams from the Oak Ridge Isochronous Cyclotron (ORIC). Among several major challenges posed by generating and accelerating adequate intensities of radioactive ion beams (RIBs), selection of the most appropriate target material for production of the species of interest is, perhaps, the most difficult. In this report, we briefly review present efforts to select target materials and to design composite target matrix/heat-sink systems that simultaneously incorporate the short diffusion lengths, high permeabilities, and controllable temperatures required to effect maximum diffusion release rates of the short-lived species that can be realized at the temperature limits of specific target materials. We also describe the performance characteristics for a selected number of target ion sources that will be employed for initial use at the HRIBF as well as prototype ion sources that show promise for future use for RIB applications
8. Pulsed power ion accelerators for inertially confined fusion
International Nuclear Information System (INIS)
Olson, C.L.
1976-01-01
Current research is described on pulsed power ion accelerators for inertial fusion, i.e., ion diodes and collective accelerators. Particle beam energy and power requirements for fusion, and basic deposition characteristics of charged particle beams are discussed. Ion diodes and collective accelerators for fusion are compared with existing conventional accelerators
9. Sealed ion accelerator tubes (survey)
International Nuclear Information System (INIS)
Voitsik, L.R.
1985-01-01
The first publications on developing commercial models of small-scale sealed accelerator tubes in which neutrons are generated appeared in the foreign press in 1954 to 1957; they were very brief and were advertising-oriented. The tubes were designed for neutron logging of oil wells instead of ampule neutron sources (Po + Be, Ra + Be). Later, instruments of this type began to be called neutron tubes from the resulting neutron radiation that they gave off. In Soviet Union a neutron tube was developed in 1958 in connection with the development of the pulsed neutron-neutron method of studying the geological profile of oil wells. At that time the tube developed was intended, in the view of its inventors, to replace standard isotope sources with constant neutron yield. A fairly detailed survey of neutron tubes was made in the studies. 8 refs., 8 figs
10. High-powered pulsed-ion-beam acceleration and transport
Energy Technology Data Exchange (ETDEWEB)
Humphries, S. Jr.; Lockner, T.R.
1981-11-01
The state of research on intense ion beam acceleration and transport is reviewed. The limitations imposed on ion beam transport by space charge effects and methods available for neutralization are summarized. The general problem of ion beam neutralization in regions free of applied electric fields is treated. The physics of acceleration gaps is described. Finally, experiments on multi-stage ion acceleration are summarized.
11. High-powered pulsed-ion-beam acceleration and transport
International Nuclear Information System (INIS)
Humphries, S. Jr.; Lockner, T.R.
1981-11-01
The state of research on intense ion beam acceleration and transport is reviewed. The limitations imposed on ion beam transport by space charge effects and methods available for neutralization are summarized. The general problem of ion beam neutralization in regions free of applied electric fields is treated. The physics of acceleration gaps is described. Finally, experiments on multi-stage ion acceleration are summarized
12. The research status of induced radioactivity in accelerator facilities
International Nuclear Information System (INIS)
Lu Feng; Deng Daping
2005-01-01
The hazards of subsequent-radiation produced by high-energy accelerator must be no ignore. The principle of induced radioactivity and the hazards to the people were introduced in this article. The radiation levels around the treatment head and in the air of the treatment room were discussed thor-oughly. Some effects of the induced radioactivity were also mentioned. At last, the article talks about some problems in present researches and some directions for the following study. (authors)
13. Folded tandem ion accelerator facility at Trombay
In the present system, negative ion beams extracted from the SNICS-II source are pre- accelerated up to 150 keV. ..... of PCs with a front-end interface using CAMAC instrumentation and uses QNX real time operating system. There are large ...
14. Recirculating induction accelerators for heavy ion fusion
International Nuclear Information System (INIS)
Barnard, J.J.; Deadrick, F.; Bangerter, R.O.
1993-01-01
We have recently completed a two-year study of recirculating induction heavy-ion accelerators (recirculators) as low-cost drivers for inertial-fusion-energy power plants. We present here a summary of that study and other recent work on recirculators
15. Pelletron ion accelerator facilities at Inter University Accelerator Centre
International Nuclear Information System (INIS)
Chopra, S.
2011-01-01
Inter University Accelerator Centre has two tandem ion accelerators, 15UD Pelletron and 5SDH-2 Pelletron, for use in different areas of research. Recently Accelerator Mass Spectrometry facility has also been added to to the existing experimental facilities of 15UD Pelletron. In these years many modifications and up gradations have been performed to 15UD Pelletron facility. A new MCSNICS ion source has been procured to produce high currents for AMS program. Two foils stripper assemblies ,one each before and after analyzing magnet, have also been added for producing higher charge state beams for LINAC and for experiments requiring higher charge states of accelerated beams. A new 1.7 MV Pelletron facility has also been recently installed at IUAC and it is equipped with RBS and Channelling experimental facility. There are two beam lines installed in the system and five more beam lines can be added to the system. A clean chemistry laboratory with all the modern facilities has also been developed at IUAC for the chemical processing of samples prior to the AMS measurements. The operational description of the Pelletron facilities, chemical processing of samples, methods of measurements and results of AMS measurements are being presented. (author)
16. High spin studies with radioactive ion beams
International Nuclear Information System (INIS)
Garrett, J.D.
1992-01-01
The variety of new research possibilities afforded by the culmination of the two frontier areas of nuclear structure: high spin and studies far from nuclear stability (utilizing intense radioactive ion beams) are discussed. Topics presented include: new regions of exotic nuclear shape (e.g. superdeformation, hyperdeformation, and reflection-asymmetric shapes); the population of and consequences of populating exotic nuclear configurations; and complete spectroscopy (i.e. the overlap of state of the art low-and high-spin studies in the same nucleus)
17. High spin studies with radioactive ion beams
Energy Technology Data Exchange (ETDEWEB)
Garrett, J D [Oak Ridge National Lab., TN (United States)
1992-08-01
The variety of new research possibilities afforded by the culmination of the two frontier areas of nuclear structure: high spin and studies far from nuclear stability (utilizing intense radioactive ion beams) are discussed. Topics presented include: new regions of exotic nuclear shape (e.g. superdeformation, hyperdeformation, and reflection-asymmetric shapes); the population of and consequences of populating exotic nuclear configurations; and, complete spectroscopy (i.e. the overlap of state of the art low- and high-spin studies in the same nucleus). (author). 47 refs., 8 figs.
18. Electron Accelerators for Radioactive Ion Beams
Energy Technology Data Exchange (ETDEWEB)
Lia Merminga
2007-10-10
The summary of this paper is that to optimize the design of an electron drive, one must: (a) specify carefully the user requirements--beam energy, beam power, duty factor, and longitudinal and transverse emittance; (b) evaluate different machine options including capital cost, 10-year operating cost and delivery time. The author is convinced elegant solutions are available with existing technology. There are several design options and technology choices. Decisions will depend on system optimization, in-house infrastructure and expertise (e.g. cryogenics, SRF, lasers), synergy with other programs.
19. Heavy Ion Acceleration at J-PARC
Science.gov (United States)
SATO, Susumu
2018-02-01
J-PARC, the Japan Proton Accelerator Research Complex, is an accelerator, which provides a high-intensity proton beam. Recently as a very attractive project, the acceleration of heavy ions produced by supplementary ion sources, called J-PARC-HI, is seriously contemplated by domestic as well as international communities. The planned facility would accelerate heavy ions up to U92+ with a beam energy 20 AGeV ( of 6.2 AGeV). The highlight of the J-PARC-HI project is its very high beam rate up to 1011 Hz, which will enable the study of very rare events. Taking advantage of this high intensity, J-PARC-HI will carry out frontier studies of new and rare observables in this energy region: (i) nuclear medium modification of chiral property of vector mesons through low-mass di-lepton signal, (ii) QCD critical pointcharacterization through event-by-event fluctuation signals of particle production, (iii) systematic measurements related to the equation of state through collective flow signal or two-particle momentum correlation signal, or (iv) the search of hyper nuclei with multi strangeness including or exceeding S = 3. The current plan of J-PARC-HI aims to carrying out the first experimental measurements in 2025.
20. Negative hydrogen ion sources for accelerators
Energy Technology Data Exchange (ETDEWEB)
Moehs, D.P.; /Fermilab; Peters, J.; /DESY; Sherman, J.; /Los Alamos
2005-08-01
A variety of H{sup -} ion sources are in use at accelerator laboratories around the world. A list of these ion sources includes surface plasma sources with magnetron, Penning and surface converter geometries as well as magnetic-multipole volume sources with and without cesium. Just as varied is the means of igniting and maintaining magnetically confined plasmas. Hot and cold cathodes, radio frequency, and microwave power are all in use, as well as electron tandem source ignition. The extraction systems of accelerator H{sup -} ion sources are highly specialized utilizing magnetic and electric fields in their low energy beam transport systems to produce direct current, as well as pulsed and/or chopped beams with a variety of time structures. Within this paper, specific ion sources utilized at accelerator laboratories shall be reviewed along with the physics of surface and volume H{sup -} production in regard to source emittance. Current research trends including aperture modeling, thermal modeling, surface conditioning, and laser diagnostics will also be discussed.
1. Induction accelerator development for heavy ion fusion
International Nuclear Information System (INIS)
Reginato, L.L.
1993-05-01
For approximately a decade, the Heavy Ion Fusion Accelerator Research (HIFAR) group at LBL has been exploring the use of induction accelerators with multiple beams as the driver for inertial fusion targets. Scaled experiments have investigated the transport of space charge dominated beams (SBTE), and the current amplification and transverse emittance control in induction linacs (MBE-4) with very encouraging results. In order to study many of the beam manipulations required by a driver and to further develop economically competitive technology, a proposal has been made in partnership with LLNL to build a 10 MeV accelerator and to conduct a series of experiments collectively called the Induction Linac System Experiments (ILSE). The major components critical to the ILSE accelerator are currently under development. We have constructed a full scale induction module and we have tested a number of amorphous magnetic materials developed by Allied Signal to establish an overall optimal design. The electric and magnetic quadrupoles critical to the transport and focusing of heavy ion beams are also under development The hardware is intended to be economically competitive for a driver without sacrificing any of the physics or performance requirements. This paper will concentrate on the recent developments and tests of the major components required by the ILSE accelerator
2. Induction accelerator development for heavy ion fusion
International Nuclear Information System (INIS)
Reginato, L.L.
1993-05-01
For approximately a decade, the Heavy Ion Fusion Accelerator Research (HIFAR) group at LBL has been exploring the use of induction accelerators with multiple beams as the driver for inertial fusion targets. Scaled experiments have investigated the transport of space charge dominated beams (SBTE), and the current amplification and transverse emittance control in induction linacs (MBE-4) with very encouraging results. In order to study many of the beam manipulations required by a driver and to further develop economically competitive technology, a proposal has been made in partnership with LLNL to build a 10 MeV accelerator and to conduct a series of experiments collectively called the Induction Linac System Experiments (ILSE).The major components critical to the ILSE accelerator are currently under development. We have constructed a full scale induction module and we have tested a number of amorphous magnetic materials developed by Allied Signal to establish an overall optimal design. The electric and magnetic quadrupoles critical to the transport and focusing of heavy ion beams are also under development. The hardware is intended to be economically competitive for a driver without sacrificing any of the physics or performance requirements. This paper will concentrate on the recent developments and tests of the major components required by the ILSE accelerator
3. Energetic ion acceleration at collisionless shocks
Science.gov (United States)
Decker, R. B.; Vlahos, L.
1985-01-01
An example is presented from a test particle simulation designed to study ion acceleration at oblique turbulent shocks. For conditions appropriate at interplanetary shocks near 1 AU, it is found that a shock with theta sub B n = 60 deg is capable of producing an energy spectrum extending from 10 keV to approx. 1 MeV in approx 1 hour. In this case total energy gains result primarily from several separate episodes of shock drift acceleration, each of which occurs when particles are scattered back to the shock by magnetic fluctuations in the shock vicinity.
4. Energetic ion acceleration at collisionless shocks
International Nuclear Information System (INIS)
Decker, R.B.; Vlahos, L.
1985-01-01
An example is presented from a test particle simulation designed to study ion acceleration at oblique turbulent shocks. For conditions appropriate at interplanetary shocks near 1 AU, it is found that a shock with theta sub B n = 60 deg is capable of producing an energy spectrum extending from 10 keV to approx 1 MeV in approx 1 hour. In this case total energy gains result primarily from several separate episodes of shock drift acceleration, each of which occurs when particles are scattered back to the shock by magnetic fluctuations in the shock vicinity
5. Control Infrastructure for a Pulsed Ion Accelerator
International Nuclear Information System (INIS)
Persaud, A.; Regis, M. J.; Stettler, M. W.; Vytla, V. K.
2016-01-01
We report on updates to the accelerator controls for the Neutralized Drift Compression Experiment II, a pulsed induction-type accelerator for heavy ions. The control infrastructure is built around a LabVIEW interface combined with an Apache Cassandra backend for data archiving. Recent upgrades added the storing and retrieving of device settings into the database, as well as ZeroMQ as a message broker that replaces LabVIEW's shared variables. Converting to ZeroMQ also allows easy access via other programming languages, such as Python.
6. Control Infrastructure for a Pulsed Ion Accelerator
Science.gov (United States)
Persaud, A.; Regis, M. J.; Stettler, M. W.; Vytla, V. K.
2016-10-01
We report on updates to the accelerator controls for the Neutralized Drift Compression Experiment II, a pulsed induction-type accelerator for heavy ions. The control infrastructure is built around a LabVIEW interface combined with an Apache Cassandra backend for data archiving. Recent upgrades added the storing and retrieving of device settings into the database, as well as ZeroMQ as a message broker that replaces LabVIEW's shared variables. Converting to ZeroMQ also allows easy access via other programming languages, such as Python.
7. Linear induction accelerator for heavy ions
International Nuclear Information System (INIS)
Keefe, D.
1976-09-01
There is considerable recent interest in the use of high energy (γ = 1.1), heavy (A greater than or equal to 100) ions to irradiate deuterium--tritium pellets in a reactor vessel to constitute a power source at the level of 1 GW or more. Various accelerator configurations involving storage rings have been suggested. A discussion is given of how the technology of Linear Induction Accelerators--well known to be matched to high current and short pulse length--may offer significant advantages for this application
8. Detection systems for radioactive ion beams; Systeme de detection en ions radioactifs
Energy Technology Data Exchange (ETDEWEB)
Savajols, H
2002-07-01
Two main methods are used to produce radioactive ion beams: -) the ISOL method (isotope separation on-line) in which the stable beam interacts with a thick target, the reaction products diffuse outside the target and are transferred to a source where they are ionized, a mass separator and a post-accelerator drive the selected radioactive ions to the right energy; -) the in-flight fragmentation method in which the stable beam interacts with a thin target, the reaction products are emitted from the target with a restricted angular distribution and a velocity close to that of the incident beam, the experimenter has to take advantage from the reaction kinetics to get the right particle beam. Characteristic time is far longer with the ISOL method but the beam intensity is much better because of the use of a post-accelerator. In both cases, the beam intensity is lower by several orders of magnitude than in the case of a stable beam. This article presents all the constraints imposed by radioactive beams to the detection systems of the reaction products and gives new technical solutions according to the type of nuclear reaction studied. (A.C.)
9. CAS Accelerator Physics (Ion Sources) in Slovakia
CERN Multimedia
CAS School
2012-01-01
The CERN Accelerator School (CAS) and the Slovak University of Technology jointly organised a specialised course on ion sources, held at the Hotel Senec, Senec, Slovakia, from 29 May to 8 June, 2012. Following some background lectures on accelerator physics and the fundamental processes of atomic and plasma physics, the course covered a wide range of topics related to ion sources and highlighted the latest developments in the field. Realistic case studies and topical seminars completed the programme. The school was very successful, with 69 participants representing 25 nationalities. Feedback from the participants was extremely positive, reflecting the high standard of the lectures. The case studies were performed with great enthusiasm and produced some excellent results. In addition to the academic programme, the participants were able to take part in a one-day excursion consisting of a guided tour of Bratislava and free time. A welcome event was held at the Hotel Senec, with s...
10. Heavy-ion accelerator research for inertial fusion
International Nuclear Information System (INIS)
1987-08-01
Thermonuclear fusion offers a most attractive long-term solution to the problem of future energy supplies: The fuel is virtually inexhaustible and the fusion reaction is notably free of long-lived radioactive by-products. Also, because the fuel is in the form of a plasma, there is no solid fuel core that could melt down. The DOE supports two major fusion research programs to exploit these virtues, one based on magnetic confinement and a second on inertial confinement. One part of the program aimed at inertial fusion is known as Heavy Ion Fusion Accelerator Research, or HIFAR. In this booklet, the aim is to place this effort in the context of fusion research generally, to review the brief history of heavy-ion fusion, and to describe the current status of the HIFAR program
11. Charge Breeding of Radioactive Ions in an Electron Cyclotron Resonance Ion Source(ECRIS) at ISOLDE
CERN Multimedia
Lindroos, M
2002-01-01
The development of an efficient charge breeding scheme for the next generation of RIB facilities will have a strong impact on the post-accelerator for several Radioactive Ion Beam (RIB) projects at European large scale facilities. At ISOLDE/CERN there will be the unique possibility to carry out experiments with the two possible charge breeding set-ups with a large variety of radioactive isotopes using identical injection conditions. One charge breeding set-up is the Penning trap/EBIS combination which feeds the REX-ISOLDE linear accelerator and which is in commissioning now. The second charge breeder is a new ECRIS PHOENIX developed at the ISN ion source laboratory at Grenoble. This ECRIS is now under investigation with a 14 GHz amplifier to characterize its performance. The experiments are accompanied by theoretical studies in computer simulations in order to optimize the capture of the ions in the ECRIS plasma. A second identical PHOENIX ECRIS which is under investigation at the Daresbury Laboratory is avai...
12. Simulations of multistage intense ion beam acceleration
International Nuclear Information System (INIS)
Slutz, S.A.; Poukey, J.W.
1992-01-01
An analytic theory for magnetically insulated, multistage acceleration of high intensity ion beams, where the diamagnetic effect due to electron flow is important, has been presented by Slutz and Desjarlais. The theory predicts the existence of two limiting voltages called V 1 (W) and V 2 (W), which are both functions of the injection energy qW of ions entering the accelerating gap. As the voltage approaches V 1 (W), unlimited beam-current density can penetrate the gap without the formation of a virtual anode because the dynamic gap goes to zero. Unlimited beam current density can penetrate an accelerating gap above V 2 (W), although a virtual anode is formed. It was found that the behavior of these limiting voltages is strongly dependent on the electron density profile. The authors have investigated the behavior of these limiting voltages numerically using the 2-D particle-in-cell (PIC) code MAGIC. Results of these simulations are consistent with the superinsulated analytic results. This is not surprising, since the ignored coordinate eliminates instabilities known to be important from studies of single stage magnetically insulated ion diodes. To investigate the effect of these instabilities the authors have simulated the problem with the 3-D PIC code QUICKSILVER, which indicates behavior that is consistent with the saturated model
13. Light Ion Biomedical Research Accelerator LIBRA
International Nuclear Information System (INIS)
Gough, R.A.
1987-01-01
LIBRA is a concept to place a light-ion, charged-particle facility in a hospital environment, and to dedicate it to applications in biology and medicine. There are two aspects of the program envisaged for LIBRA: a basic research effort coupled with a program in clinical applications of accelerated charged particles. The operational environment to be provided for LIBRA is one in which both of these components can coexist and flourish, and one that will promote the transfer of technology and knowledge from one to the other. In order to further investigate the prospects for a Light Ion Biomedical Research Accelerator (LIBRA), discussions are underway with the Merritt Peralta Medical Center MPMC) in Oakland CA, and the University of California at San Francisco (UCSF). In this paper, a brief discussion of the technical requirements for such a facility is given, together with an outline of the accelerator technology required. While still in a preliminary stage, it is possible nevertheless to develop an adequate working description of the type, size, performance and cost of the accelerator facilities required to meet the preliminary goals for LIBRA
14. The Light Ion Biomedical Research Accelerator (LIBRA)
International Nuclear Information System (INIS)
Gough, R.A.
1987-03-01
LIBRA is a concept to place a light-ion, charged-particle facility in a hospital environment, and to dedicate it to applications in biology and medicine. There are two aspects of the program envisaged for LIBRA: a basic research effort coupled with a program in clinical applications of accelerated charged particles. The operational environment to be provided for LIBRA is one in which both of these components can coexist and flourish, and one that will promote the transfer of technology and knowledge from one to the other. In order to further investigate the prospects for a Light Ion Biomedical Research Accelerator (LIBRA), discussions are underway with the Merritt Peralta Medical Center (MPMC) in Oakland, California, and the University of California at San Francisco (UCSF). In this paper, a brief discussion of the technical requirements for such a facility is given, together with an outline of the accelerator technology required. While still in a preliminary stage, it is possible nevertheless to develop an adequate working description of the type, size, performance and cost of the accelerator facilities required to meet the preliminary goals for LIBRA
15. Developments in accelerators for heavy ion fusion
International Nuclear Information System (INIS)
Keefe, D.
1985-01-01
The long term goal of Heavy Ion Fusion (HIF) is the development of an accelerator with the large beam power, large beam stored-energy, and high brightness needed to implode small deuterium-tritium capsules for fusion power. While studies of an RF linac/storage ring combination as an intertial fusion driver continue in Japan and Europe, the US program in recent times has concentrated on the study of the suitability of linear induction acceleration of ions for this purpose. Novel features required include use of multiple beams, beam current amplification in the linac, and manipulation of long beam bunches with a large velocity difference between head and tail. Recent experiments with an intense bright beam of cesium ions have established that much higher currents can be transported in a long quadrupole system than was believed possible a few years ago. A proof-of-principle ion induction linac to demonstrate beam current amplification with multiple beams is at present being fabricated at LBL
16. Developments in accelerators for heavy ion fusion
International Nuclear Information System (INIS)
Keefe, D.
1985-05-01
The long term goal of Heavy Ion Fusion (HIF) is the development of an accelerator with the large beam power, large beam stored-energy, and high brightness needed to implode small deuterium-tritium capsules for fusion power. While studies of an rf linac/storage ring combination as an inertial fusion driver continue in Japan and Europe, the US program in recent times has concentrated on the study of the suitability of linear induction acceleration of ions for this purpose. Novel features required include use of multiple beams, beam current amplification in the linac, and manipulation of long beam bunches with a large velocity difference between head and tail. Recent experiments with an intense bright beam of cesium ions have established that much higher currents can be transported in a long quadrupole system than was believed possible a few years ago. A proof-of-principle ion induction linac to demonstrate beam current amplification with multiple beams is at present being fabricated at LBL. 28 refs., 4 figs
17. Particle acceleration by electromagnetic ion cyclotron turbulence
International Nuclear Information System (INIS)
Crew, G.B.; Chang, Tom
1990-01-01
The LF EM-turbulence which furnishes energy for the acceleration of ions in various regions of the earth's magnetosphere efficiently accomplishes its transfer of energy from waves to particles through ion cyclotron resonance (ICR) with the left-hand polarized component of the turbulence; the result of this interaction is a heating of the particle distribution. A general theoretical treatment of ICR heating in a weakly inhomogeneous magnetic geometry is presented, en route to a more detailed examination of auroral ion conics' formation. A substantial simplification of the analysis of the altitude-asymptotic form of the conic distribution is obtained via the similarity transformation introduced into the properties of the electric field spectral density and the earth's dipolar magnetic field. 60 refs
18. Transport and extraction of radioactive ions stopped in superfluid helium
NARCIS (Netherlands)
Huang, WX; Dendooven, P; Gloos, K; Takahashi, N; Arutyunov, K; Pekola, JP; Aysto, J
A new approach to convert a high energy beam to a low energy one, which is essential for the next generation radioactive ion beam facilities, has been proposed and tested at Jyvaskyla, Finland. An open Ra-223 alpha-decay-recoil source has been used to produce radioactive ions in superfluid helium.
19. Method of solidifying radioactive ion exchange resin
International Nuclear Information System (INIS)
Minami, Yuji; Tomita, Toshihide
1989-01-01
Spent anion exchange resin formed in nuclear power plants, etc. generally catch only a portion of anions in view of the ion exchange resins capacity and most of the anions are sent while possessing activities to radioactive waste processing systems. Then, the anion exchange resins increase the specific gravity by the capture of the anions. Accordingly, anions are caused to be captured on the anion exchange resin wastes such that the specific gravity of the anion exchange resin wastes is greater than that of the thermosetting resins to be mixed. This enables satisfactory mixing with the thermosetting resins and, in addition, enables to form integral solidification products in which anion exchange resins and cation exchange resins are not locallized separately and which are homogenous and free from cracks. (T.M.)
20. Radioactive ion beam facility at Louvain-La-Neuve, Belgium and its features
International Nuclear Information System (INIS)
Chintalapudi, S.N.
1991-01-01
Use of radioactive ion beams for the study of nuclear structure as well as the astrophysical reaction cross sections become the current interest in physics. A full-fledged facility based on two coupled cyclotrons comprising a compact high current cyclotron and a medium energy cyclotron with an intermediate target and ion source system has been recently commissioned at the Louvain-La-Neuve University in Belgium by its accelerator group and has been successfully used for the measurement of cross sections for the primordial nucleosynthesis reactions of astrophysical interest, directly. A brief description of the system, its operational features together with some details of the target and the ion source arrangement for the production of the radioactive ion beams and their acceleration to energies required for the proposed studies is presented. Description of the reactions studied by the Louvain La Neuve group for astrophysical interest is also given. (author). 20 refs., 6 figs., 4 tabs
1. Charge breeding of radioactive isotopes at the CARIBU facility with an electron beam ion source
Science.gov (United States)
Vondrasek, R. C.; Dickerson, C. A.; Hendricks, M.; Ostroumov, P.; Pardo, R.; Savard, G.; Scott, R.; Zinkann, G.
2018-05-01
An Electron Beam Ion Source Charge Breeder (EBIS-CB) has been developed at Argonne National Laboratory as part of the californium rare ion breeder upgrade. For the past year, the EBIS-CB has been undergoing commissioning as part of the ATLAS accelerator complex. It has delivered both stable and radioactive beams with A/Q 18% into a single charge state. The operation of this device, challenges during the commissioning phase, and future improvements will be discussed.
2. Selection of RIB targets using ion implantation at the Holifield radioactive ion beam facility
International Nuclear Information System (INIS)
Alton, G.D.; Dellwo, J.
1995-01-01
Among several major challenges posed by generating and accelerating adequate intensities of RIBs, selection of the most appropriate target material is perhaps the most difficult because of the requisite fast and selective thermal release of minute amounts of the short-lived product atoms from the ISOL target in the presence of bulk amounts of target material. Experimental studies are under way at the Oak Ridge National Laboratory (ORNL) which are designed to measure the time evolution of implanted elements diffused from refractory target materials which are candidates for forming radioactive ion beams (RIBs) at the Holifield Radioactive Ion Beam Facility (HRIBF). The diffusion coefficients are derived by comparing experimental data with numerical solutions to a one-dimensional form of Fick's second law for ion implanted distributions. In this report, we describe the experimental arrangement, experimental procedures, and provide time release data and diffusion coefficients for releasing ion implanted 37 Cl from Zr 5 Si 3 and 75 As, 79 Br, and 78 Se from Zr 5 Ge 3 and estimates of the diffusion coefficients for 35 Cl, 63 Cu, 65 Cu, 69 Ga and 71 Ga diffused from BN; 35 Cl, 63 Cu, 65 Cu, 69 Ga, 75 As, and 78 Se diffused from C; 35 Cl, 68 Cu, 69 Ga, 75 As, and 78 Se diffused from Ta
3. Animal experimental investigations of the problem of the decorporation of radioactive metal ions
International Nuclear Information System (INIS)
Berner, W.
1973-01-01
Basically, it is possible to reduce the radiation exposure by excretion intensification of incorporated radioactive materials. Chelate agents have proved to be particularly effective for the accelerated elimination of radioactive metal ions. The kinetics of the distribution and excretion of 57 CoCl 2 , 65 ZnCl 2 and 203 HgCl 2 on the rat under the influence of the chelating agent penicillamin (D-ββ-dimethylcystein) was investigated and the reduction of the radiation exposure in man was calculated from the animal-experimentally gained data. At various times after the incorporation of metal ions, the whole body radioactivity and, after killing the animals, the radioactivity of the organs liver, kidney, spleen, skeleton, muscles and blood, were measured. From the course of the measured radioactivities with time, the biokinetic data of the radioactive metal ions (effective half-lives, selection factors and their components) were determined by means of regression analyses. The chelating agent was applied at different times before or after incorporation of the radioactive metal ions. (EK/LH) [de
4. Latest developments at GANIL for stable and radioactive ion beam production
International Nuclear Information System (INIS)
Jardin, P.; Barue, C.; Bajeat, O.; Canet, C.; Clement, E.; Cornell, J. C.; Delahaye, P.; Dubois, M.; Dupuis, M.; Flambard, J. L.; Fraanberg, H.; Frigot, R.; Leboucher, C.; Lecesne, N.; Lecomte, P.; Leherissier, P.; Lemagnen, F.; Leroy, R.; Maunoury, L.; Mery, A.
2010-01-01
In the frame of the SPIRAL II (Systeme de Production d'Ions Radioactifs Acceleres en Ligne Partie II) project, several developments of stable and radioactive ion production systems have been started up. In parallel, GANIL has the ambition to preserve the existing stable and radioactive beams and also to increase its range by offering new ones. In order to identify the best directions for this development, a new group called GANISOL has been formed. Its preliminary conclusions and the latest developments at GANIL are presented.
5. Heavy-Ion Fusion Accelerator Research, 1992
International Nuclear Information System (INIS)
1993-06-01
The National Energy Strategy calls for a demonstration IFE power plant by the year 2025. The cornerstone of the plan to meet this ambitious goal is research and development for heavy-ion driver technology. A series of successes indicates that the technology being studied by the HIFAR Group -- the induction accelerator -- is a prime candidate for further technology development toward this long-range goal. The HIFAR program addresses the generation of high-power, high-brightness beams of heavy ions; the understanding of the scaling laws that apply in this hitherto little-explored physics regime; and the validation of new, potentially more economical accelerator strategies. Key specific elements to be addressed include: fundamental physical limits of transverse and longitudinal beam quality; development of induction modules for accelerators, along with multiple-beam hardware, at reasonable cost; acceleration of multiple beams, merging of the beams, and amplification of current without significant dilution of beam quality; final bunching, transport, and focusing onto a small target. In 1992, the HIFAR Program was concerned principally with the next step toward a driver: the design of ILSE, the Induction Linac Systems Experiments. ILSE will address most of the remaining beam-control and beam-manipulation issues at partial driver scale. A few parameters -- most importantly, the line charge density and consequently the size of the ILSE beams -- will be at full driver scale. A theory group closely integrated with the experimental groups continues supporting present-day work and looking ahead toward larger experiments and the eventual driver. Highlights of this long-range, driver-oriented research included continued investigations of longitudinal instability and some new insights into scaled experiments with which the authors might examine hard-to-calculate beam-dynamics phenomena
6. Laser-driven Ion Acceleration using Nanodiamonds
Science.gov (United States)
D'Hauthuille, Luc; Nguyen, Tam; Dollar, Franklin
2016-10-01
Interactions of high-intensity lasers with mass-limited nanoparticles enable the generation of extremely high electric fields. These fields accelerate ions, which has applications in nuclear medicine, high brightness radiography, as well as fast ignition for inertial confinement fusion. Previous studies have been performed with ensembles of nanoparticles, but this obscures the physics of the interaction due to the wide array of variables in the interaction. The work presented here looks instead at the interactions of a high intensity short pulse laser with an isolated nanodiamond. Specifically, we studied the effect of nanoparticle size and intensity of the laser on the interaction. A novel target scheme was developed to isolate the nanodiamond. Particle-in-cell simulations were performed using the EPOCH framework to show the sheath fields and resulting energetic ion beams.
7. Radioactive Ions Production Ring for Beta-Beams
CERN Document Server
Benedetto, E; Wehner, J
2010-01-01
Within the FP7 EUROnu program, Work Package 4 addresses the issues of production and acceleration of 8Li and 8B isotopes through the Beta-Beam complex, for the production of electron-neutrino. One of the major critical issues is the production of a high enougth ion ßux, to fulÞll the requirements for physics. In alternative to the direct ISOL production method, a new ap- proach is proposed in [1]. The idea is to use a compact ring for Litium ions at 25 MeV and an internal He or D target, in which the radioactive-isotopes production takes place. The beam is expected to survive for several thousands of turns, therefore cooling in 6D is required and, according this scheme, the ionization cooling provided by the target itself and a suitable RF system would be sufÞcient. We present some preliminary work on the Production ring lat- tice design and cooling issues, for the 7Li ions, and propose plans for future studies, within the EUROnu program.
8. Recent results on reactions with radioactive beams at RIBRAS (Radioactive Ion Beams in Brazil)
Science.gov (United States)
Lépine-Szily, A.; Lichtenthäler, R.; Guimarães, V.; Arazi, A.; Barioni, A.; Benjamim, E. A.; de Faria, P. N.; Descouvemont, P.; Gasques, L. R.; E; Leistenschneider; Mendes, D. R., Jr.; Morais, M. C.; Morcelle, V.; Moro, A. M.; Pampa Condori, R.; Pires, K. C. C.; Rodriguez-Gallardo, M.; Scarduelli, V.; Shorto, J. M. B.; Zamora, J. C.
2015-04-01
We present a quick description of RIBRAS (Radioactive Ion beams in Brazil), which is a superconducting double solenoid system, installed at the Pelletron Laboratory of the University of São Paulo and extends the capabilities of the original Pelletron Tandem Accelerator of 8MV terminal voltage (8UD) by producing secondary beams of unstable nuclei. The experimental program of the RIBRAS covers the study of elastic and inelastic scattering with the objective to study the interaction potential and the reaction mechanisms between weakly bound (RIB) and halo (6He and 8B) projectiles on light, medium and heavy mass targets. With highly purified beams, the study of resonant elastic scattering and resonant transfer reactions, using inverse kinematics and thick targets, have also been included in our recent experimental program.
9. Prospects for high energy heavy ion accelerators
International Nuclear Information System (INIS)
Leemann, C.
1979-03-01
The acceleration of heavy ions to relativistic energies (T greater than or equal to 1 GeV/amu) at the beam intensities required for fundamental research falls clearly in the domain of synchrotons. Up to date, such beams have been obtained from machines originally designed as proton acccelerators by means of modified RF-programs, improved vacuum and, most importantly, altered or entirely new injector systems. Similarly, for the future, substantial changes in synchrotron design itself are not foreseen, but rather the judicious application and development of presently known principles and technologies and a choice of parameters optimized with respect to the peculiarities of heavy ions. The low charge to mass ratio, q/A, of very heavy ions demands that superconducting magnets be considered in the interest of the highest energies for a given machine size. Injector brightness will continue to be of highest importance, and although space charge effects such as tune shifts will be increased by a factor q 2 /A compared with protons, advances in linac current and brightness, rather than substantially higher energies are required to best utilize a given synchrotron acceptance. However, high yeilds of fully stripped, very heavy ions demand energies of a few hundred MeV/amu, thus indicating the need for a booster synchrotron, although for entirely different reasons than in proton facilities. Finally, should we consider colliding beams, the high charge of heavy ions will impose severe current limitations and put high demands on system design with regard to such quantities as e.g., wall impedances or the ion induced gas desorption rate, and advanced concepts such as low β insertions with suppressed dispersion and very small crossing angles will be essential to the achievement of useful luminosities
10. Charge breeding of stable and radioactive ion beams with EBIS/T devices
CERN Document Server
Kester, Oliver; Becker, R
2004-01-01
Radioactive ion beams (RIBs) are an important tool for experiments at the foremost frontier of nuclear physics. The quasi-continuous radioactive beams from target ion sources of RIB-facilities have to be accelerated to energies at and beyond the Coulomb barrier. An efficient acceleration requires a suitable A/q of the ions determined by the accelerator design, which can be reached via the stripping method or by using a charge state breeder like the REX-ISOLDE system. In order to get comparable efficiencies for a charge state breeder with the stripping scheme, the breeding efficiency in one charge state has to be optimized by narrowing the charge state distribution. In addition good beam quality and thus small emittances are required to achieve best transmission in the following accelerator, which is mandatory for high intensity RIBs. For EBIS/T devices the maximum intensity of the radioactive ion beam is a critical issue, and high current EBIS/T devices will be necessary to deal with intensities of second gen...
11. Measurement of residual radioactivity in cooper exposed to high energy heavy ion beam
Energy Technology Data Exchange (ETDEWEB)
Kim, Eunjoo; Nakamura, Takashi [Tohoku Univ., Sendai (Japan). Cyclotron and Radioisotope Center; Uwamino, Yoshitomo; Ito, Sachiko; Fukumura, Akifumi
1999-03-01
The residual radioactivities produced by high energy heavy ions have been measured using the heavy ion beams of the Heavy Ion Medical Accelerator (HIMAC) at National Institute of Radiological Sciences. The spatial distribution of residual radioactivities in 3.5 cm, 5.5 cm and 10 cm thick copper targets of 10 cm x 10 cm size bombarded by 290 MeV/u, 400 MeV/u-{sup 12}C ion beams and 400 MeV/u-{sup 20}Ne ion beam, respectively, were obtained by measuring the gamma-ray activities of 0.5 mm thick copper foil inserted in the target with a high purity Ge detector after about 1 hour to 6 hours irradiation. (author)
12. Status report on the folded tandem ion accelerator at BARC
Folded tandem ion accelerator; charged particle beams; voltage stability; Rutherford backscattering; ion optics; beam lines. Abstract. The folded tandem ion accelerator (FOTIA) facility set up at BARC has become operational. At present, it is used for elemental analysis studies using the Rutherford backscattering technique.
13. Heavy ion acceleration at parallel shocks
Directory of Open Access Journals (Sweden)
V. L. Galinsky
2010-11-01
Full Text Available A study of alpha particle acceleration at parallel shock due to an interaction with Alfvén waves self-consistently excited in both upstream and downstream regions was conducted using a scale-separation model (Galinsky and Shevchenko, 2000, 2007. The model uses conservation laws and resonance conditions to find where waves will be generated or damped and hence where particles will be pitch-angle scattered. It considers the total distribution function (for the bulk plasma and high energy tail, so no standard assumptions (e.g. seed populations, or some ad-hoc escape rate of accelerated particles are required. The heavy ion scattering on hydromagnetic turbulence generated by both protons and ions themselves is considered. The contribution of alpha particles to turbulence generation is important because of their relatively large mass-loading parameter Pα=nαmα/npmp (mp, np and mα, nα are proton and alpha particle mass and density that defines efficiency of wave excitation. The energy spectra of alpha particles are found and compared with those obtained in test particle approximation.
International Nuclear Information System (INIS)
Watanabe, Hiromasa; Tanaka, Susumu; Anazawa, Yutaka
1991-01-01
Building layout of Takasaki ion accelerator facility has been started since 1987, with the propulsion of research development of (1) cosmetic environment materials, (2) nuclear fusion reactors, (3) biotechnology, and (4) new functional materials. This paper deals with an AVF cyclotron and a tandem type accelerator, focusing on safety design, radiation safety management, and radioactive waste management. Safety design is discussed in view of radiation shielding and activation countermeasures. Radiation safety management covers radiation monitoring in the workplace, exhaust radioactivity, environment outside the facility, and the other equipments; personal monitoring; and protective management of exposure. For radiation waste management, basic concept and management methods are commented on. (N.K.)
15. Preliminary shielding estimates for the proposed Oak Ridge National Laboratory (ORNL) Radioactive Ion Beam Facility (RIBF)
International Nuclear Information System (INIS)
Johnson, J.O.; Gabriel, T.A.; Lillie, R.A.
1996-01-01
The Oak Ridge National Laboratory (ORNL) has proposed designing and implementing a new target-ion source for production and injection of negative radioactive ion beams into the Hollifield tandem accelerator. This new facility, referred to as the Radioactive Ion Beam Facility (RIBF), will primarily be used to advance the scientific communities' capabilities for performing state-of-the-art cross-section measurements. Beams of protons or other light, stable ions from the Oak Ridge Isochronous Cyclotron (ORIC) will be stopped in the RIBF target ion source and the resulting radioactive atoms will be ionized, charge exchanged, accelerated, and injected into the tandem accelerator. The ORIC currently operates with proton energies up to 60 MeV and beam currents up to 100 microamps with a maximum beam power less than 2.0 kW. The proposed RIBF will require upgrading the ORIC to generate proton energies up to 200 MeV and beam currents up to 200 microamps for optimum performance. This report summarizes the results of a preliminary one-dimensional shielding analysis of the proposed upgrade to the ORIC and design of the RIBF. The principal objective of the shielding analysis was to determine the feasibility of such an upgrade with respect to existing shielding from the facility structure, and additional shielding requirements for the 200 MeV ORIC machine and RIBF target room
16. Mutation spectrum of accelerated heavy ions
International Nuclear Information System (INIS)
Takatsuji, Toshihiro; Matsuse, Michiko; Nakazawa, Y.
2004-01-01
Using Drosophila melanogaster which has X-linked white-ivory eye-color mutation w i and two recessive genes of wing-hair mwh and flr transheterozygously located on the third chromosomes, we scored mosaic spots in eye and wing of male flies irradiated with accelerated heavy ions at the period of larvae. Results of two irradiation conditions were compared. One is that all dose were irradiated with one heavy ion spill (irradiation time was about 0.3 sec), and another was that the dose were divided into multi spills (50-100 spills, irradiation time is about 3-6 minutes). The dose was selected that the average hit of the ion to the cell nucleus was about 0.2. If some difference exists, some information must be transmitted from hit cells or the protoplast to the nucleus which is not hit. As a result, the difference was not observed, and any sign of the bystander effect was not detected. (author)
17. Accelerated physical modelling of radioactive waste migration in soil
International Nuclear Information System (INIS)
Zimmie, T.F.; De, A.; Mahmud, M.B.
1994-01-01
A 100 g-tonne geotechnical centrifuge was used to study the long-term migration of a contaminant and radioactive tracer through a saturated soil medium. The use of the centrifuge simulates the acceleration of travel time in the prototype, which is N times larger than the model, by N 2 , where N is the desired g level. For a 5 h run at 60 g, the test modelled a migration time of about 2 years for a prototype 60 times larger than the small-scale model tested. Iodine 131, used as the tracer, was injected onto the surface of the soil, and was allowed to migrate with a constant head of water through the saturated soil. End window Geiger-Mueller (G-M) tubes were used to measure the count rate of the radioactive tracer flowing through the soil. The time from the peak response of one G-M tube to the other denotes the travel time between the two points in the flow domain. The results obtained using the radioactive tracer are in good agreement with the test performed on the same model setup using potassium permanganate as tracer and with numerical flow net modelling. Radioactive tracers can be useful in the study of nonradioactive contaminants as well, offering a nonintrusive (nondestructive) method of measuring contaminant migration. (author). 18 refs., 1 tab., 7 figs
18. Production of light radioactive ion beams (RIB) using inverse kinematics
International Nuclear Information System (INIS)
Das, J.J.; Sugathan, P.; Madhavan, N.; Madhusudhana Rao, P.V.; Jhingan, A.; Varughese, T.; Barua, S.; Nath, S.; Sinha, A.K.; Kumar, B.; Zacharias, J.
2005-01-01
At Nuclear Science Centre (NSC), New Delhi, we have implemented a facility to produce low energy light radioactive ion beams (RIBs) using (p,n) type of reactions in inverse kinematics. For this purpose primary beams from the 15-UD Pelletron accelerator impinged on a thin polypropylene foil mounted on a rotating/linearly moving target assembly. For efficiently separating the secondary beam from primary beam, the existing recoil mass spectrometer (RMS) HIRA was operated with new ion optics. Suitable hardware modifications were also made. Using this facility, we have extracted a 7 Be beam of purity better than 99% and spot-size ∼4 mm in diameter. This 7 Be beam has been utilized in a variety of experiments in the energy range of 15-22 MeV. Typical beam parameters are: intensity 10 4 pps, angular spread ±30 mrad and energy spread ±0.5 MeV. Development of appropriate detector setup/target arrangement were also made to perform these experiments. In this paper, we describe the implementation of this project
19. High-spin nuclear structure studies with radioactive ion beams
International Nuclear Information System (INIS)
Baktash, C.
1992-01-01
Two important developments in the sixties, namely the advent of heavy-ion accelerators and fabrication of Ge detectors, opened the way for the experimental studies of nuclear properties at high angular momentum. Addition of a new degree of freedom, namely spin, made it possible to observe such fascinating phenomena as occurrences and coexistence of a variety of novel shapes, rise, fall and occasionally rebirth of nuclear collectivity, and disappearance of pairing correlations. Today, with the promise of development of radioactive ion beams (RIB) and construction of the third-generation Ge-detection systems (GAMMASPHERE and EUROBALL), nuclear physicists are poised to explore new and equally fascinating phenomena that have been hitherto inaccessible. With the addition of yet another dimension, namely the isospin, they will be able to observe and verify predictions for exotic shapes as varied as rigid triaxiality, hyperdeformation and triaxial-octupole shapes, or to investigate the T=O pairing correlations. In this paper, the author reviews, separately for neutron-deficient and neutron-rich nuclei, these and a few other new high-spin physics opportunities that may be realized with RIB. Following this discussion, a list of the beam species, intensities and energies that are needed to fulfill these goals is presented. The paper concludes with a description of the experimental techniques and instrumentations that are required for these studies
20. Spiral loaded cavities for heavy ion acceleration
International Nuclear Information System (INIS)
Schempp, A.; Klein, H.
1976-01-01
A transmission line theory of the spiral resonator has been performed and the calculated and measured properties will be compared. Shunt impedances up to 50 MΩ/m have been measured. In a number of high power tests the structure has been tested and its electrical and mechanical stability has been investigated. The static frequency shift due to ponderomotoric forces was between 0.2 and 50 kHz/kW dependent on the geometrical parameters of the spirals. The maximum field strength obtained on the axis was 16 MV/m in pulsed operation and 9.2 MV/m in cw, corresponding to a voltage gain per cavity of up to 0.96 MV. The results show that spiral resonators are well suited as heavy ion accelerator cavities. (author)
1. Production of a radioactive 18F ion beam for nuclear reaction studies
Science.gov (United States)
Roberts, A. D.; Nickles, R. J.; Paul, M.; Rehm, K. E.; Jiang, C. L.; Blumenthal, D. J.; Gehring, J.; Henderson, D.; Nolen, J.; Pardo, R. C.; Schiffer, J. P.; Segel, R. E.
1995-12-01
A two-stage method for generating a radioactive 18F ion beam has been developed. 18F is produced with a medical cyclotron by 11 MeV proton activation of [ 18O]water, then chemically processed off-line for use in a tandem accelerator ion source. Azeotropic distillation reduces the 18O component by 10 5, with a resulting 18O to 18F beam ratio of about 10 3. The average 18F - beam intensity per synthesis is 1 ppA over 120 min from a cesium vapor, sputter negative ion source (SNICS), with a peak intensity of 4.5 ppA.
2. Accelerated radiation damage test facility using a 5 MV tandem ion accelerator
International Nuclear Information System (INIS)
Wady, P.T.; Draude, A.; Shubeita, S.M.; Smith, A.D.; Mason, N.; Pimblott, S.M.; Jimenez-Melero, E.
2016-01-01
3. Development of bipolar pulse accelerator for intense pulsed ion beam acceleration
International Nuclear Information System (INIS)
Fujioka, Y.; Mitsui, C.; Kitamura, I.; Takahashi, T.; Masugata, K.; Tanoue, H.; Arai, K.
2003-01-01
To improve the purity of an intense pulsed ion beams a new type of pulsed ion beam accelerator named 'bipolar pulse accelerator (BPA)' was proposed. In the accelerator purity of the beam is expected. To confirm the principle of the accelerator experimental system was developed. The system utilizes B y type magnetically insulated acceleration gap and operated with single polar negative pulse. A coaxial gas puff plasma gun placed in the grounded anode was used as an ion source, and source plasma (nitrogen) of current density approx. = 25 A/cm 2 , duration approx. = 1.5 μs was injected into the acceleration gap. The ions are successfully accelerated from the grounded anode to the drift tube by applying negative pulse of voltage 180 kV, duration 60 ns to the drift tube. Pulsed ion beam of current density approx. = 40 A/cm 2 , duration approx. 60 ns was obtained at 42 mm downstream from the anode surface. (author)
4. Ion sources development at GANIL for radioactive beams and high charge state ions
International Nuclear Information System (INIS)
Leroy, R.; Barue, C.; Canet, C.; Dupuis, M.; Flambard, J.L.; Gaubert, G.; Gibouin, S.; Huguet, Y.; Jardin, P.; Lecesne, N.; Leherissier, P.; Lemagnen, F.; Pacquet, J.Y.; Pellemoine-Landre, F.; Rataud, J.P.; Saint-Laurent, M.G.; Villari, A.C.C.; Maunoury, L.
2001-01-01
The GANIL laboratory has in charge the production of ion beams for nuclear and non nuclear physics. This article reviews the last developments that are underway in the fields of radioactive ion beam production, increase of the metallic ion intensities and production of highly charges ion beams. (authors)
5. 0,01-5 MeV heavy ion accelerators
International Nuclear Information System (INIS)
Golubev, V.P.; Ivanov, A.S.; Nikiforov, S.A.; Svin'in, M.P.; Tarvid, G.V.; Troshikhin, A.G.; Fedotov, M.T.
1983-01-01
The results of development of an accelerating complex on the base of the UP-2-1 heavy ion charge exchange accelerator and IMPLANT-500 high-voltage heavy ion accelerator are given. The accelerating complex provides overlapping of the 0.01 MeV to 5 MeV energy range at accelerated beam currents of 10 -3 -10 -6 A order. The structural features of accelerators and their basic units and systems are considered. The UP-2-1 accelerator is designed for researches in the field of experimental physics and applied problem solutions. The IMPLANT-500 accelerator is designed for commercial ion-beam facilities with closed loop of silicon plate treatment
6. Production of multicharged radioactive ion beams for spiral: studies and realization of the first target-ion source system
International Nuclear Information System (INIS)
Maunoury, L.
1998-01-01
In the framework of the SPIRAL project, which concerns the production and the acceleration of a multicharged radioactive ions beam, the following part has been studied: production and ionization of the radioactive ions beam. A first target-source (nanogan II), devoted exclusively to the production of multicharged radioactive ions gas type beams, has been studied and tested. The diffusion efficiency has been deduced from the diffusion equations (Fick laws). This efficiency is governed by the following parameters: the temperature, the grains size of the target, the Arrhenius parameters and the radioactive period. Another study concerning the production targets is presented. It deals with the temperature distribution allowing an utilization of more than one month at a temperature of 2400 K. Another development (SPIRAL II) is devoted to the production of high neutron content radioactive atoms created by the uranium fission, from fast neutrons. The neutrons beam is produced by the ''stripping break-up'' of a deutons beam in a converter. (A.L.B.)
International Nuclear Information System (INIS)
2013-01-01
Collinear laser spectroscopy is a tool for the model independent determination of spins, charge radii and electromagnetic moments of nuclei in ground and long-lived isomeric states. In the context of this thesis a new offline ion source for high evaporating temperatures and an ion beam analysis system were implemented at the TRIGA-LASER Experiment at the Institute for Nuclear Chemistry at the University of Mainz. The main part of the thesis deals with the determination of the properties of radioactive praseodymium and cadmium isotopes by collinear laser spectroscopy at ISOLDE/CERN. The necessary test measurements for the spectroscopy of praseodymium ions have been conducted with the aforementioned offline ion source at the TRIGA-LASER experiment. The spectroscopy of the praseodymium ions was motivated by the observation of a modulation of the electron capture decay rates of hydrogen-like 140 Pr 58+ . The nuclear magnetic moment of the nucleus is, among others, required for the explanation of the so-called GSI Oscillations and has not been studied experimentally before. Additionally, the determined electron capture decay constant of hydrogen-like 140 Pr 58+ is lower than the one of helium-like 140 Pr 57+ . The explanation of this phenomenon requires a positive magnetic moment. During the experiment at the COLLAPS apparatus the magnetic moments of the neutron-deficient isotopes 135 Pr, 136 Pr and 137 Pr could be determined for the first time. Unfortunately, due to a too low production yield the desired isotope 140 Pr could not be studied.The systematic study of cadmium isotopes was motivated by nuclear physics in the tin region. With Z=48 two protons are missing for the shell closure and the isotopes extend from the magic neutron number N=50 to the magic neutron number N=82. The extracted nuclear properties allow tests of different nuclear models in this region. In this thesis the obtained results of the spectroscopy of the cadmium isotopes 106-124,126 Cd and their
8. A theoretical investigation of the collective acceleration of cluster ions with accelerated potential waves
International Nuclear Information System (INIS)
Suzuki, Hiroshi; Enjoji, Hiroshi; Kawaguchi, Motoichi; Noritake, Toshiya
1984-01-01
A theoretical treatment of the acceleration of cluster ions for additional heating of fusion plasma using the trapping effect in an accelerated potential wave is described. The conceptual design of the accelerator is the same as that by Enjoji, and the potential wave used is sinusoidal. For simplicity, collisions among cluster ions and the resulting breakups are neglected. The masses of the cluster ions are specified to range from 100 m sub(D) to 1000 m sub(D) (m sub(D): mass of a deuterium atom). Theoretical treatment is carried out only for the injection velocity which coincides with the phase velocity of the applied wave at the entrance of the accelerator. An equation describing the rate for successful acceleration of ions with a certain mass is deduced for the continuous injection of cluster ions. Computation for a typical mass distribution shows that more than 70% of the injected particles are effectively accelerated. (author)
9. Inertial confinement fusion systems using heavy ion accelerators as drivers
International Nuclear Information System (INIS)
Herrmannsfeldt, W.B.; Godlove, T.F.; Keefe, D.
1980-03-01
Heavy ion accelerators are the most recent entrants in the effort to identify a practical driver for inertial confinement fusion. They are of interest because of the expected efficient coupling of ion kinetic energy to the thermal energy needed to implode the pellet and because of the good electrical efficiency of high intensity particle accelerators. The beam intensities required, while formidable, lie within the range that can be studied by extensions of the theories and the technology of modern high energy accelerators
10. Acceleration of heavy-ion beams at the SF cyclotron
International Nuclear Information System (INIS)
1984-10-01
With the development of the new arc-heated cathode PIG type source, heavy-ion acceleration in the SF cyclotron has been drastically augmented, which means that a stable routine operation is being realized as well as the number of ion species is increasing. Excellent performance is also being exhibited with the arc power supply and gas feeding system required for the operation of the heavy-ion source. At present, the gaseous ions which are being accelerated are as follows: He, B, C, N, O, F, Ne, S, Ar and Xe. In the meantime, the metallic ions which are being accelerated likewise are Li, Be, Na, Mg, Al, Si, Cl, Ca, Ti, Fe and Cu. In this paper, results of mainly the research of heavy-ion acceleration conducted during the period from 1983 to July 1984 are described. (author)
11. Steady state ion acceleration by a circularly polarized laser pulse
International Nuclear Information System (INIS)
Zhang Xiaomei; Shen Baifei; Cang Yu; Li Xuemei; Jin Zhangying; Wang Fengchao
2007-01-01
The steady state ion acceleration at the front of a cold solid target by a circularly polarized flat-top laser pulse is studied with one-dimensional particle-in-cell (PIC) simulation. A model that ions are reflected by a steady laser-driven piston is used by comparing with the electrostatic shock acceleration. A stable profile with a double-flat-top structure in phase space forms after ions enter the undisturbed region of the target with a constant velocity
12. Concept for a lead-ion accelerating facility at CERN
International Nuclear Information System (INIS)
Billinge, R.; Boltezar, E.; Boussard, D.; Brouzet, E.; Cappi, R.; Raad, B. de; Doble, N.; Grafstroem, P.; Haseroth, H.; Hill, C.E.; Kissler, K.H.; Knott, J.; Linnecar, T.; Nitsch, F.; Poncet, A.; Raich, U.; Rasmussen, N.; Schoenauer, H.; Sherwood, T.R.; Siegel, N.; Tallgren, U.; Tetu, P.; Warner, D.; Weiss, M.
1990-01-01
After the successful acceleration of deuterons, alpha particles and in more recent years of oxygen and sulphur ions, interest arose for even heavier particles. This paper describes the problems associated with heavy ions. A proposal is made for a scenario which allows the CERN accelerators to cope with ions heavier than sulphur, e.g. lead. Discussed are the different options for the injector and the necessary upgrading for the circular machines. (orig.)
13. Collective ion acceleration by means of virtual cathodes
International Nuclear Information System (INIS)
Peter, W.; Faehl, R.J.; Snell, C.; Jones, M.E.
1985-01-01
Experiments on collective ion acceleration by means of the formation of a virtual cathode have been carried out for a number of years in the Soviet Union and in the United States. Recently, there has been renewed interest in the subject as a possible means of accelerating ions to very high energies. By understanding the physics underlying the acceleration process it may be possible to determine the feasibility of virtual cathode staging for very high energy ion production. For this reason, a theoretical and computational effort is underway at Los Alamos in order to clarify the basic issues of collective ion acceleration by means of virtual cathodes. To support the theoretical effort, simulations were done with the fully electromagnetic and relativistic particle-in-cell code ISIS (in a one-dimensional mode) and the electrostatic one-dimensional code BIGONE. In the simulations, an electron beam of density 6 x 10 11 cm -3 is injected into a one-dimensional box of length L. To supply the necessary ions for collective acceleration, a plasma source containing both ions and electrons was initialized near the emitting boundary. Of prime interest in this study was to understand the dynamics of virtual cathode formation and the dynamics of the acceleration process for the ions. In particular, the question of whether the ions are accelerated by a moving potential well or hydrodynamic pressure due to ambipolar expansion is of primary interest. 3 refs., 5 figs
14. Power balance limit in collective ion acceleration
International Nuclear Information System (INIS)
Olson, C.L.
1978-01-01
The power balance limit to the IREB beam front propagation velocity, as first applied to the problem of collective ion acceleration by Olson in 1973, is investigated in view of recent data of Ecker and Putnam. The beam front velocity β/sub f/c as a function of IREB impedance Z is given, showing the dependence on the power balance limit, the ionization front velocity, and the runaway cutoff. The Olson theory predictions, with no fitted parameters, are shown to be in agreement with the data. Further comparisons of β/sub f/ with respect to the IREB electron energy, the IREB current, and the neutral gas pressure are given. Various forms for the power balance limit are discussed; it is shown that inclusion of the secondary electron power loss term results in an essentially negligible correction to β/sub f/ for typical data parameters. The power balance limit used by Ecker and Putnam is shown to be simply a 3-parameter curve fit, wherein the fitted parameters must exceed their allowed physical values to obtain a reasonable fit for β/sub f/ vs Z. Further, it is shown that this curve fitting leads to serious disagreements with other aspects of the data. It is concluded that the original Olson theory adequately accounts for the data, and that the power balance limit for IREB/gas data is typically not significant except for very small values of Z
15. Diagnostics for studies of novel laser ion acceleration mechanisms
Energy Technology Data Exchange (ETDEWEB)
Senje, Lovisa; Aurand, Bastian; Wahlström, Claes-Göran [Department of Physics, Lund University, P. O. Box 118, S-221 00 Lund (Sweden); Yeung, Mark; Kuschel, Stephan; Rödel, Christian [Helmholtz-Institut Jena, D-07743 Jena (Germany); Wagner, Florian; Roth, Markus [Technische Universität Darmstadt, D-64289 Darmstadt (Germany); Li, Kun; Neumayer, Paul [ExtreMe Matter Institut, D-64291 Darmstadt (Germany); Dromey, Brendan; Jung, Daniel [Department of Physics and Astronomy, Queen' s University, Belfast BT7 1NN (United Kingdom); Bagnoud, Vincent [Helmholtz-Institut Jena, D-07743 Jena (Germany); GSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt (Germany); Zepf, Matthew [Helmholtz-Institut Jena, D-07743 Jena (Germany); Department of Physics and Astronomy, Queen' s University, Belfast BT7 1NN (United Kingdom); Kuehl, Thomas [ExtreMe Matter Institut, D-64291 Darmstadt (Germany); GSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt (Germany); Universität Mainz, D-55099 Mainz (Germany)
2014-11-15
Diagnostic for investigating and distinguishing different laser ion acceleration mechanisms has been developed and successfully tested. An ion separation wide angle spectrometer can simultaneously investigate three important aspects of the laser plasma interaction: (1) acquire angularly resolved energy spectra for two ion species, (2) obtain ion energy spectra for multiple species, separated according to their charge to mass ratio, along selected axes, and (3) collect laser radiation reflected from and transmitted through the target and propagating in the same direction as the ion beam. Thus, the presented diagnostic constitutes a highly adaptable tool for accurately studying novel acceleration mechanisms in terms of their angular energy distribution, conversion efficiency, and plasma density evolution.
16. Diagnostics for studies of novel laser ion acceleration mechanisms
International Nuclear Information System (INIS)
Senje, Lovisa; Aurand, Bastian; Wahlström, Claes-Göran; Yeung, Mark; Kuschel, Stephan; Rödel, Christian; Wagner, Florian; Roth, Markus; Li, Kun; Neumayer, Paul; Dromey, Brendan; Jung, Daniel; Bagnoud, Vincent; Zepf, Matthew; Kuehl, Thomas
2014-01-01
Diagnostic for investigating and distinguishing different laser ion acceleration mechanisms has been developed and successfully tested. An ion separation wide angle spectrometer can simultaneously investigate three important aspects of the laser plasma interaction: (1) acquire angularly resolved energy spectra for two ion species, (2) obtain ion energy spectra for multiple species, separated according to their charge to mass ratio, along selected axes, and (3) collect laser radiation reflected from and transmitted through the target and propagating in the same direction as the ion beam. Thus, the presented diagnostic constitutes a highly adaptable tool for accurately studying novel acceleration mechanisms in terms of their angular energy distribution, conversion efficiency, and plasma density evolution
17. Concept for high-charge-state ion induction accelerators
International Nuclear Information System (INIS)
Logan, B.G.; Perry, M.D.; Caporaso, G.J.
1996-01-01
This work describes a particular concept for ion induction linac accelerators using high-charge-state ions produced by an intense, short pulse laser, and compares the costs of a modular driver system producing 6.5 MJ for a variety of ion masses and charge states using a simple but consistent cost model
18. MEV Energy Electrostatic Accelerator Ion Beam Emittance Measurement
OpenAIRE
I.G. Ignat’ev; M.I. Zakharets; S.V. Kolinko; D.P. Shulha
2014-01-01
The testing equipment was designed, manufactured and tried out permitting measurements of total current, current profile and emittance of an ion beam extracted from the ion beam. MeV energy electrostatic accelerator ion H + beam emittance measurement results are presented.
19. Gamma-Ray Spectroscopy at TRIUMF-ISAC: the New Frontier of Radioactive Ion Beam Research
Science.gov (United States)
Ball, G. C.; Andreoiu, C.; Austin, R. A. E.; Bandyopadhyay, D.; Becker, J. A.; Bricault, P.; Brown, N.; Chan, S.; Churchman, R.; Colosimo, S.; Coombes, H.; Cross, D.; Demand, G.; Drake, T. E.; Dombsky, M.; Ettenauer, S.; Finlay, P.; Furse, D.; Garnsworthy, A.; Garrett, P. E.; Green, K. L.; Grinyer, G. F.; Hyland, B.; Hackman, G.; Kanungo, R.; Kulp, W. D.; Lassen, J.; Leach, K. G.; Leslie, J. R.; Mattoon, C.; Melconian, D.; Morton, A. C.; Pearson, C. J.; Phillips, A. A.; Rand, E.; Sarazin, F.; Svensson, C. E.; Sumithrarachchi, S.; Schumaker, M. A.; Triambak, S.; Waddington, J. C.; Walker, P. M.; Williams, S. J.; Wood, J. L.; Wong, J.; Zganjar, E. F.
2009-03-01
High-resolution gamma-ray spectroscopy is essential to fully exploit the unique scientific opportunities at the next generation radioactive ion beam facilities such as the TRIUMF Isotope Separator and Accelerator (ISAC). At ISAC the 8π spectrometer and its associated auxiliary detectors is optimize for β-decay studies while TIGRESS an array of segmented clover HPGe detectors has been designed for studies with accelerated beams. This paper gives a brief overview of these facilities and also presents recent examples of the diverse experimental program carried out at the 8π spectrometer.
20. High-energy acceleration of an intense negative ion beam
International Nuclear Information System (INIS)
Takeiri, Y.; Ando, A.; Kaneko, O.
1995-02-01
A high-current H - ion beam has been accelerated with the two-stage acceleration. A large negative hydrogen ion source with an external magnetic filter produces more than 10 A of the H - ions from the grid area of 25cm x 50cm with the arc efficiency of 0.1 A/kW by seeding a small amount of cesium. The H - ion current increases according to the 3/2-power of the total beam energy. A 13.6 A of H - ion beam has been accelerated to 125 keV at the operational gas pressure of 3.4 mTorr. The optimum beam acceleration is achieved with nearly the same electric fields in the first and the second acceleration gaps on condition that the ratio of the first acceleration to the extraction electric fields is adjusted for an aspect ratio of the extraction gap. The ratio of the acceleration drain current to the H - ion current is more than 1.7. That is mainly due to the secondary electron generated by the incident H - ions on the extraction grid and the electron suppression grid. The neutralization efficiency was measured and agrees with the theoretical calculation result. (author)
1. Heavy ion accelerators for inertial fusion
International Nuclear Information System (INIS)
Rubbia, C.
1992-01-01
Particle accelerators are used for accelerating the elementary, stable and separable constituents of matters to relativistic speed. These beams are of fundamental interest in the study on the ultimate constituents of matters and their interaction. Particle accelerators are the most promising driver for the fusion power reactors based on inertial confinement. The principle of inertial confinement fusion, radiation driven indirect drive, the accelerator complex and so on are described. (K.I.)
2. The radioactive ion beams facility project for the legnaro laboratories
Science.gov (United States)
Tecchio, Luigi B.
1999-04-01
In the frame work of the Italian participation to the project of a high intensity proton facility for the energy amplifier and nuclear waste transmutations, LNL is involving in the design and construction of prototypes of the injection system of the 1 GeV linac that consists of a RFQ (5 MeV, 30 mA) followed by a 100 MeV linac. This program has been already financially supported and the work is actually in progress. In this context, the LNL has been proposed a project for the construction of a second generation facility for the production of radioactive ion beams (RIBs) by using the ISOL method. The final goal consists in the production of neutron rich RIBs with masses ranging from 80 to 160 by using primary beams of protons, deuterons and light ions with energy of 100 MeV and 100 kW power. This project is proposed to be developed in about 10 years from now and intermediate milestones and experiments are foreseen and under consideration for the next INFN five year plan (1999-2003). In such period of time is proposed the construction of a proton/deuteron accelerator of 10 MeV energy and 10 mA current, consisting of a RFQ (5 MeV, 30 mA) and a linac (10 MeV, 10 mA), and of a neutron area dedicated to the RIBs production, to the BNCT applications and to the neutron physics. Some remarks on the production methods will be presented. The possibility of producing radioisotopes by means of the fission induced by neutrons will be investigated and the methods of production of neutrons will be discussed.
3. Physics with energetic radioactive ion beams
International Nuclear Information System (INIS)
Henning, W.F.
1996-01-01
Beams of short-lived, unstable nuclei have opened new dimensions in studies of nuclear structure and reactions. Such beams also provide key information on reactions that take place in our sun and other stars. Status and prospects of the physics with energetic radioactive beams are summarized
4. Laser-plasma booster for ion post acceleration
Directory of Open Access Journals (Sweden)
Satoh D.
2013-11-01
Full Text Available A remarkable ion energy increase is demonstrated for post acceleration by a laser-plasma booster. An intense short-pulse laser generates a strong current by high-energy electrons accelerated, when this intense short-pulse laser illuminates a plasma target. The strong electric current creates a strong magnetic field along the high-energy electron current in plasma. During the increase phase in the magnetic field, a longitudinal inductive electric field is induced for the forward ion acceleration by the Faraday law. Our 2.5-dimensional particle-in-cell simulations demonstrate a remarkable increase in ion energy by several tens of MeV.
5. Experimental studies of the laser-controlled collective ion accelerator
International Nuclear Information System (INIS)
Destler, W.W.; Rodgers, J.; Segalov, Z.
1989-01-01
Detailed experimental studies of a collective acceleration experiment in which a time-sequenced laser-generated ionization channel is used to control the propagation of an intense relativistic electron beamfront are presented. Ions trapped in the potential well at the beamfront are accelerated as the velocity of the beamfront is increased in a manner controlled by the time-dependent axial extent of the ionization channel. Beamfront propagation data for two different accelerating gradients are presented, together with results of ion acceleration studies for both gradients
6. Design of the radioactive ion beam facility at the LNS
International Nuclear Information System (INIS)
Migneco, E.; Alba, R.; Calabretta, L.; Ciavola, G.; Cuttone, G.; Di Giacomo, M.; Gammino, S.; Gmaj, P.; Moscatello, M.H.; Raia, G.
1992-01-01
At the Laboratorio Nazionale del Sud the existing 15 MV Tandem will be coupled to the Superconducting Cyclotron booster, which will provide light and heavy ion beams in the energy range 100-20 MeV/n. Using these beams, secondary radioactive beams can be produced by projectile fragmentation. A fragment separator will collect the secondary beam produced at energies near that of the projectile and deliver it into the experimental areas. The possibility of using an ECRIS source for the axial injection into the Cyclotron and producing radioactive ions on a thick source placed inside the Tandem preinjector is also discussed. (author) 7 refs.; 2 figs.; 1 tab
7. Method of burning ion-exchange resin contaminated with radioactivity
International Nuclear Information System (INIS)
Suzuki, Shigenori.
1986-01-01
Purpose: To process spent ion exchange resins to reduce their volume, without increasing the load on a off-gas system and in a stable state and at the same time not leaving any uncombusted portions. Method: The water slurries of the ion exchange resins contaminated with radioactive materials is dehydrated or dry combusted to reduce the water content. A binder is then added to solidify the ion exchange resin. The solidified ion exchange resins are then combusted in a furnace. This prevents the ion exchange resin from being dispersed by air and combustion gases. Furthermore, the solidified ion exchange resins in the form of small pellets burn from the surface inwards. Moreover the binder is carbonized by the combustion heat and promotes combustion to convert the ion exchange resins into a solid mass, making sure that no uncombusted portion is left. (Takahashi, M.)
8. Ion migration in ocean sediments: subseafloor radioactive waste disposal
International Nuclear Information System (INIS)
Nuttall, H.E.; Ray, A.K.; Davis, E.J.
1980-01-01
In this study of seabed disposal, analytical ion transport models were developed and used to elucidate ion migration through ocean sediments and to study the escape of ions from the ocean floor into the water column. An unsteady state isothermal diffusion model was developed for the region far from the canister to examine the effects of ion diffusion, adsorption, radioactive decay, sediment thickness and canister position. Analytical solutions were derived to represent the transient concentration profiles within the sediment, ion flux and the ion discharge rate to the water column for two types of initial conditions: instantaneous dissolution of the canister and constant canister leakage. Generalized graphs showing ion migration and behavior are presented
9. High Energy Ion Acceleration by Extreme Laser Radiation Pressure
Science.gov (United States)
2017-03-14
published in the internationally leading journal Physical Review Letters. We continued to progress this pionee 15. SUBJECT TERMS ion therapy, heavy ion ...Thomson parabola spectrometer: To separate and provide a measurement of the charge -to-mass ratio and energy spectrum of the different ion species...AFRL-AFOSR-UK-TR-2017-0015 High energy ion acceleration by extreme laser radiation pressure Paul McKenna UNIVERSITY OF STRATHCLYDE VIZ ROYAL COLLEGE
10. Diagnostics for studies of novel laser ion acceleration mechanisms
OpenAIRE
Senje, Lovisa; Yeung, Mark; Aurand, Bastian; Kuschel, Stephan; Rödel, Christian; Wagner, Florian; Li, Kun; Dromey, Brendan; Bagnoud, Vincent; Neumayer, Paul; Roth, Markus; Wahlström, Claes-Göran; Zepf, Matthew; Kuehl, Thomas; Jung, Daniel
2014-01-01
Diagnostic for investigating and distinguishing different laser ion acceleration mechanisms has been developed and successfully tested. An ion separation wide angle spectrometer can simultaneously investigate three important aspects of the laser plasma interaction: (1) acquire angularly resolved energy spectra for two ion species, (2) obtain ion energy spectra for multiple species, separated according to their charge to mass ratio, along selected axes, and (3) collect laser radiation reflecte...
11. A Study on the Establishment of Radiation Dose Estimation Procedure for Accumulated Radioactive Ions for RAON ISOL System
Directory of Open Access Journals (Sweden)
KIM Do Hyun
2017-01-01
Full Text Available For purposes of various experiments, RAON heavy ion accelerator facility has been designed in Korea. ISOL is one system of RAON accelerators to generate and separate rare isotopes. Radioactive ions generated from target-proton reactions are separated and accumulated at separation devices. The accumulated isotopes release the gamma radiations; therefore, the radiation safety must be clearly estimated. In this study, a process to evaluate radiations from the accumulated ions was proposed by modifying FISPACT code. The proposed process was validated by comparing a solution of single element decay problem. Using the process, a preliminary study for radiation doses were performed in a virtual separation devise.
12. 14 MV pelletron accelerator and superconducting ECR ion source
International Nuclear Information System (INIS)
Gupta, A.K.
2015-01-01
The BARC-TIFR 14UD Pelletron Accelerator at Mumbai has completed more than two and a half decade of successful operation. The accelerator is primarily used for basic research in the fields of nuclear, atomic and molecular, condensed matter physics and material science. The application areas include accelerator mass spectrometry, production of track-etch membranes, radioisotopes production, radiation damage studies and secondary neutron production for cross section measurement etc. Over the years, numerous developmental activities have been carried out in-house that have resulted in improving the overall performance and uptime of the accelerator and has also made possible to initiate variety of application oriented programmes. Since the SF 6 pressure vessels have been in operation for about 29 years, a comprehensive refurbishment and retrofitting work is carried out to comply with the safety recommendations. Recently, the beam trials were conducted with 18 GHz superconducting ECR (Electron Cyclotron Resonance) Ion Source system at Van-de-Graaff as per BARC Safety Council permission. Various ion beams with different charge states were extracted and mass analyzed and the beam quality was measured by recording their transverse emittance in situ. Experimental measurements pertaining to projectile X-rays Spectroscopy were carried out using variety of ion beams at variable energies. The superconducting Linac booster provides additional acceleration to the ions from Pelletron injector up to A ∼60 region with E∼5 MeV/A. In order to cover the entire mass range of the elements across the periodic table, an ECR based heavy ion accelerator was initiated under plan project. This heavy ion accelerator essentially comprises of a superconducting ECR ion source, room temperature RFQ (Radio Frequency Quadrupole) followed by superconducting Niobium resonators as accelerating elements. This talk will provide an overview of the developmental activities and the safety features
13. Installation of the Ion Accelerator for the Surface Analysis
Energy Technology Data Exchange (ETDEWEB)
Kwon, Hyeok-Jung; Kim, Han-Sung; Chung, Bo-Hyun; Ahn, Tae-Sung; Kim, Dae-Il; Kim, Cho-Rong; Cho, Yong-Sub [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2015-10-15
In this paper, an introduction to the accelerator, an installation status at KOMAC and the operation plan of the accelerator are discussed. A pelletron, which has been used over 25 years at KIGAM, is moved and installed at KOMAC in order to supply a qualified service to ion beam users. The system will be installed in September and component tests will be carried. The operation of the system starts in 2016 after it gets operation license from Nuclear Safety and Security Commission. Korea Multi-purpose Accelerator Complex (KOMAC) is operating several ion beam accelerators to provide various ion beams to users. Those are a 100 MeV proton linear accelerator, a 220 keV ion implanter for gaseous ion beams, a 150 keV metal ion implanter and a 20 keV high-current ion implanter. All of those are the machine for user service and it is important to qualify the results of the irradiation conditions for user service. For this reason, an electrostatic tandem accelerator, which has been operating over 25 years at Korea Institute of Geoscience and Mineral Resources (KIGAM), is moved to KOMAC in order to supply the qualified and quantified data on the irradiation species.
14. Studying the induced radioactivity of a varian clinac 2100C/D accelerator
International Nuclear Information System (INIS)
Lu Feng; Li Hailiang; Deng Daping; Shang Yunying; Jing Zhongjun
2008-01-01
Objective: To Study the influences of dose, time, distance and irradiation mode on induced radioactivity by measuring a Varian Clinac 2100C/D accelerator. Methods: The induced radioactivity was measured in different dose, time, distance and irradiation mode by using of 450P model dosemeter. The results was analysed. Results: The induced radioactivity is direct ratio with dose, inverse ratio with time and distance. In different irradiation mode, the induced radioactivity is different. Conclusion: The induced radioactivity level of accelerator is related with dose, time, distance and irradiation mode. (authors)
15. Pulsed vapor source for use in ion sources for heavy-ion accelerators
International Nuclear Information System (INIS)
Shiloh, J.; Chupp, W.; Faltens, A.; Keefe, D.; Kim, C.; Rosenblum, S.; Tiefenback, M.
1980-01-01
A pulsed cesium vapor source for use in ion sources for high-current heavy-ion accelerators is described. The source employs a vacuum spark in Cs and its properties are measured with a hot-filament Cs detector
16. Laser-driven ion acceleration: methods, challenges and prospects
Science.gov (United States)
2018-01-01
The recent development of laser technology has resulted in the construction of short-pulse lasers capable of generating fs light pulses with PW powers and intensities exceeding 1021 W/cm2, and has laid the basis for the multi-PW lasers, just being built in Europe, that will produce fs pulses of ultra-relativistic intensities ~ 1023 - 1024 W/cm2. The interaction of such an intense laser pulse with a dense target can result in the generation of collimated beams of ions of multi-MeV to GeV energies of sub-ps time durations and of extremely high beam intensities and ion fluencies, barely attainable with conventional RF-driven accelerators. Ion beams with such unique features have the potential for application in various fields of scientific research as well as in medical and technological developments. This paper provides a brief review of state-of-the art in laser-driven ion acceleration, with a focus on basic ion acceleration mechanisms and the production of ultra-intense ion beams. The challenges facing laser-driven ion acceleration studies, in particular those connected with potential applications of laser-accelerated ion beams, are also discussed.
17. Status report of pelletron accelerator and ECR based heavy ion accelerator programme
International Nuclear Information System (INIS)
Gupta, A.K.
2015-01-01
The BARC-TIFR Pelletron Accelerator is completing twenty seven years of round-the-clock operation, serving diverse users from institutions within and outside DAE. Over the years, various developmental activities and application oriented programs have been initiated at Pelletron Accelerator Facility, resulting into enhanced utilization of the accelerator. We have also been pursuing an ECR based heavy ion accelerator programme under XII th Plan, consisting of an 18 GHz superconducting ECR (Electron Cyclotron Resonance) ion source and a room temperature RFQ (Radio Frequency Quadrupole) followed by low and high beta superconducting niobium resonator cavities. This talk will provide the current status of Pelletron Accelerator and the progress made towards the ECR based heavy ion accelerator program at BARC. (author)
18. Collective ion acceleration via laser controlled ionization channel
International Nuclear Information System (INIS)
Destler, W.W.; O'Shea, P.G.; Rodgers, J.; Segalov, Z.
1987-01-01
Initial results from a successful laser-controlled collective ion acceleration experiment at the University of Maryland are presented. In the experiment, positive ions are trapped in the potential well at the head of an intense relativistic electron beam injected at current levels above the space charge limit. Seed ions for acceleration are provided by puff valve injection of a neutral gas cloud localized to within 3 cm of the injection point. Control over the acceleration of the well and the ions is then achieved by means of a laser-generated ionization channel produced by passing the light from a Q-switched ruby laser through a series of partially and fully reflecting mirrors in such a way as to provide time-sequenced laser ionization of a target located on the drift tube wall. Using this system, controlled acceleration of protons at a rate of approximately 40 MV/m has been demonstrated over a distance of about 50 cm
19. Generation and transport of laser accelerated ion beams
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Peter; Boine-Frankenheim, Oliver [Technische Univ. Darmstadt (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Kornilov, Vladimir; Spaedtke, Peter [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Collaboration: LIGHT-Collaboration
2013-07-01
Currently the LIGHT- Project (Laser Ion Generation, Handling and Transport) is performed at the GSI Helmholtzzentrum fuer Schwerionenforschung GmbH Darmstadt. Within this project, intense proton beams are generated by laser acceleration, using the TNSA mechanism. After the laser acceleration the protons are transported through the beam pipe by a pulsed power solenoid. To study the transport a VORPAL 3D simulation is compared with CST simulation. A criterion as a function of beam parameters was worked out, to rate the importance of space charge. Furthermore, an exemplary comparison of the solenoid with a magnetic quadrupole-triplet was carried out. In the further course of the LIGHT-Project, it is planned to generate ion beams with higher kinetic energies, using ultra-thin targets. The acceleration processes that can appear are: RPA (Radiation Pressure Acceleration) and BOA (Break-Out Afterburner). Therefore the transport of an ion distribution will be studied, as it emerges from a RPA acceleration.
20. Development of target ion source systems for radioactive beams at GANIL
Energy Technology Data Exchange (ETDEWEB)
Bajeat, O., E-mail: [email protected] [GANIL, BP 55027, 14076 CAEN Cedex 05 (France); Delahaye, P. [GANIL, BP 55027, 14076 CAEN Cedex 05 (France); Couratin, C. [GANIL, BP 55027, 14076 CAEN Cedex 05 (France); LPC Caen, 6 bd Maréchal Juin, 14050 CAEN Cedex (France); Dubois, M.; Franberg-Delahaye, H.; Henares, J.L.; Huguet, Y.; Jardin, P.; Lecesne, N.; Lecomte, P.; Leroy, R.; Maunoury, L.; Osmond, B.; Sjodin, M. [GANIL, BP 55027, 14076 CAEN Cedex 05 (France)
2013-12-15
Highlights: • For Spiral 1, a febiad ion source has been connected to a graphite target. • For Spiral 2, an oven made with a carbon resistor is under development. • We made some measurement of effusion in the Spiral 2 target. • A laser ion source is under construction. -- Abstract: The GANIL facility (Caen, France) is dedicated to the acceleration of heavy ion beams including radioactive beams produced by the Isotope Separation On-Line (ISOL) method at the SPIRAL1 facility. To extend the range of radioactive ion beams available at GANIL, using the ISOL method two projects are underway: SPIRAL1 upgrade and the construction of SPIRAL2. For SPIRAL1, a new target ion source system (TISS) using the VADIS FEBIAD ion source coupled to the SPIRAL1 carbon target will be tested on-line by the end of 2013 and installed in the cave of SPIRAL1 for operation in 2015. The SPIRAL2 project is under construction and is being design for using different production methods as fission, fusion or spallation reactions to cover a large area of the chart of nuclei. It will produce among others neutron rich beams obtained by the fission of uranium induced by fast neutrons. The production target made from uranium carbide and heated at 2000 °C will be associated with several types of ion sources. Developments currently in progress at GANIL for each of these projects are presented.
1. Heavy ion accelerator and associated development activities at IUAC
International Nuclear Information System (INIS)
Kanjilal, D.
2011-01-01
A vertical 15UD Pelletron electrostatic tandem accelerator having highest terminal voltage tested up to 16 MV has been in regular operation at Inter-University Accelerator Center (IUAC) for more than two decades. It has been providing consistently various ion beams in the energy range from a few tens of MeV to 270 MeV for scheduled experiments. A superconducting linear accelerator (LINAC) booster module having eight niobium quarter wave resonators has been designed, fabricated and installed successfully. It is fully operational for scheduled experiments. The LINAC module has been tested and used to accelerate energetic heavy ion beams from 15 UD Pelletron. A new type of high temperature superconducting electron cyclotron resonance ion source (HTS-ECRIS) has been designed, fabricated and installed successfully. It has been in regular operation as future source of highly charged ions having higher beam current for the alternate high current injector (HCI) system for the superconducting LINAC. A radio frequency quadrupole (RFQ) accelerator is being developed to accelerate highly charged particles (A/Q ∼ 6) from HTS-ECRIS to energy of 180 keV/u. The beam will then be accelerated further by drift tube linacs (DTL) to the required velocity for injection of the ion beams in to the existing superconducting LINAC booster. A low energy ion beam facility (LEIBF) having permanent magnet ECRIS on high voltage platform and a 1.7 MV Pelletron are being used for regular experiments. Details of various developmental activities related to the heavy ion accelerator and associated systems at Inter-University Accelerator Centre (IUAC) are presented. (author)
2. Heavy ion accelerator and associated development activities at IUAC
International Nuclear Information System (INIS)
Kanjilal, D.
2011-01-01
A vertical 15UD Pelletron electrostatic tandem accelerator having highest terminal voltage tested up to 16 MV has been in regular operation at Inter-University Accelerator Center (IUAC) for more than two decades. It has been providing consistently various ion beams in the energy range from a few tens of MeV to 270MeV for scheduled experiments. A superconducting linear accelerator (LINAC) booster module having eight niobium quarter wave resonators has been designed, fabricated and installed successfully. It is fully operational for scheduled experiments. The LINAC module has been tested and used to accelerate energetic heavy ion beams from 15 UD Pelletron. A new type of high temperature superconducting electron cyclotron resonance ion source (HTS-ECRlS) has been designed, fabricated and installed successfully. lt has been in regular operation as future source of highly charged ions having higher beam current for the alternate high current injector (HCI) system for the superconducting LINAC. A radio frequency quadrupole (RFQ) accelerator is being developed to accelerate highly charged particles (A/Q ∼ 6) from HTS-ECRIS to energy of 180 keV/u. The beam will then be accelerated further by drift tube linacs (DTL) to the required velocity for injection of the ion beams in to the existing superconducting LINAC booster. A low energy ion beam facility (LEIBF) having permanent magnet ECRIS on high voltage platform and a 1.7 MV Pelletron are being used for regular experiments. Details of various developmental activities related to the heavy ion accelerator and associated systems at Inter-University Accelerator Centre (IUAC) are presented. (author)
3. Engineering systems designs for a recirculating heavy ion induction accelerator
International Nuclear Information System (INIS)
Newton, M.A.; Barnard, J.J.; Reginato, L.L.; Yu, S.S.
1991-05-01
Recirculating heavy ion induction accelerators are being investigated as possible drivers for heavy ion fusion. Part of this investigation has included the generation of a conceptual design for a recirculator system. This paper will describe the overall engineering conceptual design of this recirculator, including discussions of the dipole magnet system, the superconducting quadrupole system and the beam acceleration system. Major engineering issues, evaluation of feasibility, and cost tradeoffs of the complete recirculator system will be presented and discussed. 5 refs., 4 figs
4. Biological effects of accelerated boron, carbon, and neon ions
International Nuclear Information System (INIS)
Grigoryev, Yu.G.; Ryzhov, N.I.; Popov, V.I.
1975-01-01
The biological effects of accelerated boron, carbon, and neon ions on various biological materials were determined. The accelerated ions included 10 B, 11 B, 12 C, 20 Ne, 22 Ne, and 40 Ar. Gamma radiation and x radiation were used as references in the experiments. Among the biological materials used were mammalian cells and tissues, yeasts, unicellular algae (chlorella), and hydrogen bacteria. The results of the investigation are given and the biophysical aspects of the problem are discussed
5. Resonant ion acceleration by collisionless magnetosonic shock waves
International Nuclear Information System (INIS)
Ohsawa, Y.
1985-01-01
Resonant ion acceleration ( the ν/sub rho/xΒ acceleration ) in laminar magnetosonic shock waves is studied by theory and simulation. Theoretical analysis based on a two-fluid model shows that, in laminar shocks, the electric field strength in the direction of the wave normal is about (m/sub i/m/sub e/) 1 2 times large for quasi-perpendicular shocks than that for the quasi-parallel shocks, which is a reflection of the fact that the width of quasi-perpendicular shocks is much smaller than that of the quasi-parallel shocks. Trapped ions can be accelerated up to the speed about ν/sub A/(m/sub i/m/sub e/) 1 2(M/sub A/-1) 3 2 in quasi-perpendicular shocks. Time evolution of self-consistent magnetosonic shock waves is studied by using a 2-12 dimensional fully relativistic, fully electromagnetic particle simulation with full ion and electron dynamics. Even a low-Mach-number shock wave can significantly accelerate trapped ions by the ν/sub rho/xΒ acceleration. The resonant ion acceleration occurs more strongly in quasi-perpendicular shocks, because the magnitude of this acceleration is proportional to the electric field strength
6. Physics and Technology for the Next Generation of Radioactive Ion Beam Facilities: EURISOL
CERN Document Server
Kadi, Y; Catherall, R; Giles, T; Stora, T; Wenander, F K
2012-01-01
Since the discovery of artificial radioactivity in 1935, nuclear scientists have developed tools to study nuclei far from stability. A major breakthrough came in the eighties when the first high energy radioactive beams were produced at Berkeley, leading to the discovery of neutron halos. The field of nuclear structure received a new impetus, and the major accelerator facilities worldwide rivalled in ingenuity to produce more intense, purer and higher resolution rare isotope beams, leading to our much improved knowledge and understanding of the general evolution of nuclear properties throughout the nuclear chart. However, today, further progress is hampered by the weak beam intensities of current installations which correlate with the difficulty to reach the confines of nuclear binding where new phenomena are predicted, and where the r-process path for nuclear synthesis is expected to be located. The advancement of Radioactive Ion Beam (RIB) science calls for the development of so-called next-generation facil...
7. The prototype of radioactive ion source
CERN Document Server
Aleksandrov, A V; Kot, N K; Andrighetto, A; Stroe, L
2001-01-01
The design and experimental results of the RIB source prototype are presented.A source will have the container of sup 2 sup 3 sup 5 U compounds heated up to 2200-2500 degree C. Vapors of uranium fission obtained when the ion source is irradiated by the high-energy neutron flux, are then ionized and extracted from the source. In the experiments with the prototype loaded by sup 1 sup 2 C the source working temperature 2700 degree C was reached, the carbon ion current 10 nA was obtained. The total operation time of more than 100 hours with no performance degradation was demonstrated.
8. Limitations of heavy ion synchrotron acceleration for inertial fusion
International Nuclear Information System (INIS)
Berley, D.; Danby, G.T.
1977-01-01
The potential benefits from heavy ion inertial fusion motivate the rapid development of a program to test the principle. To define the program, accelerator parameters which have not hitherto been commonly considered must be studied interactively with basic questions of space charge limitations and charge exchange. Beam lifetime and power output efficiency may ultimately lead to a linear accelerator as the choice for an ignition device. For proof of principle, however, at power levels way beyond present inertial fusion experience, synchrotrons may have applicability at lower cost. The power and energy which can be delivered by the accelerating system to the reaction chamber are limited by space charge defocussing and intra beam charge exchange scattering, both of which are beam density dependent. These put constraints on linac injector energy, synchrotron aperture, synchrotron magnetic rigidity, acceleration time, ion species and charge to mass ratio. The accelerator system considered is classical. A linear accelerator injects into a synchrotron which accelerates the ion beam to the full energy delivered to the target. The maximum energy deliverable by a synchrotron is treated in section I. The targetting parameters and the energy gained through synchrotron acceleration completely determine the synchrotron aperture. These are discussed in sections II and III. The ion range in material is treated in section IV. The problem of intrabeam scattering is considered in section V. Finally, in section VI is a discussion of examples to meet specified goals
9. Ion acceleration from relativistic laser nano-target
Energy Technology Data Exchange (ETDEWEB)
Jung, Daniel
2012-01-06
Laser-ion acceleration has been of particular interest over the last decade for fundamental as well as applied sciences. Remarkable progress has been made in realizing laser-driven accelerators that are cheap and very compact compared with conventional rf-accelerators. Proton and ion beams have been produced with particle energies of up to 50 MeV and several MeV/u, respectively, with outstanding properties in terms of transverse emittance and current. These beams typically exhibit an exponentially decaying energy distribution, but almost all advanced applications, such as oncology, proton imaging or fast ignition, require quasimonoenergetic beams with a low energy spread. The majority of the experiments investigated ion acceleration in the target normal sheath acceleration (TNSA) regime with comparably thick targets in the {mu}m range. In this thesis ion acceleration is investigated from nm-scaled targets, which are partially produced at the University of Munich with thickness as low as 3 nm. Experiments have been carried out at LANL's Trident high-power and high-contrast laser (80 J, 500 fs, {lambda}=1054 nm), where ion acceleration with these nano-targets occurs during the relativistic transparency of the target, in the so-called Breakout afterburner (BOA) regime. With a novel high resolution and high dispersion Thomson parabola and ion wide angle spectrometer, thickness dependencies of the ions angular distribution, particle number, average and maximum energy have been measured. Carbon C{sup 6+} energies reached 650 MeV and 1 GeV for unheated and heated targets, respectively, and proton energies peaked at 75 MeV and 120 MeV for diamond and CH{sub 2} targets. Experimental data is presented, where the conversion efficiency into carbon C{sup 6+} (protons) is investigated and found to have an up to 10fold (5fold) increase over the TNSA regime. With circularly polarized laser light, quasi-monoenergetic carbon ions have been generated from the same nm-scaled foil
10. Ion acceleration from relativistic laser nano-target interaction
International Nuclear Information System (INIS)
Jung, Daniel
2012-01-01
Laser-ion acceleration has been of particular interest over the last decade for fundamental as well as applied sciences. Remarkable progress has been made in realizing laser-driven accelerators that are cheap and very compact compared with conventional rf-accelerators. Proton and ion beams have been produced with particle energies of up to 50 MeV and several MeV/u, respectively, with outstanding properties in terms of transverse emittance and current. These beams typically exhibit an exponentially decaying energy distribution, but almost all advanced applications, such as oncology, proton imaging or fast ignition, require quasimonoenergetic beams with a low energy spread. The majority of the experiments investigated ion acceleration in the target normal sheath acceleration (TNSA) regime with comparably thick targets in the μm range. In this thesis ion acceleration is investigated from nm-scaled targets, which are partially produced at the University of Munich with thickness as low as 3 nm. Experiments have been carried out at LANL's Trident high-power and high-contrast laser (80 J, 500 fs, λ=1054 nm), where ion acceleration with these nano-targets occurs during the relativistic transparency of the target, in the so-called Breakout afterburner (BOA) regime. With a novel high resolution and high dispersion Thomson parabola and ion wide angle spectrometer, thickness dependencies of the ions angular distribution, particle number, average and maximum energy have been measured. Carbon C 6+ energies reached 650 MeV and 1 GeV for unheated and heated targets, respectively, and proton energies peaked at 75 MeV and 120 MeV for diamond and CH 2 targets. Experimental data is presented, where the conversion efficiency into carbon C 6+ (protons) is investigated and found to have an up to 10fold (5fold) increase over the TNSA regime. With circularly polarized laser light, quasi-monoenergetic carbon ions have been generated from the same nm-scaled foil targets at Trident with an
11. Induced radioactivity in air and water at medical accelerators
International Nuclear Information System (INIS)
Masumoto, K.; Takahashi, K.; Nakamura, H.; Toyoda, A.; Iijima, K.; Kosako, K.; Oishi, K.; Nobuhara, F.
2013-01-01
Activation of air and water has been evaluated at the 10 and 15 MeV linear electron accelerator facilities. At 15 MeV irradiation, the activity of 10-min-half-life 13 N was observed in the case of the air in the glove box. Air and water samples were also bombarded by 250 MeV protons and 400 MeV/u carbon, and the irradiation dose was 10 Gy at the isocenter. Upon the ion-chamber monitoring of the air sampled from the glove box, 15 O, 13 N, and 11 C activities were mainly observed. At the end of proton and carbon irradiation, the activity of the water was found to be about 10 kBq·cm -3 and several kBq·cm -3 , respectively. From the decay analysis of the induced activity in water, 15 O, 13 N, and 11 C were detected. (author)
12. Topical problems of accelerator and applied heavy ion physics
International Nuclear Information System (INIS)
Becker, R.; Deitinghoff, H.; Junior, P.H.; Schempp, A.
1990-12-01
These proceedings contain the articles presented at the named seminar. They deal with high-intensity linacs for heavy ions, the free-electron laser, applications of heavy-ion beams, MEQALAC, the ESR Schottky-diagnosis system, the analysis of GaAs by ion-beam methods, a light-ion synchrotron for cancer therapy, a device for the measurement of the momentum spread of ion beams, the European Hadron facility, the breakdown fields at electrons in high vacuum, a computer program for the calculation of electric quadrupoles, a focusing electrostatic mirror, storage and cooling of Ar beams, the visualization of heavy ion tracks in photographic films, the motion of ions in magnetic fields, the CERN heavy ion program, linear colliders, the beam injection from a linac into a storage ring, negative-ion sources, wake field acceleration, RFQ's, a dense electron target, the matching of a DC beam into the RFQ, electron emission and breakdown in vacuum, and 1-1.5 GeV 300 mA linear accelerator, the production of high-current positive-ion beams, high-current beam experiments at GSI, improvement of the Frankfurt EBIS, the physics of the violin, double layers, beam formation with coupled RFQ's, atomic nitrogen beam for material modification, compact superconducting synchrotron-radiation sources, industrial property rights, a RF ion source for thin film processes, beam-cavity interactions in the RFQ linac, atomic physics with crossed uranium beams, proton linacs, the interdigital H-type structure, injection of H - beams into a RFQ accelerator, the production of MOS devices by ion implantation, the application of RFQ's, the Frankfurt highly-charged ion facility, RF acceleration techniques for beam current drive in tokamaks, space-charge neutralized transport, and storage rings for synchrotron radiation and free electron lasers. (HSI)
13. Development of bipolar-pulse accelerator for intense pulsed ion beam acceleration
Energy Technology Data Exchange (ETDEWEB)
Masugata, Katsumi [Department of Electrical and Electronic System Engineering, Toyama University, 3190 Gofuku, Toyama 930-8555 (Japan)]. E-mail: [email protected]; Shimizu, Yuichro [Department of Electrical and Electronic System Engineering, Toyama University, 3190 Gofuku, Toyama 930-8555 (Japan); Fujioka, Yuhki [Department of Electrical and Electronic System Engineering, Toyama University, 3190 Gofuku, Toyama 930-8555 (Japan); Kitamura, Iwao [Department of Electrical and Electronic System Engineering, Toyama University, 3190 Gofuku, Toyama 930-8555 (Japan); Tanoue, Hisao [National Institute of Advanced Industry Science and Technology, 1-1-1, Umezono, Tsukuba-shi, Ibaraki 305-8568 (Japan); Arai, Kazuo [National Institute of Advanced Industry Science and Technology, 1-1-1, Umezono, Tsukuba-shi, Ibaraki 305-8568 (Japan)
2004-12-21
To improve the purity of intense pulsed ion beams, a new type of pulsed ion beam accelerator named 'bipolar pulse accelerator' was proposed. To confirm the principle of the accelerator a prototype of the experimental system was developed. The system utilizes By type magnetically insulated acceleration gap and operated with single polar negative pulse. A coaxial gas puff plasma gun was used as an ion source, which was placed inside the grounded anode. Source plasma (nitrogen) of current density {approx}25A/cm2, duration {approx}1.5{mu}s was injected into the acceleration gap by the plasma gun. The ions were successfully accelerated from the grounded anode to the drift tube by applying negative pulse of voltage 240kV, duration 100ns to the drift tube. Pulsed ion beam of current density {approx}40A/cm2, duration {approx}50ns was obtained at 41mm downstream from the anode surface. To evaluate the irradiation effect of the ion beam to solid material, an amorphous silicon thin film of thickness {approx}500nm was used as the target, which was deposited on the glass substrate. The film was found to be poly-crystallized after 4-shots of the pulsed nitrogen ion beam irradiation.
14. Ion Acceleration by Double Layers with Multi-Component Ion Species
Science.gov (United States)
Good, Timothy; Aguirre, Evan; Scime, Earl; West Virginia University Team
2017-10-01
Current-free double layers (CFDL) models have been proposed to explain observations of magnetic field-aligned ion acceleration in plasmas expanding into divergent magnetic field regions. More recently, experimental studies of the Bohm sheath criterion in multiple ion species plasma reveal an equilibration of Bohm speeds at the sheath-presheath boundary for a grounded plate in a multipole-confined filament discharge. We aim to test this ion velocity effect for CFDL acceleration. We report high resolution ion velocity distribution function (IVDF) measurements using laser induced fluorescence downstream of a CFDL in a helicon plasma. Combinations of argon-helium, argon-krypton, and argon-xenon gases are ionized and measurements of argon or xenon IVDFs are investigated to determine whether ion acceleration is enhanced (or diminished) by the presence of lighter (or heavier) ions in the mix. We find that the predominant effect is a reduction of ion acceleration consistent with increased drag arising from increased gas pressure under all conditions, including constant total gas pressure, equal plasma densities of different ions, and very different plasma densities of different ions. These results suggest that the physics responsible for acceleration of multiple ion species in simple sheaths is not responsible for the ion acceleration observed in these expanding plasmas. Department of Physics, Gettysburg College.
15. Advanced approaches to high intensity laser-driven ion acceleration
International Nuclear Information System (INIS)
Henig, Andreas
2010-01-01
Since the pioneering work that was carried out 10 years ago, the generation of highly energetic ion beams from laser-plasma interactions has been investigated in much detail in the regime of target normal sheath acceleration (TNSA). Creation of ion beams with small longitudinal and transverse emittance and energies extending up to tens of MeV fueled visions of compact, laser-driven ion sources for applications such as ion beam therapy of tumors or fast ignition inertial con finement fusion. However, new pathways are of crucial importance to push the current limits of laser-generated ion beams further towards parameters necessary for those applications. The presented PhD work was intended to develop and explore advanced approaches to high intensity laser-driven ion acceleration that reach beyond TNSA. In this spirit, ion acceleration from two novel target systems was investigated, namely mass-limited microspheres and nm-thin, free-standing diamond-like carbon (DLC) foils. Using such ultrathin foils, a new regime of ion acceleration was found where the laser transfers energy to all electrons located within the focal volume. While for TNSA the accelerating electric field is stationary and ion acceleration is spatially separated from laser absorption into electrons, now a localized longitudinal field enhancement is present that co-propagates with the ions as the accompanying laser pulse pushes the electrons forward. Unprecedented maximum ion energies were obtained, reaching beyond 0.5 GeV for carbon C 6+ and thus exceeding previous TNSA results by about one order of magnitude. When changing the laser polarization to circular, electron heating and expansion were shown to be efficiently suppressed, resulting for the first time in a phase-stable acceleration that is dominated by the laser radiation pressure which led to the observation of a peaked C 6+ spectrum. Compared to quasi-monoenergetic ion beam generation within the TNSA regime, a more than 40 times increase in
16. Advanced approaches to high intensity laser-driven ion acceleration
Energy Technology Data Exchange (ETDEWEB)
Henig, Andreas
2010-04-26
Since the pioneering work that was carried out 10 years ago, the generation of highly energetic ion beams from laser-plasma interactions has been investigated in much detail in the regime of target normal sheath acceleration (TNSA). Creation of ion beams with small longitudinal and transverse emittance and energies extending up to tens of MeV fueled visions of compact, laser-driven ion sources for applications such as ion beam therapy of tumors or fast ignition inertial con finement fusion. However, new pathways are of crucial importance to push the current limits of laser-generated ion beams further towards parameters necessary for those applications. The presented PhD work was intended to develop and explore advanced approaches to high intensity laser-driven ion acceleration that reach beyond TNSA. In this spirit, ion acceleration from two novel target systems was investigated, namely mass-limited microspheres and nm-thin, free-standing diamond-like carbon (DLC) foils. Using such ultrathin foils, a new regime of ion acceleration was found where the laser transfers energy to all electrons located within the focal volume. While for TNSA the accelerating electric field is stationary and ion acceleration is spatially separated from laser absorption into electrons, now a localized longitudinal field enhancement is present that co-propagates with the ions as the accompanying laser pulse pushes the electrons forward. Unprecedented maximum ion energies were obtained, reaching beyond 0.5 GeV for carbon C{sup 6+} and thus exceeding previous TNSA results by about one order of magnitude. When changing the laser polarization to circular, electron heating and expansion were shown to be efficiently suppressed, resulting for the first time in a phase-stable acceleration that is dominated by the laser radiation pressure which led to the observation of a peaked C{sup 6+} spectrum. Compared to quasi-monoenergetic ion beam generation within the TNSA regime, a more than 40 times
17. Acceleration of beam ions during major radius compression in TFTR
International Nuclear Information System (INIS)
Wong, K.L.; Bitter, M.; Hammett, G.W.
1985-09-01
Tangentially co-injected deuterium beam ions were accelerated from 82 keV up to 150 keV during a major radius compression experiment in TFTR. The ion energy spectra and the variation in fusion yield were in good agreement with Fokker-Planck code simulations. In addition, the plasma rotation velocity was observed to rise during compression
18. Collective ion acceleration by relativistic electron beams in plasmas
International Nuclear Information System (INIS)
Galvez, M.; Gisler, G.
1991-01-01
A two-dimensional fully electromagnetic particle-in-cell code is used to simulate the interaction of a relativistic electron beam injected into a finite-size background neutral plasma. The simulations show that the background electrons are pushed away from the beam path, forming a neutralizing ion channel. Soon after the beam head leaves the plasma, a virtual cathode forms which travels away with the beam. However, at later times a second, quasi-stationary, virtual cathode forms. Its position and strength depends critically on the parameters of the system which critically determines the efficiency of the ion acceleration process. The background ions trapped in the electrostatic well of the virtual cathode are accelerated and at later times, the ions as well as the virtual cathode drift away from the plasma region. The surfing of the ions in the electrostatic well produces an ion population with energies several times the initial electron beam energy. It is found that optimum ion acceleration occurs when the beam-to-plasma density ratio is near unity. When the plasma is dense, the beam is a weak perturbation and accelerates few ions, while when the plasma is tenuous, the beam is not effectively neutralized, and a virtual cathode occurs right at the injection plane. The simulations also show that, at the virtual cathode position, the electron beam is pinched producing a self-focusing phenomena
19. HEATHER - HElium Ion Accelerator for RadioTHERapy
Energy Technology Data Exchange (ETDEWEB)
Taylor, Jordan [Huddersfield U.; Edgecock, Thomas [Huddersfield U.; Green, Stuart [Birmingham U.; Johnstone, Carol [Fermilab
2017-05-01
A non-scaling fixed field alternating gradient (nsFFAG) accelerator is being designed for helium ion therapy. This facility will consist of 2 superconducting rings, treating with helium ions (He²⁺ ) and image with hydrogen ions (H + 2 ). Currently only carbon ions are used to treat cancer, yet there is an increasing interest in the use of lighter ions for therapy. Lighter ions have reduced dose tail beyond the tumour compared to carbon, caused by low Z secondary particles produced via inelastic nuclear reactions. An FFAG approach for helium therapy has never been previously considered. Having demonstrated isochronous acceleration from 0.5 MeV to 900 MeV, we now demonstrate the survival of a realistic beam across both stages.
20. Inertial confinement fusion systems using heavy ion accelerators as drivers
International Nuclear Information System (INIS)
Herrmannsfeldt, W.B.; Godlove, T.F.; Keefe, D.
1980-01-01
Heavy ion accelerators are the most recent entrants in the effort to identify a practical driver for inertial confinement fusion. They are of interest because of the expected efficient coupling of ion kinetic energy to the thermal energy needed to implode the pellet and because of the good electrical efficiency of high intensity particle accelerators. The beam intensities required, while formidable, lie within the range that can be studied by extensions of the theories and the technology of modern high energy accelerators. (orig.) [de
1. New heavy-ion-fusion accelerator research program
International Nuclear Information System (INIS)
Herrmannsfeldt, W.B.
1983-05-01
This paper will briefly summarize the concepts of Heavy Ion Fusion (HIF), especially those aspects that are important to its potential for generating electrical power. It will also note highlights of the various HIF programs throughout the world. Especially significant is that the US Department of Energy (DOE) plans a program, beginning in 1984, aimed at determining the feasibility of using heavy ion accelerators as drivers for Inertial Confinement Fusion (ICF). The new program concentrates on the aspects of accelerator design that are important to ICF, and for this reason is called HIF Accelerator Research
2. Holifield Radioactive Ion Beam Facility Development and Status
CERN Document Server
Tatum, Alan
2005-01-01
The Holifield Radioactive Ion Beam Facility (HRIBF) is a national user facility dedicated to nuclear structure, reactions, and nuclear astrophysics research with radioactive ion beams (RIBs) using the isotope separator on-line (ISOL) technique. An integrated strategic plan for physics, experimental systems, and RIB production facilities have been developed and implementation of the plan is under way. Specific research objectives are defined for studying the nature of nucleonic matter, the origin of elements, solar physics, and synthesis of heavy elements. Experimental systems upgrade plans include new detector arrays and beam lines, and expansion and upgrade of existing devices. A multifaceted facility expansion plan includes a $4.75M High Power Target Laboratory (HPTL), presently under construction, to provide a facility for testing new target materials, target geometries, ion sources, and beam preparation techniques. Additional planned upgrades include a second RIB production system (IRIS2), an external axi... 3. Removal of radioactive ions from nuclear waste solutions by electrodialysis Energy Technology Data Exchange (ETDEWEB) Sugimoto, S [Radia Industries Co. Ltd., Takasaki, Gunma (Japan) 1978-10-01 Removal of radioactive ions was studied from low and medium level radioactive waste solutions by electrodialysis using ion exchange membranes. The test solutions contained /sup 137/Cs/sup +/, /sup 106/Ru/sup 3 +/ or fission products (F.P.) as active ions and NaCl, Na/sub 2/SO/sub 4/ or Ca(NO/sub 3/)/sub 2/ as inactive coexisting salts. The decontamination factor of the active ions was in the order: /sup 137/Cs/sup +/ (greater than 99%) > /sup 90/Sr/sup 2 +/ > F.P. > /sup 106/Ru/sup 3 +/. The dialysis time required to attain the saturation was the shortest for monovalent cations K/sup +/, Cs/sup +/ and Na/sup +/, intermediate for divalent cation Sr/sup 2 +/, and the longest for trivalent cation Ru/sup 3 +/. The ratio of the decontamination factor of an active ion eta sub( a) to the desalination factor of an inactive ion eta sub( b) was nearly equal to unity for /sup 24/Na, /sup 42/K, /sup 137/Cs and /sup 90/Sr. On the other hand, the apparent selective permeability of an active ion (A/sup +/) against Na/sup +/ ion, T sub(Na/sup +/) sup( a) was higher than unity for all the active ions tested, and was in the order of /sup 137/Cs > /sup 90/Sr > /sup 42/K > /sup 24/Na, where T sub(Na/sup +/) sup( a) is defined by the ratio of ..gamma..sub( a) to ..gamma..sub(Na/sup +/) with ..gamma..sub( a) being the ratio of dilution of A in the diluate the ..gamma..sub(Na/sup +/) being that of Na/sup +/ in the same diluate. The decontamination factor of the active ions did not depend significantly on the species and concentration of the coexistent salts or on the concentration of the active ions. 4. DC and RF ion accelerators for MeV energies International Nuclear Information System (INIS) Urbanus, W.H. 1990-01-01 This thesis deals with the transport and acceleration of intense ion beams in single-ended Van de Graaff accelerators and the multiple beam rf accelerator MEQALAC (Multiple Electrostatic Quadrupole Array Linear Accelerator). Ch. 2 discusses several beam-envelope calculation techniques and describes the ion-optical components of a 1 MV, high-current, heavy-ion implantation facility and a 2 MV facility for analyzing purposes. The X-ray level of these accelerators is kept low, such that no shielding is needed, by keeping the energy of the secondary electrons sufficiently low, which is accomplished by a suppression system of small permanent magnets built in the acceleration tubes (ch. 3). Ch.'s 4,5 and 6 cover various aspects of stage II of the MEQALAC project. This stage deals with the parallel acceleration of four high-current N + beams from 40 keV to 1 MeV. Acceleration takes place in 32 rf gaps which are part of a modified interdigital H-resonator. In between the accelerating gaps, small electrostatic quadrupoles are mounted, which oppose the space charge forces of the intense ion beams. The lenses are arranged in a periodic focusing structure. A bucket-type plasma ion source is used, which produces both N + and N 2 + ions. In between the ion source and the MEQALAC section, a Low Energy Beam Transport (LEBT) section is mounted which provides for the drift space for a buncher. The latter device transforms the extracted dc beams into bunched beams which are accepted by the MEQALAC section. In ch. 4 the transport of ion beams that contain both N + and N 2 + ions, so-called mixed beams, through the LEBT section is discussed and equations for the current limit of a mixed beam are derived. Bunching of mixed N + , N 2 + beams is discussed in ch. 5. Multichannel acceleration of N + ions with the MEQALAC is discussed in ch. 6. (author). 122 refs.; 67 figs.; 1 tab 5. Accelerator mass spectrometry of 41Ca with a positive-ion source and the UNILAC accelerator International Nuclear Information System (INIS) Steinhof, A.; Henning, W.; Mueller, M.; Roeckl, E.; Schuell, D.; Korschinek, G.; Nolte, E.; Paul, M. 1987-06-01 We have made first tests investigating the performance characteristics of the UNILAC accelerator system at GSI, in order to explore the sensitivity achievable in accelerator mass spectrometry (AMS) of 41 Ca with high-current positive-ion sources. Positively charged Ca 3+ ions of up to about 100 micro-amperes electrical current were injected from a penning-sputter source and, after further stripping to Ca 9+ , accelerated to 14.3 MeV/nucleon. The combination of velocity-focussing accelerator and magnetic ion-beam transport system completely eliminated background from the other calcium isotopes. Full-stripping and detection of 41 Ca 20+ ions with a magnetic spectrograph provides separation from isobaric 41 K and, at present, a level of sensitivity of 41 Ca/Ca ≅ 2x10 -15 . Future improvements and implications for dating of Pleistoscene samples will be discussed. (orig.) 6. Laser-controlled collective ion accelerator International Nuclear Information System (INIS) O'Shea, P.G.; Destler, W.W.; Rodgers, J.; Segalov, Z. 1986-01-01 We report first results from a new collective accelerator experiment in which a laser-controlled channel of ionization is used to control the propagation of the potential well at the front of an intense relativistic electron beam injected at currents above the space-charge limit. The controlled acceleration of protons at the rate of 40 MeV/m over a distance of 45 cm is reported, in good agreement with experimental design values 7. Radioactive ion beam facilities in Europe International Nuclear Information System (INIS) Blumenfeld, Y. 2008-01-01 The past two decades have seen extraordinarily rapid development of radioactive beam physics throughout the world and in particular in Europe. The important scientific advances have stemmed from a large number of facilities. Previously existing stable beam machines have been adapted to produce rare isotope beams and dedicated facilities have come on-line. This talk gives an overview of the present European installations highlighting their complementary nature. The European roadmap calls for the construction of two next generation facilities: FAIR making use of projectile fragmentation and EURISOL based on the ISOL technique. The future FAIR facility will be described and the path towards EURISOL presented in the light of the construction of 'intermediate' generation facilities SPIRAL2, HIE ISOLDE and SPES and results from the ongoing EURISOL Design Study. 8. Naturally occurring and accelerator-produced radioactive materials: 1987 review International Nuclear Information System (INIS) Austin, J.H. 1988-03-01 From time to time, the issue as to whether the US Nuclear Regulatory Commission (NRC) should seek legislative authority to regulate naturally occurring and accelerator-produced radioactive materials (NARM) is raised. Because NARM exists in the environment, in homes, in workplaces, in medical institutions, and in consumer products, the issue of Federal controls over NARM is very old and very complex. This report presents a review of NARM sources and uses as well as incidents and problems associated with those materials. A review of previous congressional and Federal agency actions on radiation protection matters, in general, and on NARM, in particular, is provided to develop an understanding of existing Federal regulatory activity in ionizing radiation and in control of NARM. In addition, State controls over NARM are reviewed. Eight questions are examined in terms of whether the NRC should seek legislative authority to regulate NARM. The assessment of these questions serves as the basis for developing and evaluating five options. The evaluation of those options leads to two recommendations 9. An examination of medical linear accelerator ion-chamber performance International Nuclear Information System (INIS) Karolis, C.; Lee, C.; Rinks, A. 1996-01-01 Full text: The company ( Radiation Oncology Physics and Engineering Services Pty Ltd) provides medical physics services to four radiotherapy centres in NSW with a total of 6 high energy medical linear accelerators manufactured by three different companies. As part of the services, the stability of the accelerator ion chamber system is regularly examined for constancy and periodically for absolute calibration. Each accelerator ion chamber has exhibited undesirable behaviour from time to time, sometimes leading to its replacement. This presentation describes the performance of the ion chambers for some of the linacs over a period of 12-18 months and the steps taken by the manufacturer to address the problems encountered. As part of our commissioning procedure of new linacs, an absolute calibration of the accelerator output (photon and electron beams) is repeated several times over the period following examination of the physical properties of the radiation beams. These calibrations were undertaken in water using the groups calibrated ion chamber/electrometer system and were accompanied by constancy checks using an acrylic phantom and field instruments. Constancy checks were performed daily for a period of 8 weeks during the initial life of the accelerator and thereafter weekly. For one accelerator, the ion chamber was replaced 6 times in the first eighteen months of its life due to severe drifts in output, found to be due to pressure changes in one half of the chamber In another accelerator, erratic swings of 2% were observed for a period of nine months, particularly with the electron beams, before the manufacturer offered to change the chamber with another constructed from different materials. In yet another accelerator the ion chamber has shown consistent erratic behaviour, but this has not been addressed by the manufacturer. In another popular accelerator, the dosimetry was found to be very stable until some changes in the tuning were introduced resulting in small 10. Ion and electron Van de Graaff accelerators of Kyoto University International Nuclear Information System (INIS) Fukuzawa, F.; Imanishi, N.; Tomita, M.; Norisawa, K.; Yoshida, K.; Ohdaira, T. 1990-01-01 Two Van de Graaff accelerators are available at the Uji campus of Kyoto University. One is a 4MV machine, which is used for heavy ion acceleration, while the other is a 2MV machine for electron acceleration. These machines have been modified in various parts and currently used very actively in many fields of investigation. Important modifications of the 4MV machine are: use of a newly developed accelerating tube, addition of a charge-changer before the analyzing magnet, renewal of the charging belt, and development of a microbeam system for PIXE and RBS analysis. An attempt is now being made to accelerate micro-particles using the 2MV machine. The new accelerating tube has bucket type electrodes with large accelerating apertures. By charge-changing the accelerated 1+ ions to higher charge states, 2+, 3+, ..., at the entrance of the analyzing magnet, Ar ions with energies of up to 2.73, 6.21, .... MeV can be deflected to the duct. Scanning microbeam PIXE and RBS are powerful tools for analysis of spatial elemental distribution. Calculations suggest that a beam size of about 3 μm can be attained by using an object aperture of 10μm in diameter and controlling the beam divergence within 10μ rad in both directions. (N.K.) 11. Ion extraction capabilities of two-grid accelerator systems International Nuclear Information System (INIS) Rovang, D.C.; Wilbur, P.J. 1984-02-01 An experimental investigation into the ion extraction capabilities of two-grid accelerator systems common to electrostatic ion thrusters is described. This work resulted in a large body of experimental data which facilitates the selection of the accelerator system geometries and operating parameters necessary to maximize the extracted ion current. Results suggest that the impingement-limited perveance is not dramatically affected by reductions in screen hole diameter to 0.5 mm. Impingement-limited performance is shown to depend most strongly on grid separation distance, accelerator hole diameter ratio, the discharge-to-total accelerating voltage ratio, and the net-to-total accelerating voltage ratio. Results obtained at small grid separation ratios suggest a new grid operating condition where high beam current per hole levels are achieved at a specified net accelerating voltage. It is shown that this operating condition is realized at an optimum ratio of net-to-total accelerating voltage ratio which is typically quite high. The apparatus developed for this study is also shown to be well suited measuring the electron backstreaming and electrical breakdown characteristics of two-grid accelerator systems 12. The SPS as accelerator of Pb$^{82+}$ions CERN Document Server Faugier, A; Bailey, R; Blanchard, R R; Bohl, T; Brouzet, E; Burkhardt, H; Collier, Paul; Cornelis, Karel; de Rijk, G; Ferioli, F; Hilaire, A; Lamont, M; Linnecar, Trevor Paul R; Jonker, M; Niquille, C; Roy, G; Schmickler, Hermann 1996-01-01 In 1994 the CERN SPS was used for the first time to accelerate fully stripped ions of the Pb208 isotope from the equivalent proton momentum of 13 GeV/c to 400 GeV/c. In the CERN PS, which was used as injector, the lead was accelerated as Pb53+ ions and then fully stripped in the transfer line from PS to SPS. The radio frequency swing which is needed in order to keep the synchronism during acceleration is too big to have the SPS cavities deliver enough voltage for all frequencies. For that reason a new technique of fixed frequency acceleration was used. With this technique up to 70% of the injected beam could be captured and accelerated up to the extraction energy, the equivalent of 2.2 1010 charges. The beam was extracted over a 5 sec. long spill and was then delivered to different experiments at the same time. 13. About using of ion accelerators in accelerator driven systems Energy Technology Data Exchange (ETDEWEB) Chigrinov, S; Kevitskaya, A; Petlevskij, V; Rutkovskaya, C [Belarussian Academy of Sciences, Minsk-Sosny (Belarus). Radiation Physics and Chemistry Inst. 1997-12-31 The prospects of using deuteron and alpha particle beams in Accelerator Driven Molten Salt Breeder for simultaneous production of uranium 233 and of thermal power are discussed, disregarding the problems of reactor construction and design. It is shown that by replacing the proton beam by beams of deuterons or alpha particles the energy cost of one neutron can be reduced from 11.5 MeV down to 9.3-10 MeV. The average energy of neutrons increases from 17.7 MeV to 24.3 MeV or 28.2 MeV, respectively. Thus, the gain in the number of fissile nuclei and in thermal power production of at least 1.2 - 1.3 times can be expected in ACMB. (J.U.). 1 tab., 3 figs., 4 refs. 14. JAERI electrostatic accelerators for multiple ion beam application International Nuclear Information System (INIS) Ishii, Yasuyuki; Tajima, Satoshi; Takada, Isao 1993-01-01 An electrostatic accelerators facility of a 3MV tandem accelerator, a 3MV single-ended accelerator and a 400kV ion implanter was completed mainly for materials science and biotechnology research at JAERI, Takasaki. The accelerators can be operated simultaneously for multiple beam application in triple and dual beam modes. The single-ended machine was designed to satisfy an extremely high voltage stability of ±1x10 -5 to provide a submicron microbeam stably. The measured voltage stability and ripple were within the designed value. (author) 15. Collective acceleration of ions on the basis of resonance surface photoionization International Nuclear Information System (INIS) Antsiferov, V.V.; Smirnov, G.I.; Telegin, G.G. 1994-01-01 The effects of ion beam shaping and collective acceleration on the basis of resonance surface ionization are discussed. The principle diagram of the device for collective acceleration of positive ions is given. The method suggested for positive ion acceleration provides the efficiency increase, the design simplification, the size decrease and the increase in the frequency of the collective laser ion accelerator pulses 16. Health physics aspects of the Yale Heavy Ion Linear Accelerator dismantling project International Nuclear Information System (INIS) Price, K.W.; Holeman, G.R. 1976-01-01 A program for the disassembly of the Yale Heavy Ion Linear Accelerator was initiated January 1, 1975. The object of the disassembly was to render the accelerator complex free of radioactive contamination in order that the area may be used for other University purposes. In addition, any salvage of metal parts was a desirable goal of the dismantling procedure. A systematic removal of all contaminated material began immediately. Portable survey instruments, swipe surveys, and sodium iodide gamma ray spectra were used as indicators of contamination. Apparatus in the direct beam line seemed to pose the most significant hazard to personnel. As beam components were eliminated, radioactive contamination was significantly reduced. Certain accelerator parts had to be machined in order to salvage non-contaminated metal, and the health physics aspects of this procedure are described. Isotopes found in the surveys included 22 Na, 54 Mn, 60 Co, 65 Zn and 75 Se, which were predominately beam activation products of accelerator components. Final surveys indicated the area free of radioactive contamination 17. Heavy-ion fusion accelerator research, 1985 International Nuclear Information System (INIS) 1986-10-01 A plan for exploring the physics and technology of induction linac development is discussed which involves a series of increasingly sophisticated experiments. The first is the single-beam transport experiment, which has explored the physics of a single space-charge-dominated beam. Second is the multiple-beam experiment in which four independent beams will be transported and accelerated through a multigap accelerating structure. The single-beam transport experiment is described, and some results are given of stability studies and instrumentation studies. The design and fabrication of the multi-beam experiment are described, as well as results of a first round of experiments in which beam-current amplification was observed. Concurrent theoretical work, resulting in a variety of acce-leration schedules and sets of associated voltage waveforms required to implement the experiments, is also reported 18. Surface and Interface Studies with Radioactive Ions CERN Multimedia Weber, A 2002-01-01 Investigations on the atomic scale of magnetic surfaces and magnetic multilayers were performed by Perturbed Angular Correlation (PAC) spectroscopy. The unique combination of the Booster ISOLDE facility equipped with a UHV beamline and the UHV chamber ASPIC (Apparatus for Surface Physics and Interfaces at CERN) is ideally suited for such microscopic studies. Main advantages are the choice of problem-oriented radioactive probes and the purity of mass-separated beams. The following results were obtained:$\\,$i) Magnetic hyperfine fields (B$_{hf}$) of Se on Fe, Co, Ni surfaces were determined. The results prompted a theoretical study on the B$_{hf}$values of the 4sp-elements in adatom position on Ni and Fe, confirming our results and predicting unexpected behaviour for the other elements.$\\,$ii) Exemplarily we have determined B$_{hf}$values of$^{111}Cd at many different adsorption sites on Ni surfaces. We found a strong dependence on the coordination number of the probes. With decreasing coordination nu... 19. Radio-tracing 'without' radioactivity: accelerator mass spectrometry in biomedicine International Nuclear Information System (INIS) Vogel, J.S. 2005-01-01 Accelerator mass spectrometry (AMS) is a form of isotope-ratio mass spectrometry that quantifies concentrations of certain long-lived radioisotopes independently of their radioactive decay. AMS is primarily used in the geosciences for determining the age of a material that contains naturally occurring radioisotopes. AMS uses the same high specificity for enriched levels of these radioisotopes in tracing low chemical doses for long periods in biological systems, including humans. AMS provides the safety of low radiative exposure to experimental subjects and investigators, while obtaining attomole sensitivities that are not possible with stable isotope tracers because of their natural isotopic abundances. AMS isotope tracing was first applied to quantifying the genotoxicity of low level environmental chemicals in animals and later in humans. Physiologic concentrations of 14 C-labeled trace nutrients (folate, carotene, and tocopherol) are now measured directly in humans without concern about radiation. The radiative exposure is less than the commonly accepted risks of natural background radiation or the radiation fields found in high altitude air flights. AMS measures very small biological samples (such as 20 microliters of blood) that are easily obtained from human volunteers or model animals at frequent intervals for detailed analysis of kinetic profiles. This high data density enables the construction of compartmental models that elucidate nutrient behavior in tissues that cannot be directly sampled. The pharmaceutical industry is enthusiastic about AMS as a detector for 'micro-dosing' in which the human kinetics of an assuredly non-toxic dose of a candidate drug is tested early in a development project. Molecular tracing uses 3 H or 14 C as common isotopic labels, but AMS contributes to elemental tracing with certain radioisotopes having very long lives, such as 26 AL or 41 Ca. Calcium-41 is a particularly useful isotope in biomedical research because it is used 20. Selective deuterium ion acceleration using the Vulcan petawatt laser Science.gov (United States) Krygier, A. G.; Morrison, J. T.; Kar, S.; Ahmed, H.; Alejo, A.; Clarke, R.; Fuchs, J.; Green, A.; Jung, D.; Kleinschmidt, A.; Najmudin, Z.; Nakamura, H.; Norreys, P.; Notley, M.; Oliver, M.; Roth, M.; Vassura, L.; Zepf, M.; Borghesi, M.; Freeman, R. R. 2015-05-01 We report on the successful demonstration of selective acceleration of deuterium ions by target-normal sheath acceleration (TNSA) with a high-energy petawatt laser. TNSA typically produces a multi-species ion beam that originates from the intrinsic hydrocarbon and water vapor contaminants on the target surface. Using the method first developed by Morrison et al. [Phys. Plasmas 19, 030707 (2012)], an ion beam with >99% deuterium ions and peak energy 14 MeV/nucleon is produced with a 200 J, 700 fs, > 10 20 W / cm 2 laser pulse by cryogenically freezing heavy water (D2O) vapor onto the rear surface of the target prior to the shot. Within the range of our detectors (0°-8.5°), we find laser-to-deuterium-ion energy conversion efficiency of 4.3% above 0.7 MeV/nucleon while a conservative estimate of the total beam gives a conversion efficiency of 9.4%. 1. High current pulsed linear ion accelerators for inertial fusion applications International Nuclear Information System (INIS) Humphries, S. Jr.; Yonas, G.; Poukey, J.W. 1978-01-01 Pulsed ion beams have a number of advantages for use as inertial fusion drivers. Among these are classical interaction with targets and good efficiency of production. As has been pointed out by members of the accelerator community, multistage accelerators are attractive in this context because of lower current requirements, low power flow per energy conversion stage and low beam divergence at higher ion energies. On the other hand, current transport limits in conventional accelerators constrain them to the use of heavy ions at energies much higher than those needed to meet the divergence requirements, resulting in large, costly systems. We have studied methods of neutralizing ion beams with electrons within the accelerator volume to achieve higher currents. The aim is to arrive at an inexpensive accelerator that can advantageously use existing pulsed voltage technology while being conservative enough to achieve a high repetition rate. Typical output parameters for reactor applications would be an 0 + beam of 30 kA at 300 MeV. We will describe reactor scaling studies and the physics of neutralized linear accelerators using magnetic fields to control the electron dynamics. Recent results are discussed from PULSELAC, a five stage multikiloampere device being tested at Sandia Laboratories 2. The LILIA (laser induced light ions acceleration) experiment at LNF International Nuclear Information System (INIS) Agosteo, S.; Anania, M.P.; Caresana, M.; Cirrone, G.A.P.; De Martinis, C.; Delle Side, D.; Fazzi, A.; Gatti, G.; Giove, D.; Giulietti, D.; Gizzi, L.A.; Labate, L.; Londrillo, P.; Maggiore, M.; Nassisi, V.; Sinigardi, S.; Tramontana, A.; Schillaci, F.; Scuderi, V.; Turchetti, G. 2014-01-01 Laser-matter interaction at relativistic intensities opens up new research fields in the particle acceleration and related secondary sources, with immediate applications in medical diagnostics, biophysics, material science, inertial confinement fusion, up to laboratory astrophysics. In particular laser-driven ion acceleration is very promising for hadron therapy once the ion energy will attain a few hundred MeV. The limited value of the energy up to now obtained for the accelerated ions is the drawback of such innovative technique to the real applications. LILIA (laser induced light ions acceleration) is an experiment now running at LNF (Frascati) with the goal of producing a real proton beam able to be driven for significant distances (50–75 cm) away from the interaction point and which will act as a source for further accelerating structure. In this paper the description of the experimental setup, the preliminary results of solid target irradiation and start to end simulation for a post-accelerated beam up to 60 MeV are given 3. The LILIA (laser induced light ions acceleration) experiment at LNF Energy Technology Data Exchange (ETDEWEB) Agosteo, S. [Energy Department, Polytechnic of Milan and INFN, Milan (Italy); Anania, M.P. [INFN LNF Frascati, Frascati (Italy); Caresana, M. [Energy Department, Polytechnic of Milan and INFN, Milan (Italy); Cirrone, G.A.P. [INFN LNS Catania, Catania (Italy); De Martinis, C. [Physics Department, University of Milan and INFN, Milan (Italy); Delle Side, D. [LEAS, University of Salento and INFN, Lecce (Italy); Fazzi, A. [Energy Department, Polytechnic of Milan and INFN, Milan (Italy); Gatti, G. [INFN LNF Frascati, Frascati (Italy); Giove, D. [Physics Department, University of Milan and INFN, Milan (Italy); Giulietti, D. [Physics Department, University of Pisa and INFN, Pisa (Italy); Gizzi, L.A.; Labate, L. [INO-CNR and INFN, Pisa (Italy); Londrillo, P. [Physics Department, University of Bologna and INFN, Bologna (Italy); Maggiore, M. [INFN LNL, Legnaro (Italy); Nassisi, V., E-mail: [email protected] [LEAS, University of Salento and INFN, Lecce (Italy); Sinigardi, S. [Physics Department, University of Bologna and INFN, Bologna (Italy); Tramontana, A.; Schillaci, F. [INFN LNS Catania, Catania (Italy); Scuderi, V. [INFN LNS Catania, Catania (Italy); Institute of Physics of the ASCR, Prague (Czech Republic); Turchetti, G. [Physics Department, University of Bologna and INFN, Bologna (Italy); and others 2014-07-15 Laser-matter interaction at relativistic intensities opens up new research fields in the particle acceleration and related secondary sources, with immediate applications in medical diagnostics, biophysics, material science, inertial confinement fusion, up to laboratory astrophysics. In particular laser-driven ion acceleration is very promising for hadron therapy once the ion energy will attain a few hundred MeV. The limited value of the energy up to now obtained for the accelerated ions is the drawback of such innovative technique to the real applications. LILIA (laser induced light ions acceleration) is an experiment now running at LNF (Frascati) with the goal of producing a real proton beam able to be driven for significant distances (50–75 cm) away from the interaction point and which will act as a source for further accelerating structure. In this paper the description of the experimental setup, the preliminary results of solid target irradiation and start to end simulation for a post-accelerated beam up to 60 MeV are given. 4. Heavy-ion fusion accelerator research, 1988 International Nuclear Information System (INIS) 1989-05-01 This report discusses the following topics: MBE-4: The Induction-Linac Approach; Current Amplification and Acceleration Schedules; Emittance and Current Amplification; Scaling Up the Results; Progress on the Carbon-Arc Source; Injector Development; Progress Towards an ILSE Design; Beam Combination; and Focusing-System Alignment Tolerances 5. A Variable Energy CW Compact Accelerator for Ion Cancer Therapy Energy Technology Data Exchange (ETDEWEB) Johnstone, Carol J. [Fermilab; Taylor, J. [Huddersfield U.; Edgecock, R. [Huddersfield U.; Schulte, R. [Loma Linda U. 2016-03-10 Cancer is the second-largest cause of death in the U.S. and approximately two-thirds of all cancer patients will receive radiation therapy with the majority of the radiation treatments performed using x-rays produced by electron linacs. Charged particle beam radiation therapy, both protons and light ions, however, offers advantageous physical-dose distributions over conventional photon radiotherapy, and, for particles heavier than protons, a significant biological advantage. Despite recognition of potential advantages, there is almost no research activity in this field in the U.S. due to the lack of clinical accelerator facilities offering light ion therapy in the States. In January, 2013, a joint DOE/NCI workshop was convened to address the challenges of light ion therapy [1], inviting more than 60 experts from diverse fields related to radiation therapy. This paper reports on the conclusions of the workshop, then translates the clinical requirements into accelerat or and beam-delivery technical specifications. A comparison of available or feasible accelerator technologies is compared, including a new concept for a compact, CW, and variable energy light ion accelerator currently under development. This new light ion accelerator is based on advances in nonscaling Fixed-Field Alternating gradient (FFAG) accelerator design. The new design concepts combine isochronous orbits with long (up to 4m) straight sections in a compact racetrack format allowing inner circulating orbits to be energy selected for low-loss, CW extraction, effectively eliminating the high-loss energy degrader in conventional CW cyclotron designs. 6. Production of C, N, O, and Ne ions by pulsed ion source and acceleration of these ions in the cyclotron International Nuclear Information System (INIS) Nakajima, Hisao; Kohara, Shigeo; Kageyama, Tadashi; Kohno, Isao 1977-01-01 The heavy ion source, of electron bombarded hot cathode type, is usually operated by applying direct current for arc discharge. In order to accelerate Ne 6+ ion in the cyclotron, a pulsed operation of this source was attempted. Ne 6+ and O 6+ ions were accelerated successfully up to 160 MeV and more than 0.1 μA of these ion were extracted from the cyclotron. C 5+ , Ne 7+ and 22 Ne 6+ ions were also extracted with a modest intensity of beam. The intensity of C 4+ , N 4+ , N 5+ , and O 5+ ions was increased about ten times. (auth.) 7. Biological and medical research with accelerated heavy ions at the Bevalac, 1974--1977 International Nuclear Information System (INIS) Elam, S. 1977-04-01 The Bevalac, a versatile high-energy heavy-ion accelerator complex, has been in operation for less than two years. A major purpose for which the Bevalac was constructed was to explore the possibility of heavy-ion teams for therapy for certain forms of cancer. Significant progress has been made in this direction. The National Cancer Institute has recognized the advantages that these and other accelerated particles offer, and heavy ions have been included in a long-term plan for particle therapy that will assess by means of controlled therapeutic tests the value of various modalities. Since accelerated heavy ions became available, the possibility of other contributions, not planned, became apparent. We are developig a new diagnostic method known as heavy-ion radiography that has greatly increased sensitivity for soft-tissue detail and that may become a powerful tool for localizing early tumors and metastases. We have discovered that radioactive beams are formed from fragmentation of stable deflected beams. Use of these autoradioactive beams is just beginning; however, we know that these beams will be helpful in localizing the region in the body where therapy is being delivered. In addition, it has been demonstrated that instant implantation of the radioactive beam allows direct measurements of blood perfusion rates in inaccessible parts of the body, and such a technique may become a new tool for the study of fast hot atom reactions in biochemistry, tracer biology and nuclear medicine. The Bevalac will also be useful for the continuation of previously developed methods for the control of acromegaly, Cushing's disease and, on a research basis, advanced diabetes mellitus with vascular disease. The ability to make small bloodless lesions in the brain and elsewhere with heavy-ion beams has great potential for nervous-system studies and perhaps later for radioneurosurgery 8. Preliminary design of a 10 MV ion accelerator International Nuclear Information System (INIS) Fessenden, T.J.; Celata, C.M.; Faltens, A. 1986-06-01 At the low energy end of an induction linac HIF driver the beam current is limited by our ability to control space charge by a focusing system. As a consequence, HIF induction accelerator designs feature simultaneous acceleration of many beams in parallel within a single accelerator structure. As the speed of the beams increase, the focusing system changes from electrostatic to magnetic quadrupoles with a corresponding increase in the maximum allowable current. At that point the beams are merged thereby decreasing the cost of the subsequent accelerator structure. The LBL group is developing an experiment to study the physics of merging and of focusing ion beams. In the design, parallel beams of ions (C + , Al + , or Al ++ ) are accelerated to several MV and merged transversely. The merged beams are then further accelerated and the growth in transverse and longitudinal emittance is determined for comparison with theory. The apparatus will then be used to study the problems associated with focusing ion beams to a small spot. Details of the accelerator design and considerations of the physics of combining beams are presented 9. Study of radio-active ions in the atmosphere International Nuclear Information System (INIS) Renoux, A. 1965-01-01 A comparative study is made of active, deposits of radon and thoron in suspension in the atmosphere by means of α radiation counting, using ZELENY tubes, scattering equipment, filter papers or membranes. It has been possible to show the existence of small and large ions which are negative and positive, as well as of neutral radio-active nuclei; their properties are studied. A theoretical interpretation of the results is presented. The average content of radon (using the Ra A concentration) and of Th B in the air has been determined. The radioactive equilibrium between radon and its daughter products in atmospheric air are examined. The techniques developed for active radon and thoron deposits are applied to the study of artificial radio-activity, the analyses being carried out by means of γ spectrometry. (author) [fr 10. Moessbauer Effect applications using intense radioactive ion beams International Nuclear Information System (INIS) Taylor, R.D. 1990-01-01 The Moessbauer Effect is reviewed as a promising tool for a number of new solid state studies when used in combination with radioactive beam/implantation facilities. The usual Moessbauer Effect involves long-lived radioactive parents (days to years) that populate low-lying nuclear excited states that subsequently decay to the ground state. Resonant emission/absorption of recoil-free gamma rays from these states provide information on a number of properties of the host materials. Radioactive ion beams (RIB) produced on-line allow new Moessbauer nuclei to be studied where there is no suitable parent. The technique allows useful sources to be made having extremely low local concentrations. The ability to separate the beams in both Z and A should provide high specific activity ''conventional'' sources, a feature important in some applications such as Moessbauer studies in diamond anvil high pressure cells. Exotic chemistry is proposed using RIB and certain Krypton and Xenon Moessbauer isotopes 11. Development of a low-energy radioactive ion beam facility for the MARA separator Energy Technology Data Exchange (ETDEWEB) Papadakis, Philippos, E-mail: [email protected]; Moore, Iain; Pohjalainen, Ilkka; Sarén, Jan; Uusitalo, Juha [University of Jyväskylä, Department of Physics (Finland) 2016-12-15 A low-energy radioactive ion beam facility for the production and study of nuclei produced close to the proton drip line is under development at the Accelerator Laboratory of the University of Jyväskylä, Finland. The facility will take advantage of the mass selectivity of the recently commissioned MARA vacuum-mode mass separator. The ions selected by MARA will be stopped and thermalised in a small-volume gas cell prior to extraction and further mass separation. The gas cell design allows for resonance laser ionisation/spectroscopy both in-gas-cell and in-gas-jet. The facility will include experimental setups allowing ion counting, mass measurement and decay spectroscopy. 12. Modification of ion chromatograph for analyses of radioactive samples International Nuclear Information System (INIS) Curfman, L.L.; Johnson, S.J. 1979-01-01 In ion chromatographic analysis, the sample is injected through a sample loop onto an analytical column where separation occurs. The sample then passes through a suppressor column to remove or neutralize background ions. A flow-through conductivity cell is used as a detector. Depending upon column and eluent selection, ion chromatography can be used for anion or cation analyses. Ion chromatography has proven to be a versatile analytical tool for the analysis of anions in Hanford waste samples. These radioactive samples range from caustic high salt solutions to hydrochloric acid dissolutions of insoluble sludges. Instrument modifications which provide safe and convenient handling of these samples without lengthening analysis time or altering instrument performance are described 13. Studies of the mirrortron ion accelerator concept and its application to heavy-ion drivers International Nuclear Information System (INIS) Post, R.F.; Schwager, L.A.; Dougless, S.R.; Jones, B.R.; Lambert, M.A.; Larson, D.L. 1991-01-01 The Mirrortron accelerator is a plasma-based ion accelerator concept that, when implemented, should permit both higher acceleration gradients and higher peak-current capabilities than is possible with conventional induction-type accelerators. Control over the acceleration and focussing of an accelerated beam should approach that achieved in vacuum-field-based ion accelerators. In the Mirrortron a low density (10 10 to 10 11 cm -3 ) ''hot electron'' plasma is confined by a long solenoidal magnetic field capped by ''mirrors''. Acceleration of prebunched ions is accomplished by activating a series of fast-pulsed mirror coils spaced along the acceleration tube. The hot electrons, being repelled by mirror action, leave the plasma ions behind to create a localized region of high electrical gradient (up to of order 100 MV/m). At the Laboratory an experiment and analyses to elucidate the concept and its scaling laws as applied to heavy-ion drivers are underway and will be described. 4 refs., 5 figs 14. Transport of radioactive ions in soil by electrokinetics International Nuclear Information System (INIS) Buehler, M.F.; Surma, J.E.; Virden, J.W. 1994-10-01 An electrokinetic approach is being evaluated for in situ soil remediation at the Hanford Site in Richland, Washington. This approach uses an applied electric field to induce transport of both radioactive and hazardous waste ions in soil. The work discussed in this paper involves the development of a new method to monitor the movement of the radioactive ions within the soil during the electrokinetic process. A closed cell and a gamma counter were used to provide iii situ measurements of 137 Cs and 60 Co movement in Hanford soil. Preliminary results show that for an applied potential of 200 V over approximately 200 hr, 137 Cs and 60 60 were transported a distance of 4 to 5 in. The monitoring technique demonstrated the feasibility of using electrokinetics for soil separation applications 15. Investigating the contamination of accelerated radioactive beams with an ionization chamber at MINIBALL CERN Document Server Zidarova, Radostina 2017-01-01 My summer student project involved the operation and calibration of an ionization chamber, which was used at MINIBALL for investigating and determining the contamination in post-accelerated radioactive beams used for Coulomb excitation and transfer reaction experiments. 16. Inclusion of radioactive ion-exchange resins into inorganic binders International Nuclear Information System (INIS) Epimakhov, V.N.; Olejnik, M.S. 2005-01-01 The paper is devoted to inclusion of the radioactive ion-exchange resins into the portland, slag-portland and alumina cements. The degree of filling the solidified products achieves 7-10, 12 and 18.9-19.7% correspondingly under conservation of sufficient strength (not less 5 MPa). The coefficient of waste volume increasing during solidification does not exceed 1.5 under consideration of addition of 10 mass % of clay into aluminia cement [ru 17. Use of molecular ion beams from a tandem accelerator International Nuclear Information System (INIS) Faibis, A.; Goldring, G.; Hass, M.; Kaim, R.; Plesser, I.; Vager, Z. 1981-01-01 A large variety of positive molecular ion beams can be produced by gaseous charge exchange in the terminal of a tandem accelerator. After acceleration the molecules are usually dissociated by passage through a thin foil. Measurements of the break-up products provide a way to study both the structure of incident ions and the effects of electronic potentials on the internuclear interaction inside the foil. Beam intensities of a few picoamperes are quite adequate for these measurements, and the relatively high energy obtained by use of a tandem accelerator has the advantage of minimizing multiple scattering effects in the foil. The main difficulty in using the molecular beams lies in the large magnetic rigidity of singly-charged heavy molecular ions 18. New heavy-ion accelerator facility at Oak Ridge International Nuclear Information System (INIS) Stelson, P.H. 1974-01-01 Funds were obtained to establish a new national heavy-ion facility to be located at Oak Ridge. The principal component of this facility is a 25-MW tandem designed specifically for good heavy-ion acceleration, which will provide high quality beams of medium weight ions for nuclear research by itself. The tandem beams will also be injected into ORIC for additional energy gain, so that usable beams for nuclear physics research can be extended to about A = 160. A notable feature of the tandem is that it will be of the ''folded'' type, in which both the negative and positive accelerating tubes are contained in the same column. The accelerator system, the experimental lay-out, and the time schedule for the project are discussed 19. Low- to medium-β cavities for heavy ion acceleration Science.gov (United States) Facco, Alberto 2017-02-01 Acceleration of low- and medium-β heavy ions by means of superconducting (SC) linear accelerators (linacs) was made possible by the development, during four decades, of a particular class of cavities characterized by low operation frequency, several different shapes and different electromagnetic modes of operation. Their performance, initially rather poor in operating accelerators, have steadily increased along with the technological progress and nowadays the gap with the high-β, elliptical cavities is close to be filled. Initially confined to a very small number of applications, this family of cavities evolved in many directions becoming one of the most widespread in linacs. Nowadays it is present in the majority of superconducting radio-frequency ion linac projects worldwide. An overview of low- and medium-β SC cavities for heavy ions, focused on their recent evolution and achievements, will be given. 20. A study of light ion accelerators for cancer treatment International Nuclear Information System (INIS) Prelec, K. 1997-07-01 This review addresses several issues, such as possible advantages of light ion therapy compared to protons and conventional radiation, the complexity of such a system and its possible adaptation to a hospital environment, and the question of cost-effectiveness compared to other modalities for cancer treatment or to other life saving procedures. Characteristics and effects of different types of radiation on cells and organisms will be briefly described; this will include conventional radiation, protons and light ions. The status of proton and light ion cancer therapy will then be described, with more emphasis on the latter; on the basis of existing experience the criteria for the use of light ions will be listed and areas of possible medical applications suggested. Requirements and parameters of ion beams for cancer treatment will then be defined, including ion species, energy and intensity, as well as parameters of the beam when delivered to the target (scanning, time structure, energy spread). Possible accelerator designs for light ions will be considered, including linear accelerators, cyclotrons and synchrotrons and their basic features given; this will be followed by a review of existing and planned facilities for light ions. On the basis of these considerations a tentative design for a dedicated light ion facility will be suggested, a facility that would be hospital based, satisfying the clinical requirements, simple to operate and reliable, concluding with its cost-effectiveness in comparison with other modalities for treatment of cancer 1. 6 MV Folded Tandem Ion Accelerator facility at BARC International Nuclear Information System (INIS) Gupta, S.K. 2010-01-01 The 6 MV Folded Tandem Ion Accelerator (FOTIA) facility is operational round the clock and accelerated beams of both light and heavy ions are being used extensively by various divisions of BARC, Universities, lIT Bombay and other R and D labs across the country. The FOTIA is an upgraded version of the old 5.5 MV single stage Van-de-Graaff accelerator (1962-1992). Since its commissioning in the year 2000, the poor beam transmission through the 180 deg folding magnet was a matter of concern. A systematic study for beam transmission through the accelerator was carried out and progressive modifications in folding magnet chamber, foil stripper holder and improvement in average vacuum level through the accelerator have resulted in large improvement of beam transmission leading to up to 2.0 micro-amp analyzed proton beams on target. Now the utilization of the beams from the accelerator has increased many folds for basic and applied research in the fields of atomic and nuclear physics, material science and radiation biology etc. Few new beam lines after the indigenously developed 5-port switching magnet are added and the experimental setup for PIXE, PIGE, External PIXE, 4 neutron detector, Proton Induced Positron Annihilation Spectroscopy (PIPAS) setup and the general purpose scattering chamber etc have been commissioned in the beam hall. The same team has developed a Low Energy Accelerator Facility (LEAF) which delivers negative ions of light and heavy ions for application in implantation, irradiation damage studies in semiconductor devices and testing of new beam line components being developed for Low Energy High Intensity Proton Accelerator (LEHIPA) programme at BARC. The LEAF has been developed as stand alone facility and can deliver beam quickly with minimum intervention of the operator. Few more features are being planned to deliver uniform scanned beams on large targets. (author) 2. Long-pulse induction acceleration of heavy ions International Nuclear Information System (INIS) Faltens, A.; Firth, M.; Keefe, D.; Rosenblum, S.S. 1983-03-01 A long-pulse induction acceleration unit has been installed in the high-current Cs + beam line at LBL and has accelerated heavy ions. A maximum energy gain of 250 keV for 1.5 μs is possible. The unit comprises 12 independent modules which may be used to synthesize a variety of waveforms by varying the triggering times of the low-voltage trigger generators 3. Long-pulse induction acceleration of heavy ions International Nuclear Information System (INIS) Faltons, A.; Firth, M.; Keefe, D.; Rosenblum, S. 1983-01-01 A long-pulse induction acceleration unit has been installed in the high-current Cs + beam line at LBL and has accelerated heavy ions. A maximum energy gain of 250 keV for 1.5 μs is possible. The unit comprises 12 independent modules which may be used to synthesize a variety of waveforms by varying the triggering times of the low voltage trigger generators 4. Long-pulse induction acceleration of heavy-ions International Nuclear Information System (INIS) Faltens, A.; Firth, M.; Keefe, D.; Rosenblum, S.S. 1983-01-01 A long-pulse induction acceleration unit has been installed in the high-current Cs + beam line at LBL and has accelerated heavy ions. A maximum energy gain of 250 keV for 1.5 μs is possible. The unit comprises 12 independent modules which may be used to synthesize a variety of waveforms by varying the triggering times of the low voltage trigger generators 5. Transverse emittance studies of an induction accelerator of heavy ions International Nuclear Information System (INIS) Garvey, T.; Eylon, S.; Fessenden, T.J.; Hahn, K.; Henestroza, E. 1991-01-01 Current amplification of heavy ion beams is an integral feature of the induction linac approach to heavy ion fusion. As part of the Heavy Ion Fusion Accelerator Research program at LBL the authors have been studying the evolution of the transverse emittance of ion beams while they are undergoing current amplification, achieved by longitudinal bunch compression and acceleration. Experiments are conducted on MBE-4, a four beam Cs + induction linac. The space-charge dominated beams of MBE-4 are focused by electrostatic quadrupoles while they are accelerated from nominally 200 keV up to ∼ 1 MEV by 24 accelerating gaps. Initially the beams have currents of typically 4 mA to 10 mA per beam. Early experimental results showed a growth of the normalized emittance by a factor of 2 while the beam current was amplified by up to 9 times its initial value. The authors will discuss the results of recent experiments in which a mild bunch length compression rate, more typical of that required by a fusion driver, has shown that the normalized emittance can be maintained at its injection value (0.03 mm-mr) during acceleration 6. Heavy ion linear accelerator for radiation damage studies of materials Energy Technology Data Exchange (ETDEWEB) Kutsaev, Sergey V.; Mustapha, Brahim; Ostroumov, Peter N.; Nolen, Jerry; Barcikowski, Albert; Pellin, Michael; Yacout, Abdellatif 2017-03-01 A new eXtreme MATerial (XMAT) research facility is being proposed at Argonne National Laboratory to enable rapid in situ mesoscale bulk analysis of ion radiation damage in advanced materials and nuclear fuels. This facility combines a new heavy-ion accelerator with the existing high-energy X-ray analysis capability of the Argonne Advanced Photon Source. The heavy-ion accelerator and target complex will enable experimenters to emulate the environment of a nuclear reactor making possible the study of fission fragment damage in materials. Material scientists will be able to use the measured material parameters to validate computer simulation codes and extrapolate the response of the material in a nuclear reactor environment. Utilizing a new heavy-ion accelerator will provide the appropriate energies and intensities to study these effects with beam intensities which allow experiments to run over hours or days instead of years. The XMAT facility will use a CW heavy-ion accelerator capable of providing beams of any stable isotope with adjustable energy up to 1.2 MeV/u for U-238(50+) and 1.7 MeV for protons. This energy is crucial to the design since it well mimics fission fragments that provide the major portion of the damage in nuclear fuels. The energy also allows damage to be created far from the surface of the material allowing bulk radiation damage effects to be investigated. The XMAT ion linac includes an electron cyclotron resonance ion source, a normal-conducting radio-frequency quadrupole and four normal-conducting multi-gap quarter-wave resonators operating at 60.625 MHz. This paper presents the 3D multi-physics design and analysis of the accelerating structures and beam dynamics studies of the linac. 7. Heavy ion linear accelerator for radiation damage studies of materials. Science.gov (United States) Kutsaev, Sergey V; Mustapha, Brahim; Ostroumov, Peter N; Nolen, Jerry; Barcikowski, Albert; Pellin, Michael; Yacout, Abdellatif 2017-03-01 A new eXtreme MATerial (XMAT) research facility is being proposed at Argonne National Laboratory to enable rapid in situ mesoscale bulk analysis of ion radiation damage in advanced materials and nuclear fuels. This facility combines a new heavy-ion accelerator with the existing high-energy X-ray analysis capability of the Argonne Advanced Photon Source. The heavy-ion accelerator and target complex will enable experimenters to emulate the environment of a nuclear reactor making possible the study of fission fragment damage in materials. Material scientists will be able to use the measured material parameters to validate computer simulation codes and extrapolate the response of the material in a nuclear reactor environment. Utilizing a new heavy-ion accelerator will provide the appropriate energies and intensities to study these effects with beam intensities which allow experiments to run over hours or days instead of years. The XMAT facility will use a CW heavy-ion accelerator capable of providing beams of any stable isotope with adjustable energy up to 1.2 MeV/u for 238 U 50+ and 1.7 MeV for protons. This energy is crucial to the design since it well mimics fission fragments that provide the major portion of the damage in nuclear fuels. The energy also allows damage to be created far from the surface of the material allowing bulk radiation damage effects to be investigated. The XMAT ion linac includes an electron cyclotron resonance ion source, a normal-conducting radio-frequency quadrupole and four normal-conducting multi-gap quarter-wave resonators operating at 60.625 MHz. This paper presents the 3D multi-physics design and analysis of the accelerating structures and beam dynamics studies of the linac. 8. Ion Acceleration in Plasmas with Alfven Waves International Nuclear Information System (INIS) Kolesnychenko, O.Ya.; Lutsenko, V.V.; White, R.B. 2005-01-01 Effects of elliptically polarized Alfven waves on thermal ions are investigated. Both regular oscillations and stochastic motion of the particles are observed. It is found that during regular oscillations the energy of the thermal ions can reach magnitudes well exceeding the plasma temperature, the effect being largest in low-beta plasmas (beta is the ratio of the plasma pressure to the magnetic field pressure). Conditions of a low stochasticity threshold are obtained. It is shown that stochasticity can arise even for waves propagating along the magnetic field provided that the frequency spectrum is non-monochromatic. The analysis carried out is based on equations derived by using a Lagrangian formalism. A code solving these equations is developed. Steady-state perturbations and perturbations with the amplitude slowly varying in time are considered 9. Resolving key heavy-ion fusion target issues with relativistic heavy-ion research accelerators International Nuclear Information System (INIS) Arnold, R.C. 1988-01-01 Heavy-ion accelerators designed for relativistic nuclear research experiments can also be adapted for target research in heavy-ion driver inertial fusion. Needle-shaped plasmas can be created that are adequate for studying basic properties of matter at high energy density. Although the ion range is very long, the specific deposited power nevertheless increases with kinetic energy, as the focus spot can be made smaller and more ions can be accumulated in larger rings 10. Ion acceleration with ultra intense and ultra short laser pulses International Nuclear Information System (INIS) Floquet, V. 2012-01-01 Accelerating ions/protons can be done using short laser pulse (few femto-seconds) focused on few micrometers area on solid target (carbon, aluminum, plastic...). The electromagnetic field intensity reached on target (≥10 18 W.cm -2 ) allows us to turn the solid into a hot dense plasma. The dynamic motion of the electrons is responsible for the creation of intense static electric field at the plasma boundaries. These electric fields accelerate organic pollutants (including protons) located at the boundaries. This acceleration mechanism known as the Target Normal Sheath Acceleration (TNSA) has been the topic of the research presented in this thesis.The goal of this work has been to study the acceleration mechanism and to increase the maximal ion energy achievable. Indeed, societal application such as proton therapy requires proton energy up to few hundreds of MeV. To proceed, we have studied different target configurations allowing us to increase the laser plasma coupling and to transfer as much energy as possible to ions (target with microspheres deposit, foam target, grating). Different experiments have also dealt with generating a pre-plasma on the target surface thanks to a pre-pulse. On the application side, fluorescent material such as CdWO 4 has been studied under high flux rate of protons. These high flux rates have been, up to now, beyond the conventional accelerators capabilities. (author) [fr 11. Investigation of charge balance in ion accelerator TEMP–4M International Nuclear Information System (INIS) Khailov, I P; Pak, V G 2014-01-01 The paper presents the results of a study on the balance of charge in accelerator TEMP–4M operating in double-pulse mode with resistance load and ion diode. Crucially, it was found, that during the switching there is no losses of accumulated charge. It means, that all accumulated charge transferred to the load. However when the charge is transferred from the Marx generator to Blumlein line the half of accumulated charge is lost. Calibration of diagnostic equipment showed a good agreement between the calculated and experimental values of voltage and current. It means, that our diagnostic system is correct for registration parameters of the ion accelerator. A distinctive feature of the ion accelerators with self-magnetically insulated diode is that there is no need to use additional energy source for the creation of an external magnetic field. That's why the efficiency of ion diodes with an external magnetic field is not more than 10–15%. The efficiency of energy conversion in self-magnetically insulated diodes will be determined by not only the efficiency of the diode, but the energy losses in the units of the accelerator. The aim of the researches is the analysis of the balance of charge in units of the ion beams pulsed generator and definition of the most significant channels of energy loss 12. Acceleration ion focusing (IFR) and transport experiments with the recirculating linear accelerator (RLA) International Nuclear Information System (INIS) Mazarakis, M.G.; Smith, D.L.; Puokey, J.W.; Bennett, L.F.; Wagner, J.S.; Olson, W.R.; George, M.; Turman, B.N.; Prestwich, K.R.; Struve, K.W. 1992-01-01 The focusing and transport of intense relativistic electron beams in the Sandia Laboratories Recirculating Linear Accelerator (RLA) is accomplished with the aid of an ion focusing channel (IFR). We report here experiments evaluating the beam generation in the injector and its subsequent acceleration and transport through the first post-accelerating cavity. Two injectors and one type of post-accelerating cavity were studied. Beams of 6-20 kA current were injected and successfully transported and accelerated through the cavity. The transport efficiencies were 90% - 100%, and the beam Gaussian profile (4 MeV injector) and radius (5 mm) remained the same through acceleration. We describe the RLA, present the experimental results and compare them with numerical simulations. (Author) 3 refs., 7 figs 13. Ion Acceleration by Laser Plasma Interaction from Cryogenic Microjets Energy Technology Data Exchange (ETDEWEB) Propp, Adrienne [Harvard Univ., Cambridge, MA (United States) 2015-08-16 Processes that occur in extreme conditions, such as in the center of stars and large planets, can be simulated in the laboratory using facilities such as SLAC National Accelerator Laboratory and the Jupiter Laser Facility (JLF) at Lawrence Livermore National Laboratory (LLNL). These facilities allow scientists to investigate the properties of matter by observing their interactions with high-power lasers. Ion acceleration from laser plasma interaction is gaining greater attention today due to its widespread potential applications, including proton beam cancer therapy and fast ignition for energy production. Typically, ion acceleration is achieved by focusing a high power laser on thin foil targets through a mechanism called Target Normal Sheath Acceleration. However, this mechanism is not ideal for creating the high-energy proton beams needed for future applications. Based on research and recent experiments, we hypothesized that a pure liquid cryogenic jet would be an ideal target for exploring new regimes of ion acceleration. Furthermore, it would provide a continuous, pure target, unlike metal foils which are consumed in the interaction and easily contaminated. In an effort to test this hypothesis, we used the 527 nm split beam, frequency-doubled TITAN laser at JLF. Data from the cryogenic jets was limited due to the flow of current up the jet into the nozzle during the interaction, heating the jet and damaging the orifice. However, we achieved a pure proton beam with evidence of a monoenergetic feature. Furthermore, data from gold and carbon wires showed surprising and interesting results. Preliminary analysis of data from two ion emission diagnostics, Thomson parabola spectrometers (TPs) and radio chromic films (RCFs), suggests that shockwave acceleration occurred rather than target normal sheath acceleration, the standard mechanism of ion acceleration. Upon completion of the experiment at TITAN, I researched the possibility of transforming our liquid cryogenic 14. Ion Acceleration by Laser Plasma Interaction from Cryogenic Microjets International Nuclear Information System (INIS) Propp, Adrienne 2015-01-01 Processes that occur in extreme conditions, such as in the center of stars and large planets, can be simulated in the laboratory using facilities such as SLAC National Accelerator Laboratory and the Jupiter Laser Facility (JLF) at Lawrence Livermore National Laboratory (LLNL). These facilities allow scientists to investigate the properties of matter by observing their interactions with high-power lasers. Ion acceleration from laser plasma interaction is gaining greater attention today due to its widespread potential applications, including proton beam cancer therapy and fast ignition for energy production. Typically, ion acceleration is achieved by focusing a high power laser on thin foil targets through a mechanism called Target Normal Sheath Acceleration. However, this mechanism is not ideal for creating the high-energy proton beams needed for future applications. Based on research and recent experiments, we hypothesized that a pure liquid cryogenic jet would be an ideal target for exploring new regimes of ion acceleration. Furthermore, it would provide a continuous, pure target, unlike metal foils which are consumed in the interaction and easily contaminated. In an effort to test this hypothesis, we used the 527 nm split beam, frequency-doubled TITAN laser at JLF. Data from the cryogenic jets was limited due to the flow of current up the jet into the nozzle during the interaction, heating the jet and damaging the orifice. However, we achieved a pure proton beam with evidence of a monoenergetic feature. Furthermore, data from gold and carbon wires showed surprising and interesting results. Preliminary analysis of data from two ion emission diagnostics, Thomson parabola spectrometers (TPs) and radio chromic films (RCFs), suggests that shockwave acceleration occurred rather than target normal sheath acceleration, the standard mechanism of ion acceleration. Upon completion of the experiment at TITAN, I researched the possibility of transforming our liquid cryogenic 15. Phase-of-flight method for setting the accelerating fields in the ion linear accelerator International Nuclear Information System (INIS) Dvortsov, S.V.; Lomize, L.G. 1983-01-01 For setting amplitudes and phases of accelerating fields in multiresonator ion accelerators presently Δt-procedure is used. The determination and setting of two unknown parameters of RF-field (amplitude and phase) in n-resonator is made according to the two increments of particle time-of-flight, measured experimentally: according to the change of the particle time-of-flight Δt 1 in the n-resonator, during the field switching in the resonator, and according to the change of Δt 2 of the time-of-flight in (n+1) resonator without RF-field with the switching of accelerating field in the n-resonator. When approaching the accelerator exit the particle energy increases, relative energy increment decreases and the accuracy of setting decreases. To enchance the accuracy of accelerating fields setting in a linear ion accelerator a phase-of-flight method is developed, in which for the setting of accelerating fields the measured time-of-flight increment Δt only in one resonator is used (the one in which the change of amplitude and phase is performed). Results of simulation of point bunch motion in the IYaI AN USSR linear accelerator are presented 16. Heavy ion acceleration strategies in the AGS accelerator complex -- 1994 Status report International Nuclear Information System (INIS) Ahrens, L.A.; Benjamin, J.; Blaskiewicz, M. 1995-01-01 The strategies invoked to satisfy the injected beam specifications for the Brookhaven Relativistic Heavy Ion Collider (RHIC) continue to evolve, in the context of the yearly AGS fixed target heavy ion physics runs. The primary challenge is simply producing the required intensity. The acceleration flexibility available particularly in the Booster main magnet power supply and rf accelerating systems, together with variations in the charge state delivered from the Tandem van de Graaff, and accommodation by the AGS main magnet and rf systems allow the possibility for a wide range of options. The yearly physics run provides the opportunity for exploration of these options with the resulting significant evolution in the acceleration plan. This was particularly true in 1994 with strategies involving three different charge states and low and high acceleration rates employed in the Booster. The present status of this work will be presented 17. Observations of transverse ion acceleration in the topside auroral ionosphere International Nuclear Information System (INIS) Garbe, G.P.; Arnoldy, R.L.; Moore, T.E.; Kintner, P.M.; Vago, J.L. 1992-01-01 Data obtained from a sounding rocket flight which reached an apogee of 927 km and passed through several auroral arcs are reported. During portions of the flight when the rocket was not in an energetic auroral structure, the ion data are fit to a Maxwellian function which yields the plasma parameters. Throughout the middle portion of the flight when above 700 km altitude, ion distributions having a superthermal tail were measured. These ion distributions generally coexisted with a cold thermal core distribution and peaked at pitch angles slightly greater than 90 degree, which identifies them as conic distributions. These ions can be modeled using a bi-Maxwellian distribution function with a perpendicular (to B) temperature about 10 times greater than the parallel temperature of 0.15 eV. When the rocket was immersed in energetic auroral electron precipitation, two other ion distributions were observed. Transversely accelerated ions which represented bulk heating of the ambient population were observed. Transversely accelerated ions which represented bulk heating of the ambient population were observed continuously in these arcs. The characteristic perpendicular energy of the transversely bulk heated ions reached as high as 3 eV compared to typically less than 0.4 eV during nonauroral times. Cold ions flowing down the magnetic field were also continuously observed when the rocket was immersed in auroral electron precipitation and had downward speeds between 3 and 5 km/s. If one balances electric and collisional forces, these speeds translate to an electric field pointing into the atmosphere of magnitude 0.01 mV/m. A close correlation between auroral electron precipitation, measured electrostatic oxygen cyclotron waves, cold downflowing ions and transversely bulk heated ions will be shown 18. Proton and Ion Sources for High Intensity Accelerators CERN Multimedia Scrivens, R 2004-01-01 Future high intensity ion accelerators, including the Spallation Neutron Source (SNS), the European Spallation Source (ESS), the Superconducting Proton Linac (SPL) etc, will require high current and high duty factor sources for protons and negative hydrogen ions. In order to achieve these goals, a comparison of the Electron Cyclotron Resonance, radio-frequency and Penning ion sources, among others, will be made. For each of these source types, the present operational sources will be compared to the state-of-the-art research devices with special attention given to reliability and availability. Finally, the future research and development aims will be discussed. 19. Radioactive airborne species formed in the air in high energy accelerator tunnels International Nuclear Information System (INIS) Kondo, K. 2005-01-01 Many radioactive airborne species have been observed in the air of high energy accelerator tunnels during machine operation. Radiation protection against these induced airborne radioactivities is one of the key issues for radiation safety, especially at high-energy and high-intense proton accelerators such as the J-PARC (Japan Proton Accelerator Research Complex, Joint project of KEK and JAERI), which is now under construction at the TOKAI site of JAERI. Information on the chemical forms and particle sizes of airborne radioactivities is essential for the estimation of internal doses. For that purpose, the study on radioactive airborne species formed in the air of beam-line tunnels at high-energy accelerators have been extensively conducted by our group. For Be-7, Na-24, S-38, Cl-38,-39, C-11, and N-13, formed by various types of nuclear reactions including nuclear spallation reactions, their aerosol and gaseous fractions are determined by a filter technique. A parallel plate diffusion battery is used for the measurement of aerosol size distributions, and the formation of radioactive aerosols is explained by the attachment of radionuclides to ambient non-radioactive aerosols which are formed through radiation induced reactions. The chemical forms of gaseous species are also determined by using a selective collection method based on a filter technique. A review is given of the physico-chemical properties of these airborne radionuclides produced in the air of accelerator beam-line tunnels. 20. Reaching for highest ion beam intensities through laser ion acceleration and beam compression Energy Technology Data Exchange (ETDEWEB) Schumacher, Dennis; Brabetz, Christian; Blazevic, Abel; Bagnoud, Vincent; Weih, Simon [GSI Helmholtzzentrum fuer Schwerionenforschung (Germany); Jahn, Diana; Ding, Johannes; Roth, Markus [TU Darmstadt (Germany); Kroll, Florian; Schramm, Ulrich; Cowan, Tom [Helmholtzzentrum Dresden Rossendorf (Germany); Collaboration: LIGHT-Collaboration 2016-07-01 Laser ion acceleration provides access to ion sources with unique properties. To use these capabilities the LIGHT collaboration (Laser Ion Generation Handling and Transport) was founded. The aim of this collaboration is the beam transport and manipulation of laser accelerated ions with conventional accelerator structures. Therefor a dedicated beam line has been build up at GSI Helmholtzzentrum fuer Schwerionenforschung. With this beam line the manipulation of the transversal and also the longitudinal beam parameters has been achieved. It has been shown that laser generated ion beams can be transported over more than 6 meters and pulses shorter than 300 ps can be generated at this distance. This Talk will give an overview over the recent developments and plans of the LIGHT collaboration. 1. Design study of electron cyclotron resonance-ion plasma accelerator for heavy ion cancer therapy International Nuclear Information System (INIS) Inoue, T.; Sugimoto, S.; Sasai, K.; Hattori, T. 2014-01-01 Electron Cyclotron Resonance-Ion Plasma Accelerator (ECR-IPAC) device, which theoretically can accelerate multiple charged ions to several hundred MeV with short acceleration length, has been proposed. The acceleration mechanism is based on the combination of two physical principles, plasma electron ion adiabatic ejection (PLEIADE) and Gyromagnetic Autoresonance (GYRAC). In this study, we have designed the proof of principle machine ECR-IPAC device and simulated the electromagnetic field distribution generating in the resonance cavity. ECR-IPAC device consisted of three parts, ECR ion source section, GYRAC section, and PLEIADE section. ECR ion source section and PLEIADE section were designed using several multi-turn solenoid coils and sextupole magnets, and GYRAC section was designed using 10 turns coil. The structure of ECR-IPAC device was the cylindrical shape, and the total length was 1024 mm and the maximum diameter was 580 mm. The magnetic field distribution, which maintains the stable acceleration of plasma, was generated on the acceleration center axis throughout three sections. In addition, the electric field for efficient acceleration of electrons was generated in the resonance cavity by supplying microwave of 2.45 GHz 2. The intense neutron generator and future factory type ion accelerators Energy Technology Data Exchange (ETDEWEB) Lewis, W B 1968-07-01 A neutron factory is likely to sell its product in the form of isotopes. To ay neutron factories are nuclear reactors. Ion accelerators may also produce isotopes by direct interaction and, at high enough energies, mesons and hyperons. The challenge of the electrical production of neutrons goes far beyond the isotope market. It challenges the two popular concepts for long term large scale energy, the fast breeder reactor and controlled thermonuclear fusion. For this use about 4% of nuclear generated power would be applied in a feedback loop generating extra neutrons. Competition rests on operating and processing costs. The Intense Neutron Generator proposal now cancelled would have been full scale for such a use, but much further advance in accelerator engineering is required and anticipated. Perhaps most promising is the application of the ion drag principle in which rings of fast electrons are accelerated along their axis dragging ions with them by electrostatic attraction. Due to the much larger mass of the ions they can acquire much higher energy than the electrons and the process could be efficient. Such accelerators have not yet been made but experimental and theoretical studies are promising. (author) 3. The intense neutron generator and future factory type ion accelerators International Nuclear Information System (INIS) Lewis, W.B. 1968-01-01 A neutron factory is likely to sell its product in the form of isotopes. To ay neutron factories are nuclear reactors. Ion accelerators may also produce isotopes by direct interaction and, at high enough energies, mesons and hyperons. The challenge of the electrical production of neutrons goes far beyond the isotope market. It challenges the two popular concepts for long term large scale energy, the fast breeder reactor and controlled thermonuclear fusion. For this use about 4% of nuclear generated power would be applied in a feedback loop generating extra neutrons. Competition rests on operating and processing costs. The Intense Neutron Generator proposal now cancelled would have been full scale for such a use, but much further advance in accelerator engineering is required and anticipated. Perhaps most promising is the application of the ion drag principle in which rings of fast electrons are accelerated along their axis dragging ions with them by electrostatic attraction. Due to the much larger mass of the ions they can acquire much higher energy than the electrons and the process could be efficient. Such accelerators have not yet been made but experimental and theoretical studies are promising. (author) 4. Energy spectrum of neutrals formed in an ion accelerator International Nuclear Information System (INIS) Fink, J.H. 1982-01-01 This work presents an estimate of the energy distribution of the neutrals formed in the ion beam accelerator. However it does not determine the fraction of those neutrals which leave the neutral beam injector and go on into the reactor. To do that, more details of the beam line performance are needed 5. ELIMAIA: A Laser-Driven Ion Accelerator for Multidisciplinary Applications Directory of Open Access Journals (Sweden) Daniele Margarone 2018-04-01 Full Text Available The main direction proposed by the community of experts in the field of laser-driven ion acceleration is to improve particle beam features (maximum energy, charge, emittance, divergence, monochromaticity, shot-to-shot stability in order to demonstrate reliable and compact approaches to be used for multidisciplinary applications, thus, in principle, reducing the overall cost of a laser-based facility compared to a conventional accelerator one and, at the same time, demonstrating innovative and more effective sample irradiation geometries. The mission of the laser-driven ion target area at ELI-Beamlines (Extreme Light Infrastructure in Dolní Břežany, Czech Republic, called ELI Multidisciplinary Applications of laser-Ion Acceleration (ELIMAIA , is to provide stable, fully characterized and tuneable beams of particles accelerated by Petawatt-class lasers and to offer them to the user community for multidisciplinary applications. The ELIMAIA beamline has been designed and developed at the Institute of Physics of the Academy of Science of the Czech Republic (IoP-ASCR in Prague and at the National Laboratories of Southern Italy of the National Institute for Nuclear Physics (LNS-INFN in Catania (Italy. An international scientific network particularly interested in future applications of laser driven ions for hadrontherapy, ELI MEDical applications (ELIMED, has been established around the implementation of the ELIMAIA experimental system. The basic technology used for ELIMAIA research and development, along with envisioned parameters of such user beamline will be described and discussed. 6. Plasma arc pyrolysis of radioactive ion exchange resin International Nuclear Information System (INIS) Pickles, C.A.; Toguri, J.M. 1992-01-01 This paper reports on two ion exchange resins (IRN 77 and IRN 78) which were pyrolysed in a plasma-arc furnace. Both continuous and batch tests were performed. Volume reduction ratios of 10 to 1 and 10 to 3.5 were achieved for IRN 78 and IRN 77 respectively. The product of the resin pyrolysis was a char which contained the radioactive elements such as cobalt. The off-gases consisted of mainly hydrogen and carbon monoxide. There was a relatively small amount of dust in the off-gases. At the present time radioactive ion exchange resign is being kept in storage. The volume of this waste is increasing and it is important that the volume be reduce. The volume reduction ratio should be of the order of ten-to-one. Also, it is required that the radioactive elements can be collected or fixed in a form which could easily be disposed of. Plasma arc treatment offers considerable potential for the processing of the waste 7. Laser-ablation-based ion source characterization and manipulation for laser-driven ion acceleration Science.gov (United States) Sommer, P.; Metzkes-Ng, J.; Brack, F.-E.; Cowan, T. E.; Kraft, S. D.; Obst, L.; Rehwald, M.; Schlenvoigt, H.-P.; Schramm, U.; Zeil, K. 2018-05-01 For laser-driven ion acceleration from thin foils (∼10 μm–100 nm) in the target normal sheath acceleration regime, the hydro-carbon contaminant layer at the target surface generally serves as the ion source and hence determines the accelerated ion species, i.e. mainly protons, carbon and oxygen ions. The specific characteristics of the source layer—thickness and relevant lateral extent—as well as its manipulation have both been investigated since the first experiments on laser-driven ion acceleration using a variety of techniques from direct source imaging to knife-edge or mesh imaging. In this publication, we present an experimental study in which laser ablation in two fluence regimes (low: F ∼ 0.6 J cm‑2, high: F ∼ 4 J cm‑2) was applied to characterize and manipulate the hydro-carbon source layer. The high-fluence ablation in combination with a timed laser pulse for particle acceleration allowed for an estimation of the relevant source layer thickness for proton acceleration. Moreover, from these data and independently from the low-fluence regime, the lateral extent of the ion source layer became accessible. 8. Ion Beam Facilities at the National Centre for Accelerator based Research using a 3 MV Pelletron Accelerator Science.gov (United States) Trivedi, T.; Patel, Shiv P.; Chandra, P.; Bajpai, P. K. A 3.0 MV (Pelletron 9 SDH 4, NEC, USA) low energy ion accelerator has been recently installed as the National Centre for Accelerator based Research (NCAR) at the Department of Pure & Applied Physics, Guru Ghasidas Vishwavidyalaya, Bilaspur, India. The facility is aimed to carried out interdisciplinary researches using ion beams with high current TORVIS (for H, He ions) and SNICS (for heavy ions) ion sources. The facility includes two dedicated beam lines, one for ion beam analysis (IBA) and other for ion implantation/ irradiation corresponding to switching magnet at +20 and -10 degree, respectively. Ions with 60 kV energy are injected into the accelerator tank where after stripping positively charged ions are accelerated up to 29 MeV for Au. The installed ion beam analysis techniques include RBS, PIXE, ERDA and channelling. 9. Thin and thick targets for radioactive ion beam production at SPIRAL1 facility Science.gov (United States) Jardin, P.; Bajeat, O.; Delahaye, P.; Dubois, M.; Kuchi, V.; Maunoury, L. 2018-05-01 The upgrade of the Système de Production d'Ions Radioactifs Accélérés en Ligne (SPIRAL1) facility will deliver its new Radioactive Ion Beams (RIB) by summer 2017. The goal of the upgrade is an improvement of the performances of the installation in terms of isotopes species and ion charge states [1]. Ion beams are produced using the Isotope Separator On Line Method, consisting in an association of a primary beam of stable ions, a hot target and an ion source. The primary beam impinges on the material of the target. Radioactive isotopes are produced by nuclear reactions and propagate up to the source, where they are ionized and accelerated to create a RIB. One advantage of SPIRAL1 driver is the variety of its available primary beams, from carbon to uranium with energies up to 95 MeV/A. Within the SPIRAL1 upgrade, they will be combined with targets made of a large choice of materials, extending in this way the number of possible nuclear reactions (fusion-evaporation, transfer, fragmentation) for producing a wider range of isotopes, up to regions of the nuclide chart still scarcely explored. Depending on the reaction process, on the collision energy and on the primary beam power, thin and thick targets are used. As their functions can be different, their design must cope with specific constraints which will be described. After a presentation of the goals of present and future SPIRAL1 Target Ion Source System, the main target features, studies and designs under progress are presented. 10. Polarized secondary radioactive beams International Nuclear Information System (INIS) Zaika, N.I. 1992-01-01 Three methods of polarized radioactive nuclei beam production: a) a method nuclear interaction of the non-polarized or polarized charged projectiles with target nuclei; b) a method of polarization of stopped reaction radioactive products in a special polarized ion source with than following acceleration; c) a polarization of radioactive nuclei circulating in a storage ring are considered. Possible life times of the radioactive ions for these methods are determined. General schemes of the polarization method realizations and depolarization problems are discussed 11. The Holifield Radioactive Ion Beams Facility (HRIBF) - getting ready to do experiments International Nuclear Information System (INIS) Shapira, D.; Lewis, T.A. 1998-01-01 The conversion of the HHIRF facility to a Radioactive Ion Beam facility started in 1994. In this ISOL type facility the Cyclotron has been re-fitted as a driver providing high intensity proton beams which react with the target from which the radioactive products are extracted and then accelerated in the Tandem Electrostatic Accelerator to the desired energy for nuclear science studies. Facilities for nuclear physics experiments are at different stages of development: A Recoil Mass Spectrometer (RMS) with a complement of detectors at the focal plane and around the target is used primarily for nuclear structure studies. A large recoil separator combining velocity and momentum selection, with its complement of focal plane detectors, will be dedicated to measurements relevant to nuclear astrophysics. The Enge Split Pole spectrograph is being re-fitted for operation in a gas filled mode, making it a more versatile tool for nuclear reaction studies. With the new experimental equipment being commissioned and the prospects of running experiments with low intensity radioactive beams a significant effort to develop equipment for beam diagnostics is underway. Some of the efforts and results in developing beam diagnostic tools will be described 12. Staging of RF-accelerating Units in a MEMS-based Ion Accelerator Science.gov (United States) Persaud, A.; Seidl, P. A.; Ji, Q.; Feinberg, E.; Waldron, W. L.; Schenkel, T.; Ardanuc, S.; Vinayakumar, K. B.; Lal, A. Multiple Electrostatic Quadrupole Array Linear Accelerators (MEQALACs) provide an opportunity to realize compact radio- frequency (RF) accelerator structures that can deliver very high beam currents. MEQALACs have been previously realized with acceleration gap distances and beam aperture sizes of the order of centimeters. Through advances in Micro-Electro-Mechanical Systems (MEMS) fabrication, MEQALACs can now be scaled down to the sub-millimeter regime and batch processed on wafer substrates. In this paper we show first results from using three RF stages in a compact MEMS-based ion accelerator. The results presented show proof-of-concept with accelerator structures formed from printed circuit boards using a 3 × 3 beamlet arrangement and noble gas ions at 10 keV. We present a simple model to describe the measured results. We also discuss some of the scaling behaviour of a compact MEQALAC. The MEMS-based approach enables a low-cost, highly versatile accelerator covering a wide range of currents (10 μA to 100 mA) and beam energies (100 keV to several MeV). Applications include ion-beam analysis, mass spectrometry, materials processing, and at very high beam powers, plasma heating. 13. Accelerators for heavy ion inertial fusion: Progress and plans International Nuclear Information System (INIS) Bangerter, R.O.; Friedman, A.; Herrmannsfeldt, W.B. 1994-08-01 The Heavy Ion Inertial Fusion Program is the principal part of the Inertial Fusion Energy Program in the Office of Fusion Energy of the U.S. Department of Energy. The emphasis of the Heavy Ion Program is the development of accelerators for fusion power production. Target physics research and some elements of fusion chamber development are supported in the much larger Inertial Confinement Fusion Program, a dual purpose (defense and energy) program in the Defense Programs part of the Department of Energy. The accelerator research program will establish feasibility through a sequence of scaled experiments that will demonstrate key physics and engineering issues at low cost compared to other fusion programs. This paper discusses progress in the accelerator program and outlines how the planned research will address the key economic issues of inertial fusion energy 14. Heavy-ion fusion accelerator research in the USA International Nuclear Information System (INIS) Bangerter, R.O.; Godlove, T.D.; Herrmannsfeldt, W.B.; Keefe, D. 1985-01-01 In October 1983, a Heavy-Ion Fusion Accelerator Research programme (HIFAR) was established under the Office of Energy Research of the United States Department of Energy. The programme goal over the next several years is to establish a data base in accelerator physics and technology that can allow the potential of heavy ion fusion to be accurately assessed. Three new developments have taken place in the HIFAR programme. First, a decision has been made to concentrate the experimental programme on the development of multiple-beam induction linacs. Second, new beam transport experiments over a large number of quadrupole elements show that stable beam propagation occurs for significantly higher beam currents than had been believed possible a few years ago. Third, design calculations now show that a test accelerator of modest size and cost can come within a factor of three of testing almost all of the physics and technical issues appropriate to a power plant driver. (author) 15. Beam dynamics studies of the Heavy Ion Fusion Accelerator injector International Nuclear Information System (INIS) Henestroza, E.; Yu, S.S.; Eylon, S. 1995-04-01 A driver-scale injector for the Heavy Ion Fusion Accelerator project has been built at LBL. This machine has exceeded the design goals of high voltage (> 2 MV), high current (> 0.8 A of K + ) and low normalized emittance (< 1 π mm-mr). The injector consists of a 750 keV diode pre-injector followed by an electrostatic quadrupole accelerator (ESQ) which provides strong (alternating gradient) focusing for the space-charge dominated beam and simultaneously accelerates the ions to 2 MeV. The fully 3-D PIC code WARP together with EGUN and POISSON were used to design the machine and analyze measurements of voltage, current and phase space distributions. A comparison between beam dynamics characteristics as measured for the injector and corresponding computer calculations will be presented 16. Status report on electron cyclotron resonance ion sources at the Heavy Ion Medical Accelerator in Chiba CERN Document Server Kitagawa, A; Sekiguchi, M; Yamada, S; Jincho, K; Okada, T; Yamamoto, M; Hattori, T G; Biri, S; Baskaran, R; Sakata, T; Sawada, K; Uno, K 2000-01-01 The Heavy Ion Medical Accelerator in Chiba at the National Institute of Radiological Sciences (NIRS) is not only dedicated to cancer therapy, it is also utilized with various ion species for basic experiments of biomedical science, physics, chemistry, etc. Two electron cyclotron resonance (ECR) ion sources are installed for production of gaseous ions. One of them, the NIRS-ECR, is a 10 GHz ECR ion source, and is mainly operated to produce C/sup 4+/ ions for daily clinical treatment. This source realizes good reproducibility and reliability and it is easily operated. The other source, the NIRS-HEC, is an 18 GHz ECR ion source that is expected to produce heavier ion species. The output ion currents of the NIRS-ECR and the NIRS-HEC are 430e mu A for C/sup 4+/ and 1.1e mA for Ar/sup 8+/, respectively. (14 refs). 17. Micro structure processing on plastics by accelerated hydrogen molecular ions Science.gov (United States) Hayashi, H.; Hayakawa, S.; Nishikawa, H. 2017-08-01 A proton has 1836 times the mass of an electron and is the lightest nucleus to be used for accelerator in material modification. We can setup accelerator with the lowest acceleration voltage. It is preferable characteristics of Proton Beam Writer (PBW) for industrial applications. On the contrary ;proton; has the lowest charge among all nuclei and the potential impact to material is lowest. The object of this research is to improve productivity of the PBW for industry application focusing on hydrogen molecular ions. These ions are generated in the same ion source by ionizing hydrogen molecule. There is no specific ion source requested and it is suitable for industrial use. We demonstrated three dimensional (3D) multilevel micro structures on polyester base FPC (Flexible Printed Circuits) using proton, H2+ and H3+. The reactivity of hydrogen molecular ions is much higher than that of proton and coincident with the level of expectation. We can apply this result to make micro devices of 3D multilevel structures on FPC. 18. Applications of inorganic ion-exchange materials in managing radioactivity wastewater International Nuclear Information System (INIS) He Jiaheng; Li Xingliang; Li Shoujian 2007-01-01 This article introduces the application of abio-ion exchange materials in managing radioactivity wastewater, which would be useful for latter research of new inorganic materials that used in managing radioactivity wastewater. (authors) 19. Radioactive ion beam development for the SPIRAL 2 project International Nuclear Information System (INIS) Pichard, A. 2010-01-01 This thesis focuses on the study of radioactive ion beam production by the ISOL method for the SPIRAL 2 project. The production of light ion beams is studied and the potential in-target yields of two beams are appraised. The neutron-rich 15 C yield in an oxide target is estimated with simulations (MCNPx, EAF-07) and experimental data bases; the neutron-deficient 14 O yield is estimated thanks to a new measurement of the 12 C( 3 He, n) 14 O reaction excitation function. Based on thermal simulations, a first design of the production target is presented. This thermal study gives the necessary answers for the detailed design of the system able to reach a production yield 140 times higher than with SPIRAL 1. The production of radioactive ion beams coming from fissions in the UCx target is also studied and more particularly effusion and ionisation processes. A global study and an off-line tests campaign allow essential knowledge to the design of the surface ionisation source for SPIRAL 2 to be acquired. A first prototype of this ion source dedicated to alkali and alkaline-earth element production has been built and a thermal calibration performed. Ionisation efficiency and time response of the target-ion source system have been measured at different target temperatures and for different noble gases. These measurements allow evaluation of the impact of effusion and ionisation processes on the production efficiency of different alkali and noble gases isotopes as a function of their half-life. (author) [fr 20. Selection of targets and ion sources for RIB generation at the Holifield Radioactive Ion Beam Facility International Nuclear Information System (INIS) Alton, G.D. 1995-01-01 In this report, the authors describe the performance characteristics for a selected number of target ion sources that will be employed for initial use at the Holifield Radioactive Ion Beam Facility (HRIBF) as well as prototype ion sources that show promise for future use for RIB applications. A brief review of present efforts to select target materials and to design composite target matrix/heat-sink systems that simultaneously incorporate the short diffusion lengths, high permeabilities, and controllable temperatures required to effect fast and efficient diffusion release of the short-lived species is also given 1. Development of a radioactive ion beam test stand at LBNL International Nuclear Information System (INIS) Burke, J.; Freedman, S.J.; Fujikawa, B.; Gough, R.A.; Lyneis, C.M.; Vetter, P.; Wutte, D.; Xie, Z.Q. 1998-01-01 For the on-line production of a 14 O + ion beam, an integrated target--transfer line ion source system is now under development at LBNL. 14 O is produced in the form of CO in a high temperature carbon target using a 20 MeV 3 He beam from the LBNL 88'' Cyclotron via the reaction 12 C( 3 He,n) 14 O. The neutral radioactive CO molecules diffuse through an 8 m room temperature stainless steel line from the target chamber into a cusp ion source. The molecules are dissociated, ionized and extracted at energies of 20 to 30 keV and mass separated with a double focusing bending magnet. The different components of the setup are described. The release and transport efficiency for the CO molecules from the target through the transfer line was measured for various target temperatures. The ion beam transport efficiencies and the off-line ion source efficiencies for Ar, O 2 and CO are presented. Ionization efficiencies of 28% for Ar + , 1% for CO, 0.7% for O + , 0.33 for C + have been measured 2. Preliminary research results for the generation and diagnostics of high power ion beams on FLASH II accelerator International Nuclear Information System (INIS) Yang Hailiang; Qiu Aici; Sun Jianfeng; He Xiaoping; Tang Junping; Wang Haiyang; Li Jingya; Ren Shuqing; Ouyang Xiaoping; Zhang Guoguang; Li Hongyu 2004-01-01 The preliminary experimental results of the generation and diagnostics of high-power ion beams on FLASH II accelerator are reported. The high-power ion beams presently are being produced in a pinched diode. The method for enhancing the ratio of ion to electron current is to increase the electron residing time by pinching the electron flow. Furthermore, electron beam pinching can be combined with electron reflexing to achieve ion beams with even higher efficiency and intensity. The anode plasma is generated by anode foil bombarded with electron and anode foil surface flashover. In recent experiments on FLASH II accelerator, ion beams have been produced with a current of 160 kA and an energy of 500 keV corresponding to an ion beam peak power of about 80 GW. The ion number and current of high power ion beams were determined by monitoring delayed radioactivity from nuclear reactions induced in a 12 C target by the proton beams. The prompt γ-rays and diode Bremsstrahlung X-rays were measured with a PIN semi-conductor detector and a plastic scintillator detector. The current density distribution of ion beam was measured with a biased ion collector array. The ion beams were also recorded with a CR-39 detector. (authors) 3. Development of exploding wire ion source for intense pulsed heavy ion beam accelerator International Nuclear Information System (INIS) Ochiai, Y.; Murata, T.; Ito, H.; Masugata, K. 2012-01-01 A Novel exploding wire type ion source device is proposed as a metallic ion source of intense pulsed heavy ion beam (PHIB) accelerator. In the device multiple shot operations is realized without breaking the vacuum. The basic characteristics of the device are evaluated experimentally with an aluminum wire of diameter 0.2 mm, length 25 mm. Capacitor bank of capacitance 3 μF, charging voltage 30 kV was used and the wire was successfully exploded by a discharge current of 15 kA, rise time 5.3 μs. Plasma flux of ion current density around 70 A/cm 2 was obtained at 150 mm downstream from the device. The drift velocity of ions evaluated by a time-of-flight method was 2.7x10 4 m/sec, which corresponds to the kinetic energy of 100 eV for aluminum ions. From the measurement of ion current density distribution ion flow is found to be concentrated to the direction where ion acceleration gap is placed. From the experiment the device is found to be acceptable for applying PHIB accelerator. (author) 4. The light ion pulsed power induction accelerator for ETF International Nuclear Information System (INIS) Mazarakis, M.G.; Olson, R.E.; Olson, C.L.; Smith, D.L.; Bennett, L.F. 1994-01-01 Our Engineering Test Facility (ETF) driver concept is based on HERMES III and RHEPP technologies. Actually, it is a scaled-down version of the LMF design incorporating repetition rate capabilities of up to 10 Hz CW. The preconceptual design presented here provides 200-TW peak power to the ETF target during 10 ns, equal to 2-MJ total ion beam energy. Linear inductive voltage addition driving a self-magnetically insulated transmission line (MITL) is utilized to generate the 36-MV peak voltage needed for lithium ion beams. The ∼ 3-MA ion current is achieved by utilizing many accelerating modules in parallel. Since the current per module is relatively modest (∼300 kA), two-stage or one-stage extraction diodes can be utilized for the generation of singly charged lithium ions. The accelerating modules are arranged symmetrically around the fusion chamber in order to provide uniform irradiation onto the ETF target. In addition, the modules are fired in a programmed sequence in order to generate the optimum power pulse shape onto the target. This design utilizes RHEPP accelerator modules as the principal power source 5. Radiation pressure acceleration: The factors limiting maximum attainable ion energy Energy Technology Data Exchange (ETDEWEB) Bulanov, S. S.; Esarey, E.; Schroeder, C. B. [Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Bulanov, S. V. [KPSI, National Institutes for Quantum and Radiological Science and Technology, Kizugawa, Kyoto 619-0215 (Japan); A. M. Prokhorov Institute of General Physics RAS, Moscow 119991 (Russian Federation); Esirkepov, T. Zh.; Kando, M. [KPSI, National Institutes for Quantum and Radiological Science and Technology, Kizugawa, Kyoto 619-0215 (Japan); Pegoraro, F. [Physics Department, University of Pisa and Istituto Nazionale di Ottica, CNR, Pisa 56127 (Italy); Leemans, W. P. [Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Physics Department, University of California, Berkeley, California 94720 (United States) 2016-05-15 Radiation pressure acceleration (RPA) is a highly efficient mechanism of laser-driven ion acceleration, with near complete transfer of the laser energy to the ions in the relativistic regime. However, there is a fundamental limit on the maximum attainable ion energy, which is determined by the group velocity of the laser. The tightly focused laser pulses have group velocities smaller than the vacuum light speed, and, since they offer the high intensity needed for the RPA regime, it is plausible that group velocity effects would manifest themselves in the experiments involving tightly focused pulses and thin foils. However, in this case, finite spot size effects are important, and another limiting factor, the transverse expansion of the target, may dominate over the group velocity effect. As the laser pulse diffracts after passing the focus, the target expands accordingly due to the transverse intensity profile of the laser. Due to this expansion, the areal density of the target decreases, making it transparent for radiation and effectively terminating the acceleration. The off-normal incidence of the laser on the target, due either to the experimental setup, or to the deformation of the target, will also lead to establishing a limit on maximum ion energy. 6. SIS: an accelerator installation for heavy ions of high energy International Nuclear Information System (INIS) The two major sections of the report cover the scientific experimental program and the accelerator installation. Topics covered in the first include: heavy ion physics in the medium energy region; nuclear physics at relativistic energies; atomic physics loss and capture cross sections for electrons; spectroscopy of few-electron systems; atomic collision processes; biological experiments; nuclear track techniques in biology; and experiments with protons and secondary radiation. The second includes: concept for the total installation; technical description of the SIS 12; technical description of the SIS 100; status of the UNILAC injector; development options for the SIS installations; properties of the heavy ion beam; and structural work and technical supply provisions. In this SIS project proposal, an accelerator installation based on two synchrotrons is described with which atomic nuclei up to uranium can be accelerated to energies of more than 10 GeV/μ. With the SIS 12, which is the name of the first stage, heavy ion physics at intermediate energies can be pursued up to 500 MeV/μ. The second stage, a larger synchrotron, the SIS 100, has a diameter of 250 m. With this device, it is proposed to open up the domain of relativistic heavy ion physics up to 14 GeV/μ (for intermediate mass particles) and 10 GeV/μ (for uranium) 7. Generation of monoenergetic ion beams with a laser accelerator International Nuclear Information System (INIS) Pfotenhauer, Sebastian M. 2009-01-01 A method for the generation of monoenergetic proton and ion beams from a laser-based particle accelerator is presented. This method utilizes the unique space-charge effects occurring during relativistic laser-plasma interactions on solid targets in combination with a dot-like particle source. Due to this unique interaction geometry, MeV proton beams with an intrinsically narrow energy spectrum were obtained, for the first time, from a micrometer-scale laser accelerator. Over the past three years, the acceleration scheme has been consistently improved to enhance both the maximum particle energy and the reliability of the setup. The achieved degree of reliability allowed to derive the first scaling laws specifically for monoenergetic proton beams. Furthermore, the acceleration scheme was expanded on other target materials, enabling the generation of monoenergetic carbon beams. The experimental work was strongly supported by the parallel development of a complex theoretical model, which fully accounts for the observations and is in excellent agreement with numerical simulations. The presented results have an extraordinarily broad scope way beyond the current thesis: The availability of monoenergetic ion beams from a compact laser-plasma beam source - in conjunction with the unique properties of laser-produced particle beams - addresses a number of outstanding applications in fundamental research, material science and medical physics, and will help to shape a new generation of accelerators. (orig.) 8. Generation of monoenergetic ion beams with a laser accelerator Energy Technology Data Exchange (ETDEWEB) Pfotenhauer, Sebastian M. 2009-01-29 A method for the generation of monoenergetic proton and ion beams from a laser-based particle accelerator is presented. This method utilizes the unique space-charge effects occurring during relativistic laser-plasma interactions on solid targets in combination with a dot-like particle source. Due to this unique interaction geometry, MeV proton beams with an intrinsically narrow energy spectrum were obtained, for the first time, from a micrometer-scale laser accelerator. Over the past three years, the acceleration scheme has been consistently improved to enhance both the maximum particle energy and the reliability of the setup. The achieved degree of reliability allowed to derive the first scaling laws specifically for monoenergetic proton beams. Furthermore, the acceleration scheme was expanded on other target materials, enabling the generation of monoenergetic carbon beams. The experimental work was strongly supported by the parallel development of a complex theoretical model, which fully accounts for the observations and is in excellent agreement with numerical simulations. The presented results have an extraordinarily broad scope way beyond the current thesis: The availability of monoenergetic ion beams from a compact laser-plasma beam source - in conjunction with the unique properties of laser-produced particle beams - addresses a number of outstanding applications in fundamental research, material science and medical physics, and will help to shape a new generation of accelerators. (orig.) 9. Method of separating radioactive nuclides from ion exchange resins International Nuclear Information System (INIS) Suzuki, Kazunori; Saikoku, Masami; Taneta, Daisuke; Yagi, Takuro. 1987-01-01 Purpose: To enable to safely process radioactive nuclides from spent ion exchange resins by using existent processing facilities. Method: Ion exchange resins in aqueous medium are at first placed to the ultrasonic wave irradiation site and put into such a state where clads and resins are easily separatable from each other by weakening the bonding force between them. Since the clads are magnetic material such as Fe 3 O 4 or NiFe 2 O 4 , the clads can be collected in the direction of the magnetic force by exerting the magnetic field simultaneously. The collected clads are transported by means of the aqueous medium to a collecting tank by removing the effect of magnetic field, for example, by interrupting the current supply to the electromagnet. Finally, they were subjected to stabilization and fixation into inorganic hardening agent such as cement hardener. Thus, processions can be made safely by using existent facilities. (Takahashi, M.) 10. Direct Reaction Experimental Studies with Beams of Radioactive Tin Ions Energy Technology Data Exchange (ETDEWEB) Jones, K. L. [University of Tennessee, Knoxville (UTK); Ahn, S.H. [University of Tennessee, Knoxville (UTK); Allmond, James M [ORNL; Ayres, A. [University of Tennessee, Knoxville (UTK); Bardayan, Daniel W [ORNL; Baugher, T. [Michigan State University, East Lansing; Bazin, D. [Michigan State University, National Superconducting Cyclotron Laboratory (NSCL); Beene, James R [ORNL; Berryman, J. S. [Michigan State University, East Lansing; Bey, A. [University of Tennessee, Knoxville (UTK); Bingham, C. R. [University of Tennessee, Knoxville (UTK); Cartegni, L. [University of Tennessee, Knoxville (UTK); Chae, K. Y. [University of Tennessee, Knoxville (UTK)/Sungkyunkwan University, Korea; Cizewski, J. A. [Rutgers University; Gade, A. [Michigan State University, National Superconducting Cyclotron Laboratory (NSCL); Galindo-Uribarri, Alfredo {nmn} [ORNL; Garcia-Ruiz, R.F. [Instituut voor Kernen Stralingsfysica, KU Leuven, B-3001, Leuven, Belgium; Grzywacz, Robert Kazimierz [ORNL; Howard, Meredith E [ORNL; Kozub, R. L. [Tennessee Technological University (TTU); Liang, J Felix [ORNL; Manning, Brett M [ORNL; Matos, M. [Louisiana State University; McDaniel, S. [Michigan State University, East Lansing; Miller, D. [University of Tennessee, Knoxville (UTK); Nesaraja, Caroline D [ORNL; O' Malley, Patrick [Rutgers University; Padgett, S [University of Tennessee, Knoxville (UTK); Padilla-Rodal, Elizabeth [Universidad Nacional Autonoma de Mexico (UNAM); Pain, Steven D [ORNL; Pittman, S. T. [University of Tennessee (UTK) and Oak Ridge National Laboratory (ORNL); Radford, David C [ORNL; Ratkiewicz, Andrew J [ORNL; Schmitt, Kyle [ORNL; Smith, Michael Scott [ORNL; Stracener, Daniel W [ORNL; Stroberg, S. [Michigan State University, East Lansing; Tostevin, Jeffrey A [ORNL; Varner Jr, Robert L [ORNL; Weisshaar, D. [Michigan State University, East Lansing; Wimmer, K. [Michigan State University, National Superconducting Cyclotron Laboratory (NSCL)/Central Michigan University; Winkler, R. [Michigan State University, East Lansing 2015-01-01 The tin chain of isotopes provides a unique region in which to investigate the evolution of single-particle structure, spreading from N = 50 at Sn-100, through 10 stable isotopes and the N = 82 shell closure at Sn-132 out into the r-process path. Direct reactions performed on radioactive ion beams are sensitive spectroscopic tools for studying exotic nuclei. Here we present one experiment knocking out neutrons from tin isotopes that are already neutron deficient and two reactions that add a neutron to neutron-rich Sn-130. Both techniques rely on selective particle identification and the measurement of gamma rays in coincidence with charged ions. We present the goals of the two experiments and the particle identification for the channels of interest. The final results will be presented in future publications. 11. A linear radiofrequency ion trap for accumulation, bunching, and emittance improvement of radioactive ion beams International Nuclear Information System (INIS) Herfurth, F.; Dilling, J.; Kellerbauer, A. 2000-05-01 An ion beam cooler and buncher has been developed for the manipulation of radioactive ion beams. The gas-filled linear radiofrequency ion trap system is installed at the Penning trap mass spectrometer ISOLTRAP at ISOLDE/CERN. Its purpose is to accumulate the 60-keV continuous ISOLDE ion beam with high efficiency and to convert it into low-energy low-emittance ion pulses. The efficiency was found to exceed 10% in agreement with simulations. A more than 10-fold reduction of the ISOLDE beam emittance can be achieved. The system has been used successfully for first on-line experiments. Its principle, setup and performance will be discussed. (orig.) 12. Particle size of radioactive aerosols generated during machine operation in high-energy proton accelerators International Nuclear Information System (INIS) Oki, Yuichi; Kanda, Yukio; Kondo, Kenjiro; Endo, Akira 2000-01-01 In high-energy accelerators, non-radioactive aerosols are abundantly generated due to high radiation doses during machine operation. Under such a condition, radioactive atoms, which are produced through various nuclear reactions in the air of accelerator tunnels, form radioactive aerosols. These aerosols might be inhaled by workers who enter the tunnel just after the beam stop. Their particle size is very important information for estimation of internal exposure doses. In this work, focusing on typical radionuclides such as 7 Be and 24 Na, their particle size distributions are studied. An aluminum chamber was placed in the EP2 beam line of the 12-GeV proton synchrotron at High Energy Accelerator Research Organization (KEK). Aerosol-free air was introduced to the chamber, and aerosols formed in the chamber were sampled during machine operation. A screen-type diffusion battery was employed in the aerosol-size analysis. Assuming that the aerosols have log-normal size distributions, their size distributions were obtained from the radioactivity concentrations at the entrance and exit of the diffusion battery. Radioactivity of the aerosols was measured with Ge detector system, and concentrations of non-radioactive aerosols were obtained using condensation particle counter (CPC). The aerosol size (radius) for 7 Be and 24 Na was found to be 0.01-0.04 μm, and was always larger than that for non-radioactive aerosols. The concentration of non-radioactive aerosols was found to be 10 6 - 10 7 particles/cm 3 . The size for radioactive aerosols was much smaller than ordinary atmospheric aerosols. Internal doses due to inhalation of the radioactive aerosols were estimated, based on the respiratory tract model of ICRP Pub. 66. (author) 13. Ion acceleration by radiation pressure in thin and thick targets Energy Technology Data Exchange (ETDEWEB) Macchi, Andrea, E-mail: [email protected] [CNR/INFM/polyLAB, Pisa (Italy); Dipartimento di Fisica ' Enrico Fermi' , Largo Bruno Pontecorvo 3, I-56127 Pisa (Italy); Benedetti, Carlo, E-mail: [email protected] [Dipartimento di Fisica, Universita di Bologna and INFN, Via Irnerio 46, I-40126 Bologna (Italy) 2010-08-01 Radiation Pressure Acceleration (RPA) by circularly polarized laser pulses is emerging as a promising way to obtain efficient acceleration of ions. We briefly review theoretical work on the topic, aiming at characterizing suitable experimental scenarios. We discuss the two reference cases of RPA, namely the thick target ('Hole Boring') and the (ultra)thin target ('Light Sail') regimes. The different scaling laws of the two regimes, the related experimental challenges and their suitability for foreseen applications are discussed. 14. Improved beam-energy calibration technique for heavy ion accelerators International Nuclear Information System (INIS) Ferrero, A.M.J.; Garcia, A.; Gil, Salvador 1989-01-01 A simple technique for beam energy calibration of heavy-ion accelerators is presented. A thin hydrogenous target was bombarded with 12 C and 19 F, and the energies of the protons knocked out, elastically were measured at several angles using two detectors placed at equal angles on opposite sides of the beam. The use of these two detectors cancels the largest errors due to uncertainties in the angle and position at which the beam hits the target. An application of this energy calibration method to an electrostatic accelerator is described and the calibration constant of the analyzing magnet was obtained with an estimated error of 0.4 (Author) [es 15. Injection and laser acceleration of ions based on the resonant surface photoionization International Nuclear Information System (INIS) Antsiferov, V.V.; Smirnov, G.I.; Telegin, G.G. 1993-01-01 The collective effects have been investigated of the injection and acceleration of the ion beams due to the resonant surface photoionization. The considered scheme of the laser accelerator allows to obtain positive ions with relativistic velocities. 11 refs., 2 figs 16. Experimental study of ion heating and acceleration during magnetic reconnection Energy Technology Data Exchange (ETDEWEB) Hsu, S.C. 2000-01-28 This dissertation reports an experimental study of ion heating and acceleration during magnetic reconnection, which is the annihilation and topological rearrangement of magnetic flux in a conductive plasma. Reconnection is invoked often to explain particle heating and acceleration in both laboratory and naturally occurring plasmas. However, a simultaneous account of reconnection and its associated energy conversion has been elusive due to the extreme inaccessibility of reconnection events, e.g. in the solar corona, the Earth's magnetosphere, or in fusion research plasmas. Experiments for this work were conducted on MRX (Magnetic Reconnection Experiment), which creates a plasma environment allowing the reconnection process to be isolated, reproduced, and diagnosed in detail. Key findings of this work are the identification of local ion heating during magnetic reconnection and the determination that non-classical effects must provide the heating mechanism. Measured ion flows are sub-Alfvenic and can provide only slight viscous heating, and classical ion-electron interactions can be neglected due to the very long energy equipartition time. The plasma resistivity in the reconnection layer is seen to be enhanced over the classical value, and the ion heating is observed to scale with the enhancement factor, suggesting a relationship between the magnetic energy dissipation mechanism and the ion heating mechanism. The observation of non-classical ion heating during reconnection has significant implications for understanding the role played by non-classical dissipation mechanisms in generating fast reconnection. The findings are relevant for many areas of space and laboratory plasma research, a prime example being the currently unsolved problem of solar coronal heating. In the process of performing this work, local measurements of ion temperature and flows in a well-characterized reconnection layer were obtained for the first time in either laboratory or observational 17. Experimental study of ion heating and acceleration during magnetic reconnection International Nuclear Information System (INIS) Hsu, S.C. 2000-01-01 This dissertation reports an experimental study of ion heating and acceleration during magnetic reconnection, which is the annihilation and topological rearrangement of magnetic flux in a conductive plasma. Reconnection is invoked often to explain particle heating and acceleration in both laboratory and naturally occurring plasmas. However, a simultaneous account of reconnection and its associated energy conversion has been elusive due to the extreme inaccessibility of reconnection events, e.g. in the solar corona, the Earth's magnetosphere, or in fusion research plasmas. Experiments for this work were conducted on MRX (Magnetic Reconnection Experiment), which creates a plasma environment allowing the reconnection process to be isolated, reproduced, and diagnosed in detail. Key findings of this work are the identification of local ion heating during magnetic reconnection and the determination that non-classical effects must provide the heating mechanism. Measured ion flows are sub-Alfvenic and can provide only slight viscous heating, and classical ion-electron interactions can be neglected due to the very long energy equipartition time. The plasma resistivity in the reconnection layer is seen to be enhanced over the classical value, and the ion heating is observed to scale with the enhancement factor, suggesting a relationship between the magnetic energy dissipation mechanism and the ion heating mechanism. The observation of non-classical ion heating during reconnection has significant implications for understanding the role played by non-classical dissipation mechanisms in generating fast reconnection. The findings are relevant for many areas of space and laboratory plasma research, a prime example being the currently unsolved problem of solar coronal heating. In the process of performing this work, local measurements of ion temperature and flows in a well-characterized reconnection layer were obtained for the first time in either laboratory or observational 18. Selective deuterium ion acceleration using the Vulcan petawatt laser Energy Technology Data Exchange (ETDEWEB) Krygier, A. G. [Laboratoire pour l' Utilisation des Lasers Intenses, École Polytechnique, 91128 Palasiseau (France); Physics Department, The Ohio State University, Columbus, Ohio 43210 (United States); Morrison, J. T. [Propulsion Systems Directorate, Air Force Research Lab, Wright Patterson Air Force Base, Ohio 45433 (United States); Kar, S., E-mail: [email protected]; Ahmed, H.; Alejo, A.; Green, A.; Jung, D. [Centre for Plasma Physics, School of Mathematics and Physics, Queens University Belfast, Belfast BT7 1NN (United Kingdom); Clarke, R.; Notley, M. [Central Laser Facility, Rutherford Appleton Laboratory, Didcot, Oxfordshire OX11 0QX (United Kingdom); Fuchs, J.; Vassura, L. [Laboratoire pour l' Utilisation des Lasers Intenses, École Polytechnique, 91128 Palasiseau (France); Kleinschmidt, A.; Roth, M. [Institut für Kernphysik, Technische Universität Darmstadt, Schloßgartenstrasse 9, D-64289 Darmstadt (Germany); Najmudin, Z.; Nakamura, H. [The John Adams Institute, Blackett Laboratory, Department of Physics, Imperial College, London SW7 2AZ (United Kingdom); Norreys, P. [Central Laser Facility, Rutherford Appleton Laboratory, Didcot, Oxfordshire OX11 0QX (United Kingdom); Department of Physics, University of Oxford, Oxford OX1 3PU (United Kingdom); Oliver, M. [Department of Physics, University of Oxford, Oxford OX1 3PU (United Kingdom); Zepf, M. [Centre for Plasma Physics, School of Mathematics and Physics, Queens University Belfast, Belfast BT7 1NN (United Kingdom); Helmholtz Institute Jena, D-07743 Jena (Germany); Borghesi, M. [Centre for Plasma Physics, School of Mathematics and Physics, Queens University Belfast, Belfast BT7 1NN (United Kingdom); Institute of Physics of the ASCR, ELI-Beamlines Project, Na Slovance 2, 18221 Prague (Czech Republic); Freeman, R. R. [Physics Department, The Ohio State University, Columbus, Ohio 43210 (United States) 2015-05-15 We report on the successful demonstration of selective acceleration of deuterium ions by target-normal sheath acceleration (TNSA) with a high-energy petawatt laser. TNSA typically produces a multi-species ion beam that originates from the intrinsic hydrocarbon and water vapor contaminants on the target surface. Using the method first developed by Morrison et al. [Phys. Plasmas 19, 030707 (2012)], an ion beam with >99% deuterium ions and peak energy 14 MeV/nucleon is produced with a 200 J, 700 fs, >10{sup 20}W/cm{sup 2} laser pulse by cryogenically freezing heavy water (D{sub 2}O) vapor onto the rear surface of the target prior to the shot. Within the range of our detectors (0°–8.5°), we find laser-to-deuterium-ion energy conversion efficiency of 4.3% above 0.7 MeV/nucleon while a conservative estimate of the total beam gives a conversion efficiency of 9.4%. 19. Selective deuterium ion acceleration using the Vulcan petawatt laser International Nuclear Information System (INIS) Krygier, A. G.; Morrison, J. T.; Kar, S.; Ahmed, H.; Alejo, A.; Green, A.; Jung, D.; Clarke, R.; Notley, M.; Fuchs, J.; Vassura, L.; Kleinschmidt, A.; Roth, M.; Najmudin, Z.; Nakamura, H.; Norreys, P.; Oliver, M.; Zepf, M.; Borghesi, M.; Freeman, R. R. 2015-01-01 We report on the successful demonstration of selective acceleration of deuterium ions by target-normal sheath acceleration (TNSA) with a high-energy petawatt laser. TNSA typically produces a multi-species ion beam that originates from the intrinsic hydrocarbon and water vapor contaminants on the target surface. Using the method first developed by Morrison et al. [Phys. Plasmas 19, 030707 (2012)], an ion beam with >99% deuterium ions and peak energy 14 MeV/nucleon is produced with a 200 J, 700 fs, >10 20 W/cm 2 laser pulse by cryogenically freezing heavy water (D 2 O) vapor onto the rear surface of the target prior to the shot. Within the range of our detectors (0°–8.5°), we find laser-to-deuterium-ion energy conversion efficiency of 4.3% above 0.7 MeV/nucleon while a conservative estimate of the total beam gives a conversion efficiency of 9.4% 20. Predicting induced radioactivity for the accelerator operations at the Taiwan Photon Source. Science.gov (United States) Sheu, R J; Jiang, S H 2010-12-01 This study investigates the characteristics of induced radioactivity due to the operations of a 3-GeV electron accelerator at the Taiwan Photon Source (TPS). According to the beam loss analysis, the authors set two representative irradiation conditions for the activation analysis. The FLUKA Monte Carlo code has been used to predict the isotope inventories, residual activities, and remanent dose rates as a function of time. The calculation model itself is simple but conservative for the evaluation of induced radioactivity in a light source facility. This study highlights the importance of beam loss scenarios and demonstrates the great advantage of using FLUKA in comparing the predicted radioactivity with corresponding regulatory limits. The calculated results lead to the conclusion that, due to fairly low electron consumption, the radioactivity induced in the accelerator components and surrounding concrete walls of the TPS is rather moderate and manageable, while the possible activation of air and cooling water in the tunnel and their environmental releases are negligible. 1. An overview of negative hydrogen ion sources for accelerators Science.gov (United States) Faircloth, Dan; Lawrie, Scott 2018-02-01 An overview of high current (>1 mA) negative hydrogen ion (H-) sources that are currently used on particle accelerators. The current understanding of how H- ions are produced is summarised. Issues relating to caesium usage are explored. The different ways of expressing emittance and beam currents are clarified. Source technology naming conventions are defined and generalised descriptions of each source technology are provided. Examples of currently operating sources are outlined, with their current status and future outlook given. A comparative table is provided. 2. Ion exchangers in radioactive waste management: natural Iranian zeolites. Science.gov (United States) Nilchi, A; Maalek, B; Khanchi, A; Ghanadi Maragheh, M; Bagheri, A; Savoji, K 2006-01-01 Five samples of natural zeolites from different parts of Iran were chosen for this study. In order to characterize and determine their structures, X-ray diffraction and infrared spectrometry were carried out for each sample. The selective absorption properties of each zeolite were found by calculating the distribution coefficient (K(d)) of various simulated wastes which were prepared by spiking the radionuclides with (131)I, (99)Mo, (153)Sm, (140)La and (147)Nd. All the zeolite samples used in this study had extremely high absorption value towards (140)La; clinoptolite from Mianeh and analsite from Ghalehkhargoshi showed good absorption for (147)Nd; clinoptolite from Semnan and clinoptolite from Firozkoh showed high absorption for (153)Sm; mesolite from Arababad Tabas showed good absorption for (99)Mo; and finally mesolite from Arababad Tabas, clinoptolite from Semnan and clinoptolite from Firozkoh could be used to selectively absorb (131)I from the stimulated waste which was prepared. The natural zeolites chosen for these studies show a similar pattern to those synthetic ion exchangers in the literature and in some cases an extremely high selectivity towards certain radioactive elements. Hence the binary separation of radioactive elements could easily be carried out. Furthermore, these zeolites, which are naturally occurring ion exchangers, are viable economically and extremely useful alternatives in this industry. 3. Universal method for effusive-flow characterization target ion source/vapor transport systems for radioactive ion beam generation (abstract) International Nuclear Information System (INIS) Alton, G.D.; Bilheux, J.-C.; Liu, Y.; Cole, J. A.; Williams, C. 2004-01-01 Worldwide interest in the use of accelerated radioactive ion beams (RIBs) for exploring reactions important in understanding the structure of the nucleus and nuclear astrophysical phenomena has motivated the construction of facilities dedicated to their production and acceleration. Many facilities utilize the isotope-separator-on-line (ISOL) method in which species of interest are generated within a solid or liquid target matrix. Experimentally useful RIBs are often difficult to generate by this technique because of the times required for diffusion from the interior of the target material, and to effusively transport the species of interest to the ion source following diffusion release in relation to its lifetime. Therefore, these delay times must be minimized. We have developed an experimental method that can be used to determine effusive-flow times of arbitrary geometry target/vapor transport systems. The technique utilizes a fast valve to measure effusive-flow times as short as 0.1 ms for any chemically active or inactive species through any target system, independent of size, geometry and materials of construction. In this report, we provide a theoretical basis for effusive flow through arbitrary geometry vapor transport systems, describe a universal experimental apparatus for measuring effusive-flow times, and provide time spectra for noble gases through prototype RIB target/vapor-transport systems 4. Ion effects in future circular and linear accelerators International Nuclear Information System (INIS) Raubenheimer, T.O. 1995-05-01 In this paper, the author discusses ion effects relevant to future storage rings and linear colliders. The author first reviews the conventional ion effects observed in present storage rings and then discusses how these effects will differ in the next generation of rings and linacs. These future accelerators operate in a new regime because of the high current long bunch trains and the very small transverse beam emittances. Usually, storage rings are designed with ion clearing gaps to prevent ion trapping between bunch trains or beam revolutions. Regardless, ions generated within a single bunch train can have significant effects. The same is true in transport lines and linacs, where typical vacuum pressures are relatively high. Amongst other effects, the author addresses the tune spreads due to the ions and the resulting filamentation which can severely limit emittance correction techniques in future linear colliders, the bunch-to-bunch coupling due to the ions which can cause a multi-bunch instability with fast growth rates, and the betatron coupling and beam halo creation which limit the vertical emittance and beam lifetimes 5. A continuous acceleration tube of ions under 200 KV International Nuclear Information System (INIS) Mongodin, G. 1954-01-01 The realization of an Van de Graaff accelerator required, for the preliminary studies, the construction of a small proton accelerator, functioning at 200 kV in order to resolve some parasitic effects inherent to the accelerators tubes. The aim of this report is to describe the different organs of the accelerator tube, to explain the operating system and to encode their characteristics. The report first presents the ion source and the beam buncher permitting to inject in the accelerator tube particles of about 9 kV and very batched in a thin beam of circular section. Then the study explain the tube characteristics considered like optic system. A method to obtain precise calculation of particle trajectories is exposed. Aberrations of the system were discussed and balance of the currents on all electrodes inside the tube for different regimes of working were provided. The influence of the residual pressure in the tube were explained. The report finally ends on a part of the fundamental problem of the straining occurring inside the tubes accelerators under high tension. (M.B.) [fr 6. Bipolar pulse generator for intense pulsed ion beam accelerator International Nuclear Information System (INIS) Ito, H.; Igawa, K.; Kitamura, I.; Masugata, K. 2007-01-01 A new type of pulsed ion beam accelerator named ''bipolar pulse accelerator'' (BPA) has been proposed in order to improve the purity of intense pulsed ion beams. To confirm the principle of the BPA, we developed a bipolar pulse generator for the bipolar pulse experiment, which consists of a Marx generator and a pulse forming line (PFL) with a rail gap switch on its end. In this article, we report the first experimental result of the bipolar pulse and evaluate the electrical characteristics of the bipolar pulse generator. When the bipolar pulse generator was operated at 70% of the full charge condition of the PFL, the bipolar pulse with the first (-138 kV, 72 ns) and the second pulse (+130 kV, 70 ns) was successfully obtained. The evaluation of the electrical characteristics indicates that the developed generator can produce the bipolar pulse with fast rise time and sharp reversing time 7. Upgrading the Lyon cluster ion accelerator by a radiofrequency quadrupole International Nuclear Information System (INIS) Moser, H.O.; Schempp, A. 1987-02-01 The design is presented of an RFQ with variable final energy suitable to post-accelerate cluster ions from the Lyon electrostatic cluster-ion accelerator in the mass ranges from 1 to 25 μ and 1 to 50 μ to kinetic energies of 1.32-2.5 MeV and 2.64-5.0 MeV for cw and pulsed operation, respectively. Furthermore, a beam line is described which matches the electrostatically preaccelerated beam to the RFQ by use of electrostatic quadrupole triplets. When used without RFQ this beam line serves to improve beam parameters on the target, such as the particle flux density or beam divergence. The estimated costs of this project are about DM 345 000.- or FF 1 200 000.- without VAT. (orig.) [de 8. Status report on the heavy ion accelerator facility at TIFR International Nuclear Information System (INIS) Srinivasan, B. 2006-01-01 The 14 UD Pelletron Accelerator has been delivering heavy ion beams for experimental programs in Nuclear Physics and other fields. During the year beam was delivered for 72% of the time remaining after completion of certain infrastructural activities. Various developmental activities were also taken up in the laboratories associated with the Pelletron. The Superconducting Linac being constructed as a booster for the heavy ion beams from the Pelletron is in an advanced state of completion. Five of the seven cryostat modules have been assembled and tested with beam from the Pelletron. The last two remaining modules are being assembled. A new experimental beam hall has been constructed for utilization of the accelerated beam from the Linac and beam transport to one of the target areas has been carried out. (author) 9. MIAMI: Microscope and ion accelerator for materials investigations International Nuclear Information System (INIS) Hinks, J. A.; Berg, J. A. van den; Donnelly, S. E. 2011-01-01 A transmission electron microscope (TEM) with in situ ion irradiation has been built at the University of Salford, U.K. The system consists of a Colutron G-2 ion source connected to a JEOL JEM-2000FX TEM via an in-house designed and constructed ion beam transport system. The ion source can deliver ion energies from 0.5 to 10 keV for singly charged ions and can be floated up to 100 kV to allow acceleration to higher energies. Ion species from H to Xe can be produced for the full range of energies allowing the investigation of implantation with light ions such as helium as well as the effects of displacing irradiation with heavy inert or self-ions. The ability to implant light ions at energies low enough such that they come to rest within the thickness of a TEM sample and to also irradiate with heavier species at energies sufficient to cause large numbers of atomic displacements makes this facility ideally suited to the study of materials for use in nuclear environments. TEM allows the internal microstructure of a sample to be imaged at the nanoscale. By irradiating in situ it is possible to observe the dynamic evolution of radiation damage which can occur during irradiation as a result of competing processes within the system being studied. Furthermore, experimental variables such as temperature can be controlled and maintained throughout both irradiation and observation. This combination of capabilities enables an understanding of the underlying atomistic processes to be gained and thus gives invaluable insights into the fundamental physics governing the response of materials to irradiation. Details of the design and specifications of the MIAMI facility are given along with examples of initial experimental results in silicon and silicon carbide. 10. Double-layer ion acceleration triggered by ion magnetization in expanding radiofrequency plasma sources International Nuclear Information System (INIS) Takahashi, Kazunori; Charles, Christine; Boswell, Rod W.; Fujiwara, Tamiya 2010-01-01 Ion energy distribution functions downstream of the source exit in magnetically expanding low-pressure plasmas are experimentally investigated for four source tube diameters ranging from about 5 to 15 cm. The magnetic-field threshold corresponding to a transition from a simple expanding plasma to a double layer-containing plasma is observed to increase with a decrease in the source tube diameter. The results demonstrate that for the four geometries, the double layer and the accelerated ion beam form when the ion Larmour radius in the source becomes smaller than the source tube radius, i.e., when the ions become magnetized in the source tube. 11. Emittance growth from rotated quadrupoles in heavy ion accelerators International Nuclear Information System (INIS) Barnard, J.J. 1995-01-01 We derive a set of moment equations which incorporates linear quadrupolar focusing and space-charge defocusing, in the presence of rotational misalignments of the quadrupoles about the direction of beam propagation. Although the usual beam emittance measured relative to fixed transverse x and y coordinate axes is not constant, a conserved emittance-like quantity has been found. Implications for alignment tolerances in accelerators for heavy-ion inertial fusion are discussed 12. Design study of an accelerator for heavy ion fusion International Nuclear Information System (INIS) Katayama, T.; Noda, A.; Tokuda, N.; Hirao, Y. 1980-01-01 Design of a demonstration accelerator for heavy ion fusion based on a synchrotron system is briefly described. The proposed complex system of injector linac, rapid cycling synchrotron and five accumulation rings can produce a peak current 1.6 kA, peak power 32 TW and total energy 0.3 MJ. Investigations of the intrabeam scattering give a lifetime of the beam longer than the fusion cycle time of 1 sec 13. Fast neutron scintillation spectrometer in a heavy ion accelerator International Nuclear Information System (INIS) Blinov, M.V.; Gavrilov, B.P.; Ivannikova, L.L.; Kozulin, Eh.M.; Mozhaev, A.N.; Tyurin, G.P. 1984-01-01 Scintillation fast neutron spectrometer in a heavy ion accelerator is described in short. The spectrometer is used to measure characteristics of neutrons emitted in heavy ion interaction with different nuclei. Experiment was performed on the base of particle flight from 0.7 up to 2 m. Within the angle range of 0-150 deg. The technique is based on recording of two-dimensional neutron spectra obtained due to combination of the time-of-flight method and the method of recoil proton energy detection. Two measuring channels were used in the spectrometer. Each channel comprise both amplitude and time tracks. Detector on the base microchannel plates (MCP) generated a signal in passing the next ion bunch was used in order to obtain the time mark. Data from the scintillation block are recorded with respect to three parameters: recoil proton amplitude, time of neutron or γ-quantum arrival in respect of MCP-sensor pulse. Apparatus is carried out within the CAMAC standard. The spectrometer calibration within the 1-20 MeV neutron range was conducted in the Van-de-Graaf accelerator, and for higher energies - with the use of lightguides. Spectrometer time resolution for neutron energies of 0.5-50 MeV constituted 1.5-1.8 ns. The above measuring of neutron spectra from 1 /H2C+ 181 Ta and sup(20, 22)Ne+sup(181)Ta reaction have revealed a possibility of the experiment organization in heavy ion accelerators in the presence of strong neutron and γ-fields. Organization of multi-dimensional analysis combining two methods allows one to separate accelerator cycle, a region of the most reliable information, free of a low-energy gamma background and limited both by a dynamic threshold and a region of permissible energy values 14. Dedicated medical ion accelerator design study. Final report International Nuclear Information System (INIS) 1977-12-01 Results and conclusions are reported from a design study for a dedicated medical accelerator. Basing efforts on the current consensus regarding medical requirements, the resulting demands on accelerator and beam delivery systems were analyzed, and existing accelerator technology was reviewed to evaluate the feasibility of meeting these demands. This general analysis was augmented and verified by preparing detailed preliminary designs for sources of therapeutic beams of neutrons, protons and heavy ions. The study indicates that circular accelerators are the most desirable and economical solutions for such sources. Synchrotrons are clearly superior for beams of helium and heavier ions, while synchrotrons and cyclotrons seem equally well suited for protons although they have different strengths and weaknesses. Advanced techniques of beam delivery are of utmost importance in fully utilizing the advantages of particle beams. Several issues are invloved here. First, multi-treatment room arrangements are essential for making optimal use of the high dose rate capabilities of ion accelerators. The design of corresponding beam switching systems, the principles of which are already developed for physics experimental areas, pose no problems. Second, isocentric beam delivery substantially enhances flexibility of dose delivery. After several designs for such devices were completed, it was concluded that high field magnets are necessary to keep size, bulk and cost acceptable. Third, and most important, is the generation of large, homogeneous radiation fields. This is presently accomplished with the aid of scattering foils, occluding rings, collimators, ridge filters, and boluses. A novel approach, three-dimensional beam scanning, was developed here, and the most demanding components of such a system (fast-scanning magnet and power supply) were built and tested 15. Heavy-ion acceleration with a superconducting linac International Nuclear Information System (INIS) Bollinger, L.M. 1988-01-01 This year, 1988, is the tenth anniversary of the first use of RF superconductivity to accelerate heavy ions. In June 1978, the first two superconducting resonators of the Argonne Tandem-Linac Accelerator System (ATLAS) were used to boost the energy of a 19 F beam from the tandem, and by September 1978 a 5-resonator linac provided an 16 O beam for a nuclear-physics experiment. Since then, the superconducting linac has grown steadily in size and capability until now there are 42 accelerating structures and 4 bunchers. Throughout this period, the system was used routinely for physics research, and by now the total time with beam on target is 35,000 hours. Lessons learned from this long running experience and some key technical developments that made it possible are reviewed in this paper. 19 refs., 3 figs., 2 tabs 16. LIGHT - from laser ion acceleration to future applications Science.gov (United States) Roth, Markus; Light Collaboration 2013-10-01 Creation of high intensity multi-MeV ion bunches by high power lasers became a reliable tool during the last 15 years. The laser plasma source provides for TV/m accelerating field gradients and initially sub-ps bunch lengths. However, the large envelope divergence and the continuous exponential energy spectrum are substential drawbacks for many possible applications. To face this problem, the LIGHT collaboration was founded (Laser Ion Generation, Handling and Transport). The collaboration consists of several university groups and research centers, namely TU Darmstadt, JWGU Frankfurt, HI Jena, HZDR Dresden and GSI Darmstadt. The central goal is building a test beamline for merging laser ion acceleration with conventional accelerator infrastructure at the GSI facility. In the latest experiments, low divergent proton bunches with a central energy of up to 10 MeV and containing >109 particles could be provided at up to 2.2 m behind the plasma source, using a pulsed solenoid. In a next step, a radiofrequency cavity will be added to the beamline for phase rotation of these bunches, giving access to sub-ns bunch lengths and reaching highest intensities. An overview of the LIGHT objectives and the recent experimental results will be given. This work was supported by HIC4FAIR. 17. Superconducting accelerating structures for very low velocity ion beams Energy Technology Data Exchange (ETDEWEB) Xu, J.; Shepard, K.W.; Ostroumov, P.N.; Fuerst, J.D.; Waldschmidt, G.; /Argonne; Gonin, I.V.; /Fermilab 2008-01-01 This paper presents designs for four types of very-low-velocity superconducting accelerating cavity capable of providing several MV of accelerating potential per cavity, and suitable for particle velocities in the range 0.006 < v/c < 0.06. Superconducting TEM-class cavities have been widely applied to CW acceleration of ion beams. SC linacs can be formed as an array of independently-phased cavities, enabling a variable velocity profile to maximize the output energy for each of a number of different ion species. Several laboratories in the US and Europe are planning exotic beam facilities based on SC linacs. The cavity designs presented here are intended for the front-end of such linacs, particularly for the post-acceleration of rare isotopes of low charge state. Several types of SC cavities have been developed recently to cover particle velocities above 0.06c. Superconducting four-gap quarter-wave resonators for velocities 0.008 < {beta} = v/c < 0.05 were developed about two decades ago and have been successfully operated at the ATLAS SC linac at Argonne National Laboratory. Since that time, progress in simulation tools, cavity fabrication and processing have increased SC cavity gradients by a factor of 3-4. This paper applies these tools to optimize the design of a four-gap quarter-wave resonator for exotic beam facilities and other low-velocity applications. 18. Simulating electron clouds in heavy-ion accelerators International Nuclear Information System (INIS) Cohen, R.H.; Friedman, A.; Covo, M. Kireeff; Lund, S.M.; Molvik, A.W.; Bieniosek, F.M.; Seidl, P.A.; Vay, J.-L.; Stoltz, P.; Veitzer, S. 2005-01-01 Contaminating clouds of electrons are a concern for most accelerators of positively charged particles, but there are some unique aspects of heavy-ion accelerators for fusion and high-energy density physics which make modeling such clouds especially challenging. In particular, self-consistent electron and ion simulation is required, including a particle advance scheme which can follow electrons in regions where electrons are strongly magnetized, weakly magnetized, and unmagnetized. The approach to such self-consistency is described, and in particular a scheme for interpolating between full-orbit (Boris) and drift-kinetic particle pushes that enables electron time steps long compared to the typical gyroperiod in the magnets. Tests and applications are presented: simulation of electron clouds produced by three different kinds of sources indicates the sensitivity of the cloud shape to the nature of the source; first-of-a-kind self-consistent simulation of electron-cloud experiments on the high-current experiment [L. R. Prost, P. A. Seidl, F. M. Bieniosek, C. M. Celata, A. Faltens, D. Baca, E. Henestroza, J. W. Kwan, M. Leitner, W. L. Waldron, R. Cohen, A. Friedman, D. Grote, S. M. Lund, A. W. Molvik, and E. Morse, 'High current transport experiment for heavy ion inertial fusion', Physical Review Special Topics, Accelerators and Beams 8, 020101 (2005)], at Lawrence Berkeley National Laboratory, in which the machine can be flooded with electrons released by impact of the ion beam on an end plate, demonstrate the ability to reproduce key features of the ion-beam phase space; and simulation of a two-stream instability of thin beams in a magnetic field demonstrates the ability of the large-time-step mover to accurately calculate the instability 19. Hertzian spectroscopy application to excited states in accelerated ion beams Energy Technology Data Exchange (ETDEWEB) Gaillard, M L 1974-01-01 Accelerated ion beams enables the application of optical hertzian spectrometry methods to be extended to research on the excited states of free ionic systems. The photon beat method has proved especially simple to apply in beam foil geometry because of the unidirectional beam velocity while the beam gas device is suitable for experiments of the energy level crossing type. Only the resonance technique involving direct application of high-frequency magnetic fields poses serious problems because of the high HF powers necessary. So far structure intervals have been measured in ions carrying up to three charges (seven in the special case of Lamb shift measurements) with a precision of a few percent. Study of hydrogen-like or helium-like ions of high Z allows the fundamental calculations of quantum electrodynamics to be checked with regard to the Lamb shift or the spontaneous emission theory. In more complex electronic systems, optical spectroscopy of accelerated ion beams gives wavelengths with a resolution reaching 10/sup -5/, lifetimes with an accuracy better than 10% when the cascade effects are properly studied, and Lande factors with a precision of several % under present technical conditions. The photon beat method concerns hyperfine nuclear effects in light atoms of Z < = 20. (FR) 20. Repetitive pulse accelerator technology for light ion inertial confinement fusion International Nuclear Information System (INIS) Buttram, M.T. 1985-01-01 Successful ignition of an inertial confinement fusion (ICF) pellet is calculated to require that several megajoules of energy be deposited in the pellet's centimeter-sized shell within 10 ns. This implies a driver power of several hundreds of terawatts and power density around 100 TW/cm 2 . The Sandia ICF approach is to deposit the energy with beams of 30 MV lithium ions. The first accelerator capable of producing these beams (PBFA II, 100 TW) will be used to study beam formation and target physics on a single pulse basis. To utilize this technology for power production, repetitive pulsing at rates that may be as high as 10 Hz will be required. This paper will overview the technologies being studied for a repetitively pulsed ICF accelerator. As presently conceived, power is supplied by rotating machinery providing 16 MJ in 1 ms. The generator output is transformed to 3 MV, then switched into a pulse compression system using laser triggered spark gaps. These must be synchronized to about 1 ns. Pulse compression is performed with saturable inductor switches, the output being 40 ns, 1.5 MV pulses. These are transformed to 30 MV in a self-magnetically insulated cavity adder structure. Space charge limited ion beams are drawn from anode plasmas with electron counter streaming being magnetically inhibited. The ions are ballistically focused into the entrances of guiding discharge channels for transport to the pellet. The status of component development from the prime power to the ion source will be reviewed 1. Enhanced ion acceleration in transition from opaque to transparent plasmas Science.gov (United States) Mishra, R.; Fiuza, F.; Glenzer, S. 2018-04-01 Using particle-in-cell simulations, we investigate ion acceleration in the interaction of high intensity lasers with plasmas which transition from opaque to transparent during the interaction process. We show that the highest ion energies are achieved when the laser traverses the target around the peak intensity and re-heats the electron population responsible for the plasma expansion, enhancing the corresponding sheath electric field. This process can lead to an increase of up to 2x in ion energy when compared with the standard Target Normal Sheath Acceleration in opaque targets under the same laser conditions. A theoretical model is developed to predict the optimal target areal density as a function of laser intensity and pulse duration. A systematic parametric scan for a wide range of target densities and thicknesses is performed in 1D, 2D and 3D and shown consistent with the theory and with recent experimental results. These results open the way for a better optimization of the ion energy in future laser–solid experiments. 2. Activation of accelerator construction materials by heavy ions Energy Technology Data Exchange (ETDEWEB) Katrík, P., E-mail: [email protected] [GSI Darmstadt, Planckstrasse 1, D-64291 (Germany); Mustafin, E. [GSI Darmstadt, Planckstrasse 1, D-64291 (Germany); Hoffmann, D.H.H. [TU Darmstadt, Schlossgartenstraße 9, D-64289 (Germany); Pavlovič, M. [FEI STU Bratislava, Ilkovičova 3, SK-81219 (Slovakia); Strašík, I. [GSI Darmstadt, Planckstrasse 1, D-64291 (Germany) 2015-12-15 Activation data for an aluminum target irradiated by 200 MeV/u {sup 238}U ion beam are presented in the paper. The target was irradiated in the stacked-foil geometry and analyzed using gamma-ray spectroscopy. The purpose of the experiment was to study the role of primary particles, projectile fragments, and target fragments in the activation process using the depth profiling of residual activity. The study brought information on which particles contribute dominantly to the target activation. The experimental data were compared with the Monte Carlo simulations by the FLUKA 2011.2c.0 code. This study is a part of a research program devoted to activation of accelerator construction materials by high-energy (⩾200 MeV/u) heavy ions at GSI Darmstadt. The experimental data are needed to validate the computer codes used for simulation of interaction of swift heavy ions with matter. 3. Repetitive pulse accelerator technology for light ion inertial confinement fusion International Nuclear Information System (INIS) Buttram, M.T. 1985-01-01 This paper will overview the technologies being studied for a repetitively pulsed ICF accelerator. As presently conceived, power is supplied by rotating machinery providing 16 MJ in 1 ms. The generator output is transformed to 3 MV, then switched into a pulse compression system using laser triggered spark gaps. These must be synchronized to about 1 ns. Pulse compression is performed with saturable inductor switches, the output being 40 ns, 1.5 MV pulses. These are transformed to 30 MV in a self-magnetically insulated cavity adder structure. Space charge limited ion beams are drawn from anode plasmas with electron counter streaming being magnetically inhibited. The ions are ballistically focused into the entrances of guiding discharge channels for transport to the pellet. The status of component development from the prime power to the ion source will be reviewed 4. Role of resistivity gradient in laser-driven ion acceleration Directory of Open Access Journals (Sweden) L. A. Gizzi 2011-01-01 Full Text Available It was predicted that, when a fast electron beam with some angular spread is normally incident on a resistivity gradient, magnetic field generation can occur that can inhibit beam propagation [A. R. Bell et al., Phys. Rev. E 58, 2471 (1998PLEEE81063-651X10.1103/PhysRevE.58.2471]. This effect can have consequences on the laser-driven ion acceleration. In the experiment reported here, we compare ion emission from laser irradiated coated and uncoated metal foils and we show that the ion beam from the coated target has a much smaller angular spread. Detailed hybrid numerical simulations confirm that the inhibition of fast electron transport through the resistivity gradient may explain the observed effect. 5. Acceleration of heavy ions to relativistic energies and their use in physics and biomedicine International Nuclear Information System (INIS) White, M.G. 1977-01-01 The uses of accelerated heavy ions in physics and biomedicine are listed. The special properties of high energy heavy ions and their fields of applications, the desirable ions and energies, requirements for a relativistic heavy ion accelerator, and AGS and Bevalac parameters are discussed. 26 references 6. Acceleration of cluster and molecular ions by TIARA 3 MV tandem accelerator CERN Document Server Saitoh, Y; Tajima, S 2000-01-01 We succeeded in accelerating molecular and cluster ions (B sub 2 sub - sub 4 , C sub 2 sub - sub 1 sub 0 , O sub 2 , Al sub 2 sub - sub 4 , Si sub 2 sub - sub 4 , Cu sub 2 sub - sub 3 , Au sub 2 sub - sub 3 , LiF, and AlO) to MeV energies with high-intensity beam currents by means of a 3 MV tandem accelerator in the TIARA facility. These cluster ions were generated by a cesium sputter-type negative ion source. We tested three types of carbon sputter cathodes in which graphite powder was compressed with different pressures. The pressure difference affected the generating ratio of clusters generated to single atom ions extracted from the source and it appeared that the high-density cathode was suitable. We also investigated the optimum gas pressure for charge exchange in the tandem high-voltage terminal. Clusters of larger size tend to require lower pressure than do smaller ones. In addition, we were able to obtain doubly charged AlO molecular ions. (authors) 7. Ultra-relativistic ion acceleration in the laser-plasma interactions International Nuclear Information System (INIS) Huang Yongsheng; Wang Naiyan; Tang Xiuzhang; Shi Yijin; Xueqing Yan 2012-01-01 An analytical relativistic model is proposed to describe the relativistic ion acceleration in the interaction of ultra-intense laser pulses with thin-foil plasmas. It is found that there is a critical value of the ion momentum to make sure that the ions are trapped by the light sail and accelerated in the radiation pressure acceleration (RPA) region. If the initial ion momentum is smaller than the critical value, that is in the classical case of RPA, the potential has a deep well and traps the ions to be accelerated, as the same described before by simulation results [Eliasson et al., New J. Phys. 11, 073006 (2009)]. There is a new ion acceleration region different from RPA, called ultra-relativistic acceleration, if the ion momentum exceeds the critical value. In this case, ions will experience a potential downhill. The dependence of the ion momentum and the self-similar variable at the ion front on the acceleration time has been obtained. In the ultra-relativistic limit, the ion momentum at the ion front is proportional to t 4/5 , where t is the acceleration time. In our analytical hydrodynamical model, it is naturally predicted that the ion distribution from RPA is not monoenergetic, although the phase-stable acceleration mechanism is effective. The critical conditions of the laser and plasma parameters which identify the two acceleration modes have been achieved. 8. Ultra-relativistic ion acceleration in the laser-plasma interactions Energy Technology Data Exchange (ETDEWEB) Huang Yongsheng; Wang Naiyan; Tang Xiuzhang; Shi Yijin [China Institute of Atomic Energy, Beijing 102413 (China); Xueqing Yan [Institute of Heavy Ion Physics, Peking University, Beijing 100871 (China) 2012-09-15 An analytical relativistic model is proposed to describe the relativistic ion acceleration in the interaction of ultra-intense laser pulses with thin-foil plasmas. It is found that there is a critical value of the ion momentum to make sure that the ions are trapped by the light sail and accelerated in the radiation pressure acceleration (RPA) region. If the initial ion momentum is smaller than the critical value, that is in the classical case of RPA, the potential has a deep well and traps the ions to be accelerated, as the same described before by simulation results [Eliasson et al., New J. Phys. 11, 073006 (2009)]. There is a new ion acceleration region different from RPA, called ultra-relativistic acceleration, if the ion momentum exceeds the critical value. In this case, ions will experience a potential downhill. The dependence of the ion momentum and the self-similar variable at the ion front on the acceleration time has been obtained. In the ultra-relativistic limit, the ion momentum at the ion front is proportional to t{sup 4/5}, where t is the acceleration time. In our analytical hydrodynamical model, it is naturally predicted that the ion distribution from RPA is not monoenergetic, although the phase-stable acceleration mechanism is effective. The critical conditions of the laser and plasma parameters which identify the two acceleration modes have been achieved. 9. Towards polarization measurements of laser-accelerated helium-3 ions Energy Technology Data Exchange (ETDEWEB) Engin, Ilhan 2015-08-28 In the framework of this thesis, preparatory investigations for the spin-polarization measurement of {sup 3}He ions from laser-induced plasmas have been performed. Therefore, experiments aiming at an efficient laser-induced ion acceleration out of a {sup 4}He gas target were carried out at two high-intensity laser facilities: the Arcturus laser at Heinrich-Heine-Universitaet Duesseldorf as well as PHELIX at GSI Darmstadt. The scientific goal of both experiments was to investigate the ion-acceleration process in underdense plasmas by measuring the ion energy spectra and the angular distribution of the ion signal around the gas-jet target. Laser-accelerated MeV-He-ions could successfully be detected. The main acceleration direction at large angles with regard to the laser propagation direction was determined. In a second step, unpolarized {sup 3}He gas was attached in order to cross-check the experimental results with those of {sup 4}He. With the help of the achieved ion yield data, the expected rates of the fusion reaction D({sup 3}He,p){sup 4}He in the polarized case have been estimated: the information regarding the fusion proton yield from this nuclear reaction allows an experimentally based estimation for future experiments with pre-polarized {sup 3}He gas as plasma target. The experimental data is in line with supporting Particle-in-Cell (PIC) simulations performed on the Juelich supercomputers. For this purpose, the simulated target was defined as a neutral gas. The use of pre-polarized {sup 3}He gas demands a special preparation of a polarized {sup 3}He target for laser-acceleration experiments. This layout includes an (external) homogeneous magnetic holding field (field strength of ∝1.4 mT) for storing the pre-polarized gas for long time durations inside the PHELIX target chamber. For this purpose, a precise Halbach array consisting of horizontally arranged rings with built-in permanent magnets had to be designed, optimized, and constructed to deliver high 10. The Effusive-Flow Properties of Target/Vapor-Transport Systems for Radioactive Ion Beam Applications CERN Document Server Kawai, Yoko; Liu, Yuan 2005-01-01 Radioactive atoms produced by the ISOL technique must diffuse from a target, effusively flow to an ion source, be ionized, be extracted, and be accelerated to research energies in a time commensurate with the lifetime of the species of interest. We have developed a fast valve system (closing time ~100 us) that can be used to accurately measure the effusion times of chemically active or inactive species through arbitrary geometry and size vapor transport systems with and without target material in the reservoir. The effusive flow times are characteristic of the system and thus serve as figures of merit for assessing the quality of a given vapor transport system as well as for assessing the permeability properties of a given target design. This article presents effusive flow data for noble gases flowing through a target reservoir and ion source system routinely used to generate radioactive species at the HRIBF with and without disks of 6 times and 10 times compressed Reticulated Vitreous Carbon Foam (RVCF) with... 11. Ambipolar ion acceleration in an expanding magnetic nozzle Energy Technology Data Exchange (ETDEWEB) Longmier, Benjamin W; Carter, Mark D; Cassady, Leonard D; Chancery, William J; Diaz, Franklin R Chang; Glover, Tim W; Ilin, Andrew V; McCaskill, Greg E; Olsen, Chris S; Squire, Jared P [Ad Astra Rocket Company, 141 W. Bay Area Blvd, Webster, TX (United States); Bering, Edgar A III [Department of Physics and Department of Electrical and Computer Engineering, University of Houston, 617 Science and Research Building 1, Houston, TX (United States); Hershkowitz, Noah [Department of Engineering Physics, University of Wisconsin, 1500 Engineering Dr., Madison, WI (United States) 2011-02-15 The helicon plasma stage in the Variable Specific Impulse Magnetoplasma Rocket (VASIMR (registered)) VX-200i device was used to characterize an axial plasma potential profile within an expanding magnetic nozzle region of the laboratory based device. The ion acceleration mechanism is identified as an ambipolar electric field produced by an electron pressure gradient, resulting in a local axial ion speed of Mach 4 downstream of the magnetic nozzle. A 20 eV argon ion kinetic energy was measured in the helicon source, which had a peak magnetic field strength of 0.17 T. The helicon plasma source was operated with 25 mg s{sup -1} argon propellant and 30 kW of RF power. The maximum measured values of plasma density and electron temperature within the exhaust plume were 1 x 10{sup 20} m{sup -3} and 9 eV, respectively. The measured plasma density is nearly an order of magnitude larger than previously reported steady-state helicon plasma sources. The exhaust plume also exhibits a 95% to 100% ionization fraction. The size scale and spatial location of the plasma potential structure in the expanding magnetic nozzle region appear to follow the size scale and spatial location of the expanding magnetic field. The thickness of the potential structure was found to be 10{sup 4} to 10{sup 5} {lambda}{sub De} depending on the local electron temperature in the magnetic nozzle, many orders of magnitude larger than typical laboratory double layer structures. The background plasma density and neutral argon pressure were 10{sup 15} m{sup -3} and 2 x 10{sup -5} Torr, respectively, in a 150 m{sup 3} vacuum chamber during operation of the helicon plasma source. The agreement between the measured plasma potential and plasma potential that was calculated from an ambipolar ion acceleration analysis over the bulk of the axial distance where the potential drop was located is a strong confirmation of the ambipolar acceleration process. 12. Studies of ion acceleration in a one meter laser controlled collective accelerator International Nuclear Information System (INIS) Destler, W.W.; Rodgers, J.; Striffler, C.D.; Yao, R.L. 1991-01-01 The basic concept behind the Laser Controlled Beam-front Experiment has been described in detail in previous reports. In the experiment, control over the propagation of a virtual cathode at the front of an intense relativistic electron beam is achieved by a time-sequenced plasma channel produced by laser-target interactions. Ions are trapped and accelerated by the very strong electric fields (50-400 MV/m) at the virtual cathode 13. Advances in the disposal of radioactive ion exchange resins International Nuclear Information System (INIS) McCoy, S.B. 1983-01-01 During the last several years, more stringent regulations have been imposed on the disposal of low-level radioactive wastes. In particular, the disposal of high-activity ion exchange resins has been affected by the recent requirements intended to enhance waste stability. High-activity resins must now be either solidified or placed in a ''high-integrity'' container. The allowable levels of free liquids in the containers have also been reduced. Solidification of resins has long been applied at nuclear power stations, but new designs in high-integrity containers and dewatering techniques to enhance the waste stability and ensure regulatory compliance have been developed and are being introduced for use at power stations 14. Design of systems for handling radioactive ion exchange resin beads International Nuclear Information System (INIS) Shapiro, S.A.; Story, G.L. 1979-01-01 The flow of slurries in pipes is a complex phenomenon. There are little slurry data available on which to base the design of systems for radioactive ion exchange resin beads and, as a result, the designs vary markedly in operating plants. With several plants on-line, the opportunity now exists to evaluate the designs of systems handling high activity spent resin beads. Results of testing at Robbins and Meyers Pump Division to quantify the behavior of resin bead slurries are presented. These tests evaluated the following slurry parameters; resin slurry velocity, pressure drop, bead degradation, and slurry concentration effects. A discussion of the general characteristics of resin bead slurries is presented along with a correlation to enable the designer to establish the proper flowrate for a given slurry composition and flow regime as a function of line size. Guidelines to follow in designing a resin handling system are presented 15. Basic Design Study on 1-MV Electrostatic Accelerator for ion irradiation International Nuclear Information System (INIS) Cho, Yongsub; Kim, Kyeryung; Lee, Chanyoung 2014-01-01 The KOMAC (KOrea Multi-purpose Accelerator Complex) has electrostatic ion accelerators whose terminal voltages are less than 100kV. To extend ion beam irradiations with higher energy ions for industrial purposes, an electrostatic accelerator of 1-MV terminal voltage should have been studied. For industrial applications, the most important features of the accelerator are high current and high reliability for high irradiation dose and high through-put with high current and long irradiation time. The basic study on 1-MV electrostatic ion accelerator for industrial applications has been done. The key components are a high voltage power supply, an ion source, and an accelerating column. The feasibility study for fabrication is being performed. Especially the R and D for ion source is required. The 1-MV ion accelerator will be constructed with domestic companies and installed in the beam application research building, which is under construction in the site of KOMAC at Gyeongju 16. Accelerator Driven Sub-Critical System for the Radioactive Waste Transmutation International Nuclear Information System (INIS) Avramovic, I.; Pesic, M. 2008-01-01 Spent nuclear fuel discharged from nuclear power plants is the main problem during design of radioactive waste disposal. Most of the hazard stems from only a few chemical elements. The radiotoxicity of these elements can be efficiently reduced using partitioning and transmutation in fast reactors and accelerator driven subcritical systems. (author) 17. Superconducting accelerating structures for very low velocity ion beams Directory of Open Access Journals (Sweden) J. Xu 2008-03-01 Full Text Available This paper presents designs for four types of very-low-velocity superconducting (SC accelerating cavity capable of providing several MV of accelerating potential per cavity, and suitable for particle velocities in the range 0.006acceleration of ion beams. SC linacs can be formed as an array of independently phased cavities, enabling a variable velocity profile to maximize the output energy for each of a number of different ion species. Several laboratories in the U.S. and Europe are planning exotic beam facilities based on SC linacs. The cavity designs presented here are intended for the front end of such linacs, particularly for the postacceleration of rare isotopes of low charge state. Several types of SC cavities have been developed recently to cover particle velocities above 0.06c. Superconducting four-gap quarter-wave resonators for velocities 0.008<β=v/c<0.05 were developed about two decades ago and have been successfully operated at the ATLAS SC linac at Argonne National Laboratory. Since that time, progress in simulation tools, cavity fabrication, and processing have increased SC cavity gradients by a factor of 3–4. This paper applies these tools to optimize the design of a four-gap quarter-wave resonator for exotic beam facilities and other low-velocity applications. 18. Experimental methods in radioactive ion-beam target/ion source development and characterization International Nuclear Information System (INIS) Welton, R.F.; Alton, G.D.; Cui, B.; Murray, S.N. 1998-01-01 We have developed off-line experimental techniques and apparatuses that permit direct measurement of effusive-flow delay times and ionization efficiencies for nearly any chemically reactive element in high-temperature target/ion sources (TIS) commonly used for on-line radioactive ion-beam (RIB) generation. The apparatuses include a hot Ta valve for effusive-flow delay-time measurements, a cooled molecular injection system for determination of ionization efficiencies, and a gas flow measurement/control system for introducing very low, well-defined molecular flows into the TIS. Measurements are performed on a test stand using molecular feed compounds containing stable complements of the radioactive nuclei of interest delivered to the TIS at flow rates commensurate with on-line RIB generation. In this article, the general techniques are described and effusive-flow delay times and ionization efficiency measurements are reported for fluorine in an electron-beam plasma target/ion source developed for RIB generation and operated in both positive- and negative-ion extraction modes. copyright 1998 American Institute of Physics 19. Beam brilliance investigation of high current ion beams at GSI heavy ion accelerator facility. Science.gov (United States) Adonin, A A; Hollinger, R 2014-02-01 In this work the emittance measurements of high current Ta-beam provided by VARIS (Vacuum Arc Ion Source) ion source are presented. Beam brilliance as a function of beam aperture at various extraction conditions is investigated. Influence of electrostatic ion beam compression in post acceleration gap on the beam quality is discussed. Use of different extraction systems (single aperture, 7 holes, and 13 holes) in order to achieve more peaked beam core is considered. The possible ways to increase the beam brilliance are discussed. 20. Mutagenesis in human cells with accelerated H and Fe ions Science.gov (United States) Kronenberg, Amy 1994-01-01 The overall goals of this research were to determine the risks of mutation induction and the spectra of mutations induced by energetic protons and iron ions at two loci in human lymphoid cells. During the three year grant period the research has focused in three major areas: (1) the acquisition of sufficient statistics for human TK6 cell mutation experiments using Fe ions (400 MeV/amu), Fe ions (600 MeV/amu) and protons (250 MeV/amu); (2) collection of thymidine kinase- deficient (tk) mutants or hypoxanthine phosphoribosyltransferase deficient (hprt) mutants induced by either Fe 400 MeV/amu, Fe 600 MeV/amu, or H 250 MeV/amu for subsequent molecular analysis; and (3) molecular characterization of mutants isolated after exposure to Fe ions (600 MeV/amu). As a result of the shutdown of the BEVALAC heavy ion accelerator in December 1992, efforts were rearranged somewhat in time to complete our dose-response studies and to complete mutant collections in particular for the Fe ion beams prior to the shutdown. These goals have been achieved. A major effort was placed on collection, re-screening, and archiving of 3 different series of mutants for the various particle beam exposures: tk-ng mutants, tk-sg mutants, and hprt-deficient mutants. Where possible, groups of mutants were isolated for several particle fluences. Comparative analysis of mutation spectra has occured with characterization of the mutation spectrum for hprt-deficient mutants obtained after exposure of TK6 cells to Fe ions (600 MeV/amu) and a series of spontaneous mutants. 1. Source of polarized ions for the JINR accelerator complex Science.gov (United States) Belov, A. S.; Donets, D. E.; Fimushkin, V. V.; Kovalenko, A. D.; Kutuzova, L. V.; Prokofichev, Yu V.; Shutov, V. B.; Turbabin, A. V.; Zubets, V. N. 2017-12-01 The JINR atomic beam type polarized ion source is described. Results of tests of the plasma ionizer with a storage cell and of tuning of high frequency transition units are presented. The source was installed in a linac injector hall of NUCLOTRON in May 2016. The source has been commissioned and used in the NUCLOTRON runs in 2016 and February - March 2017. Polarized and unpolarized deuteron beams were produced as well as polarized protons for acceleration in the NUCLOTRON. Polarized deuteron beam with pulsed current up to 2 mA has been produced. Deuteron beam polarization of 0.6-0.9 of theoretical values for different modes of high frequency transition units operation has been measured with the NUCLOTRON ring internal polarimeter for the accelerated deuteron and proton beams. 2. Materials science and biophysics applications at the ISOLDE radioactive ion beam facility Energy Technology Data Exchange (ETDEWEB) Wahl, U., E-mail: [email protected] [Instituto Tecnologico e Nuclear, Estrada Nacional 10, 2686-953 Sacavem (Portugal); Centro de Fisica Nuclear da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa (Portugal) 2011-12-15 The ISOLDE isotope separator facility at CERN provides a variety of radioactive ion beams, currently more than 800 different isotopes from {approx}70 chemical elements. The radioisotopes are produced on-line by nuclear reactions from a 1.4 GeV proton beam with various types of targets, outdiffusion of the reaction products and, if possible, chemically selective ionisation, followed by 60 kV acceleration and mass separation. While ISOLDE is mainly used for nuclear and atomic physics studies, applications in materials science and biophysics account for a significant part (currently {approx}15%) of the delivered beam time, requested by 18 different experiments. The ISOLDE materials science and biophysics community currently consists of {approx}80 scientists from more than 40 participating institutes and 21 countries. In the field of materials science, investigations focus on the study of semiconductors and oxides, with the recent additions of nanoparticles and metals, while the biophysics studies address the toxicity of metal ions in biological systems. The characterisation methods used are typical radioactive probe techniques such as Moessbauer spectroscopy, perturbed angular correlation, emission channeling, and tracer diffusion studies. In addition to these 'classic' methods of nuclear solid state physics, also standard semiconductor analysis techniques such as photoluminescence or deep level transient spectroscopy profit from the application of radioactive isotopes, which helps them to overcome their chemical 'blindness' since the nuclear half life of radioisotopes provides a signal that changes in time with characteristic exponential decay or saturation curves. In this presentation an overview will be given on the recent research activities in materials science and biophysics at ISOLDE, presenting some of the highlights during the last five years, together with a short outlook on the new developments under way. 3. Accelerated ions as a tool in atomic physics International Nuclear Information System (INIS) Hansteen, J.M. 1977-01-01 Some of the aspects of atomic physics which are being brought into focus by the construction and completion of a new generation of heavy-ion accelerators are dealt with. Various types of processes occurring in the overlapping electron clouds are visualised in an elementary way, using among others, some recent observations on the formation of quasi-molecules and quasi-atoms. Phenomena connected with the inner electron shells in superheavy atoms are touched upon, in particular those processes possibly leading to the production of positrons. In such cases the crucial importance of an atomic Coulomb excitation mechanism is stressed. In conclusion the view is emphasized that inner shell ionization phenomena in heavy ion collisions form a bridge between processes originating respectively from nuclear and atomic physics. (Auth.) 4. Feasibility of using laser ion accelerators in proton therapy CERN Document Server Bulanov, S V 2002-01-01 The feasibility of using the laser plasma as a source of the high-energy ions for the proton radiation therapy is discussed. The proposal is based on the recent inventions of the effective ions acceleration in the experiments and through numerical modeling of the powerful laser radiation interaction with the gaseous and solid state targets. The principal peculiarity of the dependence of the protons energy losses in the tissues (the Bragg peak of losses) facilities the solution of one of the most important problems of the radiation therapy, which consists in realizing the tumor irradiation by sufficiently high and homogeneous dose with simultaneous minimization of the irradiation level, relative to the healthy and neighbouring tissues and organs 5. Report of the Accelerator Group: the light-ion injector International Nuclear Information System (INIS) 1984-01-01 Good progress was made on the various sub-systems of the light-ion injector cyclotron SPC1. The radio-frequency system, which consists of the two resonators (each with a 25 kW power amplifier) and the stabilization and control system was completed. Orbit calculations were used to determine the phase selection attainable from the combined axial and radial slits, and also to give an indication of the momentum selection which could be achieved using the radial slits. The detail design of all the extraction elements, i.e. the eletrostatic extraction channel EEK and two magnetic channel MEK1 and MEK2 has been completed. On the 15th December 1983, the first beams of ions were accelerated in SPC1. The following subsystems of SPC1 are discussed: magnets, radio-frequency systems, orbit calculations of the phase section, extraction process, vacuum system and beam diagnostics 6. Growth of nanocomposite films from accelerated C60 ions International Nuclear Information System (INIS) Pukha, V E; Zubarev, E N; Drozdov, A N; Pugachov, A T; Jeong, S H; Nam, S C 2012-01-01 A beam of accelerated C 60 ions is used to deposit superhard (∼50 GPa) carbon films that exhibit high index plasticity (∼0.13-0.14) and high conductivity (up to 3000 S m -1 ). Transmission electron microscopy, Raman spectroscopy and x-ray photoelectron spectroscopy are subsequently used to study the microstructure and bond character of the deposited films. The films consist of textured graphite nanocrystals and diamond-like amorphous carbon (DLC). The graphene plane of the nanocrystals is aligned perpendicular to the film surface. It is shown that sp 2 bonds dominate in the films. The percentage of sp 3 bonds depends on the ion energy and the substrate temperature, and does not exceed 40%. The obtained results suggest that a new nanocomposite material consisting of oriented graphite nanocrystals reinforced by a DLC matrix is synthesized. A simple model is proposed to correlate the excellent mechanical properties with the observed structure. (paper) 7. Improved ion acceleration via laser surface plasma waves excitation Energy Technology Data Exchange (ETDEWEB) Bigongiari, A. [CEA/DSM/LSI, CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex (France); TIPS/LULI, Université Paris 6, CNRS, CEA, Ecole Polytechnique, 3, rue Galilée, 94200 Ivry-sur-Seine (France); Raynaud, M. [CEA/DSM/LSI, CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex (France); Riconda, C. [TIPS/LULI, Université Paris 6, CNRS, CEA, Ecole Polytechnique, 3, rue Galilée, 94200 Ivry-sur-Seine (France); Héron, A. [CPHT, CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex (France) 2013-05-15 The possibility of enhancing the emission of the ions accelerated in the interaction of a high intensity ultra-short (<100 fs) laser pulse with a thin target (<10λ{sub 0}), via surface plasma wave excitation is investigated. Two-dimensional particle-in-cell simulations are performed for laser intensities ranging from 10{sup 19} to 10{sup 20} Wcm{sup −2}μm{sup 2}. The surface wave is resonantly excited by the laser via the coupling with a modulation at the target surface. In the cases where the surface wave is excited, we find an enhancement of the maximum ion energy of a factor ∼2 compared to the cases where the target surface is flat. 8. Development of a dual ion beam system with single accelerator for materials studies International Nuclear Information System (INIS) Suzuki, Kazumichi; Nishimura, Eiichi; Hashimoto, Tsuneyuki 1986-01-01 The dual ion beam accelerator system has been developed for simulation studies of neutron radiation damage of structural materials for nuclear fusion and fission reactors. One accelerator is used to accelerate two different kinds of ions, which are generated in the ion source simultaneously. One of these ions is selected alternatively by switching the magnetic field of the analyzing magnet, and is then accelerated to the desired energy value. The system is controlled by a microcomputer. The accelerator used in the system is a conventional 400 kV Cockcroft-Walton accelerator. The performance test by the acceleration of He + and Ar + shows that the system is capable of accelerating two ions alternatively with a switching time of less than 22 s. The beam current obtained with the microcomputer control is more than 98% of the current obtained by manual operation. (orig.) 9. Vacuum improvements for ultra high charge state ion acceleration International Nuclear Information System (INIS) Xie, Z.Q.; Lyneis, C.M.; Clark, D.J.; Guy, A.; Lundgren, S.A 1998-06-01 The installation of a second cryo panel has significantly improved the vacuum in the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory. The neutral pressure in the extraction region decreased from 1.2 x 10 -6 down to about 7 x 10 -7 Torr. The vacuum improvement reduces beam loss from charge changing collisions and enhances the cyclotron beam transmission, especially for the high charge state heavy ions. Tests with improved vacuum show the cyclotron transmission increased more than 50% (from 5.7% to 9.0%) for a Xe 27+ at 603 MeV, more than doubled for a Bi 41+ beam (from 1.9% to 4.6%) at 904 MeV and tripled for a U 47+ beam (from 1.2% to 3.6%) at 1,115 MeV. At about 5 NeV/nucleon 92 enA (2.2 pnA) for Bi 41+ and 14 enA (0.3 pnA) for U 47+ were extracted ut of the 88-Inch Cyclotron Ion beams with charge states as high as U 64+ have been produced by the LBNL AECR-U ion source and accelerated through the cyclotron for the first time. The beam losses for a variety of ultra high charge state ions were measured as a function of cyclotron pressure and compared with the calculations from the existing models 10. Vacuum improvements for ultra high charge state ion acceleration International Nuclear Information System (INIS) Xie, Z.Q.; Lyneis, C.M.; Clark, D.J.; Guy, A.; Lundgren, S.A. 1999-01-01 The installation of a second cryo panel has significantly improved the vacuum in the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory. The neutral pressure in the extraction region decreased from 1.2 x 10 -6 down to about 7 x 10 -7 Torr. The vacuum improvement reduces beam loss from charge changing collisions and enhances the cyclotron beam transmission, especially for the high charge state heavy ions. Tests with improved vacuum show the cyclotron transmission increased more than 50% (from 5.7% to 9.0%) for a Xe 27+ at 603 MeV, more than doubled for a Bi 41+ beam (from 1.9% % to 4.6%) at 904 MeV and tripled for a U 47+ beam (from 1.2% to 3.6%) at 1115 MeV. At about 5 MeV/nucleon 92 enA (2.2 pnA) for Bi 41+ and 14 enA (0.3 pnA) for U 47+ were extracted out of the 88-Inch Cyclotron Ion beams with charge states as high as U 64+ have been produced by the LBNL AECR-U ion source and accelerated through the cyclotron for the first time. The beam losses for a variety of ultra high charge state ions were measured as a function of cyclotron pressure and compared with the calculations from the existing models. (authors) 11. Visualization of complex DNA damage along accelerated ions tracks Science.gov (United States) Kulikova, Elena; Boreyko, Alla; Bulanova, Tatiana; Ježková, Lucie; Zadneprianetc, Mariia; Smirnova, Elena 2018-04-01 The most deleterious DNA lesions induced by ionizing radiation are clustered DNA double-strand breaks (DSB). Clustered or complex DNA damage is a combination of a few simple lesions (single-strand breaks, base damage etc.) within one or two DNA helix turns. It is known that yield of complex DNA lesions increases with increasing linear energy transfer (LET) of radiation. For investigation of the induction and repair of complex DNA lesions, human fibroblasts were irradiated with high-LET 15N ions (LET = 183.3 keV/μm, E = 13MeV/n) and low-LET 60Co γ-rays (LET ≈ 0.3 keV/μm) radiation. DNA DSBs (γH2AX and 53BP1) and base damage (OGG1) markers were visualized by immunofluorecence staining and high-resolution microscopy. The obtained results showed slower repair kinetics of induced DSBs in cells irradiated with accelerated ions compared to 60Co γ-rays, indicating induction of more complex DNA damage. Confirming previous assumptions, detailed 3D analysis of γH2AX/53BP1 foci in 15N ions tracks revealed more complicated structure of the foci in contrast to γ-rays. It was shown that proteins 53BP1 and OGG1 involved in repair of DNA DSBs and modified bases, respectively, were colocalized in tracks of 15N ions and thus represented clustered DNA DSBs. 12. The wondrous world of transport and acceleration of intense ion beams International Nuclear Information System (INIS) Siebenlist, F. 1987-01-01 A theoretical and experimental study of the transport, bunching and acceleration of intense ion beams in periodic focusing channels is described. The aim is to show the feasibility of accelerating high current ion beams with a Multiple Electrostatic Quadrupole Array Linear ACcelerator (MEQALAC). 83 refs.; 51 figs.; 3 tabs 13. Measurement of heat load density profile on acceleration grid in MeV-class negative ion accelerator. Science.gov (United States) Hiratsuka, Junichi; Hanada, Masaya; Kojima, Atsushi; Umeda, Naotaka; Kashiwagi, Mieko; Miyamoto, Kenji; Yoshida, Masafumi; Nishikiori, Ryo; Ichikawa, Masahiro; Watanabe, Kazuhiro; Tobari, Hiroyuki 2016-02-01 To understand the physics of the negative ion extraction/acceleration, the heat load density profile on the acceleration grid has been firstly measured in the ITER prototype accelerator where the negative ions are accelerated to 1 MeV with five acceleration stages. In order to clarify the profile, the peripheries around the apertures on the acceleration grid were separated into thermally insulated 34 blocks with thermocouples. The spatial resolution is as low as 3 mm and small enough to measure the tail of the beam profile with a beam diameter of ∼16 mm. It was found that there were two peaks of heat load density around the aperture. These two peaks were also clarified to be caused by the intercepted negative ions and secondary electrons from detailed investigation by changing the beam optics and gas density profile. This is the first experimental result, which is useful to understand the trajectories of these particles. 14. Measurement of heat load density profile on acceleration grid in MeV-class negative ion accelerator Energy Technology Data Exchange (ETDEWEB) Hiratsuka, Junichi, E-mail: [email protected]; Hanada, Masaya; Kojima, Atsushi; Umeda, Naotaka; Kashiwagi, Mieko; Yoshida, Masafumi; Nishikiori, Ryo; Ichikawa, Masahiro; Watanabe, Kazuhiro; Tobari, Hiroyuki [Japan Atomic Energy Agency, 801-1 Mukoyama, Naka 311-0193 (Japan); Miyamoto, Kenji [Naruto University of Education, 748 Nakashima, Takashima, Naruto-cho, Naruto-shi, Tokushima 772-8502 (Japan) 2016-02-15 To understand the physics of the negative ion extraction/acceleration, the heat load density profile on the acceleration grid has been firstly measured in the ITER prototype accelerator where the negative ions are accelerated to 1 MeV with five acceleration stages. In order to clarify the profile, the peripheries around the apertures on the acceleration grid were separated into thermally insulated 34 blocks with thermocouples. The spatial resolution is as low as 3 mm and small enough to measure the tail of the beam profile with a beam diameter of ∼16 mm. It was found that there were two peaks of heat load density around the aperture. These two peaks were also clarified to be caused by the intercepted negative ions and secondary electrons from detailed investigation by changing the beam optics and gas density profile. This is the first experimental result, which is useful to understand the trajectories of these particles. 15. Experimental Study of an ion cyclon resonance accelerator presentation of his thesis CERN Document Server Ramsell, C T 1999-01-01 The Ion Cyclotron Resonance Accelerator (ICRA) uses the operating principles of cyclotrons and gyrotrons. The novel geometry of the ICRA allows an ion beam to drift axially while being accelerated in the azimuthal direction. Previous work on electron cyclotron resonance acceleration used waveguide modes to accelerate an electron beam [5]. This research extends cyclotron resonance acceleration to ions by using a high field superconducting magnet and an rf driven magnetron operating at a harmonic of the cyclotron frequency. The superconducting solenoid provides an axial magnetic field for radial confinement and an rf driven magnetron provides azimuthal electric fields for acceleration. The intent of the ICRA concept is to create an ion accelerator which is simple, compact, lightweight, and inexpensive. Furthermore, injection and extraction are inherently simple since the beam drifts through the acceleration region. However, use of this convenient geometry leads to an accelerated beam with a large energy spread.... 16. Sequestration Resins for Accelerating Removal of Radioactive Contaminants International Nuclear Information System (INIS) Frattini, Paul-L.; Wells, Daniel-M.; Garcia, Susan-E.; Richard, Kohlmann; Asay, Roger; Yengoyan, Leon 2012-09-01 The Electric Power Research Institute (EPRI) is developing sequestration resins that can be used in the treatment of nuclear plant water streams for the enhanced removal of ionic cobalt. EPRI is focusing on three key areas of success: 1. Plant safety. The resins that are synthesized must be fully tested to determine that no leachable species or decomposition products (in the event of a resin bed failure) would be introduced to the plant. 2. Acceptable system performance. The resins are currently being synthesized in a powdered form for use in the reactor water clean-up and fuel pool clean-up systems that utilize pre-coatable filter elements. The resins must have effective flocking behavior; uniform application over the underlay resin and efficient removal from the septa elements after use. Bead type resins are also under development. 3. Enhanced cobalt removal. The resins are expected to out-perform the currently used ion exchange resins in the removal of ionic cobalt. During nuclear plant maintenance or refueling outages, current ion exchange resins may require several days to reduce concentrations of cobalt (for example, radio-cobalt 60 Co and 58 Co) and other activated corrosion products to safe levels in reactor coolant streams. This performance limitation often delays key maintenance activities. EPRI's resins are expected to provide at least a three-fold increase in removal capacity in light water reactor coolants. These resins also offer the potential for higher overall removal efficiencies reducing occupational exposures and waste management costs. This paper addresses issues from the range of novel resin development for radio-cobalt removal from synthesis at the bench-top level through scale-up to demonstration of use in an actual operating nuclear power plant. (authors) 17. Modeling of multi-species ion transport in cement-based materials for radioactive waste container International Nuclear Information System (INIS) Pang, X.Y.; Li, K.F.; Dangla, P. 2015-01-01 Through the conservations of heat and ions mass, a thermo-hydro-ionic model is established for radionuclide ions transport in cement-based porous barrier materials in radwaste disposal. This model is applied to the design and the safety assessment of a high-integrity container (HIC) used for near surface disposal of low- and intermediate-level radwaste. Five working cases are investigated in the safety assessment considering the internal nuclide ion release, internal heating and pressure accumulation, and external leaching. Comparative analysis shows that leaching increases concrete porosity from external side of container, internal heating of 10 K increase can considerably accelerate the nuclide transport process, and the internal pressure increases the transport rate to limited extent. It is shown that each increment of 10 mm in wall thickness will reduce the radioactivity release by 1.5 to 2 times. Together with the mechanical resistance of HIC under impact actions, the thickness of 100 mm is finally retained for design 18. Ion beam production and study of radioactive isotopes with the laser ion source at ISOLDE Science.gov (United States) Fedosseev, Valentin; Chrysalidis, Katerina; Day Goodacre, Thomas; Marsh, Bruce; Rothe, Sebastian; Seiffert, Christoph; Wendt, Klaus 2017-08-01 At ISOLDE the majority of radioactive ion beams are produced using the resonance ionization laser ion source (RILIS). This ion source is based on resonant excitation of atomic transitions by wavelength tunable laser radiation. Since its installation at the ISOLDE facility in 1994, the RILIS laser setup has been developed into a versatile remotely operated laser system comprising state-of-the-art solid state and dye lasers capable of generating multiple high quality laser beams at any wavelength in the range of 210-950 nm. A continuous programme of atomic ionization scheme development at CERN and at other laboratories has gradually increased the number of RILIS-ionized elements. At present, isotopes of 40 different elements have been selectively laser-ionized by the ISOLDE RILIS. Studies related to the optimization of the laser-atom interaction environment have yielded new laser ion source types: the laser ion source and trap and the versatile arc discharge and laser ion source. Depending on the specific experimental requirements for beam purity or versatility to switch between different ionization mechanisms, these may offer a favourable alternative to the standard hot metal cavity configuration. In addition to its main purpose of ion beam production, the RILIS is used for laser spectroscopy of radioisotopes. In an ongoing experimental campaign the isotope shifts and hyperfine structure of long isotopic chains have been measured by the extremely sensitive in-source laser spectroscopy method. The studies performed in the lead region were focused on nuclear deformation and shape coexistence effects around the closed proton shell Z = 82. The paper describes the functional principles of the RILIS, the current status of the laser system and demonstrated capabilities for the production of different ion beams including the high-resolution studies of short-lived isotopes and other applications of RILIS lasers for ISOLDE experiments. This article belongs to the Focus on 19. Unlimited Energy Gain in the Laser-Driven Radiation Pressure Dominant Acceleration of Ions OpenAIRE Bulanov, S. V.; Echkina, E. Yu.; Esirkepov, T. Zh.; Inovenkov, I. N.; Kando, M.; Pegoraro, F.; Korn, G. 2009-01-01 The energy of the ions accelerated by an intense electromagnetic wave in the radiation pressure dominated regime can be greatly enhanced due to a transverse expansion of a thin target. The expansion decreases the number of accelerated ions in the irradiated region increasing the energy and the longitudinal velocity of remaining ions. In the relativistic limit, the ions become phase-locked with respect to the electromagnetic wave resulting in the unlimited ion energy gain. This effect and the ... 20. A 1MeV, 1A negative ion accelerator test facility International Nuclear Information System (INIS) Hanada, M.; Dairaku, M.; Inoue, T.; Miyamoto, K.; Ohara, Y.; Okumura, Y.; Watanabe, K.; Yokoyama, K. 1995-01-01 For the Proof-of-Principle test of negative ion acceleration up to 1 MeV, the beam energy required for ITER, a negative ion test facility named MeV Test Facility (MTF) and an ion source/accelerator have been designed and constructed. They are designed to produce a 1 MeV H- beam at a low source pressure of 0.13Pa. The MTF has a power supply system, which constituts of a 1MV, 1A, 60 s Cockcroft-Walton type dc high energy generator and power supplies for negative ion generation and extraction (ion source power supplies). The negative ion source/accelerator is composed of a cesiated volume source and a 5-stage, multi-aperture, electrostatic accelerator. The MTF and the ion source/accelerator have been completed, and the accelertion test up to 1 MeV of the H- ions has started. (orig.) 1. The Radioactive Ion Beams in Brazil (RIBRAS) facility. Description, program, main results, future plans Energy Technology Data Exchange (ETDEWEB) Lepine-Szily, A.; Lichtenthaeler, R.; Guimaraes, V. [Instituto de Fisica, Universidade de Sao Paulo (Brazil) 2014-08-15 RIBRAS (Radioactive Ion Beams in Brazil) is a facility installed at the Institute of Physics of the University of Sao Paulo (IFUSP), Brazil. The RIBRAS system consists of two superconducting solenoids and uses the ''in-flight method'' to produce radioactive ion beams using the primary beam provided by the 8UD Pelletron Tandem of IFUSP. The ion beams produced so far by RIBRAS are {sup 6}He, {sup 8}Li, {sup 7}Be, {sup 10}Be, {sup 8}B, {sup 12}B with intensities that can vary from 10{sup 4} to 10{sup 6} pps. Initially the experimental program covered the study of elastic and inelastic scattering with the objective to study the interaction potential and the reaction mechanisms between weakly bound (RIB) and halo ({sup 6}He and {sup 8}B) projectiles on light, medium and heavy mass targets. With highly purified beams, the study of resonant elastic scattering and resonant transfer reactions, using inverse kinematics and thick targets, has also been included in our experimental program. Also, transfer reactions of astrophysical interest and fusion reactions induced by halo nuclei are part of the near-future research program. Our recent results on elastic scattering, alpha-particle production and total reaction cross sections, as well as the resonant elastic and transfer reactions, are presented. Our plans for the near future are related to the installation of a new beam line and a cave for gamma-ray detection. We intend to place in operation a large area neutron detector available in our laboratory. The long-range plans could be the move of the RIBRAS system to the more energetic beam line of the LINAC post-accelerator (10MeV/nucleon primary beams) still in construction in our laboratory. (orig.) 2. The Radioactive Ion Beams in Brazil (RIBRAS) facility. Description, program, main results, future plans Science.gov (United States) Lépine-Szily, A.; Lichtenthäler, R.; Guimarães, V. 2014-08-01 RIBRAS (Radioactive Ion Beams in Brazil) is a facility installed at the Institute of Physics of the University of São Paulo (IFUSP), Brazil. The RIBRAS system consists of two superconducting solenoids and uses the "in-flight method" to produce radioactive ion beams using the primary beam provided by the 8UD Pelletron Tandem of IFUSP. The ion beams produced so far by RIBRAS are 6He, 8Li, 7Be, 10Be, 8B, 12B with intensities that can vary from 104 to 106 pps. Initially the experimental program covered the study of elastic and inelastic scattering with the objective to study the interaction potential and the reaction mechanisms between weakly bound (RIB) and halo (6He and 8B projectiles on light, medium and heavy mass targets. With highly purified beams, the study of resonant elastic scattering and resonant transfer reactions, using inverse kinematics and thick targets, has also been included in our experimental program. Also, transfer reactions of astrophysical interest and fusion reactions induced by halo nuclei are part of the near-future research program. Our recent results on elastic scattering, alpha-particle production and total reaction cross sections, as well as the resonant elastic and transfer reactions, are presented. Our plans for the near future are related to the installation of a new beam line and a cave for gamma-ray detection. We intend to place in operation a large area neutron detector available in our laboratory. The long-range plans could be the move of the RIBRAS system to the more energetic beam line of the LINAC post-accelerator (10MeV/nucleon primary beams) still in construction in our laboratory. 3. Operation and control of ion-exchange processes for treatment of radioactive wastes International Nuclear Information System (INIS) Emelity, L.A. 1967-01-01 A manual dealing with the application of ion-exchange materials to the treatment of radioactive wastes and reviewing the facilities currently using this method. This book is one of three commissioned by the IAEA on the principal methods of concentrating radioactive wastes. The content of this document is: (i) Historical review related to removal of radioactivity; (ii) Principles of ion exchange (iii) Ion-exchange materials; (iv) Limitations of ion exchangers; (v) Application of ion exchange to waste processing; (vi) Operational procedures and experiences; (vii) Cost-of-treatment by ion-exchange. The document also gives a list of producers of ion-exchange material and defines some relevant terms. 101 refs, 31 figs, 27 tabs 4. Operation and control of ion-exchange processes for treatment of radioactive wastes Energy Technology Data Exchange (ETDEWEB) Emelity, L A [Los Alamos National Lab., NM (United States) 1967-12-01 A manual dealing with the application of ion-exchange materials to the treatment of radioactive wastes and reviewing the facilities currently using this method. This book is one of three commissioned by the IAEA on the principal methods of concentrating radioactive wastes. The content of this document is: (i) Historical review related to removal of radioactivity; (ii) Principles of ion exchange (iii) Ion-exchange materials; (iv) Limitations of ion exchangers; (v) Application of ion exchange to waste processing; (vi) Operational procedures and experiences; (vii) Cost-of-treatment by ion-exchange. The document also gives a list of producers of ion-exchange material and defines some relevant terms. 101 refs, 31 figs, 27 tabs. 5. Dynamic behavior of IREB in a collective ion acceleration experiment International Nuclear Information System (INIS) Fine, T.A.; Rhee, M.J. 1989-01-01 The authors report an experimental study of dynamic behavior of net current in conjunction with collective ion acceleration. In the presence of neutral gas, either puffed in or released from the anode foil, the IREB injected is subject to the charge and current neutralizations, resulting in a complicated time and space dependent beam distribution in the drift tube. To investigate the dynamic behavior of the current in the drift tube, typically a 0.5 MeV, 70 kA, 100 ns electron beam of 2.54 cm diam is injected through a foil anode into a drift tube of 15 cm diam. Reproducibility of experiment was improved by using a specially designed anode system with a foil changer which allowed the production of many shots of high current electron beam without disturbing the vacuum condition. The net currents were measured by a Rogowski coil built in the anode system, and a movable Faraday cup along the drift tube. The ions accelerated were diagnosed mainly by a Thomson spectrometer system placed at the end of the drift tube 6. Technology development for recirculating heavy-ion accelerators International Nuclear Information System (INIS) Newton, M.A.; Kirbie, H.C. 1993-01-01 The open-quotes recirculator,close quotes a recirculating heavy-ion accelerator has been identified as a promising approach for an inertial fusion driver. System studies have been conducted to evaluate the recirculator on the basis of feasibility and cost. The recirculator has been shown to have significant cost advantages over other potential driver schemes, but some of the performance requirements exceed the capabilities of present technology. The system studies identified the high leverage areas where advances in technology will significantly impact the cost and performance of a recirculator. One of the high leverage areas is the modulator system which generates the acceleration potentials in the induction cells. The modulator system must be capable of generating the acceleration potentials at peak repetition rates in excess of 100 kHz with variable pulse widths. LLNL is developing a modulator technology capable of driving induction cells using the latest in solid state MOSFET technology. A small scale modulator has been built and tested to prove the concept and the next version is presently being designed. The objective is to demonstrate a modulator operating at 5 kV, 1 kA, with 0.2--1 μs pulse widths while driving an induction cell at >100 kHz within the next year. This paper describes the recirculator, the technology requirements necessary to implement it and the modulator system development that is being pursued to meet these requirements 7. Basic atomic interactions of accelerated heavy ions in matter atomic interactions of heavy ions CERN Document Server Tolstikhina, Inga; Winckler, Nicolas; Shevelko, Viacheslav 2018-01-01 This book provides an overview of the recent experimental and theoretical results on interactions of heavy ions with gaseous, solid and plasma targets from the perspective of atomic physics. The topics discussed comprise stopping power, multiple-electron loss and capture processes, equilibrium and non-equilibrium charge-state fractions in penetration of fast ion beams through matter including relativistic domain. It also addresses mean charge-states and equilibrium target thickness in ion-beam penetrations, isotope effects in low-energy electron capture, lifetimes of heavy ion beams, semi-empirical formulae for effective cross sections. The book is intended for researchers and graduate students working in atomic, plasma and accelerator physics. 8. Auroral ion acceleration from lower hybrid solitary structures: A summary of sounding rocket observations Science.gov (United States) Lynch, K. A.; Arnoldy, R. L.; Kintner, P. M.; Schuck, P.; Bonnell, J. W.; Coffey, V. In this paper we present a review of sounding rocket observations of the ion acceleration seen in nightside auroral zone lower hybrid solitary structures. Observations from Topaz3, Amicist, and Phaze2 are presented on various spatial scales, including the two-point measurements of the Amicist mission. From this collection of observations we will demonstrate the following characteristics of transverse acceleration of ions (TAI) in lower hybrid solitary structures (LHSS). The ion acceleration process is narrowly confined to 90° pitch angle, in spatially confined regions of up to a few hundred meters across B. The acceleration process does not affect the thermal core of the ambient distribution and does not directly create a measurable effect on the ambient ion population outside the LHSS themselves. This precludes observation with these data of any nonlinear feedback between the ion acceleration and the existence or evolution of the density irregularities on which these LHSS events grow. Within the LHSS region the acceleration process creates a high-energy tail beginning at a few times the thermal ion speed. The ion acceleration events are closely associated with localized wave events. Accelerated ions bursts are also seen without a concurrent observation of a localized wave event, for two possible reasons. In some cases, the pitch angles of the accelerated tail ions are elevated above perpendicular; that is, the acceleration occurred below the observer and the mirror force has begun to act upon the distribution, moving it upward from the source. In other cases, the accelerated ion structure is spatially larger than the wave event structure, and the observation catches only the ion event. The occurrence rate of these ion acceleration events is related to the ambient environment in two ways: its altitude dependence can be modeled with the parameter B2/ne, and it is highest in regions of intense VLF activity. The cumulative ion outflow from these LHSS TAI is 9. Submicro and Nano Structured Porous Materials for the Production of High-Intensity Exotic Radioactive Ion Beams CERN Document Server Fernandes, Sandrina; Stora, Thierry 2010-01-01 ISOLDE, the CERN Isotope Separator On-line DEvice is a unique source of low energy beams of radioactive isotopes - atomic nuclei that have too many or too few neutrons to be stable. The facility is like a small ‘chemical factory’, giving the possibility of changing one element to another, by selecting the atomic mass of the required isotope beam in the mass separator, rather as the ‘alchemists’ once imagined. It produces a total of more than 1000 different isotopes from helium to radium, with half-lives down to milliseconds, by impinging a 1.4 GeV proton beam from the Proton Synchrotron Booster (PSB) onto special targets, yielding a wide variety of atomic fragments. Different components then extract the nuclei and separate them according to mass. The post-accelerator REX (Radioactive beam EXperiment) at ISOLDE accelerates the radioactive beams up to 3 MeV/u for many experiments. A wide international user radioactive ion beam (RIB) community investigates fundamental aspects of nuclear physics, particle... 10. Linear induction accelerator requirements for ion fast ignition International Nuclear Information System (INIS) Logan, G. 1998-01-01 Fast ignition (fast heating of DT cores afief compression) reduces driver energy (by 10 X or more) by reducing the implosion velocity and energy for a given fuel compression ratio. For any type of driver that can deliver the ignition energy fast enough, fast ignition increases the target gain compared to targets using fast implosions for central ignition, as long as the energy to heat the core after compression is comparable to or less than the slow compression energy, and as long as the coupling efficiency of the fast ignitor beam to heat the core is comparable to the overall efficiency of compressing the core (in terms of beam energy-to-DT-efficiency). Ion driven fast ignition, compared to laser-driven fast ignition, has the advantage of direct (dE/dx) deposition of beam energy to the DT, eliminating inefficiencies for conversion into hot electrons, and direct ion heating also has a more favorable deposition profile with the Bragg-peak near the end of an ion range chosen to be deep inside a compressed DT core. While Petawatt laser experiments at LLNL have demonstrated adequate light-to-hot-electron conversion efficiency, it is not yet known if light and hot electrons can channel deeply enough to heat a small portion of a IOOOxLD compressed DT core to ignition. On the other hand, lasers with chirped-pulse amplification giving thousand-fold pulse compressions have been demonstrated to produce the short pulses, small focal spots and Petawatt peak powers approaching those required for fast ignition, whereas ion accelerators that can produce sufficient beam quality for similar compression ratios and focal spot sizes of ion bunches have not yet been demonstrated, where an imposed coherent velocity tilt plays the analogous role for beam compression as does frequency chirp with lasers. Accordingly, it is the driver technology, not the target coupling physics, that poses the main challenge to ion-driven fast ignition. As the mainline HIF program is concentrating on 11. Low-energy radioactive ion beam production of 22Mg International Nuclear Information System (INIS) Duy, N.N.; Kubono, S.; Yamaguchi, H.; Kahl, D.; Wakabayashi, Y.; Teranishi, T.; Iwasa, N.; Kwon, Y.K.; Khiem, L.H.; Kim, Y.H.; Song, J.S.; Hu, J.; Ayyad, Y. 2013-01-01 The 22 Mg nucleus plays an important role in nuclear astrophysics, specially in the 22 Mg(α,p) 25 Al and proton capture 22 Mg(p,γ) 23 Al reactions. It is believed that 22 Mg is a waiting point in the αp-process of nucleosynthesis in novae. We proposed a direct measurement of the 22 Mg+α resonance reaction in inverse kinematics using a radioactive ion (RI) beam. A 22 Mg beam of 3.73 MeV/u was produced at CRIB (Center for Nuclear Study (CNS) low-energy RI Beam) facility of the University of Tokyo located at RIKEN (Japan) in 2011. In this paper we present the results about the production of the 22 Mg beam used for the direct measurement of the scattering reaction 22 Mg(α,α) 22 Mg, and the stellar reaction 22 Mg(α,p) 25 Al in the energy region concerning an astrophysical temperature of T 9 =1–3 GK 12. Accelerated radiation damage test facility using a 5 MV tandem ion accelerator Science.gov (United States) Wady, P. T.; Draude, A.; Shubeita, S. M.; Smith, A. D.; Mason, N.; Pimblott, S. M.; Jimenez-Melero, E. 2016-01-01 We have developed a new irradiation facility that allows to perform accelerated damage tests of nuclear reactor materials at temperatures up to 400 °C using the intense proton (spectrum of potential radio-active nuclides produced during the sample irradiation. The beam line capabilities have been tested by irradiating a 20Cr-25Ni-Nb stabilised stainless steel with a 3 MeV proton beam to a dose level of 3 dpa. The irradiation temperature was 356 °C, with a maximum range in temperature values of ±6 °C within the first 24 h of continuous irradiation. The sample stage is connected to ground through an electrometer to measure accurately the charge deposited on the sample. The charge can be integrated in hardware during irradiation, and this methodology removes uncertainties due to fluctuations in beam current. The measured gamma spectrum allowed the identification of the main radioactive nuclides produced during the proton bombardment from the lifetimes and gamma emissions. This dedicated radiation damage beam line is hosted by the Dalton Cumbrian Facility of the University of Manchester. 13. Modification of semiconductor materials using laser-produced ion streams additionally accelerated in the electric fields International Nuclear Information System (INIS) Rosinski, M.; Badziak, B.; Parys, P.; Wolowski, J.; Pisarek, M. 2009-01-01 The laser-produced ion stream may be attractive for direct ultra-low-energy ion implantation in thin layer of semiconductor for modification of electrical and optical properties of semiconductor devices. Application of electrostatic fields for acceleration and formation of laser-generated ion stream enables to control the ion stream parameters in broad energy and current density ranges. It also permits to remove the useless laser-produced ions from the ion stream designed for implantation. For acceleration of ions produced with the use of a low fluence repetitive laser system (Nd:glass: 2 Hz, pulse duration: 3.5 ns, pulse energy:∼0.5 J, power density: 10 10 W/cm 2 ) in IPPLM the special electrostatic system has been prepared. The laser-produced ions passing through the diaphragm (a ring-shaped slit in the HV box) have been accelerated in the system of electrodes. The accelerating voltage up to 40 kV, the distance of the diaphragm from the target, the diaphragm diameter and the gap width were changed for choosing the desired parameters (namely the energy band of the implanted ions) of the ion stream. The characteristics of laser-produced Ge ion streams were determined with the use of precise ion diagnostic methods, namely: electrostatic ion energy analyser and various ion collectors. The laser-produced and post-accelerated Ge ions have been used for implantation into semiconductor materials for nanocrystal fabrication. The characteristics of implanted samples were measured using AES 14. A new approach to characterize very-low-level radioactive waste produced at hadron accelerators International Nuclear Information System (INIS) Zaffora, Biagio; Magistris, Matteo; Chevalier, Jean-Pierre; Luccioni, Catherine; Saporta, Gilbert; Ulrici, Luisa 2017-01-01 Radioactive waste is produced as a consequence of preventive and corrective maintenance during the operation of high-energy particle accelerators or associated dismantling campaigns. Their radiological characterization must be performed to ensure an appropriate disposal in the disposal facilities. The radiological characterization of waste includes the establishment of the list of produced radionuclides, called “radionuclide inventory”, and the estimation of their activity. The present paper describes the process adopted at CERN to characterize very-low-level radioactive waste with a focus on activated metals. The characterization method consists of measuring and estimating the activity of produced radionuclides either by experimental methods or statistical and numerical approaches. We adapted the so-called Scaling Factor (SF) and Correlation Factor (CF) techniques to the needs of hadron accelerators, and applied them to very-low-level metallic waste produced at CERN. For each type of metal we calculated the radionuclide inventory and identified the radionuclides that most contribute to hazard factors. The methodology proposed is of general validity, can be extended to other activated materials and can be used for the characterization of waste produced in particle accelerators and research centres, where the activation mechanisms are comparable to the ones occurring at CERN. - Highlights: • We developed a radiological characterization process for radioactive waste produced at particle accelerators. • We used extensive numerical experimentations and statistical analysis to predict a complete list of radionuclides in activated metals. • We used the new approach to characterize and dispose of more than 420 t of very-low-level radioactive waste. 15. Regulation of naturally occurring and accelerator-produced radioactive materials. A Task Force review International Nuclear Information System (INIS) Nussbaumer, D.A.; Lubenau, J.O.; Cool, W.S.; Cunningham, L.J.; Mapes, J.R.; Schwartz, S.A.; Smith, D.A. 1977-06-01 The use of accelerator-produced radioisotopes (NARM), particularly in medicine, is growing rapidly. One NARM radioisotope, 226 Ra, is one of the most hazardous of radioactive materials, and 226 Ra is used by about 1 / 5 of all radioactive material users. Also, there are about 85,000 medical treatments using 226 Ra each year. All of the 25 Agreement States and 5 non-Agreement States have licensing programs covering NARM users. The Agreement States' programs for regulating NARM are comparable to their programs for regulating byproduct, source, and special nuclear materials under agreements with NRC. But there are 7 states who exercise no regulatory control over NARM users, and the remaining States have control programs which are variable in scope. There are no national, uniformly applied programs to regulate the design, fabrication and quality of sources and devices containing NARM or consumer products containing NARM which are distributed in interstate commerce. Naturally occurring radioactive material (except source material) associated with the nuclear fuel cycle is only partially subject to NRC regulation, i.e., when it is associated with source or special nuclear material being used under an active NRC license. The Task Force recommends that the NRC seek legislative authority to regulate naturally occurring and accelerator-produced radioactive materials for the reason that these materials present significant radiation exposure potential and present controls are fragmentary and non-uniform at both the State and Federal level 16. Development of a simple, low cost, indirect ion beam fluence measurement system for ion implanters, accelerators Science.gov (United States) Suresh, K.; Balaji, S.; Saravanan, K.; Navas, J.; David, C.; Panigrahi, B. K. 2018-02-01 We developed a simple, low cost user-friendly automated indirect ion beam fluence measurement system for ion irradiation and analysis experiments requiring indirect beam fluence measurements unperturbed by sample conditions like low temperature, high temperature, sample biasing as well as in regular ion implantation experiments in the ion implanters and electrostatic accelerators with continuous beam. The system, which uses simple, low cost, off-the-shelf components/systems and two distinct layers of in-house built softwarenot only eliminates the need for costly data acquisition systems but also overcomes difficulties in using properietry software. The hardware of the system is centered around a personal computer, a PIC16F887 based embedded system, a Faraday cup drive cum monitor circuit, a pair of Faraday Cups and a beam current integrator and the in-house developed software include C based microcontroller firmware and LABVIEW based virtual instrument automation software. The automatic fluence measurement involves two important phases, a current sampling phase lasting over 20-30 seconds during which the ion beam current is continuously measured by intercepting the ion beam and the averaged beam current value is computed. A subsequent charge computation phase lasting 700-900 seconds is executed making the ion beam to irradiate the samples and the incremental fluence received by the sampleis estimated usingthe latest averaged beam current value from the ion beam current sampling phase. The cycle of current sampling-charge computation is repeated till the required fluence is reached. Besides simplicity and cost-effectiveness, other important advantages of the developed system include easy reconfiguration of the system to suit customisation of experiments, scalability, easy debug and maintenance of the hardware/software, ability to work as a standalone system. The system was tested with different set of samples and ion fluences and the results were verified using 17. Single event simulation for memories using accelerated ions International Nuclear Information System (INIS) Sakagawa, Y.; Shiono, N.; Mizusawa, T.; Sekiguchi, M.; Sato, K.; Sugai, I.; Hirao, Y.; Nishimura, J.; Hattori, T. 1987-01-01 To evaluate the error immunity of the LSI memories from cosmic rays in space, an irradiation test using accelerated heavy ions is performed. The sensitive regions for 64 K DRAM (Dynamic Random Access Memory) and 4 K SRAM (Static Random Access Memory) are determined from the irradiation test results and the design parameters of the devices. The observed errors can be classified into two types. One is the direct ionization type and the other is the recoil produced error type. Sensitive region is determined for the devices. Error rate estimation methods for both types are proposed and applied to those memories used in space. The error rate of direct ionization exceeds the recoil type by 2 or 3 orders. And the direct ionization is susceptible to shield thickness. (author) 18. Prospects for studies of ground-state proton decays with the Holifield Radioactive Ion Beam Facility International Nuclear Information System (INIS) Toth, K.S. 1994-01-01 By using radioactive ions from the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory it should be possible to identify many new ground-state proton emitters in the mass region from Sn to Pb. During this production and search process the limits of stability on the proton-rich side of the nuclidic chart will be delineated for a significant fraction of medium-weight elements and our understanding of the proton-emission process will be expanded and improved 19. Resistance-driven bunching mode of an accelerated ion pulse International Nuclear Information System (INIS) Lee, E.P. 1981-01-01 Amplification of a longitudinal perturbation of an ion pulse in a linear induction accelerator is calculated. The simplified accelerator model consists only of an applied field (E/sub a/), distributed gap impedance per meter (R) and beam-pipe capacity per meter (C). The beam is treated as a cold, one-dimensional fluid. It is found that normal mode frequencies are nearly real, with only a very small damping rate proportional to R. This result is valid for a general current profile and is not restricted to small R. However, the mode structure exhibits spatial amplification from pulse head to tail by the factor exp(RCLv/sub o//2), where L is pulse length and v 0 is drift velocity. This factor is very large for typical HIF parameters. An initially small disturbance, when expanded in terms of the normal modes, is found to oscillate with maximum amplitude proportional to the amplification factor. Unlike the analogous problem in a circular machine, linear growth is limited in amplitude bntegrating the void fraction profile and comparing the cross-sectionally averaged void fraction with direct measurements using two quick closing valves. Results on the calibration of combinations of full-flow turbine meters, Pitot tube rakes and gamma densitometers for measuring cross-sectionally averaged mass velocity in steady steam-water flow are presented. The results are interpreted ntation 20. Prototyping of beam position monitor for medium energy beam transport section of RAON heavy ion accelerator Energy Technology Data Exchange (ETDEWEB) Jang, Hyojae, E-mail: [email protected]; Jin, Hyunchang; Jang, Ji-Ho; Hong, In-Seok [Rare Isotope Science Project, Institute for Basic Science, Daejeon (Korea, Republic of) 2016-02-15 A heavy ion accelerator, RAON is going to be built by Rare Isotope Science Project in Korea. Its target is to accelerate various stable ions such as uranium, proton, and xenon from electron cyclotron resonance ion source and some rare isotopes from isotope separation on-line. The beam shaping, charge selection, and modulation should be applied to the ions from these ion sources because RAON adopts a superconducting linear accelerator structure for beam acceleration. For such treatment, low energy beam transport, radio frequency quadrupole, and medium energy beam transport (MEBT) will be installed in injector part of RAON accelerator. Recently, development of a prototype of stripline beam position monitor (BPM) to measure the position of ion beams in MEBT section is under way. In this presentation, design of stripline, electromagnetic (EM) simulation results, and RF measurement test results obtained from the prototyped BPM will be described. 1. Recommendation for a injector-cyclotron and ion sources for the acceleration of heavy ions and polarized protons and deuterons International Nuclear Information System (INIS) Botha, A.H.; Cronje, P.M.; Du Toit, Z.B.; Nel, W.A.G.; Celliers, P.J. 1984-01-01 It was decided to accelerate both heavy and light ions with the open-sector cyclotron. The injector SPS1, was used for light ions and SPS2 for heavy ions. Provision was also made for the acceleration of polarized neutrons. To enable this, the injector must have an axial injection system. The working of a source of polarized ions and inflectors for an axial injection system is discussed. The limitations of the open-sector cyclotron on the acceleration of heavy ions are also dealt with. The following acceleration/ion source combinations are discussed: i) The open-sector cyclotron and a k=40 injector cyclotron with a Penning ion source, and a stripper between the injector and the open-sector cyclotron and also a source of polarized protons and deuterons; ii) The acceleration/ion source combination with the addition of electron beam ion sources; iii) The open-sector cyclotron and a k=11 injector cyclotron with a electron beam ion source and a source of polarized protons and deuterons 2. Ion source memory in {sup 36}Cl accelerator mass spectrometry Energy Technology Data Exchange (ETDEWEB) Pavetich, Stefan; Akhmadaliev, Shavkat; Merchel, Silke; Rugel, Georg [HZDR, Dresden (Germany); Arnold, Maurice; Aumaitre, Georges; Bourles, Didier; Martschini, Martin [ASTER, Aix-en-Provence (France); Buchriegler, Josef; Golser, Robin; Keddadouche, Karim; Steier, Peter [VERA, Vienna (Austria) 2013-07-01 Since the DREAMS (Dresden Accelerator Mass Spectrometry) facility went operational in 2011, constant effort was put into enabling routine measurements of long-lived radionuclides as {sup 10}Be, {sup 26}Al and {sup 41}Ca. For precise AMS-measurements of the volatile element Cl the key issue is the minimization of the long term memory effect. For this purpose one of the two original HVE sources was mechanically modified, allowing the usage of bigger cathodes with individual target apertures. Additionally a more open geometry was used to improve the vacuum level. To evaluate this improvement in comparison to other up-to-date ion sources, a small inter-laboratory comparison had been initiated. The long-term memory effect in the Cs sputter ion sources of the AMS facilities VERA, ASTER and DREAMS had been investigated by running samples of natural {sup 35}Cl/{sup 37}Cl-ratio and samples containing highly enriched {sup 35}Cl({sup 35}Cl/{sup 37}Cl > 500). Primary goals of the research are the time constants of the recovery from the contaminated sample ratio to the initial ratio of the sample and the level of the long-term memory effect in the sources. 3. The steering and manipulation of ion beams for low-energy heavy ion accelerators International Nuclear Information System (INIS) Beanland, D.G.; Freeman, J.H. 1976-01-01 Both electrostatic and magnetic fields are used in low-energy accelerators. Electrostatic fields are essential in the acceleration stages and they are commonly used for ion beam scanning and focussing. Magnetic fields are only infrequently used as lenses, but they are essential for mass analysis and are sometimes employed for beam steering. The electrostatic mirror is a versatile and compact lens which has hitherto received little attention for the controlled manipulation of heavy ions. In addition to energy analysis it can be used to steer, focus and scan such beams and its flexibility and usefulness can be further increased by shaping the electrostatic field in the mirror space. The use of a computer programme to model the focussing behaviour of a variety of lens shapes is described and it is shown that the focal properties of the mirror can be controlled to produce a parallel, convergent or divergent output beam. The use of mirrors for two-dimensional beam focusing is also outlined. To permit the use of the mirror system with heavy ions an apertured front plate, without field-defining gauzes, was utilized. In consequence an additional electrode was incorporated in the lens structure to prevent penetration of the positive electric field along the beam axes outside the mirror space. This factor and the compact design of the mirror, contributed to the minimisation of space-charge defocussing effects which normally militate against the use of such electrostatic lenses with high intensity ion beams. The results of experiments confirming the computer predictions are briefly described and, in conclusion some possible applications of electrostatic mirrors in electromagnetic isotope separators and low energy accelerators are outlined. (Auth.) 4. Long-pulse beam acceleration of MeV-class H(-) ion beams for ITER NB accelerator. Science.gov (United States) Umeda, N; Kashiwagi, M; Taniguchi, M; Tobari, H; Watanabe, K; Dairaku, M; Yamanaka, H; Inoue, T; Kojima, A; Hanada, M 2014-02-01 In order to realize neutral beam systems in International Thermonuclear Experimental Reactor whose target is to produce a 1 MeV, 200 A/m(2) during 3600 s D(-) ion beam, the electrostatic five-stages negative ion accelerator so-called "MeV accelerator" has been developed at Japan Atomic Energy Agency. To extend pulse length, heat load of the acceleration grids was reduced by controlling the ion beam trajectory. Namely, the beam deflection due to the residual magnetic field of filter magnet was suppressed with the newly developed extractor with a 0.5 mm off-set aperture displacement. The new extractor improved the deflection angle from 6 mrad to 1 mrad, resulting in the reduction of direct interception of negative ions from 23% to 15% of the total acceleration power, respectively. As a result, the pulse length of 130 A/m(2), 881 keV H(-) ion beam has been successfully extended from a previous value of 0.4 s to 8.7 s. This is the first long pulse negative ion beam acceleration over 100 MW/m(2). 5. Application of ion exchange processes for the treatment of radioactive waste and management of spent ion exchangers International Nuclear Information System (INIS) 2002-01-01 This report describes the ion exchange technologies currently used and under development in nuclear industry, in particular for waste management practices, along with the experience gained in their application and with the subsequent handling, treatment and conditioning of spent ion exchange media for long term storage and/or disposal. The increased role of inorganic ion exchangers for treatment of radioactive liquid waste, both in nuclear power plant operations and in the fuel reprocessing sector, is recognised in this report. The intention of this report is to consolidate the previous publications, document recent developments and describe the state of the art in the application of ion exchange processes for the treatment of radioactive liquid waste and the management of spent ion exchange materials 6. Radiation protection challenges in the management of radioactive waste from high-energy accelerators. Science.gov (United States) Ulrici, Luisa; Algoet, Yvon; Bruno, Luca; Magistris, Matteo 2015-04-01 The European Laboratory for Particle Physics (CERN) has operated high-energy accelerators for fundamental physics research for nearly 60 y. The side-product of this activity is the radioactive waste, which is mainly generated as a result of preventive and corrective maintenance, upgrading activities and the dismantling of experiments or accelerator facilities. Prior to treatment and disposal, it is common practice to temporarily store radioactive waste on CERN's premises and it is a legal requirement that these storage facilities are safe and secure. Waste treatment typically includes sorting, segregation, volume and size reduction and packaging, which will depend on the type of component, its chemical composition, residual activity and possible surface contamination. At CERN, these activities are performed in a dedicated waste treatment centre under the supervision of the Radiation Protection Group. This paper gives an overview of the radiation protection challenges in the conception of a temporary storage and treatment centre for radioactive waste in an accelerator facility, based on the experience gained at CERN. The CERN approach consists of the classification of waste items into 'families' with similar radiological and physical-chemical properties. This classification allows the use of specific, family-dependent techniques for radiological characterisation and treatment, which are simultaneously efficient and compliant with best practices in radiation protection. The storage was planned on the basis of radiological and other possible hazards such as toxicity, pollution and fire load. Examples are given of technical choices for the treatment and radiological characterisation of selected waste families, which could be of interest to other accelerator facilities. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]. 7. Design of an Acceleration / Deceleration Lens System for Ion Beam Focusing Emerging from Penning Ion Source International Nuclear Information System (INIS) El-Khabeary, H. 2007-01-01 In this study, design of the deceleration lens system has been done by using SIMION 3D version 7.0 computer program. A parallel beam of singly charged argon ions of diameter 2. mm with energy of 5 KeV emerging from Penning ion source was started at a distance of 140 mm before entering the Einzel lens system (three cylinder electrodes ). In order to design this deceleration lens system, two and three cylinder lenses with different parameters are studied. Ion beam emittance as a function of the gap width of the deceleration lens system has been studied for singly charged argon ion trajectories. Influence of the deceleration voltage applied on the deceleration electrode with different voltages of the four electrodes on the ion beam emittance has been investigated with gap widths of 3, 7, 9, 11 and 15 nun. The deceleration lens system was also used as an acceleration lens system by changing and optimising the voltage on each electrode of the deceleration lens system and of the intermediate electrode of the Einzel lens 8. Possibilities of basic and applied researches using low energy ion beams accelerators International Nuclear Information System (INIS) Morales, Roberto 1996-01-01 Full text: The availability of ion sources that allow to accelerate heavy and light ions, and the new compact accelerators have opened interesting possibilities for using in basic and applied research, Some of the research lines such as material, environmental, archaeology, bio-medicine are shown 9. Simulation of collective ion acceleration in a slow cyclotron beam mode International Nuclear Information System (INIS) Faehl, R.J.; Shanahan, W.R.; Godfrey, B.B. 1979-01-01 The use of slow cyclotron beam waves is examined as a means of accelerating ions in intense relativistic electron beams. Field magnitudes of between 10 5 -and 10 6 V/cm seem achievable in the near term, and while these will never reach the levels of beam front mechanisms, such as virtual cathodes, they will easily exceed conventional ion acceleration sources 10. Meqalac Results - Multichannel Rf Acceleration of Nitrogen-Ions to 1 Mev NARCIS (Netherlands) Wojke, R. G. C.; Bannenberg, J. G.; Vijftigschild, A. J. M.; Giskes, F. G.; Ficke, H. G.; Klein, H.; Thomae, R. W.; Schempp, A.; Weis, T.; van Amersfoort, P. W.; Urbanus, W. H. 1991-01-01 In the MEQALAC (Multiple Electrostatic Quadrupole Linear Accelerator) multiple N+ ion beams are accelerated in 32 rf gaps, which are part of a modified interdigital-H-resonator operating at 25 MHz. The transverse focusing of the intense ion beams is achieved by means of sets of miniaturized 11. High-performance control system for a heavy-ion medical accelerator Energy Technology Data Exchange (ETDEWEB) Lancaster, H.D.; Magyary, S.B.; Sah, R.C. 1983-03-01 A high performance control system is being designed as part of a heavy ion medical accelerator. The accelerator will be a synchrotron dedicated to clinical and other biomedical uses of heavy ions, and it will deliver fully stripped ions at energies up to 800 MeV/nucleon. A key element in the design of an accelerator which will operate in a hospital environment is to provide a high performance control system. This control system will provide accelerator modeling to facilitate changes in operating mode, provide automatic beam tuning to simplify accelerator operations, and provide diagnostics to enhance reliability. The control system being designed utilizes many microcomputers operating in parallel to collect and transmit data; complex numerical computations are performed by a powerful minicomputer. In order to provide the maximum operational flexibility, the Medical Accelerator control system will be capable of dealing with pulse-to-pulse changes in beam energy and ion species. 12. Alignment of Ion Accelerator for Surface Analysis using Theodolite and Laser Tracker Energy Technology Data Exchange (ETDEWEB) Ahn, Tae Sung; Seo, Dong Hyuk; Kim, Dae Il; Kim, Han Sung; Kwon, Hyeok Jung; Cho, Yong Sub [KAERI, Daejeon (Korea, Republic of) 2016-05-15 The method of ion accelerator alignment is used two ways which are a theodolite and laser tracker. For the alignment and maintenance of the proton linear accelerator, the laser tracker is typically used at KOMAC. While the device for alignment by using laser tracker is not installed in all ion accelerator components, it was used in parallel in two methods. In this paper, alignment methods are introduced and the result and comparison of each alignment method are presented. The ion accelerator for surface analysis has aligned using theodolite and laser tracker. The two ways for alignment have advantage as well as weakness. But alignment using laser tracker is stronger than using theodolite. Because it is based on alignment and position data and it is more detailed. Also since the beam distribution is smaller than accelerator component that is direction of beam progress, main component (ex. Magnet, Chamber, Pelletron tank, etc.) alignment using laser tracker is enough to align the ion accelerator. 13. High-performance control system for a heavy-ion medical accelerator International Nuclear Information System (INIS) Lancaster, H.D.; Magyary, S.B.; Sah, R.C. 1983-03-01 A high performance control system is being designed as part of a heavy ion medical accelerator. The accelerator will be a synchrotron dedicated to clinical and other biomedical uses of heavy ions, and it will deliver fully stripped ions at energies up to 800 MeV/nucleon. A key element in the design of an accelerator which will operate in a hospital environment is to provide a high performance control system. This control system will provide accelerator modeling to facilitate changes in operating mode, provide automatic beam tuning to simplify accelerator operations, and provide diagnostics to enhance reliability. The control system being designed utilizes many microcomputers operating in parallel to collect and transmit data; complex numerical computations are performed by a powerful minicomputer. In order to provide the maximum operational flexibility, the Medical Accelerator control system will be capable of dealing with pulse-to-pulse changes in beam energy and ion species 14. Ion acceleration at the earth's bow shock: A review of observations in the upstream region International Nuclear Information System (INIS) Gosling, J.T.; Asbridge, J.R.; Bame, S.J.; Feldman, W.C. 1979-01-01 Positive ions are accelerated at or near the earth's bow shock and propagate into the upstream region. Two distinctly different population of these ions, distinguished by their greatly different spectral and angular widths, can be identified there. The type of ion population observed in the upstream region is strongly correlated with the presence or absence of long-period compresive waves in the solar wind. Very few ions are accelerated in the vicinity of the shock to energies much above about 100 keV. It is not yet clear whether the most energetic ions (i.e. those near 100 keV) are accelerated at the shock or in the broad disturbed region upstream from the shock. In either case stochastic acceleration by turbulent electrostatic fields seems to be the most viable candidate for the acceleration of the most energetic particles 15. Ion acceleration at the earth's bow shock: a review of observations in the upstream region International Nuclear Information System (INIS) Gosling, J.T.; Asbridge, J.R.; Bame, S.J.; Feldman, W.C. 1979-01-01 Positive ions are accelerated at or near the earth's bow shock and propagate into the upstream region. Two distinctly different populations of these ions, distinguished by their greatly different spectral and angular widths, can be identified there. The type of ion population observed in the upstream region is strongly correlated with the presence or absence of long-period compressive waves in the solar wind. Very few ions are accelerated in the vicinity of the shock to energies much above about 100 keV. It is not yet clear whether the most energetic ions (i.e., those near 100 keV) are accelerated at the shock or in broad disturbed region upstream from the shock. In either case stochastic acceleration by turbulent electrostatic fields seems to be the most viable candidate for the acceleration of the most energetic particles 16. Shaping laser accelerated ions for future applications – The LIGHT collaboration International Nuclear Information System (INIS) Busold, S.; Almomani, A.; Bagnoud, V.; Barth, W.; Bedacht, S.; Blažević, A.; Boine-Frankenheim, O. 2014-01-01 The generation of intense ion beams from high-intensity laser-generated plasmas has been the focus of research for the last decade. In the LIGHT collaboration the expertise of heavy ion accelerator scientists and laser and plasma physicists has been combined to investigate the prospect of merging these ion beams with conventional accelerator technology and exploring the possibilities of future applications. We report about the goals and first results of the LIGHT collaboration to generate, handle and transport laser driven ion beams. This effort constitutes an important step in research for next generation accelerator technologies 17. Shaping laser accelerated ions for future applications – The LIGHT collaboration Energy Technology Data Exchange (ETDEWEB) Busold, S., E-mail: [email protected] [Institut für Kernphysik, Technische Universität Darmstadt, Schloßgartenstraße 9, D-64289 Darmstadt (Germany); Almomani, A. [Institut für angewandte Physik, Johann-Wolfgang-Goethe-Universität Frankfurt, Max von Laue Straße 1, D-60438 Frankfurt (Germany); Bagnoud, V. [GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, D-64291 Darmstadt (Germany); Helmholtz Institut Jena, Fröbelstieg 3, D-07734 Jena (Germany); Barth, W. [GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, D-64291 Darmstadt (Germany); Bedacht, S. [Institut für Kernphysik, Technische Universität Darmstadt, Schloßgartenstraße 9, D-64289 Darmstadt (Germany); Blažević, A. [GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, D-64291 Darmstadt (Germany); Helmholtz Institut Jena, Fröbelstieg 3, D-07734 Jena (Germany); Boine-Frankenheim, O. [GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, D-64291 Darmstadt (Germany); Institut für Theorie Elektromagnetischer Felder, Technische Universität Darmstadt, Schloßgartenstraße 8, D-64289 Darmstadt (Germany); and others 2014-03-11 The generation of intense ion beams from high-intensity laser-generated plasmas has been the focus of research for the last decade. In the LIGHT collaboration the expertise of heavy ion accelerator scientists and laser and plasma physicists has been combined to investigate the prospect of merging these ion beams with conventional accelerator technology and exploring the possibilities of future applications. We report about the goals and first results of the LIGHT collaboration to generate, handle and transport laser driven ion beams. This effort constitutes an important step in research for next generation accelerator technologies. 18. Electromagnetic computer simulations of collective ion acceleration by a relativistic electron beam International Nuclear Information System (INIS) Galvez, M.; Gisler, G.R. 1988-01-01 A 2.5 electromagnetic particle-in-cell computer code is used to study the collective ion acceleration when a relativistic electron beam is injected into a drift tube partially filled with cold neutral plasma. The simulations of this system reveals that the ions are subject to electrostatic acceleration by an electrostatic potential that forms behind the head of the beam. This electrostatic potential develops soon after the beam is injected into the drift tube, drifts with the beam, and eventually settles to a fixed position. At later times, this electrostatic potential becomes a virtual cathode. When the permanent position of the electrostatic potential is at the edge of the plasma or further up, then ions are accelerated forward and a unidirectional ion flow is obtained otherwise a bidirectional ion flow occurs. The ions that achieve higher energy are those which drift with the negative potential. When the plasma density is varied, the simulations show that optimum acceleration occurs when the density ratio between the beam (n b ) and the plasma (n o ) is unity. Simulations were carried out by changing the ion mass. The results of these simulations corroborate the hypothesis that the ion acceleration mechanism is purely electrostatic, so that the ion acceleration depends inversely on the charge particle mass. The simulations also show that the ion maximum energy increased logarithmically with the electron beam energy and proportional with the beam current 19. Nuclear reactions with 11C and 14O radioactive ion beams International Nuclear Information System (INIS) Guo, Fanqing 2004-01-01 Radioactive ion beams (RIBs) have been shown to be a useful tool for studying proton-rich nuclides near and beyond the proton dripline and for evaluating nuclear models. To take full advantage of RIBs, Elastic Resonance Scattering in Inverse Kinematics with Thick Targets (ERSIKTT), has proven to be a reliable experimental tool for investigations of proton unbound nuclei. Following several years of effort, Berkeley Experiments with Accelerated Radioactive Species (BEARS), a RIBs capability, has been developed at the Lawrence Berkeley National Laboratory's 88-Inch Cyclotron. The current BEARS provides two RIBs: a 11C beam of up to 2x108 pps intensity on target and an 14O beam of up to 3x104 pps intensity. While the development of the 11C beam has been relatively easy, a number of challenges had to be overcome to obtain the 14O beam. The excellent 11C beam has been used to investigate several reactions. The first was the 197Au(11C,xn)208-xnAt reaction, which was used to measure excitation functions for the 4n to 8n exit channels. The measured cross sections were generally predicted quite well using the fusion-evaporation code HIVAP. Possible errors in the branching ratios of ?? decays from At isotopes as well as the presence of incomplete fusion reactions probably contribute to specific overpredictions. 15F has been investigated by the p(14O,p)14O reaction with the ERSIKTT technology. Several 14O+p runs have been performed. Excellent energy calibration was obtained using resonances from the p(14N,p)14N reaction in inverse kinematics, and comparing the results to those obtained earlier with normal kinematics. The differences between 14N+p and 14O+p in the stopping power function have been evaluated for better energy calibration. After careful calibration, the energy levels of 15F were fitted with an R-matrix calculation. Spins and parities were assigned to the two observed resonances. This new measurement of the 15F ground state supports the disappearance of the Z = 8 20. Suppression of X-radiation from 2 MeV ion electrostatic accelerator International Nuclear Information System (INIS) Ignat'ev, I.G.; Miroshnichenko, V.I.; Sirenko, A.M.; Storizhko, V.E. 2008-01-01 The paper presents results concerning studies of X-radiation from 2 MeV ion electrostatic accelerator 'Sokol' used for nuclear microprobe analysis. The radiation protection system of the accelerator was developed and tested. Tests of the system of the accelerator show that it reduces doses rate by two orders of magnitude 1. Heavy Ion Fusion Accelerator Research (HIFAR) year-end report, April 1, 1990--September 30, 1990 International Nuclear Information System (INIS) 1990-12-01 The basic objective of the Heavy Ion Fusion Accelerator Research (HIFAR) program is to assess the suitability of heavy ion accelerators as igniters for Inertial Confinement Fusion (ICF). A specific accelerator technology, induction acceleration, is being studied at the Lawrence Berkeley Laboratory and at the Lawrence Livermore National Laboratory. The HIFAR program addresses the generation of high-power, high-brightness beams of heavy ions, the understanding of the scaling laws in this novel physics regime, and the validation of new accelerator strategies to cut costs. Key elements to be addressed include: (1) beam quality limits set by transverse and longitudinal beam physics; (2) development of induction accelerating modules, and multiple-beam hardware, at affordable costs; (3) acceleration of multiple beams with current amplification without significant dilution of the optical quality of the beams; (4) final bunching, transport, and accurate focusing on a small target 2. Transmission electron microscope interfaced with ion accelerators and its application to materials science Energy Technology Data Exchange (ETDEWEB) Abe, Hiroaki; Naramoto, Hiroshi [Japan Atomic Energy Research Inst., Takasaki, Gunma (Japan). Takasaki Radiation Chemistry Research Establishment; Hojou, Kiichi; Furuno, Shigemi; Tsukamoto, Tetsuo 1997-03-01 We have developed the transmission/analytical electron microscope interfaced with two sets of ion accelerators (TEM-Accelerators Facility) at JAERI-Takasaki. The facility is expected to provide quantitative insights into radiation effects, such as damage evolution, irradiation-induced phase transformation and their stability, through in-situ observation and analysis under ion and/or electron irradiation. The TEM-Accelerators Facility and its application to materials research are reviewed. (author) 3. Advance in the study of removal of cesium from radioactive wastewater by inorganic ion exchangers International Nuclear Information System (INIS) Wang Songping; Wang Xiaowei; Du Zhihui 2014-01-01 The excellent performance in the removal of cesium from radioactive wastewater by inorganic ion exchangers has received extensive attention due to their characteristic physico-chemical features. The paper summarized research progress of removal of cesium by different inorganic ion exchangers such as silicoaluminate, salts of hetero polyacid, hexacyanoferrate, insoluble salts of acid with multivalent metals, insoluble hydrous oxides of multivalent metals and silicotitanate and reviewed several removal systems of cesium by inorganic ion exchangers which might offer China some reference in treatment and disposal of radioactive wastewater. (authors) 4. Ion current prediction model considering columnar recombination in alpha radioactivity measurement using ionized air transportation International Nuclear Information System (INIS) Naito, Susumu; Hirata, Yosuke; Izumi, Mikio; Sano, Akira; Miyamoto, Yasuaki; Aoyama, Yoshio; Yamaguchi, Hiromi 2007-01-01 We present a reinforced ion current prediction model in alpha radioactivity measurement using ionized air transportation. Although our previous model explained the qualitative trend of the measured ion current values, the absolute values of the theoretical curves were about two times as large as the measured values. In order to accurately predict the measured values, we reinforced our model by considering columnar recombination and turbulent diffusion, which affects columnar recombination. Our new model explained the considerable ion loss in the early stage of ion diffusion and narrowed the gap between the theoretical and measured values. The model also predicted suppression of ion loss due to columnar recombination by spraying a high-speed air flow near a contaminated surface. This suppression was experimentally investigated and confirmed. In conclusion, we quantitatively clarified the theoretical relation between alpha radioactivity and ion current in laminar flow and turbulent pipe flow. (author) 5. Workshop on Accelerators for Heavy Ion Fusion: Summary Report of the Workshop Energy Technology Data Exchange (ETDEWEB) Seidl, P.A.; Barnard, J.J. 2011-04-29 The Workshop on Accelerators for Heavy Ion Fusion was held at Lawrence Berkeley National Laboratory May 23-26, 2011. The workshop began with plenary sessions to review the state of the art in HIF (heavy ion fusion), followed by parallel working groups, and concluded with a plenary session to review the results. There were five working groups: IFE (inertial fusion energy) targets, RF approach to HIF, induction accelerator approach to HIF, chamber and driver interface, ion sources and injectors. 6. Recent developments of ion sources for life-science studies at the Heavy Ion Medical Accelerator in Chiba (invited) Energy Technology Data Exchange (ETDEWEB) Kitagawa, A.; Drentje, A. G.; Fujita, T.; Muramatsu, M. [National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage, Chiba 263-8555 (Japan); Fukushima, K.; Shiraishi, N.; Suzuki, T.; Takahashi, K.; Takasugi, W. [Accelerator Engineering Corporation, Chiba (Japan); Biri, S.; Rácz, R. [Institute for Nuclear Research (Atomki), Hungarian Academy of Sciences, Bem tér 18/C, H-4026 Debrecen (Hungary); Kato, Y. [Graduate School of Engineering, Osaka University, Osaka (Japan); Uchida, T.; Yoshida, Y. [Bio-Nano Electronics Research Centre, Toyo University, Kawagoe (Japan) 2016-02-15 With about 1000-h of relativistic high-energy ion beams provided by Heavy Ion Medical Accelerator in Chiba, about 70 users are performing various biology experiments every year. A rich variety of ion species from hydrogen to xenon ions with a dose rate of several Gy/min is available. Carbon, iron, silicon, helium, neon, argon, hydrogen, and oxygen ions were utilized between 2012 and 2014. Presently, three electron cyclotron resonance ion sources (ECRISs) and one Penning ion source are available. Especially, the two frequency heating techniques have improved the performance of an 18 GHz ECRIS. The results have satisfied most requirements for life-science studies. In addition, this improved performance has realized a feasible solution for similar biology experiments with a hospital-specified accelerator complex. 7. The state of development of an intense resonance electron-ion accelerator based on Doppler effect International Nuclear Information System (INIS) Egorov, A.M.; Ivanov, B.I.; Butenko, V.I.; Ognivenko, V.V.; Onishchenko, I.N.; Prishchepov, V.P. 1996-01-01 An intense ion accelerator has been proposed and now is being developed in which accelerating and focusing electric fields in a slow wave structure are excited by an intense electron beam using the anomalous and the normal Doppler effects. The results of theoretical studies and computer simulations show the advantage of this acceleration method that will make it possible to obtain acceleration rates of the order of 10 - 100 MeV/m, and ion beam energies and currents of the order of 10-100 MeV, 1-10 A. The project and technical documentation of an experimental accelerating installation were worked out. Currently, the 5 MeV accelerator-injector URAL-5 is in operation; preliminary experiments on a small installation have been carried out; experimental investigations of an accelerating RF resonator model (in 1/2 scaling) are being performed; the accelerating test installation is being manufactured. (author). 1 tab. 12 fig., 6 refs 8. The state of development of an intense resonance electron-ion accelerator based on Doppler effect Energy Technology Data Exchange (ETDEWEB) Egorov, A M; Ivanov, B I; Butenko, V I; Ognivenko, V V; Onishchenko, I N; Prishchepov, V P [Kharkov Inst. of Physics and Technology (Ukraine) 1997-12-31 An intense ion accelerator has been proposed and now is being developed in which accelerating and focusing electric fields in a slow wave structure are excited by an intense electron beam using the anomalous and the normal Doppler effects. The results of theoretical studies and computer simulations show the advantage of this acceleration method that will make it possible to obtain acceleration rates of the order of 10 - 100 MeV/m, and ion beam energies and currents of the order of 10-100 MeV, 1-10 A. The project and technical documentation of an experimental accelerating installation were worked out. Currently, the 5 MeV accelerator-injector URAL-5 is in operation; preliminary experiments on a small installation have been carried out; experimental investigations of an accelerating RF resonator model (in 1/2 scaling) are being performed; the accelerating test installation is being manufactured. (author). 1 tab. 12 fig., 6 refs. 9. Volumetric change of simulated radioactive waste glass irradiated by electron accelerator. [Silica glass Energy Technology Data Exchange (ETDEWEB) Sato, Seichi; Furuya, Hirotaka; Inagaki, Yaohiro; Kozaka, Tetsuo; Sugisaki, Masayasu 1987-11-01 Density changes of simulated radioactive waste glasses, silica glass and Pyrex glass irradiated by an electron accelerator were measured by a ''sink-float'' technique. The density changes of the waste and silica glasses were less than 0.05 %, irradiated at 2.0 MeV up to the fluence of 1.7 x 10/sup 17/ ecm/sup 2/, while were remarkably smaller than that of Pyrex glass of 0.18 % shrinkage. Precision of the measurements in the density changes of the waste glass was lower than that of Pyrex glass possibly because of the inhomogeneity of the waste glass 10. Accelerators for Medicine CERN Multimedia CERN. Geneva 2018-01-01 This lecture will review the different applications of particle accelerators to the medical field, from cancer treatment with beams of accelerator-produced particles (photons, electrons, protons, ions and neutrons) to the generation of radioactive isotopes used in medical diagnostics, in cancer therapy and in the new domain of theragnostics. For each application will be outlined the state of the art, the potential, and the accelerator challenges to be faced to meet the increasing demand for therapeutic procedures based on accelerators. 11. Titanium carbide-carbon porous nanocomposite materials for radioactive ion beam production: processing, sintering and isotope release properties CERN Document Server AUTHOR|(CDS)2081922; Stora, Thierry 2017-01-26 The Isotope Separator OnLine (ISOL) technique is used at the ISOLDE - Isotope Separator OnLine DEvice facility at CERN, to produce radioactive ion beams for physics research. At CERN protons are accelerated to 1.4 GeV and made to collide with one of two targets located at ISOLDE facility. When the protons collide with the target material, nuclear reactions produce isotopes which are thermalized in the bulk of the target material grains. During irradiation the target is kept at high temperatures (up to 2300 °C) to promote diffusion and effusion of the produced isotopes into an ion source, to produce a radioactive ion beam. Ti-foils targets are currently used at ISOLDE to deliver beams of K, Ca and Sc, however they are operated at temperatures close to their melting point which brings target degradation, through sintering and/or melting which reduces the beam intensities over time. For the past 10 years, nanostructured target materials have been developed and have shown improved release rates of the produced i... 12. The fingerprint method for characterization of radioactive waste in hadron accelerators CERN Document Server Magistris, M 2008-01-01 Beam losses are responsible for material activation in most of the components of particle accelerators. The activation is caused by several nuclear processes and varies with the irradiation history and the characteristics of the material (namely chemical composition and size). Once at the end of their operational lifetime, these materials require radiological characterization. The radionuclide inventory depends on the particle spectrum, the irradiation history and the chemical composition of the material. As long as these factors are known and the material cross-sections are available, the induced radioactivity can be calculated analytically. However, these factors vary widely among different items of waste and sometimes they are only partially known. The European Laboratory for Particle Physics (CERN, Geneva) has been operating accelerators for high-energy physics for 50 years. Different methods for the evaluation of the radionuclide inventory are currently under investigation at CERN, including the so-calle... 13. Measurement of radioactivity in air at the linear accelerator of Kyoto University reactor facility International Nuclear Information System (INIS) Ikebe, Yukimasa; Shimo, Michikuni 1976-01-01 It is well-known that the induced activities from a number of nuclides are generated in air during the operation of high energy accelerators. Of these, measurements were performed with the linear accelerator of Kyoto University reactor facility for the purpose of the clarification of the production mechanism and behavior of radioactive aerosols. The concentration in air and the size distribution of 13 N aerosols which have aerosols as the carrier among 13 N produced by the γ-n reaction of 14 N were measured with filter packs and by diffusion method, respectively. The density of number and size distribution of non-radioactive aerosols were measured to understand the production mechanism and behavior of 13 N aerosols. For the aerosol number density, Aitken nucleus number was measured with a Pollak counter. The results obtained show that (1) under the operating condition of the linear accelerator at that measurement time, 13 N aerosol concentration was (2 to 50) x 10 -13 Ci/cm 3 while 13 N gas component concentration was (1 to 25) x 10 -12 Ci/cm 3 , i.e. the ratio was approximately 1 : 10 (2) the average size of 13 N aerosols was 0.01 to 0.04 μm, and it was found that there was positive correlation to relative humidity; (3) during the operation of the accelerator, the generation of aerosols 10 to 100 times as much as the background level was observed. The size distribution of aerosols showed a peak around 0.01 μm; and others. Examination was carried out regarding a 13 N aerosol production model based on the sticking of aerosol-free 13 N to aerosols. (Wakatsuki, Y.) 14. Design and fabrication of a Transverse Field Focussing (TFF) 180 keV negative ion accelerator International Nuclear Information System (INIS) Matuk, C.A.; Anderson, O.A.; Owren, H.M.; Paterson, J.A.; Purgalis, P. 1985-11-01 The 180 keV Transverse Field Focussing (TFF) negative ion accelerator described is the final component of a negative ion based neutral beam acceleration system which is being developed as proof-of-principle demonstration of a radiation hardened neutral beamline. The 180 keV beamline consists of: a surface conversion negative ion source, a 80 keV pre-accelerator, a TFF pumping, matching, and transport section, and the 180 keV TFF accelerator presented. This beamline is expected to provide 1 A of H - at 180 keV. In the design of the accelerator, particular importance was given to the rigidity of the accelerator electrode mounting structures and to the electrical isolation of the electrodes along with their related cooling lines. An optical alignment scheme was developed to assemble and to insure precision alignment of the electrodes 15. POLYMERS CONTAINING Cu NANOPARTICLES IRRADIATED BY LASER TO ENHANCE THE ION ACCELERATION Directory of Open Access Journals (Sweden) Mariapompea Cutroneo 2015-06-01 Full Text Available Target Normal Sheath Acceleration method was employed at PALS to accelerate ions from laser-generated plasma at intensities above 1015 W/cm2. Laser parameters, irradiation conditions and target geometry and composition control the plasma properties and the electric field driving the ion acceleration. Cu nanoparticles deposited on the polymer promote resonant absorption effects increasing the plasma electron density and enhancing the proton acceleration. Protons can be accelerated in forward direction at kinetic energies up to about 3.5 MeV. The optimal target thickness, the maximum acceleration energy and the angular distribution of emitted particles have been measured using ion collectors, X-ray CCD streak camera, SiC detectors and Thomson Parabola Spectrometer. 16. Heavy Ion Fusion Accelerator Research (HIFAR) year-end report, April 1--September 30, 1988 International Nuclear Information System (INIS) 1988-12-01 The basic objective of the Heavy Ion Fusion Accelerator Research (HIFAR) program is to assess the suitability of heavy ion accelerators as igniters for Inertial Confinement Fusion (ICF). A specific accelerator technology, the induction linac, has been studied at the Lawrence Berkeley Laboratory and has reached the point at which its viability for ICF applications can be assessed over the next few years. The HIFAR program addresses the generation of high power, high-brightness beams of heavy ions, the understanding of the scaling laws in this novel physics regime, and the validation of new accelerator strategies, to cut costs. Key elements to be addressed include: beam quality limits set by transverse and longitudinal beam physics; development of induction accelerating modules, and multiple-beam hardware, at affordable costs; acceleration of multiple beams with current amplification --both new features in a linac -- without significant dilution of the optical quality of the beams; final bunching, transport, and accurate focusing on a small target 17. Heavy Ion Fusion Accelerator Research (HIFAR) year-end report, October 1, 1987--March 31, 1988 International Nuclear Information System (INIS) 1988-06-01 The basic objective of the Heavy Ion Fusion Accelerator Research (HIFAR) program is to assess the suitability of heavy ion accelerators as igniters for Inertial Confinement Fusion (ICF). A specific accelerator technology, the induction linac, has been studied at Lawrence Berkeley Laboratory and has reached the point at which its viability for ICF applications can be assessed over the next few years. The HIFAR program addresses the generation of high-power, high-brightness beams of heavy ions, the understanding of the scaling laws in this novel physics regime, and the validation of new accelerator strategies, to cut costs. Key elements to be addressed include: beam quality limits set by transverse and longitudinal beam physics; development of induction accelerating modules, and multiple-beam hardware, at affordable costs; acceleration of multiple beams with current amplification -- both new features in a linac -- without significant dilution of the optical quality of beams; and final bunching, transport, and accurate focusing on a small target 18. Characteristics of bipolar-pulse generator for intense pulsed heavy ion beam acceleration International Nuclear Information System (INIS) Igawa, K.; Tomita, T.; Kitamura, I.; Ito, H.; Masugata, K. 2006-01-01 Intense pulsed heavy ion beams are expected to be applied to the implantation technology for semiconductor materials. In the application it is very important to purify the ion beam. In order to improve the purity of an intense pulsed ion beams we have proposed a new type of pulsed ion beam accelerator named 'bipolar pulse accelerator (BPA)'. A prototype of the experimental system has been developed to perform proof of principle experiments of the accelerator. A bipolar pulse generator has been designed for the generation of the pulsed ion beam with the high purity via the bipolar pulse acceleration and the electrical characteristics of the generator were evaluated. The production of the bipolar pulse has been confirmed experimentally. (author) 19. Ion response to relativistic electron bunches in the blowout regime of laser-plasma accelerators. Science.gov (United States) Popov, K I; Rozmus, W; Bychenkov, V Yu; Naseri, N; Capjack, C E; Brantov, A V 2010-11-05 The ion response to relativistic electron bunches in the so called bubble or blowout regime of a laser-plasma accelerator is discussed. In response to the strong fields of the accelerated electrons the ions form a central filament along the laser axis that can be compressed to densities 2 orders of magnitude higher than the initial particle density. A theory of the filament formation and a model of ion self-compression are proposed. It is also shown that in the case of a sharp rear plasma-vacuum interface the ions can be accelerated by a combination of three basic mechanisms. The long time ion evolution that results from the strong electrostatic fields of an electron bunch provides a unique diagnostic of laser-plasma accelerators. 20. A combined thermal dissociation and electron impact ionization source for radioactive ion beam generationa International Nuclear Information System (INIS) Alton, G.D.; Williams, C. 1996-01-01 The probability for simultaneously dissociating and efficiently ionizing the individual atomic constituents of molecular feed materials with conventional, hot-cathode, electron-impact ion sources is low and consequently, the ion beams from these sources often appear as mixtures of several molecular sideband beams. This fragmentation process leads to dilution of the intensity of the species of interest for radioactive ion beam (RIB) applications where beam intensity is at a premium. We have conceived an ion source that combines the excellent molecular dissociation properties of a thermal dissociator and the high ionization efficiency characteristics of an electron impact ionization source that will, in principle, overcome this handicap. The source concept will be evaluated as a potential candidate for use for RIB generation at the Holifield Radioactive Ion Beam Facility, now under construction at the Oak Ridge National Laboratory. The design features and principles of operation of the source are described in this article. copyright 1996 American Institute of Physics 1. Study of the Fixation and Migration of Radioactive Cations in a Natural Ion-Exchanger Energy Technology Data Exchange (ETDEWEB) Baetsle, L. [Centre d' Etudes de l' Energie Nucleaire, Mol (Belgium) 1960-07-01 The purpose of this study is to analyse the behaviour of Sr90 and Cs137 on natural ion-exchangers such as lignite and soil. Lignite is a substance which is found in large quantities near the Belgian Nuclear Energy Research Centre (CEN) at Mol and is particularly useful in the processing of radioactive liquid wastes because of its ion-exchange properties. The physical and chemical characteristics of lignite which have a bearing on ion exchange are given in section 1 of this paper. The various ion equilibria which affect the processing of.radioactive liquid wastes are studied in section 2, which also lists the basic factors required for calculating the rate of saturation of a lignite column. The speed of ion migration in the soil is studied along the same lines as for lignite. 2. Constraints due to the production of radioactive ion beams in the SPIRAL project International Nuclear Information System (INIS) Leroy, R.; Huguet, Y.; Jardin, P.; Marry, C.; Pacquet, J.Y.; Villari, A.C.C. 1997-01-01 The radioactive ion beams that will be delivered by the SPIRAL facility will be produced by the interaction of a stable high energy and high intensity primary ion beam delivered by the GANIL cyclotrons with a carbon target heated to 2000 deg C. During this interaction, some radioactive atoms will be created and will diffuse out of the target before entering into an electron cyclotron resonance ion source where they will be ionized and extracted. The production of radioactive ion beams with this method implies high radiation fields that activate and can damage materials located in the neighborhood of the target. Therefore, the production system which is composed of the permanent magnet ECR ion source coupled to a graphite target will be changed after two weeks of irradiation. As this ensemble will be very radioactive, this operation has to be supervised by remote control. The radiation levels around the target-ion source system and a detailed description of the different precautions that have been taken for safety and for prevention of contamination and irradiation are presented. (author) 3. A guide to radiation and radioactivity levels near high energy particle accelerators International Nuclear Information System (INIS) Sullivan, A.H. 1992-01-01 An estimate of likely radiation and radioactivity levels is needed at the design stage of an accelerator for deciding the radiation safety features to be incorporated in the infrastructure of the machine and for predicting where radiation damage possibilities will have to be taken into account. Both these aspects can have a significant influence on the machine layout and cost. Failure to make a reasonable assessment at the right time may have far reaching consequences for future costs. The purpose of this guide is to bring together basic data and methods that have been found useful in assessing radiation situations around accelerators and to provide a practical means of arriving at the radiation and induced radioactivity levels that could occur under a wide variety of circumstances. An attempt is made to present the information in a direct and unambiguous way with sufficient confidence that the necessity for large safety factors is avoided. In many cases assumptions and simplifications have been made and reliance placed on extrapolating from experimental data into regions where the basic physics is too complicated to make meaningful absolute calculations. Wherever possible such extrapolations have been tied to real or otherwise acceptable data originating from independent sources. (Author) 4. Storage ion trap of an 'In-Flight Capture' type for precise mass measurement of radioactive nuclear reaction products and fission fragments International Nuclear Information System (INIS) Tarantin, N.I. 2001-01-01 Data on nuclear masses provide a basis for creating and testing various nuclear models. A tandem system of FLNR comprised of the U-400M cyclotron, the COMBAS magnetic separator and the mass-spectrometric ion trap of an 'in-flight capture' type is considered as a possible complex for producing of the short-lived nuclei in fragmentation reactions by heavy ions and for precise mass measurement of these nuclei. The plan of scientific and technical FLNR research includes a project DRIBs for producing beams of accelerated radioactive nuclear reaction products and photofission fragments. This project proposes also precise mass measurements of the fission fragment with the help of the ion trap. The in-flight entrance of the ions and their capture in the mass-spectrometric ion trap using the monochromatizing degrader, the static electric and magnetic fields and a new invention, a magnetic unidirectional transporting ventil, is considered 5. Transport and acceleration of the high-current ion beam in magneto-isolated gap International Nuclear Information System (INIS) Karas', V.I.; Kornilov, E.A.; Manuilenko, O.V.; Fedorovskaya, O.V.; Tarakanov, V.P. 2015-01-01 The possibility of transportation and acceleration of the high-current ion beam in the magneto-isolated gap has been demonstrated. Found the parameters of the system and beams (the magnetic field produced by the coils with opposing currents, the size of the system, and the parameters of the beams), under which the uniform acceleration of the high-current ion beam all along the gap length is realized. It is shown that the quality of the ion beam, during transport and acceleration, at the exit of the gap is acceptable for many technological applications. 6. DEVELOPING THE PHYSICS DESIGN FOR NDCX-II, A UNIQUE PULSE-COMPRESSING ION ACCELERATOR International Nuclear Information System (INIS) Friedman, A.; Barnard, J.J.; Cohen, R.H.; Grote, D.P.; Lund, S.M.; Sharp, W.M.; Faltens, A.; Henestroza, E.; Jung, J.-Y.; Kwan, J.W.; Lee, E.P.; Leitner, M.A.; Logan, B.G.; Vay, J.-L.; Waldron, W.L.; Davidson, R.C.; Dorf, M.; Gilson, E.P.; Kaganovich, I. 2009-01-01 The Heavy Ion Fusion Science Virtual National Laboratory (a collaboration of LBNL, LLNL, and PPPL) is using intense ion beams to heat thin foils to the 'warm dense matter' regime at ∼ + ions to ∼1 ns while accelerating it to 3-4 MeV over ∼15 m. Strong space charge forces are incorporated into the machine design at a fundamental level. We are using analysis, an interactive 1D PIC code (ASP) with optimizing capabilities and centroid tracking, and multi-dimensional Warpcode PIC simulations, to develop the NDCX-II accelerator. This paper describes the computational models employed, and the resulting physics design for the accelerator. 7. 2D electron density profile measurement in tokamak by laser-accelerated ion-beam probe. Science.gov (United States) Chen, Y H; Yang, X Y; Lin, C; Wang, L; Xu, M; Wang, X G; Xiao, C J 2014-11-01 A new concept of Heavy Ion Beam Probe (HIBP) diagnostic has been proposed, of which the key is to replace the electrostatic accelerator of traditional HIBP by a laser-driven ion accelerator. Due to the large energy spread of ions, the laser-accelerated HIBP can measure the two-dimensional (2D) electron density profile of tokamak plasma. In a preliminary simulation, a 2D density profile was reconstructed with a spatial resolution of about 2 cm, and with the error below 15% in the core region. Diagnostics of 2D density fluctuation is also discussed. 8. Investigation on target normal sheath acceleration through measurements of ions energy distribution Energy Technology Data Exchange (ETDEWEB) Tudisco, S., E-mail: [email protected]; Cirrone, G. A. P.; Mascali, D.; Schillaci, F. [Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Sud, Via S. Sofia 62, 95123 Catania (Italy); Altana, C. [Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Sud, Via S. Sofia 62, 95123 Catania (Italy); Dipartimento di Fisica e Astronomia, Università degli Studi di Catania, Via S. Sofia 64, 95123 Catania (Italy); Lanzalone, G. [Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Sud, Via S. Sofia 62, 95123 Catania (Italy); Università degli Studi di Enna “Kore,” Via delle Olimpiadi, 94100 Enna (Italy); Muoio, A. [Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Sud, Via S. Sofia 62, 95123 Catania (Italy); Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Messina, Viale F.S. D’Alcontres 31, 98166 Messina (Italy); Brandi, F. [Consiglio Nazionale delle Ricerche, Istituto Nazionale di Ottica, Intense Laser Irradiation Laboratory, Via G. Moruzzi 1, 56124 Pisa (Italy); Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova (Italy); Cristoforetti, G.; Ferrara, P.; Fulgentini, L.; Koester, P. [Consiglio Nazionale delle Ricerche, Istituto Nazionale di Ottica, Intense Laser Irradiation Laboratory, Via G. Moruzzi 1, 56124 Pisa (Italy); Labate, L.; Gizzi, L. A. [Consiglio Nazionale delle Ricerche, Istituto Nazionale di Ottica, Intense Laser Irradiation Laboratory, Via G. Moruzzi 1, 56124 Pisa (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Largo B. Pontecorvo 3, 56127 Pisa (Italy); and others 2016-02-15 An experimental campaign aiming at investigating the ion acceleration mechanisms through laser-matter interaction in femtosecond domain has been carried out at the Intense Laser Irradiation Laboratory facility with a laser intensity of up to 2 × 10{sup 19} W/cm{sup 2}. A Thomson parabola spectrometer was used to obtain the spectra of the ions of the different species accelerated. Here, we show the energy spectra of light-ions and we discuss their dependence on structural characteristics of the target and the role of surface and target bulk in the acceleration process. 9. Investigation on target normal sheath acceleration through measurements of ions energy distribution International Nuclear Information System (INIS) Tudisco, S.; Cirrone, G. A. P.; Mascali, D.; Schillaci, F.; Altana, C.; Lanzalone, G.; Muoio, A.; Brandi, F.; Cristoforetti, G.; Ferrara, P.; Fulgentini, L.; Koester, P.; Labate, L.; Gizzi, L. A. 2016-01-01 An experimental campaign aiming at investigating the ion acceleration mechanisms through laser-matter interaction in femtosecond domain has been carried out at the Intense Laser Irradiation Laboratory facility with a laser intensity of up to 2 × 10 19 W/cm 2 . A Thomson parabola spectrometer was used to obtain the spectra of the ions of the different species accelerated. Here, we show the energy spectra of light-ions and we discuss their dependence on structural characteristics of the target and the role of surface and target bulk in the acceleration process 10. High-quality laser-accelerated ion beams for medical applications Energy Technology Data Exchange (ETDEWEB) Harman, Zoltan; Keitel, Christoph H. [Max-Planck-Institut fuer Kernphysik, Heidelberg (Germany); Salamin, Yousef I. [Max-Planck-Institut fuer Kernphysik, Heidelberg (Germany); American University of Sharjah (United Arab Emirates) 2009-07-01 Cancer radiation therapy requires accelerated ion beams of high energy sharpness and a narrow spatial profile. As shown recently, linearly and radially polarized, tightly focused and thus extremely strong laser beams should permit the direct acceleration of light atomic nuclei up to energies that may offer the potentiality for medical applications. Radially polarized beams have better emittance than their linearly polarized counterparts. We put forward the direct laser acceleration of ions, once the refocusing of ion beams by external fields is solved or radially polarized laser pulses of sufficient power can be generated. 11. A neutron beam facility for radioactive ion beams and other applications Science.gov (United States) Tecchio, L. B. 1999-06-01 In the framework of the Italian participation in the project of a high intensity proton facility for the energy amplifier and nuclear waste transmutations, LNL is involved in the design and construction of same prototypes of the injection system of the 1 GeV linac that consists of a RFQ (5 MeV, 30 mA) followed by a 100 MeV linac. This program has already been supported financially and the work is in progress. In this context LNL has proposed a project for the construction of a second generation facility for the production of radioactive ion beams (RIBs) by means of the ISOL method. The final goal is the production of neutron rich RIBs with masses ranging from 30 to 150 by using primary beams of protons, deuterons and light ions with energy of 100 MeV and 100 kW power. This project is expected to be developed in about 10 years from new and intermediate milestones and experiments are foreseen and under consideration for the next INFN five year plan (1999-2003). During that period the construction of a proton/deuteron accelerator of 10 MeV energy and 10 mA current, consisting of a RFQ (5 MeV, 30 mA) and a linac (10 MeV, 10 mA), and of a neutron area dedicated to the RIBs production and to the neutron physics, is proposed. Some remarks on the production methods will be presented. The possibility of producing radioisotopes by means of the fission induced by neutrons will be investigated and the methods of production of neutrons will be discussed. Besides the RIBs production, neutron beams for the BNCT applications and neutron physics are also planned. 12. Characteristics of the magnetic wall reflection model on ion acceleration in gas-puff z pinch International Nuclear Information System (INIS) Nishio, M.; Takasugi, K. 2013-01-01 The magnetic wall reflection model was examined with the numerical simulation of the trajectory calculation of particles. This model is for the ions accelerated by some current-independent mechanism. The trajectory calculation showed angle dependency of highest velocities of accelerated particles. This characteristics is of the magnetic wall reflection model, not of the other current-independent acceleration mechanism. Thomson parabola measurements of accelerated ions produced in the gas-puff z-pinch experiments were carried out for the verification of the angle dependency. (author) 13. Coulomb-driven energy boost of heavy ions for laser-plasma acceleration. Science.gov (United States) Braenzel, J; Andreev, A A; Platonov, K; Klingsporn, M; Ehrentraut, L; Sandner, W; Schnürer, M 2015-03-27 An unprecedented increase of kinetic energy of laser accelerated heavy ions is demonstrated. Ultrathin gold foils have been irradiated by an ultrashort laser pulse at a peak intensity of 8×10^{19} W/ cm^{2}. Highly charged gold ions with kinetic energies up to >200 MeV and a bandwidth limited energy distribution have been reached by using 1.3 J laser energy on target. 1D and 2D particle in cell simulations show how a spatial dependence on the ion's ionization leads to an enhancement of the accelerating electrical field. Our theoretical model considers a spatial distribution of the ionization inside the thin target, leading to a field enhancement for the heavy ions by Coulomb explosion. It is capable of explaining the energy boost of highly charged ions, enabling a higher efficiency for the laser-driven heavy ion acceleration. 14. Heavy ions acceleration in RF wells of 2-frequency electromagnetic field and in the inverted FEL International Nuclear Information System (INIS) Dzergach, A.I.; Kabanov, V.S.; Nikulin, M.G.; Vinogradov, S.V. 1995-03-01 Last results of the study of heavy ions acceleration by electrons trapped in moving 2-frequency 3-D RF wells are described. A linearized theoretical model of ions acceleration in a polarized spheroidal plasmoid is proposed. The equilibrium state of this plasmoid is described by the modified microcanonical distribution of the Courant-Snyder invariant (open-quotes quasienergyclose quotes of electrons). Some new results of computational simulation of the acceleration process are given. The method of computation takes into account the given cylindrical field E 011 (var-phi,r,z) and the self fields of electrons and ions. The results of the computation at relatively short time intervals confirm the idea and estimated parameters of acceleration. The heavy ion accelerator using this principle may be constructed with the use of compact cm band iris-loaded and biperiodical waveguides with double-sided 2-frequency RF feeding. It can accelerate heavy ions with a charge number Z i from small initial energies ∼ 50 keV/a.u. with the rate ∼ Z i · 10 MeV/m. Semirelativistic ions may be accelerated with similar rate also in the inverted FEL 15. A cylindrical Penning trap for capture, mass selective cooling, and bunching of radioactive ion beams International Nuclear Information System (INIS) Raimbault-Hartmann, H.; Bollen, G.; Beck, D.; Koenig, M.; Kluge, H.-J.; Schwarz, S.; Schark, E.; Stein, J.; Szerypo, J. 1997-01-01 A Penning trap ion accumulator, cooler, and buncher for low-energy ion beams has been developed for the ISOLTRAP mass spectrometer at ISOLDE/CERN. A cylindrical electrode configuration is used for the creation of a nested trapping potential. This is required for efficient accumulation of externally produced ions and for high-mass selectivity by buffer gas cooling. The design goal of a mass resolving power of about 1 x 10 5 has been achieved. Isobar separation has been demonstrated for radioactive rare-earth ion beams delivered by the ISOLDE on-line mass separator. (orig.) 16. A cylindrical Penning trap for capture, mass selective cooling, and bunching of radioactive ion beams CERN Document Server Raimbault-Hartmann, H; Bollen, G; König, M; Kluge, H J; Schark, E; Stein, J; Schwarz, S; Szerypo, J 1997-01-01 A Penning trap ion accumulator, cooler, and buncher for low energy ion beams has been developed for the ISOLTRAP mass spectrometer at ISOLDE/CERN. A cylindrical electrode configuration is used for the creation of a nested trapping potential. This is required for efficient accumulation of externally produced ions and for high mass selectivity by buffer gas cooling. The design goal of a mass resolving power of about1\\cdot 10^{5}\$ has been achieved. Isobar separation has been demonstrated for radioactive rare earth ion beams delivered by the ISOLDE on-line mass separator.
17. Design for simultaneous acceleration of stable and unstable beams in a superconducting heavy-ion linear accelerator for RISP
Science.gov (United States)
Kim, Jongwon; Son, Hyock-Jun; Park, Young-Ho
2017-11-01
The post-accelerator of isotope separation on-line (ISOL) system for rare isotope science project (RISP) is a superconducting linear accelerator (SC-linac) with a DC equivalent voltage of around 160 MV. An isotope beam extracted from the ISOL is in a charge state of 1+ and its charge state is increased to n+ by charge breeding with an electron beam ion source (EBIS). The charge breeding takes tens of ms and the pulse width of extracted beam from the EBIS is tens of μs, which operates at up to 30 Hz. Consequently a large portion of radio frequency (rf) time of the post SC-linac is unused. The post-linac is equipped also with an electron cyclotron resonance (ECR) ion source for stable ion acceleration. Thanks to the large phase acceptance of SC-linac, it is possible to accelerate simultaneously both stable and radioisotope ions with a similar charge to mass ratio by sharing rf time. This operation scheme is implemented for RISP with the addition of an electric chopper and magnetic kickers. The facility will be capable of providing the users of the ISOL and in-flight fragmentation (IF) systems with different beams simultaneously, which would help nuclear science users in obtaining a beam time as high-precision measurements often need long hours.
18. 2D accelerator design for SITEX negative ion source
International Nuclear Information System (INIS)
Whealton, J.H.; Raridon, R.J.; McGaffey, R.W.; McCollough, D.H.; Stirling, W.L.; Dagenhart, W.K.
1983-01-01
Solving the Poisson-Vlasov equations where the magnetic field, B, is assumed constant, we optimize the optical system of a SITEX negative ion source in infinite slot geometry. Algorithms designed to solve the above equations were modified to include the curved emitter boundary data appropriate to a negative ion source. Other configurations relevant to negative ion sources are examined
19. Dynamic analysis of an accelerator-based subcritical radioactive waste burning system
International Nuclear Information System (INIS)
Woosley, M.L. Jr.; Rydin, R.A.
1997-01-01
There has been a recent revival of interest in accelerator-driven subcritical fluid-fueled systems for radioactive waste management. This motivates the need for dynamic analysis of the nuclear kinetics of such systems. A physical description of the Los Alamos Accelerator-Based Conversion (ABC) concept is provided. This system is used as the basis for the kinetic study in this research. The current approach to the dynamic simulation of an accelerator-driven subcritical fluid-fueled system includes four functional blocks: A discrete ordinates model is used to calculate the flux distribution for the source-driven system (DORT); A nodal convection model is used to calculate time-dependent isotope and temperature distributions which impact reactivity (ABCcore); A nodal importance weighting model is used to calculate the reactivity impact of temperature and isotope distributions and to feed this information back to the time-dependent nodal convection model (ABCvip); A transient driver simulates system transients and records simulation data (ABCtrans). Specific transients which have been analyzed with the current modeling system are discussed. These transients include loss-of-flow and loss-of-cooling accidents, xenon and samarium transients, and cold-plug and overfueling events. The results of various transients have uncovered unpredictable behavior, unresolved design issues, and the need for active control. 11 refs., 6 figs., 1 tab
20. Heavy Ion Fusion Accelerator Research (HIFAR) year-end report, April 1, 1985-September 30, 1985
International Nuclear Information System (INIS)
1985-10-01
The heavy ion accelerator is profiled. Energy losses, currents, kinetic energy, beam optics, pulse models and mechanical tolerances are included in the discussion. In addition, computational efforts and an energy analyzer are described. 37 refs., 27 figs
1. Performance of MBE-4: An experimental multiple beam induction linear accelerator for heavy ions
International Nuclear Information System (INIS)
Warwick, A.I.; Fessenden, T.J.; Keefe, D.; Kim, C.H.; Meuth, H.
1988-06-01
An experimental induction linac, called MBE-4, has been constructed to demonstrate acceleration and current amplification of multiple heavy ion beams. This work is part of a program to study the use of such an accelerator as a driver for heavy ion inertial fusion. MBE-4 is 16m long and accelerates four space-charge-dominated beams of singly-charged cesium ions, in this case from 200 keV to 700 keV, amplifying the current in each beam from 10mA by a factor of nine. Construction of the experiment was completed late in 1987 and we present the results of detailed measurements of the longitudinal beam dynamics. Of particular interest is the contribution of acceleration errors to the growth of current fluctuations and to the longitudinal emittance. The effectiveness of the longitudinal focusing, accomplished by means of the controlled time dependence of the accelerating fields, is also discussed. 4 refs., 5 figs., 1 tab
2. Changes in acceleration rate of chloride ions depending on climatic conditions. Influence of rain
International Nuclear Information System (INIS)
Corvo, F.; Arroyave, C.; Autie, M.; Minotas, J.; Balmaseda, J.; Delgado, J.; Haces, C.
2003-01-01
Mild steel,copper and aluminum samples were exposed outdoors in two atmospheric test stations located in Havana, Cuba and Medellin, colombia. Two parallel group of samples were formed, one for each station. They were submitted to accelerated outdoor test by intermittent spraying of a salt solution (SCAB test) according to ISO 11474.98, receiving also the influence of the open atmosphere. The acceleration of corrosion rate of the three metals caused by the presence of chloride ions in both stations was determined. As expected, steel shows the higher corrosion rate and acceleration by chlorides, particularly at Cuban corrosion station. A remarkable difference in the acceleration rate of chloride ions for mild steel and copper between Cuban and Colombian acceleration rate of chloride ions of steel and copper. Steel corrosion products were analysed by Moessbauer Spectroscopy. Water absorption was also studied. The presence of magnetite, goethite and other Iron compounds was determined. (Author) 10 refs
3. Development of intense high-energy noble gas ion beams from in-terminal ion injector of tandem accelerator using an ECR ion source
Energy Technology Data Exchange (ETDEWEB)
Matsuda, M., E-mail: [email protected] [Japan Atomic Energy Agency (JAEA), Tokai Research and Development Center, 2-4 Shirakata-shirane, Tokai, Naka, Ibaraki 319-1195 (Japan); Nakanoya, T.; Hanashima, S.; Takeuchi, S. [Japan Atomic Energy Agency (JAEA), Tokai Research and Development Center, 2-4 Shirakata-shirane, Tokai, Naka, Ibaraki 319-1195 (Japan)
2011-10-21
An ECRIS-based heavy ion injector was constructed in the high-voltage terminal of JAEA-Tokai Tandem Accelerator to develop new beam species of highly charged noble gas ions. This work was associated with a lot of development to operate the ion source on the 20UR Pelletron high voltage terminal in high pressure SF{sub 6} gas environment. Highly charged ions of N, O, Ne, Ar, Kr and Xe have been accelerated satisfactorily. Operating data integrated during many years long beam delivery service are summarized.
4. MODELING AN ION EXCHANGE PROCESS FOR CESIUM REMOVAL FROM ALKALINE RADIOACTIVE WASTE SOLUTIONS
International Nuclear Information System (INIS)
Smith, F.; Hamm, Luther; Aleman, Sebastian; Michael, Johnston
2008-01-01
The performance of spherical Resorcinol-Formaldehyde ion-exchange resin for the removal of cesium from alkaline radioactive waste solutions has been investigated through computer modeling. Cesium adsorption isotherms were obtained by fitting experimental data using a thermodynamic framework. Results show that ion-exchange is an efficient method for cesium removal from highly alkaline radioactive waste solutions. On average, two 1300 liter columns operating in series are able to treat 690,000 liters of waste with an initial cesium concentration of 0.09 mM in 11 days achieving a decontamination factor of over 50,000. The study also tested the sensitivity of ion-exchange column performance to variations in flow rate, temperature and column dimensions. Modeling results can be used to optimize design of the ion exchange system
5. Laser photodetachment of radioactive ions: towards the determination of the electronegativity of astatine
CERN Multimedia
Rothe, Sebastian; Welander, Jakob Emanuel; Chrysalidis, Katerina; Day Goodacre, Thomas; Fedosseev, Valentine; Fiotakis, Spyridon; Forstner, Oliver; Heinke, Reinhard Matthias; Johnston, Karl; Kron, Tobias; Koester, Ulli; Liu, Yuan; Marsh, Bruce; Ringvall Moberg, Annie; Rossel, Ralf Erik; Seiffert, Christoph; Studer, Dominik; Wendt, Klaus; Hanstorp, Dag
2017-01-01
Negatively charged ions are mainly stabilized through the electron correlation effect. A measure of the stability of a negative ion is the electron affinity, which the energy gain by attaching an electron to a neutral atom. This fundamental quantity is, due to the almost general lack of bound excited states, the only atomic property that can be determined with high accuracy for negative ions. We will present the results of the first laser photodetachment studies of radioactive negative ions at CERN-ISOLDE. The photodetachment threshold for the radiogenic iodine isotope 128I was measured successfully, demonstrating the performance of the upgraded GANDALPH experimental beam line. The first detection of photo-detached astatine atoms marks a milestone towards the determination of the EA of this radioactive element.
6. Direction for the Future - Successive Acceleration of Positive and Negative Ions Applied to Space Propulsion
CERN Document Server
Aanesland, A.; Popelier, L.; Chabert, P.
2013-12-16
Electrical space thrusters show important advantages for applications in outer space compared to chemical thrusters, as they allow a longer mission lifetime with lower weight and propellant consumption. Mature technologies on the market today accelerate positive ions to generate thrust. The ion beam is neutralized by electrons downstream, and this need for an additional neutralization system has some drawbacks related to stability, lifetime and total weight and power consumption. Many new concepts, to get rid of the neutralizer, have been proposed, and the PEGASES ion-ion thruster is one of them. This new thruster concept aims at accelerating both positive and negative ions to generate thrust, such that additional neutralization is redundant. This chapter gives an overview of the concept of electric propulsion and the state of the development of this new ion-ion thruster.
7. Accelerator and Ion Beam Tradeoffs for Studies of Warm Dense Matter
International Nuclear Information System (INIS)
Barnard, J.J.; Briggs, R.J.; Callahan, D.A.; Davidson, R.C.; Friedman, A.; Grisham, L.; Lee, E.P.; Lee, R.W.; Logan, B.G.; Olson, C.L.; Rose, D.V.; Santhanam, P.; Sessler, A.M.; Staples, J.W.; Tabak, M.; Welch, D.R.; Wurtele, J.S.; Yu, S.S.
2006-01-01
One approach for heating a target to ''Warm Dense Matter'' conditions (similar, for example, to the interiors of giant planets or certain stages in inertial confinement fusion targets), is to use intense ion beams as the heating source (see refs.[6] and [7] and references therein for motivation and accelerator concepts). By consideration of ion beam phase-space constraints, both at the injector, and at the final focus, and consideration of simple equations of state and relations for ion stopping, approximate conditions at the target foil may be calculated. Thus, target temperature and pressure may be calculated as a function of ion mass, ion energy, pulse duration, velocity tilt, and other accelerator parameters. We connect some of these basic parameters to help search the extensive parameter space including ion mass, ion energy, total charge in beam pulse, beam emittance, target thickness and density
8. Development of ECR ion source for the HIMAC medical accelerator
International Nuclear Information System (INIS)
Kitagawa, A.; Yamada, S.; Sekiguchi, M.
1992-01-01
The development of the ECR ion source for the HIMAC injector is reported. The HIMAC facility has two types of the ion source, one is the PIG ion source and the other is the ECR ion source. The ECR ion source is especially expected long lifetime, easy operation, and easy maintenance for the medical use. Now, the system of the ion source is under construction. However, the tests of fundamental performances have been started. In the present tests, the output electrical currents of Ions are 1300 eμA of He 1+ , 210 eμA of Ne 3+ , and 100 eμA of Ar 6+ . And the good stability of the extracted beam is acquired. These performances satisfied the requirements for the radiotherapy. (author)
9. On the Acceleration and Anisotropy of Ions Within Magnetotail Dipolarizing Flux Bundles
Science.gov (United States)
Zhou, Xu-Zhi; Runov, Andrei; Angelopoulos, Vassilis; Artemyev, Anton V.; Birn, Joachim
2018-01-01
Dipolarizing flux bundles (DFBs), earthward propagating structures with enhanced northward magnetic field Bz, are usually believed to carry a distinctly different plasma population from that in the ambient magnetotail plasma sheet. The ion distribution functions within the DFB, however, have been recently found to be largely controlled by the ion adiabaticity parameter κ in the ambient plasma sheet outside the DFB. According to these observations, the ambient κ values of 2-3 usually correspond to a strong perpendicular anisotropy of suprathermal ions within the DFB, whereas for lower κ values the DFB ions become more isotropic. Here we utilize a simple, test particle model to explore the nature of the anisotropy and its dependence on the ambient κ values. We find that the anisotropy originates from successive ion reflections and reentries to the DFB, during which the ions are consecutively accelerated in the perpendicular direction by the DFB-associated electric field. This consecutive acceleration may be interrupted, however, when magnetic field lines are highly curved in the ambient plasma sheet. In this case, the ion trajectories become stochastic outside the DFB, which makes the reflected ions less likely to return to the DFB for another cycle of acceleration; as a consequence, the perpendicular ion anisotropy does not appear. Given that the DFB ions are a free energy source for instabilities when they are injected toward Earth, our simple model (that reproduces most observational features on the anisotropic DFB ion distributions) may shed new lights on the coupling process between magnetotail and inner magnetosphere.
10. An experimental program for collective acceleration of ions using intense relativistic electron beams
International Nuclear Information System (INIS)
Vijayan, T.; Raychowdhury, P.; Iyengar, S.K.
1992-01-01
A program of collective ion acceleration using intense relativistic electron beam (IREB) of 0.25-1MeV, 6-80kA, 60ns on the Kilo Ampere Linear Injector (KALI) systems to accelerate light and heavy ions to high energies approaching GeV with currents over tens of amperes, is envisaged in this report. The accelerator will make use of the intense space-charge field of electron beam in vacuum for accelerating ions which are injected into it. For ion injection, various alternatives, such as, localized gas puff, dielectric insert, laser plasma, etc. have been considered as present and long-term objectives. Among the variety of diagnostic methods chosen for characterizing the accelerated ions include range-energy in foil, CR-39 track detector, nuclear activation technique and time-of-flight for energy and species determination; ion Faraday cup for current measurement; and Thomson parabola analyzer for determining the post-acceleration charge-state. In the proposed MAHAKALI collective accelerator, protons of energy over 10 MeV and higher charge state metal ions around a GeV are predicted using a REB of 1MeV, 30kA, 60ns from KALI-5000. In present experiments using KALI-200 with REB parameters of 250keV, 60kA, 80ns, protons over a MeV and carbon and fluorine ions respectively for 12MeV and 16MeV in significant currents have been accelerated. (author). 35 refs., figs., tabs
11. Heating and acceleration of solar wind ions by turbulent wave spectrum in inhomogeneous expanding plasma
Energy Technology Data Exchange (ETDEWEB)
Ofman, Leon, E-mail: [email protected] [Department of Physics, The Catholic University of America, Washington, DC (United States); NASA Goddard Space Flight Center, Greenbelt, MD (United States); Visiting, Department of Geosciences, Tel Aviv University, Tel Aviv (Israel); Ozak, Nataly [Centre for mathematical Plasma Astrophysics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven (Belgium); Viñas, Adolfo F. [NASA Goddard Space Flight Center, Greenbelt, MD (United States)
2016-03-25
Near the Sun (< 10R{sub s}) the acceleration, heating, and propagation of the solar wind are likely affected by the background inhomogeneities of the magnetized plasma. The heating and the acceleration of the solar wind ions by turbulent wave spectrum in inhomogeneous plasma is studied using a 2.5D hybrid model. The hybrid model describes the kinetics of the ions, while the electrons are modeled as massless neutralizing fluid in an expanding box approach. Turbulent magnetic fluctuations dominated by power-law frequency spectra, which are evident from in-situ as well as remote sensing measurements, are used in our models. The effects of background density inhomogeneity across the magnetic field on the resonant ion heating are studied. The effect of super-Alfvénic ion drift on the ion heating is investigated. It is found that the turbulent wave spectrum of initially parallel propagating waves cascades to oblique modes, and leads to enhanced resonant ion heating due to the inhomogeneity. The acceleration of the solar wind ions is achieved by the parametric instability of large amplitude waves in the spectrum, and is also affected by the inhomogeneity. The results of the study provide the ion temperature anisotropy and drift velocity temporal evolution due to relaxation of the instability. The non-Maxwellian velocity distribution functions (VDFs) of the ions are modeled in the inhomogeneous solar wind plasma in the acceleration region close to the Sun.
12. Targets for production of high-intensity radioactive ion-beams
International Nuclear Information System (INIS)
Hagebo, E.; Hoff, P.; Steffensen, K.
1991-01-01
The recent developments of target systems for production of high intensity radioactive ion-beams at the ISOLDE mass separators is described. Methods for chemically selective production through separation of molecular ions are outlined and the effects of the addition of reactive gases has been studied. Results and further possible applications in the light element region are discussed. (author) 10 refs.; 9 figs.; 1 tab
13. Heavy ion beam factory for material science based on the KEK digital accelerator
Energy Technology Data Exchange (ETDEWEB)
2013-11-01
The KEK digital accelerator (DA) is an alternative to high-voltage electrostatic accelerators and conventional cyclotrons and synchrotrons, which are commonly used as swift heavy ion beam drivers. Compared with conventional accelerators, KEK-DA is capable of delivering a wider variety of ion species with various energies, as a result of its intrinsic properties. It is expected to serve as a heavy ion beam factory for research in materials science. Plans for its utilization include unique application programs, such as laboratory-based space science using virtual cosmic rays, heavy-ion mutagenesis in microorganisms, deep ion implantation, and modification of materials, which may be categorized into systematic studies of the spatial and temporal evolution of the locally and highly excited states of materials.
14. Prompt acceleration of ions by oblique turbulent shocks in solar flares
Science.gov (United States)
Decker, R. B.; Vlahos, L.
1985-01-01
Solar flares often accelerate ions and electrons to relativistic energies. The details of the acceleration process are not well understood, but until recently the main trend was to divide the acceleration process into two phases. During the first phase elctrons and ions are heated and accelerated up to several hundreds of keV simultaneously with the energy release. These mildly relativistic electrons interact with the ambient plasma and magnetic fields and generate hard X-ray and radio radiation. The second phase, usually delayed from the first by several minutes, is responsible for accelerating ions and electrons to relativistic energies. Relativistic electrons and ions interact with the solar atmosphere or escape from the Sun and generate gamma ray continuum, gamma ray line emission, neutron emission or are detected in space by spacecraft. In several flares the second phase is coincident with the start of a type 2 radio burst that is believed to be the signature of a shock wave. Observations from the Solar Maximum Mission spacecraft have shown, for the first time, that several flares accelerate particles to all energies nearly simultaneously. These results posed a new theoretical problem: How fast are shocks and magnetohydrodynamic turbulence formed and how quickly can they accelerate ions to 50 MeV in the lower corona? This problem is discussed.
15. Prompt acceleration of ions by oblique turbulent shocks in solar flares
International Nuclear Information System (INIS)
Decker, R.B.; Vlahos, L.
1985-01-01
Solar flares often accelerate ions and electrons to relativistic energies. The details of the acceleration process are not well understood, but until recently the main trend was to divide the acceleration process into two phases. During the first phase elctrons and ions are heated and accelerated up to several hundreds of keV simultaneously with the energy release. These mildly relativistic electrons interact with the ambient plasma and magnetic fields and generate hard x-ray and radio radiation. The second phase, usually delayed from the first by several minutes, is responsible for accelerating ions and electrons to relativistic energies. Relativistic electrons and ions interact with the solar atmosphere or escape from the Sun and generate gamma ray continuum, gamma ray line emission, neutron emission or are detected in space by spacecraft. In several flares the second phase is coincident with the start of a type 2 radio burst that is believed to be the signature of a shock wave. Observations from the Solar Maximum Mission spacecraft have shown, for the first time, that several flares accelerate particles to all energies nearly simultaneously. These results posed a new theoretical problem: How fast are shocks and magnetohydrodynamic turbulence formed and how quickly can they accelerate ions to 50 MeV in the lower corona. This problem is discussed
16. Modification of 300kV RF Ion Source for 1-MV Electrostatic Accelerator at KOMAC
International Nuclear Information System (INIS)
Kim, Dae-Il; Kwon, Hyeok-Jung; Park, Sae-Hoon; Cho, Yong-Sub
2015-01-01
The specifications of the 1-MV electrostatic accelerator are shown as below. High voltage power supply is electron transformer rectifier (ELV) type which was developed in Nuclear Physics Institute (Novosibirsk) for industrial electron accelerators. And accelerator column consists of alumina and metal electrode rings were 0.5m-long brazed structure which can be installed horizontally. In case of ion source for 1-MV electrostatic accelerator, it is chosen a thonemann type rf ion source and 300-kV test-stand was made up to confirm the stable operating conditions. High voltage power supply is fabricated by domestic company, and its operation has been confirming at KOMAC site. Equally, the ion source of 300-kV test-stand should be modified to install into the high voltage power supply. In this paper, modification of ion source of 300-kV test-stand for 1-MV electrostatic accelerator is presented and its processes are considered. 300-kV RF ion source and power supply are testing for the 1-MV electrostatic accelerator and trying for combination between them. The 1-MV electrostatic accelerator will be fabricated with domestic companies and tested in the beam application research building at KOMAC
17. Modification of 300kV RF Ion Source for 1-MV Electrostatic Accelerator at KOMAC
Energy Technology Data Exchange (ETDEWEB)
Kim, Dae-Il; Kwon, Hyeok-Jung; Park, Sae-Hoon; Cho, Yong-Sub [KOMAC, Gyeongju (Korea, Republic of)
2015-05-15
The specifications of the 1-MV electrostatic accelerator are shown as below. High voltage power supply is electron transformer rectifier (ELV) type which was developed in Nuclear Physics Institute (Novosibirsk) for industrial electron accelerators. And accelerator column consists of alumina and metal electrode rings were 0.5m-long brazed structure which can be installed horizontally. In case of ion source for 1-MV electrostatic accelerator, it is chosen a thonemann type rf ion source and 300-kV test-stand was made up to confirm the stable operating conditions. High voltage power supply is fabricated by domestic company, and its operation has been confirming at KOMAC site. Equally, the ion source of 300-kV test-stand should be modified to install into the high voltage power supply. In this paper, modification of ion source of 300-kV test-stand for 1-MV electrostatic accelerator is presented and its processes are considered. 300-kV RF ion source and power supply are testing for the 1-MV electrostatic accelerator and trying for combination between them. The 1-MV electrostatic accelerator will be fabricated with domestic companies and tested in the beam application research building at KOMAC.
18. New structure for accelerating heavy ions; Une nouvelle structure acceleratrice d'ions lourds
Energy Technology Data Exchange (ETDEWEB)
Pottier, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1969-06-01
A new type of accelerating structure is described which is particular suited to heavy ions (high wavelength, high shunt impedance, small size). Its properties are analyzed and compared to those of other structures (more particularly the lines). It is shown that a mode of operation exists of which the shunt impedance in the station mode has 80 per cent of its value for the progressive mode. Finally results are given obtained with a small experimental apparatus which uses this structure. (author) [French] On decrit un nouveau type de structure acceleratrice, particulierement appropriee aux ions lourds (grande longueur d'onde, forte impedance-shunt, faibles dimensions). Ses proprietes sont analysees et comparees a celles d'autres structures (plus particulierement les lignes). On met en evidence un mode de fonctionnement pour lequel l'impedance shunt en regime stationnaire vaut 80 pour cent de l'impedance shunt en regime progressif. Enfin on decrit les resultats obtenus a l'aide d'une petite machine experimentale mettant en oeuvre cette structure. (auteur)
19. MMS Observations of Protons and Heavy Ions Acceleration at Plasma Jet Fronts
Science.gov (United States)
Catapano, F.; Retino, A.; Zimbardo, G.; Cozzani, G.; Breuillard, H.; Le Contel, O.; Alexandrova, A.; Mirioni, L.; Cohen, I. J.; Turner, D. L.; Perri, S.; Greco, A.; Mauk, B.; Torbert, R. B.; Russell, C. T.; Khotyaintsev, Y. V.; Lindqvist, P. A.; Ergun, R.; Giles, B. L.; Fuselier, S. A.; Moore, T. E.; Burch, J.
2017-12-01
Plasma jet fronts in the Earth's magnetotail are kinetic-scale boundaries separating hot fast plasma jets, generally attributed to reconnection outflows, from colder ambient plasma. Jet fronts are typically associated with a sharp increase of the vertical component of the magnetic field Bz, an increase of the plasma temperature and a drop of plasma density. Spacecraft observations and numerical simulations indicate that jet fronts are sites of major ion acceleration. The exact acceleration mechanisms as well as the dependence of such mechanisms on ion composition are not fully understood, yet. Recent high-resolution measurements of ion distribution functions in the magnetotail allow for the first time to study the acceleration mechanisms in detail. Here, we show several examples of jet fronts and discuss ion acceleration therein. We show fronts that propagate in the mid-tail magnetotail both as isolated laminar boundaries and as multiple boundaries embedded in strong magnetic fluctuations and turbulence. We also show fronts in the near-Earth jet braking region, where they interact with the dipolar magnetic field and are significantly decelerated/diverted. Finally, we study the acceleration of different ion species (H+, He++, O+) at different types of fronts and we discuss possible different acceleration mechanisms and how they depend on the ion species.
20. Ion accelerator applications in medicine and cultural heritage
International Nuclear Information System (INIS)
Denker, A.; Cordini, D.; Heufelder, J.; Homeyer, H.; Kluge, H.; Simiantonakis, I.; Stark, R.; Weber, A.
2007-01-01
Formerly, accelerator laboratories were mainly dedicated to nuclear physics. Today, they are used in up-coming research fields and applications like material analysis and material science as well as biology, medicine or archaeology. Practical applications have been developed, involving hospitals, industry and even humanists in the use of accelerators. This paper focuses on some medical and analytical applications of the HMI accelerator facility, especially for eye tumour therapy and archaeology. The innovation of techniques to measure the dose distribution, the development of an automated monitoring procedure allowing an improved and accelerated patient positioning, and the implementation of a modern treatment planning system will be presented first. In the second part, the employment of accelerators in better understanding of our cultural heritage will be shown
1. Use of heavy ion accelerators in fusion reactor-related radiation-damage studies
International Nuclear Information System (INIS)
Taylor, A.; Dobson, D.A.
1974-01-01
The heavy-ion accelerator has become an important tool in the study of the fundamentals of radiation damage in fission- and fusion-reactor materials. Present facilities for such studies within the Materials Science Division at Argonne National Laboratory are provided by two complementary accelerator systems. Examples of the work carried out are discussed
2. Breakdowns and solutions in 15 UD pelletron ion accelerator facility at Inter-University Accelerator Centre, New Delhi
International Nuclear Information System (INIS)
Joshi, R.; Singh, P.; Suraj; Nishal, S.M.; Panwar, N.S.; Singh, M.P.; Kumar, R.; Prasad, J.; Sota, M.; Patel, V.P.; Sharma, R.P.; Kumar, Pankaj; Devi, K.D.; Ojha, S.; Gargari, S.; Chopra, S.; Kanjilal, D.
2013-01-01
15UD Pelletron accelerator, installed in Inter-University Accelerator Centre (IUAC), New Delhi, is a tandem ion accelerator and is performing well since its commissioning. Constant efforts have been put to keep high uptime and better performance of the accelerator for more than two decades. In recent years, the facility was improved by many modifications and up gradations. It has also gone through a few major breakdowns related to charging system and fiber optic cables. Out of two charging systems, one system failed and devices housed in tank stopped working due to the damage of fiber optic cables. The reasons for both of these breakdowns were studied thoroughly. The entire charging system and fiber optic cable network have been rebuilt and tested. The diagnostic techniques and maintenance methods for these two breakdowns will be discussed in this paper. (author)
3. Magnetic field structure of the U-120 cyclotron for heavy ions acceleration
International Nuclear Information System (INIS)
Schwabe, J.; Starzewski, J.
1975-01-01
The proposed magnetic structure makes possible the acceleration, in quasi-isochronous conditions, of ions having the ratio Z/A=0,665 - 0,1 on the U-120 cyclotron in Cracow. Simultaneously, significant improvement of the accelerated beam emittance, decrease in energy scattering down to a value of about 10 -3 , and an increase in the maximum accelerated beam energy may be obtained. (author)
4. Design studies of heavy ion linear accelerators constructed of independently phased spiral resonators
International Nuclear Information System (INIS)
Stokes, R.H.; Armstrong, D.D.
1975-01-01
Preliminary design studies are reported for two linear accelerators for heavy ions. One accelerator is a high-intensity machine which would operate with 100 percent duty factor and would produce tin ions with 6.1 MeV/A. Alternatively, it could be operated under pulsed conditions with 25 percent duty factor and would then accelerate uranium ions to 8.1 MeV/A, tin ions to 10.5 MeV/A, and all lighter ions to higher velocities. It would be injected with a positive multicharge ion source and a 4-MV single-ended dc generator. Also, design studies are reported for small postaccelerator injected by a model FN tandem. Both accelerators use three-drift-tube spiral resonators operating at room temperature. Magnetic quadrupole singlets are placed between all resonators to provide radial focussing. Each resonator is independently phased according to the velocity of the ion to be accelerated. The ability to adjust the phase of each resonator permits variations in final energy and other beam properties with great flexibility. (U.S.)
5. Regulation of naturally occurring and accelerator-produced radioactive materials: an update
International Nuclear Information System (INIS)
Bolling, L.A.; Lubenau, J.O.; Nussbaumer, D.A.
1984-10-01
In 1977, NRC published a report (NUREG-0301) of a task force review of the need for, and feasibility of, the Federal government regulating naturally occurring and accelerator-produced radioactive materials (NARM). Since that time, the Federal regulatory role has not significantly changed but State calls for increased Federal involvment have continued. In 1983, a National Governors' Association report on the NRC Agreement State program recommended amendment of the Atomic Energy Act to authorize NRC regulation of these materials. Based on that recommendation, and with the cooperation of the Conference of Radiation Control Program Directors, Inc., NRC staff undertook a review of the current status of use and regulation of NARM. This report contains the results of that review. 10 references
6. Radioactive core ions of microclusters, snowballs in superfluid helium
Energy Technology Data Exchange (ETDEWEB)
Takahashi, N. [Osaka Univ., Toyonaka (Japan). Dept. of Physics; Shimoda, T. [Osaka Univ., Toyonaka (Japan). Dept. of Physics; Fujita, Y. [Osaka Univ., Toyonaka (Japan). Dept. of Physics; Miyatake, H. [Osaka Univ., Toyonaka (Japan). Dept. of Physics; Mizoi, Y. [Osaka Univ., Toyonaka (Japan). Dept. of Physics; Kobayashi, H. [Osaka Univ., Toyonaka (Japan). Dept. of Physics; Sasaki, M. [Osaka Univ., Toyonaka (Japan). Dept. of Physics; Shirakura, T. [Osaka Univ., Toyonaka (Japan). Dept. of Physics; Itahashi, T. [Research Center for Nuclear Physics, Osaka Univ., Ibaraki (Japan); Mitsuoka, S. [Research Center for Nuclear Physics, Osaka Univ., Ibaraki (Japan); Matsukawa, T. [Naruto Univ. of Education, Tokushima (Japan); Ikeda, N. [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Morinobu, S. [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Hinde, D.J. [Australian National Univ., Canberra, ACT (Australia). Research School of Physical Sciences; Asahi, K. [Tokyo Inst. of Tech. (Japan). Dept. of Physics; Ueno, H. [Tokyo Inst. of Tech. (Japan). Dept. of Physics; Izumi, H. [Tokyo Inst. of Tech. (Japan). Dept. of Physics
1996-12-01
Short-lived beta-ray emitters, {sup 12}B, sustaining nuclear spin polarization were introduced into superfluid helium. The nuclear polarization of {sup 12}B was observed via measurement of beta-ray asymmetry. It was found that the nuclear polarization was preserved throughout the lifetime of {sup 12}B (20.3 ms). This suggests that the snowball`, an aggregation of helium atoms produced around an alien ion, constitutes a suitable milieu for freezing-out the nuclear spin of the core ion and that most likely the solidification takes place at the interior of the aggregation. (orig.).
7. Radioactive core ions of microclusters, ''snowballs'' in superfluid helium
International Nuclear Information System (INIS)
Takahashi, N.; Mitsuoka, S.; Matsukawa, T.; Ikeda, N.; Morinobu, S.; Hinde, D.J.; Asahi, K.; Ueno, H.; Izumi, H.
1996-01-01
Short-lived beta-ray emitters, 12 B, sustaining nuclear spin polarization were introduced into superfluid helium. The nuclear polarization of 12 B was observed via measurement of beta-ray asymmetry. It was found that the nuclear polarization was preserved throughout the lifetime of 12 B (20.3 ms). This suggests that the ''snowball'', an aggregation of helium atoms produced around an alien ion, constitutes a suitable milieu for freezing-out the nuclear spin of the core ion and that most likely the solidification takes place at the interior of the aggregation. (orig.)
8. Treatment of radioactive wastewaters by chemical precipitation and ion exchange
International Nuclear Information System (INIS)
Robinson, S.M.; Begovich, J.M.; Brown, C.H. Jr.; Campbell, D.O.; Collins, E.D.
1987-01-01
Precipitation and ion exchange methods are being developed at Oak Ridge National Laboratory to decontaminate wastewaters containing small amounts of 90 Sr and 137 Cs while minimizing waste generation. Distribution coefficients have been determined for strontium and cesium as functions of Ca, Na, and Mg concentrations from bench- and pilot-scale data for ion exchange resins and zeolites using actual wastewaters. Models have been used to estimate the total amount of waste that would be generated at full-scale operation. Based on these data, four process flowsheets are being tested at full-scale. 14 refs., 8 figs., 7 tabs
9. The Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory
Energy Technology Data Exchange (ETDEWEB)
Garrett, J.D. [Oak Ridge National Lab., TN (United States)
1996-12-31
The status of the new Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory (ORNL), which is slated to start its scientific program late this year is discussed, as is the new experimental equipment which is being constructed at this facility. Information on the early scientific program also is given.
10. The Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory
International Nuclear Information System (INIS)
Garrett, J.D.
1996-01-01
The status of the new Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory (ORNL), which is slated to start its scientific program late this year is discussed, as is the new experimental equipment which is being constructed at this facility. Information on the early scientific program also is given
11. High-current heavy-ion accelerator system and its application to material modification
International Nuclear Information System (INIS)
Kishimoto, Naoki; Takeda, Yoshihiko; Lee, C.G.; Umeda, Naoki; Okubo, Nariaki; Iwamoto, Eiji
2001-01-01
A high-current heavy-ion accelerator system has been developed to realize intense particle fluxes for material modification. The facility of a tandem accelerator attained 1 mA-class ion current both for negative low-energy ions and positive high-energy ions. The negative ion source of the key device is of the plasma-sputter type, equipped with mutli-cusp magnets and Cs supply. The intense negative ions are either directly used for material irradiation at 60 keV or further accelerated up to 6 MeV after charge transformation. Application of negative ions, which alleviates surface charging, enables us to conduct low-energy high-current irradiation on insulating substrates. Since positive ions above the MeV range are irrelevant for Coulomb repulsion, the facility as a whole meets the needs of high-current irradiation onto insulators over a wide energy range. Application of high flux ions provides technological merits not only for efficient implantation but also for essentially different material kinetics, which may become an important tool of material modification. Other advantages of the system are co-irradiation by intense laser and in-situ detection of kinetic processes. For examples of material modifications, we present nanoparticle fabrication in insulators, and synergistic phenomena by co-irradiation due to ions and photons. (author)
12. A detailed examination of laser-ion acceleration mechanisms in the relativistic transparency regime using tracers
Science.gov (United States)
Stark, David J.; Yin, Lin; Albright, Brian J.; Nystrom, William; Bird, Robert
2018-04-01
We present a particle-in-cell study of linearly polarized laser-ion acceleration systems, in which we use both two-dimensional (2D) and three-dimensional (3D) simulations to characterize the ion acceleration mechanisms in targets which become transparent to the laser pulse during irradiation. First, we perform a target length scan to optimize the peak ion energies in both 2D and 3D, and the predictive capabilities of 2D simulations are discussed. Tracer analysis allows us to isolate the acceleration into stages of target normal sheath acceleration (TNSA), hole boring (HB), and break-out afterburner (BOA) acceleration, which vary in effectiveness based on the simulation parameters. The thinnest targets reveal that enhanced TNSA is responsible for accelerating the most energetic ions, whereas the thickest targets have ions undergoing successive phases of HB and TNSA (in 2D) or BOA and TNSA (in 3D); HB is not observed to be a dominant acceleration mechanism in the 3D simulations. It is in the intermediate optimal regime, both when the laser breaks through the target with appreciable amplitude and when there is enough plasma to form a sustained high density flow, that BOA is most effective and is responsible for the most energetic ions. Eliminating the transverse laser spot size effects by performing a plane wave simulation, we can isolate with greater confidence the underlying physics behind the ion dynamics we observe. Specifically, supplemented by wavelet and FFT analyses, we match the post-transparency BOA acceleration with a wave-particle resonance with a high-amplitude low-frequency electrostatic wave of increasing phase velocity, consistent with that predicted by the Buneman instability.
13. Colorimetric detection and removal of radioactive Co ions using sodium alginate-based composite beads
International Nuclear Information System (INIS)
Kim, Daigeun; Jo, Ara; Yang, Hee-Man; Seo, Bum-Kyoung; Lee, Kune-Woo; Lee, Taek Seung
2017-01-01
14. Colorimetric detection and removal of radioactive Co ions using sodium alginate-based composite beads
Energy Technology Data Exchange (ETDEWEB)
Kim, Daigeun; Jo, Ara [Organic and Optoelectronic Materials Laboratory, Department of Organic Materials Engineering, Chungnam National University, Daejeon 34134 (Korea, Republic of); Yang, Hee-Man; Seo, Bum-Kyoung; Lee, Kune-Woo [Decontamination and Decommissioning Research Division, Korea Atomic Energy Research Institute, Daejeon 34057 (Korea, Republic of); Lee, Taek Seung, E-mail: [email protected] [Organic and Optoelectronic Materials Laboratory, Department of Organic Materials Engineering, Chungnam National University, Daejeon 34134 (Korea, Republic of)
2017-03-15
15. Proceedings of the Workshop on relativistic heavy ion physics at present and future accelerators
International Nuclear Information System (INIS)
Csoergoe, T.; Hegyi, S.; Lukacs, B.; Zimanyi, J.
1991-09-01
This volume contains the Proceedings of the Budapest Workshop on relativistic heavy ion physics at present and future accelerators. The topics includes experimental heavy ion physics, particle phenomenology, Bose-Einstein correlations, relativistic transport theory, quark-gluon plasma rehadronization, astronuclear physics, leptonpair production and intermittency. All contributions were indexed separately for the INIS database. (G.P.)
16. Development of heavy-ion accelerators as drivers for inertially confined fusion
International Nuclear Information System (INIS)
Herrmannsfeldt, W.B.
1979-06-01
The commercialization of inertial confinement fusion is discussed in terms of power costs. A chapter on heavy ion accelerators covers the prinicpal components, beam loss mechanisms, and theoretical considerations. Other tyopics discussed include the following: (1) heavy ion fusion implementation plan, (2) driver with accumulator rings fed by an rf LINAC, (3) single pass driver with an induction LINAC, and (4) implementation scenarios
17. A proposal for study of ion-beam induced chemical reactions using JAERI tandem accelerator
International Nuclear Information System (INIS)
1985-11-01
Problems in ion-beam induced chemical reactions using JAERI Tandem Accelerator were discussed. Research philosophy, some proposed experiments which are based on measurements during ion-beam bombardment, and main features of the experimental apparatus are briefly described in this report. (author)
18. Simulation studies of acceleration of heavy ions and their elemental compositions
International Nuclear Information System (INIS)
Toida, Mieko; Ohsawa, Yukiharu
1996-07-01
By using a one-dimensional, electromagnetic particle simulation code with full ion and electron dynamics, we have studied the acceleration of heavy ions by a nonlinear magnetosonic wave in a multi-ion-species plasma. First, we describe the mechanism of heavy ion acceleration by magnetosonic waves. We then investigate this by particle simulations. The simulation plasma contains four ion species: H, He, O, and Fe. The number density of He is taken to be 10% of that of H, and those of O and Fe are much lower. Simulations confirm that, as in a single-ion-species plasma, some of the hydrogens can be accelerated by the longitudinal electric field formed in the wave. Furthermore, they show that magnetosonic waves can accelerate all the particles of all the heavy species (He, O, and Fe) by a different mechanism, i.e., by the transverse electric field. The maximum speeds of the heavy species are about the same, of the order of the wave propagation speed. These are in good agreement with theoretical prediction. These results indicate that, if high-energy ions are produced in the solar corona through these mechanisms, the elemental compositions of these heavy ions can be similar to that of the background plasma, i.e., the corona
19. First phase plan for experimental study of heavy-ion inertial fusion accelerator
International Nuclear Information System (INIS)
Hattori, Toshiyuki; Okamura, Masahiro; Oguri, Yoshiyuki; Aida, Toshihiro; Takeuchi, Kouichi; Sasa, Kimikazu; Itoh, Takashi; Okada, Masashi; Takahashi, Yousuke; Ishii, Yasuyuki.
1993-01-01
We propose the basic experiment plan of driver for heavy-ion inertial fusion by heavy-ion linac [1-3] system and the heavy-ion cooler synchrotron. As the first phase of planning, we will improve old heavy-ion accelerator system that accelerate small intensity around Cl ion with charge to mass ratio of 1/4 up to 2.4 MeV/amu. The injector of the system will exchange from the 1.6 MV Peletron Tandem accelerator to an RFQ type linac with an ECR heavy-ion source. According to building up the power sources of RF and focusing magnet, then it is able to accelerate intense around Xe ion with charge to mass ratio of 1/6 up to 2.4 MeV/amu. At the next stage of it, we will construct a heavy-ion cooler synchrotron having magneticrigidity of 3 or 6 Tm and begin to study about HIF driver. (author)
20. Recent radioactive ion beam program at RIKEN and related topics | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8257247805595398, "perplexity": 4408.30981805615}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589251.7/warc/CC-MAIN-20180716095945-20180716115945-00616.warc.gz"} |
http://www.tutorialpoint.org/Filter/nonlinear-estimation-literature-review-page9.html | tutorialpoint.org
# Nonlinear Estimation
## 2 Literature review on quadrature based nonlinear estimation (Cont'd...)
### Smolyak's rule
A numerical approximation for the following integral can be expressed as [Wasilkowski 1995] [Jia 2012a]. $$\begin{split} &I_{n,L}(f)=\int_{\Re^n}f(x)\aleph(x;0,I_n)\\&\approx \sum_{q=L-n}^{L-1}(-1)^{L-1-q}C^{n-1}_{L-1-q}\sum_{\Xi\in\textbf{N}_q^n}(I_{l_1} \otimes I_{l_2} \otimes...\otimes I_{l_n})(f) \end{split}$$ where $I_{n,L}$ represents the numerical evaluation of $n$-dimensional system with the accuracy level $L$. This means that the approximation is exact for all the polynomials having degree upto $(2L-1)$. $C$ stands for the binomial coefficient i.e. $C_k^n=n!/k!(n-k)!$. $I_{l_j}$ is the single dimensional quadrature rule with the accuracy level $l_j\in\Xi$ and $\Xi \triangleq (l_1,l_2,...,l_n)$, $\otimes$ stands for the tensor product and $N_q^n$ is set of possible values of $l_j$ given as
Above Equation can be written as \begin{align} \begin{split} I_{n,L}(f)&\approx \sum_{q=L-n}^{L-1}(-1)^{L-1-q}C^{n-1}_{L-1-q}\sum_{\Xi\in\textbf{N}_q^n}\sum_{q_{s_1}\in X_{l_1}}\sum_{q_{s_2}\in X_{l_2}} \\ &...\sum_{q_{s_n}\in X_{l_n}}f(q_{s_1},q_{s_2},...,q_{s_n})w_{s_1}w_{s_2}...w_{s_n} \end{split} \end{align}
where $X_{l_j}$ is the set of quadrature points for the single dimensional quadrature rule $I_{l_j}$, $[q_{s_1},q_{s_2},...,q_{s_n}]^T$ is a Sparse-grid quadrature (SGQ) point. $q_{s_j}\in X_{l_j}$ and $w_{s_j}$ is the weight associated with $q_{s_j}$. Some SGQ points occure multiple times, that could be counted once by adding their weight. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.9931609630584717, "perplexity": 503.2790833302025}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249556231.85/warc/CC-MAIN-20190223223440-20190224005440-00391.warc.gz"} |
https://www.physicsforums.com/threads/does-bott-periodicity-imply-homotopy-equivalences.827505/ | # Does Bott periodicity imply homotopy equivalences?
1. Aug 13, 2015
### nonequilibrium
Hello!
Trying to learn some basics of (topological) K-theory and came up with the following question:
From what I can gather, we can define (complex, topological) K-theory as $K^n(X) = [X, B^n Gr^\infty(m)]$ with m going to infinity (indeed for m large enough, the answer is independent of it) and where B is taking the classifying space (this means: for any topological space X, we define BX such that $\Omega (B X) = X$ where $\Omega$ takes the loop space).
Let me know if so far I have made a mistake. As an illustration this tells us $K^0(X) = [X,Gr^\infty]$ (where I have implicitly taken the limit $m \to \infty$) which indeed classifies vector bundles on X up to (stable) isomorphism/equivalence.
So Bott periodicity tells us $K^n(X) \cong K^{n+2}(X)$. In other words it tells us $[X, B^n Gr^\infty] \cong [X, B^{n+2} Gr^\infty]$. My question is: have I made a mistake, or does Bott periodicity imply
$$\boxed{ B^n Gr^\infty \simeq B^{n+2} Gr^\infty} \;?$$
To focus on a specific example, let's take n = -1. Then this would tell us that the classifying space of the infinite Grassmannian is homotopic to U(n) (for n large enough). Is this true?...
EDIT: It seems wikipedia agrees with the above bold statements. However, not completely. For example it implies that in fact $B^2 Gr^\infty \simeq \mathbb Z \times Gr^\infty$. This seems weird, as I wouldn't expect $[X, Gr^\infty ] \cong [X, \mathbb Z \times Gr^\infty ]$ ... Do we have to take reduced cohomology/mod out by something to make it all work, or does it work like this anyway and do I just fail to see it?
2. Aug 14, 2015
### nonequilibrium
Aha, I have realized the answer. The key point is that $[X,Y] \cong [X,Y \times \mathbb Z]$ since in these contexts we are looking at *base point preserving* maps, which are insensitive to the number of disconnected components. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9610028266906738, "perplexity": 411.1785020386688}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647777.59/warc/CC-MAIN-20180322053608-20180322073608-00449.warc.gz"} |
https://people.maths.bris.ac.uk/~matyd/GroupNames/320/C4xDic20.html | Copied to
clipboard
## G = C4×Dic20order 320 = 26·5
### Direct product of C4 and Dic20
Series: Derived Chief Lower central Upper central
Derived series C1 — C20 — C4×Dic20
Chief series C1 — C5 — C10 — C2×C10 — C2×C20 — C2×Dic10 — C2×Dic20 — C4×Dic20
Lower central C5 — C10 — C20 — C4×Dic20
Upper central C1 — C2×C4 — C42 — C4×C8
Generators and relations for C4×Dic20
G = < a,b,c | a4=b40=1, c2=b20, ab=ba, ac=ca, cbc-1=b-1 >
Subgroups: 374 in 110 conjugacy classes, 55 normal (31 characteristic)
C1, C2, C4, C4, C4, C22, C5, C8, C8, C2×C4, C2×C4, Q8, C10, C42, C42, C4⋊C4, C2×C8, Q16, C2×Q8, Dic5, C20, C20, C20, C2×C10, C4×C8, Q8⋊C4, C2.D8, C4×Q8, C2×Q16, C40, C40, Dic10, Dic10, C2×Dic5, C2×C20, C4×Q16, Dic20, C4×Dic5, C10.D4, C4⋊Dic5, C4×C20, C2×C40, C2×Dic10, C20.44D4, C405C4, C4×C40, C4×Dic10, C2×Dic20, C4×Dic20
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D5, Q16, C22×C4, C2×D4, C4○D4, D10, C4×D4, C2×Q16, C4○D8, C4×D5, D20, C22×D5, C4×Q16, Dic20, C2×C4×D5, C2×D20, C4○D20, C4×D20, D407C2, C2×Dic20, C4×Dic20
Smallest permutation representation of C4×Dic20
Regular action on 320 points
Generators in S320
(1 202 107 46)(2 203 108 47)(3 204 109 48)(4 205 110 49)(5 206 111 50)(6 207 112 51)(7 208 113 52)(8 209 114 53)(9 210 115 54)(10 211 116 55)(11 212 117 56)(12 213 118 57)(13 214 119 58)(14 215 120 59)(15 216 81 60)(16 217 82 61)(17 218 83 62)(18 219 84 63)(19 220 85 64)(20 221 86 65)(21 222 87 66)(22 223 88 67)(23 224 89 68)(24 225 90 69)(25 226 91 70)(26 227 92 71)(27 228 93 72)(28 229 94 73)(29 230 95 74)(30 231 96 75)(31 232 97 76)(32 233 98 77)(33 234 99 78)(34 235 100 79)(35 236 101 80)(36 237 102 41)(37 238 103 42)(38 239 104 43)(39 240 105 44)(40 201 106 45)(121 306 178 247)(122 307 179 248)(123 308 180 249)(124 309 181 250)(125 310 182 251)(126 311 183 252)(127 312 184 253)(128 313 185 254)(129 314 186 255)(130 315 187 256)(131 316 188 257)(132 317 189 258)(133 318 190 259)(134 319 191 260)(135 320 192 261)(136 281 193 262)(137 282 194 263)(138 283 195 264)(139 284 196 265)(140 285 197 266)(141 286 198 267)(142 287 199 268)(143 288 200 269)(144 289 161 270)(145 290 162 271)(146 291 163 272)(147 292 164 273)(148 293 165 274)(149 294 166 275)(150 295 167 276)(151 296 168 277)(152 297 169 278)(153 298 170 279)(154 299 171 280)(155 300 172 241)(156 301 173 242)(157 302 174 243)(158 303 175 244)(159 304 176 245)(160 305 177 246)
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40)(41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160)(161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200)(201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240)(241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280)(281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320)
(1 261 21 241)(2 260 22 280)(3 259 23 279)(4 258 24 278)(5 257 25 277)(6 256 26 276)(7 255 27 275)(8 254 28 274)(9 253 29 273)(10 252 30 272)(11 251 31 271)(12 250 32 270)(13 249 33 269)(14 248 34 268)(15 247 35 267)(16 246 36 266)(17 245 37 265)(18 244 38 264)(19 243 39 263)(20 242 40 262)(41 197 61 177)(42 196 62 176)(43 195 63 175)(44 194 64 174)(45 193 65 173)(46 192 66 172)(47 191 67 171)(48 190 68 170)(49 189 69 169)(50 188 70 168)(51 187 71 167)(52 186 72 166)(53 185 73 165)(54 184 74 164)(55 183 75 163)(56 182 76 162)(57 181 77 161)(58 180 78 200)(59 179 79 199)(60 178 80 198)(81 306 101 286)(82 305 102 285)(83 304 103 284)(84 303 104 283)(85 302 105 282)(86 301 106 281)(87 300 107 320)(88 299 108 319)(89 298 109 318)(90 297 110 317)(91 296 111 316)(92 295 112 315)(93 294 113 314)(94 293 114 313)(95 292 115 312)(96 291 116 311)(97 290 117 310)(98 289 118 309)(99 288 119 308)(100 287 120 307)(121 236 141 216)(122 235 142 215)(123 234 143 214)(124 233 144 213)(125 232 145 212)(126 231 146 211)(127 230 147 210)(128 229 148 209)(129 228 149 208)(130 227 150 207)(131 226 151 206)(132 225 152 205)(133 224 153 204)(134 223 154 203)(135 222 155 202)(136 221 156 201)(137 220 157 240)(138 219 158 239)(139 218 159 238)(140 217 160 237)
G:=sub<Sym(320)| (1,202,107,46)(2,203,108,47)(3,204,109,48)(4,205,110,49)(5,206,111,50)(6,207,112,51)(7,208,113,52)(8,209,114,53)(9,210,115,54)(10,211,116,55)(11,212,117,56)(12,213,118,57)(13,214,119,58)(14,215,120,59)(15,216,81,60)(16,217,82,61)(17,218,83,62)(18,219,84,63)(19,220,85,64)(20,221,86,65)(21,222,87,66)(22,223,88,67)(23,224,89,68)(24,225,90,69)(25,226,91,70)(26,227,92,71)(27,228,93,72)(28,229,94,73)(29,230,95,74)(30,231,96,75)(31,232,97,76)(32,233,98,77)(33,234,99,78)(34,235,100,79)(35,236,101,80)(36,237,102,41)(37,238,103,42)(38,239,104,43)(39,240,105,44)(40,201,106,45)(121,306,178,247)(122,307,179,248)(123,308,180,249)(124,309,181,250)(125,310,182,251)(126,311,183,252)(127,312,184,253)(128,313,185,254)(129,314,186,255)(130,315,187,256)(131,316,188,257)(132,317,189,258)(133,318,190,259)(134,319,191,260)(135,320,192,261)(136,281,193,262)(137,282,194,263)(138,283,195,264)(139,284,196,265)(140,285,197,266)(141,286,198,267)(142,287,199,268)(143,288,200,269)(144,289,161,270)(145,290,162,271)(146,291,163,272)(147,292,164,273)(148,293,165,274)(149,294,166,275)(150,295,167,276)(151,296,168,277)(152,297,169,278)(153,298,170,279)(154,299,171,280)(155,300,172,241)(156,301,173,242)(157,302,174,243)(158,303,175,244)(159,304,176,245)(160,305,177,246), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320), (1,261,21,241)(2,260,22,280)(3,259,23,279)(4,258,24,278)(5,257,25,277)(6,256,26,276)(7,255,27,275)(8,254,28,274)(9,253,29,273)(10,252,30,272)(11,251,31,271)(12,250,32,270)(13,249,33,269)(14,248,34,268)(15,247,35,267)(16,246,36,266)(17,245,37,265)(18,244,38,264)(19,243,39,263)(20,242,40,262)(41,197,61,177)(42,196,62,176)(43,195,63,175)(44,194,64,174)(45,193,65,173)(46,192,66,172)(47,191,67,171)(48,190,68,170)(49,189,69,169)(50,188,70,168)(51,187,71,167)(52,186,72,166)(53,185,73,165)(54,184,74,164)(55,183,75,163)(56,182,76,162)(57,181,77,161)(58,180,78,200)(59,179,79,199)(60,178,80,198)(81,306,101,286)(82,305,102,285)(83,304,103,284)(84,303,104,283)(85,302,105,282)(86,301,106,281)(87,300,107,320)(88,299,108,319)(89,298,109,318)(90,297,110,317)(91,296,111,316)(92,295,112,315)(93,294,113,314)(94,293,114,313)(95,292,115,312)(96,291,116,311)(97,290,117,310)(98,289,118,309)(99,288,119,308)(100,287,120,307)(121,236,141,216)(122,235,142,215)(123,234,143,214)(124,233,144,213)(125,232,145,212)(126,231,146,211)(127,230,147,210)(128,229,148,209)(129,228,149,208)(130,227,150,207)(131,226,151,206)(132,225,152,205)(133,224,153,204)(134,223,154,203)(135,222,155,202)(136,221,156,201)(137,220,157,240)(138,219,158,239)(139,218,159,238)(140,217,160,237)>;
G:=Group( (1,202,107,46)(2,203,108,47)(3,204,109,48)(4,205,110,49)(5,206,111,50)(6,207,112,51)(7,208,113,52)(8,209,114,53)(9,210,115,54)(10,211,116,55)(11,212,117,56)(12,213,118,57)(13,214,119,58)(14,215,120,59)(15,216,81,60)(16,217,82,61)(17,218,83,62)(18,219,84,63)(19,220,85,64)(20,221,86,65)(21,222,87,66)(22,223,88,67)(23,224,89,68)(24,225,90,69)(25,226,91,70)(26,227,92,71)(27,228,93,72)(28,229,94,73)(29,230,95,74)(30,231,96,75)(31,232,97,76)(32,233,98,77)(33,234,99,78)(34,235,100,79)(35,236,101,80)(36,237,102,41)(37,238,103,42)(38,239,104,43)(39,240,105,44)(40,201,106,45)(121,306,178,247)(122,307,179,248)(123,308,180,249)(124,309,181,250)(125,310,182,251)(126,311,183,252)(127,312,184,253)(128,313,185,254)(129,314,186,255)(130,315,187,256)(131,316,188,257)(132,317,189,258)(133,318,190,259)(134,319,191,260)(135,320,192,261)(136,281,193,262)(137,282,194,263)(138,283,195,264)(139,284,196,265)(140,285,197,266)(141,286,198,267)(142,287,199,268)(143,288,200,269)(144,289,161,270)(145,290,162,271)(146,291,163,272)(147,292,164,273)(148,293,165,274)(149,294,166,275)(150,295,167,276)(151,296,168,277)(152,297,169,278)(153,298,170,279)(154,299,171,280)(155,300,172,241)(156,301,173,242)(157,302,174,243)(158,303,175,244)(159,304,176,245)(160,305,177,246), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320), (1,261,21,241)(2,260,22,280)(3,259,23,279)(4,258,24,278)(5,257,25,277)(6,256,26,276)(7,255,27,275)(8,254,28,274)(9,253,29,273)(10,252,30,272)(11,251,31,271)(12,250,32,270)(13,249,33,269)(14,248,34,268)(15,247,35,267)(16,246,36,266)(17,245,37,265)(18,244,38,264)(19,243,39,263)(20,242,40,262)(41,197,61,177)(42,196,62,176)(43,195,63,175)(44,194,64,174)(45,193,65,173)(46,192,66,172)(47,191,67,171)(48,190,68,170)(49,189,69,169)(50,188,70,168)(51,187,71,167)(52,186,72,166)(53,185,73,165)(54,184,74,164)(55,183,75,163)(56,182,76,162)(57,181,77,161)(58,180,78,200)(59,179,79,199)(60,178,80,198)(81,306,101,286)(82,305,102,285)(83,304,103,284)(84,303,104,283)(85,302,105,282)(86,301,106,281)(87,300,107,320)(88,299,108,319)(89,298,109,318)(90,297,110,317)(91,296,111,316)(92,295,112,315)(93,294,113,314)(94,293,114,313)(95,292,115,312)(96,291,116,311)(97,290,117,310)(98,289,118,309)(99,288,119,308)(100,287,120,307)(121,236,141,216)(122,235,142,215)(123,234,143,214)(124,233,144,213)(125,232,145,212)(126,231,146,211)(127,230,147,210)(128,229,148,209)(129,228,149,208)(130,227,150,207)(131,226,151,206)(132,225,152,205)(133,224,153,204)(134,223,154,203)(135,222,155,202)(136,221,156,201)(137,220,157,240)(138,219,158,239)(139,218,159,238)(140,217,160,237) );
G=PermutationGroup([[(1,202,107,46),(2,203,108,47),(3,204,109,48),(4,205,110,49),(5,206,111,50),(6,207,112,51),(7,208,113,52),(8,209,114,53),(9,210,115,54),(10,211,116,55),(11,212,117,56),(12,213,118,57),(13,214,119,58),(14,215,120,59),(15,216,81,60),(16,217,82,61),(17,218,83,62),(18,219,84,63),(19,220,85,64),(20,221,86,65),(21,222,87,66),(22,223,88,67),(23,224,89,68),(24,225,90,69),(25,226,91,70),(26,227,92,71),(27,228,93,72),(28,229,94,73),(29,230,95,74),(30,231,96,75),(31,232,97,76),(32,233,98,77),(33,234,99,78),(34,235,100,79),(35,236,101,80),(36,237,102,41),(37,238,103,42),(38,239,104,43),(39,240,105,44),(40,201,106,45),(121,306,178,247),(122,307,179,248),(123,308,180,249),(124,309,181,250),(125,310,182,251),(126,311,183,252),(127,312,184,253),(128,313,185,254),(129,314,186,255),(130,315,187,256),(131,316,188,257),(132,317,189,258),(133,318,190,259),(134,319,191,260),(135,320,192,261),(136,281,193,262),(137,282,194,263),(138,283,195,264),(139,284,196,265),(140,285,197,266),(141,286,198,267),(142,287,199,268),(143,288,200,269),(144,289,161,270),(145,290,162,271),(146,291,163,272),(147,292,164,273),(148,293,165,274),(149,294,166,275),(150,295,167,276),(151,296,168,277),(152,297,169,278),(153,298,170,279),(154,299,171,280),(155,300,172,241),(156,301,173,242),(157,302,174,243),(158,303,175,244),(159,304,176,245),(160,305,177,246)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40),(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160),(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200),(201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240),(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280),(281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320)], [(1,261,21,241),(2,260,22,280),(3,259,23,279),(4,258,24,278),(5,257,25,277),(6,256,26,276),(7,255,27,275),(8,254,28,274),(9,253,29,273),(10,252,30,272),(11,251,31,271),(12,250,32,270),(13,249,33,269),(14,248,34,268),(15,247,35,267),(16,246,36,266),(17,245,37,265),(18,244,38,264),(19,243,39,263),(20,242,40,262),(41,197,61,177),(42,196,62,176),(43,195,63,175),(44,194,64,174),(45,193,65,173),(46,192,66,172),(47,191,67,171),(48,190,68,170),(49,189,69,169),(50,188,70,168),(51,187,71,167),(52,186,72,166),(53,185,73,165),(54,184,74,164),(55,183,75,163),(56,182,76,162),(57,181,77,161),(58,180,78,200),(59,179,79,199),(60,178,80,198),(81,306,101,286),(82,305,102,285),(83,304,103,284),(84,303,104,283),(85,302,105,282),(86,301,106,281),(87,300,107,320),(88,299,108,319),(89,298,109,318),(90,297,110,317),(91,296,111,316),(92,295,112,315),(93,294,113,314),(94,293,114,313),(95,292,115,312),(96,291,116,311),(97,290,117,310),(98,289,118,309),(99,288,119,308),(100,287,120,307),(121,236,141,216),(122,235,142,215),(123,234,143,214),(124,233,144,213),(125,232,145,212),(126,231,146,211),(127,230,147,210),(128,229,148,209),(129,228,149,208),(130,227,150,207),(131,226,151,206),(132,225,152,205),(133,224,153,204),(134,223,154,203),(135,222,155,202),(136,221,156,201),(137,220,157,240),(138,219,158,239),(139,218,159,238),(140,217,160,237)]])
92 conjugacy classes
class 1 2A 2B 2C 4A 4B 4C 4D 4E 4F 4G 4H 4I ··· 4P 5A 5B 8A ··· 8H 10A ··· 10F 20A ··· 20X 40A ··· 40AF order 1 2 2 2 4 4 4 4 4 4 4 4 4 ··· 4 5 5 8 ··· 8 10 ··· 10 20 ··· 20 40 ··· 40 size 1 1 1 1 1 1 1 1 2 2 2 2 20 ··· 20 2 2 2 ··· 2 2 ··· 2 2 ··· 2 2 ··· 2
92 irreducible representations
dim 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 type + + + + + + + + - + + + - image C1 C2 C2 C2 C2 C2 C4 D4 D5 Q16 C4○D4 D10 D10 C4○D8 C4×D5 D20 Dic20 C4○D20 D40⋊7C2 kernel C4×Dic20 C20.44D4 C40⋊5C4 C4×C40 C4×Dic10 C2×Dic20 Dic20 C2×C20 C4×C8 C20 C20 C42 C2×C8 C10 C8 C2×C4 C4 C4 C2 # reps 1 2 1 1 2 1 8 2 2 4 2 2 4 4 8 8 16 8 16
Matrix representation of C4×Dic20 in GL4(𝔽41) generated by
9 0 0 0 0 9 0 0 0 0 1 0 0 0 0 1
,
40 1 0 0 5 35 0 0 0 0 15 3 0 0 38 35
,
25 30 0 0 12 16 0 0 0 0 17 38 0 0 1 24
G:=sub<GL(4,GF(41))| [9,0,0,0,0,9,0,0,0,0,1,0,0,0,0,1],[40,5,0,0,1,35,0,0,0,0,15,38,0,0,3,35],[25,12,0,0,30,16,0,0,0,0,17,1,0,0,38,24] >;
C4×Dic20 in GAP, Magma, Sage, TeX
C_4\times {\rm Dic}_{20}
% in TeX
G:=Group("C4xDic20");
// GroupNames label
G:=SmallGroup(320,325);
// by ID
G=gap.SmallGroup(320,325);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,253,344,58,1684,102,12550]);
// Polycyclic
G:=Group<a,b,c|a^4=b^40=1,c^2=b^20,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
×
𝔽 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9735801219940186, "perplexity": 1858.6006833251145}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989012.26/warc/CC-MAIN-20210509183309-20210509213309-00531.warc.gz"} |
http://www.dummies.com/how-to/content/how-to-determine-the-measure-of-an-angle-whose-ve0.navId-407427.html | Of the three places an angle’s vertex can be in relation to a circle (inside, on, or outside the circle), the two types of angles that have their vertex on a circle — inscribed angles and tangent-chord angles — are the ones that come up in the most problems and are therefore the most important.
• Inscribed angle: An inscribed angle, like angle BCD in the above figure on the left, is an angle whose vertex lies on a circle and whose sides are two chords of the circle.
• Tangent-chord angle: A tangent-chord angle, like angle JKL in the above figure on the right, is an angle whose vertex lies on a circle and whose sides are a tangent and a chord of the circle.
Measure of an angle on a circle: The measure of an inscribed angle or a tangent-chord angle is one-half the measure of its intercepted arc.
For example, in the above figure,
Make sure you remember the simple idea that an angle on a circle is half the measure of the arc it intercepts (or if you look at it the other way around, the arc measure is double the angle). If you forget which is half of which, try this: Draw a quick sketch of a circle with a 90° arc (a quarter of the circle) and an inscribed angle that intercepts the 90° arc. You’ll see right away that the angle is less than 90°, telling you that the angle is the thing that’s half of the arc, not vice versa.
Congruent angles on a circle:
• If two inscribed or tangent-chord angles intercept the same arc, then they’re congruent (see the below figure on the left).
• If two inscribed or tangent-chord angles intercept congruent arcs, then they’re congruent (see the below figure on the right).
Time to see these ideas in action.
Using the figure above, solve the following problem:
The key to this problem is to just use the inscribed angle formula over and over. Remember — the angle is half the arc; the arc is twice the angle.
You’ve got the measures of the first three: 110°, 40°, and 120° respectively. That adds up to 270°.
Note: This triangle idea also gives you a good way to check your results — do the angles add up to 180°?
That does add up to 180°, so it checks, which leads to the following tip.
Whenever possible, check your answers with a method that’s different from your original solution method. This is a much more effective check of your results than simply going through your work a second time looking for mistakes. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8003851175308228, "perplexity": 447.81210048487094}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783393533.44/warc/CC-MAIN-20160624154953-00191-ip-10-164-35-72.ec2.internal.warc.gz"} |
http://www.oalib.com/search?kw=Wei%20Yin&searchField=authors | Home OALib Journal OALib PrePrints Submit Ranking News My Lib FAQ About Us Follow Us+
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APC: Only $99 Submit 2019 ( 86 ) 2018 ( 846 ) 2017 ( 848 ) 2016 ( 858 ) Search Results: 1 - 10 of 61263 matches for " Wei Yin " All listed articles are free for downloading (OA Articles) Page 1 /61263 Display every page 5 10 20 Item American Journal of Industrial and Business Management (AJIBM) , 2014, DOI: 10.4236/ajibm.2014.41007 Abstract: This paper develops the basic model of the buy-back contract by introducing the fairness to investigate how the dominant supplier decides the wholesale price, whether the buy-back contract can achieve coordination and how the fairness influences the wholesale price. It is found that, under Stackelberg game between the retailer and the dominant supplier, the buy-back contract cannot coordinate the supply chain whether the fairness is incorporated or not. Furthermore, the optimal wholesale price under Stackelberg game is larger than the initial wholesale price, which can achieve coordination. Moreover, the optimal wholesale price decreases with the retailer’s fairness, while it increases with the supplier’s fairness. Wei Yin Asian Social Science , 2009, DOI: 10.5539/ass.v4n8p137 Abstract: Society has assigned different expectation and obligation to male and female. And this difference is shown in many ways, especially in clothing. Society prescribes standard costume for both sexes. Human clothing represents great otherness because of the gender differences. This dissertation is to discuss the relationship between gender differences and costume. Technology and Investment (TI) , 2017, DOI: 10.4236/ti.2017.84016 Abstract: Intellectual property operation platform serves as an important bridge between promoting and realizing the value of intellectual property. And the construction and improvement of it holds the key to improve the level of intellectual property application and implement Chinese IPR strategy. Moreover, the coming of “Internet +” era creates a favorable environment for intellectual property operation platforms. The purpose of this paper is to explore how to build an intellectual property rights operation platform which has overall function under the background of “Internet +”, then to create a “one-stop” solution for intellectual property operation under demand orientation. The second step is to strengthen the external linkage between intellectual property operation platform and other platforms to integrate resources. The third step is to design the internal business module of intellectual property operation platform, emphasize the compatibility of different subjects’ interest in the platform and avoid the technical, legal and economic risks in the construction process of intellectual property operation platform. Chinese Science Bulletin , 2010, DOI: 10.1007/s11434-010-3119-2 Abstract: In the past decade, the asymmetric Morita-Baylis-Hillman (MBH)/aza-Morita-Baylis-Hillman (aza-MBH) reaction has attracted great attention because it leads to the formation of densely functionalized products in a catalytic and atom-economic way. The MBH/aza-MBH adducts can be further applied in a wide variety of organic synthesis, such as peptide synthesis and heterocyclic compounds synthesis. After a lot of attempts to improve the enantioselectivity, many types of chiral organocatalysts have been identified as highly enantioselective organocatalysts in MBH/aza-MBH reaction. Especially, certain “privileged chiral catalysts” are highly enantioselective in MBH/aza-MBH reaction, which are designed and developed through introducing bi-/multi-functional groups on the so-called “privileged structures” such as cinchona alkaloids, BINAP/BINOL. This review summarizes the exciting advances about the design and development of chiral catalysts derived from “privileged structures” and their applications in asymmetric MBH/aza-MBH reaction. Journal of Inequalities and Applications , 2011, DOI: 10.1155/2011/479576 Abstract: Journal of Inequalities and Applications , 2011, Abstract: Let , the authors introduce in this paper a class of the hypersingular Marcinkiewicz integrals along surface with variable kernels defined by , where with . The authors prove that the operator is bounded from Sobolev space to space for , and from Hardy-Sobolev space to space for . As corollaries of the result, they also prove the boundedness of the Littlewood-Paley type operators and which relate to the Lusin area integral and the Littlewood-Paley function. Physics , 2013, DOI: 10.1103/PhysRevC.88.015804 Abstract: The three-body force (TBF) effect on the neutrino emissivity in neutron star matter and the total neutrino emissivity of neutron stars have been investigated within the framework of the Brueckner-Hartree-Fock approach by adopting the AV18 two-body interaction plus a microscopic TBF. The neutrino emissivity from the direct Urca process turns out to be much larger than that from the modified Urca process. Inclusion of the TBF reduces strongly the density thresholds of the direct Urca processes involving electrons and muons. The TBF effect on the total neutrino emissivity of neutron stars is shown to be negligibly weak for neutron stars with small masses. For neutron stars with large masses, the TBF effect becomes visible and inclusion of the TBF may enhance the total neutrino emissivity by about 50% for neutron stars with a given mass of$M=1.6M_{\odot}$. Wei-Yin Loh Mathematics , 2006, DOI: 10.1214/074921706000000464 Abstract: Although regression trees were originally designed for large datasets, they can profitably be used on small datasets as well, including those from replicated or unreplicated complete factorial experiments. We show that in the latter situations, regression tree models can provide simpler and more intuitive interpretations of interaction effects as differences between conditional main effects. We present simulation results to verify that the models can yield lower prediction mean squared errors than the traditional techniques. The tree models span a wide range of sophistication, from piecewise constant to piecewise simple and multiple linear, and from least squares to Poisson and logistic regression. Mathematics , 2015, DOI: 10.1016/j.na.2015.03.022 Abstract: In this paper we mainly investigate the Cauchy problem of a two-component Novikov system. We first prove the local well-posedness of the system in Besov spaces$B^{s-1}_{p,r}\times B^s_{p,r}$with$p,r\in[1,\infty],~s>\max\{1+\frac{1}{p},\frac{3}{2}\}$by using the Littlewood-Paley theory and transport equations theory. Then, by virtue of logarithmic interpolation inequalities and the Osgood lemma, we establish the local well-posedness of the system in the critical Besov space$B^{\frac{1}{2}}_{2,1}\times B^{\frac{3}{2}}_{2,1}$. Moreover, we present two blow-up criteria for the system by making use of the conservation laws. Mathematics , 2014, Abstract: In this paper we mainly investigate the Cauchy problem of the finite extensible nonlinear elastic (FENE) dumbbell model with dimension$d\geq2\$. We first proved the local well-posedness for the FENE model in Besov spaces by using the Littlewood-Paley theory. Then by an accurate estimate we get a blow-up criterion. Moreover, if the initial data is perturbation around equilibrium, we obtain a global existence result. Our obtained results generalize recent results in [8].
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http://klotza.blogspot.com/2016/01/ | ## Tuesday, 26 January 2016
### Adding gravity to the nuclear liquid drop model: stabilizing the all-neutron atom.
The liquid drop model is a formula used to calculate the excess mass of an atomic nucleus based on the different factors that contribute to its total energy. It can tell us whether a given nucleus with a certain number of protons and neutrons will be stable or unstable, and informs us that an all-neutron nucleus is always unstable. However, if we modify the model slightly to include gravitational attraction, we can find how many neutrons are required to make a stable nucleus, and use this to estimate the minimum mass of a neutron star. I think it's a neat application of various physics concepts, so I'm sharing it with you, the readers of this blog.
Exactly like this.
The Liquid Drop Model
The liquid drop model, also known as the semi-empirical mass formula, is an equation used for predicting the binding energy of a nucleus, such that the total mass of the nucleus is the sum of the protons, the neutrons, and the mass due to the binding energy. If the total mass of the system is lower than just a pile of free protons and neutrons (e.g. the binding energy is negative), the nucleus will be bound, and if it is greater than the mass of the particles alone, it will not be bound*. It does a pretty good job at explaining nuclear masses, but is not perfect. The variables in the formula are the number of protons, Z, the number of neutrons, N, and their sum, A=N+Z. The nucleus is treated as a spherical "drop" with a volume proportional to the number of particles that make it up. Typically, there are five terms in the formula:
Each term has a unique scaling with the nucleon numbers, and the strength of each term is determined by the value of the individual Greek prefactors, with dimensions of energy (they are 15.4, 16.9, 0.7, 22.4, and 11.1 in mega electron volts, from alpha to epsilon). I'll briefly discuss what each term means and motivate its scaling. The first is the residual strong attraction**, which is the only term that is always binding (negative). The attraction is so short-range that it can be treated as an interaction between neighbouring protons or neutrons, and the number of neighbour-pairs is proportional to the number of particles, which is why it is linear. The second term has to do with surface-to-volume ratio (the number of particles at the surface scales as the 2/3 power of the volume), and the fact that particles at the surface of the nucleus will have less binding partners than interior particles. This term is most relevant for nuclei smaller than iron, that can increase their binding energy by undergoing fusion. The third term is the electrostatic repulsion between protons, and has the same form as the electric potential of a charged sphere: proportional to the two charges multiplied in Coulomb's force law, and inversely proportional to the radius which goes as the cube-root of volume. The fourth term, which will become more important later in this post, is minimized when the number of protons and neutrons is the same. This can be understood in terms of the Pauli exclusion principle: only two of each kind of particle can be in the same energy level, so each additional pair must have a higher energy. If there are more neutrons than protons, some of the higher energy neutrons can become lower energy protons and overall the excess energy decreases. Or vice versa, if there are more protons. An excess difference between the number of protons or neutrons can lead to either kind of beta decay (although the Coulomb term tends to bias nuclei towards having more neutrons than protons). The last term has to do with the fact that it's energetically favourable to have an even number of protons and an even number of neutrons so that the spins of the particles can align (sort of like a magnetic attraction between pairs, if you will), so an odd number of either will make the energy more positive (bad), while an even number will make it more negative (good).
From Wikipedia's article on the topic, demonstrating that extra neutrons mean extra energy.
So just to give a basic example, if we have iron-56, Z=26, N=30, A=56, and the formula gives us -490 MeV, about half the mass of a proton. The nuclear mass of iron-56 is 55.935 amu, the sum of the protons and neutrons is 56.429 amu, so the difference is 0.494 amu or 460 MeV, so the formula was pretty close, if I did the math right. It's not perfect, but it works. Another thing this model is good at, which is left as an exercise to the reader, is calculating the ideal proton:neutron ratio as a function of A.
The All-Neutron Atom
Neutrons are unstable, because they outweigh a proton by 2.5 electron masses, and will decay into a proton, an electron, and a neutrino after about 15 minutes if left alone. They are stable when part of a nucleus with protons. Could agglomerates of neutrons be stable? There has been some experimental evidence of unstable isotopes emitting correlated neutrons, indicating they perhaps transiently formed a "dineutron." What does the liquid drop model say about this?
If we substitute A=N, Z=0 into the equation, the Coulomb term goes away, but the symmetry term is always there. Now that the binding and symmetry terms are both linear functions of N, ignoring the surface and pairing terms, we have the binding energy going as $N\cdot(\delta-\alpha)$, and because the absolute value of delta is bigger than alpha, the total binding energy is always positive, meaning that bound states of neutrons cannot exist. A clump of ten neutrons would become ten clumps of one neutron and then would become ten protons.
Astute students of physics will realize that the above model does not take into account all the fundamental interactions: every particle exerts a gravitational attraction on every other particle. For charged protons, this is typically like 40 orders of magnitude weaker than the electrostatic repulsion and is totally irrelevant, but neutrons do not experience electrostatic repulsion. Perhaps if we had enough neutrons, the gravitational attraction would overcome the "symmetry"-induced instability of neutronium.
If we add a Newtonian gravitational term to the all-neutron liquid drop model, the negative binding energy scales as the square of the number of neutrons (divided by the cube-root), while the instability scales linearly. Thus, for a very very large number of neutrons, we might expect a stable state to be reached. Let's write down the new equation...
I'm going to go out on a limb and make the assumption that this will be a large number of neutrons, which lets us neglect the surface and pairing terms. I did make one slight change for the Newtonian term: I've explicitly included the mass and radius of the neutron (roughly a femtometer), whereas the charge and radius of the proton were embedded in the definition of gamma in the old Coulomb term. The Newtonian prefactor is on the order of $10^-{36}$ MeV. So, how many neutrons are required for an all-neutron nucleus to be gravitationally stable? We can set $E_B$ to zero and solve for N.
Lots of neutrons.
So by modifying an equation used to predict the mass of nuclei with 1 to 300 neutrons, we have derived a result of $10^{55}$ neutrons to be gravitationally stable. This gives a mass of about $10^{28}$ kg or about 1% the mass of the sun.
Now, stellar-sized gravitationally bound agglomerates of neutrons already sort of exist; they are called neutron stars. They are not 100% neutrons; they have a crust that is still full of protons. The interior structure and composition of a neutron star are also not fully known (it's not even known whether their radius gets bigger or smaller as a function of mass), and the core is basically the "here be dragons" of stellar astrophysics. What is known, however, is that a neutron star must be at least 1.44 times the mass of the sun (the Chandrasekhar limit), because below that it can still be supported by electron degeneracy pressure, and the star is a white dwarf.
The gravitational neutron drop model underpredicted the minimum neutron star size by two orders of magnitude. I still think it's impressive, however, that we extrapolated the model by 53 orders of magnitude beyond its intended use and were only off by another two orders.
Neutron Stars
At this point in the post I'll mention that this calculation was not my idea. I saw it in a talk by John Michael Pearson at McGill in 2014. It was a nuclear talk about stars, which is good because nuclear talks about nuclear physics and astrophysics talks about astrophysics are both too technical for a general physicist, but when someone has to talk to people outside their own speciality, the talks become more accessible. In his talk he introduced this calculation, and then went on to refine it to get a better answer. In particular, he was interested in using this type of reasoning and precise nuclear mass data to derive an upper-bound to the neutron star mass (before it collapses into a black hole), which could be compared to observations of very large neutron stars to verify their description of the nuclear physics. He mentioned in the talk that the recent discovery of a very large neutron star had already ruled out one of his models.
He has a paper on it here, and he got $10^{56}$ neutrons (not sure where our divergence lies, perhaps in a factor of 3/5 that I dropped, or maybe I have to take into account the surface terms), within one order of magnitude of the Chandrasekhar limit, before refining his calculation with nuclear physics that is far beyond what I have encountered.
The way neutron star models are typically derived is by constraining the internal density of the star to the pressure by assuming hydrostatic equilibrium, and further constraining the pressure to the density using nuclear physics***. Because gravitational fields in neutron stars are so intense it becomes necessary to make general relativistic corrections to the hydrostatic equilibrium, so it gets pretty complicated.
So, just to summarize, by adding a gravitational attraction to the liquid drop model, you can make a wild extrapolation and get logarithmically-almost the correct answer, which I think is cool.
*I have read mixed conventions of whether the binding energy is additive and negative, or subtractive and positive. The sentence "adding a negative binding energy reduces the mass and makes the nucleus stable, and a larger magnitude of this energy makes it more stable" describes my convention. If this doesn't quite make sense, imagine pulling the protons and neutrons out of the nucleus and considering how that increases the total energy, and then compare the bound energy to the energy of all the particles at infinity, sort of like gravitational potential. If this still doesn't make sense...leave a comment.
**Sort of like the van der Waals version of the strong nuclear force. There's a misconception that the strong force holds nucleons together, but it actually holds quarks together inside nucleons, and the residual force holds nucleons together.
***I'm now talking about something I don't really understand so it sounds vague.
## Monday, 18 January 2016
### The Simpson-Hawking Donut Universe
Your idea of a donut shaped universe is intriguing, Homer. I may have to steal it.-Stephen Hawking, The Simpsons.
In a 1999 episode of The Simpsons, Stephen Hawking discusses a donut-shaped universe with Homer, before punching him in the face with his robotic boxing glove. Is this just a joke by the writers playing on Homer's love of donuts, or does it hint at something deeper? A donut-shaped universe does have physical implications, and observational searches for them neither confirm nor explicitly reject the Simpson-Hawking donut universe.
The mathematical structure resembling a donut is called a torus. It's the shape that is generated if you take a rectangle, attach two opposite sides together so that it forms a cylinder, and than attaching the two circular ends of the cylinder together.
A torus.
A torus is the geometry of the game Asteroids and many others, where going off the screen on one side makes you appear on the others. Solving physics problems on a toroidal geometry can be pretty useful, because you don't have to deal with boundary conditions (Onsager's solution to the square-lattice Ising model is such an example). Conceptually, this cosmic looparound is comforting, avoiding both the edges of the universe and the fact that there are none.
It looks like a rectangle but it's a donut.
Our universe apparently has three spatial dimensions, so if it were donut shaped it would have to be a 3-torus, which is beyond my ability to visualize as its enclosed volume is some kind of hyperdonut in four dimensional space. But what the physical implications of the universe being a 3-donut, and can we look for them?
Even before getting into cosmology, one might want to consider special relativity in a torus. Because two inertial observes can move with respect to one another and cross each others' path multiple times, the so-called twin paradox cannot be resolved by requiring that one of the twins has to change directions in order to compare the elapsed time. The resolution is that in a toroidal spacetime, there is a preferred reference frame, which is the one that makes a given side of the torus appear shortest. So, special relativity in the land of donuts is not the same as the version we are familiar with. This challenges our Copernican sensibilities, because there will be some place and frame from which the universe appears smallest.
Homer Simpson, you are accused of breaking half the Lorentz symmetry of the planet of the donuts.
Considering a cosmological torus, light that is emitted and travels far enough would reach the point where it was emitted, so if we looked far enough we might see another Earth. However, we live in a universe that used to be a hot opaque plasma, so light from that epoch reaches us in the form of the cosmic microwave background, which is seen in all directions, and we can't see beyond that. So even if we can't see another Milky Way, we could detect the donutness of the universe. Consider Earth in a toroidal universe. Light is emitted from some distant point in all directions. Instead of only one of those light rays reaching Earth, many of them take a different path, each arriving at Earth in a different direction. When we look up at the sky, we would see multiple versions of the same image, in a circle whose angular size depended on the relative size of the torus and distance to the source. This took me a while to figure out, so I drew a crappy MS Paint drawing to illustrate it.
Yellow, red, and green all go from the star thingy to Earth in different directions, arriving at different angles in the sky.
As was the case in the photon decay paper, the cosmic microwave background is the most distant light source we have, so this has the best chance of being duplicated by the topology of the universe. To see if this is the case we can look at measurements of the temperature anisotropy of the universe, such as those taken by the WMAP satellite. That's what these guys did, and by their non-observation of obvious cosmic circles (the analysis was considerably more detailed), they placed the bounds of the size of any potential torus at about 78 billion lightyears. I am not sure whether this should be compared with the radius (46 billion lightyears) or diameter (92 billion) of the observable universe. There are a number of independent analyses of this, and to my surprise they do not really rule out the donut universe, although they do not support it either.
If the size of the universe exceeds the size of the torus, the "intersection" will appear at multiple points on the sky.
So, the jury is still out on the Simpson-Hawking donut universe. Did Hawking himself every discuss this? In a 1992 paper on chronology projection, he did brush over it slightly:
"For example, if the initial surface is a three-torus, the Cauchy horizon will also be a three-torus, and the generators can be nonrational curves that do not close up on themselves. However, this kind of behavior is unstable."
However, this kind of behavior is unstable.
## Monday, 4 January 2016
### A Living Ising Model: Bacterial Vortex Lattices
Today I read an interesting paper in Nature Physics by Hugo Wioland and friends, called "Ferromagnetic and antiferromagnetic order in bacterial vortex lattices." A lot of Nature Physics is devoted to solid state physics which I personally don't find too interesting, so I almost glossed over until I saw the "bacterial vortex" at the end of the title. In the paper, they grew bacterial colonies in circular cavities that spontaneously rotated, and showed that each colony vortex can behave the way atoms do in magnetic solids, and use it as a jumping-off point to model complex living systems with lattice physics.
A bacterial vortex, taken from the supplemental material of the paper. The graininess is due to me trying to convert from mov to gif and is not part of the paper. The colonies are 50 microns in diameter.
The bacteria, Bacillus subtilis, is covered in flagella which are constantly waving around. The bacteria cannot occupy the same space as one another and so organize themselves in such a way as to avoid that, and influence each other through hydrodynamic interactions of the beating flagella. When they are packed into these circular cavities, they fill the space, and when the flagella beat coherently the colonies start to rotate. One rotating colony they call a bacterial vortex, and they can rotate clockwise or counterclockwise with varying magnitude.
Four connected colonies. The top left and bottom right spin counterclockwise, and the top right and bottom left spin clockwise. (You can see this in the movies from the paper)
The circular cavities are arranged in a lattice, either square or triangular, with a gap of a certain size connecting each one. Tuning the size of the gaps tunes the interactions between cavities, which are mediated by the row of bacteria on the edge of each circle next to the walls. If the gaps are narrow, the bacteria do not move through and they interact hydrodynamically through the flagella beats, and want to move in the same direction as their neighbour across the gap, which makes the vortices spin in opposite directions. If the gaps are wide, bacteria tend to line up along the walls of the gap, such that a row of bacteria will do a "180" going from one cavity to the next, meaning neighbours will move in opposite directions and thus the vortices will spin in the same direction.
Diagram from the paper of inter-vortex interactions. If the gaps are small, they bacteria at the gaps interact hydrodynamically and move in the same Cartesian direction. If the gaps are wide the bacteria move along the edges, making adjacent cavities rotate the same way. I can foresee my explanation being confusing and unsatisfactory.
This is cool and all, but at this point I should take a step back and actually explain why they are doing this experiment.
Physics is hard. There are very few complex problems that can be exactly solved, but there are computational methods that can get approximate solutions. One of these is called lattice field theory, where space and time are broken into finite-size steps (sites on a lattice), and interactions between adjacent lattice sites are considered and the system is simulated with a computer.
One of the simplest but most ubiquitous lattice models is called the Ising Model*, which is used to understand magnetic materials. In the Ising model, there is a lattice of "spins" that can either be "up" (+1) or "down" (-1), and the total energy of the system depends on whether each spin is pointing the same direction or the opposite direction as its neighbor**. (Imagine two adjacent wire loops with electrical current going around them, and consider the torques they exert on each other if the current is going in opposite directions. Then try to consider a thousand loops.) Materials where the spins want to point in the same direction are ferromagnetic (like iron) and materials where the spins want to point in opposite directions as their neighbor are called antiferromagnetic (like chromium). Solving the Ising model can be complicated, but it's much simpler than considering the interactions of $10^{23}$ interacting atoms.
A two dimensional Ising lattice, showing ferromagnetic order (left) and antiferromagnetic order (right).
The authors wanted to see they could apply the Ising model to a living system, so the created these bacterial vortices to see if they obeyed Ising-like behaviour. From a thermodynamic standpoint, living matter is substantially more complicated than inert matter: it's constantly producing its own energy and is never in equilibrium. There is a whole relatively new branch of physics just dedicated to studying the thermodynamics of active matter. A network of colonies, each a network of bacteria, each a network of interacting proteins of incredible complexity, would be essentially impossible to model from a "bottom up" approach, but mapping it onto the Ising model would allow its large scale behaviour to be predicted and studied, and may open the door to more generally studying the physics of living systems.
Back to the results of the paper. You may recall that I said that for lattices with narrow gaps, the adjacent bacterial vortices spin oppositely, and for wide gaps adjacent vortices spin in the same direction. The former case corresponds to antiferromagnetism, and the latter to ferromagnetism. By changing the size of the gaps, they can ordain what kind of "magnet" these bacterial colonies will be. The critical size where the behaviour crosses over is about 8 microns.
Left: An antiferromagnetic bacterial vortex lattice, where adjacent cavities tend to spin in opposite directions (alternating green and purple). Right: A ferromagnetic lattice, where neighbors tend to spin in the same direction, with domains of green and purple.
To make the whole thing slightly cooler, they explain the spin-spin interactions between adjacent vortices in terms of an "edge current" of the outer layer bacteria moving along the walls in the opposite direction as all the bacteria in the middle. This is analogous to certain quantum materials such as a quantum hall state in a two dimensional electron gas (a "thin cold semiconductor" doesn't sound as neat), where the electrons propagate in the opposite direction along the outside of the material. Many-body quantum mechanics and bacterial fluid mechanics do not have much in common, but both can be described by this lattice model. I generally think it's neat that these colonies can be modelled as a lattice interacting spins the same way that atoms in a magnet can, even though the first kind of spin is the net motion of the bacteria and the second kind is the intrinsic angular momentum of an electron.
People invariably ask what the practical applications of a given paper are. I will quote the how-we-will-save-the-world-if-we-get-more-funding section from the last paragraph, where the authors state: "Improved prevention strategies for pathogenic biofilm formation, for example, will require detailed knowledge of how bacterial flows interact with complex porous surface structures to create the stagnation points at which biofilms can nucleate."
Overall, very cool paper.
*Named after Ernst Ising and also a good name for a physics hockey team.
**Still haven't decided to go with American or Canadian spelling on this one. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8281604051589966, "perplexity": 447.4715074832465}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320261.6/warc/CC-MAIN-20170624115542-20170624135542-00010.warc.gz"} |
https://blogs.helsinki.fi/quantitative-communication/data-analysis/visualising-data/ | # Correlation and regression
In the Descriptive statistics section we used a scatter plot to draw two continuous variables, age and salary, against each other. On the basis of the picture we were not able to determine if there was any association between the variables. For studying the linear relationship between two continuous variables a measure called the Pearson product-moment correlation coefficient (“correlation” in short) can be used. It is a measure of a linear relationship, not a curvilinear one. It does not take a stand on any kind of causality (such as X is a cause of Y), but describes the strength of the association.
The symbol of the Pearson correlation is $\rho$ or r and in reality it is a standardized measure of covariance (“co-variation”). The standardized values can vary between -1 and +1, where 1 indicates perfect positive (linear) relationships, -1 a perfect negative (liner) relationship, and 0 stands for no correlation at all. For the correlation to be considered “weak” or “strong” depends on the study and data, but usually more than $\pm$ 0.3 to 0.5 is expected. For example, correlation between age and salary in our example is 0.124, which is, although statistically significant $(p<.05)$, very weak.
The correlation coefficient is easily calculated by any statistical package, but the results are not meaningful unless there is a linear relationship between the variables. The distributions of the variables should also be approximately symmetrical for correlation to be meaningful. For example, the presence of outliers would severely harm the results of a correlation coefficient as seen in the classical example by Anscombe[1] in the figure below.
It is good to note how misleading correlation coefficients (or any other single statistics) can be. Therefore, graphical explorations are necessary. In the Anscombe’s quartet above the first plot shows the correlation as it should be, the second shows a curvilinear relationship, the third shows the effect of an outlier, and the fourth shows the effect of an extreme outlier. If the data is biased and the outliers are a necessary part of the data (not random errors), the Pearson correlation should not be used. In such cases, Spearman’s rank correlation can be used, which is a similar measure to the Pearson correlation, but is not influenced by the effect of outliers.
Linear regression
Once we have familiarized ourselves with the basic idea of correlation, it is time to move on to linear regression, which is a technique for modeling the relationship between two or more variables. The scatterplot in the figure below depicts the regression line that passes through the dots, representing the observations. This regression line is similar to a linear polynomial function that can be represented as a linear equation having a constant “a” (the intersection with Y-axis), the slope “b” (coefficient for defining how steep the line is), and the variables x and y, whose relationship the function describes. This type of equation for a linear line takes the following form: $y=a+bx$, and can be thought of as what goes in as x comes out as y. It is important to note that theoretically speaking we are not dealing with associations any more, but making a causal claim that from x follows y. When x changes, y changes in a way specified by the right side of the equation. In the language of regression analysis, x is called the independent variable (the one that is not influenced; also “predictor”) and y is called the dependent variable (the one that is dependent on x). The symbol for constant is $\beta_{0}$ (“beta”) and for coefficient(s) $\beta_{x}$.
If you take a look at the plot in the figure above, age and salary are depicted as a linear line, and the equation describing the position and slope of the line is also labeled. In the equation y stands for “salary”, and x for “age”. The numbers 2340 and 10.23 are estimates for $\beta_{0}$ and $\beta_{1}$. The $R^{2}$ in the top left of the plot is the coefficient of determination, which describes how well the line – the linear model – fits the data, i.e. how well the line accounts for the variation of the observations. $R^{2}$ can be interpreted as a percentage. In this instance the model captures no more than 1.5% of the variation.
The equation can be written in the following way: $y_{salary}=2340+10.23\times x_{age}$. The constant $\beta_{0}$ is 2340 and the coefficient $\beta_{1}$ is 10.23. How to interpret the model? First, the coefficient is positive, so age has a positive effect on salary. Secondly, the constant (or intercept) is 2340. So if age is 0, the salary would be 2340 when $\beta_{1}$ cancels out. The interesting part, the effect of the age on salary (read: the effect of x on y) is described by the coefficient $\beta_{1}$. It is interpreted in the following way: when x increases by 1 unit (which is 1 year in this case), y will increase by 10.23. So each time we get one year older, our salary increases by 10.23 euros according to the model.
The idea of a regression model is to predict the values of y on the basis of the values of one or more x variables. Let’s try to predict the salary for a 40-year-old person. We start by inserting 40 in place of x so that the right of the equation will be 2340+10.23*40, which yields 2749. This a very simple linear model. Considering the low coefficient of determination (98.5% was not explained), the next task of a researcher is to find better predictors, i.e. x-variables that can predict changes in y. The motive for using regression analysis is that it allows us to add as many x variables into the equation as needed. The regression analysis will account for them all together, considering their simultaneous effect on y. The motive for adding new predictors to the equation comes both from theoretical and statistical reasons, i.e. we know that x influences y under certain conditions and $R^{2}$ increases accordingly. Linear regression analysis also has some constraints, however. Most importantly, the dependent variable need to be continuous. Independent variable(s) need to be discrete/continuous or dichotomous. All variables need to be more or less normally distributed, and independent variables should not correlate strongly together (a condition called multicollinearity).
Let’s add two new variables into the regression equation. We introduce a new variable called “education”, which is dichotomous and hence can take two values: “1” standing for “person has a university/college degree” and “0” for “person does not have a university/college degree” (i.e. they have a degree lower than that or no degree at all). We are interested in testing the effect of a university/college degree on the predicted salary. The second new variable is “gender”, testing the effect of “being female” (=1) on the predicted salary. The regression equation is now
$y_{salary}=\beta_{0}+\beta_{1}x_{1(age)}+\beta_{2}x_{2(education)}+\beta_{3}x_{3(gender)}$
The output of the regression analysis is in the table below.
From the table we can see that the effect of age is 16.787, meaning that each year yields this much extra to the salary. The constant is now 2117.362, meaning that this is the value when both age, education, and gender are zero. The effect of education is that if a person has a college/university degree, 766.969 will be multiplied by 1, and hence added to the salary. The same goes if a person is female, but this time we subtract 592.928 from the salary. Let’s make the same prediction as above for a 40-year-old female with a college/university degree. The salary is now 2117.362 + 16.787*40 + 766.969*1 – 592.928*1 = 2962.883. Which one of the predictors is stronger? Beta values in the table are standardized values for B’s, making it possible to compare their effects on y. It seems to be that education is the strongest one, having almost twice as big an effect as age. t-tests at the right end of the table show whether the predictors are statistically significant in the model (p-values should be <0.05).
From the other output table below we can also see that $R^{2}$ increased from 1.5% to 24.8% (“adjusted $R^{2}$” accounts for the error caused by increasing the number of predictors), so it is a big change in the goodness of fit of the model. The standard error of estimate is 791.659, and it is a measure of error in the model. It can be interpreted as the average deviation of the predicted values (salaries given by the model) from the observed values (the observed salaries in the data).
The difference between observed and predicted values is called residual variation in regression analysis and it can be marked with e for “error”: $y=\beta_{0}+\beta_{1}x_{1}+e$. This means that y is equal to the model plus the rest of the variation of y that is not captured by the model. If we modify the equation slightly, we can say that $e=y-\left(\beta_{0}+\beta_{1}x_{1}\right)$. Technically speaking, the goal of a regression analysis is to minimize the amount of errors. This happens usually by the procedure called least square estimation, which is done by finding such values for $\beta_{0}$ and $\beta_{1}$ that the sum of the squared differences between y and $\left(\beta_{0}+\beta_{1}x_{1}\right)$ become as small as possible.
Finally, a researcher needs to assess how well the model actually fits to the data. This is typically done by examining the residual variance, i.e. the part of the variation that was not explained by the model. For this purpose a residual plot can be drawn. If the residual variance is normally distributed and varies in an unsystematic manner around the predicted values, we can state that the model is quite a good predictor of the values for y.
[1] Anscombe, F. J. (1973). Graphs in statistical analysis.The American Statistician, 27(1), 17-21. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 24, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8874521255493164, "perplexity": 366.20366005995106}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027316785.68/warc/CC-MAIN-20190822064205-20190822090205-00003.warc.gz"} |
http://math.stackexchange.com/questions/48905/a-neighborhood-of-an-intersection-point | # a neighborhood of an intersection point
if a point $x$ is in the intersection of two spaces $X$ and $Y$ suppose we know explicitly a neighborhood of $x$ in $X$, can we take the same neighborhood of $x$ in $Y$. More specifically, if the neighborhood of $x$ in $X$ is homeomorphic to $\mathbb R^n$ can we say that if the neighborhood of $x$ in $Y$ is $\mathbb R^k$ then $k$ must be equal to $n$?
-
Take $Z$ to be the subspace of $\mathbb{R}^3$ consisting of the union of $X=$ the x-y plane and $Y =$ the z-axis. Take $x\in X\cap Y$ to be the origin (the only thing it can be). Then a small open ball around $x$ (in $\mathbb{R}^3$) intersects $X$ in a small open 2-d ball and intersects $Y$ in a small open 1-d ball.
So, no, you can't conclude $k=n$.
If I understood well, X,Y are manifolds and x is in W=$X\cap Y$, and the manifolds intersect in the "right way" (transversally),the dimension of the intersection will be equal to the dimension of the ambient space minus the sum of the codimensions.
Edit: After searching, I found we can say even more: the transversal intersection of submanifolds of a manifold is a submanifold; if Z is the intersection, and p is in Z, then we can show that actually, there is a coordinate chart around p in which X corresponds to $R^r x {0}$ and Y corresponds to ${0} x R^s$, (I think these are an inmersion and a submersion) so that $Z=X \cap Y$, corresponds to ${0} x R^k x {0}$ (where r=dim(X), s=dim(Y), and k=(r+s)). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.953498125076294, "perplexity": 135.1125842888239}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246661733.69/warc/CC-MAIN-20150417045741-00000-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/how-to-derive-the-solution-for-potential-flow-around-a-circular-cylinder.579799/ | # How to derive the solution for potential flow around a circular cylinder
1. Feb 21, 2012
### meldraft
Hey all,
I've been trying for a while now to derive the following solution, for a circular cylinder under uniform flow:
$$φ(r,θ)=U(r+\frac{R^2}{r})cos θ$$
where φ is the flow potential that satisfies Laplace's equation, as defined in this article:
http://en.wikipedia.org/wiki/Potential_flow_around_a_circular_cylinder
I know how to solve laplace's equation in a rectangular domain, using separation of variables, but here I am at a loss. I simply can't figure out how to implement the circular geometry into the rectangular domain.
To make it more clear, I am assuming a rectangular domain with a circle inside. The domain has a Dirichlet condition on two opposite sides (flow velocity), and a Neuman condition on the surface of the sphere and on the other two sides of the rectangle.
Since this solution is on wikipedia, I figured that it would be well documented, but, after scouring the internet and my books for days, I simply can't find how it's derived anywhere. If someone could provide a link or some help in deriving the solution, I would be grateful
2. Feb 22, 2012
### meldraft
shameless bump :tongue: Searching around the internet I found a proof that basically uses the potential at infinity to formulate the solution, so there was no actual solution of the PDE.
An idea a colleague had was that maybe it is possible to solve the PDE for the cylinder with boundaries at infinity, and then solve the rectangle with the boundaries of my problem, and superpose the solutions? This seems likely in principle, but something doesn't really sit right with this approach. Namely, since the flow around the cylinder is generated by the boundary conditions on the rectangular domain, it is pretty unlikely that I will get any meaningful results without properly implementing that boundary condition in the cylindrical problem. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8830649852752686, "perplexity": 224.89238012060008}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267159570.46/warc/CC-MAIN-20180923173457-20180923193857-00014.warc.gz"} |
https://brilliant.org/discussions/thread/titus-lemma-part-1/ | # Titu's Lemma (Part 1)
Titu's lemma
The Inequality
Let $x_1, x_2, ..., x_n$ be real numbers and $y_1, y_2, ..., y_n$ be positive real numbers.
Then, the following inequality holds,
$\frac{x_1^2}{y_1} + \frac{x_2^2}{y_2} + ... + \frac{x_n^2}{y_n} \ge \frac{(x_1 + x_2 + ... + x_n)^2}{y_1 + y_2 + ... + y_n}$
Why is this true? Actually, this inequality follows from the Cauchy-Schwarz Inequality.
$(\frac{x_1^2}{y_1} + \frac{x_2^2}{y_2} + ... + \frac{x_n^2}{y_n})(y_1 + y_2 + ... + y_n) \ge (x_1 + x_2 + ... + x_n)^2$
Examples
$1.$ Prove Nesbitt Inequality :
$\frac{a}{b + c} + \frac{b}{a + c} + \frac{c}{b + a} \ge \frac{3}{2}$
Solution :
We can't see any squares terms on the numerators, so wishful thinking motivates us to create them.
How can we create the square terms? Squaring the whole left hand side is very messy, and a much simpler way is to multiply the numerators and denominators of the fractions by $a, b, c$ respectively.
Now, the way to proceed is clear, as by Titu's Lemma we get
$\frac{a^2}{ab + ac} + \frac{b^2}{ab + bc} + \frac{c^2}{bc + ac}$
$\ge \frac{(a + b + c)^2}{2(ab + bc + ca)}$
Now, we just have to prove that $2(a + b + c)^2 \ge 6(ab + bc + ca)$, which can be rewritten as
$(a + b + c)^2 \ge 3(ab + bc + ca)$, which can be rewritten as $a^2 + b^2 + c^2 \ge ab + bc + ca$,
The last inequality follows from $\frac{1}{2}[(a - b)^2 + (b - c)^2 + (a - c)^2] \ge 0$.
Problems
$1.$ Prove that for all positive real numbers $x, y, z$
$\frac{2}{x + y}+\frac{2}{y + z}+\frac{2}{z + x} \ge \frac{9}{x + y + z}$
Note by Zi Song Yeoh
6 years, 2 months ago
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Hi, Here is your answer We can write $\frac{2}{x+y}+\frac{2}{y+z}+\frac{2}{z+x}$ as $\frac{(\sqrt{2})^2}{x+y}+\frac{(\sqrt{2})^2}{z+y}+\frac{(\sqrt{2})^2}{x+z}$ So as to use The above mentioned inequality. So after applying the inequality, we get, $\frac{(\sqrt{2})^2}{x+y}+\frac{(\sqrt{2})^2}{z+y}+\frac{(\sqrt{2})^2}{x+z} \geq \frac{(3\sqrt{2})^2}{2(x+y+z)}=\frac{9}{x+y+z}$
- 6 years, 2 months ago
There is a minor typo at the end of your solution. The $3$ should be inside the bracket.
- 6 years, 2 months ago
Got it.Sorry!
- 6 years, 2 months ago
I multiplied up and down by 2...follows the same steps though.....Cheers!
- 6 years, 2 months ago
Is it not possible by setting $x+y+z=1$ and then applying the lemma?
- 4 years, 5 months ago
Very direct application question
- 5 years, 1 month ago
Stay tuned for Part 2!
- 6 years, 2 months ago
- 6 years, 2 months ago
Pretty interesting is name of this. Except Titu's lemma (sometimes written as T2 lemma), you can also find it as SQ lemma (like ...escu), or (at least in Czech and Slovak republic) as CS-fractionfighter (CS stands for Cauchy-Schwartz)
- 6 years, 2 months ago
Many also call it Cauchy "in fractional form," which is similar to your last name.
- 6 years, 2 months ago
Some even call it Cauchy in Engel Form
- 2 years, 3 months ago
I did a similar method but slightly more intuitive..
First observe $9 = 3^2$, therefore, we can try to create the sum of the numerators of the fractions in LHS to be $3$.
Also, observe that there is a common multiple of $2$ in the numerator in LHS, so divide the LHS and RHS with $2$ to get: $\frac{1}{x+y} + \frac{1}{y+z}+\frac{1}{z+x}\geq \frac{9}{2(x+y+z)}$
Then using Titu's Lemma, we get $\frac{1}{x+y} + \frac{1}{y+z}+\frac{1}{z+x}\geq \frac{(1+1+1)^2}{2(x+y+z)} = \frac{9}{2(x+y+z)}$. We are done.
- 5 years, 10 months ago
This is NOT Titu's lemma. This inequality was published in 1997 in russian language in journal KVANT by Nairi Sedrakyan, Sedrakyan not only wrote the inequality in this form, but he has shown how this inequality can be used to prove different inequalities and called his article About applications of one useful inequality. In russian speaking countries it is called Sedrakyan's inequality. Here is the link of the first page of that article http://kvant.mccme.ru/pdf/1997/02/42.pdf But in english speaking countries this inequality sometimes is called Engel's form or Titu's Lemma. Because Arthur Engel has included it in his book published in 1998 and Titu Andreescu has included it in his book published in 2003. Both authors were familiar with russian language mathematics literature and Sedrakyan's works, but none of them cited the original source of the work. Moreover, Sedrakyan devotes a whole separate chapter to the applications of this inequality in his book Inequalities. Methods of proving published in 2002 in russian.
- 2 years, 3 months ago
other method for 1)
$A.M \geq H.M$
$s = a + b + c$
$\dfrac{a}{s - a} + \dfrac{b}{s - b} + \dfrac{c}{s - c} = \dfrac{s}{s - a} - 1 + \dfrac{s}{s - b} - 1 + \dfrac{s}{s - c} - 1$
$\dfrac{\dfrac{s}{s - a} + \dfrac{s}{s - b} + \dfrac{s}{s - c}}{3} \geq \dfrac{3}{\dfrac{s - a + s - b + s - c}{s}}$
$\dfrac{\dfrac{s}{s - a} + \dfrac{s}{s - b} + \dfrac{s}{s - c}}{3} \geq \dfrac{3}{2}$
$\dfrac{\dfrac{s}{s - a} - 1 + \dfrac{s}{s - b} - 1 + \dfrac{s}{s - c} - 1 }{3} \geq \dfrac{1}{2}$
$\dfrac{s}{s - a} - 1 + \dfrac{s}{s - b} - 1 + \dfrac{s}{s - c} - 1 \geq \dfrac{3}{2}$
$\dfrac{a}{b + c} + \dfrac{b}{a + c} + \dfrac{c}{b + c} \geq \dfrac{3}{2}$
- 5 years, 1 month ago
Actually, this is a special case of Holder's Inequality
- 6 years, 2 months ago
Can you add this to Titu's Lemma? Thanks @Zi Song Yeoh
Staff - 5 years, 4 months ago
very nice way to prove it
- 5 years, 2 months ago
@Zi Song Yeoh @Calvin Lin Thanks , this note was quite useful. For saying thank you I created this problem : click here. Hope you enjoy it :)
- 4 years, 4 months ago
Wishful thinking does motivate us indeed.
Also nice notes
- 2 years, 5 months ago
$2\left(\sum_{cyc} \frac1{x+y}\right) \geq 2\cdot \frac{(1+1+1)^2}{2(x+y+z)} = \frac9{x+y+z}$
- 1 year, 9 months ago
Cauchy Schwarz inequality states, [(x+y)+(y+z)+(z+x)].[1/(x+y)+1/(y+z)+1/(z+x)]≥(1+1+1)^2...........(£)
Hence the rearrangement of the above proves the requirement
Also Eqn. (£) can be produced by AM-GM
- 1 year, 9 months ago | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 44, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9858691096305847, "perplexity": 1914.1118628074782}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145818.81/warc/CC-MAIN-20200223154628-20200223184628-00404.warc.gz"} |
https://socialsci.libretexts.org/Learning_Objects/Teaching_Materials/Exploring_Public_Speaking_Accessible_PowerPoint_Slides/Language%3A_Exploring_Public_Speaking_Accessible_PowerPoint_Slides_for_Chapter_10 | # Language: Exploring Public Speaking Accessible PowerPoint Slides for Chapter 10
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This link will take you to Exploring Public Speaking Chapter 10 PowerPoint slides.
Note: These slides are for use as a student study guide, not necessarily for lectures. You may want to edit and reduce some of the wordiness if you use them as lecture slides.
Language: Exploring Public Speaking Accessible PowerPoint Slides for Chapter 10 is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8460032343864441, "perplexity": 1582.5456016547653}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104293758.72/warc/CC-MAIN-20220704015700-20220704045700-00005.warc.gz"} |
https://mdtpmodules.org/geom/geom-2/lesson-3/practice-2/ | # GEOM 2 | Lesson 3 | Practice (Finding Angles)
Refer back to the concept of arc tan, or inverse tan, to understand the concept of inverse sine and inverse cosine. Watch(Tangent) https://mdtpmodules.org/geom-2-lesson-2-watch/
Reminder: the angle of elevation and angle of depression have the same measure.
Use the following problems to apply the inverse tangent, sine, and cosine functions:
1) Find the angle of elevation to the airplane from the ground:
2) Find the measure of angle A. Which ratio did you use and why?
3) Find the measure of angle A and the measure of angle F. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9782078862190247, "perplexity": 956.0187896519157}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107882102.31/warc/CC-MAIN-20201024051926-20201024081926-00638.warc.gz"} |
https://www.physicsforums.com/threads/spring-question.15042/ | # Spring question!
1. Feb 24, 2004
### lollypop
hello, if anyone can help me figure this out, it will be appreciated.
the problem is the following:
An 80.0-kg man jumps from a height of 2.50 m onto a platform mounted on springs. As the springs compress, he pushes the platform down a maximum distance of 0.240 m below its initial position, and then it rebounds. The platform and springs have negligible mass.
a)What is the man's speed at the instant he depresses the platform 0.120 m?
b)If the man just steps gently onto the platform, what maximum distance would he push it down?
I found the potential energy when the man hits the spring by U=mgh,
i also need the spring constant and this is where i get confused on how to get it.
Do i use F=kx, the F being the weight???and then plug in to find w=0.5kx^2, and then finally find v??
I also get confused as to which distances to use on the equations
Any help would be great!
thanks.
[?]
2. Feb 24, 2004
### NateTG
At the point where the spring is fully compressed you've got:
$$PE_{spring}=mgh$$
for the second part you've got:
$$kx=mg$$
which is also relatively easy to solve.
3. Feb 24, 2004
### lollypop
thanks for ur reply NateTG, but still I get confused on how to get the constant k, on the equations u sent, they use x as distance, which distance should i use??
4. Feb 24, 2004
### NateTG
Let's find $$k$$
$$mgh=\frac{1}{2}kx^2$$
so
$$k=\frac{2mgh}{x^2}$$
where h is the height the man dropped, and x is the spring displacement.
5. Feb 24, 2004
### lollypop
hey thanks!, i got the first part for the velocity ,but the equation that you gave me for the second part, to find the distance as the man steps on the spring kx=mg is not giving me the right answer, is there another way of finding that distance???
6. Feb 24, 2004
### NateTG
I get
$$k=373332 N/m$$
so I get a displacement of $$2cm$$ what do you get?
7. Feb 24, 2004
### lollypop
i get for the first part k=68055 N/m, which gave me a velocity
of 6.06 m/s, which is right.
But when i use that same k for the second part, i get 0.0115 m
for the displacement, and it says its wrong.
8. Feb 25, 2004
### NateTG
Hmm, do you know what the correct answer is supposed to be? You would get a different equation if you try disregard friction, and solve part 2 with energy.
9. Feb 25, 2004
### lollypop
no, i don't know the answer,i put the answer on a website and it tells me wheter i'm right or not. I still have 6 tries left
I supposed the answer would be smaller than 0.240 m which was the compression when the man jumped, I plugged in yours, 2 cm , 0.02 m , and is also wrong.i'll keep trying with what u said about not using friction and doing it with kinetic, thanks.
10. Feb 25, 2004
### lollypop
hey, i think they wanted more sig figs, the anwer was 0.0210 m,
i just requested it, because i got the same as you did when i worked it out.
11. Feb 25, 2004
### Tom McCurdy
mgy=1/2kx^2
mgy=1/2kx^2
is all you need for these problems
hold on While I do the calculations
12. Feb 25, 2004
### Tom McCurdy
Worked out
MGY
80*2.5*9.8=1960
1960=1/2K*.254^2
K=68055.55556
Then you can F=-kx
F=-16333.3333
you shoudl be able to solve the rest fairly easily... if i did it right hope i helped in some way
Similar Discussions: Spring question! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8994501829147339, "perplexity": 1545.8730124513067}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607846.35/warc/CC-MAIN-20170524131951-20170524151951-00413.warc.gz"} |
https://infoscience.epfl.ch/record/217948 | Infoscience
Conference paper
# Caching Gaussians: Minimizing Total Correlation on the Gray–Wyner Network
We study a caching problem that resembles a lossy Gray–Wyner network: A source produces vector samples from a Gaussian distribution, but the user is interested in the samples of only one component. The encoder first sends a cache message without any knowledge of the user’s preference. Upon learning her request, a second message is provided in the update phase so as to attain the desired fidelity on that component. The cache is efficient if it exploits as much of the correlation in the source as possible, which connects to the notions of Wyner’s common information (for high cache rates) and Watanabe’s total correlation (for low cache rates). For the former, we extend known results for 2 Gaussians to multivariates by showing that common information is a simple linear program, which can be solved analytically for circulant correlation matrices. Total correlation in a Gaussian setting is less well-studied. We show that for bivariates and using Gaussian auxiliaries it is captured in the dominant eigenvalue of the correlation matrix. For multivariates the problem is a more difficult optimization over a non-convex domain, but we conjecture that circulant matrices may again be analytically solvable. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8537163138389587, "perplexity": 760.1949233490519}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917124371.40/warc/CC-MAIN-20170423031204-00236-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/651358/if-k-is-composite-which-of-its-prime-factors-dominates-its-divisibility-into | If $k$ is composite, which of its prime factors dominates its divisibility into $n!$ for $n$ large?
Suppose we have a fixed (generally composite) $k$, and we want to find the largest power of $k$ that divides $n!$ for $n$ large.
If $k$ is square-free, we need only consider the behavior of the largest prime $p$ dividing $k$: if $p^i | n!$, then certainly $q^i|n!$ for any prime $q<p$, and so $k^i|n!$.
Most of the time, when $k$ is composite, a similar argument is possible and we need only consider a single prime factor of $k$. Legendre's formula for the prime factorization of $n!$ tells us that the highest power of $p$ dividing $n!$ is $$\sum_{j=1}^\infty \left\lfloor \frac{n}{p^j}\right\rfloor = \frac{n}{p-1} + O(\log n) \, .$$ So, for a fixed prime power $p^a$, the largest power of $p^a$ that divides $n!$ is $\frac{n}{a(p-1)} + o(n)$.
It follows that, if $k=p_1^{a_1}\dots p_n^{a_n}$, then we need only consider those $p_i$ which minimize $a_i(p_i-1)$. Most of the time there will only be one such $p_i$, in which case our life is no harder than it was when $k$ was square-free.
For example, if $k=24$, then we are interested only in the divisibility of $n!$ by the prime powers $8$ and $3$. The above analysis tells us that the largest power of $8$ that divides $n!$ is roughly $\frac{n}{3(2-1)}=\frac{n}{3}$, while the largest power of $3$ that divides $n!$ is roughly $\frac{n}{3-1}=\frac{n}{2}$. So the largest power of $24$ that divides $n!$ is always the same as the largest power of $8$ that divides $n!$, for $n$ sufficiently large.
However, there are exceptions!
For example, if $k=12=2^2 \cdot 3$, then the largest power of both $4$ and $3$ that divides $n!$ will be roughly $\frac{n}{2}$. Numerical experimentation suggests that $n!$ usually has more than twice as many factors of $2$ as it has factors of $3$, but the number of exceptions is large (for $n<10^7$, the factors of $2$ are the scarce ones about $17\%$ of the time, and that number seems to decrease only slowly as $n$ increases).
Can anything be said about which prime factor of $k$ will be the most scarce, in cases where the basic asymptotic analysis given above isn't strong enough?
This comes down to the relative size of the exponents of the primes dividing $n!,$ because your power is limited by the smallest exponent ratio for each prime, the exponent in $n!$ divided by the exponent in your given $k.$
I happen to know that the exponent of prime $p$ in $\operatorname{lcm} (1,2,\ldots,n)$ is proportional to $1 / \log p,$ so that the exponent of $2$ over the exponent of $3$ is approximately $\log 3 / \log 2.$
I'm trying to think if the limiting proportions are the same for factorials, using Legendre's theorem. And i would need to say no. For large $n,$ Legendre's theorem says that the exponent ratio for small primes $p,q$ may be calculated by ignoring the "floor" symbols, giving a limiting exponent ratio of $(q-1)/(p-1).$
So, for each prime factor $p$ of your $k,$ calculate $$\frac{n}{(p-1) \, a}$$ where $$p^a \parallel k.$$ The smallest value of this ratio is a good estimate for your biggest power.
• Agreed. Unless I'm misunderstanding what you're saying, the limiting proportions in your last sentence are precisely the computation I did in my question, and the fundamental problem is that (unlike in the case of $\operatorname{lcm}$) they wind up being rational. – Micah Jan 25 '14 at 23:16
• @Micah, I see, you do have that in your post. I guess the message is that, when this is not good enough, one must put back the floor signs to get exact ratios. You might try reading articles by Jean-Louis Nicolas and Guy Robin. I'm not sure any by Robin are in English, all French. I am thinking of the papers using superior highly composite numbers and colossally abundant numbers. Robin worked up what he called operations research methods for finding all highly composite numbers between two s.h.c. numbers. Heavy number crunching. – Will Jagy Jan 25 '14 at 23:27
• – Will Jagy Jan 25 '14 at 23:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9073119759559631, "perplexity": 118.58549630017808}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250606226.29/warc/CC-MAIN-20200121222429-20200122011429-00147.warc.gz"} |
https://collegephysicsanswers.com/openstax-solutions/emf-induced-rotating-1000-turn-200-cm-diameter-coil-earths-500-times-10-5-t | Question
An emf is induced by rotating a 1000-turn, 20.0 cm diameter coil in the Earth’s $5.00 \times 10^{-5} \textrm{ T}$ magnetic field. What average emf is induced, given the plane of the coil is originally perpendicular to the Earth’s field and is rotated to be parallel to the field in 10.0 ms?
$157 \textrm{ mV}$
Solution Video | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9659538865089417, "perplexity": 640.776598376322}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657176116.96/warc/CC-MAIN-20200715230447-20200716020447-00105.warc.gz"} |
https://math.stackexchange.com/questions/3135753/conditional-expectation-of-geometric-brownian-motion | # Conditional expectation of geometric brownian motion
Given a geometric Brownian motion $$S ( t ) = e ^ { \mu t + \sigma B ( t ) }$$, I'm trying to calculate $$E [ S ( t ) | \mathcal { F } ( s ) ]$$ where $$\mathcal { F } ( s )$$ is the history of the process. Here is my try:
This is conditioned on history of the process $$\mathcal { F } ( s )$$, so we need to rewrite $$B(t)$$ as $$B ( s ) + ( B ( t ) - B ( s ) )$$
\begin{align*} S ( t ) &= e ^ { \mu t + \sigma B ( t ) }\\ &= e ^ { \mu t + \sigma (B ( s ) + ( B ( t ) - B ( s ) )) }\\ &= e ^ { \mu t + \sigma B ( s ) + \sigma\left( B ( t ) - B ( s ) \right) } \end{align*}
\begin{align*} \mathbb{E}[S ( t )|\mathcal { F } ( s )] &= \mathbb{E}[e ^ { \mu t + \sigma B ( s ) + \sigma\left( B ( t ) - B ( s ) \right) }]\\ &= \mathbb{E}[e ^ { \mu t + \sigma B ( s )}e^{\sigma\left( B ( t ) - B ( s ) \right) }]\\ \end{align*}
Edit: Now here is my problem: I see that many online solutions proceed as following
$$\mathbb{E}[S ( t )|\mathcal { F } ( s )] = e ^ { \mu t + \sigma B ( s )}\mathbb{E}[e^{\sigma\left( B ( t ) - B ( s ) \right) }]=e ^ { \mu t + \sigma B ( s )}e^{\sigma^{2}(t-s)/2}$$
But I don't understand 2 things:
1. How the first term comes out of expectation.
2. What does it mean when we say Using moment generating function, we know that $$\mathbb{E}[e^{\sigma B_t}]=e^{\frac{1}{2}\sigma^2t},\qquad \sigma\in\mathbb{R}.$$
$$\mathcal F(s)$$ is the filtration of $$B(t)$$ for $$t, hence, $$B(s)$$ is $$\mathcal F(s)$$-measurable; this means that, for any measurable function $$f(\cdot)$$, $$\mathbf E[ f\big(B(s)\big)|\mathcal F(s)] = f\big(B(s)\big).$$
To compute $$\mathbf E[\mathrm e^{\mu t + \sigma B(s)}\mathrm e^{\sigma (B(t) - B(s))}| \mathcal F(s)]$$ we use two facts
1. $$\mathrm e^{\mu t + \sigma B(s)}$$ is $$\mathcal F(s)$$-measurable, so it goes out of the conditional expectation (it acts as a constant);
2. Brownian motion has independent and Gaussian increments; so $$B(t)-B(s)$$ is independent of $$\mathcal F(s)$$ and is a Gaussian random variable with zero mean and variance equal to the increment $$t-s$$.
The first fact allows you to move out the first part from the expectation; the second fact allows you to write that $$\mathbf E[\mathrm e^{\sigma (B(t) - B(s))}| \mathcal F(s)] = \mathbf E[\mathrm e^{\sigma Y}]$$ where $$Y\sim N(0,t-s)$$; then, using the moment generating formula, you have the value of the expectation.
$$\mathbb{E}[S ( t )|\mathcal { F } ( s )] = e ^ { \mu t + \sigma B ( s )}\mathbb{E}[e^{\sigma\left( B ( t ) - B ( s ) \right) }]=e ^ { \mu t + \sigma B ( s )}e^{\sigma^{2}(t-s)/2}$$
• This is what the question states; I don't see how you are answering any of the points raised by the poster. – Riccardo Sven Risuleo Mar 5 '19 at 16:27
• @RiccardoSvenRisuleo I made an edit to my problem after his answer. – Blade Mar 5 '19 at 16:57
• I apologize for that then! – Riccardo Sven Risuleo Mar 5 '19 at 16:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 26, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9967416524887085, "perplexity": 192.89808752664547}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153980.55/warc/CC-MAIN-20210730185206-20210730215206-00700.warc.gz"} |
http://unapologetic.wordpress.com/2007/05/22/functors/?like=1&_wpnonce=d19428bcb3 | # The Unapologetic Mathematician
## Functors
As with all the other algebraic structures we’ve considered, we’re interested in the “structure-preserving maps” between categories. In this case, they’re called “functors”.
A functor $F$ from a category $\mathcal{C}$ to a category $\mathcal{D}$ consists of two functions, both also called $F$. One sends objects of $\mathcal{C}$ to objects of $\mathcal{D}$, and the other sends morphisms of $\mathcal{C}$ to morphisms of $\mathcal{D}$. Of course, these are subject to a number of restrictions:
• If $m$ is a morphism from $X$ to $Y$ in $\mathcal{C}$, then $F(m)$ is a morphism from $F(X)$ to $F(Y)$ in $\mathcal{D}$.
• For every object $X$ of $\mathcal{C}$, we have $F(1_X)=1_{F(X)}$ in $\mathcal{D}$ — identities are sent to identities.
• Given morphisms $f:X\rightarrow Y$ and $g:Y\rightarrow Z$ in $\mathcal{C}$, we have $F(g\circ f)=F(g)\circ F(f)$ in $\mathcal{D}$ — a functor preserves compositions.
It’s tempting at this point to think of a “category of categories”, but unfortunately this gets hung up on the same hook as the “set of sets”. A lot of the intuition goes through, however, and we do have a category $\mathbf{Cat}$ of small categories (with only a set of objects and a set of morphisms) and functors between them.
Every category $\mathcal{C}$ comes with an identity functor $1_\mathcal{C}$. This is an example of an “endofunctor” (in analogy with “endomorphism”).
Every category of algebraic structures we’ve considered — $\mathbf{Grp}$, $\mathbf{Mon}$, $\mathbf{Ring}$, $R-\mathbf{mod}$, etc. — comes with a “forgetful” functor to the category of sets. Remember that a group (for example) is a set with extra structure on top of it, and a group homomorphism is a function that preserves the group structure. If we forget all that extra structure we’re just left with sets and functions again.
To be explicit, there is a functor $U:\mathbf{Grp}\rightarrow\mathbf{Set}$ that sends a group $(G,\cdot)$ to its underlying set $G$. It sends a homomorphism $f:G\rightarrow H$ to itself, now considered as a function on the underlying sets. It should be apparent that this sends the identity homomorphism on the group $G$ to the identity function on the set $G$, and that it preserves compositions. The same arguments go through for rings, monoids, $R$-modules.
In fact, there are other forgetful functors that behave in much the same way. A ring is an abelian group with extra structure, so we can forget that structure to get a functor from $\mathbf{Ring}$ to $\mathbf{Ab}$ — the category of abelian groups. An abelian group, in turn, is a restricted kind of group. We can forget the restriction to get a functor from $\mathbf{Ab}$ to $\mathbf{Grp}$.
Now for some more concrete examples. Remember that a monoid is a category with one object. So what’s a functor between such monoids? Consider monoids $M$ and $N$ as categories. Then there’s only one object in each, so the object function is clear. We’re left with a function on the morphisms sending the identity of $M$ to the identity of $N$ and preserving compositions — a monoid homomorphism!
What about functors between preorders, considered as categories? Now all the constraints are on the object function. Consider preorders $(P,\leq)$ and $(Q,\preceq)$ as categories. If there is an arrow from $a$ to $b$ in $P$ then there must be an arrow from $F(a)$ to $F(b)$. That is, if $a\leq b$ then $F(a)\preceq F(b)$. Functors in this case are just order-preserving functions.
These two examples show how the language of categories and functors subsumes both of these disparate notions. Preorder relations translate into the existence of certain arrows, which functors must then preserve, while monoidal multiplications translate into compositions of arrows, which functors must then preserve. The categories of (preorders, order-preserving functions) and (monoids, monoid homomorphisms) both find a natural home with in the category of (small categories, functors).
May 22, 2007 - Posted by | Category theory
1. [...] Transformations and Functor Categories So we know about categories and functors describing transformations between categories. Now we come to transformations between functors [...]
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2. [...] algebras — were all asserted to be the “free” constructions. This makes them functors from the category of vector spaces over to appropriate categories of -algebras, and that means [...]
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3. [...] closely, we’ll find that what we’ve defined as a presheaf is actually a contravariant functor from this category to the category of sets! For every arrow we have an arrow — in the [...]
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4. [...] that we ended up defining a presheaf as a functor. Given our topological space we set up the partial order category , flipped it around to so the [...]
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https://la.mathworks.com/help/wavelet/gs/from-fourier-analysis-to-wavelet-analysis.html | ## From Fourier Analysis to Wavelet Analysis
### Inner Products
Both the Fourier and wavelet transforms measure similarity between a signal and an analyzing function. Both transforms use a mathematical tool called an inner product as this measure of similarity. The two transforms differ in their choice of analyzing function. This results in the different way the two transforms represent the signal and what kind of information can be extracted.
As a simple example of the inner product as a measure of similarity, consider the inner product of vectors in the plane. The following MATLAB® example calculates the inner product of three unit vectors, $\left\{u,v,w\right\}$, in the plane:
`$\begin{array}{l}\left\{\left(\begin{array}{c}\sqrt{3}/2\\ 1/2\end{array}\right),\left(\begin{array}{c}1/\sqrt{2}\\ 1/\sqrt{2}\end{array}\right),\left(\begin{array}{c}0\\ 1\end{array}\right)\right\}\\ \end{array}$`
```u = [sqrt(3)/2 1/2]; v = [1/sqrt(2) 1/sqrt(2)]; w = [0 1]; % Three unit vectors in the plane quiver([0 0 0],[0 0 0],[u(1) v(1) w(1)],[u(2) v(2) w(2)]); axis([-1 1 0 1]); text(-0.020,0.9371,'w'); text(0.6382,0.6623,'v'); text(0.7995,0.4751,'u'); % Compute inner products and print results fprintf('The inner product of u and v is %1.2f\n', dot(u,v)) fprintf('The inner product of v and w is %1.2f\n', dot(w,v)) fprintf('The inner product of u and w is %1.2f\n', dot(u,w))```
Looking at the figure, it is clear that u and v are most similar in their orientation, while u and w are the most dissimilar.
The inner products capture this geometric fact. Mathematically, the inner product of two vectors, u and v is equal to the product of their norms and the cosine of the angle, θ, between them:
`$\begin{array}{l}=|\text{}\text{ }|u|\text{ }||\text{ }|v|\text{ }|\mathrm{cos}\left(\theta \right)\\ \end{array}$`
For the special case when both u and v have unit norm, or unit energy, the inner product is equal to cos(θ) and therefore lies between [-1,1]. In this case, you can interpret the inner product directly as a correlation coefficient. If either u or v does not have unit norm, the inner product may exceed 1 in absolute value. However, the inner product still depends on the cosine of the angle between the two vectors making it interpretable as a kind of correlation. Note that the absolute value of the inner product is largest when the angle between them is either 0 or $\pi$ radians (0 or 180 degrees). This occurs when one vector is a real-valued scalar multiple of the other.
While inner products in higher-dimensional spaces like those encountered in the Fourier and wavelet transforms do not exhibit the same ease of geometric interpretation as the previous example, they measure similarity in the same way. A significant part of the utility of these transforms is that they essentially summarize the correlation between the signal and some basic functions with certain physical properties, like frequency, scale, or position. By summarizing the signal in these constituent parts, we are able to better understand the mechanisms that produced the signal.
### Fourier Transform
Fourier analysis is used as a starting point to introduce the wavelet transforms, and as a benchmark to demonstrate cases where wavelet analysis provides a more useful characterization of signals than Fourier analysis.
Mathematically, the process of Fourier analysis is represented by the Fourier transform:
`$F\left(\omega \right)={\int }_{-\infty }^{\infty }f\left(t\right){e}^{-j\omega t}dt.$`
which is the integral (sum) over all time of the signal f(t) multiplied by a complex exponential. Recall that a complex exponential can be broken down into real and imaginary sinusoidal components. Note that the Fourier transform maps a function of a single variable into another function of a single variable.
The integral defining the Fourier transform is an inner product. See Inner Products for an example of how inner products measure of similarity between two signals. For each value of ω, the integral (or sum) over all values of time produces a scalar, F(ω), that summarizes how similar the two signals are. These complex-valued scalars are the Fourier coefficients. Conceptually, multiplying each Fourier coefficient, F(ω), by a complex exponential (sinusoid) of frequency ω yields the constituent sinusoidal components of the original signal. Graphically, the process looks like
Because ${e}^{j\omega t}$ is complex-valued, F(ω) is, in general, complex-valued. If the signal contains significant oscillations at an angular frequency of ${\omega }_{0}$, the absolute value of $F\left({\omega }_{0}\right)$ will be large. By examining a plot of $|F\left(\omega \right)|$ as a function of angular frequency, it is possible to determine what frequencies contribute most to the variability of f(t).
To illustrate how the Fourier transform captures similarity between a signal and sinusoids of different frequencies, the following MATLAB code analyzes a signal consisting of two sinusoids of 4 and 8 Hertz (Hz) corrupted by additive noise using the discrete Fourier transform.
```rng(0,'twister'); Fs = 128; t = linspace(0,1,128); x = 2*cos(2*pi*4*t)+1.5*sin(2*pi*8*t)+randn(size(t)); xDFT = fft(x); Freq = 0:64; subplot(211); plot(t,x); xlabel('Seconds'); ylabel('Amplitude'); subplot(212); plot(Freq,abs(xDFT(1:length(xDFT)/2+1))) set(gca,'xtick',[4:4:64]); xlabel('Hz'); ylabel('Magnitude'); ```
Viewed as a time signal, it is difficult to determine what significant oscillations are present in the data. However, looking at the absolute value of the Fourier transform coefficients as function of frequency, the dominant oscillations at 4 and 8 Hz are easy to detect.
### Short-Time Fourier Transform
The Fourier transform summarizes the similarity between a signal and a sinusoid with a single complex number. The magnitude of the complex number captures the degree to which oscillations at a particular frequency contribute to the signal's energy, while the argument of the complex number captures phase information. Note that the Fourier coefficients have no time dependence. The Fourier coefficients are obtained by integrating, or summing, over all time, so it is clear that this information is lost. Consider the following two signals:
Both signals consist of a single sine wave with a frequency of 20 Hz. However, in the top signal, the sine wave lasts the entire 1000 milliseconds. In the bottom plot, the sine wave starts at 250 and ends at 750 milliseconds. The Fourier transform detects that the two signals have the same frequency content, but has no way of capturing that the duration of the 20 Hz oscillation differs between the two signals. Further, the Fourier transform has no mechanism for marking the beginning and end of the intermittent sine wave.
In an effort to correct this deficiency, Dennis Gabor (1946) adapted the Fourier transform to analyze only a small section of the signal at a time -- a technique called windowing the signal. Gabor's adaptation is called the short-time Fourier transform (STFT). The technique works by choosing a time function, or window, that is essentially nonzero only on a finite interval. As one example consider the following Gaussian window function:
`$w\left(t\right)=\sqrt{\frac{\alpha }{\pi }}{e}^{-\alpha {t}^{2}}$`
The Gaussian function is centered around t=0 on an interval that depends on the value of α. Shifting the Gaussian function by τ results in:
`$w\left(t-\tau \right)=\sqrt{\frac{\alpha }{\pi }}{e}^{-\alpha {\left(t-\tau \right)}^{2}},$`
which centers the Gaussian window around τ. Multiplying a signal by $w\left(t-\tau \right)$ selects a portion of the signal centered at τ. Taking the Fourier transform of these windowed segments for different values of τ, produces the STFT. Mathematically, this is:
`$F\left(\omega ,\tau \right)=\int f\left(t\right)w\left(t-\tau \right){e}^{-j\omega t}dt$`
The STFT maps a function of one variable into a function of two variables, ω and τ. This 2-D representation of a 1-D signal means that there is redundancy in the STFT. The following figure demonstrates how the STFT maps a signal into a time-frequency representation.
The STFT represents a sort of compromise between time- and frequency-based views of a signal. It provides some information about both when and at what frequencies a signal event occurs. However, you can only obtain this information with limited precision, and that precision is determined by the size of the window.
While the STFT compromise between time and frequency information can be useful, the drawback is that once you choose a particular size for the time window, that window is the same for all frequencies. Many signals require a more flexible approach -- one where you can vary the window size to determine more accurately either time or frequency.
Instead of plotting the STFT in three dimensions, the convention is to code $|F\left(\omega ,\tau \right)|$ as intensity on some color map. Computing and displaying the STFT of the two 20-Hz sine waves of different duration shown previously:
By using the STFT, you can see that the intermittent sine wave begins near 250 msec and ends around 750 msec. Additionally, you can see that the signal's energy is concentrated around 20 Hz. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 14, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9537372589111328, "perplexity": 347.2991611593606}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103642979.38/warc/CC-MAIN-20220629180939-20220629210939-00452.warc.gz"} |
https://physics-network.org/what-determines-the-period-of-a-spring/ | # What determines the period of a spring?
Mass on a spring – Where a mass m attached to a spring with spring constant k, will oscillate with a period (T). Described by: T = 2π√(m/k). By timing the duration of one complete oscillation we can determine the period and hence the frequency.
## What is a period in physics spring?
The period of a spring-mass system is proportional to the square root of the mass and inversely proportional to the square root of the spring constant.
## What is the period of a spring measured in?
The unit of the period is a second (s) and the unit of the frequency is Hertz or s–1 (Hz = 1/s).
## Is the period of a spring constant?
As the spring constant k increases, the period decreases. which gives the period T for a mass m attached to a spring with spring constant k.
## What’s the unit of period?
A time period (denoted by ‘T” ) is the time taken for one complete cycle of vibration to pass a given point. As the frequency of a wave increases, the time period of the wave decreases. The unit for time period is ‘seconds’.
## What is the formula for period?
time is called T, the period of oscillation, so that ωT = 2π, or T = 2π/ω. The reciprocal of the period, or the frequency f, in oscillations per second, is given by f = 1/T = ω/2π.
## What is period of oscillation?
Period is the time taken by the particle for one complete oscillation. It is denoted by T. The frequency of the oscillation can be obtained by taking the reciprocal of the frequency.
## Why does the period of a spring depend on mass?
Bigger mass means you would get more period because there’s more inertia, and it’s also affected by the spring constant. Bigger spring constant means you’d have less period because the force from the spring would be larger.
## What is Hooke’s Law in oscillation?
The simplest type of oscillations and waves are related to systems that can be described by Hooke’s law: F=−kx, F = − k x , where F is the restoring force, x is the displacement from equilibrium or deformation, and k is the force constant of the system.
## What is the frequency of a spring?
The natural frequency of one spring is √25000 (N/m) /12.5 (kg) /(2×3.14) ≒ 7.12 (Hz).
## Does period depend on length?
The period of a pendulum does not depend on the mass of the ball, but only on the length of the string.
## What is unit of spring constant?
Introduction To Spring Constant k is known as the spring constant or stiffness constant. Unit of spring constant is N/m.
## What is the symbol of period?
A period, also known as a “full stop” in British English, is a punctuation mark that looks like a tiny circle or dot. It appears at the bottom of a written line and directly follows the preceding character without a space.
## What is period in 11th physics?
Total amount of time taken by an object to complete one revolution is called Period. The object in that time completes the revolution of a circular path.
## What is the period of a frequency?
The corresponding period is the time duration of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example, if a heart beats at a frequency of 120 times a minute (2 hertz), its period, T—the time interval between beats—is half a second (60 seconds divided by 120 beats).
## What is period and frequency in physics?
Definition of Period and Frequency Period refers to the amount of time it takes a wave to complete one full cycle of oscillation or vibration. Frequency, on the contrary, refers to the number of complete cycles or oscillations occur per second. Period is a quantity related to time, whereas frequency is related to rate.
## What is a period of a function?
The distance between the repetition of any function is called the period of the function. For a trigonometric function, the length of one complete cycle is called a period. For any trigonometry graph function, we can take x = 0 as the starting point.
## What is the difference between frequency and period?
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency.
## What is relationship between period and frequency?
The number of times a cycle is completed in a second is the frequency. The time taken to complete one vibration is called time period. Frequency and time period is inversely proportional, the number of vibrations per second is frequency. f = 1 t f=\frac1t f=t1 or t = 1 f t=\frac1f t=f1.
## How do you find the period of harmonics?
Step 1: Identify the argument of the cosine function in the simple harmonic equation. Step 2: Find the number multiplied by t . This is the angular frequency of simple harmonic motion. Step 3: Find the period by substituting the angular frequency found in step 2 into the equation T=2πω T = 2 π ω .
## Does velocity affect period of spring?
The period would remain the same. Explanation: When it comes to the period of a spring, the velocity of the object has no effect.
## What is time period of simple pendulum?
The time period of a simple pendulum is equal to the time it takes to complete one Oscillation. T=2π√lg→ Length of the string of the pendulum. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9547970294952393, "perplexity": 392.98824189242674}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710421.14/warc/CC-MAIN-20221210074242-20221210104242-00827.warc.gz"} |
https://wordpandit.com/number-system-decimals-and-fractions-test-2/ | Select Page
• This is an assessment test.
• To draw maximum benefit, study the concepts for the topic concerned.
• Kindly take the tests in this series with a pre-defined schedule.
## Number System: Decimals and Fractions Test-2
Congratulations - you have completed Number System: Decimals and Fractions Test-2.You scored %%SCORE%% out of %%TOTAL%%.You correct answer percentage: %%PERCENTAGE%% .Your performance has been rated as %%RATING%%
Question 1
If p = 0.009 and q =0.0009 then what will be the value of p x q
A 0.000081 B 81 x 10-5 C 0.00081 D 0.0000081
Question 1 Explanation:
Simply first multiply 9 by 9 and then count the number of digits after the decimal value
The number of digits after the decimal of both the numbers is the actual position of decimal in the result of their multiplication: 0.009 x 0.0009 = 0.0000081
Question 2
If P= (0.008 +6.987+0.8+55.986-5.5-4.76), then the value of P in fractions will be
A (53521 / 1000) B (53522/1000) C (53521/100) D (535521/1000)
Question 2 Explanation:
=> (0.008 +6.987+0.8+55.986) = 63.781
=>(-5.5-4.76) = -10.26
=> 63.781-10.26 = 53.521
So the right answer is option A
Question 3
Which is the greatest among the following numbers?
A ½ B 19/29 C 689/987 D 899/999
Question 3 Explanation:
Just divide each of the following extract the decimal form and get the answer as option D
899/999 = 0.89
689/987 = 0.67
19/29 = 0.65
½ =0.5
Question 4
If numerator of any fraction is increased by 1 it becomes equal to 1/2 and if we decrease 2 from the denominator of the original fraction then it also remains same, then the fraction is:
A 11/22 B 1/2 C 3/4 D 7/16
Question 4 Explanation:
Option 1: 11/22 is already equal to ½ but in the statement we are given that when the fraction is increased by 1 in the numerator then it becomes ½. This is not possible in the given case.
½ is not the right choice because when we increase 1 with 1, then it becomes 2 and numerator will become 2 and the fraction will convert into the natural number 1
¾ same as in case of ½
7/16 is the right answer (7+1)/16 =1/2 and 7/14=1/2
Question 5
Which of the following has the least value?
A 29/2291 B 23/1357 C 19/1691 D none
Question 5 Explanation:
Option A is 29/2291 = 1/79
Option B is 23/1357 = 1/59
Option C is 19/1691 = 1/89
Out of the above, clearly option C is the lowest value.
Once you are finished, click the button below. Any items you have not completed will be marked incorrect.
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http://eprints.iisc.ac.in/7808/ | # The Role of Special Functions in a Viscous Flow Problem Involving Two Cylinders
Chakrabarti, A and Hamsapriye, * (2000) The Role of Special Functions in a Viscous Flow Problem Involving Two Cylinders. In: Mechanics Research Communications, 27 (1). pp. 123-130.
PDF THE_ROLE_OF_SPECIAL_FUNCTIONS_IN_A_VISCOUS_FLOW_PROBLEM.pdf Restricted to Registered users only Download (314kB) | Request a copy
## Abstract
The theoretical understanding of slow, axi-symmetric, steady, creeping motion of viscous fluids, in the cylindrical geometry ${(\rho,\phi,z)}$ denoting the cylindrical coordinates of a material point in standard notations can be completed by determining the Stokes's stream function $\psi(\rho,z)$ (independent of ${\phi}$, because of axisymmetry), which is known (see [4]) to satisfy a fourth order partial differential equation (PDE) as given by (see also the Appendix):
Item Type: Journal Article Copyright of this article belongs to Elsevier. Division of Physical & Mathematical Sciences > Mathematics T M Devendrappa 18 Aug 2006 19 Sep 2010 04:29 http://eprints.iisc.ac.in/id/eprint/7808 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9630888104438782, "perplexity": 1847.139219682834}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578530527.11/warc/CC-MAIN-20190421100217-20190421122217-00094.warc.gz"} |
http://aghomeworkxggw.casestudyhouse26.com/latex-thesis-symbols.html | Latex thesis symbols
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# Latex thesis symbols
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How can I make LaTeX use symbols (*, †, ‡, and so on) instead of numbers to mark footnotes? (The numbers are confusing because I use superscripted numbers for. When you define terms, you need to remember that they will be sorted by makeindex or xindy. While xindy is a bit more LaTeX aware, it does it by omitting latex macros
## Latex thesis symbols
Jan 04, 2015 · How to Write a Great Master Thesis? Best (and worst) practices from choosing a topic to handing in - Duration: 1:20:57. ElmarDJuergens 14,719 views Mathematics environments . LaTeX needs to know beforehand that the subsequent text does indeed contain mathematical elements. This is because LaTeX typesets maths.
Auburn University requires a dissertation for all Ph.D. degrees and a thesis for many master’s degrees. The thesis or dissertation is a demonstration of the student. 1.1 Summary. Org is a mode for keeping notes, maintaining TODO lists, and project planning with a fast and effective plain-text system. It also is an authoring system.
Masters/Doctoral Thesis Description: This template provides a full framework for writing a graduate level thesis. It is carefully structured and separated into. Academic & Research Computing Getting Started with LATEX LATEX Tutorial You can either print this document or follow it on line. About LATEX
phd-thesis-template - A LaTeX / XeLaTeX / LuaLaTeX PhD thesis template for Cambridge University Engineering Department (CUED) Consider the following piece of LaTeX code: \begin{tabular}{p{1in}p{1in}} A & B\\ C & D\\ \end{tabular} How can I make the contents of each cell aligned in the center. NEW!! Up-to-date (2016) Caltech thesis templates can be found in Caltech's Featured Templates section of the website. Students are not required to have an Overleaf.
LaTeX Information: Training Materials, Examples, Links Instructional Material. Academic and Research Computing (ARC) provides materials for self-paced on-line. Printing a list of abbreviations or symbols is one of these things (like so many) LaTeX provides a very simple and elegant solution for. The nomencl package. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8585659861564636, "perplexity": 3993.8018636235843}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118831.16/warc/CC-MAIN-20170423031158-00565-ip-10-145-167-34.ec2.internal.warc.gz"} |
http://www.gemini.edu/science/maxat/comparative/comparative.html | On the Comparative Performance of an 8m NGST and a Ground Based 8m Optical/IR Telescope
F.C. Gillett and M. Mountain
Abstract.
The potential 1-20µm imaging and spectroscopic sensitivity of a cooled 8m NGST in space is compared to that of a 8m ground-based telescope. For 2.5µm an 8m NGST may achieve a signal-to-noise ratio (SNR) advantage in the range 100 to 1000 for both imaging observations and for spectroscopic observations up to R=1000. In the 1 to 2.5µm regime an 8m NGST may achieve a SNR advantage for imaging of ~10, while for spectroscopic observations the SNR advantage is expected to be substantially less and could approach unity for R1000.
1. Introduction
The NGST science drivers dictate a telescope of 4m diameter or larger and imaging and spectroscopic capability optimized for the 1-5µm range and extending over the 0.6 to 20µm wavelength range with image quality at least as good as that of HST. While contemplating in more detail the design parameters of the NGST telescope and its instrumentation capabilities, it is essential to anticipate the likely state of ground-based astronomical observational capability at the time of the launch of NGST, expected to be no sooner than 2007.
Currently, ground-based astronomy is undergoing a fundamental revolution throughout the world. Shortly after the beginning of the 21st century, well before the launch of NGST, at least a dozen 8m class optical/IR ground-based telescopes will be in operation. A recent assessment of plans in this area is compiled in SPIE Volume 2871 (ed Ardeberg, 1996). These include Keck I and II telescopes (10m diameter, in operation on Mauna Kea, HI), Hobby-Eberly telescope (9.2m effective diameter, first light in mid 1996 on Mt. Fowlkes, TX), Subaru telescope (8.2m, first light mid 1998 on Mauna Kea, HI), VLT telescopes (four - 8m diameter telescopes, first light mid 1998 on Paranal, Chile), Gemini -North and -South (8m diameter, first light at the end of 1998 on Mauna Kea, HI, and mid 2001 on Cerro Pachon, Chile), the LBT telescope (2x8.4m dia, first light 2001 for a single optical train, 1 to 2 years later for the combined beam, on Mt Graham, AZ), and the Spanish GTC Project (10m diameter, first light planned for 2002, on La Palma).
Many of these telescopes are located on excellent sites for IR observations, with low water vapor and very good seeing. Spectroscopic instrumentation with resolutions ranging up to at least 100,000 at optical and IR wavelengths are planned and/or under development for these telescopes, including 2-d spectroscopy, multi-slit and wide field multi-object spectroscopic capability in the 1-5µm range. One can reasonably expect that these telescopes will continue to be equipped with state of the art instrumentation and detector arrays, covering the whole range of optical/IR wavelengths accessible from the ground.
Given the pace of Adaptive Optics applications in ground-based astronomy, one can also confidently predict that many of these telescopes will be equipped with Adaptive Optics systems based on Laser beacons, capable of providing near diffraction limited images at 1µm and longward, over most of the sky. Thus it is very likely that by the time NGST is launched, these ground-based 8m class observatories will be undertaking what can be done from the ground, exploiting Adaptive Optics, the most advanced detector arrays, and the most advanced technologies for high throughput, high resolution, multi-object spectroscopy covering a wide range of spectral resolutions.
It is essential to understand how the NGST will build on the investigations to be carried out with this collection of ground-based telescopes and how the parameters of the NGST telescope, e.g. collecting area and image quality, and instrumentation, e.g. wavelength coverage, field of view and spectral resolution should be optimized for scientific return given the likely activities of this unprecedented armada of very large ground-based optical/IR telescopes.
The obvious advantage of NGST compared to ground-based optical/IR telescopes is freedom from the effects of the earth's atmosphere. Absorption by molecules in the earth's atmosphere precludes astronomical observations from the ground over about 25% of 1-5µm regime and roughly 33% over the 1-25µm regime while the NGST would have unobstructed access to the whole wavelength range. This unobscured access will be important for many astronomical problems, but is probably not compelling by itself.
Turbulence in the atmosphere distorts the wavefront passing through, leading to rapidly varying degradation of the images of external sources while, for NGST, any degradation of diffraction limited performance will be the result of distortions in the telescope and instruments plus pointing/tracking errors. With the rapid development of Adaptive Optics, it is anticipated that ground-based telescopes in the 8m class will be capable of nearly diffraction limited image quality for wavelengths longward of 1µm. Achieving significantly better images at these wavelengths with NGST is likely to be a major cost driver.
Airglow emission from the earth's upper atmosphere, due primarily to rotation/vibration OH lines, dominants the dark sky background in the 0.6 to 2.3µm range for good ground-based astronomical sites. At longer wavelengths, thermal emission from molecules in the lower atmosphere and from the ambient temperature telescope itself dominates over all other backgrounds.
Outside the earth's atmosphere, the sky background over this spectral range is the result of scattering by and emission from interplanetary dust grains and astronomical sources. The NGST telescope and instruments will be cooled so their contribution to the IR background shortward of 25µm is negligible. It is in this area that NGST's fundamental advantage is anticipated, allowing the NGST to detect and study sources too faint to be seen from the ground. The remainder of this paper examines the comparative sensitivity performance of large ground-based telescopes and NGST. The comparison is illustrative rather than exhaustive, with several simplifying assumptions and arbitrary choices for parameters.
2. Sensitivity Comparison
We choose to simplify the sensitivity comparison in a variety of ways;
• Focus on 1-5µm spectral region, the optimized core of NGST wavelength coverage, with extension to longer wavelengths.
• Illustrate the comparison in the atmospheric ''windows'', where the effect of the atmosphere on telescope sensitivity is minimized. These atmospheric windows are assigned nominal properties based on modeling and observations. No attempt is made to model details within a window.
• Compare Signal to Noise Ratios (SNR) for the detection of point sources with a range of assumptions concerning spectral resolution (R = 5 (Imaging), 100, 1000, 10,000) and detector performance that are judged to be scientifically interesting possibilities for NGST, and technically reasonable.
• In order to include the effect of photon statistics for the source itself, the SNR comparison is made for a point source of flux density that achieves a SNR = 10 with a total integration time of 10,000 sec for the NGST assumptions.
• Assume that the array pixels convert photons into photoelectrons with unity gain, and that all the photon sources obey Poisson statistics. Then the SNR of an observation with exposure time t is given by (see e.g. Gillett, 1987):
SNR = Is · t/N(t)
where Is = 1.5·107 ·Ac ·qe ·Ta ·Tt ·Ti ·1/R ·fv ·f electrons/sec is the signal photocurrent, with Ac as the telescope collecting area in meters2 , Ta, Tt, Ti are the atmosphere, telescope and instrument transmission respectively, qe is the detector quantum efficiency, R is the spectral resolution /, fv is the source strength in Jansky's, and f is the fraction of source photons collected. The measurement noise is given by:
N(t) = (Is ·t + Ibg ·t + n ·Idc ·t + n ·N2r )1/2
where Ibg = 1.5·107·Ac·qe·Tt·Ti·1/R·· electron/s is the background photocurrent, where is the sky background surface brightness in Jansky's per square arcsec, is solid angle in square arcsec that encloses the fraction f of the point source flux, n is the number of pixels required to cover while Idc and Nr are the detector dark current and read noise per pixel.
We assume that k observations with exposure time t can be combined with the resultant SNR given by SNR(k·t) = SNR(t)·k0.5.
The values for parameters used in the comparison are discussed briefly below.
2.1. Telescope size/Collecting area (Ac) and throughput (Ti, Ta, Tt)
Calculations are based on the collecting area of one 8m diameter ground-based telescope with a small central obscuration. It should be noted that several ground-based observatories are planning to combine 2 or more 8m telescopes (e.g. Keck, LBT, VLT).
We also assume that the NGST has the same collecting area even though the NGST concepts range from 4m to 8m diameter. There is clear advantage in SNR for increased collecting area, and an optimistic version of NGST has been adopted for this illustration. The product of telescope and instrument transmission is taken to be 0.5 for both the ground-based telescope and NGST. The atmospheric transmission is taken as 0.95 and applies only to the ground-based telescope.
2.2. Image Size ()
For the 8m ground-based telescope, the imaging performance is assumed to be consistent with a moderately good Adaptive Optics capability, roughly corresponding to a Strehl Ratio of 0.8 at K and less at H and J and diffraction limited at L and beyond.
For the NGST is assumed that it delivers the same image size as the 8m ground-based telescope. Significant deviations from a circular aperture, i.e. petals and or large central obscuration will reduce the concentration of energy within the central core of the diffraction pattern. In addition, for smaller NGST diameter than 8m, the diffraction limited solid angle will increase inversely proportional to the diameter squared.
In all cases, it is assumed that the image area is covered by four pixels in order to achieve spatial resolution roughly commensurate with the image quality. The parameters adopted are a beam size of 0.01 square arcsec and f=0.7 for < 3.5µm and beam size 0.01·( /3.5µm) square arcsec with f=0.5 for 3.5µm.
2.3. Background ()
For the 8m ground-based telescope, several sources of background photons are important in this wavelength regime. Beyond 2.3µm the background for a ground-based telescope is overwhelmingly dominated by thermal emission from the telescope and atmosphere (see Figure 1). The telescope contribution is taken to be at an ambient temperature greybody of 0 deg C with emissivity of 3%, and the atmospheric contribution is calculated for a high altitude site like MK with 1mm precipitable water vapor at an ambient temperature at ground level of 0 deg C.
Shortward of 2.3µm OH airglow emission becomes significant and is the dominant source of background emission in the H and J bands. This background is concentrated in a relatively small number of very narrow lines. For imaging observations with broad band filters and low resolution spectroscopy, the lines are averaged to produced the background, however at higher spectral resolution, most of the spectral elements will be OH-line free.
Figure 1. Typical IR background emission for a low background ground-based telescope at a good, high altitude site like Mauna Kea. Thermal emission from the telescope and atmosphere dominate the background beyond 2.3µm, while OH airglow lines dominate at the shorter IR wavelengths. Also shown is 2x the minimum sky background from space as measured by COBE.
For the R=100 and 1000 comparisons, two options are evaluated:
• The OH lines are averaged to produce the background, and
• The observations are carried out at a resolution of 5000, and pixels contaminated by OH emission are deleted from the spectrum, with the remaining spectral elements combined to achieve an effective spectral resolution of 100 or 1000 (see e.g. Herbst, 1994). It is assumed that 10% of the pixels are lost because of contamination by OH lines, and that the recombined spectra have SNR given by SNR(R) = SNR(5000)·(5000/R)0.5. The technique achieves a substantially reduced background for the spectroscopic observations: however, the resulting sensitivity is more dependent on detector performance, and for the same array size, spectral coverage is reduced.
For the NGST, the sky background is taken to be 2x the minimum sky background observed by COBE (Hauser, 1994). The NGST telescope is assumed to be passively cooled to near 30K, thus contributing essentially no background in the wavelength range considered here.
The backgrounds in the 1-3µm regime are summarized in Figure 2. In addition the photocurrent generated by these backgrounds for the 8m telescope parameters adopted here is also indicated for spectroscopic observations. The photocurrents are extremely low, less than 0.01e/sec/pixel at R=1000, leading to a critical dependence of NGST (and the ground-based telescope) sensitivity on detector properties.
2.4. Detector Performance (Id, Nr, qe)
It is assumed that the arrays for both NGST and the ground-based telescope have the same performance even though experience has shown that generally ground-based facilities can more rapidly deploy advanced technology of this type. Two cases are considered here: 1) Photon noise limited performance; except for the quantum efficiency, the detectors are perfect, i.e. dark current and read noise are negligibly small, and 2) Extrapolation of current performance; in this case the adopted read noise and dark current are improvements beyond the current state-of-the-art for InSb arrays operating over the 1-5.5µm range. For wavelengths longward of 5.5µm, the assumptions are significant improvements compared to current low temperature performance of Si:As IBC arrays. Parameters adopted for these two cases are listed in Table 1.
Wavelength range 1µm to 5.5µm 5.5µm to 25µm Parameter Id Nr qe Id Nr qe Photon noise limited 0 0 80% 0 0 40% Extrapolation of current performance 0.02 e/sec 4e 80% 10 e/sec 30e 40% Table 1. Assumed array characteristics.
Figure 2. Near IR sky background surface brightness. Also indicated is the corresponding background photocurrent for the assumed 8m telescope parameters. References: Minimum sky background measured by COBE - Hauser (1994). OH line emission and Background between the OH lines - Maihara, et al (1993)
2.5. Integration Time (t)
The maximum single exposure time is taken to be 1000 sec for NGST, assumed to be limited by the effects of charged particle hits on the detector. Variable Cosmic Ray fluxes are the space equivalent of ''weather'', and are expected to be highly variable. For the ground-based telescope, shielded from much of the cosmic ray fluence, the maximum single exposure integration time is taken as 4000 sec. The SNR comparison is evaluated at SNR = 10 and total integration time of 10,000 sec, i.e. ten 1000 sec exposures on NGST and 2.5 4000 sec exposures for the ground-based 8 m telescope.
3. Discussion
The results of this illustrative comparison are shown in Figures 3 and 4. Figure 3 shows the sensitivity vs wavelength for imaging and R=1000 spectroscopy for both the NGST and 8m ground-based models. Figure 4 shows the relative SNR for NGST compared to the 8m ground-based telescope, for R=5, 100, 1000, and 10000, respectively.
For wavelengths longer than 2.5µm, an 8m NGST will have a SNR advantage compared to ground-based 8m class telescopes in excess of a factor of 10 and approaching a factor of 1000 at all spectral resolutions. This spectral regime is currently being probed from space with a cooled telescope by ISO, and will be explored to levels beyond ground-based sensitivities by SIRTF, but NGST retains a huge performance advantage compared to either of these space missions, because as its much larger collecting area and improved diffraction limited image quality. An 8m NGST would be unsurpassed scientifically in this regime. Because of the low background photon flux in space, detector performance becomes the dominant noise source for R100.
In the 1-2.5µm range the NGST sensitivity advantage compared to the ground-based 8m telescope is substantially reduced due to the very rapid decrease in thermal emission from the atmosphere and ambient temperature telescope in the 2-3µm regime. For broad band imaging the 8m NGST has a SNR advantage of about a factor of 10 as a result of the ~100x lower background in space compared to the OH line emission in this spectral region. If the extrapolated detector performance can be obtained, NGST imaging observations are likely to be background limited. Under background limited conditions, the SNR is roughly proportional to (Ac/)1/2; thus, a smaller NGST telescope or poorer imaging performance would lead to a reduced SNR advantage for 1-2.5µm imaging.
Detector performance will be a major issue for spectroscopic observations with R100 because of the very low photocurrents anticipated in this spectral regime for both ground-based and space-based telescopes. Because of the very low backgrounds, depending on assumptions as to relative image quality, maximum integration times, and collecting area, it is possible that ground-based facilities may have a SNR advantage compared to NGST for spectroscopic observations in this wavelength range. Under detector noise limited conditions, the SNR is proportional to Ac, thus the size of the NGST telescope will be critical to its spectroscopic performance compared to ground-based telescopes.
Figure 3. Point source sensitivity for the NGST and 8m ground-based telescope models for SNR=10 with 10,000 sec total exposure time for the parameters discussed in the text and assuming the extrapolated detector performance.
Figure 4. Relative point source SNR of an 8m NGST compared to 8m ground-based telescope for R=5 (imaging), 100, 1000, and 10,000.
Solid square - extrapolated detector performance, averaging OH lines
Solid triangle - photon noise limited performance, averaging OH lines
Open circle - extrapolated detector performance, between OH lines
Open triangle - photon noise limited performance, between OH lines
Source photon noise is a significant factor for NGST observations shortward of 5µm at R100 and SNR10.
References
1. Ardeberg, A. 1996, SPIE, vol 2871, ``Optical Telescopes of Today and Tomorrow''
2. Gillett, F.C. 1987, ``Infrared Astronomy with Arrays'',ed. C.G. Wynn-Williams and E.E. Backlin, University of Hawaii, pg 3
3. Hauser, M.G. 1994, IAU Symposium 168
4. Herbst, T.M. 1994, PASP, 106, 1298
5. Maihara, T., Iwamuro, F., Yamashita, T., Hall, D.N.B., Cowie, L.L., Tokunaga, A.T., and Pickles, A.J. 1993, PASP, 105, 940 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9172970056533813, "perplexity": 3123.5213765600515}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988725451.13/warc/CC-MAIN-20161020183845-00486-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://math.tutorcircle.com/number-sense/how-to-calculate-ratios-into-percentages.html | Sales Toll Free No: 1-800-481-2338
# How to Calculate Ratios Into Percentages?
TopIn actual life, circumstances may arise where we may need to convert the ratios or Proportions to percentages. This mathematical operations is of wide use in the fields where business analyses, accounting, management of test scores etc. are required to be done. So, how to calculate ratios into percentages? For this we first need to know the fact that the percentages are always measured as per hundred slices. If a Percentage has to be specified as a ratio, the denominator is itself equal to 100. Similarly, to convert the fraction into corresponding percentage we multiply the fraction by 100. Use of scientific calculators may lead to simplified calculations.
Let us consider an example to understand how to convert ratios or Fractions to percentages? Suppose we wish to convert the Ratio 44: 50 or "44 to 50 to its corresponding percentage value. We first replace the colon to from ratio and write it in form of a fraction as 44 /50.
We either multiply fraction by 100 and calculate final result as the percentage value or directly solve fraction and then multiplying it with 100. Let us multiply the fraction by 100 as follows:
44 /50 * 100 = 44 * 2 = 88 %
If we first solve fraction and bring it in decimal form and then multiply decimal number by 100, we get same result:
44 /50 = 0.88
Multiplying it with 100 we get: 0.88 * 100 = 88 % or percent.
Thus we see that, percentages will lie within 100 parts of original value till the numerator in the fraction is less than or equal to the denominator. In case where the numerator goes above the denominator we get percentage value more than 10 percent. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9771534204483032, "perplexity": 566.7886108743425}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164046334/warc/CC-MAIN-20131204133406-00066-ip-10-33-133-15.ec2.internal.warc.gz"} |
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# Visual Complex Analysis by Tristan Needham
by Greg Bernhardt
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Admin P: 8,416 Author: Tristan Needham Title: Visual Complex Analysis Amazon Link: http://www.amazon.com/Visual-Complex...8719763&sr=8-1 Prerequisities: Contents: Table of Contents: Geometry and Complex Arithmetic Introduction Historical Sketch Bombelli's "Wild Thought" Some Terminology and Notation Practice Symbolic and Geometric Arithmetic Euler's Formula Introduction Moving Particle Argument Power Series Argument Sine and Cosine in Terms of Euler's Formula Some Applications Introduction Trigonometry Geometry Calculus Algebra Vectorial Operations Transformations and Euclidean Geometry Geometry Through the Eyes of Felix Klein Classifying Motions Three Reflections Theorem Similarities and Complex Arithmetic Spatial Complex Numbers? Exercises Complex Functions as Transformations Introduction Polynomials Positive Integer Powers Cubics Revisited Cassinian Curves Power Series The Mystery of Real Power Series The Disc of Convergence Approximating a Power Series with a Polynomial Uniqueness Manipulating Power Series Finding the Radius of Convergence Fourier Series The Exponential Function Power Series Approach The Geometry of the Mapping Another Approach Cosine and Sine Definitions and Identities Relation to Hyperbolic Functions The Geometry of the Mapping Multifunctions Example: Fractional Powers Single-Valued Branches of a Multifunction Relevance to Power Series An Example with Two Branch Points The Logarithm Function Inverse of the Exponential Function The Logarithmic Power Series General Powers Averaging over Circles The Centroid Averaging over Regular Polygons Averaging over Circles Exercises Mobius Transformations and Inversion Introduction Definition of Mobius Transformations Connection with Einstein's Theory of Relativity Decomposition into Simple Transformations Inversion Preliminary Definitions and Facts Preservation of Circles Construction Using Orthogonal Circles Preservation of Angles Preservation of Symmetry Inversion in a Sphere Three Illustrative Applications of Inversion A Problem on Touching Circles Quadrilaterals with Orthogonal Diagonals Ptolemy's Theorem The Riemann Sphere The Point at Infinity Stereographic Projection Transferring Complex Functions to the Sphere Behaviour of Functions at Infinity Stereographic Formulae Mobius Transformations: Basic Results Preservation of Circles, Angles, and Symmetry Non-Uniqueness of the Coefficients The Group Property Fixed Points Fixed Points at Infinity The Cross-Ratio Mobius Transformations as Matrices Evidence of a Link with Linear Algebra The Explanation: Homogeneous Coordinates Eigenvectors and Eigenvalues Rotations of the Sphere Visualization and Classification The Main Idea Elliptic, Hyperbolic, and Loxodromic types Local Geometric Interpretation of the Multiplier Parabolic Transformations Computing the Multiplier Eigenvalue Interpretation of the Multiplier Decomposition into 2 or 4 Reflections Introduction Elliptic Case Hyperbolic Case Parabolic Case Summary Automorphisms of the Unit Disc Counting Degrees of Freedom Finding the Formula via the Symmetry Principle Interpreting the Formula Geometrically Introduction to Riemann's Mapping Theorem Exercises Differentiation: The Amplitwist Concept Introduction A Puzzling Phenomenon Local Description of Mappings in the Plane Introduction The Jacobian Matrix The Amplitwist Concept The Complex Derivative as Amplitwist The Real Derivative Re-examined The Complex Derivative Analytic Functions A Brief Summary Some Simple Examples Conformal = Analytic Introduction Conformality Throughout a Region Conformality and the Riemann Sphere Critical Points Degrees of Crushing Breakdown of Conformality Branch Points The Cauchy-Riemann Equations Introduction The Geometry of Linear Transformations The Cauchy-Riemann Equations Exercises Further Geometry of Differentiation Cauchy-Riemann Revealed Introduction The Cartesian Form The Polar Form An Intimation of Rigidity Visual Differentiation of log(z) Rules of Differentiation Composition Inverse Functions Addition and Multiplication Polynomials, Power Series, and Rational Functions Polynomials Power Series Rational Functions Visual Differentiation of the Power Function Visual Differentiation of exp(z) Geometric Solution of E' = E 232 An Application of Higher Derivatives: Curvature Introduction Analytic Transformation of Curvature Complex Curvature Celestial Mechanics Central Force Fields Two Kinds of Elliptical Orbit Changing the First into the Second The Geometry of Force An Explanation The Kasner-Arnol'd Theorem Analytic Continuation Introduction Rigidity Uniqueness Preservation of Identities Analytic Continuation via Reflections Exercises Non-Euclidean Geometry Introduction The Parallel Axiom Some Facts from Non-Euclidean Geometry Geometry on a Curved Surface Intrinsic versus Extrinsic Geometry Gaussian Curvature Surfaces of Constant Curvature The Connection with Mobius Transformations Spherical Geometry The Angular Excess of a Spherical Triangle Motions of the Sphere A Conformal Map of the Sphere Spatial Rotations as Mobius Transformations Spatial Rotations and Quaternions Hyperbolic Geometry The Tractrix and the Pseudosphere The Constant Curvature of the Pseudosphere A Conformal Map of the Pseudosphere Beltrami's Hyperbolic Plane Hyperbolic Lines and Reflections The Bolyai-Lobachevsky Formula The Three Types of Direct Motion Decomposition into Two Reflections The Angular Excess of a Hyperbolic Triangle The Poincare Disc Motions of the Poincare Disc The Hemisphere Model and Hyperbolic Space Exercises Winding Numbers and Topology Winding Number The Definition What does "inside" mean? Finding Winding Numbers Quickly Hopf's Degree Theorem The Result Loops as Mappings of the Circle The Explanation Polynomials and the Argument Principle A Topological Argument Principle Counting Preimages Algebraically Counting Preimages Geometrically Topological Characteristics of Analyticity A Topological Argument Principle Two Examples Rouche's Theorem The Result The Fundamental Theorem of Algebra Brouwer's Fixed Point Theorem Maxima and Minima Maximum-Modulus Theorem Related Results The Schwarz-Pick Lemma Schwarz's Lemma Liouville's Theorem Pick's Result The Generalized Argument Principle Rational Functions Poles and Essential Singularities The Explanation Exercises Complex Integration: Cauchy's Theorem Introduction The Real Integral The Riemann Sum The Trapezoidal Rule Geometric Estimation of Errors The Complex Integral Complex Riemann Sums A Visual Technique A Useful Inequality Rules of Integration Complex Inversion A Circular Arc General Loops Winding Number Conjugation Introduction Area Interpretation General Loops Power Functions Integration along a Circular Arc Complex Inversion as a Limiting Case General Contours and the Deformation Theorem A Further Extension of the Theorem Residues The Exponential Mapping The Fundamental Theorem Introduction An Example The Fundamental Theorem The Integral as Antiderivative Logarithm as Integral Parametric Evaluation Cauchy's Theorem Some Preliminaries The Explanation The General Cauchy Theorem The Result The Explanation A Simpler Explanation The General Formula of Contour Integration Exercises Cauchy's Formula and Its Applications Cauchy's Formula Introduction First Explanation Gauss' Mean Value Theorem General Cauchy Formula Infinite Differentiability and Taylor Series Infinite Differentiability Taylor Series Calculus of Residues Laurent Series Centred at a Pole A Formula for Calculating Residues Application to Real Integrals Calculating Residues using Taylor Series Application to Summation of Series Annular Laurent Series An Example Laurent's Theorem Exercises Vector Fields: Physics and Topology Vector Fields Complex Functions as Vector Fields Physical Vector Fields Flows and Force Fields Sources and Sinks Winding Numbers and Vector Fields The Index of a Singular Point The Index According to Poincare The Index Theorem Flows on Closed Surfaces Formulation of the Poincare-Hopf Theorem Defining the Index on a Surface An Explanation of the Poincare-Hopf Theorem Exercises Vector Fields and Complex Integration Flux and Work Flux Work Local Flux and Local Work Divergence and Curl in Geometric Form Divergence-Free and Curl-Free Vector Fields Complex Integration in Terms of Vector Fields The Polya Vector Field Cauchy's Theorem Example: Area as Flux Example: Winding Number as Flux Local Behaviour of Vector Fields Cauchy's Formula Positive Powers Negative Powers and Multipoles Multipoles at Infinity Laurent's Series as a Multipole Expansion The Complex Potential Introduction The Stream Function The Gradient Field The Potential Function The Complex Potential Examples Exercises Flows and Harmonic Functions Harmonic Duals Dual Flows Harmonic Duals Conformal Invariance Conformal Invariance of Harmonicity Conformal Invariance of the Laplacian The Meaning of the Laplacian A Powerful Computational Tool The Complex Curvature Revisited Some Geometry of Harmonic Equipotentials The Curvature of Harmonic Equipotentials Further Complex Curvature Calculations Further Geometry of the Complex Curvature Flow Around an Obstacle Introduction An Example The Method of Images Mapping One Flow Onto Another The Physics of Riemann's Mapping Theorem Introduction Exterior Mappings and Flows Round Obstacles Interior Mappings and Dipoles Interior Mappings, Vortices, and Sources An Example: Automorphisms of the Disc Green's Function Dirichlet's Problem Introduction Schwarz's Interpretation Dirichlet's Problem for the Disc The Interpretations of Neumann and Bocher Green's General Formula Exercises References Index
P: 1,666 I bought it and did not like it. For one, it's not visual. Complex Analysis in my opinion is very visual and they did not in my opinion capture this visual component of the subject well at all. Sorry I can't give examples, I looked on my bookshelf and seem not to have it anymore.
P: 714 This is one of my favourite mathematics books. It has a strong "style" to it that some people may not like, and it is probably not the best book to use for a first course. However, as a supplemental text or a second course, it would be awesome. I deeply love Complex Analysis because of this book.
P: 768
## Visual Complex Analysis by Tristan Needham
I haven't worked through the entirety of the text, but the section on Mobius transformations and their relationship linear projective transformations is honestly the most insightful and clear that I've ever read. The book is worth the price for that chapter alone.
Related Discussions Calculus & Beyond Homework 10 Calculus 3 General Math 0 Science & Math Textbooks 0 Science & Math Textbooks 0 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9477126598358154, "perplexity": 1290.6689763221523}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999654003/warc/CC-MAIN-20140305060734-00022-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/questions/41741/conflict-with-biblatex-and-custom-class | # conflict with biblatex and custom class
I am customizing apa6e for a large report. I need the functionality of apa6e's leavefloats option. But when that option is passed to the class, biblatex-apa doesn't work, giving me an error about the argument of \MakeLowercase having an extra }.
By removing leavefloats, everything works perfectly. I can't figure out why exactly from reading the code, I'd appreciate if someone can point me in the right direction.
A latex example:
\documentclass[leavefloats]{apa6e}
\usepackage[american]{babel}
\usepackage{csquotes}
\usepackage[style=apa, backend=biber]{biblatex}
\DeclareLanguageMapping{american}{american-apa}
\bibliography{books}
\title{Test}
\shorttitle{Test}
\author{Johnny B. Good}
\authornote{\ldots}
\abstract{\ldots}
\begin{document}
\maketitle
This is my example \parencite{good}.
\newpage
\printbibliography
\end{document}
The accompanying bib file:
@Book{good,
author={Johnny B. Good},
title={My great book},
publisher={Good Publishing},
year={1910}
}
-
A MWE example would be useful. – egreg Jan 20 '12 at 17:05
The command authornotes is undefined. The correct one is authornote. Avoid the command \bibliography instead use \addbibresource{books.bib}. With this modification your example works without any errors. – Marco Daniel Jan 20 '12 at 18:15
@MarcoDaniel Thanks! this is exactly what I needed. If you can add it as an answer I can accept it :) – ravl1084 Jan 21 '12 at 17:00
@ravl1084: Done ;-) – Marco Daniel Jan 21 '12 at 17:36
The error in your code based on the command \authonotes. This command is undefined. The correct one is \authornote (without "s").
Next thing. Please use \addbibresource instead of \bibliography. The manual of biblatex explains the differences and the advantages of \addbibresource. However \addbibresource expect the filename with the extension.
\addbibresource{books.bib} | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8695828914642334, "perplexity": 4262.55939546589}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1419447561188.130/warc/CC-MAIN-20141224185921-00057-ip-10-231-17-201.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/79343/is-the-axiom-of-universes-harmless | # Is the axiom of universes 'harmless'?
Usually when you start studying category theory you see the usual definition: a category consists of a class $Ob(\mathcal{C})$ of objects, etc.
If you take ZFC to be your system of axioms, then a "class" (a proper one) is something which you can't formally use, since everything in the universe of discourse is a set.
Some people (MacLane? Grothendieck?) were understandably worried about this. Cutting down on the history which I am unqualified to give an accurate account of, there is the definition of Grothendieck universe.
If we add the following axiom of universes to ZFC, then we can get around having to use classes:
Axiom of universes (U): every set is contained in some universe.
Now, it can be proven that the axiom of universes is equivalent to the
Inaccesible cardinal axiom: for every cardinal μ, there is an inaccessible cardinal κ which is strictly larger.
which was proven to be independent of ZFC. Hence we can work in ZFC+U and do category theory with the concern of dealing with proper classes put at rest.
This seems to be now a standard approach to a good foundation of category theory.
My question, to put it informally, is: how innocent is the axiom of universes?
What I mean by this is: how do we know it does not have unexpected consequences which may alter the rest of mathematics? The motivation was to give a good foundation of category theory, but it would be unreasonable to give a great foundation that altered the rest of ordinary mathematics.
To give an example, we now that adding the axiom of choice to ZF has some startling consequences. For example, the Banach-Tarski paradox. How do we know that ZFC+U does not have some equally startling consequences? Why are we at rest with adding this axiom to our foundation of mathematics? Isn't this a rather delicate question? How much do we know about how good is the universe approach? (I would say a foundation for category theory is better than another one if it solves the 'proper classes issue' and it has less impact on the rest of mathematics.)
-
Just to comment on your last sentence, that is to say "ZFC+A proper class of inaccessible cardinals" is enough to solve all "proper class" issues. However this is not just "a single inaccessible" assumption, and it is quite heavier than assuming the existence of one or two inaccessible cardinals (however not even close to something like Mahlo cardinals). It does not solve all proper classes issues, especially not in set theory. The Russell paradox tells us not that we are limited by set theory, but rather that we are limited. You can never describe your system from within itself. – Asaf Karagila Nov 5 '11 at 22:28
If you only need one ‘level’ of classes, then NBG may provide a satisfactory solution. Mac Lane only assumes the existence of one universe in Categories for the Working Mathematician. But the truth of the matter is that the working categorist would rather have at least a countable infinity of levels, so that we can talk about such things as the category of all functors $\textbf{CRing} \to \textbf{Set}$ (relevant, for example, in Grothendieck's functor of points approach to algebraic geometry). – Zhen Lin Nov 5 '11 at 22:47
If you read French you may want to consult the contribution by Bourbaki to SGA 4.1. – t.b. Nov 5 '11 at 23:16
Related: This MO thread. – Quinn Culver Dec 3 '11 at 17:31
Bruno, I'm not 100% clear about what you are trying to understand with this question. Modern mathematics is a lot more open to paradoxical results (e.g. Banach-Tarski Banach-Tarski) and the parts depending on universes (i.e. mild large cardinals) are not too horrible to endure. It seems that many people have accepted large cardinals, and even stronger axioms than universes. – Asaf Karagila Dec 7 '11 at 23:10
What I mean by this is: how do we know it does not have unexpected consequences which may alter the rest of mathematics?
I will give a couple remarks, and also link to these MathOverflow discussions:
(1) In set theory, the study of large cardinals (much "larger" than just inaccessible) has been very fruitful. The existence of many of these large cardinals requires the existence of inaccessibles. So set theorists are interested in these large cardinals because of their useful (perhaps "startling") consequences. If there were no interesting consequences, set theorists would find other things to look at.
(2) From the skeptical POV, we don't know what the consequences might be. It could be that ZFC is consistent but ZFC plus the universe axiom is inconsistent. Many people come to feel that they have some intuition that the existence of universes is not inconsistent with ZFC. This belief often comes from thinking about the way that the cumulative hierarchy works. On the other hand, there is a manuscript by Kiselev (link) in which he claims to prove that the existence of even one inaccessible cardinal is inconsistent with ZFC.
We do know that ZFC cannot prove that there is even one inaccessible cardinal. And we know we cannot prove in ZFC that the existence of an inaccessible is consistent, because of limitations coming from the incompleteness theorems. So any argument that inaccessibles are consistent will have to use methods that cannot be formalized in ZFC.
(3) Temporarily adopt a Platonistic perspective, at least for the sake of argument. From this position, each "axiom" is either true or false, but it cannot alter the properties of mathematical objects, which exist separately from the axioms used to study them. Of course we can prove false statements from false axioms, but we can't actually change the objects themselves.
(4) Now temporarily reject Platonism, and think only about formal proofs. Then it will not make any difference to my conception of mathematics if someone else adopts an axiom that I don't accept. I will simply put a * beside all the theorems that use this axiom, and count them as dubious at best. I might even reprove some of the theorems without the new axiom just so I know they are OK. In this way, my personal conception of mathematics would also be unchanged by other people using different axioms.
I think that (3) and (4) start to indicate the way that philosophical issues will enter in when we ask about the effects of different axioms on "mathematics".
-
I will leave it to another user to discuss the exact strength of the universe axioms in set theory. There is a lot to say about that.
The thing that I want to point out is that, for the actual applications of the category-theoretic methods to number theory, such as Fermat's Last Theorem (FLT), it appears that the use of universes can be eliminated. For example, Colin McLarty published an article (ref, preprint) in the Bulletin of Symbolic Logic in 2010 in which he states:
"This paper aims to explain how and why three facts coexist:
1. Universes organize a context for the rather explicit arithmetic calculations proving FLT or other number theory.
2. Universes can be eliminated in favor of ZFC by known devices though this is never actually done (and this remains far stronger than PA).
3. The great proofs in cohomological number theory, such as Wiles [1995] or Deligne [1974], or Faltings [1983], use universes in fact."
The key claim I want to highlight is (2): many people believe that methods using universes are not needed for concrete results such as Wiles' theorem, and in principle the proofs can be rewritten without them. I am in no position to judge the claim but it seems to be accepted by quite a few people who have looked into the matter. There is an open conjecture that Fermat's Last Theorem can be proved in Peano Arithmetic and even in much weaker theories, and at present we have no reason to suspect that FLT cannot be proved in Peano Arithmetic.
This makes the foundational question of universes more interesting: they are used, clearly, but working number theorists know how to avoid them if desired, which leaves a sort of tension. This is the issue McLarty is getting at in his paper.
McLarty's most recent progress announcement indicates he has made even more progress since his 2010 paper.
-
Concerning 3. I'm no expert at all, but I distinctly remember this MO thread. – t.b. Nov 5 '11 at 23:56
This answer is very interesting as a comment: since the bounty is coming to an end, I will award it to you. I do not consider it really answers the question, as you point out in the first paragraph yourself, hence I will still leave this question without a checkmark. – lentic catachresis Dec 10 '11 at 15:55
@Bruno Stonek: Thank you! I will do my best to write an answer to the question separately, in return. I expected someone else would write one, so I hesitated. But I can say something at least. I will write it tomorrow. – Carl Mummert Dec 11 '11 at 2:45
@CarlMummert: Great! I'm looking forward to it :) – lentic catachresis Dec 11 '11 at 17:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8144852519035339, "perplexity": 444.70317815923516}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119646554.36/warc/CC-MAIN-20141024030046-00318-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/electric-field-of-a-solenoid.112821/ | # Electric field of a solenoid
1. Mar 3, 2006
### Reshma
A long solenoid with radius 'a' and 'n' turns per unit length carries a time-dependent current $I(t)$ in the $\phi$ direction. Find the electric field (magnitude and direction) at a distance 's' from the axis (both inside and outside the solenoid), in quasi-static approximation.
What's quasi-static approximation? Anyway, without much prior thought I applied the flux rule :
$$\varepsilon = \int \vec E \cdot d\vec l = -{d\Phi \over dt}$$
$\vec B = \mu_0 nI \hat z$, $\vec A = \pi a^2 \hat z$
$$\Phi = \mu_0 nI \pi a^2$$
$$\int \vec E \cdot d\vec l =-{d ( \mu_0 nI \pi a^2)\over dt}$$
$$E2\pi a = -( \mu_0 n \pi a^2){dI\over dt}$$
Before I proceed to the final step, someone please check my work.
2. Mar 3, 2006
### Galileo
Since you have a time varying current, the electromagnetic field created by the solenoid varies with time. The electromagnetic 'news' travels at the speed of light though.
In this case you are working with a time varying currents, but you are using the apparatus of magnetostatics, like Biot-Savart and Ampère's Law (e.g. Your equation for B came from magnetostatics). Your answers are only approximately correct, but the deviation is small if the current is 'static enough', i.e. it doesn't vary quickly. The approximation is called the quasi-static approximation.
You are looking at a distance 's' from the solenoid axis right? So $\oint \vec E \cdot d\vec l=E2\pi s$. Also, the flux through the surface bounding your Amperian loop is $\mu_0 n \pi a^2$ only outside the loop, where $s\geq a$.
3. Feb 5, 2011
### Khalid Hameed
By the quasi static appriximation we mean that B=mu_0 nI (s<a) and B= 0 (s>a)
then why E is not zero outside(s>a)? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9239373803138733, "perplexity": 1260.0193629837413}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698540409.8/warc/CC-MAIN-20161202170900-00092-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(Guichard)/15%3A_Multiple_Integration/15.3%3A_Moment_and_Center_of_Mass | $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$
# 15.3: Moment and Center of Mass
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
Using a single integral we were able to compute the center of mass for a one-dimensional object with variable density, and a two dimensional object with constant density. With a double integral we can handle two dimensions and variable density.
Just as before, the coordinates of the center of mass are
$$\bar x={M_y\over M} \qquad \bar y={M_x\over M},$$
where $$M$$ is the total mass, $$M_y$$ is the moment around the $$y$$-axis, and $$M_x$$ is the moment around the $$x$$-axis. (You may want to review the concepts in Section 9.6.)
The key to the computation, just as before, is the approximation of mass. In the two-dimensional case, we treat density $$\sigma$$ as mass per square area, so when density is constant, mass is $$(\hbox{density})(\hbox{area})$$. If we have a two-dimensional region with varying density given by $$\sigma(x,y)$$, and we divide the region into small subregions with area $$\Delta A$$, then the mass of one subregion is approximately $$\sigma(x_i,y_j)\Delta A$$, the total mass is approximately the sum of many of these, and as usual the sum turns into an integral in the limit:
$$M=\int_{x_0}^{x_1}\int_{y_0}^{y_1} \sigma(x,y)\,dy\,dx,$$
and similarly for computations in cylindrical coordinates. Then as before
\eqalign{ M_x &= \int_{x_0}^{x_1}\int_{y_0}^{y_1} y\sigma(x,y)\,dy\,dx\cr M_y &= \int_{x_0}^{x_1}\int_{y_0}^{y_1} x\sigma(x,y)\,dy\,dx.\cr }
Example $$\PageIndex{1}$$
Find the center of mass of a thin, uniform plate whose shape is the region between $$y=\cos x$$ and the $$x$$-axis between $$x=-\pi/2$$ and $$x=\pi/2$$. Since the density is constant, we may take $$\sigma(x,y)=1$$.
It is clear that $$\bar x=0$$, but for practice let's compute it anyway. First we compute the mass:
\begin{align*} M&=\int_{-\pi/2}^{\pi/2} \int_0^{\cos x} 1\,dy\,dx \\[5pt]&=\int_{-\pi/2}^{\pi/2} \cos x\,dx \\[5pt]&=\left.\sin x\right|_{-\pi/2}^{\pi/2}=2.\end{align*}
Next,
\begin{align*} M_x&=\int_{-\pi/2}^{\pi/2} \int_0^{\cos x} y\,dy\,dx \\[5pt]&=\int_{-\pi/2}^{\pi/2} {1\over2}\cos^2 x\,dx\\[5pt]&={\pi\over4}.\end{align*}
Finally,
\begin{align*} M_y&=\int_{-\pi/2}^{\pi/2} \int_0^{\cos x} x\,dy\,dx \\[5pt]&=\int_{-\pi/2}^{\pi/2} x\cos x\,dx\\[5pt]&=0.\end{align*}
So $$\bar x=0$$ as expected, and $$\bar y=\pi/4/2=\pi/8$$. This is the same problem as in example 9.6.4; it may be helpful to compare the two solutions.
Example $$\PageIndex{2}$$
Find the center of mass of a two-dimensional plate that occupies the quarter circle $$x^2+y^2\le1$$ in the first quadrant and has density $$k(x^2+y^2)$$. It seems clear that because of the symmetry of both the region and the density function (both are important!), $$\bar x=\bar y$$. We'll do both to check our work.
Jumping right in:
\begin{align*} M&=\int_0^1 \int_0^{\sqrt{1-x^2}} k(x^2+y^2)\,dy\,dx \\[5pt]&=k\int_0^1 x^2\sqrt{1-x^2}+{(1-x^2)^{3/2}\over3}\,dx. \end{align*}
This integral is something we can do, but it's a bit unpleasant. Since everything in sight is related to a circle, let's back up and try polar coordinates. Then $$x^2+y^2=r^2$$ and
\begin{align*} M&=\int_0^{\pi/2} \int_0^{1} k(r^2)\,r\,dr\,d\theta \\[5pt]&=k\int_0^{\pi/2}\left.{r^4\over4}\right|_0^1\,d\theta \\[5pt]&=k\int_0^{\pi/2} {1\over4}\,d\theta \\[5pt]&=k{\pi\over8}.\end{align*}
Much better. Next, since $$y=r\sin\theta$$,
\begin{align*} M_x&=k\int_0^{\pi/2} \int_0^{1} r^4\sin\theta\,dr\,d\theta \\[5pt]&=k\int_0^{\pi/2} {1\over5}\sin\theta\,d\theta \\[5pt]&=k\left.-{1\over5}\cos\theta\right|_0^{\pi/2}={k\over5}.\end{align*}
Similarly,
\begin{align*} M_y&=k\int_0^{\pi/2} \int_0^{1} r^4\cos\theta\,dr\,d\theta \\[5pt]&=k\int_0^{\pi/2} {1\over5}\cos\theta\,d\theta \\[5pt]&=k\left.{1\over5}\sin\theta\right|_0^{\pi/2}={k\over5}.\end{align*}
Finally, $$\bar x = \bar y = {8\over5\pi}$$.
### Contributors
• Integrated by Justin Marshall. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9937930703163147, "perplexity": 873.1172161526239}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583857993.67/warc/CC-MAIN-20190122161345-20190122183345-00235.warc.gz"} |
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