content
string | pred_label
string | pred_score
float64 |
|---|---|---|
4 TYPES OF VOR CHECKS
Your airplanes VOR received must be checked every 30 days for IFR Operations and there are multiple ways pilot's can check their VORs. How are they performed? What do you need to annotate?
Here's what you need to know.
VOR Checks:
VOR Receivers are required to be checked every 30 days for IFR Flight Operations. However, it is also important for VFR Pilot’s to check their aircraft’s VOR Receivers.
What to Write (SLED)
Signature (of pilot performing the check)
Location (of the check)
Error (amount of error detected during check)
Date (of the check)
VOT (VOR Test Facility)
A VOT is coded to emit the 360 Radial in all directions around the facility.
This means the airplane’s VOR Receiver should read either: 360 FROM or 180 TO, regardless of the aircraft’s location in relation to the VOR.
How the check is done:
1. Tune and Identify the VOT.
2. Twist the OBS Knob to center the CDI Needle.
3. Check for proper TO/FROM Indication.
4. The radial selected must be within:
5. +/- 4 degrees of 360 or 180.
Ground Check
With a VOR Ground Check:
• The Pilot must park the airplane in the designated ground spot.
• The Pilot must tune and identify the correct VOR.
• The Pilot must use the ground check sign to know:
• Which radial he/she should be on.
• Whether he/she should have a TO or a FROM Indication.
How the check is done:
1. Park aircraft in designated check spot.
2. Tune and Identify the Correct VOR.
3. Twist the OBS Knob to center the CDI Needle.
4. Check for proper TO/FROM Indication.
5. The radial selected must be within:
6. +/- 4 degrees of Designated Radial.
Airborne Check
With an Airborne VOR check:
• The Pilot must position the airplane over the designated location.
• The Pilot must tune and identify the correct VOR.
• The Pilot must use the information in the Chart Supplement to know:
• Which radial he/she should be on.
• Whether he/she should have a TO or a FROM Indication.
How the check is done:
1. Position aircraft over designated check spot.
2. Tune and Identify the Correct VOR.
3. Twist the OBS Knob to center the CDI Needle.
4. Check for proper TO/FROM Indication.
5. The radial selected must be within:
6. +/- 6 degrees of Designated Radial.
Dual VOR Check
With a Dual VOR check, the airplane must be equipped with 2 VOR Receivers.
How the check is done:
1. The pilot tunes both VOR Receivers to the same VOR.
2. The pilot centers both CDI Needles.
3. Check for proper TO/FROM Indications.
4. With both CDI Needles Centered:
5. The Selected Radials should be within 4 degrees of each other.
VOR Check Summary:
• VOT = +/- 4
• Ground Check = +/- 4
• Airborne Check = +/- 6
• Dual Check = within 4 degrees of each other
Author - Nate Hodell
CFI/CFII/MEI/ATP - Creator of wifiCFI - Owner of Axiom Aviation Flight School.
This information is included in the Navigation Aids: VOR Lessons on wifiCFI. Sign up today to watch videos, listen to podcasts, take lesson quizzes, join live webinars, print lesson quicktakes, and more by clicking this link >
where aviation comes to study
worldwide site members: 27,532
|
__label__pos
| 0.930287 |
How to Convert A Hexadecimal Number to Decimal in Excel
Sometimes we use hexadecimal numbers to mark products in daily life, and we want to convert these hexadecimal numbers to decimal numbers in some situations. We can convert number between two number types by convert tool online, actually we can also convert numbers by function in excel as well. In excel, =HEX2DEC(number) can help you to convert hexadecimal number to decimal properly, and on the other side, you can use =DEX2HEX(number) to convert decimal to hexadecimal number.
1. Convert Hex Number to Decimal in Excel
As we mentioned above, we can use HEX2DEC function to convert numbers conveniently. Just prepare a table with two columns, one column is used for recording HEX numbers, the second column is used for saving the converted decimal numbers.
Convert A Hexadecimal Number to Decimal 1
Step1: in B1 enter the formula:
=HEX2DEC(A2)
Convert A Hexadecimal Number to Decimal 2
Step2: Click Enter to get returned value. So 21163 in B2 is the mapping decimal number for 52AB.
Convert A Hexadecimal Number to Decimal 3
Step3: Drag the fill handle down to fill the following cells.
Convert A Hexadecimal Number to Decimal 4
Verify that all hexadecimal numbers are converted to decimal numbers correctly. You can also double check the result by convert tool online to make sure the result is correct.
Note:
Sometimes hexadecimal numbers are displayed like 0x52AB, user can remove 0x before 52AB and then use HEX2DEC function to convert number.
2. Convert Decimal to Hex Number in Excel
Prepare another table, the first column is Decimal, the second column is Hex Number.
Convert A Hexadecimal Number to Decimal 5
Step1: in B10 enter the formula:
=HEX2DEC(A2)
Convert A Hexadecimal Number to Decimal 6
Step2: Click Enter to get returned value. So 4D2 in B10 is the mapping hex number for 1234.
Convert A Hexadecimal Number to Decimal 7
Step3: Drag the fill handle down to fill the following cells.
Convert A Hexadecimal Number to Decimal 8
Note:
There are some other functions to convert numbers between different types. See below screenshot.
Convert A Hexadecimal Number to Decimal 9
Convert A Hexadecimal Number to Decimal 10
Convert A Hexadecimal Number to Decimal 11
3. Video: Converting Hex Numbers to Decimal and Decimal to Hex
In this video, we’ll explore two essential skills: converting Hexadecimal numbers to Decimal and Decimal numbers to Hex in Excel.
4. SAMPLE FIlES
Below are sample files in Microsoft Excel that you can download for reference if you wish.
|
__label__pos
| 0.998641 |
skip to Main Content
What is In Vitro Fertilization?
An Overview of IVF
In Vitro fertilization (IVF) has become the most popular choice of treatment for couples with various types of infertility. It is generally accepted as the most successful and fastest method available to achieve pregnancy. While it was initially reserved for patients with blocked, damaged, or absent fallopian tubes (tubal factor infertility), IVF is now also used to overcome infertility caused by endometriosis, male factor (sperm) issues, diminished egg quality, ovulatory problems, or other unexplained reasons.
IVF is an advanced method of assisted reproduction in which the man’s sperm and the woman’s eggs are combined in a laboratory where fertilization occurs, and the resultant embryos are then transferred to the woman’s uterus (embryo transfer) in hopes of achieving a pregnancy. Initially, the patient undergoes ovulation enhancement (superovulation) with a combination of injectable fertility medications that results in the development of multiple eggs in both ovaries. When the eggs have sufficiently matured, the transvaginal ultrasound-guided egg retrieval procedure is then performed in the office, with an anesthesiologist present to provide complete pain relief. The patient is discharged home soon after the procedure.
On the day the eggs are harvested, the partner provides a semen specimen from which the sperm are isolated in the laboratory, and used to fertilize the eggs. If a significant male factor is present, such as low sperm concentrations, or a diminished percentage of normal appearing sperm (morphology) or normally motile sperm (motility), intracytoplasmic sperm injection (ICSI) is an extremely useful modality that is employed to maximize the chances for fertilization.
ICSI
Intracytoplasmic Sperm Injection (ICSI — pronounced “ick-see”) is a technique of gamete (sperm/egg) micro-manipulation, or assisted fertilization, in which individual sperm are captured in a microscopic glass pipette and meticulously injected directly into the individual eggs. The resultant fertilized eggs (early embryos) are then allowed to grow and mature in the sterile laboratory conditions in a manner similar to that of standard IVF. In cases where there is a complete absence of sperm in the ejaculate, such as in gentlemen who have previously undergone a vasectomy, microsurgical epididymal sperm aspiration (MESA) or testicular sperm extraction (TESE) is performed by a specialized urologist here in our office for retrieval of the sperm, and ICSI is then carried out.
Embryo Transfer
An appropriate number of fertilized eggs (pre-embryos) are returned into the patient’s uterus three days later following the egg retrieval via Day 3 embryo transfer, or in select cases, the embryos are cultured for an additional 2-3 days and a blastocyst transfer is performed. We are extremely careful to limit the number of embryos transferred so as to help avoid a high order multiple pregnancy (3 or more fetuses) from occurring.
To learn more, please contact us online or by phone at 732-339-9300, or please continue reading on our Frequently Asked Questions page.
Back To Top
|
__label__pos
| 0.934772 |
Genesis, 1-3
Genesis, 1-3
Without blaming serpent, Eve or Adam, what do you think is the crime which gets Adam and Eve thrown out of the garden? To say it another way, what is this knowledge which God wants to keep human beings from having?
Eusa Story (Blackboard)
What is Eusa’s crime?
In what way does his story retell the shut-down of the Garden of Eden?
Galileo (Blackboard and Copernicus film: https://www.youtube.com/watch?v=zHUWP9zu4W8)
On the night of January 7, 1610, Galileo has a new “superlative instrument.” He writes, “When I inspected the celestial constellations through a spyglass, Jupiter presented himself.”
p. 64—What does Galileo see when he looks up at Jupiter?
p. 65—Why does he decide, on January 8, to look at Jupiter again?
p. 65–What does he see, on that second night (January 8) when he looks at Jupiter again?
pp. 65-85—Between January 8 and March 1, 1610, what does Galileo do every night that the weather is clear?
p. 85—What does Galileo know for certain by March 1, 1610?
(film) Briefly describe Galileo’s scientific achievement
(film) Briefly describe Galileo’s trial for heresy
(film) Briefly describe the advance of science since Galileo’s day
GALILEO’S OBSERVATIONS OF THE MOON
1—1610: What was happening in your home country at this time?
2—Is Galileo the 1st to create a telescope?
3—With his own self-made telescope, how close is he able to make the moon appear?
4—How far is the moon, actually, from the Earth? How many “terrestrial diameters?”
5—On the 4th or 5th day after “conjunction,” the moon appears to have horns. Explain. See page 40.
6—On Earth, when the sun rises and its light catches the peak of a mountain, what light reaches the valleys on either side of the mountain?
7—How well-lit are the valleys when the sun rises high in the sky?
8—If the surface of the moon is covered with mountains, why does the moon appear to be almost perfectly round? See page 49.
9—Galileo believes that the moon, like the Earth, has an atmosphere. Is he right? See pages 50—51.
10—Even when the moon is dark, it isn’t perfectly dark. It’s as if some faint light is shining on it. Where does this light come from? See pages 53—56.
11—Based on your general knowledge, in what way or ways can you imagine that Galileo’s observations may get him in trouble with the Catholic Church?
The 6th Extinction ppt slides
#6 Describe the trajectory of human population from 4000 BC to 2100 AD (projected)
#9 How does Darwin explain extinction?
#15 How does E. O. Wilson explain extinction?
#19-20 How long have there been human beings? How long have there been ginkgo trees?
#21 What is the relationship between megafauna extinctions around the world and the spread of human beings?
#28 Karl Marx almost seems to admire the “subjection of Nature’s forces to man” which has happened during the brief “rule” of the bourgeoisie. Explain.
The 6th Extinction (text)
Chapter 1—Why are the golden frogs dying? What change in the world is causing the frogs to die?
Chapter 2—pp. 27-28 What does Jefferson write about “the economy of nature,” and what does he expect Lewis & Clark to find on their expedition to the West?
p. 29 How does Cuvier arrive at the conclusion that the bones of a mastodon belong to an “espece perdue (lost species)?”
p. 44 “The thread of operations is broken,” Cuvier writes. Explain.
Chapter 3 pp. 48-52 Lyell, like Darwin, is a “uniformitarian.” Explain.
p. 69 How does Darwin explain extinction?
Chapter 4 pp 74-78 in 1977, Walter Avarez sends soil samples to a colleague, Frank Asaro. In 1980, Walter Alvarez and his father, Luis Alvarez, publish a paper, “Extraterrestrial Cause for the Cretaceous-Tertiary Extinction.” What is their theory? What is their evidence ?
p. 91 Paul Taylor says about the death of the ammonites that, in certain moments, “the rules of the survival game” abruptly change. How is this a restatement of Cuvier’s idea that “the thread of operations is broken?” How does this theory put a major dent in Darwin’s theory of how extinctions take place?
Chapter 5 pp. 107-108 Paul Crutzen argues that the Earth is now in a new phase of extinction which he calls the Anthropocene. Name 5 geologic-scale processes which people are now causing.
Chapter 6 p. 113 How much CO2 will there be in the air by 2050? What global warming effects can be expected?
pp. 113-114 How much of this CO2 finds its way into the world’s oceans? How much more acidic will the oceans be than they were at the start of the Industrial Revolution?
pp. 116-117 How do the underwater CO2 vents along the sides of the Italian island, Castello Aragonese, offer scientists an “underwater time machine?”
pp. 121-124 How does ocean acidification increase “the cost of calcification?”
Chapter 7 pp. 128-130 How do coral reefs get built? How do they change the world?
pp. 136-137 With ocean acidification, what will happen to the world’s coral reefs? What will happen to their “tenants?”
Chapter 8 pp. 151-153 Imagine walking from the North Pole to the equator. To what degree are there more species in the tropics than anywhere else? Describe 3 theories to explain this difference.
p. 161 According to Darwin, how do species respond to temperature change?
p. 167 Describe 2 different predictions for the % of species loss by 2050, based on temperature change alone.
Chapter 9 p. 176 How much ice-free “wildlands” exist today?
p. 177 what is a “fishbone” pattern of deforestation?
p. 186 As a result of tropical deforestation, how many insect species are being lost every year?
p. 189 Describe the “dark synergy” between fragmentation and global warming.
Chapter 10 p. 197 What is meant by word, “Pangaea?”
pp. 204-205 just as golden frogs and other amphibians are being wiped out by chytrid fungus, little brown bats are being wiped out by white nose syndrome. How are human beings to blame?
pp. 205-208 What is an “introduced species?” How can it be argued that human beings are causing a “New Pangaea?”
Chapter 11 p. 221 Human beings “have brought (the Sumatran rhinoceros) so low that it seems only heroic human efforts can save it.” Explain.
p. 226 “What happened to all these Brobdingnagian animals? Cuvier, who was the first to note their disappearance, believed they had been done in by the most recent catastrophe: ‘a revolution on the surface of the earth’ that took place just before the start of recorded history.” Explain.
p. 234 It appears that the Anthropocene era does not begin with the Industrial Revolution, but with the dispersal of human beings around the earth. Comment.
Chapter 12 pp.246-247 Neanderthals are gone, but something like 4% of our genes today are, in fact, Neanderthal genes. Explain.
p. 249 Human children do not seem to be brighter than ape children except in one regard. What is it?
Chapter 13 p. 260 What is the Frozen Zoo?
Order a unique copy of this paper
(550 words)
Approximate price: $22
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
• 24/7 support
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
• Expert Proofreading
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)
Our guarantees
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
Money-back guarantee
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.
Read more
Zero-plagiarism guarantee
Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.
Read more
Free-revision policy
Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.
Read more
Privacy policy
Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.
Read more
Fair-cooperation guarantee
By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.
Read more
Calculate the price of your order
550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
$26
The price is based on these factors:
Academic level
Number of pages
Urgency
|
__label__pos
| 0.999951 |
Frequently Asked Questions
We have put together a list of Frequently Asked Questions to help you understand better what’s involved with Chiropractic and our Body in Balance clinic. If you can’t find the answer to your question, please phone us or use the form at the bottom of the page and we will answer your question directly.
Does treatment hurt?
Treatment is usually painless, and most patients look forward to and enjoy the experience (children often laugh!).
Sometimes though, especially after the first one or two treatments there may be a temporary reaction to treatment such as soreness similar to that felt after a work out, or tiredness (usually resulting in a good night’s sleep)
I saw on Trevor MacDonalds Tonight programme on TV that back problems can be cured by taking fillings out it was reported by Jonathan Maitland – is this true?
The TV programme showed the opinion of one practitioner regarding one specific patient. As a Chiropractor, I am trained to take a full history and carry out a through examination of a patient – following on from this I will share my findings and recommend a treatment programme.
Chiropractors may refer a patient for other tests or to other healthcare professionals. Each patient is different and the approach that an individual chiropractor may take in each case can vary, but has the aim of treating the problem through chiropractic treatment and then seeking to prevent re-occurrence in the future through individual exercise programmes, diet and lifestyle advice.
We describe this as a patient focused package of care. Along with my fellow chiropractors in the UK, I am regulated by the government appointed regulator, the General Chiropractic Council and abide by their strict codes of practice.
As a BCA member I have completed a minimum four-year full-time degree level education in chiropractic and am required by the regulator to demonstrate continuous learning and professional development each year.
How long will a visit to the Pain Relief Centre take?
Please click the following link to our “What to Expect” section on the Start Here page. You will find all the relevant details as well as an overview of the treatments and therapies we offer.
What does a chiropractor do?
A chiropractor checks your spine, and often your limbs, jaw and cranial bones, to see if you have any misalignment’s, stiffness or instability. When you have a misalignment, your spinal bones (vertebrae) create havoc with your nervous system and cerebro-spinal fluid flow.
This interference disturbs the neurological impulses flowing from your brain to your body and from your body back to your brain. Your brain then can no longer keep the body healthy.
As a result this can cause a negative effect on the body, a weakened immune system, arthritis and other diseases.
Do I need to contact my GP?
Only if you want to, or if you need a referral letter for private medical cover. We may, with your permission send a report to your GP to keep your medical records up to date.
Are Chiropractors ‘real’ doctors?
In the sense that doctor means ‘educator’ then yes, most chiropractors spend time educating their patients about health and well-being. Something medical doctors ironically rarely have time for.
In the legal sense, yes again, chiropractors can call themselves doctors as long as they make it clear they are not medical doctors.
Chiropractors are trained similar to medical doctors for the first two years, but then spend much more time on neurology, orthopedics, physical assessment, radiology and radiography.
Medical doctors spend this time learning about drugs, surgery and disease.
Is there any parking at the clinics?
At Body In Balance in Brookmans Park, you will find free parking right by the clinic.
How long will it take to get better?
As every body is unique this is very difficult to answer until you have been examined. It also depends on what you mean by ‘better’. Most people mean ‘how long before I’m out of pain?’ Pain can start to reduce right from the very first treatment or may take several sessions.
At Body In Balance our initial objective is to relieve the pain. Once we achieve this we work with you to help to “fix” the underlying problem and help you to get ‘better’ from a medical point of view.
A rough guide can be given though, as most people feel relief within 6-8 treatments over a few weeks, whereas to be healed to prevent reoccurrences would usually take a minimum of 3 months of care for simple cases in healthy, active people.
The longer you have had a problem, and the poorer your general condition and health, the longer it will take. The longer you leave a problem the more attention will be required to rectify it.
Can I have Chiropractic care after surgery?
Yes. Some techniques can be used directly after surgery to help speed up the healing process. If you had surgery for a specific problem and you still have pain – do not give up hope, chiropractic, and the correct exercise, has helped many people recover.
Can people with osteoporosis get chiropractic care?
Of course. When developing a care plan the unique circumstances of each patient are considered. There are many ways to adjust the spine.
The method selected will be best suited to your age, size and condition. Also, we can give you up to date advice on how to combat osteoporosis including what exercise to do, what foods and drinks to avoid that weaken your bones, and what supplements and foods may be of benefit.
How can chiropractic treatment benefit you?
Alleviates pain and discomfort. Helps you return to normal activity. Prevents recurrence. Promotes good health and well-being – please see articles in download section for more details.
What do chiropractors treat?
The primary goal for a chiropractor is to remove interference from your body’s own capacity to heal. So in a medical sense chiropractors treat nothing in particular, but can help in almost all health conditions.
For a list of the main problems seen by chiropractors please go to our Start Here page
What is the difference between Chiropractic and Osteopathy?
Well to be honest there can be more similarities than differences. Both try to improve health by mainly working on your spine.
What differs are the techniques learned at college. Some chiropractic and osteopathic techniques are very gentle, and some can seem very rough.
Very often it is the practitioner themselves that are the difference, rather than the profession. On the whole though osteopathic treatment tends to take longer to perform.
A final difference is that chiropractors learn to take and interpret X-rays.
Find Us and Contact Us
Address
9 Bradmore Green
Brookmans Park
Hertfordshire AL9 7QW
Phone
Use the form below to contact Body In Balance
|
__label__pos
| 0.969608 |
Asbestos health problem
Over time, accumulated asbestos fibers can cause tissue inflammation and scarring, which can affect breathing and lead to serious health problems low levels of asbestos fibers are present in the air, water, and soil. Asbestos poses health risks only when fibres are present in the air that people breathe health risks of asbestos also find out how to properly handle a potential asbestos problem asbestos, if inhaled, can cause cancer and other diseases on this page. People who get health problems from inhaling asbestos have usually been exposed to high levels of asbestos for a long time the symptoms of these diseases do not usually appear until about 20 to 30 years after the first exposure to asbestos. In general, the greater the exposure to asbestos, the greater the chance of developing harmful health effects disease symptoms may take many years to develop following exposure asbestos-related conditions can be difficult to identify. Asbestos an environmental and a health problem by dr hussein fatehy mahmoud phd-fccp -mcts consultant pulmonologist abbassia chest hospital cairo-egypt 2 agenda asbestos overview asbestos- an environmental problem asbestos-a health problem role of egyptian press media in asbestos banning role of egyptian government in asbestos banning take.
asbestos health problem Asbestos deaths remain a public health problem : shots - health news exposure to the tiny fibers in asbestos can lead people who work around the material to develop mesothelioma, a cancer of the.
Asbestosis is a serious long-term lung condition caused by prolonged exposure to asbestos asbestos is a whitish material that was used in buildings for insulation, flooring and roofing in the past, but is now no longer used. The port allegany asbestos health program (paahp) is a unique, community-run program that resulted from the successful cooperative efforts of a labor union, a corporation, community health care providers, and a medical school. Asbestos still kills around 5000 workers each year, this is more than the number of people killed on the road around 20 tradesman die each week as a result of past exposure however, asbestos is not just a problem of the past it can be present today in any building built or refurbished before the.
The world trade center health registry estimates about 410,000 people were exposed to a host of toxins including asbestos during the rescue, recovery and clean-up efforts that followed 9/11 people most affected by asbestos at ground zero were people assigned to rescue survivors. Workers exposed to asbestos have an increased risk of developing lung cancer this risk is greatly increased if the person smokes it is very difficult to distinguish lung cancer caused by asbestos and that caused by smoking or other environmental pollutants, so it is often very difficult to get a clear diagnosis of asbestos-related lung cancer. Asbestos in some form is in millions of homes, but i haven't been able to find statistics on the health effects of asbestos exposure in the home that doesn't mean they aren't there, but the cases of health problems from occupational exposure dominate. In may 2018, the epa published a document known as the “problem formulation of the risk evaluation for asbestos,” which establishes the scientific approach the epa will take in evaluating. Hd historic stock footage - story of asbestos mining and mfg 1920s - duration: 11:38 buyout footage historic film archive 11,743 views.
The legal limit for safe exposure to asbestos in the workplace is now 01 fiber/ml, so any asbestos measurement in the home of 01 fiber/ml or greater is a health concern. Once they are trapped in the body, the fibers can cause health problems asbestos is most hazardous when it is friable the term friable means that the asbestos is easily crumbled by hand, releasing fibers into the air. Asbestosis is a lung disease that develops when asbestos fibers cause scarring in your lungs the scarring restricts your breathing and interferes with the ability of oxygen to enter your bloodstream.
asbestos health problem Asbestos deaths remain a public health problem : shots - health news exposure to the tiny fibers in asbestos can lead people who work around the material to develop mesothelioma, a cancer of the.
Asbestos can cause health problems when inhaled into the lungs breathing in very small, airborne asbestos fibres has been associated with diseases such as asbestosis, mesothelioma and lung cancer. The environmental impact of asbestos used in the past as a common part of construction materials, asbestos continues to pose major risks to human health and the environment once it was discovered that it caused health problems, products that contained asbestos were discontinued, but the risks remain. Health problems associated with exposure to asbestos breathing asbestos mainly causes problems in the lungs and the membrane that surrounds the lungs, including: asbestosis : scarring of lung tissue that causes breathing problems, usually in workers exposed to asbestos in workplaces before the federal government began regulating asbestos use. Health problems attributed to asbestos include: asbestosis - a lung disease first found in textile workers, asbestosis is a scarring of the lung tissue resulting from the production of growth factors that stimulate fibroblasts (the scar-producing lung cells) to proliferate and synthesize the scar tissue in response to injury by the inhaled.
• “asbestos” is a commercial name, not a mineralogical definition, given to a variety of six naturally occurring fibrous minerals these minerals possess high tensile strength, flexibility, resistance to chemical and thermal degradation, and electrical resistance.
• Tigerite – geologically compressed blue asbestos white asbestos is also known as ‘serpentine’, as its’ fibres are bendy all the rest are called ‘amphibole’, as their crystals are constructed in columns (and so more rigid and liable to snap into tiny fragments.
• Install asbestos cement pipe, primarily because of issues with handling, there appears to be no concern for health of consumers receiving the water and no programmes to specifically replace asbestos cement pipe for this reason.
Asbestos becomes a health risk when its fibres are released into the air and breathed in breathing in asbestos fibres can cause asbestosis, lung cancer and mesothelioma asbestos was once used in australia in more than 3,000 different products including fibro, flue pipes, drains, roofs, gutters, brakes, clutches and gaskets. Asbestos use continued to grow through most of the 20th century until public knowledge of the health hazards of asbestos dust led to its outlawing by courts and legislatures in mainstream construction and fireproofing in most countries. What is asbestos asbestos is the name given to a group of naturally occurring minerals that are resistant to heat and corrosion asbestos has been used in products, such as insulation for pipes (steam lines for example), floor tiles, building materials, and in vehicle brakes and clutches. Knowledge or suspicion of health issues existed for a long time: the health issues related to asbestos were known, suspected, or reported, for decades, with modern medical coverage dating back to the 19th century.
asbestos health problem Asbestos deaths remain a public health problem : shots - health news exposure to the tiny fibers in asbestos can lead people who work around the material to develop mesothelioma, a cancer of the. asbestos health problem Asbestos deaths remain a public health problem : shots - health news exposure to the tiny fibers in asbestos can lead people who work around the material to develop mesothelioma, a cancer of the. asbestos health problem Asbestos deaths remain a public health problem : shots - health news exposure to the tiny fibers in asbestos can lead people who work around the material to develop mesothelioma, a cancer of the.
Asbestos health problem
Rated 3/5 based on 14 review
2018.
|
__label__pos
| 0.895392 |
Home | | Chemistry | General properties of Lanthanides
Chapter: 11th 12th std standard Class Organic Inorganic Physical Chemistry Higher secondary school College Notes
General properties of Lanthanides
General properties of Lanthanides
The Lanthanide series include fifteen elements i.e. lanthanum (57 La) to lutetium (71 Lu). Lanthanum and Lutetium have no partly filled 4f- subshell but have electrons in 5d-subshell.
The position of f block elements in the periodic table, is explained above.
The elements in which the extra electron enters ( n- 2 )f orbitals are called f- block elements. These elements are also called as inner transition elements because they form a transition series within the transition elements. The f-block elements are also known as rare earth elements. These are divided into two series.
i) The Lanthanide series (4f-block elements)
ii) The Actinide series (5f- block elements )
The Lanthanide Series
The Lanthanide series include fifteen elements i.e. lanthanum (57 La) to lutetium (71 Lu). Lanthanum and Lutetium have no partly filled 4f- subshell but have electrons in 5d-subshell. Thus these elements should not be included in this series. However, all these elements closely resemble lanthanum and hence are considered together.
General properties of Lanthanides
1. Electronic configuration
The electronic configuration of Lanthanides are listed in the table . The fourteen electrons are filled in Ce to Lu with configuration [54 Xe ]4f1-14 5d1 6s2
2. Oxidation states
The common oxidation state exhibited by all the lanthanides is +3 (Ln3+) in aqueous solutions and in their solid compounds. Some elements exhibit +2 and +4 states as uncommon oxidation states.
La - +3
Ce - +3, +4, +2
Pr - +3, +4
Nd - +3, +4, +2
3. Radii of tripositive lanthanide ions
The size of M3+ ions decreases as we move through the lanthanides from lanthanum to lutetium. This steady decrease in ionic radii of M3+ cations in the lanthanide series is called Lanthanide contraction.
Cause of lanthanide contraction
The lanthanide contraction is due to the imperfect shielding of one 4f electron by another in the same sub shell. As we move along the lanthanide series, the nuclear charge and the number of 4f electrons increase by one unit at each step. However, due to imperfect shielding, the effective nuclear charge increases causing a contraction in electron cloud of 4f-subshell.
Consequences of lanthanide contraction
Basicity of ions
i) Due to lanthanide contraction, the size of Ln3+ ions decreases regularly with increase in atomic number. According to Fajan's rule, decrease in size of Ln3+ ions increase the covalent character and decreases the basic character between Ln3+ and OH- ion in Ln(OH)3. Since the order of size of Ln3+ ions
are
La3+> Ce3+ ............... >Lu3+
ii) There is regular decrease in their ionic radii.
iii) Regular decrease in their tendency to act as reducing agent, with increase in atomic number.
iv) Due to lanthanide contraction, second and third rows of d-block transistion elements are quite close in properties.
v) Due to lanthanide contraction, these elements occur together in natural minerals and are difficult to separate.
Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail
11th 12th std standard Class Organic Inorganic Physical Chemistry Higher secondary school College Notes : General properties of Lanthanides |
Privacy Policy, Terms and Conditions, DMCA Policy and Compliant
Copyright © 2018-2023 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.
|
__label__pos
| 0.985058 |
Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Screen reader users: click this link for accessible mode. Accessible mode has the same essential features but works better with your reader.
Patents
1. Advanced Patent Search
Publication numberUS4053739 A
Publication typeGrant
Application numberUS 05/713,470
Publication dateOct 11, 1977
Filing dateAug 11, 1976
Priority dateAug 11, 1976
Also published asCA1097407A1, DE2735204A1, DE2735204C2
Publication number05713470, 713470, US 4053739 A, US 4053739A, US-A-4053739, US4053739 A, US4053739A
InventorsRobert Lynn Miller, Robert Neal Weisshappel
Original AssigneeMotorola, Inc.
Export CitationBiBTeX, EndNote, RefMan
External Links: USPTO, USPTO Assignment, Espacenet
Dual modulus programmable counter
US 4053739 A
Abstract
The inventive counter is operable to divide an input signal by the sum of two binary numbers, A and B. Each number is stored in memory. These numbers are alternately preset into a binary counter which also receives the input signal. A logic gate monitors the counter output and changes state when the number previously preset in the counter equals the accumulated count. The gate state transition is used to preset the counter with the alternate stored number. Thus, the process continues whereby the output from the logic gate represents the input signal divided by the sum of A and B.
Images(1)
Previous page
Next page
Claims(5)
We claim:
1. A multiple modulus counter for dividing a signal having a frequency f by a divisor N = M1 + M2 + . . . + Mx, where N, M1, M2, . . . , Mx are selected numbers, comprising:
counter means including an input for receiving the signal to be divided, an output for producing a signal representative of the count of signals received at the input, and means to input a preset count state;
a plurality of Mx preset means, each actuable to preset one of the numbers M1 . . . Mx into the counter means;
control means responsive to the count state at the counter output to sequentially actuate a successive one of the preset means in response to the counter counting to the count preset into the counter by the preceding preset means, the control means producing an output waveform having transitions corresponding to the actuation of predetermined preset means,
whereby the control means output waveform is of a frequency f/N.
2. A dual modulus counter for dividing a signal having a frequency f by a divisor N = A + B, where N, A and B are selected numbers, comprising:
counter means including an input for receiving the signal to be divided, an output for producing a signal representative of the count of signals received at the input, and means to input a preset count state;
first preset means actuable to preset the count A in the counter means;
second preset means actuable to preset the count B in the counter means; and
control means responsive to the count state at the counter output to sequentially actuate the second and first preset means in response to the counter counting the numbers A and B, respectively, the control means producing an output waveform having transitions at the times of actuating the first and second preset means,
whereby the control means output waveform is of a frequency f/N.
3. A frequency synthesizer comprising:
a reference signal source for generating a reference signal of frequency f;
a phase comparator for producing at its output an error signal representative of the phase difference of signals received at its input;
means for coupling the reference signal source to the first phase comparator input;
a signal controlled oscillator for producing an oscillator signal of predetermined frequency at its output responsive to a received control signal;
means for processing the phase comparator error signal and producing a control signal in response thereto;
means for coupling the produced control signal to the signal controlled oscillator;
prescaler means actuable to frequency divide the oscillator signal by one of two predetermined divisors P, P';
a dual modulus divider for frequency dividing the output from the prescaler by alternate stored divisors A and B, where A and B are selected numbers, the dual modulus divisor including means to actuate the prescaler means from its P divisor to its P' divisor upon transition from the A divisor to the B divisor and from its P' divisor to its P divisor upon transition from the B divisor to the A divisor; and
means for coupling the output from the dual modulus divider to the comparator second input,
whereby the oscillator signal tends to assume the frequency f/(AP + BP').
4. The frequency synthesizer of claim 3 wherein P' = P + 1.
5. The frequency divisor of claim 3 wherein the dual modulus divider comprises:
counter means including an input for receiving the prescaler output signal, an output for producing a signal representative of the count of signals received at the input, and means to input a preset count state;
first preset means actuable to preset the count A in the counter means;
second preset means actuable to preset the count B in the counter means; and
control means responsive to the count state at the counter output to sequentially actuate the second and first preset means in response to the counter counting the numbers A and B, respectively, the control means producing an output waveform having transitions at the times of actuating the first and second preset means.
Description
BACKGROUND OF THE INVENTION
The present invention pertains to the electronic signal processing art and, in particular, to a programmable frequency counter.
Programmable frequency counters have been well known in the electronic processing art, particularly in the frequency synthesizer field. Frequency synthesizers commonly employ standard phase lock loop circuitry wherein a reference frequency oscillator signal may be divided by a selected one of a plurality of divisors thus providing an output signal of desired frequency. Previous techniques employed in digital frequency synthesizers have used, in the feedback portion of a conventional phase lock loop, a variable prescaler, and first and second counters. The first counter has been programmable and is used to divide the output of the variable prescaler by a fixed number (N). The second counter, often referred to as a swallow counter, has been used to switch the variable prescaler to a new divisor, or modulus, which new modulus is present during the counting of "N". As is discussed at page 10-3 of the Motorola "McMOS HANDBOOK", printed 1974 by Motorola, Inc., the total divisor NT of the feedback loop is given by:
NT = (P + 1)A + P(N - A)
where, the variable modulus prescaler operates between two divisors P and P+1, the swallow counter has a fixed divisor A, and the programmable divider has the divisor N.
While the above described frequency synthesizer provided the desired function, it requires a large number of parts and thus is expensive to manufacture. It is desirable, therefore, to provide the frequency synthesizer function using fewer parts.
SUMMARY OF THE INVENTION
It is an object of this invention, therefore, to provide an improved dual modulus programmable counter which is particularly suited for application in frequency synthesizers.
It is a particular object of the invention to provide the above dual modulus programmable counter which employs a minimum of components and, therefore, results in a minimum cost.
Briefly, according to the invention, a multiple modulus divider divides a signal having a frequency f by a divisor N = N1 + M2 + . . . + Mx, where N, M1, M2, . . . , Mx are selected numbers. The improved counter comprises a counter means which includes an input for receiving the signal to be divided, an output for producing a signal representative of the count of signals received at the input, and means to input a preset count state. Also included are a plurality of Mx preset means, each of which is actuable to preset one of the numbers M1 . . . Mx into the counter means. A control means responds to the count state at the counter output to sequentially actuate successive ones of the preset means in response to the counter counting to the count preset into the counter by the preceeding preset means. The control means produces an output waveform having transitions corresponding to the actuation of the predetermined preset means whereby the control means output waveform is of a frequency f/N.
The improved dual modulus programmable counter may be used in combination with further components to comprise a frequency synthesizer. In particular, additional frequency synthesizer components comprise a reference signal source for generating a reference signal frequency f. This signal is coupled, via appropriate means, to the first input of a phase comparator which compares this signal to the signal received at its second input, and produces an error signal representative of the phase difference therebetween at its output. The phase comparator error signal is processed for application to the control signal of a signal controlled oscillator which, in turn, responds by producing an oscillator signal of predetermined frequency. The output from the signal controlled oscillator couples to a prescaler which is actuable to frequency divide the oscillator signal by one of two predetermined divisors P, P'. The aforementioned dual modulus divider frequency divides the output from the prescaler by alternate stored divisors A and B, where A and B are selected numbers. The divisor includes means to actuate the prescaler means from its P divisor to its P' divisor upon transition from the A divisor to the B divisor, and from its P' divisor to its P divisor upon transition from the B divisor to the A divisor. The output from the divider is coupled to the comparator second input whereby the oscillator signal tends to assume the frequency f/(AP' + BP).
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic diagram illustrating the inventive dual modulus counter; and
FIG. 2 is a schematic diagram illustrating a frequency synthesizer which employs the inventive counter.
DESCRIPTION OF THE PREFERRED EMBODIMENT OF THE INVENTION
Referring to FIG. 1, a signal of frequency f, which is to be divided by a divisor N, is applied at the input 12 of a standard binary counter 10. The binary counter 10, operating in the well known manner, produces a signal at its output terminal 14 in response to a predetermined count of the input signal f. The binary counter 10 also has preset count input terminals 16, 18. A binary number coupled to one of the preset count inputs 16, 18 will activate the counter 10 to the binary number. In the present preferred embodiment of the invention, binary counter 10 is of the count-down type which means that a count state preset at the input terminals 16 or 18 will be decremated one count for each received input pulse at input 12. The binary counter 10 responds to counting down to a zero count state by changing its output logic state at output terminal 14.
A change in the output state at output 14 of binary counter 10 activates the "C" input 22 of a conventional control flip-flop 24. Flip-flop 24 has a first "Q" output 26 and a second "Q" output 28. The control flip-flop 24 responds to transition state changes at its input 22 to alternately activate the Q output 26 high and low, with the Q output 28 correspondingly low and high.
The Q output 28 of the flip-flop 24 couples to the input terminals 32, 42 of a pair of preset storage registers 30, 40, respectively. Each register 30, 40 is programmed to contain a preset number. In this case preset register 30 contains the number A and preset register 40 contains the number B. Upon suitable activation at their inputs 32, 42 each register 30, 40 applies the number stored therein to the preset input terminals 16, 18 of the binary counter 10, activating the count in the same to the appropriate number A, B. Each number A, B corresponds to a modulus with which the input signal f will be divided. In this preferred embodiment of the invention a dual modulus system is provided. Thus, there are two preset registers 30, 40 each containing the number A, B respectively. In a generalized system, any one of a number of divisors of modulus M1 + M2 + . . . + Mx might be used, in which case there would be a preset register for each, each containing the appropriate number M1, M2, . . . Mx. For purposes of clarity the following discussion deals primarily with a dual modulus counter. Nonetheless, it should be understood that anyone of ordinary skill in the art could practice the invention by constructing a counter having more than two moduli.
Operation of the dual modulus programmable counter of FIG. 1 may be understood as follows.
Assume initially that the Q output 28 of the flip-flop 24 has activated preset register 30 to place the count A into the binary counter 10. Thus, each successive count of the input signal f reduces the counter by one whereby, finally, the counter reaches a count of zero. At this time the counter output 14 makes a transition thereby activating the control input 22 of the flip-flop 24. At this point the Q output 26 and Q output 28 of flip-flop 24 make a transition to the opposite logic state. This transition causes the second preset register 40 to input the count B into the binary counter 10. Now successive input counts at input 12 of binary counter 10 due to the input signal f reduce the count state of the counter 10 until it again reaches zero, at which point an output transition at output 14 once again activates the control input 22 of the flip-flop 24, thus activating preset register 30 to again input the count A into the binary counter 10.
Henceforth, the cycle repeats and the Q output 26 of the flip-flop 24 assumes a waveform having a frequency f/N, where N = A + B. Thus, with a minimum of components at input signal f is divided by two moduli A, B, thereby dividing the input signal f by the sum of the two moduli, N. As is discussed with reference to FIG. 2, the fact that the control flip-flop 24 produces an output transition after the A count period renders the instant dual modulus programmable counter extremely useful in frequency synthesizer applications.
FIG. 2 illustrates the preferred embodiment of a frequency synthesizer which employs the novel dual modulus programmable counter. There a standard phase lock loop chain includes a reference oscillator 100 which produces a reference signal of frequency f. The signal f is fed to the first input 112 of a phase detector 110. Phase detector 110 has a second input 114 and an output 116. Acting in the conventional manner, the phase detector 110 produces an error signal at its output 116, which error signal is representative of the phase difference between signals received at the input terminals 112, 114.
In the conventional manner, the output error signal at output terminal 116 is low pass filtered through a low pass filter circuit 118 and applied to the control input 122 of a voltage controlled oscillator 120. The voltage controlled oscillator 120 produces an oscillator signal of predetermined frequency at its output 124 responsive to a control signal received at its control input 122. This oscillator output signal is the output signal fout of the frequency synthesizer.
The output terminal 124 of the voltage controlled oscillator 120 also feeds to the input terminal 132 of a variable modulus prescaler 130. The variable modulus prescaler 130 responds to a signal at its divisor input 134 to divide signals received at its input terminal 132 by either one of two moduli P, or P' reproducing the output frequency divided signal at its output terminal 136. In the preferred embodiment of the invention, P' = P + 1, however it should be understood that the selection of the P' modulus is one of individual designer's choice. The frequency divided output 136 of the variable modulus prescaler 130 is applied to the input terminal 142 of the dual modulus programmable counter 150. The dual modulus programmable counter 150 is seen to be identical to the preferred embodiment thereof illustrated in FIG. 1. For example, input terminal 142 is the input of a binary counter 140 corresponding to the binary counter 10 of FIG. 1. Binary counter 140 has an output 144 which feeds to the control input 152 of a control flip-flop 154. The control flip-flop 154 has a Q output 156 and a Q output 158. The Q output 158 actuates the inputs 162, 172 of the preset storage registers 160, 170 respectively. As before, each preset register 160, 170 contains preset numbers A, B, respectively, which, upon actuation via the input terminals 162, 172 feed their corresponding number into the binary counter 140 via the preset input terminals 146, 148.
The Q output 156 of the flip-flop 154 feeds to the modulus control terminal 134 of the variable modulus prescaler 130. A transition in logic state at input 134 causes the variable modulus prescaler 130 to alternate between the P and P+1 divisors. Finally, the Q output 158 of the control flip-flop 154 feeds to the second input 114 of the phase comparator 110.
Operation of the frequency synthesizer of FIG. 2 is understood as follows.
The reference oscillator 100 feeds a signal of frequency f to the first input 112 of the phase detector 110. Phase detector 110, in turn, produces an error signal at its output 116 which, when low pass filtered via the filter 118, controls the voltage controlled oscillator 120. The oscillator output signal from the voltage controlled oscillator 120 is frequency divided by the variable modulus prescaler 130. Assuming that the variable modulus prescaler 130 is activated to its P modulus, the variable modulus prescaler 130 will produce an output transition at its output terminal 136 when it has counted P counts in the oscillator signal. At this time the first count is received by the binary counter 140 at its input 142. Stored within the binary counter 140 initially is the binary number A. Thus, this binary preset count is decremented by one count. This process continues until the variable modulus prescaler 130 counts to the number P, A times. After the binary counter 140 has counted down from its preset input A, it produces an output at output terminal 144 which in turn is applied to the control input 152 of the control flip-flop 144. This transition at the control input 152 causes the Q output 156 and Q output 158 to flip to their opposite states. Thus, the Q output 156 activates the variable modulus prescaler 130 to begin dividing by its second modulus P+1. Also, the Q output 158 causes the number B stored in register 170 to be fed into the binary counter 40. Now, the binary counter 140 does not change its output state at its output terminal 144 until the variable modulus prescaler has counted P+1 counts a total of B times.
Thereafter, the cycle repeats whereby the waveform at the Q output 158 of the flip-flop 154 is of a frequency fout /Nt, where Nt = A(P) + B(P+1). Now, in the conventional manner, the waveform fout /Nt is phase compared with the reference oscillator 100 signal f, whereby the two tend to phase lock producing the output signal fout = f/NT.
Thus, the dual modulus programmable counter 150 replaces the variable counter and the swallow counter of the prior art when used in a frequency synthesizer which provides an output signal which is the frequency division of a reference signal. Since the inventive dual modulus programmable counter does not require both a programmable counter, and a swallow counter, as has been known in the prior art, a significant reduction in parts count, and thus cost, has been achieved.
While a preferred embodiment of the invention has been described in detail, it should be understood that many modifications and variations thereto are possible, all of which fall within the true spirit and scope of the invention.
Patent Citations
Cited PatentFiling datePublication dateApplicantTitle
US3353104 *Jun 14, 1965Nov 14, 1967Ltv Electrosystems IncFrequency synthesizer using fractional division by digital techniques within a phase-locked loop
US3594551 *Nov 29, 1966Jul 20, 1971Electronic CommunicationsHigh speed digital counter
US3605025 *Jun 30, 1969Sep 14, 1971Sperry Rand CorpFractional output frequency-dividing apparatus
US3714589 *Dec 1, 1971Jan 30, 1973Lewis RDigitally controlled phase shifter
US3959737 *Nov 18, 1974May 25, 1976Engelmann Microwave Co.Frequency synthesizer having fractional frequency divider in phase-locked loop
US3982199 *Jan 6, 1975Sep 21, 1976The Bendix CorporationDigital frequency synthesizer
Referenced by
Citing PatentFiling datePublication dateApplicantTitle
US4184068 *Nov 14, 1977Jan 15, 1980Harris CorporationFull binary programmed frequency divider
US4231104 *Apr 26, 1978Oct 28, 1980Teradyne, Inc.Generating timing signals
US4241408 *Apr 4, 1979Dec 23, 1980Norlin Industries, Inc.High resolution fractional divider
US4316151 *Feb 13, 1980Feb 16, 1982Motorola, Inc.Phase locked loop frequency synthesizer using multiple dual modulus prescalers
US4325031 *Feb 13, 1980Apr 13, 1982Motorola, Inc.Divider with dual modulus prescaler for phase locked loop frequency synthesizer
US4327623 *Mar 31, 1980May 4, 1982Nippon Gakki Seizo Kabushiki KaishaReference frequency signal generator for tuning apparatus
US4330751 *Dec 3, 1979May 18, 1982Norlin Industries, Inc.Programmable frequency and duty cycle tone signal generator
US4357527 *Jan 25, 1979Nov 2, 1982Tokyo Shibaura Denki Kabushiki KaishaProgrammable divider
US4390960 *Nov 21, 1980Jun 28, 1983Hitachi, Ltd.Frequency divider
US4468797 *Feb 3, 1982Aug 28, 1984Oki Electric Industry Co., Ltd.Swallow counters
US4559613 *Jun 29, 1982Dec 17, 1985The United States Of America As Represented By The Secretary Of The Air ForceDigital frequency synthesizer circuit
US4574385 *Feb 16, 1984Mar 4, 1986Rockwell International CorporationClock divider circuit incorporating a J-K flip-flop as the count logic decoding means in the feedback loop
US4651334 *Dec 24, 1984Mar 17, 1987Hitachi, Ltd.Variable-ratio frequency divider
US4658406 *Aug 12, 1985Apr 14, 1987Andreas PappasDigital frequency divider or synthesizer and applications thereof
US4891825 *Feb 9, 1988Jan 2, 1990Motorola, Inc.Fully synchronized programmable counter with a near 50% duty cycle output signal
US5065415 *Feb 21, 1990Nov 12, 1991Nihon Musen Kabushiki KaishaProgrammable frequency divider
US5066927 *Sep 6, 1990Nov 19, 1991Ericsson Ge Mobile Communication Holding, Inc.Dual modulus counter for use in a phase locked loop
US5195111 *Aug 13, 1991Mar 16, 1993Nihon Musen Kabushiki KaishaProgrammable frequency dividing apparatus
US5202906 *Dec 23, 1987Apr 13, 1993Nippon Telegraph And Telephone CompanyFrequency divider which has a variable length first cycle by changing a division ratio after the first cycle and a frequency synthesizer using same
US5235531 *Dec 13, 1991Aug 10, 1993Siemens AktiengesellschaftMethod and arrangement for dividing the frequency of an alternating voltage with a non-whole-numbered division factor
US5495505 *Dec 20, 1990Feb 27, 1996Motorola, Inc.Increased frequency resolution in a synthesizer
US5781459 *Apr 16, 1996Jul 14, 1998Bienz; Richard AlanMethod and system for rational frequency synthesis using a numerically controlled oscillator
US5842006 *Sep 6, 1995Nov 24, 1998National Instruments CorporationCounter circuit with multiple registers for seamless signal switching
US6035182 *Jan 20, 1998Mar 7, 2000Motorola, Inc.Single counter dual modulus frequency division apparatus
US6072404 *Apr 29, 1997Jun 6, 2000Eaton CorporationUniversal garage door opener
US6725245May 3, 2002Apr 20, 2004P.C. Peripherals, IncHigh speed programmable counter architecture
USRE32605 *Jun 28, 1985Feb 16, 1988Hitachi, Ltd.Frequency divider
WO1981002371A1 *Jan 5, 1981Aug 20, 1981Motorola IncAn improved frequency synthesizer using multiple dual modulus prescalers
WO1981002372A1 *Jan 5, 1981Aug 20, 1981Motorola IncImproved divider with dual modulus prescaler
WO1982003477A1 *Mar 30, 1982Oct 14, 1982Inc MotorolaFrequency synthesized transceiver
Classifications
U.S. Classification708/103, 377/52, 331/25, 331/1.00A, 331/16, 377/47
International ClassificationG06F7/68, H03K23/66, H03L7/193, H03L7/18
Cooperative ClassificationH03K23/665, H03L7/193, H03L7/18, H03K23/667, G06F7/68
European ClassificationH03K23/66P, H03K23/66S, G06F7/68, H03L7/18, H03L7/193
|
__label__pos
| 0.927167 |
IBM Certification Questions
Q:
Which of the following extenders allows data to be presented in a three dimensional format?
A) DB2 AVI Extender B) DB2 XML Extender
C) DB2 Text Extender D) DB2 Spatial Extender
Answer & Explanation Answer: D) DB2 Spatial Extender
Explanation:
Report Error
View Answer Workspace Report Error Discuss
Filed Under: IBM Certification
3 1193
Q:
Which of the following DB2 data types CANNOT be used to contain the date an employee was hired?
A) CLOB B) TIME
C) VARCHAR D) TIMESTAMP
Answer & Explanation Answer: B) TIME
Explanation:
Report Error
View Answer Workspace Report Error Discuss
Filed Under: IBM Certification
4 1163
Q:
With database logging, where are transaction records first placed?
A) in the logical log buffer B) in the primary chunk
C) in the physical buffer D) in a temporary database table
Answer & Explanation Answer: A) in the logical log buffer
Explanation:
Report Error
View Answer Workspace Report Error Discuss
Filed Under: IBM Certification
4 1088
Q:
The DBA can set the registry variable DB2_HASH_JOIN on or off because:
A) hash joins may require more resources to run. B) hash joins are not used unless outer joins are requested.
C) If hash joins are enabled, no other join method can be used. D) Hash joins are only needed when the tables are portioned using hash keys.
Answer & Explanation Answer: A) hash joins may require more resources to run.
Explanation:
Report Error
View Answer Workspace Report Error Discuss
Filed Under: IBM Certification
4 1073
Q:
Suppose a System z customer has a new CIO. The CIO is concerned about continuing operations and recovery following a catastrophe.Which of the following addresses this issue?
A) GDPS B) TAM
C) DR D) WASS
Answer & Explanation Answer: A) GDPS
Explanation:
Report Error
View Answer Workspace Report Error Discuss
Filed Under: IBM Certification
2 1035
|
__label__pos
| 0.999626 |
What determines the CICSGLBL parms MONITOR value after CICS region is recycled?
Document ID : KB000045768
Last Modified Date : 14/02/2018
Show Technical Document Details
Summary:
This knowledge document details a usage scenario of the UTRPARM(CICSGLBL) MONITOR parameter and how to initialize it, and modify it after the CICS region is recycled.
Here is a scenario that was described by a user of the CA Mainframe Application Tuner (CA MAT):
The client was interested in finding out where the CICSGLBL parms were loaded from.
1. They changed UTRPARM(CICSGLBL) MONITOR from YES to NO and reran the TUNS transaction in a CICS region. Nothing changed, it stayed YES.
2. They then recycled the CA MAT address space and again ran the TUNS transaction with no change, it stayed YES.
3. They then recycled CICS and the PLT ran and the region came up with Monitor=NO, it changed to NO.
4. They then reran the CICS transaction TUNS and the TDQ showed Monitor=YES.
Here was their question: They want to know what is in place that allowed Monitoring to go back to YES if it was coded in CA MAT as NO and a recycle of CICS was also NO but when TUNS was entered it changed to YES?
Said another way: What has to be done if we don't initialize CA MAT from the CICS PLT?
Instructions:
From the list of scenarios in the Summary above:
1. When CICS region starts with PLT (TC00CPLT) and without SIT parameter
r'INITPARM=(TCnnFSET='SERVERID=xxxxxxxx')
where 'nn' is CICS release number
'xxxxxxxx' is the MAT server name that it will get the CICS parameter
or with SIT parameter
'INITPARM=(TCnnFSET='SERVERID=xxxxxxxx')
but MAT server is not ACTIVE, internal programmatic CICSDFLT parameters are used.
The DEFAULT values are:
MONITOR=YES
MAXTRANS=2000
RESET_TRAN=TUNS
COLLECT_TRAN=TUNC
COLLECT=1
The messages in CICS MSGUSR would indicate it is 'CICSDFLT'.
2. When CICS region starts with PLT (TC00CPLT) and with SIT parameter
'INITPARM=(TCnnFSET='SERVERID=xxxxxxxx')
where 'nn' is CICS release number
'xxxxxxxx' is the MAT server name that will get the CICS parameter
and MAT server is ACTIVE
and MAT server start with CICSGLBL
and there is no entry in CICSREGN for this CICS region
The values in CICSGLBL will be used and the messages in CICS MSGUSR would indicate it is 'CICSGLBL'.
3. When CICS region start with PLT (TC00CPLT) and with SIT parameter
'INITPARM=(TCnnFSET='SERVERID=xxxxxxxx')
where 'nn' is CICS release number
'xxxxxxxx' is the MAT server name that it will get the CICS parameter
and MAT server is ACTIVE
and MAT server start with CICSGLBL
and there is a matching entry in CICSREGN for this CICS region
The values in CICSREGN will be used.
The messages in CICS MSGUSR would indicate it is 'CICSREGN'.
4. When CICS region start without PLT (TC00CPLT) and later would like to START CA MAT CICS exits, enter 'TUNS' (RESET TRAN) on a CICS terminal would set CICSDFLT parameter values.
enter 'TUNS serverid' on a CICS terminal would set parameters from this MAT 'serverid'
5. If CICS started with a set of parameter values and would like to change afterwards, you can change the parameters either in CICSREGN or CICSGLBL:
recycle MAT server,
enter 'TUNS serverid' on a CICS terminal
This would set parameters from this MAT 'serverid'. There is no need to recycle CICS. After you change the parameters and recycle CA MAT server, you can enter 'TUNS serverid' on a CICS terminal. This will change the parameter without a recycle of CICS.
|
__label__pos
| 0.931782 |
Hung-Che
Published
Facemask ATM + Reminder
Fear not ol' forgetful geezers for I have a solution for the ever-existing problem in these pandemic time of forgetting face mask!!
BeginnerShowcase (no instructions)58
Facemask ATM + Reminder
Things used in this project
Story
Read more
Code
Face mask ATM
Arduino
#include <LiquidCrystal.h>
#include <Keypad.h>
LiquidCrystal lcd(12,11,A4,A5,13,10);
const byte ROWS = 4;
const byte COLS = 4;
const int pirPin = A3;
char keys[ROWS][COLS] = {
{'7','8','9','C'},
{'1','2','3','A'},
{'4','5','6','B'},
{'*','0','#','D'}
};
byte rowPins[ROWS] = { 2, 3, 4, 5 };
byte colPins[COLS] = { 6, 7, 8, 9 };
Keypad kpd = Keypad( makeKeymap(keys), rowPins, colPins, ROWS, COLS );
int fm = 0;
void setup() {
Serial.begin(9600);
lcd.begin(16, 2);
pinMode(pirPin, INPUT);
}
void loop() {
//case 1: when there is no face mask
int fm_temp = 0;
while(fm==0){
lcd.setCursor(0,0);
lcd.print("Number of mask:");
lcd.setCursor(0,1);
lcd.print("Max 100: ");
//input number of face mask
char key = kpd.getKey();
if(key){
if(key == '0') fm_temp = fm_temp * 10 + 0;
if(key == '1') fm_temp = fm_temp * 10 + 1;
if(key == '2') fm_temp = fm_temp * 10 + 2;
if(key == '3') fm_temp = fm_temp * 10 + 3;
if(key == '4') fm_temp = fm_temp * 10 + 4;
if(key == '5') fm_temp = fm_temp * 10 + 5;
if(key == '6') fm_temp = fm_temp * 10 + 6;
if(key == '7') fm_temp = fm_temp * 10 + 7;
if(key == '8') fm_temp = fm_temp * 10 + 8;
if(key == '9') fm_temp = fm_temp * 10 + 9;
if(key == 'A') fm_temp = fm_temp / 10;
lcd.setCursor(9,1);
lcd.print(fm_temp);
lcd.print(" ");
if(key == 'D'){
//if number exceeds 100, reset fm to -1
if(fm_temp > 100){
fm = -1;
}else{
fm = fm_temp;
}
fm_temp = 0;
}
}
}
//case 2: when there is one or more face mask
while(fm>0){
lcd.setCursor(0,0);
lcd.print("Current amount:");
lcd.setCursor(0,1);
lcd.print(fm);
lcd.print(" ");
//algorithm for each time motion sensor detects something
int pirStat = digitalRead(pirPin);
if(pirStat == HIGH){
Serial.print("I got chu");
tone(A1, 100, 500);
delay(5000);
if(fm > 1){
fm--;
}else if(fm == 1){
fm = -2;
}
}
}
//case 3: when fm exceeds 100 and need to be reset
while(fm==-1){
lcd.setCursor(0,0);
lcd.print("Invalid number!");
lcd.setCursor(0,1);
lcd.print("Any key to redo ");
char key = kpd.getKey();
if(key){
fm = 0;
}
}
//case 4: when fm runs out and needs to be refilled
while(fm ==-2){
lcd.setCursor(0,0);
lcd.print("Out of facemask!");
lcd.setCursor(0,1);
lcd.print("Any key to input");
char key = kpd.getKey();
if(key){
fm = 0;
}
}
}
Credits
Hung-Che
Hung-Che
2 projects • 7 followers
High School Junior
Comments
|
__label__pos
| 0.998995 |
Skip to main content
A consistent long-lasting pattern of spatial variation in egg size and shape in blue tits (Cyanistes caeruleus)
Abstract
Background
Interspecies variation in avian egg shape and size is understandable in terms of adaptation, allometry and phylogeny. Within-species variation in egg properties influences offspring fitness and can be explained by differences in allocation of resources into reproductive components of life history in mulidimensionally variable environments. Egg size is inherently traded-off with clutch size, which may also be true of egg shape in some cases. We investigated long-term variation in egg shape and size between two geographically close populations of blue tits Cyanistes caeruleus in relation to clutch size and habitat differences.
Results
The main finding is that there exists a persistent long-lasting pattern of spatial variation of egg size and shape between the two study populations of blue tits, 10 km apart, controlling for clutch size. Eggs in the urban park site were on average larger in volume and less spherical in shape than eggs in the forest site over 12 years of this study. Egg sizes were negatively associated with clutch sizes. Egg shape was not correlated with clutch size.
Conclusions
Our findings suggest that the pattern of variation in egg size and shape results from different trophic richness of the breeding habitats of the study populations, demanding different allocation of resources and, especially, from the contrasting difference in the availability of calcium.
Background
The avian egg is an evolutionarily elaborated version of the eggs of amniotes, in general, and the eggs of theropods, in particular [1]. In addition to containing the genetic equipment, it stores all the nutrients needed by the embryo to develop successfully [2]. At the level of class Aves, egg sizes are allometrically related to female body sizes, yet the relationship shows some differences between taxa and modes of development within birds [3]. Also the shape of bird eggs shows remarkable taxonomic diversity, with characteristic phylogenetically constrained patterns [2, 4, 5]. Inter-species variation in egg shape was found to be associated with avian flight adaptations [4], which, however, does not explain within-species variation. It seems reasonable to consider within-species variation in egg size as part of reproductive allocation strategy and seek its explanation within the framework of life-history theory [6].
Within species, different measures of nestling/fledgling performance, such as rates of growth and development, hatchability and chances to fledge, are usually positively affected by egg sizes [7, 8], at least to some threshold egg size, above which nestling performance increases no further [9]. In optimal environmental conditions birds would be expected to lay eggs of minimum size which still maximizes chances of nestling survival. Although producing eggs smaller than that size would be costly in terms of fitness, the negative effects can be overridden by parental care of nestlings, especially by adequate feeding [9, 10] which may be possible if the nestling stage coincides with the time of rich food abundance. If the amount of energy and nutrients allocated to a single egg affects not only its own size, but also the size of the subsequent eggs in a clutch, a trade-off between egg size and clutch size should arise because it is ultimately the number of surviving offspring which is the currency of fitness [6, 11, 12]. Optimal allocation of resources into individual eggs in the whole clutches is a key component of reproductive strategy that is certainly dependent on resource richness in the breeding habitat [6]. Because resources, including macronutrients and micronutrients, tend to be limited and variable in time and space (habitat), constraints on optimal allocation arise, and, therefore, some level of plasticity is favoured by natural selection [13]. Fitness may be locally maximised by different, resource-dependent allocation, resulting in producing clutches and eggs of different size in different habitats.
Egg shape is not usually considered in the context of intraspecies life-history variation, but it was hypothesised that optimal shape should depend on the number of eggs in the clutch in view of the way eggs are incubated [14]. Eggs of optimal shape should best fit the brood patch of incubating parents to be most efficiently maintained at an appropriate level of temperature for embryos to develop, resulting in clutches of different size having different optimal shapes of eggs [14]. In the case of larger clutches, it is not possible for all eggs to be in contact with the brood patch at the same time because they are distributed in layers within the nest cup and must be systematically rearranged to be uniformly warmed [15, 16]. If there is an optimal clutch-size-dependent shape of eggs, a pattern of relationship between egg shape and clutch size should be observable in avian populations because deviations from the optimal shape would be selected against [17]. In a study on fitness consequences of variation in egg shape in common blackbirds Turdus merula and great tits Parus major Encabo et al. [17] did not find any relationship between egg shapes and clutch sizes. This suggests that some other factors, perhaps limiting resources needed by females during the process of egg formation, should be taken into consideration. Calcium is a micronutrient whose availability is known to be often limiting for breeding birds during the stage of egg formation and nestling growth [7, 18,19,20,21,22]. Calcium availability seems to be able both to modify optimality criteria for egg shape and to generate its own selection pressures on egg shape and size.
The structure of eggshell is critically important for an avian embryo to develop normally into a hatchling that would have a chance to survive to fledging and then to the reproductive maturity [7, 22]. The shell must meet physiological functions associated with the embryo’s water management and gas exchange during incubation, which takes place in a nest containing the whole clutch. Hence it must be strong enough for eggs not to be damaged in the crush from incubating adults and other eggs. In fact, the shell must be produced quickly, in passerine in 1 day, and for just one egg at a time, because of egg fragility and bird mobility, with flight being especially prone to cause egg damage [2, 4]. In most small passerine birds eggshells are formed on the basis of the daily income of calcium, with no stored reserves available [7]. The availability of calcium may constrain a possibility of forming eggs of most profitable size in terms of fitness, which may generate selection pressures on the most compact and strong shapes. These factors may influence a balance between egg size and clutch size. In general, as economical a use of calcium as possible would be expected in calcium-poor habitats, where even defective eggshells are regularly recorded [18]. Calcium-poor habitats with otherwise good trophic conditions for breeding may generate selection for locally adaptive sizes and shapes of eggs as well as clutch sizes.
This study concerns blue tits Cyanistes caeruleus breeding in two areas that are contrastingly different in habitat properties, especially in terms of trophic conditions [23] and in terms of calcium availability [24]. One site is rich in caterpillars, the optimal food of nestlings, but poor in calcium, whereas the other site is poor in caterpillars, but rich in calcium [23, 24]. Bańbura et al. [24] revealed that eggs laid by blue tits in the calcium-poor area are on average smaller than in the calcium-rich area, with clutch sizes being larger in the former than in the latter. In this study we analyse a much larger dataset collected over 12 years of breeding. In particular, we focus on egg shape as well as on egg size. If the inter-habitat difference in egg traits resulted only from the association with clutch size, it should disappear after statistically correcting for variation in clutch size. If the difference remains after the adjustment, it must result from properties of the habitats compared. We expect that eggs should be not only smaller on average, but also more spherical in the calcium-poor area because round eggs make more economical use of calcium [14].
The aims of this study are to:
1. 1.
check if variation in egg volume between two spatially close populations of blue tits represents a consistent long-term pattern.
2. 2.
test if there exists any consistent pattern of variation in egg shape.
3. 3.
examine if variation in egg size and shape is associated with clutch size.
Methods
Study sites
This study was carried out between 2002 and 2013 as part of a long-term research project on the breeding biology of nestbox breeding populations of hole-nesting birds in two study sites within and near Łódź, central Poland. The study sites represent structurally different habitats of an urban parkland and a deciduous forest, 10 km apart. The urban park site (51°45’N; 19°24′E) is an 80 ha area that is composed of the zoological and botanical gardens, located in the SW part of the city of Łódź. The forest study site (51°50’N; 19°29′E) is a 130 ha area in the interior part of a mature mixed-deciduous forest (Łagiewniki Forest; 1250 ha in total), bordering on the NE suburbia of Łódź. The tree cover of the park area is highly fragmented and arranged to be useful for the purpose of animal and plant exposition, with trees constituting a mixture of many exotic and native species, deciduous and coniferous. This study site has a lot of open space, pathways, fences and buildings. Predominating tree species in the forest study area are pedunculate oaks Quercus robur and sessile oaks Quercus petraea. The tree canopy of this area is almost continuous and it also covers most of a small number of pathways crossing the forest.
Some characteristics of the study sites influence the availability of calcium for laying females. In the Łagiewniki Forest as a whole, including the study area, there has been a long-term tendency for water bodies and streams to dry up over the last 30–40 years. Water bodies in the urban park site are stabilised by artificial supply of water and, in addition, considerable parts of this area are watered as part of plant growing procedures. Soils of the Łagiewniki Forest are acidic, with pH < 5, whereas in the park site pH is higher (pH > 6) [25]. There are many artificial sources of calcium in the park area (lime, grit, buildings, pathways and so on), whereas such sources are lacking in the forest. The assemblage of shelled snails during the time of this study in the park site contained abundant synanthropic species, such as Arianta arbustorum, Cepaea nemoralis, and Punctum pygmaeum, which are completely absent from the forest [24]. Density of shelled snails is several times lower in the forest than in the park site [24].
Wooden nestboxes with a removable front panel [26] were erected on trees at a height c. 3 m above the ground level in both the study sites, c. 200 in the urban park site and 300 in the forest site. The nestboxes were distributed in a grid, keeping a distance of about 50 m between them. Mean density of nestboxes was similar in both study sites, 2.2–2.3 per 1 ha [27].
Egg data
The field procedure in our study routinely starts in early spring (late March) from inspections of nestboxes to find signs of nest building and to determine nesting species. Then study sites are visited daily to record clutch initiation dates and clutch sizes in occupied nestboxes. Measurements of length and breadth of each egg in all clutches were taken with dial sliding calipers to the nearest 0.1 mm. Accidentally, eggs in a small fraction of clutches were not measured for technical reasons. This study is based on 8572 (3445 in the park site and 5127 in the forest site) eggs from 781 complete clutches (322 in the park site and 781 in the forest site) of blue tits measured over 12 years.
Based on lengths (L) and breadths (B) of individual eggs, volume (V) was calculated applying Hoyt’s [28] formula, V = 0.51 * L * B2 and shape (sphericity index, SH) was calculated according to the formula, SH = (B/L) * 100 [17, 29]. The B/L index is the reciprocal of the L/B index [29], thus indicating egg sphericity, which increases with egg breadth increasing in relation to egg length. These indices of individual egg shape and volume were data points analysed in this study.
Statistical analyses
Because eggs in clutches tend to be similar in size to each other, their measurements cannot be treated as independent data records [30]. Accordingly, we calculated the intra-clutch repeatability of egg volume and egg shape for the whole data set, applying the intra-class correlation based on variance components obtained from one-way anovas [30], with standard errors estimated following Becker [31].
Egg volumes and shapes were analysed as dependent variables in separate linear mixed models in relation to year and site factors and clutch size as a covariate. Modeling started from models that included the first order interactions between all of the independent variables; non-significant interactions were deleted to leave the final model containing only significant interactions and all independent variables [32]. Clutch ID was included as a random effect in the models to control for clustering that resulted from eggs being laid in clutches (thus lacking independence from those in the same clutch), which was associated with degrees of freedom being estimated using the Satterthwaite method [33]. Statistical computing was performed using IBM SPSS Statistics 22 [33].
Results
Both egg volume and shape show high variation between clutches and low variation within clutches, resulting in substantial repeatability (egg volume: R = 0.782 ± 0.027 (SE), F780;7791 = 40.1, p < 0.0001 and egg shape: R = 0.714 ± 0.026 (SE), F780;7791 = 40.1, p < 0.0001).
Egg volume
The most striking result concerning egg volume in the study populations of blue tits was that the eggs showed a consistent pattern of variation between sites. Eggs in the urban park site were on average 5% larger than eggs in the forest site every year of the study (total mean volumes: 1.181 cm3 ± 0.005 (SE) v. 1.124 cm3 ± 0.004 (SE)). The data were modeled using two separate models. In the first model, which included year as categorical variable (12 years), neither effects of the two-way interactions nor of the year factor were significant (Table 1, Fig. 1). The site factor and the clutch size covariate had significant effects on egg volume, with the effect of clutch size being negative (Table 1, Fig. 2). The second model treated year as a continuous variable (Table 1). Because effects of the two-way interactions were non-significant in this model either, the main effects could be considered separately. While the effect of site remained highly significant, a significant negative effect of years was also revealed, with the clutch size covariate being non-significant (Table 1). This means that the eggs of the blue tits studied tended to reduce in size over time and that the tendency was consistently parallel in the two populations (Fig. 1).
Table 1 Summary of linear mixed models of egg volume of blue tits in relation to year, site and clutch size. Two separate models are shown: (i) with year as a categorical factor and (ii) with year as a continuous variable. Clutch ID included as a random effect
Fig. 1
figure 1
Mean volumes of blue tit eggs in the urban parkland site (squares) and the forest study site (triangles) during 2002–2013. Means ± standard errors are given
Fig. 2
figure 2
Relationship between the per-clutch mean egg volume and clutch size for 781 clutches of blue tits
Egg shape
Since the egg shape measure used in this study might not be independent of egg volume, the models examining egg shape included egg volume as a covariate in addition to year, site, clutch size and all two-way interactions. Two separate models were considered: the first one treated year as a categorical factor, while the second one included year as a continuous covariate (Table 2). Both final models showed a very similar pattern with a significant effect of the site – egg volume interaction (Table 2). This interaction in both the models resulted from egg sphericity being negatively correlated with egg volume in the forest site, but not in the urban park site (Table 2). The effect of site was not entangled in any interactions and, hence, was considered separately, showing a significant variation between the two study populations (Table 2, Fig. 3). Eggs were slightly more spherical in the forest population than in the urban park population (total mean sphericity: 76.992% ± 0.149 (SE) v. 76.026% ± 0.161 (SE), respectively). No differences in egg shape among years nor any trend over time were found (Table 2). Egg shape was not found to be dependent on clutch size (Table 2).
Table 2 Summary of linear mixed models of egg shape (sphericity) of blue tits in relation to year, site, clutch size and egg volume. Two separate models are shown: (i) with year as a categorical variable and (ii) with year as a continuous variable. Clutch ID included as a random effect
Fig. 3
figure 3
Mean shape indices of blue tit eggs in the urban parkland site (squares) and the forest study site (triangles) during 2002–2013. Means ± standard errors are given
Discussion
This study found that egg shape as well as egg size may differ between spatially close populations of a small passerine. The main finding is that there exists a persistent long-lasting pattern of spatial variation of egg size and shape between the two study populations of blue tits, 10 km apart. Eggs in the urban park site were on average larger in volume and less spherical in shape than eggs in the forest site. Egg volume tended to decrease over the years in parallel between the urban park and the forest. We found no year-to-year variation in the case of egg shape.
Offspring size and number during particular breeding attempts as well as over the whole reproductive life of the individual are fundamental life-history traits [6]. The trade-off between egg size and clutch size in birds is a particular case of a more general pattern of trade-off between offspring size and number that is inevitable when the limited resources are allocated between individual offspring in a particular breeding attempt [6, 11, 34]. In wild bird populations living in heterogenous environments the negative relationship between egg size and clutch size expected from the trade-off may be masked by the effect of female (pair) body condition, where high condition females are capable of laying both big eggs and big clutches [35, 36]. The model of Charnov et al. [12] proposes that in the case of birds that produce relatively big clutches, such as tits (Cyanistes, Parus) or flycatchers (Ficedula), the masking effect may be weaker than in species laying clutches of smaller size. Accordingly, a significant negative correlation is usually found in species laying larger clutches [37,38,39,40]. In our study we also found such a significant negative correlation in blue tits.
Our study, based on individual eggs, controlling for clustering in clutches, considers egg shape (sphericity) as well as egg size (volume). Both egg volume and shape proved to be highly repeatable within clutches, which is typical of birds [24, 30]. Egg indices of both size (volume) and shape (sphericity) are derived from the basic linear measurements of eggs that are routinely taken in the field [28, 29]. Adamou et al. [41] have recently shown that these indices are good approximations of principal component measures of size and shape of eggs. However, in contrast to principal component indicators of shape, the measures of shape derived from egg linear dimensions, including the index of sphericity used in this study, may not be independent of egg volume. To control for this lack of independence, we used egg volume as a covariate in models explaining egg shape. The difference in average egg sizes between the blue tit populations nesting at the park site and the forest site for 2002–2009 was shown by Bańbura et al. [24]. Their analysis was based on per-clutch mean volumes and linear dimensions of a sub-set of the whole egg dataset. Our present findings more powerfully confirm the existence of a stable, long-lasting pattern of difference in egg volume and, in addition, in egg shape between the study populations inhabiting the urban park site and the forest site. We found that egg volumes significantly decreased over the years in a parallel manner in both the study sites. No consistent change over time was found in the case of egg sphericity.
Inter-annual, usually rather slight variation in egg size has been reported for many species of birds [41,42,43]. It was suggested that under current global warming, some trends in inter-annual variation in egg traits might be expected in different bird species [44], which in fact came true in several cases, yet sometimes trends were in an unexpected direction [45,46,47]. The latter is also the case in our present study, where we found a decreasing trend in egg volumes instead of an increasing trend that would be expected from earlier arguments [44]. In agreement with the global trend, air temperature in Poland, from the scale of the whole country to the local scale of our study area, is known to have been increasing over the last hundred years [48]. This increase manifests itself in both annual mean temperatures and in spring temperatures, resulting, however, not only in warming, but also in more frequent and less predictable extreme weather events [48], which may not be favourable to breeding birds. As far as we know, no data on inter-year variation in egg traits of blue tits are available in the literature, whereas there are a few reports concerning different populations of another parid species, the great tit. Jarvinen and Pryl [49] found no differences between years in egg volumes or linear dimensions in a south Finland population of this species. Slight inter-year variation in egg size and shape, entangled in interactions of the year factor with other factors, was reported by Ojanen et al. [50] for north Finland. Hõrak et al. [51] found significant year-to-year variation in egg volume and shape, with no clear pattern, in rural and urban populations of great tits in Estonia; a significant difference in egg volume between 2 years was also shown by Mӓnd et al. [52] in the same country. The differences most probably result from effects of year-to-year differences in ecological conditions prevailing during the time of egg formation on resource allocation between egg size and clutch size [9, 46, 53].
Spatial variation in egg volume and linear dimensions was analysed on the scale of entire Europe in the case of great tits, but not blue tits [54]. Small-scale spatial or habitat effects were also more often studied in great tits. Hõrak et al. [51] showed that eggs in an urban park site in Tartu, Estonia, were on average smaller than in a rural forest site (the distance between the study sites c. 5 km). By contrast, Riddington and Gosler [55] found that great tit eggs in Oxfordshire village and urban gardens were heavier (larger) than in the forest habitat of Wytham Wood (the distance between the gardens and Wytham Wood c. 2 km). Mӓnd et al. [52] reported that eggs in the deciduous forest site tended to be larger than eggs in the coniferous forest site in Estonia (the study sites to c. 10 km apart). Hargitai et al. [56] discovered that eggshells in an urban park were thicker than in a woodland site in great tits (the distance between the sites c. 20 km). Slight variation in egg size [57] and shape [58] was shown to be related to the altitude of nest sites in ultramarine tits (African blue tits) Cyanistes teneriffe ultramarinus in Algeria. In our study populations we previously found a significant between-habitat difference in mean egg sizes of blue tits, but no of great tits [24]. This difference in the patterns of egg size and shape variation between the tit species is confirmed by the present study on blue tits and our new data on great tits (in preparation). A very similar pattern of inter-habitat variation in egg volume was revealed for the same tit species in Burgundy, with no difference in great tits and a significant difference in blue tits, and with eggs being larger in urban habitats than in the forest (the study sites 40–100 km apart) [59]. Apart from our study, we are not aware of any other results describing clear patterns of variation in egg shape as well as egg size between habitats in European blue tits. The persistent difference in egg size and shape between sites with parallel fluctuations across the years of the study suggest that there exists a long-lasting difference between the sites, on the one hand, and a cause of year-to-year variation which is common for the two sites, on the other hand.
The basic idea behind our study system was to encompass study sites of contrasting habitats to be studied in a long-term perspective. As a consequence, we established our nestbox study areas in a large urban park habitat and in an interior part of a deciduous forest, assuming that the former would represent a sub-optimal habitat, while the latter would be the optimal habitat for nesting tits. The breeding density of blue tits is variable over the years, and with the grand mean values of 3.4 pairs/10 ha in the forest and 3.8 pairs/10 ha in the park, it is relatively low in comparison with the values typical of West European populations of this species [40], which is also true of great tits (own data). We estimate that 90–95% of breeding pairs of both tit species nests in nestboxes, even if both study sites are also rich in natural holes. Thus, the potential nest sites are superabundant. Of the available nestboxes, no more than 35% are occupied by all hole-nesting species in the forest site, with the corresponding figure for the park site being 60%, still leaving many holes free. The age structure seems not to much differ between the forest and the park populations – the proportion of the first-year adults is 41–44% against 56–59% of older adults in both the sites (own data, in preparation). The blue tits are typically single-brooded, with very rare, exceptional second breeding attempts.
In terms of the abundance of leaf-eating caterpillars, as key food for nestlings, the contrast between the forest and the urban park study sites is considerable. The leaf-eating caterpillars are on average three times more abundant in the forest site than in the park site, which leads to the corresponding difference between the sites in their suitability for rearing nestling tits [23, 27, 60, 61]. It is well known that tits and some other insectivorous species lay larger clutches in optimal habitats than in suboptimal ones because clutch size tends to be adjusted to the trophic conditions during the chick-rearing phase [9, 62,63,64,65].
In accordance with the difference between our study sites in the abundance of caterpillars, clutches of blue tits are on average larger in the forest site than in the urban park area, with some variation between years occurring [23, 60]. In fact, it is not only the abundance of leaf-eating caterpillars that differs between the two study sites. Insects and other arthropods in general are distinctly more abundant in the forest site than in the urban park site [66, 67], which creates more favourable trophic conditions for breeding insectivorous birds. On the other hand, the forest site is characterised by a five to six times lower density of shelled snails than the urban park site, with the latter area being home for abundant human-associated snails, such as Cepaea spp. [24]. It was shown by many authors that poor availability of shells and other sources of calcium is limiting for females during the time of egg formation, when the demands for calcium are highest [18, 19, 53, 68]. We suggest that this is also the case with blue tits in our forest study site. High availability of insect food and poor availability of calcium may maintain a pressure on females to move a balance in resource allocation towards producing smaller eggs because any potential initial disadvantages can be compensated for at the nestling stage. When considered separately in field experiments on blue tits in Scotland, the quality of supplemental food had positive effect, whereas supplemental calcium had no effect on egg sizes [69, 70]. Obviously, the experimental supplements used by Ramsay and Houston [69, 70] were transient factors, while the trophic characteristics of our study sites are enduring factors, both of which can have effects on egg size but at a different level. Transient factors may result in a release from trophic limitation, when supplementary food and/or micronutrients are provided, or in the limitation becoming even more severe, when the resources are reduced. Enduring factors generate selection pressures for economical use of resources, which can run adaptive changes in female physiology and oviduct morphology [4], resulting in producing smaller ova, needing less calcium. Transient factors would be expected to determine rather eggshell thickness than egg size or shape.
The difference in clutch size between our study sites may suggest that smaller mean egg sizes in the forest site than in the urban park site could potentially result just from different allocation of resources. However, we excluded such an effect in statistical analysis by including clutch size as a covariate in the models. Thus, the persistent difference in egg sizes between the study populations was shown to be independent of clutch size, which suggests that blue tits in the forest site lay smaller eggs than expected from their clutch size and from the respective trade-off between egg size and clutch size in comparison with the urban park site. Eggs laid in the forest site are not only smaller than eggs in the park site, but also tend to be more round, with roundness being the most calcium-saving shape of eggs [14]. Moreover, the eggs tend to become less spherical with the increasing volume in the forest, while no such tendency occurs in the park.
In contrast to egg sizes being related to clutch size, we found no correlation between egg shape and clutch size. We expected that such a correlation should occur in blue tits. Because blue tits lay some of the largest clutch sizes of any passerine [40] and a clutch in our study populations is on average composed of over 11 eggs [27], the eggs must be arranged in layers within the nest cup. As a consequence, to expose all eggs of a clutch to an appropriate temperature during incubation, females rotate and rearrange them regularly to enable them to be uniformly warmed by the brood patch, to allow air to circulate around eggs, and to dissipate heat when the eggs are too warm [14, 15, 17, 71, 72]. The physical shape, considered along the roundness-elongation axis, may directly influence feasibility of getting a space-saving arrangement of eggs within the whole clutch, which should be also affected by clutch size [14, 17]. It seems reasonable to expect that from the point of view of the space-saving three-dimensional arrangement of eggs in the space of nest cup, larger clutches should contain more elongated eggs. However, the acts of rotation and rearrangement of eggs by incubating females may expose eggs to elevated risks of breakage. They may be greater with increasing clutch size and with declining calcium availability. On the other hand, more spherical eggs form a stronger structure for a given, limited amount of calcium [14]. All this may account for our results that eggs in the forest site are more spherical than eggs in the urban park site and that it happens at least in some years that egg sphericity is positively related with clutch size. Analogously, Kouidri et al. [58] found that egg sphericity in North African ultramarine tit tended to increase with clutch size at high altitude, where ecological conditions were harsh. Gosler et al. [73] found that great tit eggs were more spherical in calcium-poor surroundings.
Thus, the patterns in egg shape variation seem to complement the pattern of variation in egg sizes in the study populations of blue tits. They both support the hypothesis that the availability of calcium may be the most important factor that affects variation in egg size and shape, resulting in the existence of stable spatial patterns. Under poor calcium availability, females would be expected to lay smaller and more spherical eggs than under rich calcium availability.
Conclusions
We found in this study that both egg size and shape show consistent patterns of variation between two spatially close populations of blue tits. The difference in egg volumes between the two sites goes beyond the difference expected from the trade-off with clutch size, which is also true of egg shape. Overall, the patterns of variation in egg traits we found and their stability over time suggest that there may be different optimal sizes and shapes of eggs between the caterpillar-rich-calcium-poor habitat and the caterpillar-poor-calcium-rich habitat.
References
1. 1.
Deeming DC, Ruta M. Egg shape changes at the theropoid-bird transition, and a morphometric study of amniote eggs. R Soc Open Sci. 2014;1:140311.
Article PubMed PubMed Central Google Scholar
2. 2.
Birkhead T. The most perfect thing. London: Bloomsbury; 2016.
Google Scholar
3. 3.
Birchard GF, Deeming DC. Egg allometry: influences of phylogeny and the altricial-precocial continuum. In: Deeming DC, Reynolds SJ, editors. Nests, eggs, and incubation. Oxford: Oxford University Press; 2015. p. 97–112.
Chapter Google Scholar
4. 4.
Stoddard MC, Yong EH, Akkaynak D, Sheard C, Tobias JA, Mahadevan L. Avian egg shape: form, function, and evolution. Science. 2017;356:1249–54.
Article PubMed CAS Google Scholar
5. 5.
Duursma DE, Gallagher RV, Price J, Griffith SC. Variation in avian egg shape and nest structure is explained by climatic conditions. Sci Rep. 2018;8:4141.
Article CAS Google Scholar
6. 6.
Stearns SC. The evolution of life histories. Oxford: Oxford University Press; 1992.
Google Scholar
7. 7.
Perrins CM. Eggs, egg formation and the timing of breeding. Ibis. 1996;138:2–15.
Article Google Scholar
8. 8.
Krist M. Egg size and offspring quality: a meta-analysis in birds. Biol Rev. 2011;86:692–716.
Article PubMed Google Scholar
9. 9.
Martin TE. Food as a limit on breeding birds: a life-history perspective. Ann Rev Ecol Syst. 1987;18:453–87.
Article Google Scholar
10. 10.
Ricklefs RE. Components of variance in measurments of nestling european starlings (Sturnus vulgaris) in southeastern Pennsylvania. Auk. 1984;101:319–33.
Article Google Scholar
11. 11.
Smith CC, Fretwell SD. The optimal balance between size and number of offspring. Am Nat. 1974;108:499–506.
Article Google Scholar
12. 12.
Charnov EL, Downhower JF, Brown LP. Optimal offspring sizes in small litters. Evol Ecol. 1995;9:57–63.
Article Google Scholar
13. 13.
Stearns SC. The evolutionary significance of reaction norms. Bioscience. 1989;39:436–46.
Article Google Scholar
14. 14.
Barta Z, Székely T. The optimal shape of avian eggs. Funct Ecol. 1997;11:656–62.
Article Google Scholar
15. 15.
Boulton RL, Cassey P. How avian incubation behaviour influences egg surface temperatures: relationships with egg position, development and clutch size. J Avian Biol. 2012;43:289–96.
Article Google Scholar
16. 16.
Šálek ME, Zárybnická M. Different temperature and cooling patterns at the blunt and sharp egg poles reflect the arrangement of eggs in an avian clutch. PLoS One. 2015;10:e0117728.
Article PubMed PubMed Central CAS Google Scholar
17. 17.
Encabo SI, Barba E, Gil-Delgado JA, Monrós JS. Fitness consequences of egg shape variation: a study on two passerines and comments on the optimal egg shape model. Ornis Fennica. 2001;78:83–92.
Google Scholar
18. 18.
Graveland J. Avian eggshell formation in calcium-rich and calcium-poor habitats: importance of shells and anthropogenic calcium sources. Can J Zool. 1996;74:1035–44.
Article Google Scholar
19. 19.
Mänd R, Tilgar V, Leivits A. Calcium, snails, and birds: a case study. Web Ecol. 2000;1:63–9.
Article Google Scholar
20. 20.
Dhondt AA, Hochachka WM. Variations in calcium use by birds during the breeding season. Condor. 2001;103:592–8.
Article Google Scholar
21. 21.
Wilkin T, Gosler AG, Garant D, Reynolds SJ, Sheldon BC. Calcium effects on life-history traits in a wild population of the great tit (Parus major): analysis of long-term data at several spatial scales. Oecologia. 2009;159:463–72.
Article PubMed Google Scholar
22. 22.
Reynolds SJ, Perrins CM. Dietary calcium availability and reproduction in birds. Cur Onith. 2010;17:31–74.
Google Scholar
23. 23.
Marciniak B, Nadolski J, Nowakowska M, Loga B, Bańbura J. Habitat and annual variation in arthropod abundance affects blue tit Cyanistes caeruleus reproduction. Acta Ornithol. 2007;42:53–62.
Article Google Scholar
24. 24.
Bańbura M, Sulikowska-Drozd A, Kaliński A, Skwarska J, Wawrzyniak J, Kruk A, Zieliński P, Bańbura J. Egg size variation in Blue Tits Cyanistes caeruleus and Great tit Parus major in relation to habitat differences in snail abundance. Acta Ornithol. 2010;45:121–9.
Article Google Scholar
25. 25.
Liszewski S. (Red.) Atlas Miasta Łodzi. Łódź: ŁTN; 2002.
Google Scholar
26. 26.
Lambrechts MM, Adriaensen F, Ardia DR, Artemyev AV, Atiénzar F, Bańbura J, Barba E, Bouvier JC, Camprodon J, Cooper CB, Dawson RD, Eens M, Eeva T, Faivre B, Garamszegi LZ, Goodenough AE, Gosler AG, Grégoire A, Griffith CG, Gustafsson L, Johnson LL, Kania W, Keišs O, Llambias PE, Mainwaring MC, Mänd R, Massa B, Mazgajski TD, Møller AP, Moreno J, Naef-Daenzer B, Nilsson J-Å, Norte AC, Orell M, Otter KA, Park CR, Perrins CR, Pinowski J, Porkert J, Potti J, Remes V, Richner H, Rytkönen S, Shiao MT, Silverin B, Slagsvold T, Smith HG, Sorace A, Stenning MJ, Stewart I, Thompson CF, Tryjanowski P, Török J, van Noordwijk AJ, Winkler DW, Ziane N. The design of artificial nestboxes for the study of secondary hole-nesting birds: a review of methodological inconsistencies and potential biases. Acta Ornithol. 2010;45:1–26.
Article Google Scholar
27. 27.
Glądalski M, Bańbura M, Kaliński A, Markowski M, Skwarska J, Wawrzyniak J, Zieliński P, Cyżewska I, Mańkowska D, Bańbura J. Effects of human-related disturbance on breeding success of urban and non-urban blue tits (Cyanistes caeruleus). Urban Ecosyst. 2016;19:1325–34.
Article Google Scholar
28. 28.
Hoyt DF. Practical methods of estimating volume and fresh weight of bird eggs. Auk. 1979;96:73–7.
Google Scholar
29. 29.
Hoyt DF. The effect of shape on the surface-volume relationships of birds’ eggs. Condor. 1976;78:343–9.
Article Google Scholar
30. 30.
Bańbura J, Zieliński P. Within-clutch repeatability of egg dimensions in the black-headed Gull Larus ridibundus. J Ornithol. 1990;131:305–10.
Article Google Scholar
31. 31.
Becker WA. Manual of quantitative genetics. Washington: Academic Enterprises; 1984.
Google Scholar
32. 32.
Crawley MJ. Statistical Computing: An introduction to data analysis using S-plus. Chichester: Wiley; 2002.
Google Scholar
33. 33.
Heck RH, Thomas SL, Tabata LN. Multilevel and Longitudinal modeling with IBM SPSS. New York: Routledge; 2010.
Google Scholar
34. 34.
Pick JL, Hutter P, Ebneter C, Ziegler AK, Giordano M, Tschirren B. Artificial selection reveals the energetic expense of producing larger eggs. Front Zool. 2016;13:38.
Article PubMed PubMed Central CAS Google Scholar
35. 35.
van Noordwijk AJ, de Jong G. Acquisition and allocation of resources: their influence on variation in life histories. Am Nat. 1986;128:137–42.
Article Google Scholar
36. 36.
de Jong G, van Noordwijk AJ. Acquisition and allocation of resources: genetic (co)variances, selection, and life histories. Am Nat. 1992;139:749–70.
Article Google Scholar
37. 37.
Ojanen M, Orell M, Väisänen RA. Egg and clutch sizes in four passerine species in northern Finland. Ornis Fennica. 1978;55:60–8.
Google Scholar
38. 38.
Järvinen A, Väisänen RA. Egg size and related reproductive traits in a southern passerine Ficedula hypoleuca breeding in an extreme northern environment. Ornis Scand. 1983;14:253–62.
Article Google Scholar
39. 39.
Ekman J, Johansson-Allende A. Egg size investments of tits; does number conflict with size? In: Blondel J, Gosler A, Lebreon JD, McCleery R, editors. Population biology of passerine birds. Berlin: Springer; 1990. p. 247–55.
Chapter Google Scholar
40. 40.
Stenning M. The blue tit. London: Poyser; 2018.
Google Scholar
41. 41.
Adamou AE, Tabib R, Kouidri M, Ouakid ML, Glądalski M, Bańbura J. Avian Biol Res. 2018;11:1–8.
Article Google Scholar
42. 42.
Ojanen M. Significance of variation in egg traits in birds, with special reference to passerines. Acta Unv Oul A 154 Biol. 1983;20:1–61.
Google Scholar
43. 43.
Robertson GJ. Annual variation in common eider egg size: effects of temperature, clutch size, laying date, and laying sequence. Can J Zool. 1995;73:1579–87.
Article Google Scholar
44. 44.
Järvinen A. Global warming and egg size of birds. Ecography. 1994;17:108–10.
Article Google Scholar
45. 45.
Tryjanowski P, Sparks TH, Kuczyński L, Kuźniak S. Should avian egg size increase as a result of global warming? A case study using the red-backed shrike (Lanius collurio). J Ornithol. 2004;145:264–8.
Article Google Scholar
46. 46.
Potti J. Temperature during egg formation and the effect of climate warming on egg size in a small songbird. Acta Oecol. 2008;33:387–93.
Article Google Scholar
47. 47.
Skwarska J, Kaliński A, Wawrzyniak J, Bańbura M, Glądalski M, Markowski M, Zieliński P, Anna B, Bańbura J. Variation in egg sizes of pied flycatchers Ficedula hypoleuca in Central Poland; a long-term decreasing trend. Acta Ornithol. 2015;50:85–94.
Article Google Scholar
48. 48.
Chojnacka-Ożga L, Ożga W. Air temperature anomalies in experimental forests in Rogów in 1924-2015. Forest Res Papers. 2018;79:37–44.
Google Scholar
49. 49.
Järvinen A, Pryl M. Egg dimension of the great tit Parus major in southern Finland. Ornis Fennica. 1989;66:69–74.
Google Scholar
50. 50.
Ojanen M, Orell M, Väisänen RA. Role of heredity in egg size variation in the great tit Parus major and the pied flycatcher Ficedula hypoleuca. Ornis Scand. 1979;10:22–8.
Article Google Scholar
51. 51.
Hõrak P, Mänd R, Ots I, Leivits A. Egg size in the great tits Parus major: individual, habitat and geographic differences. Ornis Fennica. 1995;72:97–114.
Google Scholar
52. 52.
Mänd R, Tilgar V, Kilgas P, Mägi M. Manipulation of laying effort reveals habitat-specific variation in egg production constaints in great tits ( Parus major). J Ornithol. 2007;148:91–7.
Article Google Scholar
53. 53.
Perrins CM. Tits and their caterpillar food supply. Ibis. 1991;133:49–54.
Article Google Scholar
54. 54.
Encabo SI, Barba E, Gil-Delgado JA, Monrós JS. Geographical variation in egg size of the great tit Parus major: a new perspective. Ibis. 2002;144:623–31.
Article Google Scholar
55. 55.
Riddington R, Gosler AG. Differences in reproductive success and parental qualities between habitats in the great tit Parus major. Ibis. 1995;137:371–8.
Article Google Scholar
56. 56.
Hargitai R, Nagy G, Nyiri Z, Bervoets L, Eke Z, Eens M, Tӧrӧk J. Effects of breeding habitat (woodland versus urban) and mental pollution on the egg characteristics of great tits (Parus major). Sci Tot Env. 2016;544:31–8.
Article CAS Google Scholar
57. 57.
Chabi Y, Benyacoub S, Bańbura J. Egg-size variation in Algerian populations of the blue tit (Parus caeruleus ultramarinus): effects of altitude and habitat. Rev Ecol (Terre Vie). 2000;55:183–92.
Google Scholar
58. 58.
Kouidri M, Adamou AE, Bańbura A, Oukaid ML, Chabi Y, Bańbura J. High egg size variation in African blue tits Cyanistes caeruleus ultramarinus on the periphery of species range. Acta Ornithol. 2015;50:205–12.
Article Google Scholar
59. 59.
Bailly J, Scheifler R, Berthe S, Clement-Demange VA, Leblond M, Pasteur B, Faivre B. From eggs to fleding: negative impact of urban habitat on reproduction in two tit species. J Ornithol. 2016;157:377–92.
Article Google Scholar
60. 60.
Glądalski M, Bańbura M, Kaliński A, Markowski M, Skwarska J, Wawrzyniak J, Zieliński P, Cyżewska, Bańbura J. Inter-annual and inter-habitat variation in breeding performance of blue tits (Cyanistes caeruleus) in Central Poland. Ornis Fennica. 2015;92:34–42.
Google Scholar
61. 61.
Glądalski M, Bańbura M, Kaliński A, Markowski M, Skwarska J, Wawrzyniak J, Zieliński P, Cyżewska I, Bańbura J. Differences in the breeding success of blue tits Cyanistes caeruleus between a forest and an urban area: a long-term study. Acta Ornithol. 2017;52:59–68.
Article Google Scholar
62. 62.
Perrins CM. Population fluctuations and clutch size in the great tit Parus major L. J Anim Ecol. 1965;34:601–47.
Article Google Scholar
63. 63.
Perrins C. British tits. London: Collins; 1979.
Google Scholar
64. 64.
Murphy EC, Haukioja E. Clutch size in nidicolous birds. Curr Ornithol. 1986;4:141–79.
Google Scholar
65. 65.
Pettifor RA, Perrins CM, McCleery RH. Individual optimization of clutch size in great tits. Nature. 1988;336:160–2.
Article Google Scholar
66. 66.
Nadolski J, Marciniak B, Nowakowska M, Szczepko K, Kowalczyk JK. Preliminary results of quantitative investigation of the insect fauna of Łódź. In: Indykiewicz P, Barczak T, editors. Fauna miast Europy Środkowej 21. wieku. Bydgoszcz: Logo; 2004. p. 37–48.
Google Scholar
67. 67.
Nowakowska M. Zróżnicowanie sezonowe i środowiskowe potencjalnej bazy pokarmowej ptaków owadożernych: konsekwencje dla rozrodu sikor bogatki Parus major i modrej Parus caeruleus. Ph D Thesis. Łódź: Univeristy of Łódź; 2007.
Google Scholar
68. 68.
Nager RG. The challenges of making eggs. Ardea. 2006;94:323–46.
Google Scholar
69. 69.
Ramsay SL, Houston DC. Nutritional constraints on egg production in the blue tit: a supplementary feeding study. J Anim Ecol. 1997;66:649–57.
Article Google Scholar
70. 70.
Ramsay SL, Houston DC. Do acid rain and calcium supply limit eggshell formation for blue tits (Parus caeruleus) in the U.K.? J Zool Lond. 1999;247:121–5.
Article Google Scholar
71. 71.
Boulton RL, Cassey P. How avian incubation behaviour influences egg surface temperatures: relationships with egg position, development and cluth size. J Avian Biol. 2012;43:289–96.
Article Google Scholar
72. 72.
Bueno-Enciso J, Barrientos R. Incubation behavior of blue Cyanistes caeruleus and great tits Parus major in a Mediterranean habitat. Acta Ornithol. 2017;52:21–34.
Article Google Scholar
73. 73.
Gosler AG, Higham JP, Reynolds J. Why are birds’ eggs speckled? Ecol Lett. 2005;8:1105–13.
Article Google Scholar
Download references
Acknowledgements
We thank E. Wróblewska, A. Jaksa, D. Mańkowska and J. Białek for their help and consent to conducting research in the areas under their administration. We thank A.P. Cowie for linguistic consultation. Critical comments of two anonymous referees greatly helped us revise the manuscript. We are very grateful to them.
Funding
The study was financially supported by the University of Łódź.
Availability of data and materials
The datasets used and analysed during the current study are available from the corresponding author on reasonable request.
Author information
Affiliations
Authors
Contributions
MB and JB carried out the analyses and drafted the manuscript. JB and PZ designed the study. MB, MG, AK, MM, JS, JW, PZ and JB conducted the field study. MG, AK, MM, JS, JW and PZ improved several subsequent versions of the manuscript. All authors read and approved the final manuscript.
Corresponding author
Correspondence to Jerzy Bańbura.
Ethics declarations
Ethics approval
The field study and all procedures were performed under the licenses from The General Directorate for Environmental Protection, The Regional Directorate for Environmental Protection in Łódź, The Local Ethical Committee for Research on Animals and Polish Bird Ringing Centre.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Reprints and Permissions
About this article
Verify currency and authenticity via CrossMark
Cite this article
Bańbura, M., Glądalski, M., Kaliński, A. et al. A consistent long-lasting pattern of spatial variation in egg size and shape in blue tits (Cyanistes caeruleus). Front Zool 15, 34 (2018). https://doi.org/10.1186/s12983-018-0279-4
Download citation
• Received:
• Accepted:
• Published:
• DOI: https://doi.org/10.1186/s12983-018-0279-4
Keywords
• Egg shape
• Egg volume
• Life history
• Passerine
• Spatial variation
|
__label__pos
| 0.536215 |
Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Screen reader users: click this link for accessible mode. Accessible mode has the same essential features but works better with your reader.
Patents
1. Advanced Patent Search
Publication numberUS6942158 B2
Publication typeGrant
Application numberUS 10/697,011
Publication dateSep 13, 2005
Filing dateOct 31, 2003
Priority dateNov 21, 2002
Fee statusPaid
Also published asDE10353373A1, DE10353373B4, US20040099738
Publication number10697011, 697011, US 6942158 B2, US 6942158B2, US-B2-6942158, US6942158 B2, US6942158B2
InventorsJohn Deryk Waters
Original AssigneeHewlett-Packard Development Company, L.P.
Export CitationBiBTeX, EndNote, RefMan
External Links: USPTO, USPTO Assignment, Espacenet
Memory tag and a reader
US 6942158 B2
Abstract
A memory tag comprising a resonant circuit part, a memory, a detector module and an output generator module, the resonant circuit part being operable to generate an output signal in response to a signal from a reader, the amplitude of the output signal dependent on the magnitude of the signal from the reader, the detector module being responsive to the magnitude of the output signal such that, when the magnitude of the output signal is relatively low, the detector module causes the output generator module to transmit an identifier signal, and when the magnitude of the output signal is relatively high, the detector module connects the memory to the resonant circuit part.
Images(4)
Previous page
Next page
Claims(28)
1. A memory tag comprising a resonant circuit part, a detector module and an output generator module, the resonant circuit part being operable to generate an output signal in response to a reader signal from a reader, the magnitude of the output signal being dependent on the magnitude of the reader signal, the detector module being responsive to the magnitude of the output signal such that, when the magnitude of the output signal is relatively low, the detector module causes the output generator module to transmit an identifier signal which is configured to cause the reader to increase the magnitude of the reader signal from a first level to a second relatively high level, and when the magnitude of the output signal is relatively high as a result of the tag receiving the second relatively high magnitude reader signal from the reader, the detector module is operable to cause the tag to move to an operating mode.
2. A memory tag according to claim 1 comprising a memory, wherein the detector module is operable in response to the reader signal being at the second relatively high level, to cause the tag to move to the operating mode by connecting the memory to the resonant circuit part.
3. A memory tag according to claim 1 comprising a rectifying circuit part responsive to the output signal of the resonant circuit part to generate an output voltage, and wherein the detector module is responsive to the magnitude of the output voltage.
4. A memory tag according to claim 3 wherein the tag comprises a memory and wherein the detector module is operable to move the tag to an operating mode by connecting the memory to the rectifying circuit part when the output signal is relatively high, and operable to disconnect the memory from the rectifying circuit part when the magnitude of the output signal is relatively low.
5. A memory tag according to claim 1 wherein the resonant circuit part comprises a switch, wherein when the magnitude of the output signal is relatively low the output generator module is operable to control the switch to transmit the identifier signal, and when the magnitude of the output signal is relatively high, the memory is operable to control the switch.
6. A memory tag according to claim 1 wherein the output generator module comprises a pseudorandom binary sequence generator to generator an identifier signal comprising a pseudorandum binary sequence.
7. A memory tag according to claim 1 wherein the resonant circuit part is operable to provide inductive coupling to a reader wherein the reader signal is received via the inductive coupling.
8. A memory tag comprising a resonant circuit part, a detector module, an output generator module and a memory, the resonant circuit being operable to generate an output signal in response to a reader signal from a reader, the magnitude of the output signal being dependent on the magnitude of the reader signal, the detector module being operable in response to the output signal such that when the magnitude of the output signal received by the memory tag is relatively low, the detector module causes the output generator module to transmit an identifier signal configured to induce the reader to increase the magnitude of the reader signal from a normal finite level to a higher level, and when the magnitude of the output signal is relatively high in response to the magnitude of the reader signal being increased to the higher level, the detector module is operable to connect the memory to the resonant circuit part.
9. A reader to read a memory tag, the reader being operable to transmit a reader signal to a memory tag, the reader further being operable to receive a signal from a memory tag, the reader:
being operable to transmit the reader signal to the memory tag at a first, relatively low power, and in response to an identifier signal being issued from the memory tag in response to receipt of the reader signal having the first relatively low power, and
being operable to transmit a reader signal to the memory tag at a second, relatively high power whereby the reader is switched from a low power search mode to a high power read mode.
10. A reader according to claim 9 comprising a resonant circuit part and a signal generator operable to supply a drive signal to the resonant circuit part, the reader further comprising an amplitude modulator to control the amplitude of the drive signal supplied from the signal generator to the resonant circuit part.
11. A reader according to claim 9 comprising a output signal identifier module, operable to identify the identifier signal from the memory tag.
12. A reader according to claim 11 wherein the reader comprises a correlator operable to identify the identifier signal.
13. A reader according to claim 9 operable to provide inductive coupling to the memory tag wherein the reader signal is transmitted via the inductive coupling.
14. A reader to read a memory tag, the reader comprising a resonant circuit part, an interrogator, and an identifier signal module, the interrogator module being operable to transmit a reader signal at a first, relatively low power to a memory tag, receive a signal from the memory tag which is generated by the memory tag in response to receipt of the first, relatively low power reader signal, and pass the received signal to the identifier signal module, the identifier signal module being operable to identify the identifier signal and generate an instruction to the interrogator module to generate a reader signal at a second, relatively high power.
15. A system comprising a memory tag and a reader, the memory tag having a resonant circuit part, a detector module, an output generator module and a memory holding data, the reader comprising a resonant circuit part operable to transmit a reader signal to the memory tag and receive a signal from the memory tag, the reader being operable to transmit a reader signal to the memory tag at a first relatively low power wherein,
the resonant circuit part of the memory tag, in response to the reader signal, generates an output signal having a first, relatively low magnitude,
the detector module is responsive to the first relatively low magnitude of the output signal to cause the output generator module to transmit an identifier signal,
the reader is operable to receive the identifier signal from the memory tag and identify the identifier signal, and generate a reader signal at a second, relatively high power,
the resonant circuit part of the tag is operable to generate an output signal having a second, relatively high magnitude, the detector module being responsive to the output signal having a second, relatively high magnitude to connect the memory to the resonant circuit part, and
the memory tag is operable to send a signal to the reader to transmit the data held in the memory to the reader.
16. A method of operating a memory tag comprising the steps of detecting a reader signal received from a reader, and, when the magnitude of the reader signal received by the tag is relatively low, transmitting an output identifier signal from the tag to the reader to induce the reader to increase the power of the reader signal, and when the magnitude of the reader signal received by the tag is relatively high as a result of the reader receiving the output identifier signal, moving to an operating mode by using the received reader signal with the relatively high magnitude, to energize the memory tag.
17. A method according to claim 16 wherein the step of moving to an operating mode comprises permitting operation of a memory of the memory tag.
18. A memory tag comprising a resonant circuit part, a detector module and an output generator module, the resonant circuit part being operable to generate a first relatively low magnitude output signal and a second relatively high magnitude output signal respectively in response to a first reader signal and a second reader signal which are respectively issued from a reader at first and second power levels, the magnitude of the first output signal being variable with the magnitude of the first reader signal which is lower in power than the second reader signal, the detector module being responsive to the relatively low magnitude of the first output signal such that the detector module transmits an identifier signal which is configured to induce the reader to issue the second relatively high power level reader signal, and in response to the second output signal, which is induced by the second relatively high power level reader signal, the detector module is operable to cause the tag to move to an operating mode.
19. A memory tag according to claim 18 comprising a memory, wherein the detector module is operable to cause the tag to move to an operating mode by connecting the memory to the resonant circuit part.
20. A memory tag according to claim 18 comprising a rectifying circuit part responsive to the first and second output signals of the resonant circuit part to generate respective output voltages, and wherein the detector module is responsive to the respective magnitudes of the output voltages.
21. A memory tag according to claim 20 wherein the tag comprises a memory and wherein the detector module is operable to energize the tag into the operating mode by connecting the memory to the rectifying circuit part in response to the second output signal, and operable to disconnect the memory from the rectifying circuit part in response to the first output signal.
22. A memory tag according to claim 18 wherein the resonant circuit part comprises a switch, wherein in response to the first output signal, the output generator module is operable to control the switch to transmit the identifier signal, and in response to the second output signal, the memory is operable to control the switch.
23. A memory tag according to claim 18 wherein the output generator module comprises a pseudorandom binary sequence generator to generator an identifier signal comprising a pseudorandum binary sequence.
24. A memory tag according to claim 18 wherein the resonant circuit part is operable to provide inductive coupling to a reader wherein the reader signal is received via the inductive coupling.
25. A method of operating a reader for reading a memory tag comprising:
generating a reader signal normally having a first, relatively low power during a low power search mode,
detecting an identifier signal from a memory tag which is produced by the memory tag in response to receipt of the reader signal having the first relatively low power, and
inducing a high-power read mode by generating, in response to detection of the identifier signal, a reader signal at a second, relatively high power to excite the memory tag into an operating mode wherein data can be transmitted from the memory tag and read by the reader.
26. A method according to claim 25, wherein the step of exciting the memory tag into an operative mode comprises: connecting a memory to a resonant circuit in response to the reader signal being at the second relatively high level.
27. A method according to claim 26 further comprising:
using a rectifying circuit part responsive to the output signal of the resonant circuit to generate an output voltage, and
using the output voltage to control a detector module.
28. A method according to claim 25 wherein the tag comprises a memory and a detector module and wherein the detector module is operable to excite the tag into an operating mode by:
connecting the memory to a rectifying circuit when the output signal is relatively high, and
disconnecting the memory from the rectifying circuit part when the magnitude of the output signal is relatively low.
Description
FIELD OF THE INVENTION
This invention relates to a memory tag powered by a signal generated by a reader, and a reader.
BACKGROUND OF THE INVENTION
Memory tags in the form of Radio Frequency Identification (RFID) tags are well known in the prior art, and the technology is well established (see for example: RFID Handbook, Klaus Finkenzeller, 1999, John Wiley & Sons). RFID tags come in many forms but all comprise an integrated circuit with information stored on it and a coil which enables it to be interrogated by a read/write device generally referred to as a reader. Until recently RFID tags have been quite large, due to the frequency they operate at (13.56 MHz) and the size of coil they thus require, and have had very small storage capacities. Such RFID tags have tended to be used in quite simple applications, such as for file tracking within offices or in place of or in addition to bar codes for product identification and supply chain management.
Much smaller RFID tags have also been developed, operating at various frequencies. For example Hitachi-Maxell have developed “coil-on-chip” technology in which the coil required for the inductive link is on the chip rather than attached to it. This results in a memory tag in the form of a chip of 2.5 mm square, which operates at 13.56 MHz. In addition Hitachi has developed a memory tag referred to as a “mu-chip” which is a chip of 0.4 mm square and operates at 2.45 GHz. These smaller memory tags can be used in a variety of different applications. Some are even available for the tagging of pets by implantation.
Although it is known to provide tags with their own power source, in many applications the tag is also powered by the radio frequency signal generated by the reader. Such a known system is shown in FIG. 1 where a reader is indicated generally at 10 and a tag at 12. The reader 10 comprises a radio frequency generator 13 and a resonant circuit part 11, in the present example comprising an inductor 14 and a capacitor 15 connected in parallel. The inductor 14 comprises a antenna. The resonant circuit part will have a particular resonant frequency in accordance with the capacitance and inductance of the capacitor 15 and the inductor 14, and the frequency generator 13 is operated to generate a signal at that resonant frequency.
The tag 12 similarly comprises a resonant circuit part generally illustrated at 16, a rectifying circuit part generally indicated at 17 and a memory 18. The resonant circuit part 16 comprises an inductor 19 which again comprises in this example a loop antenna, and a capacitor 20. The resonant circuit part 16 will thus have a resonant frequency set by the inductor 19 and capacitor 20. The resonant frequency of the resonant circuit part 16 is selected to be the same as that of the reader 10. The rectifying part comprises a forward-biased diode 21 and a capacitor 22 and thus effectively acts as a half-ware rectifier.
When the reader 10 and the tag 12 are sufficiently close, a signal generated by the frequency generator 13 will cause the resonant circuit part 11 to generate a reader signal comprising a high frequency electromagnetic field. When the resonant circuit part 16 is moved within this field, a current will be caused to flow in the resonant circuit part 16, drawing power from the time varying magnetic field generated by the reader. The rectifying circuit part 17 will then serve to smooth the voltage across the resonant frequency part and provide a power supply storage. The rectifying circuit part 17 is sufficient to supply a sufficiently stable voltage to the memory 18 for the memory to operate.
It is possible however, when no tag 12 is sufficiently close to the reader 10, the electromagnetic field generated by the reader 10 could be coupled to other objects, particularly objects containing metal, such as a glass frame a pen or such wires as may be found on a desk. This may be undesirable. It is possible in such circumstances, the reader would not meet prescribed legal regulations or guidelines relating to the level of radiated power from radio transmitters. However, it will be apparent that simply reducing the power of the signal transmitted by the reader will reduce both the range at which the reader may operate and the power available for operation of the tag 32. An aim of the present invention is to reduce or overcome the above problem.
SUMMARY OF THE INVENTION
According to one aspect of the invention, we provide a memory tag comprising a resonant circuit part, a detector module and an output generator module, the resonant circuit part being operable to generate an output signal in response to a reader signal from a reader, the amplitude of the output signal dependent on the magnitude of the reader signal, the detector module being responsive to the magnitude of the output signal such that, when the magnitude of the output signal is relatively low, the detector module causes the output generator module to transmit an identifier signal, and when the magnitude of the output signal is relatively high, the detector module is operable to cause the tag to move to an operating mode.
The tag may comprise a memory, wherein the detector module may be operable to cause the tag to move to an operating mode by connecting the memory to the resonant circuit part.
The tag may comprise a rectifying circuit part which is responsive to the output signal of the resonant circuit part to generate an output voltage, and the detector module may be responsive to the magnitude of the output voltage.
The detector module may be operable to connect the memory to the rectifying circuit part when the output signal is relatively high and to disconnect the memory from the rectifying circuit part when the magnitude of the output signal is relatively low.
The resonant circuit part may comprise a variable capacitance element, wherein when the magnitude of the output signal is relatively low the output generator module is operable to control the variable capacitance element, and when the magnitude of the output signal is relatively high, the memory is operable to control the variable capacitance element.
The output generator module may comprise a pseudorandom binary sequence generator and wherein the pseudorandom binary sequence generator is operable to control the variable capacitance element to transmit the pseudorandom binary sequence to a reader.
The resonant circuit part may be operable to provide inductive coupling to a reader wherein the reader signal is received via the inductive coupling.
According to a second aspect of the invention, we provide a reader to read a memory tag, the reader comprising a resonant circuit part operable to transmit a reader signal to a memory tag, the reader further being operable to receive a signal from a memory tag, the reader being operable to transmit the signal to the memory tag at a first, relatively low power, and in response to an identifier signal from a memory tag, being operable to transmit a signal to the memory tag at a second, relatively high power.
A resonant circuit part and a signal generator may be operable to supply a drive signal to the resonant circuit part, the reader further comprising an amplitude modulator to control the amplitude of the drive signal supplied from the signal generator to the resonant circuit part.
An identifier signal module may be provided, operable to identify the identifier signal from the memory tag.
The identifier signal module may comprise a correlator operable to identify the identifier signal.
The reader may be operable to provide inductive coupling to the memory tag wherein the reader signal is transmitted via the inductive coupling.
According to a third aspect of the invention, we provide a method of operating a memory tag comprising the steps of detecting a signal received from a reader, and, when the magnitude of the signal is relatively low, transmitting an output identifier signal and when the magnitude of the signal is relatively high, permitting operation of the memory tag.
The step of moving to an operating mode may comprise permitting operation of a memory of the memory tag.
According to a fourth aspect of the invention, we provide a method of operating a reader for reading a memory tag comprising generating a signal having a first, relatively low power, detecting an identifier signal from a memory tag, and in response to detection of the identifier signal, generating a signal at a second, relatively high power.
BRIEF DESCRIPTION OF THE DRAWINGS
The embodiments of the present invention will now be described by way of example only with reference to the accompanying drawings wherein;
FIG. 1 is a diagrammatic illustration of a known reader and memory tag,
FIG. 2 is a diagrammatic illustration of a reader and a memory tag embodying the present invention, and
FIG. 3 is a diagrammatic illustration of a particular reader and memory tag embodying the present invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring now to FIG. 2, a tag embodying the present invention is shown at 30 and a reader shown at 31. The tag 30 comprises a resonant circuit part 32 and a rectifying circuit part 33, together with a memory 34. The resonant circuit part 32 comprises an inductor L2 shown at 35 which comprises an antenna of suitable form and a capacitor L2 shown at 36 connected in parallel in like manner to the tag 12 of FIG. 1. The resonant circuit part 32 further comprises a switch S1 shown at 37 as a field effect transistor (FET) which is switchable between a high resistance, where it acts as an open switch, and a low resistance, where it acts as a closed switch, by applying an appropriate voltage to line 37 a. The rectifying circuit part 33 comprises a diode D1 shown at 40 connected to the resonant circuit part 32 in a forward biased direction and a capacitor C4 shown at 41 connected in parallel with the components of the resonant circuit part 32. The rectifying circuit part 33 operates in like manner to the rectifying circuit part 17 of FIG. 1 as a half-wave rectifier to provide power to the memory 34 when the tag 30 receives a reader signal generated by the reader 31.
The tag 30 further comprises a detector module 42 and an output identifier generator 43. The detector module 42 is connected to the output of the rectifying circuit part 33. The detector module 42 is further operable to control a second switch S2 shown at 44 to connect one of the memory and the identifier signal generator module 43 to the switch S1, and a third switch S3 as shown at 45 connected between the output of the rectifying circuit part 32 and the memory 34. The detector module 42 is responsive to the magnitude of the output voltage of the rectifying circuit part 32 to control the switches S2 S3. When the output voltage has a relatively low magnitude, the detector module 42 is operable to set switch S3 open and connect switch S2 to the identifier signal module 43. When the output voltage has a relatively high magnitude, the detector module 42 is operable to cause the tag 30 to move to an operating mode by closing switch S3, connecting the memory to the rectifying circuit 32, and setting switch S2 to connect the memory 34 to the first switch S1.
The identifier signal generated by the identifier signal generator module 43 may be a pseudorandom binary sequence as discussed below, or may be any appropriate signal to indicate the presence of the tag 30, such as a repeating short sequence of bits, or a serial number corresponding to the tag 30, or indeed any other signal as desired. Different tags 30 or types of tag 30 mat be operable to generate different pseudorandom binary sequences to identify the tag 30 as well as detectably indicate the presence of the tag.
In the present example, the tag 30 is provided on a CMOS chip. The a resonant circuit part 32, excluding the antenna, and the rectifying circuit part 33 occupy an area of approximately 0.5 mm2. The memory 34 in this example is a non-volatile memory providing 1 Mbit of capacity and is of an area of approximately 1 mm2. The memory may for example use FRAM (ferroelectric random access memory) or MRAM (magnetoresistive random access memory). The antenna is provided on the chip and may have only a few turns, for example 5, or in this case one turn. The tag 30 will be of generally square shape in plan view and have an external dimension D for the length of each side of approximately 1 mm
The reader 31 comprises an interrogator module 46 connected to an inductor 47 in the present example an antenna, to provide inductive coupling between the tag 30 and the reader 31. When the switch S1 is closed, it causes an increased current to flow in the resonant circuit part 32, which can be detected by the reader 31 as a drop in voltage across the inductor 47 providing a data output 48. The reader 31 further comprises an identifier signal module 49 connected to the data output 48 operable to identify the identifier signal transmitted by the tag 30 and generate a high power instruction on line 50. The interrogator module 46 is operable to supply a signal to the inductor 47 at a first, relatively low power and, in response to the high power instruction received on line 50, to supply a signal to the inductor at a second relatively high power.
As discussed above, the tag 30 will have a dimension D of about 1 mm, and the reader 31 will be operable to communicate with the tag over a relatively short range, for example approximately 2D, but the distance over which the tag 30 and reader 31 can communicate effectively will vary with the exact details of their construction.
The tag 30 and reader 31 are operable as follows. The reader 31 is initially in “search mode”, that is a tag 30 is not sufficiently close to the antenna 47 for inductive coupling to occur. The interrogator module 46 generates an output reader signal of relatively low power.
When a tag 30 comes sufficiently close to the antenna 47 to provide inductive coupling, for example within about 2D, the reader signal will cause the rectifying circuit part 32 to generate an output voltage having a relatively low magnitude as discussed hereinbefore. The detector module 42 will cause switch S3 to be open and switch S2 connected to the identifier signal generator module 43 as shown in FIG. 2. Sufficient power will be supplied to the tag 30 to operate the identifier signal generator module 43 such that it transmits an appropriate identifier signal. Conveniently, the identifier signal operator module 43 will comprise a pseudorandom binary sequence generator which may simply be assembled out of a shift register and XOR gates in known manner. Such a functionality will require very little power to operate, particularly when provided as part of a CMOS integrated circuit. The module 43 modulates the resonant frequency of the resonant circuit part 32 by operating the switch S1 in accordance with the pseudorandom binary signal. For example, the output of the identifier signal operator module 43 may simply be a series of pulses of relatively high or low voltage encoding the bits of the identifier signal passed to the switch S1. The switch S1 will be open or closed depending on the voltage of the signal, thus transmitting the identifier signal to the reader 31. The interrogator 46 transmits the received data 48 to the identifier signal module 49. On detecting the identifier signal from the tag 30, the identifier signal module 49 will send a high power instruction on a line 50 to the interrogator 46 to switch to high power operation. The interrogator 45 will then send a relatively high power signal to the antenna 47. This will cause the rectifying circuit part 32 to generate a signal comprising an output voltage having a relatively high magnitude which is detected by the detector module 42. The detector module 42 then closes switch S3, connecting the memory 34 to the rectifying circuit part 32, and toggles switch S2 to connect the memory 34 to first switch S1. The tag 30 may then operate to read data from the memory 34 to the reader 31. In particular, a program stored in the memory 34 may be operable to read data held in the memory 34 and control the switch S1 by transmitting a signal having a particular voltage on line 34 a, for example encoding binary digits by pulses of relatively high or low voltage.
Referring now to FIG. 3, a particular embodiment of a memory tag and reader are shown at 30′ and 31′ respectively. The reader 31′ comprises a resonant circuit part 51 which comprises an inductor L1 shown at 52, in this example an antenna and a capacitor C1 shown at 53 connected in parallel. A signal generator 54 is connected to the resonant circuit part 51 to provide a drive signal.
The reader 31′ further comprises a demodulator, generally shown at 55. The demodulator 55 comprises a splitter 56 connected to the frequency generator to split off a part of the drive signal to provide a reference signal. A coupler 57 is provided to split off part of a reflected signal reflected back from the resonant circuit part 51, and pass the reflected signal to a multiplier shown at 58. The multiplier 58 multiplies the reflected signal received from the coupler 57 and the reference signal received from the splitter 56 and passes the output to a low pass filter 59. The low pass filter 59 passes the signal corresponding the phase difference between the reference signal and the reflected signal to an output 60. An amplitude modulator is shown at 61 operable to control the amplitude of the drive signal supplied from the frequency generator 54 to the resonant circuit part 51.
The memory tag 32′ is the same as the memory tag 32 of FIG. 2 except that the switch S1 37 has been replaced with a variable capacitance element generally indicated at 37′ comprising a switch S1′ shown at 38 and a capacitor C3 shown at 39. Operation of the switch S138 will switch the capacitor C3 in and out of the resonant circuit part 32′, thus changing the resonant frequency of the resonant circuit part 32′ causing a relative phase shift in the signal reflected from the resonant circuit part 51. The switch S1′ may comprise an FET and be operable in like manner to the switch 37 as discussed herein before.
In the reader 31′ the reference signal from the splitter 56 will be of the form
S(t)=A cos(ωt)
and the reflected signal R(t) will be of the form
R(t)=a cos(ωt+φ(t))
• where
• A=amplitude of the reference signal,
• a=amplitude of the reflected signal
• φ(t)=the relative phase and
• ω=the frequency of the drive signal generated by the frequency source 45.
R(t) is multiplied by the carrier reference signal S(t) at the multiplier 58, producing a resulting signal a A 2 cos ( 2 ω t + φ ( t ) ) + a A 2 cos ( φ ( t ) )
The first of these terms, the second harmonic, is simply filtered by the low pass filter 59 leaving the second term that comprises the phase difference between the reference and reflected signals. It is a known effect of resonant circuits that when the circuit passes a signal which has a frequency less than the resonant frequency of the circle, a phase lag is introduced to the signal frequency, whilst when the frequency is greater than that of the resonant circuit, a phase lead is induced. Thus, by modulating the frequency of the reflected signal by changing the resonant frequency of the resonant circuit part 32′ of the tag 30′, the reflected signal will have a phase difference relative to the reference signal from the frequency source 54 which may easily be measured by the demodulator as discussed above.
An identifier signal module is shown at 49 connected to the output 60 and operable to control the amplitude modulator 61. In this example, the identifier signal module comprises a correlator. Correlators are particularly useful for identifying weak repetitive signals, and in this example the correlator 48 is operable to identify the pseudorandom binary sequence transmitted by the tag 30. The correlator is operable to control the amplitude modulator 55 to switch the modulator between a relatively low amplitude signal and a relatively high amplitude signal to generate a relatively low or relatively high amplitude output.
The embodiment of FIG. 3 is particularly advantageous in that the data is transmitted from the memory tag 30′ without significantly affecting the output voltage of the rectifying circuit part 33, and the correlator 49 simply receive the identifier signal from the demodulator 55 used to read data from the tag 30′.
The reader 31, 31′ may be provided as a device or a component of a device having any appropriate function or application as desired. For example, a reader might comprise a device whose intended principle function is simply to act as a stand-alone reader. The small size of the reader would permit it to be intergrated into small devices, such as a key fob or pen. The reader may have a display or other understandable output means, or may be suitably adapted to connect another device. It might be envisaged for example that a reader is provided with a suitable memory into which the contents of the memory of a tag are read, and an interface to enable the reader to be connected to another device such as a personal computer to enable the content of the reader memory to be downloaded.
A reader might be provided with a connection to a computer, such that the reader functions as a peripheral of the computer operable to read a tag and supply the read information to the computer for any appropriate application, or indeed write information to the tag. In this example, it might be envisaged that the reader be provided on a computer mouse or a keyboard. It might also be envisaged that a printer be provided with a reader, such that the printer could retrieve a document stored on a tag and print a copy of the document.
A reader may also be provided integrated in or provided as part of a portable device. For example, a personal digital assistant (PDA) might be provided with a reader such that a user may read from and write to a memory tag with the reader and view the retrieved information on a screen of the PDA. Similarly, it might be envisaged that a reader might be built into a mobile telephone, or be connectable thereto to enable information transmitted via the mobile telephone to be read from or written to the memory tag, and made available to a user via the screen of the telephone or as an audible output.
In all of the examples, it will be apparent that the information read from or written to the memory tag may comprise any appropriate type or format as desired, for example text, images, programs, sound files or movie files.
It will of course be apparent that the reader 31 31′ may be provided with any appropriate implementation as desired to switch between a relatively low power search mode and a relatively high power mode where data may be read from or to the tag 30. In a preferred embodiment, the resonant frequency of the resonant circuit part 42, and hence the frequency of the signal generated by the frequency source 45 is about 2.45 GHz, and the resonant frequency of the resonant circuit part 32 is modulated by about 0.05 GHz either side of this reference frequency. At this frequency, component values for the inductors for the capacitors are small, allowing easy integration of the circuit and require relatively small early areas of silicon on an integrated circuit. It is particularly desirable that the circuit for the memory tag 30 30′ be provided as a integrated circuit, for example as a CMOS integrated circuit. Switches S1′, S2, S3 may advantageously be provided as field effect transmitters which are particularly suitable for provision as part of a CMOS integrated circuit.
The tag 30 30′ is particularly advantageous in that it may be used with a CMOS integrated circuit. It is known that the power requirements of a CMOS integrated circuit are proportional to the square of the operating voltage, the capacitance of all the gates found on the circuit and the operation frequency. The pseudorandom binary sequence generator 43 may operate at a relatively low rate, for example on the order of 100 kilobits per second instead of 10 megabits per second for the normal read/write operation of the tag, and may be relatively simply implemented to, for example, provide a repeating sequence of 127 bits at a relatively low power. The correlator 49 is operable to detect the sequence of 127 bits with high confidence, even though the signal generated by the tag may be generated at a relatively low power.
In the present specification “comprises” means “includes or consists of” and “comprising” means “including or consisting of”.
The features disclosed in the foregoing description, or the following claims, or the accompanying drawings, expressed in their specific forms or in terms of a means for performing the disclosed function, or a method or process for attaining the disclosed result, as appropriate, may, separately, or in any combination of such features, be utilised for realising the invention in diverse forms thereof.
Patent Citations
Cited PatentFiling datePublication dateApplicantTitle
US5073781 *Jan 31, 1991Dec 17, 1991Texas Instruments Deutschland GmbhTransponder
US5305008 *Sep 4, 1992Apr 19, 1994Integrated Silicon Design Pty. Ltd.Transponder system
US5471212Apr 26, 1994Nov 28, 1995Texas Instruments IncorporatedMulti-stage transponder wake-up, method and structure
US5523749 *Apr 3, 1992Jun 4, 1996Integrated Silicon Design Pty. Ltd.Identification system for simultaneously interrogated labels
US6265963 *Jun 23, 2000Jul 24, 2001Micron Technology, Inc.Methods of processing wireless communication, methods of processing radio frequency communication, and related systems
US6398116Jun 22, 1998Jun 4, 2002Angewandte Digital GmbhChip card with at least two coil devices for transferring data and/or energy
US6476708Mar 20, 1998Nov 5, 2002Hid CorporationDetection of an RFID device by an RF reader unit operating in a reduced power state
US20020089448 *Jan 9, 2002Jul 11, 2002Juraj PoliakReceiver designed to pick up an electromagnetic signal and system using such a receiver
DE4002801A Title not available
WO1999030401A1Dec 4, 1998Jun 17, 1999Atmel CorporationMinimum voltage radio frequency identification
Non-Patent Citations
Reference
1"Keyless entry", http://www.all-electronics.de/news4d4b4303e11,print/html, Sep. 1, 2002.
2"Transponder: Arten und Reichweiten", http://web.archive.org/web/20021115010650/Http://www.nur-sicherheit.de/themen/zutrittskontrolle/identi.htm, as of Nov. 15, 2002.
3"Verfolgungsjagd durchs Autowerk", IEE Automatisierung + Datentechnik, Mar. 2002.
4English Translation of a German Office Action dated Aug. 27, 2004 issued in corresponding German Application No. 103 53 373.7-53, (6 pp.), Applicant: Hewlett-Packard Co.
Referenced by
Citing PatentFiling datePublication dateApplicantTitle
US7183925 *Feb 3, 2003Feb 27, 2007Koninklijke Philips Electronics N.V.Interactive system using tags
US7603082 *Jun 23, 2005Oct 13, 2009Stmicroelectronics S.A.Impedance matching of an electromagnetic transponder reader
US8441099 *Sep 29, 2010May 14, 2013Semiconductor Energy Laboratory Co., Ltd.Wireless chip
US8914665Jul 6, 2006Dec 16, 2014Hewlett-Packard Development Company, L.P.Reading or storing boot data in auxiliary memory of a tape cartridge
US9058550 *Feb 5, 2013Jun 16, 2015Google Technology Holdings LLCMobile devices with RFID capabilities and corresponding memory write methods
US20050140504 *Feb 3, 2003Jun 30, 2005Koninklijke Philips Electronics N.V.Interactive system using tags
US20050225437 *Aug 19, 2004Oct 13, 2005Fujitsu LimitedInformation processing apparatus for receiving predetermined information, and program product and method therefor
US20050285718 *Jun 23, 2005Dec 29, 2005Stmicroelectronics, S.A.Impedance matching of an electromagnetic transponder reader
US20060057762 *Sep 13, 2004Mar 16, 2006Shoei-Lai ChenMethod of building electronic label for electronic device
US20060178816 *Jan 30, 2006Aug 10, 2006Hewlett-Packard Development Company, L.P.Methods, articles and computer program products for providing travel directions
US20070101113 *Jul 6, 2006May 3, 2007Evans Rhys WData back-up and recovery
US20100045441 *Nov 15, 2007Feb 25, 2010Nxp, B.V.Near field communication (nfc) activation
US20110012183 *Sep 29, 2010Jan 20, 2011Semiconductor Energy Laboratory Co., Ltd.Wireless chip
US20140191041 *Feb 5, 2013Jul 10, 2014Motorola Mobility LlcMobile devices with rfid capabilities and corresponding memory write methods
Classifications
U.S. Classification235/492, 340/572.1, 340/10.2
International ClassificationH04B5/00, G06K19/07
Cooperative ClassificationH04B5/0062, G06K19/0723, H04B5/0012, H04B5/0056
European ClassificationH04B5/00C, G06K19/07T, H04B5/00R
Legal Events
DateCodeEventDescription
Oct 31, 2003ASAssignment
Owner name: HEWLETT-PACKARD DEVELOPMENT COMPANY, L.P., TEXAS
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:HEWLETT-PACKARD LIMITED;REEL/FRAME:014658/0537
Effective date: 20031028
Mar 13, 2009FPAYFee payment
Year of fee payment: 4
Feb 26, 2013FPAYFee payment
Year of fee payment: 8
|
__label__pos
| 0.80365 |
x
Digital Engineering: The Transforming Landscape
• LinkedIn
• Twitter
• Copy
• |
• Shares 0
• Reads 174
Author
• Ali kidwaiContent Architect
The goal is to turn data into information, and information into insights.
18-February-2021
Featured
• Data Engineering
• Cloud Computing
• Data Science
More than 500 years ago, as Leonardo da Vinci experimented with his flying machines, he inked drawings and mocked up physical models before getting down to create his marvels of design. His techniques set the threshold for modern engineering. Going ahead in time, the emergence of computer-aided drafting (CAD) systems in the 20th century automated the drawing process for engineers, and CAD evolved into computer-aided design by adding 3-D modeling and manufacturing planning to software capabilities. Moving ahead, now we have digital twins: dynamic and realistic computer-based instantiations of actual systems and devices.
Digital twins serve as the most accurate replicas of physical objects allowing scientists and engineers to test out the capability and feasibility of their ideas before coming up with critical real-life decisions. The digital twins have moved from trial-and-error-based engineering to systematic, science-based engineering and optimization.
It is made possible by high-performance computing (HPC) advances, now we can utilize digital twins to virtually explore trade spaces, component interaction and performance, operations and manufacturing processes over a system's life cycle or a device in support of performance-based maintenance.
Digital engineering is more than the advanced technology that integrates the data by taking the advantage of a digital skillset. It is the practice in which new applications are delivered and conceived.
Encompassing the utility, methodologies, and process of creating new end-to-end digital products, digital engineering leverages technology and data to produce improvements to applications—or even entirely new solutions.
In the hyper-competitive modern technological world, connectivity and social networking are the norms. Consumers seek value for their investment; thus, they are active participants in the product design process to make sure that the product meets the market demand. Digitizing manufacturing gives automated customization, analytical simulations, and flexible models to deliver personalized manufacturing to consumers.
Fortunately, industries today have new technologies like - big data, cloud computing, mobile, and IoT that help weave in the digital thread to form a directional flow of information. These technologies connect various enterprise sectors for ease of operations, collaboration, quality management, and product traceability. This is particularly crucial in the aerospace industry where components are complex, demand for high quality with zero tolerances must be met, and expense reduction is crucial.
From an engineering perspective, modeling has extremely improved and continues to evolve. The initial 2D modeling techniques have advanced to 3D modeling techniques meshed with analytical simulations to determine the models' workability under numerous conditions. Gradually, 3D models are now printable in what is called 3D printing through pairing computer-aided manufacturing (CAM) and skilled coding.
The result of 3D printing is additive manufacturing techniques that are applicable for both actual production and prototyping. Additive manufacturing processes best align with model-based engineering (MBE) practices and digital 3D models.
For instance, Boeing's 787 Dreamliner whose titanium parts were 3D printed. Additive manufacturing facilitates creating new products and is influential in the design process as complex components can be easily machined, and the number of assembly parts is reduced.
It is clear enough that digital engineering has significantly affected the performance in completing the tasks. A wide array of benefits is offered in cost, safety, quality, and program designs. Following, the role of digital engineering is believed to be able to maximize the penetration to the marketplace so that the products are more acceptable.
This cannot be separated from the increasing reputation as the industry with digital engineering gains its popularity. In line with it, there are numerous benefits as engineers consider the use of digital engineering and here, they are.
1. The use of advanced technology in conducting the projects helps to enhance the confidence toward the project outcomes, enrich the knowledge, reduce the costs and minimize the risk to take.
2. The collaborative environment that involves people from different backgrounds is thought to be the best solution to develop and validate all the ongoing projects. Here, the digitalized systems become the core as the projects are carried out.
3. With the use of digital engineering, it helps the engineers to plan the design with maximum efficiency so that it can maximize the value of the assets.
4. It is undeniable that digital engineering also plays its role to both identify and mitigate the health, risks, and safety of all the construction personnel and the assets.
5. Advanced technology is also significantly important to do rapid tests on determining the solutions virtually and some identifications and validations. This becomes the best solution for the clients as well.
Electric Vehicles
Electric vehicles continue to challenge traditional automotive practices by subsidizing economic and environmental factors. Environmental agencies and industries are pushing for green energy, & digital engineering will be the most viable solution to environmental protection measures and energy.
According to the forecast that by 2030, there will be over 125 million electric cars in the world. This prediction is based on the 54% growth of about 3.1 million electric cars in 2017. With this advancement, digital engineering will continue to play an instrumental role in the automotive industry.
Spacecrafts
SpaceX, a private organization by Elon Musk, has had a breakthrough into outer space to land contracts from governmental agencies venturing into space and NASA. Designing a rocket takes a team of skilled engineers, avionics and structures. The Falcon rocket designed at SpaceX amalgamates product data management (PDM) software and finite element analysis (FEA) coordinated by Siemens' Teamcenter software solution. The complete SpaceX systems have NX software that gives virtual mockups of the Falcon rocket to offer interfaces to designers and engineering components. SpaceX has entirely digitized its operations at its factory through the design stage, manufacturing, and processing. Eventually, digital engineering has propelled SpaceX as the only private company venturing into space.
Virtual Training
Boeing's group of airplane manufacturers has embraced digital engineering. The organization uses an advanced digital toolkit collaborating AR, advanced analytics, cloud computing and IoT to resolve complex issues in the aerospace industry. Augmented reality assists train workers virtually on the production process, therefore reducing real-time training on production floors. Presently, Boeing has a research project on AR with the Digital Manufacturing and Design Innovation Institute (DMDII), a non-profit federal company committed to developing advanced manufacturing technologies and improving American manufacturing competitiveness. By tapping capability sharing, the two organizations utilize 3D cameras with advanced image processing and computer vision algorithms to create a simple, intuitive approach to augmented reality. Therefore, an expert can record instructions while performing a complex operation using innate digital work instructions and unveil it to others for training objectives, thereby increasing training resource availability and reducing expenditures.
Digital Engineering can be viewed as a more collaborative and informed way of working. It is facilitated by digital processes and technological advancements to enable more productive planning methods, operations, designing, & maintaining assets. Through integration and data capture, it seeks to add value to a project at delivery and beyond. Ultimately, the processes entailed in digital engineering are constantly transforming, and the development of disruptive technologies will always persist.
About Author
digital engineering
Ali kidwai
Content Architect
The goal is to turn data into information, and information into insights.
Generally Talks About
• Data Engineering
• Cloud Computing
• Data Science
Related blog
|
__label__pos
| 0.809366 |
www.adichemistry.com
ATOMIC STRUCTURE
< Early Atomic models Atomic structure: TOC Hydrogen atomic spectrum >
NATURE OF LIGHT & QUANTUM THEORY
The early theories describing the atomic structure are based on classical physics. However these theories could not explain the behavior of atom completely. The modern view of atomic structure is based on quantum theory introduced by Max Planck.
Before learning the quantum theory, it is necessary to understand the nature of light.
LIGHT
Light is considered as an electromagnetic radiation. It consists of two components i.e., the electric component and the magnetic component which oscillate perpendicular to each other as well as to the direction of path of radiation.
electromagnetic radiation representation
The electromagnetic radiations are produced by the vibrations of a charged particle. The properties of light can be explained by considering it as either wave or particle as follows (dual nature).
WAVE NATURE OF LIGHT
According to the wave theory proposed by Christiaan Huygens, light is considered to be emitted as a series of waves in all directions. The following properties can be defined for light by considering the wave nature.
Wavelength (λ): The distance between two successive similar points on a wave is called as wavelength. It is denoted by λ.
Units: cm, Angstroms (Ao), nano meters (nm), milli microns (mµ) etc.,
Note:
1 Ao = 10-8 cm.
1 nm= 10-9m = 10-7cm
Frequency (ν): The number of vibrations done by a particle in unit time is called frequency. It is denoted by 'ν'.
Units: cycles per second = Hertz = sec-1
Velocity (c): Velocity is defined as the distance covered by the wave in unit time. It is denoted by 'c'.
Velocity of light = c = 3.0 x 108 m.sec-1 = 3.0 x 1010 cm.sec-1
Note: For all types of electromagnetic radiations, the velocity is a constant value. The relation between velocity (c), wavelength (λ) and frequency (ν) can be given by following equation.
velocity = frequency x wavelength
c = νλ
Wave number (): The number of waves spread in a length of one centimeter is called wave number. It is denoted by . It is the reciprocal of wavelength, λ.
units: cm-1, m-1
Amplitude: The distance from the midline to the peak or the trough is called amplitude of the wave. It is usually denoted by 'A' (a variable). Amplitude is a measure of the intensity or brightness of light radiation.
PARTICLE NATURE OF LIGHT
Though most of the properties of light can be understood by considering it as a wave, some of the properties of light can only be explained by using particle (corpuscular) nature of it. Newton considered light to possess particle nature. In the year 1900, in order to explain black body radiations, Max Planck proposed Quantum theory by considering light to possess particle nature.
PLANCK'S QUANTUM THEORY
Black body: The object which absorbs and emits the radiation of energy completely is called a black body. Practically it is not possible to construct a perfect black body. But a hollow metallic sphere coated inside with platinum black with a small aperture in its wall can act as a near black body. When the black body is heated to high temperatures, it emits radiations of different wavelengths.
The following curves are obtained when the intensity of radiations are plotted against the wavelengths, at different temperatures.
Following are the conclusions that can be drawn from above graphs.
1) At a given temperature, the intensity of radiation increases with wavelength and reaches a maximum value and then starts decreasing.
2) With increase in temperature, the wavelength of maximum intensity (λmax) shifts towards lower wavelengths. According to classical physics, energy should be emitted continuously and the intensity should increase with increase in temperature. The curves should be as shown by dotted line.
In order to explain above experimental observations Max Planck proposed the following theory.
Quantum theory:
1) Energy is emitted due to vibrations of charged particles in the black body.
2) The radiation of energy is emitted or absorbed discontinuously in the form of small discrete energy packets called quanta
3) Each quantum is associated with definite amount of energy which is given by the equation E=hν.
Where
h = planck's constant = 6.625 x 10-34 J sec = 6.625 x10-27 erg sec
ν= frequency of radiation
4) The total energy of radiation is quantized i.e., the total energy is an integral multiple of hν. It can only have the values of 1 hν or 2 hν or 3 hν. It cannot be the fractional multiple of hν.
5) Energy is emitted and absorbed in the form of quanta but propagated in the form of waves.
EINSTEIN'S GENERALIZATION OF QUANTUM THEORY
Einstein generalized the quantum theory by applying it to all types of electromagnetic radiations. He explained photoelectric effect using this theory.
Photoelectric Effect: The ejection of electrons from the surface of a metal, when the metal is exposed to light of certain minimum frequency, is called photoelectric effect
The frequency of light should be equal or greater than a certain minimum value characteristic of the metal. This is called threshold frequency, νo
The photoelectric effect cannot be explained by considering the light as wave. Einstein explained photoelectric effect by applying quantum theory as follows:
1. All electromagnetic radiations consists of small discrete energy packets called photons. These photons are associated with definite amount of energy given by the equation E=hν.
2. Energy is emitted, absorbed as well as propagated in the form of photons only.
3. The electron is ejected from the metal, only when a photon of sufficient energy strikes the electron. When a photon strikes the electron, some part of the energy of photon is used to free the electron from the attractive forces in the metal atom and the remaining part is converted into kinetic energy.
hν = W + K.E
Where
W = energy required to overcome the attractions
K.E = kinetic energy of the electron
Since the frequency corresponding to the minimum energy required to overcome the attraction is called threshold frequency, νo, the above equation can be written as:
hν = hνo + K.E
or
K.E = hνo- hν = h(νo- ν)
< Early Atomic models Atomic structure: TOC Hydrogen atomic spectrum >
Author: Aditya vardhan Vutturi
|
__label__pos
| 0.996864 |
Satellites Orbiting Earth
How a Satellite Works
Satellites are very complex machines that require precise mathematical calculations in order for them to function. The satellite has tracking systems and very sophisticated computer systems on board. Accuracy in orbit and speed are required for the satellite to keep from crashing back down to Earth. There are several different types of orbits that the satellite can take. Some orbits are stationary and some are elliptical.”Satellite Orbit”
Low Earth Orbit
A satellite is in “Low Earth Orbit” when it circles in an elliptical orbit close to Earth. Satellites in low orbit are just hundreds of miles away. These satellites travel at high speeds preventing gravity from pulling them back to Earth. Low Orbit Satellites travel approximately 17,000 miles per hour and circle the Earth in an hour and a half.
Polar Orbit
This is how a satellite travels in a polar orbit.
This is how a satellite travels in a polar orbit. These orbits eventually pass the entire surface of the Earth.
Polar Orbiting Satellites circle the planet in a north-south direction as Earth spins beneath it in an east-west direction. Polar Orbits enable satellites to scan the entire surface of the Earth. Like pealing an orange peal in a circular motion from top to bottom. Remote sensing satellites, weather satellites, and government satellites are almost always in polar orbit because of the coverage. Polar orbits cover the Earth’s surface thoroughly. The polar obit occupied by a satellite has a constant location in which it passes over. ALL POLAR ORBITING SATELLITES INTERSECT The North Pole at their same point. While one Polar orbit satellite is over America, another Polar Satellite is passing over the North Pole. So the North Pole has a constant flow of UHF and higher microwaves hitting it. The illustration shows that the common passing point for Polar Orbiting Satellites is over the North Pole.
A polar orbiting satellite will pass over the Earths equator at a different longitude on each of its orbits; however, Polar Orbiting satellites pass over the North Pole every time. Polar orbits are often used for earth mapping, earth observation, weather satellites, and reconnaissance satellites. This orbit has a disadvantage. No one spot of the Earth’s surface can be sensed continuously from a satellite in a polar orbit.
This is from U.S. Army Information Systems Engineering Command.
“In order to fulfill the military need for protected communication service, especially low probability of intercept/detection (LPI/LPD), to units operating north of 65 degree northern latitude, the space communications architecture includes the polar satellite system capability. An acceptable approach to achieving this goal is to fly a low capacity EHF system in a highly elliptical orbit, either as a hosted payload or as a “free-flyer,” to provide service during a transition period, nominally 1997-2010. A single, hosted EHF payload is already planned. Providing this service 24 hours-a-day requires a two satellite constellation at high earth orbit (HEO). Beyond 2010, the LPI/LPD polar service could continue to be provided by a high elliptical orbit HEO EHF payload, or by the future UHF systems.” (quote from www.fas.org)
THERE IS A CONSTANT 24 HOUR EHF AND HIGHER MICROWAVE TRANSMISSION PASSING OVER THE NORTH POLE!
“Geo Synchronous” Orbit
This is how a satellite travels in a Equitorial orbit
This is how a satellite travels in a “Geo Synchronous” orbit. Equatorial orbits are also called “Geostationary”. These satellites follow the rotation of the Earth.
A satellite in a “Geo Synchronous” orbit hovers over one spot and follows the Earths spin along the equator. Go to this link for more information on “Geo synchronous Orbits”. Earth takes 24 hours to spin on its axis. In the illustration you can see that an “Geo Synchronous” Orbit follows the equator and never covers the North or South Poles. The footprints of “Geo Synchronous” orbiting satellites do not cover the polar regions, so communication satellites in “Geo Synchronous” orbits in cannot be accessed in the northern and southern polar regions.
Because the “Geo Synchronous” satellite does not move from the area that it covers, these satellites are used for telecommunications, gps trackers, television broadcasting, government, and internet. Because they are stationary, their orbits are much farther from the Earth than the Polar orbiting satellites. If a stationary satellite is too close to the Earth, it will crash back down at a faster rate. They say there are about 300 “Geo Synchronous” satellites in orbit right now. Of course, these are the satellites that the public is allowed to know about, that are not governmentally classified.
Satellite Anatomy
This is the Atatomy of a Satellite.
This is the Anatomy of a Satellite.
A satellite is made up of several instruments that work together to operate the satellite during its mission. This illustration to the left demonstrates the parts of a satellite.
The command and data system controls all of the satellite functions. This is a very complex computer system that communicates all of the satellite flight operations, where the satellite points, and any other mathematical operations.
The Pointing control directs the satellite in order for the satellite to keep a steady flight path. This system is a complex sensor instrument that keeps the satellite pointing in the same direction. The satellite uses a propulsion system called “momentum wheels” that adjusts the position of the satellite into its proper place. Scientific observation satellites have more precise propulsion systems than do communications satellites.
The Communications system has a transmitter, a receiver, and various antennas to transmit data to the Earth . On Earth, Ground control sends instructions and data to the satellite’s computer through the Antenna. Pictures, data, television, radio, and many other data is sent by the satellite back to practically everyone on Earth.
The Power system needed power and operate the satellite is an efficient solar panel array that obtains energy from the Sun’s rays. Solar arrays make electricity from the sunlight and store the electricity in rechargeable batteries.
The Payload is what a satellite needs to perform its job. A weather satellite would have a payload that consist of an Image sensor, digital camera, telescope, and other thermal and weather sensing devices.
The Thermal Control is the protection required to prevent damage to the satellite’s instrumentation and components in. Satellite are exposed to extreme temperature changes. Temperatures range from 120 degrees below zero to 180 degrees above zero. Heat distribution units and thermal blankets to protect the electronics and components from temperature damage.
Satellite Footprints
A single satellite footprint
Here you can see one footprint covers an enormous area.
Geostationary satellites have a very broad view of Earth. The footprint of one Echo Starbroadcast satellite covers almost all of North America. They stay over the Earth at same the same location so we always know where they are. Direct contact with the satellite can be made because Equatorial Satellites are fixed.
Many communications satellites travel in Equatorial orbits, including those that relay TV signals into our homes; However, the size of the footprint of one satellite covers the entire Northern America.
The multi path effect that occurs when satellite transmissions are obstructed by topographical entities also provides insight on microwave global warming. Microwaves are being bombarded upon our planet. Our planet absorbs and obstructs the waves from space. Microwaves penetrate through all of our atmosphere and bounce and echo off of the Earth. Imagine the footprint overlaps that are being produced by the thousands of satellites in orbit right now?
coverage 8 pic
Here you can see the footprint overlapping the that satellites make. Each satellite covers an enormous area.
The closer the satellite is to something the more power will be exerted on the object. The farther the waves have to go the less power they will have. Because the atmosphere is so much closer to the satellite, there is a stronger beam of energy going through the clouds and atmosphere. This stronger power causes a higher rate of warming in the atmosphere than it does on the surface of the Earth.
The illustration to the right shows how eight satellites microwave an enormous part of our Earth. When the radio signals reflect off of surrounding terrain; buildings, canyon walls, hard ground multi path issues occur due to multiple waves doubling over themselves. These delayed signals can cause poor signals. Ultimately, the water, ice, and Earth are absorbing and reflecting microwaves in many different directions. Microwaves passing through Earths atmospheres are causing radio frequency heating at the molecular level.
System spectral efficiency
“In wireless networks, the system spectral efficiency is a measure of the quantity of users or services that can be simultaneously supported by a limited radio frequency bandwidth in a defined geographic area.” The capacity of a wireless network can be measured by calculating the maximum simultaneous phone calls over 1 MHz frequency spectrum. This is measured in Erlangs//MHz/cell, Erlangs/MHz/sector, Erlangs/MHz/site, or Erlangs/MHz/km measurements. Modern day cell phones take advantage of this type of transmission. These cell phones transmit a microwave transmission that is twice the frequency of a microwave oven in your home.
This is a misconception of how microwave frequencies travel.
This is a misconception of how microwave frequencies travel.
An example of a spectral efficiency can be found in the satellite RADARSAT-1. In 1995 RADARSAT-1, an Earth observation satellite from Canada, was launched in an orbit above the Earth. RADRASAT-1 provides images of the Earth, scientific and commercial, used in agriculture, geology, hydrology, arctic surveillance, oceanography, cartography, ice and ocean monitoring, forestry, detecting ocean oil slicks, and many other applications. This satellite uses continuous high microwave transmissions. A Synthetic Aperture Radar (SAR) system is a type of sensor that images the Earth at a single microwave frequency of 5.3 GHz. SAR systems transmit microwaves towards the surface of the Earthy and record the reflections from the surface. This satellite can image the Earth during any time and in any atmospheric condition.
This is how microwave frequencies travel
This is how microwave frequencies actually travel.
A Common misconception about microwave transmissions is that the transmission is directly beaming straight into the receiving antennae. (See misconception illustration) This however, is not true. Transmissions are spread into the air in a spherical direction. The waves travel in every direction until they find a receiver or some dielectric material to pass into.
When a microwave transmission is sent to a receiving satellite dish the transmission is sent in a spherical direction. (See how microwaves travel illustration) The signal passes through all parts of that sphere until it finds a connection. All microwaves, not received by an antennae, pass through the dielectric material in the earth. Dielectric material is primarily water and ice.
Advertisements
The Celestial Sphere
Humans perceive in Euclidean space -> straight lines and planes. But, when distances are not visible (i.e. very large) than the apparent shape that the mind draws is a sphere -> thus, we use a spherical coordinate system for mapping the sky with the additional advantage that we can project Earth reference points (i.e. North Pole, South Pole, equator) onto the sky. Note: the sky is not really a sphere!
From the Earth’s surface we envision a hemisphere and mark the compass points on the horizon. The circle that passes through the south point, north point and the point directly over head (zenith) is called the meridian.
This system allows one to indicate any position in the sky by two reference points, the time from the meridian and the angle from the horizon. Of course, since the Earth rotates, your coordinates will change after a few minutes.
The horizontal coordinate system (commonly referred to as the alt-az system) is the simplest coordinate system as it is based on the observer’s horizon. The celestial hemisphere viewed by an observer on the Earth is shown in the figure below. The great circle through the zenith Z and the north celestial pole P cuts the horizon NESYW at the north point (N) and the south point (S). The great circle WZE at right angles to the great circle NPZS cuts the horizon at the west point (W) and the east point (E). The arcs ZN, ZW, ZY, etc, are known as verticals.
The two numbers which specify the position of a star, X, in this system are the azimuth, A, and the altitude, a. The altitude of X is the angle measured along the vertical circle through X from the horizon at Y to X. It is measured in degrees. An often-used alternative to altitude is the zenith distance, z, of X, indicated by ZX. Clearly, z = 90 – a. Azimuth may be defined in a number of ways. For the purposes of this course, azimuth will be defined as the angle between the vertical through the north point and the vertical through the star at X, measured eastwards from the north point along the horizon from 0 to 360°. This definition applies to observers in both the northern and the southern hemispheres.
It is often useful to know how high a star is above the horizon and in what direction it can be found – this is the main advantage of the alt-az system. The main disadvantage of the alt-az system is that it is a local coordinate system – i.e. two observers at different points on the Earth’s surface will measure different altitudes and azimuths for the same star at the same time. In addition, an observer will find that the star’s alt-az coordinates changes with time as the celestial sphere appears to rotate.
Celestial Sphere:
To determine the positions of stars and planets on the sky in an absolute sense, we project the Earth’s spherical surface onto the sky, called the celestial sphere.
The celestial sphere has a north and south celestial pole as well as a celestial equator which are projected reference points to the same positions on the Earth surface. Right Ascension and Declination serve as an absolute coordinate system fixed on the sky, rather than a relative system like the zenith/horizon system. Right Ascension is the equivalent of longitude, only measured in hours, minutes and seconds (since the Earth rotates in the same units). Declination is the equivalent of latitude measured in degrees from the celestial equator (0 to 90). Any point of the celestial (i.e. the position of a star or planet) can be referenced with a unique Right Ascension and Declination.
The celestial sphere has a north and south celestial pole as well as a celestial equator which are projected from reference points from the Earth surface. Since the Earth turns on its axis once every 24 hours, the stars trace arcs through the sky parallel to the celestial equator. The appearance of this motion will vary depending on where you are located on the Earth’s surface.
Note that the daily rotation of the Earth causes each star and planet to make a daily circular path around the north celestial pole referred to as the diurnal motion.
|
__label__pos
| 0.946131 |
Chiropractic and Bedwetting
Aug 18, 2022
Chiropractic
Welcome to McKinnon Marie, your trusted source for alternative and natural medicine. In this article, we will explore how chiropractic care can help with bedwetting issues, providing you with a comprehensive understanding of the topic.
Understanding Bedwetting
Bedwetting, medically known as nocturnal enuresis, is a common issue, especially in children. It refers to involuntary urination during sleep. While it can be distressing for both children and parents, it is important to remember that bedwetting is typically a developmental phase that most children outgrow with time.
How Chiropractic Care Can Help
Chiropractic care offers a holistic approach to addressing bedwetting concerns. By focusing on the nervous system and overall spinal health, chiropractors can identify and correct any potential underlying issues contributing to the problem.
The Spine and Nervous System Connection
The spine plays a crucial role in the proper functioning of the nervous system. Misalignments or subluxations in the spine can disrupt communication between the brain and other parts of the body, potentially affecting bladder control. Chiropractic adjustments aim to realign the spine, allowing for optimal nerve function and restoring balance to the body.
Reducing Interference and Restoring Balance
Chiropractors use gentle, non-invasive techniques to address spinal misalignments. These adjustments promote proper nerve flow, enhancing the function of the bladder and reducing bedwetting episodes. By restoring balance to the body, chiropractic care provides a natural and drug-free solution for individuals struggling with bedwetting.
The Benefits of Chiropractic Care for Bedwetting
Choosing chiropractic care for bedwetting offers several advantages:
• Non-Invasive: Chiropractic adjustments are gentle and non-invasive, making them a safe option for children and adults alike.
• Addressing Underlying Causes: Chiropractors focus on identifying and resolving the root cause of bedwetting, rather than just treating the symptoms.
• Drug-Free Solution: Chiropractic care provides a natural alternative to medication, reducing the need for pharmaceutical intervention.
• Improving Overall Well-being: Through spinal adjustments, chiropractic care promotes overall health and well-being, supporting the body’s ability to function optimally.
• Complementary Approach: Chiropractic care can be used alongside other treatments or therapies, enhancing their effectiveness.
Consult with Our Experts at McKinnon Marie
At McKinnon Marie, we take a patient-centered approach to alternative and natural medicine. Our experienced chiropractors specialize in addressing bedwetting concerns and providing comprehensive care.
If you or your child are experiencing bedwetting issues, we invite you to schedule a consultation with our team. Our chiropractors will assess your specific situation, develop a personalized treatment plan, and guide you on a journey towards improved well-being.
Trust McKinnon Marie for exceptional alternative and natural medicine solutions. Contact us today to learn more about chiropractic care for bedwetting.
Jayson Jeffries
Great info on bedwetting!
Nov 8, 2023
Mike Dempsey
I never knew chiropractic care could be related to bedwetting. It's fascinating to learn about these potential connections.
Aug 4, 2023
Steven Gerhardt
I've always been curious about alternative medicine. This article provides valuable insight into the potential benefits of chiropractic care for bedwetting.
Jul 4, 2023
Tim Hopper
I appreciate the detailed explanation of how chiropractic care can provide relief for bedwetting. It's an eye-opening read.
Apr 7, 2023
Jason Threat
As a parent, I'm eager to learn about non-invasive solutions for bedwetting. This article offers valuable information.
Mar 20, 2023
Jeff Emmot
The potential link between chiropractic care and bedwetting is intriguing. I'm eager to learn more about this connection.
Feb 10, 2023
Mecca Robbins
Interesting read. I appreciate the comprehensive explanation of how chiropractic care can potentially help with bedwetting.
Jan 23, 2023
Xavier Luna
Thanks for shedding light on this issue. It's important to explore alternative treatments for bedwetting.
Jan 22, 2023
Kim Guinn
I've heard about the effectiveness of chiropractic care for various issues, so it's great to see it explored in the context of bedwetting.
Dec 4, 2022
Al Venzon
It's great to see alternative medicine being explored for common issues like bedwetting. Thanks for bringing attention to this topic.
Oct 21, 2022
Jamie Lowe
This is a fascinating topic! I've never considered the connection between chiropractic care and bedwetting before.
Oct 13, 2022
|
__label__pos
| 0.511192 |
Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Screen reader users: click this link for accessible mode. Accessible mode has the same essential features but works better with your reader.
Patents
1. Advanced Patent Search
Publication numberUS7598037 B2
Publication typeGrant
Application numberUS 11/485,203
Publication dateOct 6, 2009
Filing dateJul 12, 2006
Priority dateSep 27, 2005
Fee statusPaid
Also published asUS7863003, US20070072213, US20100041570
Publication number11485203, 485203, US 7598037 B2, US 7598037B2, US-B2-7598037, US7598037 B2, US7598037B2
InventorsAlexander N. Perov, Darrell P. Chandler
Original AssigneeU Chicago Argonne, Llc
Export CitationBiBTeX, EndNote, RefMan
External Links: USPTO, USPTO Assignment, Espacenet
Method for implementing non-destructive quality control of substrates and printed biological microarrays
US 7598037 B2
Abstract
A method and apparatus are provided for implementing non-destructive quality control of substrates and printed biological microarrays. A method and apparatus are provided for implementing quality control of gel-based microarrays prepared by dispensing a gel-forming composition on a solid substrate. The method utilizes the difference between the wettability properties of a supporting substrate and a gel, where the gel is hydrophilic. Condensation of vapor of a chemically inert water-soluble liquid, such as water or glycerol, on the surface of a substrate under inspection creates a layer of tiny droplets that affect both transmission and scattering of light on the surface. A pattern of condensation, characterized by spatial distribution, average size of the droplets and spacing between the droplets, reflects variation in wetting properties of the substrate. The pattern of condensation circumscribes printed microarray features to be non-destructively imaged and analyzed.
Images(4)
Previous page
Next page
Claims(16)
1. A method for implementing non-destructive quality control of substrates for receiving microarray features of biological microarrays in an automated machine vision system, said method comprising the steps of:
creating a layer of condensate droplets of a chemically inert water-soluble liquid on a surface of a substrate under inspection; said condensate droplets being densely spaced droplets having an average size substantially less than the microarray features; said layer of condensate droplets affecting both transmission and scattering of light on the surface; said layer of said condensate droplets of said chemically inert water-soluble liquid evaporating without any residue;
illuminating said surface of said substrate under inspection;
detecting an image of said illuminated surface of said substrate under inspection; and
identifying a pattern of condensate droplets from said detected image of said surface of said substrate under inspection, said pattern characterized by spatial distribution, average size of the droplets and spacing between the droplets, reflecting variation in wetting properties of the substrate; and utilizing said identified pattern with the automated machine vision system for visually detecting an area indicating presence of undesirable variation of wettability and rejecting said substrate under inspection, responsive to detecting the area indicating presence of undesirable variation of wettability.
2. A method for implementing non-destructive quality control of substrates for biological microarrays as recited in claim 1 wherein the step of creating a layer of condensate droplets includes using water for said chemically inert water-soluble liquid.
3. A method for implementing non-destructive quality control of substrates for biological microarrays as recited in claim 1 wherein the step of creating a layer of condensate droplets includes using glycerol for said chemically inert water-soluble liquid.
4. A method for implementing non-destructive quality control of substrates for biological microarrays as recited in claim 1 wherein said chemically inert water-soluble liquid is in a vapor phase and wherein the steps of creating a layer of condensate droplets includes providing said surface of said substrate under inspection within a thermally insulated chamber, and flowing carrier gas through said chamber, said carrier gas transporting said chemically inert water-soluble liquid in vapor phase.
5. A method for implementing non-destructive quality control of substrates for biological microarrays as recited in claim 4 wherein the step of flowing carrier gas through said chamber includes using a selected one of air or nitrogen for said carrier gas.
6. A method for implementing non-destructive quality control of substrates for biological microarrays as recited in claim 1 wherein the steps of identifying a pattern of condensate droplets on said surface of said substrate under inspection includes illuminating said surface of said substrate under inspection, collecting a digital image, and filtering said digital image.
7. A method for implementing non-destructive quality control of substrates for biological microarrays as recited in claim 6 further includes performing digital analysis of said digital image.
8. A method for implementing non-destructive quality control of substrates for biological microarrays as recited in claim 7 further includes calculating statistical characteristics and metrics for at least a portion of said digital image to identify characteristic features associated with non-uniform wettability, localized contaminations and dust particles.
9. A method for implementing non-destructive quality control of substrates for biological microarrays as recited in claim 8 further includes rejecting said substrate responsive to said calculated characteristics and metrics being outside predefined upper and lower tolerance margins; and further includes experimentally determining said predefined upper and lower tolerance margins.
10. A method for implementing non-destructive quality control of substrates for biological microarrays as recited in claim 8 further includes calculating a histogram for said digital image; and calculating a standard deviation for at least a portion of said histogram for said digital image.
11. A method for implementing non-destructive quality control of printed biological microarrays in an automated machine vision system, said method comprising the steps of:
creating a layer of condensate droplets of a chemically inert water-soluble liquid on a surface of a microarray under inspection; said condensate droplets being densely spaced droplets having an average size of at least ten times smaller than microarray features said layer of condensate droplets affecting both transmission and scattering of light on the surface; said layer of said condensate droplets of said chemically inert water-soluble liquid evaporating without any residue;
illuminating said surface of said microarray under inspection;
detecting an image of said illuminated surface of said microarray under inspection; and
identifying a pattern of condensate droplets from said detected image of said surface of said microarray under inspection, said pattern characterized by spatial distribution, average size of the droplets and spacing between the droplets, reflecting variation in wetting properties of said surface of said microarray; and utilizing said identified pattern with the automated machine vision system for visually detecting a presence of undesirable variation of microarray features; and rejecting said microarray under inspection responsive to visually detecting the presence of undesirable variation of microarray features.
12. A method for implementing non-destructive quality control of printed biological microarrays as recited in claim 11 wherein said chemically inert water-soluble liquid includes a selective one of water and glycerol.
13. A method for implementing non-destructive quality control of printed biological microarrays as recited in claim 11 wherein said chemically inert water-soluble liquid is in a vapor phase and wherein the steps of creating a layer of condensate droplets includes providing said surface of said substrate under inspection within a thermally insulated chamber, and flowing carrier gas through said chamber, said carrier gas transporting said chemically inert water-soluble liquid in vapor phase; said carrier gas including a selected one of air or nitrogen.
14. A method for implementing non-destructive quality control of printed biological microarrays as recited in claim 11 wherein the step of identifying a pattern of condensate droplets on said surface of said microarray under inspection further includes the steps of collecting and processing said image to circumscribe said microarray features to be inspected for presence of said microarray features, morphology of said microarray features, pitch of said microarray features, and regularity of said microarray features.
15. A method for implementing non-destructive quality control of printed biological microarrays as recited in claim 14 further includes processing said image to circumscribe microarray features to be inspected for predefined quantifiable attributes of said microarray features.
16. A method for implementing non-destructive quality control of printed biological microarrays as recited in claim 11 wherein said microarrays are gel-based microarrays.
Description
This application claims the benefit of U.S. Provisional Application No. 60/721,041, filed on Sep. 27, 2005.
CONTRACTUAL ORIGIN OF THE INVENTION
The United States Government has rights in this invention pursuant to Contract No. W-31-109-ENG-38 between the United States Government and Argonne National Laboratory.
FIELD OF THE INVENTION
The present invention relates to a method and apparatus for the quality control of printed microarrays. More specifically, this invention relates to a method and apparatus for implementing non-destructive quality control of solid substrates for biological microarrays; and a method and apparatus for implementing quality control of microarrays fabricated by contact or non-contact deposition techniques. A preferred embodiment of the invention pertains to quality control of gel-element microarrays, typically prepared by dispensing a gel-forming composition on a solid substrate, such as glass or plastic surfaces.
DESCRIPTION OF THE RELATED ART
Variations in substrate quality, for example, chemical or physical non-uniformities, substantially affect the quality of microarrays during the printing process, significantly decrease the yield of useable microarrays from any one manufacturing lot, and cause substantial variability in their bio-analytical characteristics and response or irreproducibility of their analytical characteristics. Likewise, variations in microarray feature quality, for example, spot morphology or probe density, substantially affect microarray bio-analytical characteristics and response or irreproducibility of their analytical characteristics.
A rapid and non-destructive method and decision criteria for substrate and microarray feature quality control and quality assurance is therefore required in order to improve overall manufacturing process control, and subsequent reproducibility and performance of microarrays.
Known methods of substrate characterization rely either on sophisticated equipment such as atomic force microscope or infrared Fourier spectrometers, or test printing on certain selected slides. None of these techniques are rapid, reliable, or non-destructive. Known methods for characterizing microarray features on printed microarrays include staining with fluorescent dyes, or functional tests of selected microarrays from individual batches. In either case, the present methods do not allow non-destructive, quantitative, thorough inspection of each and every substrate and each and every microarray, which is the preferred solution for production scale-up and successful commercialization of microarray-based diagnostic tests.
In order to illustrate the present invention, we describe methods and techniques for quality control and quality assurance of gel-element microarrays, manufactured via co-polymerization chemistry and conventional contact printing robotics on either glass or plastic substrates. A preferred embodiment for performing substrate and microarray inspection is an optical system that can detect and quantify missing, deformed or misplaced array elements as well as particles of dirt or other contamination on the microarray substrate. For those skilled in the art and in the spirit of the invention, however, it is understood that the invention is broadly applicable to many types of printed microarrays and substrates.
Typical gel compositions used to form the elements of a gel-element microarray are transparent, colorless, rather thin (<10 micron), and have a refractive index that does not differ much from that of glass or plastic. For this reason, gel-element features are very difficult to visualize other than by staining them with some dye, a procedure that usually leaves the microarray contaminated and unsuitable for subsequent diagnostic tests or biological analyses.
Important objects of the present invention are to provide a method and apparatus for implementing non-destructive quality control of substrates for biological microarrays.
Important objects of the present invention are to provide a method and apparatus for implementing quality control of microarray features deposited by contact and non-contact printing methods.
Important objects of the present invention are to provide a method and apparatus for implementing quality control of gel-based microarrays prepared by dispensing a gel-forming composition on a solid substrate.
Other important aspects of the present invention are to provide such method and apparatus for implementing non-destructive quality control of substrates for biological microarrays; such method and apparatus for implementing quality control of microarray features deposited by contact and non-contact printing methods; and such method and apparatus for implementing quality control of gel-based microarrays prepared by contract dispensing a gel-forming composition on a solid substrate; each substantially without negative effect and that overcome some of the disadvantages of prior art arrangements.
SUMMARY OF THE INVENTION
In brief, a method and apparatus are provided for implementing non-destructive quality control of substrates and for implementing non-destructive quality control of printed microarrays. Condensation of vapor of a chemically inert water-soluble liquid, such as water vapor or another chemically neutral and relatively volatile liquid, such as glycerol, on the surface of a substrate under inspection creates a layer of tiny droplets that affect both transmission and scattering of light on the surface. A pattern of condensation, characterized by spatial distribution, average size of the droplets and spacing between the droplets, is used to identify variation in wetting properties of the substrate.
The method of the invention enables the detection, visually or by machine, of areas of a specific type of vapor condensation on the printed microarray, which indicates the presence of undesirable variations of wettability and/or substrate contaminations, and circumscribes microarray features to be inspected for presence and absence, morphology, pitch regularity, and other geometrical and quantifiable attributes.
In accordance with features of the invention, in more hydrophobic regions the droplets are smaller and more densely spaced, so these regions are brighter in reflected light and less transparent in transmitted light. These variations in brightness and transparency are distinct and are easily observed and analyzed directly by the operator or by means of an automated machine vision system. The test is non-destructive as the condensate readily evaporates and leaves both the substrate and microarray features uncontaminated.
A method and apparatus are provided for implementing quality control of microarrays prepared by dispensing a gel-forming composition on a solid substrate. The method utilizes the difference between wettability properties of the solid substrate and a gel, where the gel is hydrophilic. Condensation of water vapor on a solid substrate surface results in formation of multiple densely spaced small droplets on the surface between the array elements while the array elements remain clear. Since the droplets reduce transmittance of the substrate due to light scattering, the array becomes visible in both transmitted and reflected light. Evaluation of the array quality is performed visually by the operator using a microscope or with an automated machine vision system. Since the condensate evaporates without any residue, the test is non-destructive.
In accordance with features of the invention, the method of the invention enables automating the quality control of microarray substrates and printed microarrays, enabling decision making of acceptance or rejection of substrates and completely fabricated microarrays based on analysis of the digital image of a condensation pattern.
BRIEF DESCRIPTION OF THE DRAWINGS
The present invention together with the above and other objects and advantages may best be understood from the following detailed description of the preferred embodiments of the invention illustrated in the drawings, wherein:
FIG. 1 is a schematic and block diagram representation illustrating apparatus for implementing methods for non-destructive quality control of substrates for biological microarrays; for implementing methods for quality control of microarray features deposited by contact and non-contact printing; and for implementing methods for quality control of gel-based microarrays prepared by contract printing of a gel-forming composition on a glass or plastic substrate in accordance with the preferred embodiment;
FIGS. 2A and 2B respectively are a substrate image histogram with signal intensity shown along a horizontal axis and number of pixels shown along a vertical axis, and a display of a region of interest (ROI) together illustrating defects of microarray substrates and characteristic features of the substrate image histogram associated with the defects detected with the apparatus of FIG. 1 in accordance with the preferred embodiment; and
FIG. 3 is a flow chart illustrating exemplary steps for implementing methods for non-destructive quality control of substrates for biological microarrays in accordance with the preferred embodiment.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
As used in the following description and claims, the following definitions apply:
A biological microarray is defined herein as an array of biomolecular probes immobilized at spatially ordered locations on a solid substrate.
A biomolecular probe is defined as a synthetic or natural compound capable of specific interaction with biological molecules such as DNA, RNA, or protein.
Biomolecular probes may be delivered to the immobilization sites on the substrate by any known dispensing technique, either contact or non-contact.
The process of dispensing probes onto a substrate is defined as a printing method. Accordingly, microarrays fabricated by printing are referred to as printed microarrays, as opposed to microarrays fabricated by synthesizing the probes on the substrate, in situ. In the process of printing, the probes are typically dispensed on the substrates as one component of an aqueous solution.
In the preferred embodiment, the printing solution is a gel-forming composition, which, upon gel polymerization, considerably enhances the immobilization capacity of the substrate by creating a highly porous three-dimensional polymer structure directly on each immobilization site. Microarrays fabricated in this manner are referred to as gel-element or gel-based microarrays.
The material immobilized onto discrete sites on the substrate during microarray manufacture is defined as a microarray feature, which is in contradistinction to the surrounding surface of the substrate.
To allow high-density printing and improve feature morphology, the wettability of microarray substrates is typically adjusted to prepare a moderately hydrophobic surface, where the preferred contact angle for the printed solution is in the range of 40 to 80 degrees. The surface chemistry of the substrate is typically modified to provide conditions for either direct immobilization of the probes onto the substrate surface; or to immobilize discrete gel-elements onto the substrate surface. Optically, microarray substrates are preferably transparent, black or reflective. In each case, the substrate surface is normally polished to minimize undesirable light scattering.
Microarray substrates can consist of glass, for example a standard microscope slide, plastics or other materials, such as silicon or sapphire.
While the following detailed description generally refers to the condensation of water vapor, the present invention is not limited to the condensation of water vapor, it should be understood that a chemically inert water-soluble liquid, or chemically neutral and relatively volatile liquid, such as glycerol, could be used to implement methods of the invention. Likewise, it should be understood that the present invention is not limited to gel-element microarrays; it should be understood that various array surfaces and printed microarrays could be analyzed and assessed in accordance with the methods of the invention.
In accordance with features of the preferred embodiments, methods are provided for implementing non-destructive quality control of substrates and microarray features for biological microarrays. Condensation of water vapor on the surface of a substrate under inspection is provided to create a layer of tiny droplets that affect both transmission and scattering of light on that surface. The pattern of condensation, characterized by spatial distribution of average size of the droplets and spacing between them, reflects variations of wetting properties of the substrate: in more hydrophobic regions, the droplets are smaller and spaced more densely, so these regions are brighter in reflected light and less transparent in transmitted light. These variations of brightness and transparency are distinct and can be easily observed and analyzed either directly, by the operator, or by an automated machine vision or imaging system. The test is non-destructive as the condensate readily evaporates leaving the microarray uncontaminated.
The gel that forms the elements of gel-element arrays is transparent, colorless, thin, such as less than 10 micron, and has a refractive index that does not differ much from that of glass or plastic. For this reason, gel-based arrays are very difficult to visualize. Staining the gel-based arrays with some dye that could render them visible typically causes irreversible contamination of the array.
In accordance with features of the preferred embodiments, a quality-control method for mass production of gel-based microarrays manufactured by contact printing of gel-forming composition on glass or plastic substrates is provided that can detect missing, deformed or misplaced array elements as well as dust particles and other possible contaminations on the microarray substrate. In contrast to the gel-supporting surface, gel-elements are hydrophilic. Condensation of water vapor on the microarray results in formation of multiple densely spaced small droplets on the substrate surface between the array elements while the array elements remain clear. Since the droplets substantially reduce transmittance of the substrate due to increased light scattering, the microarray elements become distinctly visible and circumscribed in both transmitted and reflected light. Evaluation of the microarray quality can be performed either visually by the operator using a microscope or by means of an automated machine vision system. The test is non-destructive as the water vapor condensate evaporates without any residue.
Having reference now to the drawings, in FIG. 1 there is shown an exemplary automated quality control apparatus generally designated by the reference character 100 for implementing non-destructive quality control of substrates for biological microarrays and implementing non-destructive quality control for mass production of gel-based microarrays in accordance with the preferred embodiment.
Automated quality control apparatus 100 includes a computer 102 coupled to a detector such as a charge coupled device (CCD) camera 104. Automated quality control apparatus 100 includes a ring illuminator 106 and a positioner 108 provided with the CCD camera 104, for example, for sequentially illuminating a surface 110 of one substrate 112 under test. As shown in FIG. 1, each of the plurality of substrates 112 carries a respective pattern of printed microarray elements 114.
It should be understood that substrates 112 without microarray elements 114 advantageously are processed using the automated quality control apparatus 100 for implementing non-destructive quality control of substrates
Automated quality control apparatus 100 includes a thermally insulated chamber 120 that receives the plurality of substrates 112 carrying the respective microarray elements 114 with the surface 110 under test of each of the plurality of substrates 112 disposed within the chamber. A source of moist warm air, for example, having a temperature greater than room temperature, and the moist air having a dew point higher than the temperature of the substrate, is applied to an input port 122 of the thermally insulated chamber 120. A carrier gas at the input port 122 of the thermally insulated chamber 120, such as air, nitrogen, argon, or the like, transports a liquid in vapor phase, such as water vapor, glycerol vapor, or other liquid vapor. The thermally insulated chamber 120 includes an exhaust port 124 located at an opposite end from the input port 122. Condensation of water vapor is provided on the surface 110 of the substrate 112 under inspection to create a layer of tiny droplets that affect both transmission and scattering of light on that surface.
FIGS. 2A and 2B together illustrate exemplary defects of microarray substrates and characteristic features of the substrate image histogram associated with the defects detected with the apparatus 100. In FIGS. 2A and 2B, local contaminations and dust particles on a reverse side are illustrated. In the histogram of FIG. 2A, an arrow indicates a median.
In accordance with features of the preferred embodiments of the invention, automated quality control of substrates, such as illustrated in the exemplary steps of the flow chart of FIG. 3, advantageously is based on the following practical considerations:
Features of the substrate surface 110 that may affect sample transfer from the pin to the substrate and/or cause subsequent droplet migration are those with a characteristic linear scale comparable to or exceeding the mean droplet diameter used to form microarray features 114.
The largest droplets of the water vapor condensate are typically at least ten times smaller than the droplets of microarray elements 114.
Defects of the substrate working surface 110 can be classified into one of the following three categories: (1) relatively smooth variations of wettability due to inhomogeneous chemical activation; (2) localized spots of abnormally high wettability due to accidental chemical contamination; (3) particulate contaminations which are typically hydrophilic. In a condensation pattern recorded in reflected light, the latter two categories (2) and (3) give characteristic distinct dark spots.
Particulate contaminations on the reverse side of the substrate 112 should generally be considered as a reason for substrate rejection because they may readily be transferred to the working surfaces 110 in the process of substrate handling. In contrast to the particles on the working surface 110, those located on the reverse side of the substrate are bright in reflected light.
Referring now to FIG. 3, there are shown exemplary steps for implementing methods for non-destructive quality control of substrates for biological microarrays in accordance with the preferred embodiment starting with image processing at a block 300. First the image is smoothed using an appropriate imaging analysis technique such as a numerical filtering algorithm for calculating a moving average as indicated in a block 302. The purpose of filtering is to eliminate small-scale signal variations caused by light scattering on individual droplets of the condensate. Then the computer generates a histogram of the image as indicated in a block 304 and analyzes the image histogram to identify characteristic features associated with localized contaminations and dust particles, such as shown in FIG. 2.
Checking for a peak signal in a low intensity region and a high intensity region is performed as indicated in respective decision blocks 306 and 308. The substrate is rejected if a peak signal is identified in the low intensity region or the high intensity region as indicated in a block 309. If the substrate has not been rejected based on histogram analysis at decision blocks 306 and 308, its average wettability and spatial variations of the wetting properties are evaluated, for example, by calculating a median intensity as indicated in a block 310 and by calculating a standard deviation of the signal, as indicated in a block 314, respectively. At blocks 310 and 314, the calculations may be restricted to the Region of Interest (ROI) defined as a region on a substrate 112 designated for array printing. The calculated median and standard deviations are compared to predetermined tolerance margins as indicated in respective decision blocks 312 and 316. The substrate is accepted as indicated in a block 318 if both the median signal intensity and the standard deviation fall within tolerance margins that are assumed to be determined experimentally. The image processing is completed as indicated in a block 320.
Having reference again to FIG. 3, those skilled in the art will understand that various different pattern recognition techniques can be applied to a digital microarray image to extract information and create decision logic for quality control and quality assurance of printed microarrays.
While the present invention has been described with reference to the details of the embodiments of the invention shown in the drawing, these details are not intended to limit the scope of the invention as claimed in the appended claims.
Patent Citations
Cited PatentFiling datePublication dateApplicantTitle
US20020095073 *Nov 27, 2001Jul 18, 2002Jacobs Alice A.Clinically intelligent diagnostic devices and mehtods
US20040063098 *Sep 26, 2002Apr 1, 2004Hargreaves John S.Peptide or nucleic acid display; surface hydroxyl number by hydrolysis
US20050227358 *Apr 1, 2004Oct 13, 2005Mcentee John FMethods of determining a quality of an array substrate
Non-Patent Citations
Reference
1 *Taylor et al "Impact of surface chemistry and blocking stratagies on DNA microarrays" Nucleic Acids Research, 2004, vol. 31, No. 16e87.
Classifications
U.S. Classification435/6.11, 435/283.1, 435/287.2, 435/6.19, 422/68.1, 422/82.05, 435/288.7
International ClassificationC12M1/00, C12Q1/68, G01N15/06
Cooperative ClassificationG06T7/0004, C12Q1/6837, G06T2207/30072
European ClassificationG06T7/00B1, C12Q1/68B10A
Legal Events
DateCodeEventDescription
Mar 14, 2013FPAYFee payment
Year of fee payment: 4
Nov 3, 2006ASAssignment
Owner name: ENERGY, UNITED STATES DEPARTMENT OF, DISTRICT OF C
Free format text: CONFIRMATORY LICENSE;ASSIGNOR:UNIVERSITY OF CHICAGO, THE;REEL/FRAME:018482/0304
Effective date: 20060926
Sep 28, 2006ASAssignment
Owner name: U CHICAGO ARGONNE LLC, ILLINOIS
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:UNIVERSITY OF CHICAGO, THE;REEL/FRAME:018385/0618
Effective date: 20060925
Owner name: U CHICAGO ARGONNE LLC,ILLINOIS
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:UNIVERSITY OF CHICAGO, THE;US-ASSIGNMENT DATABASE UPDATED:20100309;REEL/FRAME:18385/618
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:UNIVERSITY OF CHICAGO, THE;US-ASSIGNMENT DATABASE UPDATED:20100225;REEL/FRAME:18385/618
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:UNIVERSITY OF CHICAGO, THE;US-ASSIGNMENT DATABASE UPDATED:20100316;REEL/FRAME:18385/618
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:UNIVERSITY OF CHICAGO, THE;US-ASSIGNMENT DATABASE UPDATED:20100323;REEL/FRAME:18385/618
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:UNIVERSITY OF CHICAGO, THE;US-ASSIGNMENT DATABASE UPDATED:20100427;REEL/FRAME:18385/618
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:UNIVERSITY OF CHICAGO, THE;US-ASSIGNMENT DATABASE UPDATED:20100511;REEL/FRAME:18385/618
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:UNIVERSITY OF CHICAGO, THE;REEL/FRAME:18385/618
Jul 12, 2006ASAssignment
Owner name: CHICAGO, THE UNIVERSITY OF, ILLINOIS
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:PEROV, ALEXANDER N.;CHANDLER, DARRELL P.;REEL/FRAME:018057/0693
Effective date: 20060710
|
__label__pos
| 0.667629 |
KinFitSim - a software package to fit kinetic data
Тип работы:
Реферат
Предмет:
Физико-математические науки
Узнать стоимость
Детальная информация о работе
Выдержка из работы
UDC 541. 14
KINFITSIM — A SOFTWARE PACKAGE TO FIT KINETIC DATA
SVIR I. B., KLYMENKO A. V., PLATZM. S.
A new software package, KinFitSim, for fitting and simulating kinetic data is presented. The KinFitSim package can be used in either chemical research or for educational purposes.
The KinFitSim package obtains the best-fit kinetic parameters — rate constants, amplitudes and others — to any selected chemical mechanism, displays the calculated and experimental absorbance versus time plots and presents the best fit data in a report to the user. The KinFitSim package has more mathematical possibilities for good kinetic and fitting simulations and a modern interface with new possibilities for users than previous packages that fit kinetic data such as KINSIM and KSIM.
The KinFitSim package consists of two general parts. The first part of the software package is a kinetic simulator (KS), which computes the time dependence of the concentrations of all species involved in a user defined reaction mechanism of any order, with defined rate constants of reactions. KS can work as a separate program. The second part of the software package is a fitting simulator (FS). FS computes the best-fit rate constants to experimental kinetic data and calculated results for a user selected reaction mechanism (in KS) by a non-linear regression procedure. FS starts it’s work after obtaining the calculated results in KS and loading the experimental data.
Kinetic Simulator (KS)
Reaction mechanism
In KS work the user first defines the reaction mechanism. Then the reaction scheme is solved to yield the corresponding ordinary differential equations (ODE) of the kinetic system.
Chemical reactions are conventionally presented by stoichiometric equations, which show the proportion of reacting species in the reaction. Thus the chemical reaction can be presented by equation [1]
Z aiYi = 0 (1)
where Yi is a chemical species, щ & gt- 0 for reaction products and & lt- 0 for reactants. a is a stoichiometric
vector, which can be written as, а = я- p where я and p are the positive vectors which correspond to products and reactants. In general we have several chemical reactions and the corresponding matrix a. Stoichiometric vectors of reactions are the columns of matrix a.
If j -th reaction goes with rate #j, then the concentration change can be written as
y = У0 +"#, (2)
where y is the concentrations vector and yo is the initial concentrations vector.
After differentiation of equation (2), we obtained the system of ODEs for the concentrations of all species:
y'- = ar, (3)
where r is a vector of reactions rates.
The rate expression can be written as
rj = kj П У?'-, (4)
i
where kj is a rate constant of j -th reaction. Simulation methods
The user then specifies several parameters such as the initial concentrations of reactants and rate constants, the desired numerical method for solving the ODE system and other parameters (run time, desired accuracy, etc.) to simulate the specified reaction mechanism with the selected method. Three general numerical methods are implemented in KS for solving the ODEs [1−4]: the Euler method, the Runge-Kutta method and Gear methods, including the Adams-Moulton method. These methods can solve both stiff and non-stiffODE systems.
The Euler and Runge-Kutta methods are one-step methods used for solving non-stiff systems of ODEs. A more complicated case is a stiff system of ODEs, which can not be solved by explicit Euler and Runge-Kutta methods. The Gear method was used for such systems. This Gear method is a modification of the Adams-Moulton method.
Definition of stiff ODE system.
The initial value problem
y- Ax y)=o- y (a) = yo- x є [a, b],
is stiff in segment I c [a, b], if for each x є I when the following conditions are held
1) Re (^) & lt- 0, i = 1,2,…, n-
2) S (x) = max Re (-li) / min Re (-li) & gt->- 1,
i =1,…, n / i=1,…, n
where Ai are the eigenvalues of Jacobian dfj dy, which are calculated in x point.
The ratio S (x) is called «the local stiffness coefficient» ofthe initial value problem. The stiff system is a problem with large Lipshitz constants or is a problem where there is a large difference between the time constants.
The corrector iterations in the stiff-stable Gear method must be performed with the Newton method. According to Newton’s method we must iteratively solve the linear systems of algebraic equations until the required accuracy is met.
132
РИ, 2001, № 1
Fitting Simulator (FS)
The second part of the KinFitSim package is FS, which includes KS as a subprogram. The least squares method is used to obtain the best fit to experimental data. When using FS one first inputs the experimental data and a reaction mechanism is specified. The user then selects the parameters to be used in the kinetic and data simulation, and chooses the method for the minimization procedure such as the gradient-search method or the Marquardt method [5−8].
The method of least squares
The method of least squares [5] is based on the hypothesis that the optimum description of a set of data is one that minimizes the weighted sum of the squares
of the deviation of the data y from the fitting function
y (tj). FS solves the minimization problem for the goodness-of-fit factor
2 N (І2
x = 2 wjyj -y (tj V, (5)
j=0 aeQ' v 7
where aj indicates a unit vector in the direction of the a j coordinate axis.
In order to determine the gradient, we estimate the partial derivatives numerically:
Vr2 & gt- aj-x4j
J j d aj Aaj '
where Aa j is a step size by which a j is changed in order to determine the derivative.
The gradient has both magnitude and dimensions and,
if the dimensions of the various parameters a j are not
the same (which is usually the case), the components of the gradient do not have the same dimensions. We
define dimensionless parameters bj by rescaling each
of the parameters a j using the step sizes Aa j as the scaling constants, so that
Q:
t1 & lt- a (& lt- a{U, i = 1,
(6)
bj =
aj
Aaj '
where y j are the measured variables, t j are the time values, wj is the weight of value yj, yf j) are values
of the function calculated at tj by KS, aand a (U
J l l
are lower and upper bounds of aj variation.
The method of least squares consists of determining the values ofthe unknown parameters aj, j = 1,…, m ofthe
function y (t) that yields a minimum for the function % 2
given in equation (5). For non-linear fitting problems, there are several ways of finding this minimum value. We use either the gradient-search method [5−8] or Marquardt method [5,6] for solving the above mentioned minimization problem.
Gradient-search method
In the gradient-search method of least squares [5], all the parameters a j are incremented simultaneously,
with relative magnitudes adjusted so that the resultant direction of travel in parameter space is along the gradient (or direction of maximum variation) of2. The gradient V2 is a vector that points in the direction in which у increases most rapidly and has components
2
in parameter space equal to the rate of change of % along each axis:
V — m
j=is aj
The derivative with respect to b j then becomes
^db~Aaj *2 (aj+Aaj)_^2 W.
Now we define the dimensionless gradient у with unit magnitude and components
yj
d2/Э bj
1
my 2 і 2
Тдх2/д bj i=1V
The direction that the gradient-search method follows is the direction of steepest descent, which is the opposite of the gradient у.
The main iterative formula of the gradient-search method is
aM = Jk)+Jk) dk), k = 0,1,^,
where k is the iteration index, c№ is the step size (adjustable coefficient) in the direction ofvector dJk).
The components of the vector & amp-/k) are
Scj = -yj Aaj.
The adjustable coefficient orA) is used at each iteration to avoid overshooting the minimum, which we search
РИ, 2001, № 1
133
for. The adjusting of or?'- begins by setting its to value unity. If the inequality
T2 [ a (k+1 j& lt-^2 [ Jk) j (7)
is met the value of c№ (and therefore the value of Jk+1) is accepted and a new iteration begins. In the
other case the value of the adjustable coefficient is divided by two and the inequality (7) is tested again. This
2
algorithm is used to ensure that function % decreases at each iteration.
The minimization procedure can drive the solution of the constraint region. A reasonable way to return to the range of parameter variation is a projection of the found
point Jk+1
onto the area Q. The new iteration formula in this case is
Jk+1 = +"*W), k = 0,1,… (8)
whereq (x) is a projection of the x point onto the region Q.
If q is a hyperparallelepiped (as in our case) the projection can be written as
Ыx) i
(/) ^ (/)
(l) ^ ^ (m)
Xj, aj & gt- & lt- Xj & lt- aj & gt-,
(m) ^ (m)
a} & gt-, Xj & gt- a}
/ 1 i
j = 1,…, m ,
(9)
Student i mine-
Date:
Solvent Temperature: r-Jcime of Precursor Laser Wavelength: Monitoring Wavelength:
Report
about KhtFitSint results
Alexey Klyiiieuko 11 05 01 15: 28 13
3501
Mechanism name: Altsorbancc (350 nm)
At K 11 & gt-?L 2. At Ki2 & gt-C t 3. 2Bt & gt-D
K-] K-2 K-3
Output equations: A* X + R*X2 + C*X?& gt-+D*XЛ
Applied methods in KS Ruler FS: Отжііеі il -seal'-d i
Initial parameters vain es
I Optimized parameters values
K+l 3R6 K+l 3 233 928
Ki2 1H5 К12 99 380. 82
K+3 1R5 K+3 93 775. 93
XI 1 XI 9 654 822
X2 0.1 X2 0 3 928 265
X3 1 X3 0. 9 735 624
X4 5 X4 4. 179 795
Z2vi jlue before filling: 0. 2 991 093 Xі value after fiUme: 0. 115 696
Fig. 1. The report about the KinFitSim work
The Marquardt method
A more sophisticated approach to the minimization is
2
to use second partial derivatives of % to determine changes in the gradient along the search path. This
2
method is equivalent to approximating the Ж hypersurface by a parabolic surface. As a result of the
2
parabolic expansion of x one obtains a matrix equation
P = 8a-q, (10)
where p and 8a are row matrices and 7 is a symmetric matrix of order m with
Pi
5/
d aj
and Vjj
22
д X
d a j d aj
We can solve equation (10) to yield parameter increments Saj. The main iterative formula of this method is
similar to (8) with c№ = 1. If the search is already close to the minimum, this method does decrease the number of steps needed, but at the expense of more elaborate computation. This method is usually named the Gauss-Newton method.
One disadvantage of this method is that, although it converges quite rapidly to the point of minimum ^2
from points nearby, it cannot be relied on to approach the minimum with any accuracy from a point outside
the region where x hypersurface is approximately parabolic.
A convenient algorithm (Marquardt) can be obtained by increasing the diagonal terms of the matrix 7 by a factor
(l + t). Equation (10) then becomes
, _vjj t1 + ^) for j =j,
P = Sarj with 4jj — |^jj for j ф j _ (11)
The following algorithm of choosing 2, was proposed by Marquardt [6]:
1. Compute xja}.
2. Start initially with 2 = 0. 001.
3. Compute 8a and xja + Sa) with this choice of 2.
4. If xja + Sa) & gt- X2{a), increase 2 by a factor 10 and repeat step 3.
5. If X2(a + Sa) & lt- X2(a, decrease 2 by a factor 10, consider a'- = a + 8a to be the new starting point and return to step 3 substituting a'- for a.
134
РИ, 2001, № 1
Input and output parameters
The KinFitSim package has a user-friendly interface for the PC, which allows convenient input-output. The user can easily obtain the calculated values for any reaction scheme and change any parameters in any stage of KinFitSim work. The KinFitSim package allows one to examine, to save and to print any graphical charts generated by KS and FS (theoretical and/or experimental). The user can correct the experimental data by hands in the special editor regime. The package produces a report, which contains the calculated and experimental graphical plots, and a list of the best-fit parameter values.
Fig. 1 shows a report of KinFitSim work: the initial and best-fit parameters. Fig. 2 demonstrates the calculated and experimental data before fitting and Fig.3 shows these curves after fitting. Fig. 2 and Fig. 3 correspond to information in the report (Fig. 1) about the chemical scheme, the applied numerical methods in KS and FS, initial and optimized parameters, and all other values.
Comparison of KinFitSim with KINSIM and KSIM
We compared the work of KinFitSim package with similar results of other packages: KIN SIM (Version 3.4 for PC, Chemical Kinetic Simulation System: B.A. Barshop, R.F. Wrenn, C. Frieden (1983) Anal. Biochem. 130: 134−145- C.T. Zimmerle, K. Patane, C. Frieden (1987) Biochemistry 26: 6545−6552- Dr. Bryce Plapp (1990), Biochemistry Department, The University of Iowa) and KSIM (Version 2.0 by Neil C. Millar, 1994).
There are four main differences between KinFitSim and other packages:
РИ, 2001, № 1
1. Limitations: KINSIM and KSIM have limitations for step count: the simulation stops when the time reaches the maximum time scale, or after 1000 steps for KSIM and 1024 steps for KINSIM, whichever happens sooner. KinFitSim can do simulations with an unlimited step count.
2. Kinetic simulating, the KINSIM package has two methods for ODE solving: Gear method and flux tolerance method (Euler method). The KSIM program uses the Runge-Kutta method and Gear method for kinetic simulation. KinFitSim has three methods for numerical simulation of ODEs: Euler, Runge-Kutta and Gear (Adams-Moulton in case of non-stiff systems) methods.
3. Fitting procedure: KS IM uses the Marquardt method for fitting to ten standard functions only (linear, exponential, hyperbolic, etc.). KINSIM uses the least squares method for fitting the calculated curves by optimization method of second order: Gauss-Newton and Marquardt methods. KinFitSim has three optimization methods for solving the non-linear regression problem: gradient-search method, Marquardt method and Gauss-Newton as a particular case of Marquardt method. The user can apply one, two or all three methods for one fitting procedure and change it easily in FS. The first order gradient-search method is often more efficient than the second order methods like Gauss-Newton or Marquardt methods. This occurs because there is less computational work for numerical approximation ofpartial derivatives of the X2 function. The gradient-search method needs m +1 calculations of
X
3 2
for gradient approximation versus — m
л- m +1 2
135
2
calculations of % for approximation of matrix of second partial derivatives in second order methods.
4. Input-output parameters: KINSIM and KSIM packages were written for the MS-DOS operating system and therefore they lack a user-friendly interface. KINSIM and KSIM require the creation a number of additional files for saving transient information in the course of the normal work of these packages. The KinFitSim package has a modern Windows interface with possibilities of easy input and output (save and print) of all parameters and all graphical plots (calculated and experimental) at any stage of work of our package.
Computing
The KinFitSim package consist of original programs written by the authors in Delphi 5 and run on a PC with Pentium III 800 MHz processor and 256 Mb of RAM.
Conclusion
The KinFitSim package offers more mathematical possibilities for good kinetic and fitting simulations and a modern interface with new possibilities for users than previous packages: KINSIM and KSIM. The KinFitSim package can be used in chemical research and for educational purposes. Students can apply and study the fitting procedure with various optimization methods and study each method using different initial, simulation parameters and various kinetic schemes.
Acknowledgements
We thank Dr. George McBane (The Ohio State University, USA) for interesting discussion of kinetic fitting problems and his kind help to the authors. Creation of KinFitSim was supported by grant from The US National Science Foundation for joint work during February of 2001 for Dr Irina Svir and Alexey 136
Klymenko in the group of Professor Matthew S. Platz in The Ohio State University.
References: 1. Современные численные методы для решения обыкновенных дифференциальных уравнений / Под ред. Дж. Холла и Дж. М. Ватта. М.: Мир, 1979. 312с. 2. БахваловН. С. Численные методы. М.: Наука, 1973. 632 с.
3. Хайрер Э, Нёрсетт С., Баннер Г. Решение обыкновенных дифференциальных уравнений. Нежесткие задачи: Пер. с англ. М.: Мир, 1990. 512 с. 4. Gear C. W. Numerical initial value problem in ordinary differential equations. Prentice-Hall, 1971. 253p. 5. Bevington P. R, Robinson D. K. Data reduction and error analysis for the physical sciences. McGraw-Hill, Inc. 1992. 6. Marquardt D.W. An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 1963. Vol. 11. Р. 431- 444. 7. Химмельблау Д. Прикладное нелинейное программирование. М.: Мир, 1975. 534 с. 8. Евдокимов, А Г. Минимизация функций и ее применение к задачам потокораспределения в инженерных сетях. Х.: Вища шк., 1985. 280 с.
Поступила в редколлегию 15. 03. 2001
Irina B. Svir, Kand. Phys. -Math. Sci., Senior Scientist, doctorant of Biomedical Electronics Department Kharkov State Technical University of RadioElectronics. Scientific interests: mathematical and computer modeling of physicochemical problems. Address: KTURE, Dept. Biomedical Electronics, 14 Lenina Avenue, Kharkov 61 166. E-mail: svir@kture. kharkov. ua
Alexey V. Klymenko, Master of Science in Applied Mathematics, Kharkov State Technical University of RadioElectronics. Scientific interests: numerical methods and programming. Address: KTURE, Dept. Biomedical Electronics, 14 Lenina Avenue, Kharkov — 61 166.
Matthew S. Platz, Professor of Chemistry, Newman and Wolfrom Laboratory Ohio State University. Scientific interests: photochemistry, physical-organic chemistry. Address: 100 West 18th Avenue, Columbus, OH 432 101 185, USA.
РИ, 2001, № 1
ПоказатьСвернуть
Заполнить форму текущей работой
|
__label__pos
| 0.877673 |
518
I am working on Linux with the GCC compiler. When my C++ program crashes I would like it to automatically generate a stacktrace.
My program is being run by many different users and it also runs on Linux, Windows and Macintosh (all versions are compiled using gcc).
I would like my program to be able to generate a stack trace when it crashes and the next time the user runs it, it will ask them if it is ok to send the stack trace to me so I can track down the problem. I can handle the sending the info to me but I don't know how to generate the trace string. Any ideas?
• 2
What OS, what shell? – Paul Tomblin Sep 16 '08 at 20:44
• 2
backtrace and backtrace_symbols_fd are not async-signal-safe. you should not use these function in signal handler – Parag Bafna Jun 14 '12 at 9:08
• 7
backtrace_symbols calls malloc, and so must not be used in a signal handler. The other two functions (backtrace and backtrace_symbols_fd) do not have this problem, and are commonly used in signal handlers. – cmccabe Aug 2 '12 at 20:01
• 1
@cmccabe that is incorrect backtrace_symbols_fd usually does not call malloc but may if something goes wrong in its catch_error block – Sam Saffron Dec 17 '13 at 22:24
• 2
It "may" in the sense that there is no POSIX spec for backtrace_symbols_fd (or any backtrace); however, GNU/Linux's backtrace_symbols_fd is specified to never call malloc, as per linux.die.net/man/3/backtrace_symbols_fd . Therefore, it is safe to assume that it will never call malloc on Linux. – codetaku Jul 17 '14 at 14:42
29 Answers 29
446
For Linux and I believe Mac OS X, if you're using gcc, or any compiler that uses glibc, you can use the backtrace() functions in execinfo.h to print a stacktrace and exit gracefully when you get a segmentation fault. Documentation can be found in the libc manual.
Here's an example program that installs a SIGSEGV handler and prints a stacktrace to stderr when it segfaults. The baz() function here causes the segfault that triggers the handler:
#include <stdio.h>
#include <execinfo.h>
#include <signal.h>
#include <stdlib.h>
#include <unistd.h>
void handler(int sig) {
void *array[10];
size_t size;
// get void*'s for all entries on the stack
size = backtrace(array, 10);
// print out all the frames to stderr
fprintf(stderr, "Error: signal %d:\n", sig);
backtrace_symbols_fd(array, size, STDERR_FILENO);
exit(1);
}
void baz() {
int *foo = (int*)-1; // make a bad pointer
printf("%d\n", *foo); // causes segfault
}
void bar() { baz(); }
void foo() { bar(); }
int main(int argc, char **argv) {
signal(SIGSEGV, handler); // install our handler
foo(); // this will call foo, bar, and baz. baz segfaults.
}
Compiling with -g -rdynamic gets you symbol info in your output, which glibc can use to make a nice stacktrace:
$ gcc -g -rdynamic ./test.c -o test
Executing this gets you this output:
$ ./test
Error: signal 11:
./test(handler+0x19)[0x400911]
/lib64/tls/libc.so.6[0x3a9b92e380]
./test(baz+0x14)[0x400962]
./test(bar+0xe)[0x400983]
./test(foo+0xe)[0x400993]
./test(main+0x28)[0x4009bd]
/lib64/tls/libc.so.6(__libc_start_main+0xdb)[0x3a9b91c4bb]
./test[0x40086a]
This shows the load module, offset, and function that each frame in the stack came from. Here you can see the signal handler on top of the stack, and the libc functions before main in addition to main, foo, bar, and baz.
• 50
There's also /lib/libSegFault.so which you can use with LD_PRELOAD. – CesarB Oct 23 '08 at 15:05
• 6
It looks like the first two entries in your backtrace output contain a return address inside the signal handler and probably one inside sigaction() in libc. While your backtrace appears to be correct, I have sometimes found that additional steps are necessary to ensure the actual location of the fault appears in the backtrace as it can be overwritten with sigaction() by the kernel. – jschmier Mar 27 '10 at 19:11
• 7
What would happen if the crash comes from inside malloc? Wouldn't you then hold a lock and then get stuck as "backtrace" tries to allocate memory? – Mattias Nilsson Apr 17 '12 at 6:39
• 7
catchsegv is not what the OP needs but is awesome for catching segmentation faults and getting all the information. – Matt Clarkson Jan 30 '13 at 10:45
• 7
For ARM, I had to also compile with -funwind-tables. Otherwise my stack depth was always 1 (empty). – jfritz42 Apr 10 '13 at 20:17
115
Linux
While the use of the backtrace() functions in execinfo.h to print a stacktrace and exit gracefully when you get a segmentation fault has already been suggested, I see no mention of the intricacies necessary to ensure the resulting backtrace points to the actual location of the fault (at least for some architectures - x86 & ARM).
The first two entries in the stack frame chain when you get into the signal handler contain a return address inside the signal handler and one inside sigaction() in libc. The stack frame of the last function called before the signal (which is the location of the fault) is lost.
Code
#ifndef _GNU_SOURCE
#define _GNU_SOURCE
#endif
#ifndef __USE_GNU
#define __USE_GNU
#endif
#include <execinfo.h>
#include <signal.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ucontext.h>
#include <unistd.h>
/* This structure mirrors the one found in /usr/include/asm/ucontext.h */
typedef struct _sig_ucontext {
unsigned long uc_flags;
struct ucontext *uc_link;
stack_t uc_stack;
struct sigcontext uc_mcontext;
sigset_t uc_sigmask;
} sig_ucontext_t;
void crit_err_hdlr(int sig_num, siginfo_t * info, void * ucontext)
{
void * array[50];
void * caller_address;
char ** messages;
int size, i;
sig_ucontext_t * uc;
uc = (sig_ucontext_t *)ucontext;
/* Get the address at the time the signal was raised */
#if defined(__i386__) // gcc specific
caller_address = (void *) uc->uc_mcontext.eip; // EIP: x86 specific
#elif defined(__x86_64__) // gcc specific
caller_address = (void *) uc->uc_mcontext.rip; // RIP: x86_64 specific
#else
#error Unsupported architecture. // TODO: Add support for other arch.
#endif
fprintf(stderr, "signal %d (%s), address is %p from %p\n",
sig_num, strsignal(sig_num), info->si_addr,
(void *)caller_address);
size = backtrace(array, 50);
/* overwrite sigaction with caller's address */
array[1] = caller_address;
messages = backtrace_symbols(array, size);
/* skip first stack frame (points here) */
for (i = 1; i < size && messages != NULL; ++i)
{
fprintf(stderr, "[bt]: (%d) %s\n", i, messages[i]);
}
free(messages);
exit(EXIT_FAILURE);
}
int crash()
{
char * p = NULL;
*p = 0;
return 0;
}
int foo4()
{
crash();
return 0;
}
int foo3()
{
foo4();
return 0;
}
int foo2()
{
foo3();
return 0;
}
int foo1()
{
foo2();
return 0;
}
int main(int argc, char ** argv)
{
struct sigaction sigact;
sigact.sa_sigaction = crit_err_hdlr;
sigact.sa_flags = SA_RESTART | SA_SIGINFO;
if (sigaction(SIGSEGV, &sigact, (struct sigaction *)NULL) != 0)
{
fprintf(stderr, "error setting signal handler for %d (%s)\n",
SIGSEGV, strsignal(SIGSEGV));
exit(EXIT_FAILURE);
}
foo1();
exit(EXIT_SUCCESS);
}
Output
signal 11 (Segmentation fault), address is (nil) from 0x8c50
[bt]: (1) ./test(crash+0x24) [0x8c50]
[bt]: (2) ./test(foo4+0x10) [0x8c70]
[bt]: (3) ./test(foo3+0x10) [0x8c8c]
[bt]: (4) ./test(foo2+0x10) [0x8ca8]
[bt]: (5) ./test(foo1+0x10) [0x8cc4]
[bt]: (6) ./test(main+0x74) [0x8d44]
[bt]: (7) /lib/libc.so.6(__libc_start_main+0xa8) [0x40032e44]
All the hazards of calling the backtrace() functions in a signal handler still exist and should not be overlooked, but I find the functionality I described here quite helpful in debugging crashes.
It is important to note that the example I provided is developed/tested on Linux for x86. I have also successfully implemented this on ARM using uc_mcontext.arm_pc instead of uc_mcontext.eip.
Here's a link to the article where I learned the details for this implementation: http://www.linuxjournal.com/article/6391
• 10
On systems using GNU ld, remember to compile with -rdynamic to instruct the linker to add all symbols, not only used ones, to the dynamic symbol table. This allows backtrace_symbols() to convert addresses to function names – jschmier Mar 26 '10 at 20:00
• 1
Also, you need to add "-mapcs-frame" option to GCC''s command line to generate stack frames on ARM platform – qehgt Feb 1 '12 at 15:53
• 3
This may be too late but can we use addr2line command somehow to get the exact line where the crash occurred? – enthusiasticgeek Oct 24 '12 at 18:26
• 4
On more recent builds of glibc uc_mcontext does not contain a field named eip. There is now an array that needs to be indexed, uc_mcontext.gregs[REG_EIP] is the equivalent. – mmlb Dec 14 '12 at 14:57
• 4
For ARM, my backtraces always had depth 1 until I added the -funwind-tables option to the compiler. – jfritz42 Apr 10 '13 at 16:10
112
It's even easier than "man backtrace", there's a little-documented library (GNU specific) distributed with glibc as libSegFault.so, which was I believe was written by Ulrich Drepper to support the program catchsegv (see "man catchsegv").
This gives us 3 possibilities. Instead of running "program -o hai":
1. Run within catchsegv:
$ catchsegv program -o hai
2. Link with libSegFault at runtime:
$ LD_PRELOAD=/lib/libSegFault.so program -o hai
3. Link with libSegFault at compile time:
$ gcc -g1 -lSegFault -o program program.cc
$ program -o hai
In all 3 cases, you will get clearer backtraces with less optimization (gcc -O0 or -O1) and debugging symbols (gcc -g). Otherwise, you may just end up with a pile of memory addresses.
You can also catch more signals for stack traces with something like:
$ export SEGFAULT_SIGNALS="all" # "all" signals
$ export SEGFAULT_SIGNALS="bus abrt" # SIGBUS and SIGABRT
The output will look something like this (notice the backtrace at the bottom):
*** Segmentation fault Register dump:
EAX: 0000000c EBX: 00000080 ECX:
00000000 EDX: 0000000c ESI:
bfdbf080 EDI: 080497e0 EBP:
bfdbee38 ESP: bfdbee20
EIP: 0805640f EFLAGS: 00010282
CS: 0073 DS: 007b ES: 007b FS:
0000 GS: 0033 SS: 007b
Trap: 0000000e Error: 00000004
OldMask: 00000000 ESP/signal:
bfdbee20 CR2: 00000024
FPUCW: ffff037f FPUSW: ffff0000
TAG: ffffffff IPOFF: 00000000
CSSEL: 0000 DATAOFF: 00000000
DATASEL: 0000
ST(0) 0000 0000000000000000 ST(1)
0000 0000000000000000 ST(2) 0000
0000000000000000 ST(3) 0000
0000000000000000 ST(4) 0000
0000000000000000 ST(5) 0000
0000000000000000 ST(6) 0000
0000000000000000 ST(7) 0000
0000000000000000
Backtrace:
/lib/libSegFault.so[0xb7f9e100]
??:0(??)[0xb7fa3400]
/usr/include/c++/4.3/bits/stl_queue.h:226(_ZNSt5queueISsSt5dequeISsSaISsEEE4pushERKSs)[0x805647a]
/home/dbingham/src/middle-earth-mud/alpha6/src/engine/player.cpp:73(_ZN6Player5inputESs)[0x805377c]
/home/dbingham/src/middle-earth-mud/alpha6/src/engine/socket.cpp:159(_ZN6Socket4ReadEv)[0x8050698]
/home/dbingham/src/middle-earth-mud/alpha6/src/engine/socket.cpp:413(_ZN12ServerSocket4ReadEv)[0x80507ad]
/home/dbingham/src/middle-earth-mud/alpha6/src/engine/socket.cpp:300(_ZN12ServerSocket4pollEv)[0x8050b44]
/home/dbingham/src/middle-earth-mud/alpha6/src/engine/main.cpp:34(main)[0x8049a72]
/lib/tls/i686/cmov/libc.so.6(__libc_start_main+0xe5)[0xb7d1b775]
/build/buildd/glibc-2.9/csu/../sysdeps/i386/elf/start.S:122(_start)[0x8049801]
If you want to know the gory details, the best source is unfortunately the source: See http://sourceware.org/git/?p=glibc.git;a=blob;f=debug/segfault.c and its parent directory http://sourceware.org/git/?p=glibc.git;a=tree;f=debug
• 1
"Possibility 3. Link with libSegFault at compile time" does not work. – Hans Kratz Jan 23 '13 at 18:05
• 4
@crafter: What do you mean "does not work". What have you tried, on what language/compiler/toolchain/distribution/hardware ? Did it fail to compile ? To catch error ? To produce output at all ? To produce hard-to-use output ? Thank you for details it will help everyone. – Stéphane Gourichon Mar 31 '14 at 9:33
• 1
'best source is unfortunately the source' ... Hopefully, some day, the man page for catchsegv will actually mention SEGFAULT_SIGNALS. Until then, there's this answer to refer to. – greggo Jul 3 '14 at 16:06
• I can't believe I've been programming C for 5 years and never heard of this :/ – DavidMFrey Mar 16 '16 at 12:44
• 5
@StéphaneGourichon @HansKratz To link with libSegFault you'll have to add -Wl,--no-as-needed to the compiler flags. Otherwise, ld will indeed not link against libSegFault, because it recognizes that the binary doesn't use any of its symbols. – Phillip Jul 28 '16 at 8:49
75
Even though a correct answer has been provided that describes how to use the GNU libc backtrace() function1 and I provided my own answer that describes how to ensure a backtrace from a signal handler points to the actual location of the fault2, I don't see any mention of demangling C++ symbols output from the backtrace.
When obtaining backtraces from a C++ program, the output can be run through c++filt1 to demangle the symbols or by using abi::__cxa_demangle1 directly.
• 1 Linux & OS X Note that c++filt and __cxa_demangle are GCC specific
• 2 Linux
The following C++ Linux example uses the same signal handler as my other answer and demonstrates how c++filt can be used to demangle the symbols.
Code:
class foo
{
public:
foo() { foo1(); }
private:
void foo1() { foo2(); }
void foo2() { foo3(); }
void foo3() { foo4(); }
void foo4() { crash(); }
void crash() { char * p = NULL; *p = 0; }
};
int main(int argc, char ** argv)
{
// Setup signal handler for SIGSEGV
...
foo * f = new foo();
return 0;
}
Output (./test):
signal 11 (Segmentation fault), address is (nil) from 0x8048e07
[bt]: (1) ./test(crash__3foo+0x13) [0x8048e07]
[bt]: (2) ./test(foo4__3foo+0x12) [0x8048dee]
[bt]: (3) ./test(foo3__3foo+0x12) [0x8048dd6]
[bt]: (4) ./test(foo2__3foo+0x12) [0x8048dbe]
[bt]: (5) ./test(foo1__3foo+0x12) [0x8048da6]
[bt]: (6) ./test(__3foo+0x12) [0x8048d8e]
[bt]: (7) ./test(main+0xe0) [0x8048d18]
[bt]: (8) ./test(__libc_start_main+0x95) [0x42017589]
[bt]: (9) ./test(__register_frame_info+0x3d) [0x8048981]
Demangled Output (./test 2>&1 | c++filt):
signal 11 (Segmentation fault), address is (nil) from 0x8048e07
[bt]: (1) ./test(foo::crash(void)+0x13) [0x8048e07]
[bt]: (2) ./test(foo::foo4(void)+0x12) [0x8048dee]
[bt]: (3) ./test(foo::foo3(void)+0x12) [0x8048dd6]
[bt]: (4) ./test(foo::foo2(void)+0x12) [0x8048dbe]
[bt]: (5) ./test(foo::foo1(void)+0x12) [0x8048da6]
[bt]: (6) ./test(foo::foo(void)+0x12) [0x8048d8e]
[bt]: (7) ./test(main+0xe0) [0x8048d18]
[bt]: (8) ./test(__libc_start_main+0x95) [0x42017589]
[bt]: (9) ./test(__register_frame_info+0x3d) [0x8048981]
The following builds on the signal handler from my original answer and can replace the signal handler in the above example to demonstrate how abi::__cxa_demangle can be used to demangle the symbols. This signal handler produces the same demangled output as the above example.
Code:
void crit_err_hdlr(int sig_num, siginfo_t * info, void * ucontext)
{
sig_ucontext_t * uc = (sig_ucontext_t *)ucontext;
void * caller_address = (void *) uc->uc_mcontext.eip; // x86 specific
std::cerr << "signal " << sig_num
<< " (" << strsignal(sig_num) << "), address is "
<< info->si_addr << " from " << caller_address
<< std::endl << std::endl;
void * array[50];
int size = backtrace(array, 50);
array[1] = caller_address;
char ** messages = backtrace_symbols(array, size);
// skip first stack frame (points here)
for (int i = 1; i < size && messages != NULL; ++i)
{
char *mangled_name = 0, *offset_begin = 0, *offset_end = 0;
// find parantheses and +address offset surrounding mangled name
for (char *p = messages[i]; *p; ++p)
{
if (*p == '(')
{
mangled_name = p;
}
else if (*p == '+')
{
offset_begin = p;
}
else if (*p == ')')
{
offset_end = p;
break;
}
}
// if the line could be processed, attempt to demangle the symbol
if (mangled_name && offset_begin && offset_end &&
mangled_name < offset_begin)
{
*mangled_name++ = '\0';
*offset_begin++ = '\0';
*offset_end++ = '\0';
int status;
char * real_name = abi::__cxa_demangle(mangled_name, 0, 0, &status);
// if demangling is successful, output the demangled function name
if (status == 0)
{
std::cerr << "[bt]: (" << i << ") " << messages[i] << " : "
<< real_name << "+" << offset_begin << offset_end
<< std::endl;
}
// otherwise, output the mangled function name
else
{
std::cerr << "[bt]: (" << i << ") " << messages[i] << " : "
<< mangled_name << "+" << offset_begin << offset_end
<< std::endl;
}
free(real_name);
}
// otherwise, print the whole line
else
{
std::cerr << "[bt]: (" << i << ") " << messages[i] << std::endl;
}
}
std::cerr << std::endl;
free(messages);
exit(EXIT_FAILURE);
}
• Thank you for this, jschmier. I created a little bash script to feed the output of this into the addr2line utility. See: stackoverflow.com/a/15801966/1797414 – arr_sea Apr 5 '13 at 19:02
• 3
Don't forget to #include <cxxabi.h> – Bamaco Jul 7 '14 at 19:52
• 1
Good documentation, and a straightforward header file has been posted here since 2008... panthema.net/2008/0901-stacktrace-demangled very similar to your approach :) – kevinf Oct 23 '14 at 20:25
• abi::__cxa_demangle seems to be not the async-signal-safe, so the signal handler can deadlock somewhere in malloc. – orcy Nov 27 '15 at 6:41
33
Might be worth looking at Google Breakpad, a cross-platform crash dump generator and tools to process the dumps.
21
You did not specify your operating system, so this is difficult to answer. If you are using a system based on gnu libc, you might be able to use the libc function backtrace().
GCC also has two builtins that can assist you, but which may or may not be implemented fully on your architecture, and those are __builtin_frame_address and __builtin_return_address. Both of which want an immediate integer level (by immediate, I mean it can't be a variable). If __builtin_frame_address for a given level is non-zero, it should be safe to grab the return address of the same level.
12
ulimit -c <value> sets the core file size limit on unix. By default, the core file size limit is 0. You can see your ulimit values with ulimit -a.
also, if you run your program from within gdb, it will halt your program on "segmentation violations" (SIGSEGV, generally when you accessed a piece of memory that you hadn't allocated) or you can set breakpoints.
ddd and nemiver are front-ends for gdb which make working with it much easier for the novice.
• 5
Core dumps are infinitely more useful than stack traces because you can load the core dump in the debugger and see the state of the whole program and its data at the point of the crash. – Adam Hawes Feb 4 '09 at 13:07
• 1
The backtrace facility that others have suggested is probably better than nothing, but it is very basic -- it doesn't even give line numbers. Using core dumps, on the other hand, let's you retroactively view the entire state of your application at the time it crashed (including a detailed stack trace). There might be practical issues with trying to use this for field debugging, but it is definitely a more powerful tool for analyzing crashes and asserts during development (at least on Linux). – nobar Oct 26 '10 at 13:36
10
Some versions of libc contain functions that deal with stack traces; you might be able to use them:
http://www.gnu.org/software/libc/manual/html_node/Backtraces.html
I remember using libunwind a long time ago to get stack traces, but it may not be supported on your platform.
• 7
Wow, you answered the question before it was asked (look at the times). – Jeroen Noten Mar 30 '15 at 12:50
10
It's important to note that once you generate a core file you'll need to use the gdb tool to look at it. For gdb to make sense of your core file, you must tell gcc to instrument the binary with debugging symbols: to do this, you compile with the -g flag:
$ g++ -g prog.cpp -o prog
Then, you can either set "ulimit -c unlimited" to let it dump a core, or just run your program inside gdb. I like the second approach more:
$ gdb ./prog
... gdb startup output ...
(gdb) run
... program runs and crashes ...
(gdb) where
... gdb outputs your stack trace ...
I hope this helps.
• 3
You can also call gdb right from your crashing program. Setup handler for SIGSEGV, SEGILL, SIGBUS, SIGFPE that will call gdb. Details: stackoverflow.com/questions/3151779/… The advantage is that you get beautiful, annotated backtrace like in bt full, also you can get stack traces of all threads. – Vi. Jun 30 '10 at 22:20
• You can also get backtrace easier than in the answer: gdb -silent ./prog core --eval-command=backtrace --batch -it would show backtrace and close debugger – Grzegorz Bazior Jan 2 at 8:00
10
Ive been looking at this problem for a while.
And buried deep in the Google Performance Tools README
http://code.google.com/p/google-perftools/source/browse/trunk/README
talks about libunwind
http://www.nongnu.org/libunwind/
Would love to hear opinions of this library.
The problem with -rdynamic is that it can increase the size of the binary relatively significantly in some cases
• 2
On x86/64, I have not seen -rdynamic increase binary size much. Adding -g makes for a much bigger increase. – Dan Mar 24 '10 at 6:46
• 1
I noticed that libunwind does not have functionality to get the line number, and I guess (did not test) unw_get_proc_name returns the function symbol (which is obfuscated for overloading and such) instead of the original name. – Herbert Nov 24 '14 at 20:10
• 1
That's correct. It gets very tricky to do this correctly, but I've had excellent success with gaddr2line there is lots of practical information here blog.bigpixel.ro/2010/09/stack-unwinding-stack-trace-with-gcc – Gregory Nov 25 '14 at 20:53
10
Thank you to enthusiasticgeek for drawing my attention to the addr2line utility.
I've written a quick and dirty script to process the output of the answer provided here: (much thanks to jschmier!) using the addr2line utility.
The script accepts a single argument: The name of the file containing the output from jschmier's utility.
The output should print something like the following for each level of the trace:
BACKTRACE: testExe 0x8A5db6b
FILE: pathToFile/testExe.C:110
FUNCTION: testFunction(int)
107
108
109 int* i = 0x0;
*110 *i = 5;
111
112 }
113 return i;
Code:
#!/bin/bash
LOGFILE=$1
NUM_SRC_CONTEXT_LINES=3
old_IFS=$IFS # save the field separator
IFS=$'\n' # new field separator, the end of line
for bt in `cat $LOGFILE | grep '\[bt\]'`; do
IFS=$old_IFS # restore default field separator
printf '\n'
EXEC=`echo $bt | cut -d' ' -f3 | cut -d'(' -f1`
ADDR=`echo $bt | cut -d'[' -f3 | cut -d']' -f1`
echo "BACKTRACE: $EXEC $ADDR"
A2L=`addr2line -a $ADDR -e $EXEC -pfC`
#echo "A2L: $A2L"
FUNCTION=`echo $A2L | sed 's/\<at\>.*//' | cut -d' ' -f2-99`
FILE_AND_LINE=`echo $A2L | sed 's/.* at //'`
echo "FILE: $FILE_AND_LINE"
echo "FUNCTION: $FUNCTION"
# print offending source code
SRCFILE=`echo $FILE_AND_LINE | cut -d':' -f1`
LINENUM=`echo $FILE_AND_LINE | cut -d':' -f2`
if ([ -f $SRCFILE ]); then
cat -n $SRCFILE | grep -C $NUM_SRC_CONTEXT_LINES "^ *$LINENUM\>" | sed "s/ $LINENUM/*$LINENUM/"
else
echo "File not found: $SRCFILE"
fi
IFS=$'\n' # new field separator, the end of line
done
IFS=$old_IFS # restore default field separator
9
ulimit -c unlimited
is a system variable, wich will allow to create a core dump after your application crashes. In this case an unlimited amount. Look for a file called core in the very same directory. Make sure you compiled your code with debugging informations enabled!
regards
• 4
The user is not asking for a core dump. He's asking for a stack trace. See delorie.com/gnu/docs/glibc/libc_665.html – Todd Gamblin Sep 16 '08 at 20:54
• 1
a core dump will contain the call stack at the moment of the crash, won't it? – Mo. Sep 16 '08 at 20:57
• 3
You're assuming he's on Unix, and using Bash. – Paul Tomblin Sep 16 '08 at 20:58
• 2
If you are using tcsh, you have to do limit coredumpsize unlimited – sivabudh Nov 10 '10 at 19:46
9
Forget about changing your sources and do some hacks with backtrace() function or macroses - these are just poor solutions.
As a properly working solution, I would advice:
1. Compile your program with "-g" flag for embedding debug symbols to binary (don't worry this will not impact your performance).
2. On linux run next command: "ulimit -c unlimited" - to allow system make big crash dumps.
3. When your program crashed, in the working directory you will see file "core".
4. Run next command to print backtrace to stdout: gdb -batch -ex "backtrace" ./your_program_exe ./core
This will print proper readable backtrace of your program in human readable way (with source file names and line numbers). Moreover this approach will give you freedom to automatize your system: have a short script that checks if process created a core dump, and then send backtraces by email to developers, or log this into some logging system.
8
win: How about StackWalk64 http://msdn.microsoft.com/en-us/library/ms680650.aspx
• StackWalk64 requires that you ship debug symbols with your code. That's generally not desirable, as it makes reverse-engineering your application a whole lot easier. On Windows, there is a way easier solution, that provides way better information: Use WER and have it write a mini dump on unhandled exceptions. A single registry is required to enable this. – IInspectable Feb 17 '18 at 14:26
8
You can use DeathHandler - small C++ class which does everything for you, reliable.
• The best shows line numbers (correct line numbers) – Dawid Drozd Jun 21 '13 at 7:29
• 1
unfortunately it uses execlp() to perform addr2line calls... would be nice to fully stay in the own program (which is possible by including the addr2line code in some form) – example Aug 26 '14 at 14:39
7
Look at:
man 3 backtrace
And:
#include <exeinfo.h>
int backtrace(void **buffer, int size);
These are GNU extensions.
6
See the Stack Trace facility in ACE (ADAPTIVE Communication Environment). It's already written to cover all major platforms (and more). The library is BSD-style licensed so you can even copy/paste the code if you don't want to use ACE.
5
I can help with the Linux version: the function backtrace, backtrace_symbols and backtrace_symbols_fd can be used. See the corresponding manual pages.
4
*nix: you can intercept SIGSEGV (usualy this signal is raised before crashing) and keep the info into a file. (besides the core file which you can use to debug using gdb for example).
win: Check this from msdn.
You can also look at the google's chrome code to see how it handles crashes. It has a nice exception handling mechanism.
• SEH does not help in producing a stack trace. While it could be part of a solution, that solution is harder to implement and provides less information at the expense of disclosing more information about your application than the real solution: Write a mini dump. And set up Windows to do this automatically for you. – IInspectable Feb 17 '18 at 14:28
4
I found that @tgamblin solution is not complete. It cannot handle with stackoverflow. I think because by default signal handler is called with the same stack and SIGSEGV is thrown twice. To protect you need register an independent stack for the signal handler.
You can check this with code below. By default the handler fails. With defined macro STACK_OVERFLOW it's all right.
#include <iostream>
#include <execinfo.h>
#include <signal.h>
#include <stdlib.h>
#include <unistd.h>
#include <string>
#include <cassert>
using namespace std;
//#define STACK_OVERFLOW
#ifdef STACK_OVERFLOW
static char stack_body[64*1024];
static stack_t sigseg_stack;
#endif
static struct sigaction sigseg_handler;
void handler(int sig) {
cerr << "sig seg fault handler" << endl;
const int asize = 10;
void *array[asize];
size_t size;
// get void*'s for all entries on the stack
size = backtrace(array, asize);
// print out all the frames to stderr
cerr << "stack trace: " << endl;
backtrace_symbols_fd(array, size, STDERR_FILENO);
cerr << "resend SIGSEGV to get core dump" << endl;
signal(sig, SIG_DFL);
kill(getpid(), sig);
}
void foo() {
foo();
}
int main(int argc, char **argv) {
#ifdef STACK_OVERFLOW
sigseg_stack.ss_sp = stack_body;
sigseg_stack.ss_flags = SS_ONSTACK;
sigseg_stack.ss_size = sizeof(stack_body);
assert(!sigaltstack(&sigseg_stack, nullptr));
sigseg_handler.sa_flags = SA_ONSTACK;
#else
sigseg_handler.sa_flags = SA_RESTART;
#endif
sigseg_handler.sa_handler = &handler;
assert(!sigaction(SIGSEGV, &sigseg_handler, nullptr));
cout << "sig action set" << endl;
foo();
return 0;
}
3
I would use the code that generates a stack trace for leaked memory in Visual Leak Detector. This only works on Win32, though.
• And requires that you ship debug symbols with your code. In general not desirable. Write a mini dump and set up Windows to do it automatically for you on unhandled exceptions. – IInspectable Feb 17 '18 at 14:29
3
I have seen a lot of answers here performing a signal handler and then exiting. That's the way to go, but remember a very important fact: If you want to get the core dump for the generated error, you can't call exit(status). Call abort() instead!
3
The new king in town has arrived https://github.com/bombela/backward-cpp
1 header to place in your code and 1 library to install.
Personally I call it using this function
#include "backward.hpp"
void stacker() {
using namespace backward;
StackTrace st;
st.load_here(99); //Limit the number of trace depth to 99
st.skip_n_firsts(3);//This will skip some backward internal function from the trace
Printer p;
p.snippet = true;
p.object = true;
p.color = true;
p.address = true;
p.print(st, stderr);
}
2
In addition to above answers, here how you make Debian Linux OS generate core dump
1. Create a “coredumps” folder in the user's home folder
2. Go to /etc/security/limits.conf. Below the ' ' line, type “ soft core unlimited”, and “root soft core unlimited” if enabling core dumps for root, to allow unlimited space for core dumps.
3. NOTE: “* soft core unlimited” does not cover root, which is why root has to be specified in its own line.
4. To check these values, log out, log back in, and type “ulimit -a”. “Core file size” should be set to unlimited.
5. Check the .bashrc files (user, and root if applicable) to make sure that ulimit is not set there. Otherwise, the value above will be overwritten on startup.
6. Open /etc/sysctl.conf. Enter the following at the bottom: “kernel.core_pattern = /home//coredumps/%e_%t.dump”. (%e will be the process name, and %t will be the system time)
7. Exit and type “sysctl -p” to load the new configuration Check /proc/sys/kernel/core_pattern and verify that this matches what you just typed in.
8. Core dumping can be tested by running a process on the command line (“ &”), and then killing it with “kill -11 ”. If core dumping is successful, you will see “(core dumped)” after the segmentation fault indication.
1
On Linux/unix/MacOSX use core files (you can enable them with ulimit or compatible system call). On Windows use Microsoft error reporting (you can become a partner and get access to your application crash data).
1
As a Windows-only solution, you can get the equivalent of a stack trace (with much, much more information) using Windows Error Reporting. With just a few registry entries, it can be set up to collect user-mode dumps:
Starting with Windows Server 2008 and Windows Vista with Service Pack 1 (SP1), Windows Error Reporting (WER) can be configured so that full user-mode dumps are collected and stored locally after a user-mode application crashes. [...]
This feature is not enabled by default. Enabling the feature requires administrator privileges. To enable and configure the feature, use the following registry values under the HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\Windows Error Reporting\LocalDumps key.
You can set the registry entries from your installer, which has the required privileges.
Creating a user-mode dump has the following advantages over generating a stack trace on the client:
• It's already implemented in the system. You can either use WER as outlined above, or call MiniDumpWriteDump yourself, if you need more fine-grained control over the amount of information to dump. (Make sure to call it from a different process.)
• Way more complete than a stack trace. Among others it can contain local variables, function arguments, stacks for other threads, loaded modules, and so on. The amount of data (and consequently size) is highly customizable.
• No need to ship debug symbols. This both drastically decreases the size of your deployment, as well as makes it harder to reverse-engineer your application.
• Largely independent of the compiler you use. Using WER does not even require any code. Either way, having a way to get a symbol database (PDB) is very useful for offline analysis. I believe GCC can either generate PDB's, or there are tools to convert the symbol database to the PDB format.
Take note, that WER can only be triggered by an application crash (i.e. the system terminating a process due to an unhandled exception). MiniDumpWriteDump can be called at any time. This may be helpful if you need to dump the current state to diagnose issues other than a crash.
Mandatory reading, if you want to evaluate the applicability of mini dumps:
0
If your program crashes, it's the operating system itself that generates crash dump information. If you're using a *nix OS, you simply need to not prevent it from doing so (check out the ulimit command's 'coredump' options).
0
I forgot about the GNOME tech of "apport", but I don't know much about using it. It is used to generate stacktraces and other diagnostics for processing and can automatically file bugs. It's certainly worth checking in to.
0
It looks like in one of last c++ boost version appeared library to provide exactly what You want, probably the code would be multiplatform. It is boost::stacktrace, which You can use like as in boost sample:
#include <filesystem>
#include <sstream>
#include <fstream>
#include <signal.h> // ::signal, ::raise
#include <boost/stacktrace.hpp>
const char* backtraceFileName = "./backtraceFile.dump";
void signalHandler(int)
{
::signal(SIGSEGV, SIG_DFL);
::signal(SIGABRT, SIG_DFL);
boost::stacktrace::safe_dump_to(backtraceFileName);
::raise(SIGABRT);
}
void sendReport()
{
if (std::filesystem::exists(backtraceFileName))
{
std::ifstream file(backtraceFileName);
auto st = boost::stacktrace::stacktrace::from_dump(file);
std::ostringstream backtraceStream;
backtraceStream << st << std::endl;
// sending the code from st
file.close();
std::filesystem::remove(backtraceFileName);
}
}
int main()
{
::signal(SIGSEGV, signalHandler);
::signal(SIGABRT, signalHandler);
sendReport();
// ... rest of code
}
In Linux You compile the code above:
g++ --std=c++17 file.cpp -lstdc++fs -lboost_stacktrace_backtrace -ldl -lbacktrace
Example backtrace copied from boost documentation:
0# bar(int) at /path/to/source/file.cpp:70
1# bar(int) at /path/to/source/file.cpp:70
2# bar(int) at /path/to/source/file.cpp:70
3# bar(int) at /path/to/source/file.cpp:70
4# main at /path/to/main.cpp:93
5# __libc_start_main in /lib/x86_64-linux-gnu/libc.so.6
6# _start
Your Answer
By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.
Not the answer you're looking for? Browse other questions tagged or ask your own question.
|
__label__pos
| 0.577779 |
Zaleplon and Tinnitus - a phase IV clinical study of FDA data
Summary:
Tinnitus is reported only by a few people who take Zaleplon.
The phase IV clinical study analyzes which people take Zaleplon and have Tinnitus. It is created by eHealthMe based on reports of 1,610 people who have side effects while taking Zaleplon from the FDA, and is updated regularly.
Phase IV trials are used to detect adverse drug outcomes and monitor drug effectiveness in the real world. With medical big data and AI algorithms, eHealthMe is running millions of phase IV trials and makes the results available to the public. Our original studies have been referenced on 600+ medical publications including The Lancet, Mayo Clinic Proceedings, and Nature.
On Feb, 02, 2023
1,610 people reported to have side effects when taking Zaleplon.
Among them, 4 people (0.25%) have Tinnitus.
What is Zaleplon?
Zaleplon has active ingredients of zaleplon. It is often used in insomnia. eHealthMe is studying from 1,690 Zaleplon users for its effectiveness, alternative drugs and more.
What is Tinnitus?
Tinnitus (a ringing in the ears) is found to be associated with 3,241 drugs and 2,780 conditions by eHealthMe.
Number of Zaleplon and Tinnitus reports submitted per year:
Could Zaleplon cause Tinnitus?
Time on Zaleplon when people have Tinnitus *:
• < 1 month: 100 %
• 1 - 6 months: 0.0 %
• 6 - 12 months: 0.0 %
• 1 - 2 years: 0.0 %
• 2 - 5 years: 0.0 %
• 5 - 10 years: 0.0 %
• 10+ years: 0.0 %
Gender of people who have Tinnitus when taking Zaleplon *:
• female: 25 %
• male: 75 %
Age of people who have Tinnitus when taking Zaleplon *:
• 0-1: 0.0 %
• 2-9: 0.0 %
• 10-19: 0.0 %
• 20-29: 33.33 %
• 30-39: 0.0 %
• 40-49: 33.33 %
• 50-59: 0.0 %
• 60+: 33.33 %
Common drugs people take besides Zaleplon *:
1. Zolpidem Tartrate: 1 person, 25.00%
2. Zoloft: 1 person, 25.00%
3. Aleve: 1 person, 25.00%
4. Allegra Allergy: 1 person, 25.00%
5. Ampyra: 1 person, 25.00%
6. Ativan: 1 person, 25.00%
7. Clonazepam: 1 person, 25.00%
8. Crestor: 1 person, 25.00%
9. Cymbalta: 1 person, 25.00%
10. Flonase: 1 person, 25.00%
Common side effects people have besides Tinnitus *:
1. Urinary Tract Infection: 1 person, 25.00%
2. Urinary Retention (the inability to completely or partially empty the bladder): 1 person, 25.00%
3. Bipolar Disorder (mood disorder): 1 person, 25.00%
4. Drowsiness: 1 person, 25.00%
5. Drug Ineffective: 1 person, 25.00%
6. Ejaculation Delayed: 1 person, 25.00%
7. Gait Disturbance: 1 person, 25.00%
8. Hearing Loss: 1 person, 25.00%
9. Joint Pain: 1 person, 25.00%
10. Nausea (feeling of having an urge to vomit): 1 person, 25.00%
Common conditions people have *:
1. Urination - Excessive Volume: 1 person, 25.00%
2. Narcolepsy (brain's inability to regulate sleep-wake cycles normally): 1 person, 25.00%
3. Multiple Sclerosis (a nervous system disease that affects your brain and spinal cord. it damages the myelin sheath): 1 person, 25.00%
4. Migraine (headache): 1 person, 25.00%
5. Fatigue (feeling of tiredness): 1 person, 25.00%
* Approximation only. Some reports may have incomplete information.
Do you take Zaleplon and have Tinnitus?
Check whether Tinnitus is associated with a drug or a condition
How to use the study?
You can discuss the study with your doctor, to ensure that all drug risks and benefits are fully discussed and understood.
Related studies
How severe was Tinnitus and when was it recovered:
Expand to all the drugs that have ingredients of zaleplon:
Alternative drugs to, pros and cons of Zaleplon:
Common Zaleplon side effects:
Browse all side effects of Zaleplon:
a b c d e f g h i j k l m n o p q r s t u v w x y z
Tinnitus treatments and more:
COVID vaccines that are related to Tinnitus:
Common drugs associated with Tinnitus:
All the drugs that are associated with Tinnitus:
Common conditions associated with Tinnitus:
All the conditions that are associated with Tinnitus:
How the study uses the data?
The study uses data from the FDA. It is based on zaleplon (the active ingredients of Zaleplon) and Zaleplon (the brand name). Other drugs that have the same active ingredients (e.g. generic drugs) are not considered. Dosage of drugs is not considered in the study.
Who is eHealthMe?
With medical big data and proven AI algorithms, eHealthMe provides a platform for everyone to run phase IV clinical trials. We study millions of patients and 5,000 more each day. Results of our real-world drug study have been referenced on 600+ medical publications, including The Lancet, Mayo Clinic Proceedings, and Nature. Our analysis results are available to researchers, health care professionals, patients (testimonials), and software developers (open API).
WARNING, DISCLAIMER, USE FOR PUBLICATION
WARNING: Please DO NOT STOP MEDICATIONS without first consulting a physician since doing so could be hazardous to your health.
DISCLAIMER: All material available on eHealthMe.com is for informational purposes only, and is not a substitute for medical advice, diagnosis, or treatment provided by a qualified healthcare provider. All information is observation-only. Our phase IV clinical studies alone cannot establish cause-effect relationship. Different individuals may respond to medication in different ways. Every effort has been made to ensure that all information is accurate, up-to-date, and complete, but no guarantee is made to that effect. The use of the eHealthMe site and its content is at your own risk.
If you use this eHealthMe study on publication, please acknowledge it with a citation: study title, URL, accessed date.
Recent studies on eHealthMe:
|
__label__pos
| 0.585172 |
use strict; use Win32::OLE qw(in); use HTML::Template; { package Wrapper::Notes::Template; use strict; use File::Spec; sub new { my ($class,$document, $attachmentdir) = @_; my $self = { document => $document, attachments => $attachmentdir }; bless $self, $class; $self; }; sub document { $_[0]->{document} }; sub param { my ($self,@args) = @_; if (scalar @args) { my $result; if ($_[1] eq 'Attachments') { my $result = []; my $body = $self->document->GetFirstItem('Body'); my @attachments = grep { warn join ":",$_->{Name}, $_->{Type},$_->{Text}; $_->{Type} == 4 } (@{$self->document->Items()}); mkdir $self->{attachments}; for my $attname (@attachments) { my $url = File::Spec->catfile($self->{attachments},$attname); $url = File::Spec->rel2abs($url); #warn "Extracting $attname to $url"; my $f = $self->document->getAttachment($attname); if ($f) { $f->extractFile($url); push @$result, { name => $attname, url => $url }; }; }; return $result; } elsif ($_[1] eq 'EmbeddedObjects') { my $result = []; my $body = $self->document->GetFirstItem('Body'); my $attachments = $body->EmbeddedObjects; if ($attachments) { mkdir $self->{attachments}; for my $att (Win32::OLE::in $attachments) { warn $att->{Type}; my $url = File::Spec->catfile($self->{attachments},$att->{Name}); $url = File::Spec->rel2abs($url); $att->extractFile($url); push @$result, { name => $att->{Name}, url => $url }; }; }; return $result; } else { $result = $self->document->{$_[1]}; }; if (ref $result) { return [ map { "value" => $_ }, @$result ]; } else { $result; }; } else { return (map { $_->Name } (Win32::OLE::in ($self->document->Items()))), "Attachments", "EmbeddedObjects"; }; }; }; my ($server,$database) = ('server','mail/corion.nsf'); my $Notes = Win32::OLE->new('Notes.NotesSession') or die "Cannot start Lotus Notes Session object.\n"; my ($Version) = ($Notes->{NotesVersion} =~ /\s*(.*\S)\s*$/); print "The current user is $Notes->{UserName}.\n"; print "Running Notes \"$Version\" on \"$Notes->{Platform}\".\n"; my $Database = $Notes->GetDatabase($server, $database); my $AllDocuments = $Database->AllDocuments; my $Count = $AllDocuments->Count; print "There are $Count documents in the database.\n"; my $Index = 4419; while (++$Index <= $Count) { my $Document = $AllDocuments->GetNthDocument($Index); my $wrapper = Wrapper::Notes::Template->new($Document,sprintf "email/mail.%05g",$Index); my $template = HTML::Template->new( filename => 'lotus-email.tmpl', die_on_bad_params => 0, loop_context_vars => 1, associate => [ $wrapper ], case_sensitive => 1, ); my $outfile = sprintf "email/mail.%05g.html", $Index; open MAIL, ">", $outfile or die "Couldn't create '$outfile' : $!\n"; $template->output( print_to => *MAIL ); close MAIL; last unless $Index <= 4420; # magic number! }
|
__label__pos
| 0.999614 |
Accelerator Physics
Second Edition
I
Accelerator Physic
Second E d i t i o n S. Y. Lee
Department of Physics, Indiana University
\jjjp World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONGKONG • TAIPEI • BANGALOf
Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataioguing-in-Publication Data A catalogue record for this book is available from the British Library.
ACCELERATOR PHYSICS (Second Edition) Copyright © 2004 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.
ISBN 981-256-182-X 981-256-200-1 (pbk)
To the memory of my parents
Preface
Since the appearance of the first edition in 1999, this book has been used as a textbook or reference for graduate-level "Accelerator Physics" courses. I have benefited from questions, criticism and suggestions from colleagues and students. As a response to these suggestions, the revised edition is intended to provide easier learning explanations and illustrations. Accelerator Physics studies the interaction between the charged particles and electromagnetic field. The applications of accelerators include all branches of sciences and technologies, medical treatment, and industrial processing. Accelerator scientists invent many innovative technologies to produce beams with qualities required for each application. This textbook is intended for graduate students who have completed their graduate core-courses including classical mechanics, electrodynamics, quantum mechanics, and statistical mechanics. I have tried to emphasize the fundamental physics behind each innovative idea with least amount of mathematical complication. The textbook may also be used by undergraduate seniors who have completed courses on classical mechanics and electromagnetism. For beginners in accelerator physics, one begins with Sees. 2.1-2.4 in Chapter 2, and follows by Sees. 3.1-3.2 for the basic betatron and synchrotron motion. The study continues onto Sees. 2.5, 2.8, and 3.7 for chromatic aberration and collective beam instabilities. After these basic topics, the rf technology and basic physics of linac are covered in Sees. 3.5, 3.6, 3.8 in Chapter 3. The basic accelerator physics course ends with physics of electron storage rings in Chapter 4. I have chosen the Frenet-Serret coordinate-system of (x, s, z) for the transverse radially-outward, longitudinally-forward, and vertical unit base-vectors with the righthand rule: z = x x I. I have also chosen positive-charge to derive the equations of betatron motion for all sections of the Chapter 2, except a discussion of ±-signs in Eq. (2.29). The sign of some terms in Hill's equation should be reversed if you solve the equation of motion for electrons in accelerators. The convention of the rf-phase differs in linac and synchrotron communities by 4>\mac = ^synchrotron — (TT/2) • To be consistent with the synchrotron motion in Chapter 3, I have chosen the rf-phase convention of the synchrotron community to describe the synchrotron equation of motion for linac in Sec. 3.8. In this revised edition, I include two special topics: free electron laser (FEL) vii
viii
PREFACE
and beam-beam interaction in Chapter 5. In 2000, several self-amplified spontaneous emission (SASE) FEL experiments have been successfully demonstrated. Many light source laboratories are proposing the fourth generation light source using high gain FEL based on the concept of SASE and high-gain harmonic generation (HGHG). Similarly, the success of high luminosity B-factories indicates that beam-beam interaction remains very important to the basic accelerator physics. These activities justify the addition of two introductory topics to the accelerator physics text. Finally, the homework is designed to solve a particular problem by providing step-by-step procedures to minimize frustrations. The answer is usually listed at the end of each homework problem so that the result can be used in practical design of accelerator systems. I would appreciate very much to receive comments and criticism to this revised edition. S.Y. Lee Bloomington, Indiana, U.S.A. November, 2004
Preface to the first edition
The development of high energy accelerators began in 1911 when Rutherford discovered the atomic nuclei inside the atom. Since then, high voltage DC and rf accelerators have been developed, high-field magnets with excellent field quality have been achieved, transverse and longitudinal beam focusing principles have been discovered, high power rf sources have been invented, high vacuum technology has been improved, high brightness (polarized/unpolarized) electron/ion sources have been attained, and beam dynamics and beam manipulation schemes such as beam injection, accumulation, slow and fast extraction, beam damping and beam cooling, instability feedback, etc. have been advanced. The impacts of the accelerator development are evidenced by many ground-breaking discoveries in particle and nuclear physics, atomic and molecular physics, condensed-matter physics, biomedical physics, medicine, biology, and industrial processing. Accelerator physics and technology is an evolving branch of science. As the technology progresses, research in the physics of beams propels advancement in accelerator performance. The advancement in type II superconducting material led to the development of high-field magnets. The invention of the collider concept initiated research and development in single and multi-particle beam dynamics. Accelerator development has been impressive. High energy was measured in MeV's in the 1930's, GeV's in the 1950's, and multi-TeV's in the 1990's. In the coming decades, the center of mass energy will reach 10-100 TeV. High intensity was 109 particles per pulse in the 1950's. Now, the AGS has achieved 6 x 1013 protons per pulse. We are looking for 1014 protons per bunch for many applications. The brilliance of synchrotron radiation was about 1012 [photons/s mm2 mrad2 0.1% (AA/A)] from the first-generation light sources in the 1970's. Now, it reaches 1021, and efforts are being made to reach a brilliance of 1029 - 1034 in many FEL research projects. This textbook deals with basic accelerator physics. It is based on my lecture notes for the accelerator physics graduate course at Indiana University and two courses in the U.S. Particle Accelerator School. It has been used as preparatory course material for graduate accelerator physics students doing thesis research at Indiana University. The book has four chapters. The first describes historical accelerator development. The second deals with transverse betatron motion. The third chapter concerns synchrotron motion and provides an introduction to linear accelerators. The fourth deals with synchrotron radiation phenomena and the basic design principles
ix
x
PREFACE TO THE FIRST EDITION
of low-emittance electron storage rings. Since this is a textbook on basic accelerator physics, topics such as nonlinear beam dynamics, collective beam instabilities, etc., are mentioned only briefly, in Chapters 2 and 3. Attention is paid to deriving the action-angle variables of the phase space coordinates because the transformation is basic and the concept is important in understanding the phenomena of collective instability and nonlinear beam dynamics. In the design of synchrotrons, the dispersion function plays an important role in particle stability, beam performance, and beam transport. An extensive section on the dispersion function is provided in Chapter 2. This function is also important in the design of low-emittance electron storage ring lattices. The SI units are used throughout this book. I have also chosen the engineer's convention of j = —i for the imaginary number. The exercises in each section are designed to have the student apply a specific technique in solving an accelerator physics problem. By following the steps provided in the homework, each exercise can be easily solved. The field of accelerator physics and technology is multi-disciplinary. Many related subjects are not extensively discussed in this book: linear accelerators, induction linacs, high brightness beams, collective instabilities, nonlinear dynamics, beam cooling physics and technology, linear collider physics, free-electron lasers, electron and ion sources, neutron spallation sources, muon colliders, high intensity beams, vacuum technology, superconductivity, magnet technology, instrumentation, etc. Nevertheless, the book should provide the understanding of basic accelerator physics that is indispensable in accelerator physics and technology research. S.Y. Lee Bloomington, Indiana, U.S.A. January, 1998
2 Electrostatic Accelerators I. 1 Transfer Matrix and Stability of Betatron Motion II.3 Floquet Transformation xi vii ix 1 4 5 6 6 9 17 18 19 19 20 22 23 23 24 24 24 35 36 37 39 41 41 42 47 47 51 52 .2 Courant-Snyder Parametrization II.4 Radio-Frequency (RF) Accelerators I.1 High Energy and Nuclear Physics III.2 Solid-State and Condensed-Matter Physics III.1 Natural Accelerators I.1 Acceleration Cavities II.Contents Preface Preface to the first edition 1 Introduction I Historical Developments I.3 Other Applications Exercise 2 Transverse Motion I Hamiltonian for Particle Motion in Accelerators I.3 Other Important Components III Accelerator Applications III.3 Induction Accelerators I.4 Particle Motion in Dipole and Quadrupole Magnets Exercise II Linear Betatron Motion II.3 Equation of Betatron Motion I.2 Accelerator Magnets II.5 Colliders and Storage Rings I.2 Magnetic Field in Frenet-Serret Coordinate System I.1 Hamiltonian in Frenet-Serret Coordinate System I.6 Synchrotron Radiation Storage Rings II Layout and Components of Accelerators II.
9 Mechanisms of emittance dilution and diffusion Exercise Off-Momentum Orbit IV. Action. Flexible momentum compaction (FMC) lattices C.7 Experimental Measurements of Dispersion Function IV.8 Beam Injection and Extraction III. 7T jump schemes B.4 Lattice Design Strategy Exercise Linear Coupling VI.4 Dispersion Suppression and Dispersion Matching IV.3 Experimental Measurement of Linear Coupling CONTENTS 57 60 65 66 67 73 85 85 91 92 101 105 108 110 115 117 121 129 129 133 136 139 141 143 145 146 146 149 155 156 157 161 172 173 178 178 183 184 186 186 189 193 III IV V VI . FMC in double-bend (DB) lattices IV.3 Application of Dipole Field Error III.5 Courant-Snyder Invariant and Emittance II.1 Closed-Orbit Distortion due to Dipole Field Errors III.1 Dispersion Function IV.9 Minimum {H) Modules Exercise Chromatic Aberration V.7 Transverse Spectra III.I Chromaticity Measurement and Correction V.2 %-Function.4 Action-Angle Variable and Floquet Transformation II. and Integral Representation IV.6 Transport Notation IV.2 Effects of an isolated Linear Coupling Resonance VI.2 Extended Matrix Method for the Closed Orbit III.2 Nonlinear Effects of Chromatic Sextupoles V. Other similar FMC modules D.6 Stability of Betatron Motion: A FODO Cell Example II.5 Achromat Transport Systems IV.3 Chromatic Aberration and Correction V.6 Application of quadrupole field error III.5 Basic Beam Observation of Transverse Motion III.3 Momentum Compaction Factor IV.8 Transition Energy Manipulation A.4 Quadrupole Field (Gradient) Errors III.8 Effect of Space-Charge Force on Betatron Motion Exercise Effect of Linear Magnet Imperfections III.1 The Linear Coupling Hamiltonian VI.xii II.7 Symplectic Condition II.
5 Summary of Synchrotron Equations of Motion Exercise II Adiabatic Synchrotron Motion II.2 RF Phase Modulation and Parametric Resonances III.1 Normalized Phase-Space Coordinates III.4 Frequency Spread and Landau Damping Exercise IX Synchro-Betatron Hamiltonian Exercise 3 Synchrotron Motion I Longitudinal Equation of Motion I.4 Small-Amplitude Synchrotron Motion at the UFP II.5 RF Voltage Modulation III.3 Measurements of Synchrotron Phase Modulation III.6 Measurement of RF Voltage Modulation Exercise xiii 196 197 197 202 202 209 211 212 213 216 216 220 221 225 228 232 237 239 240 244 245 246 247 248 249 251 252 253 255 258 259 261 263 268 268 271 277 280 288 295 297 .2 Bucket Area II. 1 Nonlinear Resonances Driven by Sextupoles VII.3 Small-Amplitude Oscillations and Bunch Area II.1 Fixed Points II.1 Impedance VIII.1 The Synchrotron Hamiltonian I.4 Betatron Tunes and Nonlinear Resonances Exercise VIII Collective Instabilities and Landau Damping VIII.5 Linear Coupling Using Transfer Matrix Formalism Exercise VII Nonlinear Resonances VII.CONTENTS VI.4 Some Practical Examples I.4 Linear Coupling Correction with Skew Quadrupoles VI.6 Experimental Tracking of Synchrotron Motion Exercise III RF Phase and Voltage Modulations III.2 The Synchrotron Mapping Equation I.3 Effect of Wakefield on Transverse Wave VIII.2 Higher-Order Resonances VII.2 Transverse Wave Modes VIII.4 Effects of Dipole Field Modulation III.5 Synchrotron Motion for Large-Amplitude Particles II.3 Evolution of Synchrotron Phase-Space Ellipse I.3 Nonlinear Detuning from Sextupoles VII.
Shunt impedance C.3 Particle Acceleration by EM Waves A. HOMs 301 302 305 308 309 312 315 317 318 320 322 326 326 327 334 340 343 343 345 353 356 359 362 363 367 369 373 381 383 383 387 387 388 388 389 390 391 392 395 396 399 401 . Exercise VII Longitudinal Collective Instabilities VII.1 Historical Milestones VIII.2 Nonlinear Synchrotron Motion at 7 « 7T IV.4 Beam Loading Compensation and Robinson Instability .2 Fundamental Properties of Accelerating Structures A.3 Beam Loading VI. Alvarez structure E. . G.5 The QI Dynamical Systems Exercise V Beam Manipulation in Synchrotron Phase Space V. traveling wave.2 Collective Microwave Instability in Coasting Beams VII. .1 Pillbox Cavity VI. and coupled cavity linacs .4 Synchrotron Motion with Nonlinear Phase Slip Factor IV.xiv IV CONTENTS Nonadiabatic and Nonlinear Synchrotron Motion IV.2 Capture and Acceleration of Proton and Ion Beams V. Standing wave. EM waves in a cylindrical wave guide B.2 Low Frequency Coaxial Cavities VI.7 The Barrier RF Bucket Exercise VI Fundamentals of RF Systems VI. Loaded wave guide chain and the space harmonics F.1 Longitudinal Spectra VII.3 Longitudinal Impedance VII. .I RF Frequency Requirements V. 3 Beam Manipulation Near Transition Energy IV. Transit time factor B.6 Double rf Systems V.. 1 Linear Synchrotron Motion Near Transition Energy IV. Phase velocity and group velocity C. TM modes in a cylindrical pillbox cavity D.4 Microwave Single Bunch Instability Exercise VIII Introduction to Linear Accelerators VIII.5 Beam Stacking and Phase Displacement Acceleration V.3 Bunch Compression and Rotation V.4 Debunching V. The quality factor Q VIII.
1 Non-relativistic Reduction I.2 Interaction of the Radiation Field with the Beam I. 1 Damping of Synchrotron Motion II.7 Radiation Integrals II.4 Quantum Fluctuation Exercise II Radiation Damping and Excitation II.8 Beam Lifetime Exercise III Emittance in Electron Storage Rings III.2 The Coherent Beam-Beam Effects II. FODO cell lattice B.3 Frequency and Angular Distribution I. Three-bend achromat III. Minimizing emittance in a combined function DBA E.1 The beam-beam force II. Minimum (H)-function lattice D.4 Longitudinal Particle Dynamics in a Linac VIII.2 Radiation Field for Particles at Relativistic Velocities I.CONTENTS VIII.6 Vertical Beam Width II.2 Insertion Devices III.1 Emittance of Synchrotron Radiation Lattices A.3 Experiments on High Gain FEL Generation Exercise II Beam-Beam Interaction II.4 Radiation Excitation and Equilibrium Energy Spread II.3 Damping Rate Adjustment II. Double-bend achromat (Chasman-Green lattice) C.5 Radial Bunch Width and Distribution Function II.5 Transverse Beam Dynamics in a Linac Exercise 4 Physics of Electron Storage Rings I Fields of a Moving Charged Particle I.3 Nonlinear Beam-Beam Effects xv 402 407 410 417 422 424 424 427 433 435 437 438 441 445 448 453 455 456 456 462 466 467 467 469 473 475 476 478 486 489 497 498 500 506 509 510 513 517 519 521 .1 Small Signal Regime I.2 Damping of Betatron Motion II.3 Beam Physics of High Brightness Storage Rings Exercise 5 Special Topics in Beam Physics I Free Electron Laser (FEL) I.
2 Langevin Equation of Motion II.1 Cauchy Integral Formula III.2 Fixed Points I.4 Fokker-Planck Equation B Numerical Methods and Physical Constants I Fourier Transform I.7 Vector Operation V Maxwell's equations V.xvi CONTENTS II.4 Some Simple Fourier Transforms II Model Independent Analysis III Model Independent Analysis II.3 Digital Filtering I.3 Poisson Bracket I.6 Gauss' and Stokes' theorems IV. . 522 II.2 Dispersion Relation IV Useful Handy Formulas IV.2 Cylindrical waveguides V.5 Floquet Theorem II Stochastic Beam Dynamics II.3 Voltage Standing Wave Ratio 533 533 533 534 534 535 536 537 537 538 539 541 543 543 544 544 545 546 546 547 548 549 549 549 550 551 551 551 551 552 552 553 553 553 554 554 556 .2 The Hankel transform IV.I Lorentz Transformation of EM fields V.1 Canonical Transformations I.3 Accelerator Modeling III Cauchy Theorem and the Dispersion Relation III. 1 Generating functions for the Bessel functions IV. 2 Independent Component Analysis II.4 Liouville Theorem I.4 Experimental Observations and Numerical Simulations .2 Discrete Fourier Transform I. .B e a m Interaction in Linear Colliders 525 Exercise 527 A Basics of Classical Mechanics I Hamiltonian Dynamics I.3 The complex error function IV. .3 Stochastic Integration Methods II.5 B e a m .l Central Limit Theorem II.5 Cylindrical Coordinates IV.1 Nyquist Sampling Theorem I.4 A multipole expansion formula IV.
CONTENTS VI Physical Properties and Constants xvii 557 561 563 571 Bibliography Index Symbols and Notations .
D. I have benefited greatly from the collaboration with Drs. and Y. H. Yan and Prof. who made many useful suggestions to this revised edition. V. M. Kang. Your comments and corrections will be highly appreciated. Cousineau. Beltran. Li. A. Fung. M. I would like to thank S. Huang. Jeon. During the course of this work. The responsibility for all errors lies with me. K. C.Y. Guo. Bai. I owe special thanks to Prof.Acknowledgments I would like to thank students and colleagues. xviii .M. X. Ranjbar. Huang. Wang. Breitzmann. particularly D. Y. Y. Zhang. Chao. S. W. X. K. I owe special thanks to Margaret Dienes for editing the first edition of this book. Jau-Jiun Hsiao for making critical suggestions to the new chapter in this revised edition. David Caussyn. Ng. I would like to thank Angela Bellavance for pointing out mis-prints during a USPAS program in 2001. Ellison. Riabko. A. who helped me polish the lecture notes into a book form.
etc. These include electromagnetism. The counting rate in a detector is given by £u. In recent years. and Robert Schrieffer in 1957. waste treatment. Fine meshed superconducting wires are usually used in high-field magnets. plasma physics. High energy was measured in MeV's in the 1930's. As physicists probe deeper into the inner structure of matter. in biological and medical research with synchrotron light sources. where a is the cross-section of a reaction process. Understanding of the microscopic basis of superconductivity was achieved by John Bardeen. solid-state properties of materials. and quantum physics. and is about 1014 ppp in the 1990's. Advances in technology have allowed remarkable increases in energy and luminosity2 for fundamental physics research.G. The beam intensity was about 109 particles per pulse (ppp) in the 1950's. 1 . and is measured in TeV's in the 1990's. Leon Cooper. The race to build modern particle accelerators began in 1911 when Rutherford discovered the nucleus by scattering a-particles off Aluminum foil. Accelerators have also been used for radiotherapy. accelerators have found many applications: they are used in nuclear and particle physics research. The commonly used dimension is cm"2 s" 1 . etc. atomic physics. Since 1970. superconductivity. The physics and technology of accelerators and storage rings involves many branches of science.1 nonlinear mechanics. in industrial applications such as ion implantation and lithography. in material science and medical research with spallation neutron sources. and indeed new energy frontiers usually lead to new physics discoveries. High temperature superconductor was discovered by K. high energy and high luminosity colliders have become basic tools in nuclear and particle physics research. 2 The luminosity C is denned as the probability of particle encountering rate per unit area in a collision process (see Exercise 1. when men built bows and arrows for hunting. Mueller and J. Bednorz in 1986. A major application of particle accelerators is experimental nuclear and particle physics research. spin dynamics. high energy provides new territory for potential discoveries. Superconducting thin films deposited on the cavity surface are used for superconducting cavities.Chapter 1 Introduction The first accelerator dates back to prehistoric-historic times. The evolution of 1 Superconductivity was discovered by Heike Kamerlingh Onnes in 1911.A. food sterilization. The Meissner effect was discovered in 1933.7).
. high-brilliance photon beams from high-brightness electron beams in storage rings3 have been extensively used in biomedical and condensed-matter physics research.- . .6). 1.fi^&$rf~~~'**' n"*""u""! ••»•"«" — .1%Aw/w)) is plotted _ $• as a function photon beam {"„«««. | . . • « . innovative ideas provide substantial jump in beam enPTP"V el &y- _ y .J°t-=Tvr""°° -^ § photons/(mm 2 mrad 2 s •^ — ~ 1 ^ ^ 2 : • | (0. is plotted as a function of time._\ 5 and average Photon » * " " " * * " . .-.5 Brilliance denned as In 2 ^ ^ .„. i .-. 1980 2000 year ° Rectifier generator In recent years. 1Q6 J c v i T ^ 1940 1960 i . /ri™»)HT' „»"'" .S y S e a t e d by high . 102 108 _ Br. ..=.2 shows the peak photon brilliance (number of photons/(mm2 mrad2 s (0. .2 CHAPTER! INTRODUCTION accelerator development can be summarized by the Livingston chart shown in Fig. . I.. .tr^l^. Note * n a ' . . i . .S quality electron beams in • storage rings and m hnacs.° I | | ^jf jrfp -^--^rfi o 'CPQ_—&-^P Electron lin a c » J P j ^ T ^ H«*ron Synchrotron (strong focusing) TTlP -1-Ile HflsTlpH U d 4 I l e U llTIP 1 1 I l e m l b S s | < 109 _1 S . > l o 2 1 I " I " " I ^' " I " " 1 U I lo18 " = £ B I ' I \ IQ15 _ g* S lol2 l i | | I 1 1 | o 2 « ! * g I I" " I" " I' ' l ^ ' I l I TOW «»->*«~' ""^r * S K W M ..-*"V« _ .„!<. . .^fLe—^=_Ji c'°1°"°". o /—\ / ^ / »SLSXl^p^ ^ \ x " " I . — - pjg u r e U .. i . / »siin ^ ^ „ .io24 • .i<J 10~ 2 I I I " I Z j A 10" 1 10° 101 photon energy (keV) 102 1 0 " 2 10" 1 10° 101 photon energy (keV) Besides being used for fundamental material science research. .1 10 c.1.^ygtf—® g Proton lln. which is beam energy doubling in every two years.c . Figure 1." ctor '° cu " d . xhe Livingston Chart: The equivalent fixed target proton beam energy versus time in years. 2020 2040 drawn to guide the trend.loie _ s"ctLo1u." ' ~~~~. _ 10 28 / ^ ^ ^ \ t i g u r e 1. .„ — ^ \ • ..m.1% Aw/w)) as a function of photon beam energy from storage rings and linacs.2: The peak . KE = s/(2m p c 2 ) (see Exercise 1.„. i . high-intensity neu3 The brightness of a beam is denned as the beam's intensity divided by its phase-space volume. 'I'0** \ — lO 1311 TESU LCLS ' — Undulator (8-8 GeV) v '• - 8 . Cu _tJ" K c K • ? e n e l . • ' s ' ' 10 2 0 - — ^ l . where the equivalent fixed target proton energy.
Frontiers in accelerator physics and technology research Accelerator physics is a branch of applied science. and b and t quarks. wakefield control. wakefields.+/J. This led to the discovery of W and Z bosons. high-field superconducting magnets and the stability of high-brightness beams are important issues. and higher luminosity leads to higher precision in experimental results. a high-intensity proton source can be used to drive secondary beams such as kaons.ACCELERATOR PHYSICS 3 tron sources driven by powerful proton beam sources may provide energy amplification for future global energy needs.~ collider studies are also of current interest. China. dedicated meson factories such as the $-factory at Frascati National Laboratory in Italy and the B-factories at SLAC and Cornell in the U. . high acceleration gradients. Some of these topics in beam physics are as follows. the CERN Linear Collider (CLIC). Stochastic cooling has been successfully applied to accumulate anti-protons. and condensed-matter physics 4 See e. synchrotron light sources with high-brightness electron beams are used in medical. Innovations in technology give rise to new frontiers in beam physics research. and muons. Some proposed e+e~ colliders are the Next Linear Collider (NLC). biological. For lepton colliders. Taking advantage of radiation cooling. and high power rf sources are important. 1997). Ionization cooling is needed for muon beams in fi+fJ.~ colliders.g. • High-brightness beams: Beam-cooling techniques have been extensively used in attaining high-brightness hadron beams. • High energy: For high energy hadron accelerators such as the Tevatron at Fermilab. Since higher energy leads to new discoveries.S. With high-intensity y u beams. the National Spallation Neutron Source Design Report (Oak Ridge. Current research topics include high rf power sources. the Large Hadron Collider (LHC) at CERN.4 Furthermore. • High luminosity: To provide a detailed understanding of CP violation and other fundamental symmetry principles of interactions. the Japan Linear Collider (JLC). High intensity heavy-ion beams have also been actively pursued for inertial fusion evaluation. and at KEK in Japan were built in the 1990's. and the Tau-Charm factory is being contemplated in Beijing. which employs superconducting rf cavities. pions. Since the neutron flux from spallation neutron sources is proportional to the proton beam power. and the contemplated Very Large Hadron Collider (VLHC). /J. high acceleration gradient structures. etc.. physics and technology for high-intensity low-loss proton sources are important. and the TeV Superconducting Linear Accelerator (TESLA). the frontiers of accelerator physics research are classified into the frontiers of high energy and high brightness. Electron cooling and laser cooling have been applied to many low energy storage rings used in atomic and nuclear physics research.
high power rf sources. space-charge effects. Since the magnetic force is perpendicular to both v and B. Petti and A. novel acceleration techniques. Lennox. food sterilization.3) e. This book deals only with the fundamental aspects of accelerator physics. sterilization of medical tools. ARNS 44. the charged particle will move on a circular arc.33564 x p [GeV/c/u]. P. . First. high gradient accelerating structures. Recent research topics in accelerator physics include beam cooling. etc. beam-beam interactions. nonlinear beam dynamics. A high power tunable free-electron laser would be useful for chemical and technical applications. beam manipulation techniques. reliability. when the magnetic flux density is perpendicular to v. etc. beam instrumentation development.g. INTRODUCTION research. etc.1) The charge particle can only gain or lose its energy by its interaction with the electric field E. • Accelerator applications: The medical use of accelerators for radiation treatment.L. The momentum rigidity of the charged particle is Bp [T-m] = ? = ^ x 3. 155 (1994). and ease in operation. In particular. magnet technology. beam-cooling physics and technologies. I Historical Developments A charged particle with charge q and velocity v in the electromagnetic fields (E.. rf physics and technology. etc. (1. ion sources. etc.5 isotope production.4 CHAPTER 1. nonlinear beam dynamics. the bending radius is where m and p = mv are the mass and momentum of the particle. q Z 5 See (1. collective beam instability. material testing. electron-beam welding. requires safety. Higher beam power density with minimum beam loss can optimize safety in industrial applications such as ion implantation. B) is exerted by the Lorentz's force F: F = q(E + vxB).. It serves as an introduction to more advanced topics such as collective beam instabilities.J. Sub-picosecond photon beams would be important to time-resolved experiments. the technical achievements in accelerator physics of past decades will be described. Accelerator technology research areas include superconducting materials.
etc. to the surprise of many physicists. Barnett et al. S. This discovery created an era of search for high-voltage sources for particle acceleration that can produce high-intensity high-energy particles for the study of nuclear transmutation.H. 1997. stable or radioactive ions. 7See J. Rutherford employed a particles escaping the Coulomb barrier of Ra and Th nuclei to investigate the inner structure of atoms. heavy elements have been measured with energies up to 3 x 1020 eV. Interest in the relativistic heavy ion collider (RHIC) was amplified by the cosmic ray emulsion experiments. high vacuum components for attaining excellent beam lifetime. 323 (1983) and R. 1998). Sci. 19. Simpson. Feb. p. p. undulators and wigglers to produce high brilliance photon beam. 31. Rutherford also used a particles to induce the first artificial nuclear reaction. continuous (CW. . Pions were discovered in 1947 in emulsion experiments. and others. the existence of a positively charged nucleus with a diameter less than 10"11 cm.6 He demonstrated. Nuclei range from n and H to Ni. They are designed to accelerate electrons (leptons) or hadrons. Neddermeyer. Anderson. and A and Ze are the atomic mass number and charge of the particle. Cosmic rays Cosmic rays arise from galactic source accelerators. An event with energy 3 x 1020 eV had been recorded in 1991 by the Fly's Eye atmospheric-fluorescence detector in Utah (see Physics Today. a + 14N — 17O > + H. 6The kinetic energy of a particles that tunnel through the Coulomb barrier to escape the nuclear force is typically about 6 MeV. Accelerators are classified as follows. (Particle Data Group) D54. Jan.I. I. Ann. and the revolution of quantum mechanics in the early 20th century. In 1919. Accelerators are composed of ion sources. Phys. in no specific chronological order.I Natural Accelerators Radioactive accelerators In 1911. Nucl. cavity and magnet components that can generate and maintain electromagnetic fields for beam acceleration and manipulation. DC or coasting beam) or bunched and pulsed.A. 33. electrostatic or radio frequency. Rev.7 Muons were discovered in cosmic-ray emulsion experiments in 1936 by CD. devices to detect beam motion. Accelerators can be classified as linear or circular. targets for producing secondary beams. This led to the introduction of Bohr's atomic model. Rev. 1 (1996). HISTORICAL DEVELOPMENTS 5 where Bp is measured in Tesla-meter. and the momentum is measured in GeV/c per amu.
J.G. it has the brand name Pelletron. the rectifier units are replaced by an electrostatic charging belt. which increases the peak acceleration voltage. Nucl. (1. ds*is the differential for the line integral that surrounds the surface area. Phys.6 CHAPTER 1. Cockcroft-Walton electrostatic accelerator In 1930. INTRODUCTION 1.4) J Js Here £ is the induced electric field. Van de Graaff. Van de Graaff developed the electrostatic charging accelerator. Prog. R. 1. 704 (1934). 1 (1946). and the high-voltage terminal and the acceleration tube are placed in a common tank with compressed gas for insulation.10 Today the voltage attained in tandem accelerators is about 25 MV. John Douglas Cockcroft and Ernst Thomas Sinton Walton developed a highvoltage source by using high-voltage rectifier units. they reached 400-kV terminal voltage to achieve the first man-made nuclear transmutation: p + Li — » 2 He.D. economical. Buechner. The cascade type of X-ray tube is called the Coolidge tubes. When the Van de Graaff accelerator is used for electron acceleration. Rep. J.W. Since then. 195 (1960). Cockcroft and Walton shared 1951 Nobel Prize in physics. 11. Cockcroft and E. dS is the differential for the 8 J. Soc.J.9 In the Van de Graaff accelerator. Inst. Van de Graaff. when the magnetic flux changes. Placement of the high-voltage terminal at the center of the tank and use of the chargeexchange process in the tandem accelerator can increase the beam energy for nuclei. In 1932. Proc.J. and reliable radio frequency quadrupole (RFQ) accelerators. 1 0 R. 619 (1932).3 Induction Accelerators According to Faraday's law of induction. Methods 8. 9 R. $ is the total magnetic flux. Walton. $= f B-dS. A136. More recently. . Trump. the induction electric field along a beam path is given by ie-ds = $. A137.2 Electrostatic Accelerators X-ray tubes William David Coolidge in 1926 achieved 900-keV electron beam energy by using three X-ray tubes in series. Cockcroft-Walton accelerators have been widely used in first-stage ion-beam acceleration. they are being replaced by more compact.T. 229 (1932). Van de Graaff and tandam accelerators In 1931.S. Roy.8 The maximum achievable voltage was limited to about 1 MV because of sparking in air. and W. A144.
in Proc.K.1: Induction linac projects and achievements Laboratory / (kA) E (MeV) Beam width Repetition (ns) rate (Hz) ETA II LLNL 3 70 50 I ETA III LLNL 2 6 50 2000 ATA | LLNL | 10 | 50 | 50 | 1000 Project B: Betatron Let p be the mean radius of the beam pipe in a basic magnet configuration of a betatron. 1591 (1986). Table 1. R. A: Induction linac The induction linac was invented by N. Hyder. IEEE Trans. Barletta. Neil.J. Lett.C. Lett.I HISTORICAL DEVELOPMENTS 7 surface integral. Christofilos and R. Zi (1.12 A linear induction accelerator (LIA) employs a ferrite core arranged in a cylindrically symmetric configuration to produce an inductive load to a voltage gap. Beal.S. IEEE Trans. J or £ =-Bwp. Nucl.A. 1988). 3149 (1985).K. et al. NS 16. and V.J. LINAC96 (1996). Accel.5) will use magnetic field as a synonym for magnetic flux density. Eds.B..E.g. R. Rose. (Plenum Press. Christofilos in the 50's for the acceleration of high-intensity beams. 71 (1980). R. 57. Prono.C. Miller. the electric field at the voltage gap along the beam axis is used to accelerate the beam. Review of new developments in the field of induction accelerators. The induced electric field can be used for beam acceleration. 11. 3144 (1985). 13 See e. D.J. Part. Rev. NS32. 294 (1958) and references therein. and A. J. the induced electric field along the beam axis is given. Nucl. IEEE Trans.13 Table 1. Miller. A. Guenther. G. Sci. Caporaso.. NS32. If the total magnetic flux enclosed by the beam circumference is ramped up by a time-dependent magnetic flux density. G. N.W. 54. NATO ASI on High Brightness Transport in Linear Induction Accelerators. according to Faraday's law of induction. W. Phys.H.1 lists the achievements of some LIA projects. Nucl. Sci.B. Briggs. e. Sci. by <b £ • ds = 2np£ = np2Bm. Phys. M. Rev. and B is the "magnetic field"11 enclosed by the contour C. 2588 (1985). Hester. Each LIA module can be viewed as a low-Q 1:1 pulse transformer. in Proc.F. A properly pulsed stack of LIA modules can be used to accelerate high-intensity short-pulse beams with a gradient of about 1 MeV/m and a power efficiency of about 50%. Caporaso. 12 See 11 We .g. Simon Yu. When an external current source is discharged through the circuit.
8
CHAPTER 1. INTRODUCTION
Here £ is the induced electric field, and Bm is the average magnetic flux density inside the circumference of the beam radius. Thefinalparticle momentum can be obtained by integrating Newton's law, p = e£, i.e. p=-eBmp = eBgp, or Bg = -Bm. (1.6)
The betatron principle that the guide field Bg is equal to 1/2 of the average field Bm, was first stated by R. Wiederoe in 1928. u Figure 1.3 is a schematic drawing of a betatron, where particles circulate in the vacuum chamber with a guide field Bg, and the average flux density enclosed by the orbiting particle is £?av.
Figure 1.3: Schematic drawing of a betatron. The guidefieldfor beam particles is jBg, and the average flux density enclosed by the orbiting path is B av . It took many years to understand the stability of transverse motion. This problem was solved in 1941 by D. Kerst and R. Serber.15 When the magnetic field is shaped according to B, = £ > „ ( * ) " , (1.7)
where R is the reference orbit radius, r is the beam radius, and n is the index of focusing given by (see Exercise 1.14)
R fdBA
. .
Let x = r — R and z be small radial and vertical displacements from a reference orbit, then the equations of motion become — +cj2nz = 0, -—+L)2{l-n)x = 0. (1.9)
14In 1922, Joseph Slepian patented the principle of applying induction electric field for electron beam acceleration in the U.S. patent 1645304. 15D. Kerst and R. Serber, Phys. Rev. 60, 53 (1941). See also Exercise 1.14. Since then, the transverse particle motion in all types of accelerators has been called betatron motion.
I. HISTORICAL DEVELOPMENTS
9
Thus the motion is stable if 0 < n < 1. The resulting frequencies of harmonic oscillations are fx = foy/1 — n and fz = foy/n, where / 0 = W/2TT is the revolution frequency. In 1940 D. Kerst was the first to operate a betatron to achieve 2.3 MeV. In 1949 he constructed a 315-MeV betatron16 at the University of Chicago with the parameters p = 1.22 m, B% = 9.2 kG, Einj = 80 - 135 keV, / inj = 13 A. The magnet weighed about 275 tons and the repetition rate was about 6 Hz. The limitations of the betatron principle are (1) synchrotron radiation loss (see Chapter 4) and (2) the transverse beam size limit due to the intrinsic weak-focusing force.
1.4
Radio-Frequency (RF) Accelerators
Since the high-voltage source can induce arcs and corona discharges, it is difficult to attain very high voltage in a single acceleration gap. It would be more economical to make the charged particles pass through the acceleration gap many times. This concept leads to many different rf accelerators,17 which can be classified as linear (RFQ, linac) and cyclic (cyclotron, microtron, and synchrotron). Accelerators using an rf field for particle acceleration are described in the following subsections.
<u
o
Wideroe Linac
i
I —
I
-
i
i i
RF source S~\
r^
g->czi
c—i c—i i — i — i
i -+
Figure 1.4: Schematic drawing of the Wiederoe rf LINAC structure. Wideroe used a 1-MHz, 25-kV oscillator to make 50-kV potassium ions.
A. LINAC
In 1925 G. Ising pointed out that particle acceleration can be achieved by using an alternating radio-frequency field. In 1928 R. Wiederoe reported the first working rf accelerator, using a 1-MHz, 25-kV oscillator to produce 50-kV potassium ions (see Fig. 1.4). In 1931 D.H. Sloan and E.O. Lawrence built a linear accelerator using a 10-MHz, 45 kV oscillator to produce 1.26 MV Hg+ ion.18 An important milestone
Kerst et. a!., Phys. Rev. T8, 297 (1950). rf sources are classified into VHF, UHF, microwave, and millimeter waves bands. The microwave bands are classified as follows: L band, 1.12-1.7 GHz; S band, 2.6-3.95 GHz; C band, 3.95-5.85 GHz; X band, 8.2-12.4 GHz; K band, 18.0-26.5 GHz; millimeter wave band, 30-300 GHz. See also Exercise 1.2. 18 D.H. Sloan and E.O. Lawrence, Phys. Rev. 38, 2021 (1931).
17 The 16 D.W.
10
CHAPTER 1.
INTRODUCTION
in rf acceleration is the discovery of the phase-focusing principle by E. M. McMillan and V. Veksler in 1945 (see Ref. [17] and Chap. 2, Sec. IV.3). Since the length of drift tubes is proportional to J3X/2, it would save space by employing higher frequency rf sources. However, the problem associated with a high frequency structure is that it radiates rf energy at a rate of P = UriCVl (1.10)
where w,f is the rf frequency, C is the gap capacitance, and VT{ is the rf voltage. The rf radiation power loss increases with the rf frequency. To eliminate rf power loss, the drift tube can be placed in a cavity so that the electromagnetic energy is stored in the form of a magnetic field (inductive load). At the same time, the resonant frequency of the cavity can be tuned to coincide with that of the accelerating field. In 1948 Louis Alvarez and W.K.H. Panofsky constructed the first 32-MV drifttube linac (DTL or Alvarez linac) for protons.19 Operational drift-tube linacs for protons are the 200-MeV linacs at BNL and Fermilab, and the 50-MeV linacs at KEK and CERN. In the 1970's Los Alamos constructed the first side-coupled cavity linac (CCL), reaching 800 MeV. Fermilab upgraded part of its linac with the CCL to reach 400 MeV kinetic energy in 1995. The coupled cavity drift tube linac (CCDTL) that combines CCL and DTL has been shown to be efficient in accelerating high intensity low energy proton beams. After World War II, rf technology had advanced far enough to make magnetron and klystron20 amplifiers that could provide rf power of about 1 MW at 3 GHz (S band). Today, the highest energy linac has achieved 50-GeV electron energy operating at S band (around 2.856 GHz) at SLAC, and has achieved an acceleration gradient of about 20 MV/m, fed by klystrons with a peak power of 40 MW in a l-/xs pulse length. To achieve 100 MV/m, about 25 times the rf power would be needed. The next linear collider (NLC), proposed by SLAC and KEK, at a center-of-mass energy of 500 GeV to 2 TeV beam energy, calls for X band with an acceleration gradient of 50 MV/m or more. The required klystron peak power is about 50 MW in a pulse duration is about 1.5 us. The peak power is further enhanced by pulse compression schemes.
Alvarez, Phys. Rev. 70, 799 (1946). klystron, invented by Varian brothers in 1937, is a narrow-band high-gain rf amplifier. The operation of a high power klystron is as follows. A beam of electrons is drawn by the induced voltage across the cathode and anode by a modulator. The electrons are accelerated to about 400 kV with a current of about 500 A. As the beam enters the input cavity, a small amount of rf power (< 1 kW) is applied to modulate the beam. The subsequent gain cavities resonantly excite and induce micro-bunching of the electron beam. The subsequent drift region and penultimate cavity are designed to produce highly bunched electrons. The rf energy is then extracted at the output cavity, which is designed to decelerate the beam. The rf power is then transported by rf waveguides. The wasted electrons are collected at a water-cooled collector. If the efficiency were 50%, a klystron with the above parameters would produce 100 MW of rf power. See also E.L. Ginzton, "The $100 idea", IEEE Spectrum, 12, 30 (1975).
20The 19L.
I HISTORICAL DEVELOPMENTS
11
Superconducting cavities have also become popular in recent years. At the Continuous Electron Beam Accelerator Facility (CEBAF) at the Thomas Jefferson National Accelerator Laboratory in Virginia, about 160 m of superconducting cavity was installed for attaining a beam energy up to 4 GeV in 5 paths using 338 five-kW CW klystrons. During the LEP-II upgrade more than 300 m of superconducting rf cavity was installed for attaining an almost 100-GeV beam energy. Many accelerator laboratories, such as Cornell and Fermilab in the U.S. and DESY in Germany, are collaborating in the effort to achieve a high-gradient superconducting cavity for a linear collider design called the TeV Superconducting Linear Accelerator (TESLA). Normally, a superconducting cavity operates at about 5-10 MV/m. After extensive cavity wall conditioning, single-cell cavities have reached beyond 25 MV/m.21 B: RFQ In 1970,1.M. Kapchinskij and V.A. Teplyakov invented a low energy radio-frequency quadrupole (RFQ) accelerator - a new type of low energy accelerator. Applying an rf electric field to the four-vane quadrupole-like longitudinally modulated structure, a longitudinal rf electric field for particle acceleration and a transverse quadrupole field for focusing can be generated simultaneously. Thus the RFQs are especially useful for accelerating high-current low-energy beams. Since then many laboratories, particularly Los Alamos National Laboratory (LANL), Lawrence Berkeley National Laboratory (LBNL), and CERN, have perfected the design and construction of RFQ's, which are replacing Cockcroft-Walton accelerators as injectors to linac and cyclic accelerators. C: Cyclotron
The synchrotron frequency for a non-relativistic particle in a constant magnetic field is nearly independent of the particle velocity, i.e.,
wsyn =
e-Bo
7m
« wcyc = , * m
eB0
(1-11)
where 7 « 1 for non-relativistic particles, Bo is the magnetic field, and m is the particle mass. In 1929 E.O. Lawrence combined the idea of a constant revolution frequency and Ising's idea of the rf accelerator (see Sec. I.4A of Wiederoe linac), he invented the cyclotron.22 Historical remarks in E.O. Lawrence's Nobel lecture are
reach 30 MV/m and beyond. 22 E.O. Lawrence and N.E. Edlefsen, Science, 72, 376 (1930). See e.g. E.M. McMillan, Early Days in the Lawrence Laboratory (1931-1940), in New directions in physics, eds. N. Metropolis, D.M. Kerr, Gian-Carlo Rota, (Academic Press, Inc., New York, 1987). The cyclotron was coined by Malcolm Henderson, popularized by newspaper reporters; see M.S. Livingston, Particle Accelerators: A Brief History, (Harvard, 1969).
21See
e.g., J. Garber, Proc. PAC95, p. 1478 (IEEE, New York 1996). Single-cell cavities routinely
12
reproduced below:
CHAPTER 1.
INTRODUCTION
One evening early in 1929 as I was glancing over current periodicals in the University library, I came across an article in a German electrical engineering journal by Wideroe on the multiple acceleration of positive ions. . . . This new idea immediately impressed me as the real answer which I had been looking for to the technical problem of accelerating positive ions, . . . Again a little analysis of the problem showed that a uniform magnetic field had just the right properties - that the angular velocity of the ion circulating in the field would be independent of their energy so that they would circulate back and forth between suitable hollow electrodes in resonance with an oscillating electric field of a certain frequency which has come to be known as the cyclotron frequency. Now this occasion affords me a felicitous opportunity in some measure to correct an error and an injustice. For at that time I did not carefully read Wiederoe's article and note that he had gotten the idea of multiple acceleration of ions from one of your distinguished colleagues, Professor G. Ising, who in 1924 published this important principle. It was several years had passed that I became aware of Professor Ising's prime contribution. I should like to take this opportunity to pay tribute to his work for he surely is the father of the developments of the methods of multiple acceleration.
If two D plates (dees) in a constant magnetic field are connected to an rf electric voltage generator, particles can be accelerated by repeated passage through the rf gap, provided that the rf frequency is an integer multiple of the cyclotron frequency, a/rf = huj0. On January 2, 1931 M.S. Livingston demonstrated the cyclotron principle by accelerating protons to 80 keV in a 4.5-inch cyclotron, where the rf potential applied across the the accelerating gap was only 1000 V. In 1932 Lawrence's 11inch cyclotron reached 1.25-MeV proton kinetic energy that was used to split atoms, just a few months after this was accomplished by the Cockcroft-Walton electrostatic accelerator. Since then, many cyclotrons were designed and built in Universities.23 Figure 1.5 shows a schematic drawing of a classical cyclotron. The momentum p and kinetic energy T of the extracted particle are p = rwyPc and T = mc2(7 - 1) = p2/[(j + l)m]. Using Eq. (1.3), we obtain the kinetic energy per amu as
A-(7+l)muUJ
=K
{A) '
(L12)
where BoRo = Bp is the magnetic rigidity, Z and A are the charge and atomic mass numbers of the particle, mu is the atomic mass unit, and K is called the K-value or bending limit of a cyclotron. In the non-relativistic limit, the /{"-value is equal to the proton kinetic energy T in MeV, e.g. K200 cyclotron can deliver protons with 200 MeV kinetic energy.
23 M.S. Livingston, J. Appl. Phys, 15, 2 (1944); 15, 128 (1944); W.B. Mann, The Cyclotron, (Wiley, 1953); M.E. Rose, Phys. Rev., 53, 392 (1938); R.R. Wilson, Phys. Rev., 53, 408 (1938); Am. J. Phys., 11, 781 (1940); B.L. Cohen, Rev. Sci. Instr., 25, 562 (1954).
I. HISTORICAL
DEVELOPMENTS
13
F j ;I I • • i \ \ \ '. ', i \ (~)rf n i l i .' C i i ; i! D |"^ \\ \ \ \ \ \ ion source ,' ; ; ; I \ \ \ \ \ \ ^, .•'','•!'/
Figure 1.5: Schematic drawing of a classical cyclotron. Note that the radial distance between adjacent revolutions becomes smaller as the turn number increases [see Eq. (1.13)].
septum
The iron saturates at a field of about 1.8 T (depending slightly on the quality of iron and magnet design). The total volume of iron-core is proportional to the cubic power of the beam rigidity Bp. Thus the weight of iron-core increases rapidly with its K-value: Weight of iron = W ~ K15 ~ (Bp)3, where Bp is the beam rigidity. Typically, the magnet for a K-100 cyclotron weighs about 160 tons. The weight problem can be alleviated by using superconducting cyclotrons.24 The design of beam extraction systems in cyclotrons is challenging. Let VQ be the energy gain per revolution. The kinetic energy at ./V revolutions is K^ = eiVVo = e2B2r2/2m, where e is the charge, m is the mass, B is the magnetic field, and r is the beam radius at the ./V-th revolution. The radius r of the beam at the iV-th revolution becomes
r =I
(^) "V*.
(U3)
i.e. the orbiting radius increases with the square root of the revolution number N. The beam orbit separation in successive revolutions may becomes small, and thus the septum thickness becomes a challenging design problem. Two key difficulties associated with classical cyclotrons are the orbit stability and the relativistic mass effect. The orbit stability problem was partially solved in 1945 by D. Kerst and R. Serber (see Exercise 1.14). The maximum kinetic energy was limited by the kinetic mass effect. Because the relativistic mass effect can destroy particle synchronism [see Eq. (1.11)], the upper limit of proton kinetic energy attainable in a cyclotron is about 12 MeV (See Exercise 1.4.).25 Two ideas proposed to solve the dilemma are the isochronous cyclotron and the synchrocyclotron.
24 See 25 H.
H. Blosser, in Proc. 9th Int. Conf. on Cyclotrons and Applications, p. 147 (1985). Bethe and M. Rose, Phys. Rev. 52, 1254 (1937).
14
CHAPTER 1.
INTRODUCTION
Isochronous cyclotron
In 1938 R.H. Thomas pointed out that, by using an azimuthal varying field, the orbit stability can be retained while maintaining the isochronism. The isochronous cyclotron is also called the azimuthal varying field (AVF) cyclotron. From the cyclotron principle, we observe that
where Eo = me2 and ui is the angular revolution frequency. Thus, to maintain isochronism with constant w, the B field must be shaped according to
Bz = ^
e
= ^E{p) = ^\l-mY/2.
ec* ec2 [ V c / J
(1.15)
When the magnetic flux density is shaped according to Eq. (1.15), the focusing index becomes n < 0, and the vertical orbit is unstable. Orbit stability can be restored by shaping the magnetic pole-face. In 1938 L.H. Thomas introduced pole plates with hills and valleys in an isochronous cyclotron to achieve vertical orbit stability.26 Such isochronous cyclotrons are also called AVF cyclotrons. The success of sector-focused cyclotron led by J.R. Richardson et al. led to the proliferation of the separate sector cyclotron, or ring cyclotron in the 1960's.27 It gives stronger "edge" focusing for attaining vertical orbit stability. Ring cyclotrons are composed of three, four, or many sectors. Many universities and laboratories built ring cyclotrons in the 1960's.
Synchrocyclotron
Alternatively, synchronization between cyclotron frequency and rf frequency can be achieved by using rf frequency modulation (FM). FM cyclotrons can reach 1-GeV proton kinetic energy.28 The synchrocyclotron uses the same magnet geometry as the weak-focusing cyclotrons. Synchronism between the particle and the rf accelerating voltage is achieved by ramping the rf frequency. Because the rf field is cycled, i.e. the rf frequency synchronizes with the revolution frequency as the energy is varied, synchrocyclotrons generate pulsed beam bunches. Thus the average intensity is low. The synchrocyclotron is limited by the rf frequency detuning range, the strength of the magnet flux density, etc. Currently two synchrocyclotrons are in operation, at CERN and at LBL.
Thomas, Phys. Rev. 54, 580 (1938). Willax, Proc. Int. Cyclotron Conj. 386 (1963). 28 For a review, see R. Richardson, Proc. 10th Int. Conj. on Cyclotrons and Their Applications, IEEE CH-1996-3, p. 617 (1984).
27 H.A. 26 L.H.
I. HISTORICAL DEVELOPMENTS D: Microtron
15
As accelerating rf cavities are expensive, it would be economical to use the rf structure repetitively: microtrons, originally proposed by V. Veksler in 1944, are designed to do this. Repetitive use requires synchronization between the orbiting and the rf periods. For example, if the energy gain per turn is exactly equal to the rest mass of the electron, the cyclotron frequency at the n — 1 passage is given by <4.-i = — , (1-16) nm0 i.e., the orbit period is an integral multiple of the fundamental cyclotron period. Thus, if the rf frequency tuTf is an integral multiple of the fundamental cyclotron frequency, the particle acceleration will be synchronized. Such a scheme or its variation was invented by V. Veksler in 1945. The synchronization concept can be generalized to include many variations of magnet layout, e.g. the race track microtron (RTM), the bicyclotron, and the hexatron. The resonance condition for the RTM with electrons traveling at the speed of light is given by AW nArf = 2 T T — , (1.17) ecB where AE is the energy gain per passage through the rf cavity, B is the bending dipole field, Arf is the rf wavelength, and n is an integer. This resonance condition simply states that the increase in path length is an integral multiple of the rf wavelength. Some operational microtrons are the three-stage MAMI microtron at Mainz, Germany,29 and the 175-MeV microtron at Moscow State University. Several commercial models have been designed and built by Scanditron. The weight of the microtron also increases with the cubic power of beam energy. E: Synchrotrons, weak and strong focusing After E.M. McMillan and V. Veksler discovered the phase focusing principle of the rf acceleration field in 1945, a natural evolution of the cyclotron was to confine the particle orbit in a well-defined path while tuning the rf system and magnetic field to synchronize particle revolution frequency.30 The first weak-focusing proton synchrotron, with focusing index 0 < n < 1, was the 3-GeV Cosmotron in 1952 at BNL.
e.g., H. Herminghaus, in Proc. 1992 EPAC, p. 247 (Edition Frontieres, 1992). Goward and D.E. Barnes converted a betatron at Telecommunication Research Laboratory into a synchrotron in August 1946. A few months earlier, J.R. Richardson, K. MacKenzie, B. Peters, F. Schmidt, and B. Wright had converted the fixed frequency 37-inch cyclotron at Berkeley to a synchro-cyclotron for a proof of synchrotron principle. A research team at General Electric Co. at Schenectady built a 70 MeV electron synchrotron to observe synchrotron radiation in October 1946. See also E.J.N. Wilson, 50 years of synchrotrons, Proc. of the EPAC96 (1996).
30Prank 29see
16
CHAPTER 1.
INTRODUCTION
A 6-GeV Bevatron constructed at LBNL in 1954, led to the discovery of antiprotons in 1955. An important breakthrough in the design of synchrotron came in 1952 with the discovery of the strong-focusing or the alternating-gradient (AG) focusing principle by E.D. Courant, H.S. Snyder and M.S. Livingston.31 Immediately, J. Blewett invented the electric quadrupole and applied the alternating-gradient-focusing concept to linac32 solving difficult beam focusing problems in early day rf linacs. Here is Some
Recollection on the Early History of Strong Focusing in the publication BNL 51377 (1980) by E.D. Courant: Came the summer of 1952. We have succeeded in building the Cosmotron, the world's first accelerator above one billion volts. We heard that a group of European countries were contemplating a new high-energy physics lab with a Cosmotron-like accelerator (only bigger) as its centerpiece, and that some physicists would come to visit us to learn more about the Cosmotron. . . . Stan (Livingston) suggested one particular improvement: In the Cosmotron, the magnets all faced outward. This made it easy to get negative secondary beam from a target in the machine, but much harder to get positive ones. Why not have some magnets face inward so that positive secondaries could have a clear path to experimental apparatus inside the ring? . . . I did the calculation and found to my surprise that the focusing would be strengthened simultaneously for both vertical and horizontal motion. ... Soon we tried to make the gradients stronger and saw that there was no theoretical limit - provided the alterations were made more frequent as the gradient went up. Thus it seemed that aperture could be made as small as one or two inches against 8 x 24 inches in the Cosmotron, 12 x 48 in the Bevatron, and even bigger energy machines as we then imagined them. With these slimmer magnets, it seemed one could now afford to string them out over a much bigger circles, and thus go to 30 or even 100 billion volts.
The first strong-focusing 1.2 GeV electron accelerator was built by R. Wilson at Cornell University. Two strong-focusing or alternating-gradient (AG) proton synchrotrons, the 28-GeV CERN PS (CPS) and the 33-GeV BNL AGS, were completed in 1959 and 1960 respectively. The early strong-focusing accelerators used combined-function magnets, i.e., the pole-tips of dipoles were shaped to attain a strong quadrupole field. For example, the bending radius and quadrupole field gradients of AGS magnets are respectively p = 85.4 m, and Bx = (dB/dx) = ±4.75 T/m at B — 1.15 T. This corresponds to a focusing index of n = ±352. The strengths of a string of alternating focusing and defocussing lenses were adjusted to produce net strong focusing effects in both planes. The strong focusing idea was patented by a U.S. engineer, N.C. Christofilos,33
Courant, H.S. Snyder and M.S. Livingston, Phys. Rev. 88, 1188 (1952). Blewett, Phys. Rev. 88, 1197 (1952). 33 N.C. Christofilos, Focusing system for ions and electrons, U.S. Patent No. 2736799 (issued 1956). Reprinted in The Development of High Energy Accelerators, M.S. Livingston, ed. (Dover, New York, 1966).
3 2 J. 31 E.D.
I. HISTORICAL DEVELOPMENTS
17
living in Athens, Greece. Since then, the strong-focusing (AG) principle and a cascade of AG synchrotrons, proposed by M. Sands,34 has become a standard design concept of high energy accelerators. Since the saturation properties of quadrupole and dipole fields in a combined function magnet are different, there is advantage in machine tuning with separate quadrupole and dipole magnets. The Fermilab Main Ring was the first separate function accelerator.35 Most present-day accelerators are separate-function machines. For conventional magnets, the maximum dipole field strength is about 1.5 T and the maximum field gradient is approximately I/a [T/m] (see Exercise 1.12), where o is the aperture of the quadrupole in meters. For superconducting magnets, the maximum field and field gradient depends on superconducting coil geometry, superconducting coil material, and magnet aperture.
1.5
Colliders and Storage Rings
The total center-of-mass energy obtainable by having an energized particle smash onto a stationary particle is limited by the kinematic transformation (see Exercise 1.6). To boost the available center-of-mass energy, two beams are accelerated to high energy and made to collide at interaction points.36 Since the lifetime of a particle beam depends on the vacuum pressure in the beam pipe, stability of the power supply, intrabeam Coulomb scattering, Touschek scattering, quantum fluctuations, collective instabilities, nonlinear resonances, etc., accelerator physics issues have to be evaluated in the design, construction, and operation of colliders. Beam manipulation techniques such as beam stacking, bunch rotation, stochastic beam cooling, invented by S. Van de Meer,37 electron beam cooling, invented by Budker in 1966,38 etc., are essential in making the collider a reality. The first proton-proton collider was the intersecting storage rings (ISR) at CERN completed in 1969. ISR was the test bed for physics ideas such as stochastic beam cooling, high vacuum, collective instabilities, beam stacking, phase displacement acceleration, nonlinear beam-beam force, etc. It reached 57 A of single beam current at 30 GeV. It stopped operation in 1981. The first electron storage ring (200 MeV) was built by B. Touschek et al. in 1960
34M. 35The
a cascade of accelerators including proton linac, rapid cycling booster synchrotron, and a separate function Main Ring. 36 A.M. Sessler, The Development of Colliders, LBNL-40116, (1997). The collider concept was patented by R. Wiederoe in 1943. The first collider concept based on "storage rings" was proposed by G.K. O'Neill in Phys. Rev. Lett. 102, 1418 (1956). 3 7 S. Van de Meer, Stochastic Damping of Betatron Oscillations in the ISR, CERN internal report CERN/ISR-PO/72-31 (1972). 38 See e.g., H. Poth, Phys. Rep. 196, 135 (1990) and references therein.
Sands, A proton synchrotron for 300 GeV, MURA Report 465 (1959). Fermi National Accelerator Laboratory was established in 1967. The design team adopted
18
CHAPTER 1. INTRODUCTION
in Rome. It had only one beam line and an internal target to produce positrons, and it was necessary to flip the entire ring by 180° to fill both beams. Since the Laboratoire de l'Accelerateur Lineaire (LAL) in Orsay had a linac, the storage ring was transported to Orsay in 1961 to become the first e+e~ collider. The StanfordPrinceton electron-electron storage ring was proposed in 1956 but completed only in 1966. The e~e" collider moved from Moscow to Novosibirsk in 1962 began its beam collision in 1965. Since the 1960's, many e+e~ colliders have been built. Experience in the operation of high energy colliders has led to an understanding of beam dynamics problems such as beam-beam interactions, nonlinear resonances, collective (coherent) beam instability, wakefield and impedance, intrabeam scattering, etc. Some e+e~ colliders now in operation are CESR at Cornell, SLC and PEP at SLAC, PETRA and DORIS at DESY, VEPP's at Novosibirsk, TRISTAN at KEK, and LEP at CERN. The drive to reach higher energy provided the incentive for the high power klystron. The power compression method SLED (SLAC Energy Development), originated by P. Wilson, D. Farkas, H. Hogg, et al., paved the way to the SLAC Linear Collider (SLC). High energy lepton colliders such as NLC, JLC, and CLIC are expanding linear accelerator technology. On the luminosity frontier, the ^-factory at Frascati and B-factories such as PEP-II at SLAC and TRISTAN-II at KEK aim to reach 1033"34 crn"2 s""1. Proton-antiproton colliders include the Tevatron at Fermilab and SppS at CERN. The discovery of type-II superconductors39 led to the successful development of superconducting magnets, which have been successfully used in the Tevatron to attain 2-TeV cm. energy, and in HERA to attain 820-GeV proton beam energy. At present, the CERN LHC (14-TeV cm. energy) and the BNL RHIC (200-GeV/u heavy ion cm. energy) are under construction. The (40-TeV) SSC proton collider in Texas was canceled in October 1993. Physicists are contemplating a very large hadron collider with about 60-100 TeV beam energy.
1.6
Synchrotron Radiation Storage Rings
Since the discovery of synchrotron light from a then high energy (80-MeV) electron synchrotron in 1947, the synchrotron light source has become an indispensable tool in basic atomic and molecular physics, condensed-matter physics, material science, biological, chemical, and medical research, and material processing. Worldwide, about 70 light sources are in operation or being designed or built. Specially designed high-brightness synchrotron radiation storage rings are classified into generations. Those in the first generation operate in the parasitic mode
39Type II superconductors allow partial magnetic flux penetration into the superconducting material so that they have two critical fields BC\(T) and BC2(T) in the phase transition, where T is the temperature. The high critical field makes them useful for technical applications. Most type II superconductors are compounds or alloys of niobium; commonly used alloys are NbTi and NbaSn.
II. S.. Eds. 1 Acceleration Cavities The electric fields used for beam acceleration are of two types: the DC acceleration column and the rf cavity. booster synchrotrons. new acceleration schemes such as inverse free-electron laser acceleration. plasma wakefield acceleration. the advanced light source (ALS) at Lawrence Berkeley National Laboratory. and colliders. Vo /) is the effective peak accelerating voltage..40 The DC acceleration column is usually used in low energy accelerators such as the Cockcroft-Walton. the beam pulse is usually prebunched and chopped into appropriate sizes. etc. Some basic accelerator components are described in the following subsections. Before injection into various types of accelerators. laser . Third-generation light sources produce high-brilliance photon beams from insertion devices using dedicated high-brightness electron beams. (1996) and reference therein.. chopper. There are research efforts toward fourth generation light sources based on free electron laser from a long undulator.18) where AV = VQ sin(wrft + <> is the effective gap voltage. For a particle with charge e. These include the advanced photon source (APS) at Argonne National Laboratory. 40In recent years. (1. where charged ions are extracted by a high-voltage source to form a beam.g. storage rings. Figure 1. etc. No. the Japan synchrotron radiation facility (JSRF). 398. wrf is the rf frequency. and 4> is the phase angle. II.6 is a schematic drawing of a small accelerator complex at the Indiana University Cyclotron Facility. Chattopadhyay. pre-accelerators such as the high-voltage source or RFQ. The rf acceleration cavity provides a longitudinal electric field at an rf frequency that ranges from a few hundred kHz to 10-30 GHz. AIP Conf. et al. LAYOUT AND COMPONENTS OF ACCELERATORS 19 from existing high energy e+e~ colliders. Low frequency rf cavities are usually used to accelerate hadron beams. Particle beams are produced from ion sources. drift-tube linac (DTL). the European synchrotron radiation facility (ESRF). the energy gain/loss per passage through a cavity gap is AE = eAV. The beams can be injected into a chain of synchrotrons to reach high energy. have been proposed for high-gradient accelerators. See e. Van de Graaff. II Layout and Components of Accelerators A high energy accelerator complex is composed of ion sources. and high frequency rf cavities to accelerate electron beams. The second generation comprises dedicated low-emittance light sources. Advanced Accelerator Concepts. etc. buncher/debuncher. The beam can be accelerated by a DC accelerator or RFQ to attain the proper velocity needed for a drift-tube linac. Proc.
the Cooler Injector Synchrotron (CIS) at the Indiana University Cyclotron Facility.2 Accelerator Magnets Accelerator magnets requires stringent field uniformity condition in order to minimize un-controllable beam orbit distortion and beam loss. The circumference is 17. The superconducting magnets employ superconducting coils to produce high field magnets. and a transfer line are shown to illustrate the basic structure of an accelerator system.36 m. . the CIS synchrotron with 4 dipoles. Accelerator magnets are also classified into conventional iron magnets and superconducting magnets. Accelerator magnets are classified into field type of dipole magnets for beam orbit control.6: A small accelerator. DTL. The synchronization is achieved by matching the rf frequency with particle velocity. INTRODUCTION Figure 1.20 CHAPTER 1. The source. sextupole and higher-order multipole magnets for the control of chromatic and geometric aberrations. chopper. debuncher. Acceleration of the bunch of charged particles to high energies requires synchronization and phase focusing. and the phase focusing is achieved by choosing a proper phase angle between the rf wave and the beam bunch. The conventional magnets employ iron or silicon-steel with OFHC copper conductors. quadrupole magnets for beam size control. II. RPQ.
the superconducting coils are arranged to simulate the cosine-theta like distribution.8 T. and the total integrated dipole field is I Bdl = 2-rrpo/e = 2nBp.9 = / Bdl = -— Bdl. The iron plate can be C-shaped for a C-dipole (see Exercise 1.II.10 and the left plot of Fig. and Bp = po/e is the momentum rigidity of the beam. superconducting coils can be used. A gap between the iron yoke is used to shape dipole field. 1. that requires DC magnetic field. Figure 1. the maximum attainable field for iron magnet is about 1. To attain a higher dipole field. the pole shape is designed to attain uniform field in the gap. (1. The rectangular blocks shown in the left plot are oxygen free high conductivity (OFHC) copper coils. courtesy of R. the bending angle 6 is given by . These magnets are called superconducting magnets. The total bending angle for a circular accelerator is 2TT. Solid block of high permeability soft-iron can also be used for magnets in the transport line or cyclotrons. Gupta at LBNL). courtesy of G. .20) The conventional dipole magnets are made of laminated silicon-steel plates for the return magnetic flux for minimizing eddy current loss and hysteresis loss.7 T magnet flux. (1.7). For superconducting magnets. Berg at IUCF) and an SSC superconducting dipole magnet (right.7: The cross-sections of a C-shaped conventional dipole magnet (left. or H-shaped for H-dipole. LAYOUT AND COMPONENTS OF ACCELERATORS 21 Dipoles Dipole magnets are used to guide charged particle beams along a desired orbit.19) P o Jsi Bp Jsi where po is the momentum of the beam. Since iron saturates at about 1. From the Lorentz force law. For conventional magnets.
vacuum ports 4 1 B. II.7 shows the cross-section of the highfieldSSC dipole magnets.. * * « « • . e. INTRODUCTION Superconducting magnets that use iron to enhance the attainable magnetic field is also called superferric magnets. Quadrupoles A stack of laminated iron plates with a hyperbolical profile can be used to produce quadrupole magnet (see Exercise 1.22) Lil-. s.3 Other Important Components Other important components in accelerators are ion sources. azimuthal. 1. Electron Cyclotron Resonance Ion Sources and ECR Plasma (Inst. Bristol. the Lorentz force for a particle with charge e and velocity v along the J direction is given by F = evBi§ x {zx + xz) = —evB\ZZ + evB\XX. beam current and beam loss. New York. For a charged particle passing through the center of a quadrupole. R. 24) in a quadrupole. the magnetic field and the Lorentz force are zero. beam dump. where s — vt is the longitudinal distance along the s direction.. (1. Pub. Wolf. and x. of Phys. Geller. 1995).. The right plot of Fig. emittance meters. and z are the unit vectors in the horizontal.g. Bp ox d?z n we obtain d2x n (1 .22 CHAPTER 1. For high field magnets. z) from the center. 77m. where the magnetic field of an ideal quadrupole is given by B = B1(zx + xz). . ed.41 monitors for beam position. Handbook of Ion Sources (CRC Press. At a displacement (a. blocks of superconducting coils are used to simulate the cosine-theta current distribution (see Exercise 1. Defining the focusing index as „ =* .9).21) where B\ = dBz/dx evaluated at the center of the quadrupole. The equations of motion become 1d^_eBL (1. 5-12 T. and vertical directions. 1996).12).^LZ vl at1 jmv (123) vl at1 jmv Thus a focusing quadrupole in the horizontal plane is also a defocussing quadrupole in the vertical plane and vice versa.
For high energy experiments. and other nonlinear magnets for nonlinear stopband correction. The Tevatron at Fermilab facilitated the discovery of the top quark in 1995. power supplies. Computer control software retrieves beam signals. For synchrotron radiation applications in electron storage rings. Observation of a parton-like structure inside a proton provided proof of the existence of elementary constituents known as quarks. The LHC (7-TeV on 7-TeV proton-proton collider) at CERN will lead high energy physics research at the beginning of the 21st century. high energy accelerators are needed. wigglers and undulators are used to enhance the photon beam quality. beam stacking accumulation.1 fm) studies of the electromagnetic properties of nuclei. beam orbit and stopband correctors. Ill III. f2. Tevatron (1-TeV on 1-TeV proton-antiproton collider). The CEBAF 4-6-GeV continuous electron beams allow high resolution (0. sophisticated particle detectors are the essential sources of discovery. The timing and operation of all accelerator components (including experimental devices) are controlled by computers. sextupoles. such as the B-factories at SLAC and KEK and the ^-factory at DA$NE. High luminosity colliders. stochastic beam cooling. . etc. LEP (50-100-GeV on 50-100-GeV e+e~ collider) led the way in high energy physics in the 1990's. octupoles. The RHIC (100-GeV/u on 100-GeV/u heavy ion collider) will provide important information on the phase transitions of quark-gluon plasma. W*1 • • •. High energy accelerators have provided essential tools in the discovery of p. skew quadrupoles.l Accelerator Applications High Energy and Nuclear Physics To probe into the inner structure of the fundamental constituents of particles. etc. High energy colliders such as HERA (30-GeV electrons and 820-GeV protons). will provide dedicated experiments for understanding the symmetry of the fundamental interactions. Historical advancement in particle and nuclear physics has always been linked to advancement in accelerators.III. orbit bumps. Z°. etc. and septum. ACCELERATOR APPLICATIONS 23 and pumps. Radioactive beams may provide nuclear reactions that will lead to understanding of the nucleo-synthesis of elements in the early universe. SLC (50-GeV on 50-GeV e+e" collider). kickers. The advance in computer hardware and software provides advanced beam manipulation schemes such as slow beam extraction. J/^. The IUCF cyclotron has provided the opportunity to understand the giant Ml resonances in nuclei. and sets proper operational conditions for accelerator components.
proton and heavyion beams have become popular in cancer radiation therapy because these beam particles deposit most of their energy near the end of their path. Beam lithography is used in industrial processing. Beams have been used in radiation sterilization. Bert M. isotope production for radionuclide therapy. (a) Estimate the magnetic rigidity of proton beams at the IUCF Cooler Ring (kinetic energy 500 MeV). Since the discovery of X-ray in 1895.24 CHAPTER 1. and strategic equipment. p. Patent 2787564). INTRODUCTION III. and radiation treatments. etc. In particular. p is the beam momentum. Phys. . diagnosis. biology. By controlling the beam energy. Shockley in 1954 (U. Nath. and insulators. Radiation has been used in the manufacture of polymers. 43see e. invented by W. and neutron back-scattering have provided important tools for solid-state and condensed-matter physics research. Neutron sources have been important sources for research aimed at understanding the properties of metals. and biochemistry. and Ze is the charge of the particle.43 etc.42 synchrotron radiation sources.— . RHIC (momentum 250 GeV/c). Show that the magnet rigidity Bp is related to the particle momentum p by R \rp i _ P _ \ 3. what is the total length of dipole needed for each of these accelerators? 42The ion implantation.3357 p [GeV/c] for singly charged particles j G e V / .2 Solid-State and Condensed-Matter Physics Ion implantation. radiation has been used in medical imaging. solid-state physics. Coursey and R.g. c ] for particles with charge Ze ' &P Limj . ships. 3 Other Applications Electron beams can be used to preserve and sterilize agricultural products. 25. Particle beams have been used to detect defects and metal fatigue of airplanes. Radiation can be used to terminate unwanted tumor growth with electron. III. or ion beams. radiation hardening for material processing. Today. semiconductors. Free-electron lasers with short pulses and high brightness in a wide spectrum of frequency ranges have been used extensively in medical physics. proton. (b) If the maximum magnetic flux density for a conventional dipole is 1. Exercise 1: Basics 1. most of the beam energy can be deposited in the cancerous tumor with little damage to surrounding healthy cells.| 3^57 p where B is the magnetic flux density. p is the bending radius. has become an indispensable tool in the semiconductor industry. April 2000.7 Tesla.S. Tevatron (momentum 1 TeV/c) and SSC (momentum 20 TeV/c).
.l)uio.6 mm. The total power radiated by an accelerated charged particle is given by Larmor's formula: 1 2e2t>2 _ 1 2e2 dp^ dp. and 7 is the relativistic energy factor. Modern Microwave Technology (Prentice Hall.F. what is the equivalent field gradient? 4. Assuming that you can build a capacitor with a minimum capacitance of C = 1 pF. For an order of magnitude estimation. 5. if a sinusoidal voltage Vrt — t^costt/pt is applied to the dees. (a) Estimate the space-charge force for the SSC low energy booster at injection with kinetic energy 800 MeV and NQ = 1010 particles per bunch. If this force is exerted by a quadrupole.HIC). and the beam size is 3 /jm.. the maximum attainable kinetic energy is \/2eVmc2/n. show that a test charged particle traveling along at the same velocity as the beam.C. f e 2 JV o—n. experiences a repulsive space-charge force.r o 6 2 2r . (b) What happens if the test charged particle travels in the opposite direction in the head-on collision process? Estimate the space-charge force for the e+e~ colliding beam at SLC. the rms bunch length is as = 0. where the beam parameters are E = 47 GeV and NB = 2 x 1010. The resonance frequency of a LC circuit is / r = l/2-Ky/LC. what is the total length of dipoles needed in each accelerator? 2. (a) Let ip be the rf phase of the particle. 5 T (Tevatron) and 6./w. Use the following steps. NJ. 1987).5 mm thick will yield an inductance of about 3 x 10~7 H. Englewood Cliffs.6 T (SSC). ~ 47re0 3c3 ~~ 4TT€0 3m 2 c 3 ( dr ' dr ' "See V. Integrate this equation and show that the maximum kinetic energy attainable is \j2eVmc'1. where WQ = eB/m is the cyclotron frequency. with rms bunch length as = 2 m and beam diameter 4 mm. where e and m are the charge and mass of the particle. r - a r> a ( 2^607" 7 where 7 = l / \ / l . Veley./ 3 2 and e is the charge of the beam particle. Consider a uniform cylindrical beam with N particles per unit length in a beam of radius o. Here the number of particles per unit length is N = NB/(\/2nas).EXERCISE 1 25 (c) If superconducting magnets are used with magnetic fields B = 3. a 5-cm-radius single loop with wire 0. Show that the equation of motion in a uniform acceleration approximation is dip/dt = (7" 1 . (b) Denning a variable q = acos^>. where a = 2u>oeV/irmc2. the synchronous frequency is cj = eB/ym = UJQ/J. show that the equation of motion becomes {q/\/a2 — q2)dq = (27 — 2)UIQ dj. in the uniform acceleration approximation.5 T (R. dy2/dt — acostp. In a cyclotron. v. what value of inductance L is needed to attain 3 GHz resonance frequency? What is your conclusion from this exercise? Can you use a conventional LC circuit for microwave tuning? 44 3. to prove that.
dp _ 1 dE where w = j3c/p. INTRODUCTION where dr = dt/y is the proper time and pM is the four-momentum. and p is the bending radius. p. the gradient of the accelerating cavities will increase by a factor of 10. Classical Electrodynamics. The ratio of radiation power loss to power supply from an external accelerating source is = P _ 1 2e2 dE _ 2 re dE dE/dt ~ 47reo3m2c3«.78 x l(T 18 [m/(GeV) 3 ] for protons. . and p is the radius of curvature in the dipole. where the circulating beam currents are respectively 3 mA and 70 mA. 1 7.85 x l(r 5 [m/(GeV) 3 ] for electrons.26 CHAPTER 1. I is the total beam current. Assuming that electrons gain energy from 1 GeV to 47 GeV in 3 km at SLC. The radiated power becomes where ro is the classical radius of the particle. 45See J. what is the ratio of power loss to power supply? In the Next Linear Collider (NLC). The radiative energy loss per revolution of an isomagnetic storage ring becomes i. Calculate the energy dissipation per revolution for electrons at energy E = 50 GeV and 100 GeV in LEP. where p = 3096. Find the energy loss per turn for protons in SSC. Jackson. 2nd ed.(rf^) ~ S m c 2 ^ ' 1 where re = 2. and = 7 4nr0 3(mc 2 ) 3 = f 8. p changes direction while the change in energy per revolution is small..6 Tesla at 20 TeV. The power radiated 1 2e2 dp 2 = 1 2e2 dE 2 47re o 3m 2 c 3 Mr 47re0 3m 2 c 3 1 dx ' ' where dE/dx is the rate of energy change per unit distance. i. iii. ii. where the magnetic field is 6.e. Uo = ^CyE^/p. the circumference is 87120 m.853 m. the motion is along a straight path.45 (a) In a linear accelerator. What will be the ratio of radiation power loss to power supply? What is your conclusion from this exercise? (b) In a circular accelerator.175 m and the circumference is 26658. m is the mass.D.82 x 10~15 m is the classical radius of the electron. and the bending radius is 10187 m. Find the synchrotron radiation power loss per unit length in LEP and SSC. 468 (1975). Show that the power radiated per unit length in dipoles for a beam is where Ug is the energy loss per revolution.
(a) In fixed target experiments. is a measure of the probability (rate) of particle encounters per unit area in a collision process. What is the advantage of stretching the beam pulse length to 1 s in this experiment? (b) When two beams collide head-on. where si = s + fict. z. the luminosity is given by C = (dNB/dt)retarget. where the beam repetition rate is 0. „ 6+(62 + [l. s2 = s — fict. the luminosity is reduced by a factor exp{—b2/4a2}. and p\ and pi are the normalized distribution functions for these two bunches. L [cm~ 2 s~ 1 ]. f is the encountering frequency. z. . Consider a fixed target experiment. The luminosity. Show that the total energy for a head-on collision of two beams at an energy of 7 cm mc 2 each is equivalent to a fixed target collision at the laboratory energy of 7771c2 with 7 = 27c2m . + 1 [e_s]2)m+^a+{a2+s2)y2) 6 +(b2 + s2)V2\ where I is the length of the solenoid. beam particle per pulse is 1013. and the target thickness is 4 mg/cm 2 Au foil. the beam pulse length is 150 ns. Ni and JV2 are the numbers of particles. where dNB/dt is the number of beam particles per second on target. and ntarget is the target thickness measuring the number of atoms per cm2.4 Hz. show that the luminosity for two bunches with identical distribution profiles is £=fN1N1 4naxaz Show that when two beams are offset by a horizontal distance 6. 8.1. Using a Gaussian bunch distribution. Here NB is the number of particles per pulse (bunch) and / is the pulse repetition rate. where (dNB/dt) = NBf. J is the current density. b are the inner and outer cylindrical radii respectively.a2. the luminosity is £ = 2fNiN2[ pi(z. and CTS are respectively the horizontal and vertical rms bunch widths and the rms bunch length. 7. and s is the distance from one end of the solenoid. Thus the total counting rate of a physics event is it = (TphysA where <Tphys is the cross-section of a physics process. Find the instantaneous and average luminosities of the fixed target experiment. a. si)p2{x.EXERCISE 1 27 6.s ] 2 )i/ 2 . 1 p ( w ) = f x2 z2 s2 \ (2*)^axazas ^ { " ^ f " &f " 2^f) ' where crx. Show that the magnetic field on the axis of a circular cylindrical winding of uniform cross-section is Hs) = — {(t-°n»a+ia2 o^ ML. s2)dxdzdsd{fict). The average luminosity is given by (C) = (dNB/dt)ntATget.
J. where I\ is the total dipole current and (r. where y+ and y_ are the complex coordinates y = x + jz at an infinitesimal distance from the current sheet. INTRODUCTION (a) For an ideal solenoid.A. From elementary physics. 2568 (1966). R. where S is the cross-section area of the solenoid.28 CHAPTER 1. Apply this theorem to show that the cosine-theta current distribution on a circular cylinder gives rise to a pure dipole field inside the cylinder. the current / is positive if it points out of paper. show that the magnetic field becomes46 where n is the number of turns per unit length.z) = I*1 where j is an imaginary number. Note that the total energy stored in the magnet is given by the magnetic energy. and yo = xo + JZQ is the position of the current filament. (a) Show that the 2D magnetic field at location y = x + jz for a long straight wire is Bz(x.a). show that the magnetic field inside the current sheet is Bz = -ti0Ii/4a. 4689 (1967).47 (b) If the current per unit area of an infinitely long circular current sheet is X(r. Phys. High-field superconducting dipoles are normally made of current blocks that simulate the cosinetheta distribution.z)+jBx(x.B(y_) = jMdl/dy).6 -> a. . (b) For an ideal solenoid. and dl/dy is the current per unit length. This is the cosine-theta current distribution for a dipole. Bx = 0. the field at a distance r from a long straight wire carrying current / is B = ^oI/2-nr along a direction tangential to a circle with radius r around the wire. (c) The Beth current sheet theorem states that the magnetic fields in the immediate neighborhood of a two-dimensional current sheet are B(y+) . <j>) are the cylindrical coordinates with x = r cos <j> and z = r sin <j>. show that the inductance is L = non2(S = non2 x volume of the solenoid. <j>) = ( / i / 2 o ) cos <f> 5{r . Beth. 38. 9. 46Set 47See s = 1/2. and / is the current in each turn. 37. Appl.
Show that the dipole field of a window-frame dipole with two sheets of parallel plates having infinite permeability is given by B = fioNI/g = HQUI. show that the magnetic potential is <&m = —Kxz. where g is the gap between two parallel plates. Use the following identities: iry _ 4y ^ t a n h _ _ _ ^ _______ 1 Try _ 2 c o t h ___ 4y ^—^ + _ ^ _ _ _ _ . where N is the number of turns. Following Maxwell's equation.oN2(. g is the gap between two iron plates. Show that the inductance is L = /j. where NI is the number of ampere-turns per pole. The total power dissipation is P = [NI)2R. The achievable gradient is B\ = Bv0\e tip/a.Y. 151 (1991). where R = pi/A is the resistance. The inductance in an ideal quadrupole is _ 8M0iV2l 2 a2 (Xc o4 8noN2e 12x? j R i a2 2 X" where xc is the distance of the conductor from the center of the quadrupole.EXERCISE 1 29 10. A as the cross-sectional area of the conductor. and n = N/g is the number of turns per unit gap length. A300. Show that the magnetic field at the coordinate y = x + jz. Meth. Nucl.w/g = nan2 x volume of the dipole. Lee. between two sheets of parallel plates with infinite permeability is 48 Bz + jBx = Of tanh E i l l l + coth to!) 1. 1 . I is the current in each turn. In reality. with B = —V$ m . due to a thin current wire located at coordinates yo = XQ + jzo. The pole-tip field is jBpoie tip = Ka. where I and w are the length and width of the dipole. V x B = 0 in the current-free region. where wc is the width of the pole. Thus the pole shapes of quadrupoles are hyperbolic curves with xz = o 2 /2.Show that the gradient field is Bx = 2naNI/a2. and a is the half-aperture of the quadrupole. Inst. 12. The current flows in the xxz direction. and the magnetic field can be derived from a magnetic potential. For a quadrupole field with Bz = Kx. 48S. 11. Bx = Kz.9 Tesla. The equipotential curve is xz = constant. <&m. and p is the resistivity of the coil. To avoid the magnetic field saturation in iron. x2 should be replaced by x\ + xcwc. the pole-tip field in a quadrupole is normally designed to be less than 0.
INTRODUCTION 13. where fields are all transverse with phase velocity up = u/k. where Z = \fJTjl is the intrinsic impedance of the medium. the inductance per unit length is where the integral is carried out between two conductors. where / = Xvp is the current per unit length.z)e-^ks-ut\ H(f. the capacitance per unit length is C = X/V.30 CHAPTER 1. and df= dxx + dzz. For a transverse guided field propagating in the +s direction.~ . we assume E{r. show that lH-dr = X/eZ = Xvp.Z) = -V_L#E. because of the transverse nature of the electromagnetic field. t) = Hx(x. (a) Show that the frequency ui and the wave number k of the electromagnetic wave satisfy the dispersion relation UJ — fc/^/e/J. and surrounded by isotropic and homogeneous medium with permittivity e and permeability [i. z and s form the basis of an orthonormal coordinate system. where the external charge and current are zero. Show that there is a general relation: C L = /ie = 1/«|. z)e-^ks-ut\ B± = tfj_. where C and L are the capacitance and the inductance per unit length.t) = Ex{x. the electric field can be represented by £(Z. where V = cj>i — <j>2 is the potential difference between two conductors. Consider a pair of conductors with cross-sections independent of the azimuthal coordinate s. where <f> is the electric potential. By definition. VxE = on . . (b) Show that. (c) Similarly. Let x. and Vj_ is the transverse gradient with respect to the transverse coordinates. Using Ampere's law.Z). Maxwell's equations are V-(eE) = 0. The characteristic impedance of the transmission line is given by Rc = y/L/C = V/I. and A is the charge per unit length on conductors. Show that the transverse electromagnetic fields satisfy the static electromagnetic field equation. and the transverse plane wave obeys the relation H = ^ sxEj_.
. Kerst and R. For charged ion beams.5 RG174/U 0. (a) Assume that the vertical component of the magnetic flux density is B . there are thermionic sources.. show that the equations of motion become £ + wg(l-n)£ = 0. Rev. where UJQ = v/R = eBo/jm is the angular velocity of the orbiting particle. laser-driven electron sources.) > where n is the field index. In the cylindrical coordinate system.=fl0(l)-«Bb(l-B4^ + . etc. the transverse oscillations of charged particles in linear or circular accelerators are generally called betatron oscillations. 15. 60.z are respectively the radially outward and vertically upward directions. Ion sources are indispensable to all applications in accelerators.152 98. C + wg< = 0.307 93. Br. r ^ = Type Diameter Capacitance Inductance [cm] [pF/m] LuH/m] RG58/U 0. Show that the radial magnetic field with BT = 0 at z = 0 is nB0 (dBz\ V dr ) T = R R (b) Using i = (r-R)/R and ( = z/R. Show that the stability of betatron motion requires 0 < n < 1.73 I 96..8 | | Rc Delay time [Q] [ns/m] 50 50 50 | 14. Derive the transverse equations of motion for electrons in a betatron49 by the following procedures. 6 is the azimuthal angle. the equation of motion for electrons is at at where f.4 RG218/U I 1.EXERCISE 1 31 (d) Show that the capacitance and the inductance per unit length of a coaxial cable with inner and outer radii r\ and r-i are 2ne T P 1 r2 n—/—v> L = 7rln~ • In(r2/ri) 2vr r\ Fill out the following table for some commonly used coaxial cables. For electron beams. there are many different configurations for generating plasma 49See D.Bz are the radial and vertical components of the magnetic flux density. and 9 = v/r is the angular velocity. Phys. 53 (1941). Because of this seminal work. Serber. rf gun sources.
. INTRODUCTION sources for beam extraction.50 Charged ion beams are usually drawn from a spacecharge ion source at zero initial velocity.00861 16. 188 (1988). The Paraxial Ray Equation: In the free space. and Ar+ ion sources are given by the following table. Phys. N + . AIP Conf. The flow of charged ions is assumed to be laminar. and is the perveance of the ion source. proton. Rev. (j> is the azimuthal coordinate. Proc. Let s be the distance coordinate between the parallel plates with a = 0 at the emitter. s) for the cylindrical coordinates in paraxial geometry. Proc. Here the microperveance is defined as 1 fj. where r is the radial distance from the axis of symmetry. the condition of maximum space-charge shielding is equivalent to V = 0 and dV/ds = 0 at s = 0. See also A. Large Ion Beams (Wiley. the electric potential obeys the Laplace equation V2V = 0. and v is the velocity of the ion. 492 (1911). and s is the longitudinal coordinate. show that the Poisson equation becomes ds2 e0 \2e) where J = pv is the current density. Child.P = 1 x 10" 6 A/V 3 / 2 .0545 | 0. where Vo is the extraction voltage at the anode.32 CHAPTER 1.D.0272 | 0.51 (c) Show that the space-charge perveance parameters for electron. No. Symp. Rev. New York.P) 2. 1988). deuteron. AIP Conf. e and m are the charge and mass of the ion. 210 (1990). No. 51 C. 32. I D+ I He+ I N+ I A+ 1 e I p X (fJ.334 0. Forrester. In the space-charge dominated limit. 32. 0. Langmuir. The relation of the current to the extraction voltage is called Child's law.0385 ~0. Proc. The Poisson equation becomes d?V _ p where V is the electric potential. Phys. Production and Neutralization of Negative Ions and Beams. Int. and eo is the permittivity. The maximum beam current occurs when the electric field becomes zero at the emitter.g. He + . (b) For a space-charge dominated beam. p is the ion density in the parallel plate.0146 [ 0. Show that the maximum current is J = X^o3/V. the electric field between the anode and the cathode is maximally shielded by the beam charge. we expand the 50 See e. Assume a simplified geometry of two infinite parallel plates so that the the motion of ions is one-dimensional. and s = o at the anode.T. I. Using the basis vectors (f. 450 (1913). on Electron Beam Ion Sources. (a) In the non-relativistic limit with laminar flow.
1/(3) T/(5) where VJj correspond to nth-derivative of Vb with respect to s. . This result is the basis of beam position monitor design.K. known as the paraxial ray equation. Pierce. 1943). Introduction to Electron Optics. Show that the equation of motion for the radial coordinate. s) and the electric field E = Err + Ess are VW V(r. The multipole expansion can be obtained by using the identity cosn<? + jsinn9 = e^nB. (Oxford. Electron Optics and the Electron Microscope. Consider a line charge inside an infinitely long circular conducting cylinder with radius b. where a is the distance from the center of the cylinder. a sin <f>). Show that the induced surface charge density on the cylinder is 53 (b 6 \ a( A 2nb b2 + a2- b2 . Theory and Design of Electron Beams. where the overdot represents the time derivative. F. Radio Engineers' Handbook. csin<£). 1945). . The paraxial ray equation can be used to analyze the beam envelope in electrostatic accelerators. (Van Nostrand. 53 Let the image charge be located at c = (ccos<£.4>) '<Pvl) = -5S[1 + 2 SU) A f °° /a\n cosn <*-"4 1 where <^w is the angular coordinate of the cylindrical wall surface. The induced surface charge density is a = eoEr.52 17.R.EXERCISE 1 33 position vector as R = rr + ss.c? 2ba cos(<£ w . . and (j> is the phase angle with respect to the x axis. Zworykin et al. 1950). 52 V. The line-charge density per unit length is A. Let VQ(S) be the electric potential on the axis of symmetry. The electric field is E = —V$. (Wiley. becomes Vr" + \v'r> + -V"r = 0. Cosslett. (McGraw-Hill. we obtain c = b2/a and Ai = —A. and the coordinates of the line charge are a = (a cos <j>. J. The equation of motion for a non-relativistic particle in the electric field is mR = eE.s)=V0(s)-^rr*-^rri y(4) + ---. Terman. Show that the electric potential V(r. 1949).. where V replaces Vo for simplicity and the prime is the derivative with respective to s. then the electric potential for infinite line charges at f is $(r) = In \r — a -I In r — cl. Using the condition EQ = 0 on the conducting wall surface in the cylindrical coordinate. V.E.
.
Lattice design has to take these field errors into account. control and feedback-correction of collective beam instabilities. A closed orbit in a linac is the orbit with zero betatron oscillation amplitude. In the first-order approximation. In actual accelerators. the resulting closed orbits will also depend on the particle momentum. beam distribution. The dispersion function. we derive the particle Hamiltonian in the Frenet-Serret coordinate system. magnetic field errors are unavoidable. 1A closed orbit in a synchrotron is defined as a particle trajectory that closes on itself after a complete revolution. This defines a closed orbit. Betatron motion around the closed orbit is determined by an arrangement of quadrupoles. where p0 is the momentum of a reference particle. high-intensity and high-brightness beams require measurement and correction of linear and nonlinear resonances. It is now used for transverse motion in all types of accelerators. the method discussed in this chapter can also be applied to a linac or a transport line. therefore the closed orbit and the betatron motion will be perturbed. since the bending angle of a dipole depends on the particle momentum. where the betatron motion is equivalent to an initial value problem. Serber on the transverse particle motion in a betatron. Particle motion with a small deviation from the closed orbit will oscillate around the closed orbit.Chapter 2 Transverse Motion In an accelerator. the deviation of the closed orbit is proportional to the fractional off-momentum deviation (p — Po)/Po. 2In principle. We discuss the Floquet transformation to action-angle variables. defined as the derivative of the closed orbit with respect to the fractional off-momentum variable. we examine the properties of linear betatron motion. and the chromatic aberration of the betatron motion play a major role in the accelerator's performance. In particular. bending magnets are needed to provide complete revolution of the particle beam. Various aspects of transverse particle motion in synchrotrons will be discussed in this chapter. In synchrotrons. Kerst and R. II. 35 . Furthermore. The terminology of betatron motion is derived from the seminal work of D. I.2 In Sec. called the accelerator lattice. In Sec. and measurement. the transverse particle motion is divided into a closed orbit1 and a small-amplitude betatron motion around the closed orbit.
(2. The energy and momentum of the particle can be expressed as E = ymc2 = mc2dt/dT and p = rwyv' = mdf/dr. Section IV deals with the off-momentum closed orbit and its implications for longitudinal synchrotron motion. and (x. we study the effects of linear magnetic imperfections (dipole and quadrupole field errors) and their application in beam manipulation. In Sec. (2. and properties of the envelope function. B = V x A. v = df/dt is the velocity. and p is the mechanical momentum. Section VIII introduces the basic concept of transverse collective instabilities and Landau damping.V $ .36 CHAPTER 2.2) The canonical momentum P = dL/dv = p + eA. (2.1) at where p = ymv is the relativistic kinetic momentum. (2. . • • • pairs are conjugate phase-space coordinates. and 7 = l / \ / l — v2/c2 is the relativistic Lorentz factor.3) and Hamilton's equations of motion are dH X~WX' Px~ p_JJI dx' e ' {2A) where the overdot is the derivative with respect to time t. Ill. and Section VI describes linear betatron coupling.dA/dt. ^=F = e(E + vxB). Section IX lays out a general framework for the synchrotronbetatron coupling Hamiltonian.1) can be derived from Lagrange's equation d_ (dL\ _d£_() where the Lagrangian is L = —mc2Jl — v2/c2 — e$+ev-A. and also with the lattice design strategies for variable 7T and minimum dispersion action. m is the mass. The electric and magnetic fields are related to the vector potential A and the scalar potential $ by E = . Px). Section V describes the chromatic aberration and its correction. e is the charge. we examine the effects of low-order nonlinear resonances. The Hamiltonian for particle motion is given by H = P-v-L = c[m2c2 + {P. Thus Eq. where r is the proper time with dt/dr = 7. I Hamiltonian for Particle Motion in Accelerators The motion of a charged particle in electromagnetic field E and B is governed by the Lorentz force. VII. In Sec. TRANSVERSE MOTION beam emittance.eA)2}1'2 + e$.
9) 3 Using Eq. Z'(S) = -T(S)X{S) . ?o(s) is the reference orbit.8) P(s) where the prime denotes differentiation with respect to s. 2.6) where p(s) defines the radius of curvature. HAMILTONIAN FOR PARTICLE MOTION IN ACCELERATORS 37 Figure 2. (2. where s is the arc length measured along the closed orbit from a reference initial point. The particle trajectory around the reference orbit can be expressed as r(s) = fo(s) + xx(s) + zz(s) . x.I Hamiltonian in Frenet-Serret Coordinate System Let fo(s) be the reference orbit (see Fig. and T(S) is the torsion of the curve. . Here x and z are betatron coordinates. I. we find a centr i p etai = \d2r0/dt2\ = {ds/dt)2\(d/ds)(df0/ds)\ = v21(ds/ds)|. where v = ds/dt is the tangential velocity.5) The unit vector perpendicular to the tangent vector and on the tangential plane is3 x{s) = ~p(s)^ . (2. s and z form the orthonormal basis for the right-handed Frenet-Serret curvilinear coordinate system with x'{s) = -priis) + T{S)Z{S). s and i form the basis of the curvilinear coordinate system.7) The vectors x. where r(s) = 0.5). we discuss only plane geometry.I. (2.1). The magnitude of the bending radius is p = ^2/acentripetal = \ds/ds\.1: Curvilinear coordinate system for particle motion in synchrotrons. (2. Any point in the phase space can be expressed by r = TQ + xx + zz. The tangent unit vector to the closed orbit is given by i(s) = d*&. The unit vector orthogonal to the tangential plane is given by z(s) = x{s) x s{s) . For simplicity. (2. (2.
s.[fo(s) + xx(s) + zz{s)\ . (2. z) are (see Appendix A) ps = -d-~ = {l+xlp)P-s. — ps as the new Hamiltonian. z). dH x = —. >Px ~ ^ ' z dps_ . _dp1 ~ a 'Pz ~ 13~- . The conjugate momenta for the coordinates (x. dH .10) where P is the momentum in the Cartesian coordinate system. A x m2c2 + ^ + lyjp + (p.ps = --^-. . and the conjugate phase-space coordinates given by x.pz. s.px.11). A s = (l + x/p) A .e. . (2.z . The transformation reduces the degrees of freedom from three to two. 1/. 1 dp^ ~ KTi x _ ~ dp. we find .13) Note that As and ps are not simply the projections of vectors A and P in the s direction.1OJ dH at opx ox opz oz This is Hamilton's equations of motion with s as the independent variable. Hamilton's equation becomes .17) ~ atr' When the scalar and vector potentials 4> and A are independent of time. But the price to pay is that the new Hamiltonian depends on the new variable s.s .eAzfj =A-x. opz oz .z. _ ap. dH z=—.px = -—-. s. In the new coordinate system. ops os . z.^ 1 = P. ox Px = -?h oz = p.-H. (2.eAxf + (p.14) The next step is to use s as the independent variable instead of time t [16]. dH .X. i. Using the relation dH = (dH/dpx)dpx + {dH/dps)dps — 0 or ds s \apx) \dpsj dpx where the prime denotes differentiation with respect to s. Because of the repetitive nature of the accelerator. dH . (2. .38 CHAPTER 2.—. Az =A . z) = -P.p2 = . .12) (2. dH s= ^—. a _ ap. us Px = . t. opx ox .AX and Az are obtained by substituting the vector A in Eq. TRANSVERSE MOTION To express the equation of motion in terms of the reference orbit coordinate system (x. x.11) The new Hamiltonian becomes { (n - PA \2 ~\ 1/2 where AS. (2. the new Hamiltonian —ps is also time independent. (2. we perform a canonical transformation by using the generating function F3(P.
The total energy and momentum of the particle are E = H — e<j) and p = JE2/c2 — m2c2. t.eAzf) . -H). The periodic nature of the new Hamiltonian can be fruitfully exploited in the analysis of linear and nonlinear betatron motion.A2) hs dz _ ~ 1 dAs hs dz' °z~ _ 1 d{hsA2) hs dx 1 dAs ~ hsdx' KZ-1 (2. In accelerator applications.eAs. (2. 1.I. \dA. we can assume Ax = Az = 0. (x. 8A3 dx dz J s + 1 [dfoAa) 9AJ . for an accelerator with transverse magnetic fields.20) V$ = —X + ——S + —Z. z.eA°> where the phase-space coordinates are (x.z)x + Bz{x. furthermore. HAMILTONIAN FOR PARTICLE MOTION IN ACCELERATORS 39 the dependence of the new Hamiltonian on s is periodic. we expand the Hamiltonian up to second order in px and pz H « -p (l + ^ + i ± ^ [(px . hz = 1. The new Hamiltonian H = -ps is then given by k=.pz. we consider only the case with zero electric potential with $ = 0.19) In the Frenet-Serret coordinate system. s. /I2 = A • 5.eA>)2]V2 .{l+f) [ ( g T^ ) 2 -mV -{p* ~eA*)2 -{pz .21) > . z)..z)z. the scale factor becomes hx = l. We have hs = 1 + .px.2 Magnetic Field in Frenet-Serret Coordinate System (2. z' fts hs [~dx~~~~ds~\ ds hs ds where ^ = A • x.eAxf + (Pz . The two-dimensional magnetic field can be expressed as B = Bx(x. Since the transverse momenta px and pz are much smaller than the total momentum. ox hs os dz V. where _ 1 d(h.z. and A3 = A.A = ! \d(hsA1) | 8A2 | d(hsA3)l hs dx [ ds /is [dx dx ds dz \x+[dz dz dz J' 9$ 1 d$ 3$ vy v A v 1 [ ^ 3 _ d(hsA2)] .
an are called 2(n + l)th multipole coefficients with dipole 6o.. n> = 1 cm.Normally the normalization constant Bo is chosen as the main dipole field strength such that bo — I. The resulting magnetic flux density is given by4 oo Bz + jBx = Bo £ ( b n + jan){x + jz)n 71=0 (2.S. dipole roll do. 4The multipole expansion of the magneticfieldis usually rescaled to obtain Bz + jBx = BQ n=O ^(bn+JanX^^r. 62.BZ (see Exercise 2.1. skew sextupole 02. in our coordinate system. .3). sextupole 62. quadrupole 6i. Thus we have Bobo = —[Bp]/p. Using Maxwell's equation V x B = 0.24) where j is the imaginary number. skew quadrupole ai. The resulting bn and an coefficients are dimensionless. For straight geometry with hs = 1. In Europe.6) oz hs oz ox hs ox and As can be obtained through power series expansion General solutions of BX.40 CHAPTER 2. (2-27) where.x=z=o n ~ Bon\ dx" B = l = 0 ' ( b) where bn. and for RHIC and Tevatron. 5 Note that the multipole convention used in Europe differs from that in the U. we have d i d A d idAs_ o~I—5 <"5~T—3~ u\i. The complex 2D magnetic field representation in Bz + jBx is called the Beth representation (see Exercise 1. r\> = 2. the — and + signs are used for particles with positive and negative charges respectively. p is the bending radius. etc. where Bp is the momentum rigidity of the beam. physicists use 61.E ( ^ +io») (^ + ^ ) n .5 The effective multipole field on the beams becomes 1 -I 00 — (Bz + jBx) = T .10). TRANSVERSE MOTION with As = hsA2.02 for quadrupole and skew quadrupole.25) with bn .54 cm. and As can be expanded in power series as As = Sosft g *££{* + jzr 1 ] . ai for dipole and dipole roll.2. Vb where r^ is a reference radius. For high energy accelerators such as the SSC and LHC. and Bz = ^ and Bx = ~"^ 1 . (2. we obtain V\AS = 0..Bon! 3x. 5ft[.] represents the real part. and bo = 1. etc.
29) by changing the time variable to the coordinate of orbital distance s._dH_ opz . Bz = -Bo + -—^x = ^Bo + BlX.4 Particle Motion in Dipole and Quadrupole Magnets We consider a on-momentum particle with p = Po. expand the magnetic field up to first order in x and z. (2.29) can be derived through Newton's law of acceleration (see Exercise 2. i.3 Equation of Betatron Motion Disregarding the effect of synchrotron motion (see Sec.] represents the imaginary part of the expression.1. B = . ox Bx = —^z = BlZ. the betatron equations of motion become Pl ..e.e. and e is the charge of a particle.V $ m (see Exercise 2. 1.. i. B P \\ P) (2-29) I Bpp y p) where we neglect higher-order terms. (2. ox (2. 1. the magnetic field can also be derived from a scalar magnetic potential $ m . Alternatively. _ dH az With the transverse magnetic fields of Eq. p is the momentum of the particle.__dH_ ox . Hamilton's equations of betatron motion are given by . Po is the momentum of a reference particle. HAMILTONIAN FOR PARTICLE MOTION IN ACCELERATORS 41 Since V x B = 0 in the current free region.22). the upper and lower signs correspond to the positive and negative charged particle respectively._dH_ opx .3).I. The sign convention is chosen such that Bp is positive. Eq.2). The scalar magnetic potential is *m = -Bo3 [ £bj~^YL(^+ J * H Ln=0 J (2-28) where 3[. Bp = po/e is the magnetic rigidity. The equations of motion are given by ~ m ~± B p ' Z~^ TU 7 B p ' which can be transformed into Eq. (2.e.30) . IX).1. x" = f/v2s. i.
we have Kx = —Kz. and makes an angle 9/2 with the pole-faces in the rectangular dipole.31) and (2. where 1/p = 0.g.2: Schematic drawing of the particle trajectory in a sector dipole and in a rectangular dipole.32) are given below. A weak focusing accelerator requires 0 < n(s) < 1. • The focusing functions Kx. z" + Kz(s)z = 0. For a strong-focusing accelerator. Eq. Some observations about the linear betatron equations (2. to be discussed in next section. (2. Thus Eqs. This means that a horizontally focusing quadrupole is also a vertically defocussing quadrupole and vice versa. Such a dipole is called a sector dipole with perpendicular entrance and exit angles to the edge of the dipole field (see Fig.2. The solution of Hill's equation satisfies the Floquet theorem. where the entrance and exit angles of particle trajectories are not perpendicular to the dipole edge. The betatron equation of motion.2a).42 CHAPTER 2. there is an edge focusing/defocussing effect (see Exercise 2. • A horizontal bending dipole has a focusing function Kx = 1/p2. \ / (b) rectangular dipole • In a quadrupole. Kz are periodic functions of the longitudinal coordinate s.2). Kx = l/p2^Kl{s). and Kz = 0. (2. For non-sector type dipoles. becomes x" + Kx(s)x = 0. and the quadrupole gradient function B\ = dBz/dx is evaluated at the closed orbit. Kz = ±/fi(s). n(s) ss ±350 for the AGS. Note that the particle orbit is perpendicular to the pole-faces of the sector dipole magnet.31) and (2. \ / \ / \ 1 (a) sector dipole e/2/K / \ \ \ e' / JKj/Z / \ Figure 2. \ / \ . e.32) where Ki(s) = Bi(s)/Bp is the effective focusing function. (2.31) (2. TRANSVERSE MOTION where Bo/Bp = 1/p signifies the dipole field in defining a closed orbit.29). . and the upper and lower signs correspond respectively to the positive and negative charged particles. 2. \n\ 3> 1. The focusing index is given by n(s) = p2 Ki(s).32) are Hill's equations with periodic boundary conditions.
z) be local polar coordinates inside a dipole. Let (x.s. Expressing the scalar potential in power series of particle coordinates.z). show that '-»+•*-%. 1 + z/p & ' Derive Eq. where 6 = s/p is the angle associated with the reference orbit. *=E V.S. The particle coordinate is r — (p + x)x + zz.29) through the following geometric argument. . Thus the electric field and magnetic field can be expanded by scalar potentials with B = . and show that P2 - Bp{l+ p> ' Z ~ W1 + p> ' where the prime is the derivative with respect to s. transverse magnetic fields are o = ?_^£ 1 + x/p dz ' o z 1 dA. 2. The momentum of the particle is p = ymr. and p is the radius of curvature.(2.. where d9 = vsdt/(p + x). ds = pd9. 3.z). i. (a) Using Eq. with B = Bxx + Bzz. where both scalar potentials satisfy the Laplace equation & with V 2 $ . ' % where Bp = ymvs/e is the momentum rigidity and vs is the longitudinal velocity. In the curvilinear coordinates (x. (2. dp/dt = ymr.e. and the overdot corresponds to the derivative with respect to time t.3*. s. (c) Transform the time coordinate to the longitudinal distance s with ds — pd9. Derive Eq. where p is the bending radius. we then have _ 2 -.V $ m . show that f = xx + (p + x)9s + zz. (2. where j is constant in the static magnetic field.19). Inside the vacuum chamber of an accelerator. Similarly. f=[x-(p + x)82]x + [2x9 + (p + x)9]s + zz. In the Prenet-Serret coordinate system (x.1 1. where $ stands for either $ m or < e = 0. (b) Using dp/dt = ev x B. (2.1 43 Exercise 2.29) from the Hamiltonian of Eq. . E = . we have V x B = 0 and V x E = 0.V $ e . 92$ + a? + TTTx^rnrx &) =0xizi 1 5 .8). v *= TTW[1+hx]^] * 1 d .A ^jv .EXERCISE 2.. 1 <9$N where h = 1/p.
3tj+2.l)h2Aid . show that the magnetic potential.i(3i .3i(i - l)h2Ai_2:j+2 . etc. this serves as a general method for deriving the magnetic field map.19) for the particle motion in the solenoid is H = -p+ ^-[(p» . Assuming yloo = 0. the potential for a quadrupole is given by the ^4n term and the skew quadrupole arises from the A20 term.eAxf + {pzeAz)2}. TRANSVERSE show that Aij satisfies the following iteration relation: Aij+2 = -A'lj . show that the vector potential can be expressed as A=-[lrbo(s)-±rHo'(S) + --j 4>. Bz = z-£b2k+i(x2 + z2)k.l)2h3Ai-u + ih'A'^j . and (j> = (—zx + xz)/r.44 CHAPTER 2. 6A word of caution: the magnetic potential obtained here can not be used as the potential in the Hamiltonian of Eq. (b) The Hamiltonian of Eq. is6 $ = -Booz+±A2o{x2-z2) + Anxz+l-A3o{x3-3xz2) + \B'oW +\A2lx2z + UB'0'0 . In particular. up to the fourth order with i + j< < 4. where r = xx + zz.xz3) \A[IXZ\ 4. (2.ihA'Uj -3ihAi-ld+2 -i{i . r = \jx2 + z2. However.(3i + MOTION l)hAi+1J . (2. . Show that the vector potential is In a cylindrical coordinate system. and AQI — —Boo i n a rectangular coordinate system with h = h' = 0. where the prime is the derivative with respect to s.6x2z2 + z4) +±A2'0(-3x2z2 + z") + \A31(x*z .18).i(i .Aig = 0. The field components in the current-free region of an axial symmetric solenoid are 00 OO OO Bx = xJ2b2k+l(x2 k=0 + z2)k. k=0 Bs = Y2hk(x2 + z2)k. k=0 (a) Show that the coefficients are 2(feTi)*"' W^)h'2k+l' b2k+1 = b2k+2 = where the prime is the derivative with respect to s.Ai+2j .A21)z3 + ^-A40(x4 .l)(t - 2)h3Ai-.
2gx' . included in the g' terms. (c) Up to third order. .7 For normal multipoles with mid-plane symmetry with Bz{z) = Bx(-z). The linearized equation can be solved analytically. provides both horizontal and vertical focusing. Note also that the effects of the ends of a solenoid. b. i.^-x(x2 + z2). p.1 Show that the lineaxized equation of motion is (see also Exercise 2. Bx = zJ2 ^z2\ i.k=0 OO OO Bs = z £ «#****. have been included to obtain this Hill's equation in the rotating frame. Letting y = x + jz. show that the equation of motion is x" + 2gz'+g'z z"-2gx'-g'x = ^z'(x2 + z2) + ^-z(x2 + z \ = -^-x'(x2 + z2) .k=0 i.6. CERN 85-19.k=O OO where a. Transforming the coordinates into the rotating frame with y = ye-je{s)^ where g = fs rf Jo show that the system is decoupled. and the decoupled equation of motion becomes y" + g2y = 0.EXERCISE 2. 45 where g = ebo/2p = eB^/2p is the strength of the solenoid. 25 (1985). the most general form of expansion is Bz = £ b^z2". in the rotating frame. Bs(z) = -Bs{-z). Steffen. Thus the solenoidal field. c can be determined from Maxwell's equations: V x B = 0 and V • B = 0. Bx(z) = -Bx(-z). independent of the direction of the solenoidal field. Show that Maxwell's equations give the following relations: ai'k = WTibi+1*' Ci'k + p Ci .g'x = 0. Consider the transverse magnetic field in the Prenet-Serret coordinate system. Z o 5.1 >* = 2 T T 1 6 ^ ' 7 See K.2) x" + 2gz' + g'z = 0. show that the coupled equation of motion becomes y"-j2gy'-jg'y = 0. z" .
0\. where p —> oo.o 3 + — ^ p } 1} + ~p(B2'° + 1 7 + —] Bs 1 D + 2[Bl'° " ( ~ o '''' = BjiOz + ( J B i .n " * ' = Bloz + 2B2.^ ^ + ^{x+iz)z2 l + ---. B z ( z = 0 ) = B o f i + B l f l x + B 2 f i x 2 + B 3 f l x 3 + •••. the end field has an octupole-like magnetic multipole field. Thus for a finite length quadrupole with B[ 0 ^ 0.46 CHAPTER 2. R'" .0 ~ ^~^~' *> OR 0.e.^ ^)a. Show that in a pure multipole magnet.oxz + 3Bs. Assuming that we can measure the Bz at the mid-plane as a function of x. where S^o are functions of s..o + Blfix + B2iOx2-(B2fi -{SB3yo H Bx . 2B2. where j is the complex number. the magnetic field can be expanded as Bz+jBx = YJBn»{x n=0 +3 z T .lrr.n . s.-°i. .0 +^ .ox3 (B'°<°Vnn-r2J- 1/n (-D2.^ > ) ^ + ( ^ .ox2z--{3B3. i. 1 1" —2~) + 21. o .o + -g h0. show that the field map is Bz = Bo. B + ^)z2 B + B3. TRANSVERSE MOTION where the prime is the derivative with respect to s.2.
we study. we can apply the Floquet theorem (see Appendix A. The nominal betatron tunes are ux = 6. Sec. the Courant-Snyder invariant and emittance. (2. where four combined function magnets are arranged to form a basic focusing-defocussing periodic (FODO) cell.7 and vz = 6.Bi{s)/Bp. (2. betatron tune. The total length of a repetitive cell is 19. LINEAR BETATRON MOTION 47 II Linear Betatron Motion Particle motion around a closed orbit is called betatron motion.34) 8The focusing functions are Kx = l/p2 + B1(s)/Bp and Kz(s) = -B1{s)/Bp for negative charged particles. For example. BF BF BD BD ] • • • • s=0 BE s=L Figure 2.0208186 m~2. Let y. Since the amplitude of betatron motion is small. y' represent either horizontal or vertical phase-space coordinates. and L is the length of a periodic structure in an accelerator.3: A schematic drawing of the Fermilab booster lattice. .33) where Kx = 1/p2 . the linearized betatron equation of motion governed by Hill's equation x" + Kx{s)x = 0. 1 Transfer Matrix and Stability of Betatron Motion Because accelerator components usually have uniform or nearly uniform magnetic fields.889612 m and focusing function Kp = 0. The accelerator is made of 24 such FODO cells. Fig. A small trim focusing quadrupole is used to change the betatron tune.0244817 m~2 and Ku = -0.3 shows a schematic drawing of the Fermilab booster lattice. and thus the superperiod of the machine is 24. and the envelope equation. (2.II.7588448 m. z" + Kz{s)z = 0. Floquet transformation. 2. In this section we study linear betatron motion. Kz(s) = B^/Bp. It consists of four combined-function magnets of length 2. then Eq.33) becomes y" + Ky(s)y = 0.8. II. 8 The focusing functions are periodic with Kx<z(s + L) = KXyZ(s). 1.5) to facilitate the design of an accelerator lattice. the focusing functions KXtZ(s) are piecewise constant. Exploiting the periodic nature. in this section. and B^s) = dBz/dx evaluated at the closed orbit.
35) ! acoshiyf^Ks + b). (2.e. we neglect the subscript y hereafter. K> 0.— -fesinVKe\ .2/2 of Hill's equation. The transfer matrix for a constant focusing function K is [I cos^KE . we can express the solution of Eq.34) as y(a) = M{s\so)y{so). we obtain detM = 1. For any two linearly independent solutions 2/1. Since K is finite. . The solutions of Hill's equation with constant Ky are9 a cos{y/Ks + b). the transfer matrix for a > quadrupole reduces to i J > ^defocussing = ( 1/y i )' (2.48 CHAPTER 2. s) = yiy'2 . Letting be the betatron state-vector. K = 0.)-(*>) IW (2. as + b.38) Since the Wronskian obeys W(s) — [det M]W(so). f = \imt^ol/(Ke). M(s\sQ) = < ( 1 i ) / cosh J\K\£ v { VvWnhy^ •^focusing — [ _-i I f -j=sinh J\K\£\ v 1*1 Jl_ cosh^f^ J K < 0: defocussing quad. convention for the transfer matrix of a thin-lens quadrupole is M q u a d =(_ 1 1 / / JJ. (2. (2. where / > 0 for a focusing quadrupole and / < 0 for a defocussing quadrupole. In this case. where £ = s — SQ. K < 0.y[y2.39) where / is the focal length given by10 10The 9To simplify our notation. the Wronskian is independent of time. *(.37) where M(S\SQ) is the betatron transfer matrix. dW W(yi. TRANSVERSE MOTION with the periodic condition Ky(s + L) = Ky{s). i. ff = 0: drift space „ n t . -£• = 0. y and j / must be continuous.y2. and the integration constants a and 6 are determined by the initial values of y0 and y'o.— .— K > 0: focusing quad. In thin-lens approximation with £ — 0.
(2. (2.43) where C and S" are the derivatives of C and 5 with respect to s. (2. « '*«')• 49 (240) where 6 = £/p is the orbiting angle and p is the bending radius. This means that the effect of a dipole with a small bending angle is equivalent to that of a drift space.*>) . e. M{SM = ( ^ j J£.45) where {yo. S(s0. LINEAR BETATRON MOTION Similarly. we obtain detM(s|s 0 ) = W(C. s0) = 1.44).so)y'o. The transfer matrix for any intervals made up of subintervals is just the product of the transfer matrices of the subintervals. s0) = 0. (2. C"(s0.g. using the Wronskian of Eq.s) = 1. the solution of a second-order differential equation can be expressed as y(s) = C(s.so)yo + S(s. s0) = 1. so) = 0. In the small-angle approximation.so)yo + S'{s. y'(s) = C'(s.y'o) and {y. (2-41) where £ is the length of the dipole. and. M(s 2 |s 0 ) = M{s2\Sl)M(Sl\so). S'{s0.33) can be expressed in terms of the transfer matrix as11 yW = MWeoMo).y') are the particle phase-space coordinates at the entrance and exit of accelerator elements. . the transfer matrix for a pure sector dipole with Kx = 1/p2 is « < > = (->* .So) an< i S(S.44) Thus the solution of Eq. The 2x2 matrix M depends only on the function K(s) between s and s0. u The transfer matrix for the uncoupled betatron motion can be expressed as /x\ \ x' \ fMx(s2]Sl) 0 /x\ \ I x'\ \z'/1 I * \z'/2 V ° M2(s2\Sl)J \ z ' where the M's are the 2x2 transfer matrices. (2. (2.so)y'o.S. particle motion can be tracked through accelerator elements.42) Using these matrices. Combining all segments.II. and yo and y'o are the initial phase-space coordinates at SQ. The solutions C(s. the transfer matrix becomes Ms(S>s0)=(J I ) .SQ) are respectively called the cosine-like and sine-like solutions with boundary conditions C(s0.
e. we obtain M{s2 + L\Sl) = M(s2)M(s2\Sl) = M(s2\Sl)M(Sl). A2 = e-J'*. M(s) = M(s + L\s) = Mn---M2Mu where the Mi's are the transfer matrices of the constituent elements. Using the periodicity condition. A2 be the eigenvalues and V\.3 has 24 superperiods. the eigenvalues are the reciprocals of each other. (y°)=av1+bv2.50) (2. (2.e. Thus a necessary condition for orbit stability is to have a real betatron phase advance <£. The transfer matrix for passing through P superperiods is M(s + PL\s) = [M(s)] P .48) Thus M(s 2 ) and M(si) are related by a similarity transformation: M(s 2 ) = M(s2\s1)M{s1)[M{83\s1)]-1.46) where V\ and v2 are the eigenvectors associated with eigenvalues Ai and X2 respectively. and $ is complex if Trace (M) > 2. Let Trace(M) = 2cos($). 2. (2. and the LEP at CERN has 8. (2. Since M has a unit determinant. The transfer matrix M of one repetitive period composed of n elements is a periodic function of s with a period L. The eigenvalue satisfies the equation A2 . Ai = 1/A2. This implies that the transfer matrix of a periodic section has identical eigenvalues.52) . We find that $ is real if Trace(M) < 2. > Expressing the initial condition of beam coordinates (yoi2/o) a s a l i n e a r superposition of the eigenvectors.47) (2. the Fermilab booster shown in Fig. The number of identical modules that form a complete accelerator is called the superperiod P. i. we find that the particle coordinate after the mth revolution becomes (Vj) = Mm (Vj) = aX^+bX^v. The eigenvalues are Ai=e J *. For example. the AGS at BNL has 12. v2 be the corresponding eigenvectors of the matrix M. Let Ai.49) where 3 is the betatron phase advance of a periodic cell. i.50 CHAPTER 2.Trace(M)A + 1 = 0. (2. The necessary and sufficient condition for stable orbital motion is that all matrix elements of the matrix [M(s)]m remain bounded as m increases. Let L be the length of a module with K(s + L) = K{s).. or |Trace(M)| < 2. TRANSVERSE MOTION An accelerator is usually constructed with repetitive modules.e. and Ai + \2 = Trace(M). (2. and for passing through m revolutions becomes [M(s)] mP .51) The stability of particle motion requires that A^" and \™ not grow with m. i.
the values of the Courant-Snyder parameters 02. 7i V 7i/ afa = a i . 2 Courant-Snyder Parametrization The most general form for matrix M with unit modulus can be parametrized as . .57 ) We note that 7 is constant in a drift space._ / cos $ + a sin $ M= .54) The ambiguity in the sign of sin<& can be resolved by requiring /? to be a positive definite number if |Trace(M)| < 2.56) V7/2 V Ml -2M 21 M 22 Ml ATA where My are the matrix elements of M(s2\si). and by requiring Im(sin$)>0 if |Trace(M)| > 2. LINEAR BETATRON MOTION 51 II. This ambiguity will be resolved when the matrix is tracked along the accelerator elements.7 i « = -(«-s*)//5*.72 at S2 are related to Qi. M" 1 = I cos $ . ./?i.12 $ is the phase advance. /3 and 7 are Courant-Snyder parameters. 1. . = Icos$ +Jsin$. (2. .„. + (i^)!.7i at S\ by (P\ a = ( Mf. we obtain the De Moivere's theorem: Mk = (I cos $ + J sin $)* = I cosfc"J>+ J sin fc$.48).T .55) Using the similarity transformation of Eq. (2. and s* = Q1/71 is the location for an extremum of the betatron amplitude function with a(s*) = 0.J sin $. -MnMai -2MnM12 MUM22 + M12M21 M\2 -M12M22 \ \\a (0\ .53) where a. and 7 parameters have nothing to do with the relativistic Lorentz factor.^2. The definition of the phase factor $ is still ambiguous up to an integral multiple of 2TT. f). (2. . Using the property of matrix J.JJ. \ —7 sin < P cos < — a sin $ J J > /?sin$ \ T . and 3 = (- - ) ' with Trace(J) = °> J 2 = .. (2. T . 12The a. 72 = 7i = l/£*. The evolution of the betatron amplitude function in a drift space is &= i +1l ( s _-y =/s . . The evolution of betatron functions is shown in the following examples.I or ^7 = 1 + a2. I is the unit matrix. (2.„. P* ( 2 .
> = ^2. where the focusing function K(s) satisfies K(s) = K(s+L). y*(s) = o w f s j e " * ' .w'2 — w'(s2). and w and ip are the amplitude and phase functions. Let s2 — S\ = L be the length of a periodic beam line.w2w'1 sin ip ' 2 wiw2smip Mcos'iA \ smtp .60) (2. Eq.61) Here. (2. Any solution of Eq.^ = ipfa) -ip(si). (2. and the prime is the derivative with respect to s. w[ — w'(si). Since K{s) is real. Eq. we set the periodic boundary conditions to the amplitude and phase functions: u>i = w2 = w.61) is the betatron phase equation.34) is a linear superposition of the linearly independent solutions y and y*. (2.4r = 0. Sec 1. (2. (2. 7 2 = 7 l + 2 a 1 / / + /3 1 // 2 . 4. and we have chosen a normalization for the amplitude and phase functions. Eq.34) can be solved by using the Floquet transformation: y(s) = s w ( s ) ^ w . Thus a thin-lens quadrupole gives rise to an angular kick to the betatron amplitude function without changing its magnitude.5). (2. a2 = <*i + A / / . the evolution of betatron function is given by ft = ft. Passing through a thin-lens quadrupole.( .3 Floquet Transformation Since the focusing function K(s) is a periodic function. TRANSVERSE MOTION 2. Thus the mapping matrix M(s2\si) can be obtained easily as / V^ cos ip .58) where / is the focal length of the quadrupole.52 CHAPTER 2. Using the Floquet theorem (see Appendix A. (2.59) where a is a constant.60) is called the betatron envelope equation. .w2 = w{s2). w[ = w'2 = w'. tp(si + L) — tp(si) = $. II. the amplitude and phase functions satisfy w" + Kw .1 ^ c o s f i + wiwismip/ where w\ = w(si).
67). which will be referred to as the betatron amplitude function.l [ l + (|)2j= 0 ) or a' = Kf3-±(l + a2).53).67) reduces to the CourantSnyder parametrization of Eq. ^2 are values of betatron amplitude functions at si and s2 respectively. we obtain (2. The betatron phase advance is -Cm i^» + ^ . and ft) <*2.62) to Eq. .53). from Eq.60). where s2 = S\ + L with Kfa) = K(si). 71. and we have defined the betatron amplitude matrix B(s) and its inverse as We note. Applying Floquet theorem to a repetitive period. (2. LINEAR BETATRON MOTION 53 Equating the matrix M of a complete period in Eq. (265) Here the amplitude function j3(s) is also the local wave number of betatron oscillations. (2. or (/?) = L/$. (2. we obtain ft = ft>.63) (2. (2. «i.II. we have $ = L/{P). (2. a = ~ww' = -P/2. ax = a 2 . we obtain w2 = 0. ^ = •0(s2) — V'(si). The Courant-Snyder parameter a is related to the slope of the betatron amplitude function. The betatron wavelength is A^ = 2TT(/?}. and the transfer matrix of Eq.64) Thus the amplitude of the betatron motion is proportional to the square root of the Courant-Snyder parameter /3(s). (2.66) The transfer matrix from S\ to s2 in any beam transport line becomes ( y^(cos ip + ai sin ip) \/P\h sin i> \ ( v% 0 \ / cos^ sinV\/^7 ° ^ = B(s2)( C0S^ ^^B" 1 ^). Substituting /? = w2 back into Eq. (2. that the linear betatron motion becomes coordinate rotation after the normalization of the phase-space coordinates with the B" 1 matrix. (2-67) where A. In the smooth approximation.
and its derivative is periodic.4) is made of a pair of focusing and defocussing quadrupoles with or without dipoles in between. is called Floquet transformation. FODO CELL «F/S | | B (2J1) (2. 2. w-kfm 0 +^ =0 .e. {^QF 0 QD 0 ^QF}. fy are constants to be determined from initial conditions.34) becomes y(s) = aJfWJcoa[il>y{8)+ty] with %{s) = f -r-f^. or Qy. The phase change per revolution is P$. This is a pseudoharmonic oscillation with varying amplitude /J*/2(s). and QF and QD indicate the focusing and defocussing quadrupoles. The betatron tune vy. Example 1: FODO cell in thin-lens approximation A FODO cell (Fig. where /o is the revolution frequency.72) The phase function <j>y increases by 2n in one revolution. JO Py(S) (2. I . defined as the number of betatron oscillations in one revolution. from y(s) to the amplitude and phase functions /3s(s) and <j>y(s). . 1 B Figure 2. where the transfer ma« F / 2 trix for the dipoles (B) can be apEH proximated by drift spaces. The local betatron wavelength is A = 2irPv{s). We define new variables r/ a n d </>y:13 ""f.4: A schematic plot of a FODO cell.54 Betatron tune CHAPTER 2. is •fc-^-s/ WY (269) The betatron oscillation frequency is vyfo. i. Thus t h e linear b e t a t r o n motion is in fact a simple harmonic motion.70) where a. (2. Hill's equation can be transformed to «D I . TRANSVERSE MOTION We consider an accelerator of circumference C = PL with P identical superperiods. The general solution of Eq. 13 This transformation.
we have 2Lt (1 . 15The transfer matrices of dipoles are represented by those of drift spaces. and (3F and aF are values of the betatron amplitude functions at the center of the focusing quadrupole.sin($/2)) sin^ ' ° PD = Q D = (2J5) at the center of the defocussing quadrupole. Insertions (or straight sections) are usually used for physics experiments. FODO cells are usually repetitively used for beam transport in arcs and transport lines. The transfer matrix for vertical motion can be obtained by reversing focusing and defocussing elements. We can also use the transfer matrix of Eq. and Arid. (2. The accelerator lattice is usually divided into arcs and insertions. and the corresponding CourantSnyder parameters are values of the betatron amplitude functions at that position.2.74) sin$ The parameter $ is the phase advance per cell. rf cavities.. is15 .^ | or sinf = ^- (2-73) 2 M l + sin(*/2)) 0.U !)(!?)(! !)(!?)(-*!) = / l-$ 2L1(l + ^ ) \ V-^(l-|?) 1-$ ) where / is the magnitude of the focal lengths for the focusing and defocussing quadrupoles. (2. point = — ^ (2 . injection and extraction systems. The above procedure can be performed at any position of the FODO cell. point = ± c o s ( $ / 2 ) (2™) at the midpoint between the QF and the QD. The betatron tune for a machine with N FODO cells is v = N$/2TT. in the thin-lens approximation. Arcs are curved sections that transport beams for a complete revolution.8). Because of the repetitive nature of FODO cells. "mid. and L\ is the drift length between quadrupoles.14 The transfer matrix for the horizontal betatron motion. (2.II LINEAR BETATRON MOTION 55 where O represents either a dipole or a drift space.Sin2 . etc. the transfer matrix can be identified with the Courant-Snyder parametrization of Eq. For example.53) to obtain cos$=^Trace(M) = l .J . where we neglect the effect of 1/p2 focusing and edge focusing.67) to find the betatron amplitude functions at other locations (see Exercise 2. .
i. The solid and dashed lines in the upper plot of Fig. The AGS lattice can be well approximated by 60 FODO cells with a phase advance of 52. Px 1 + sin $/2 . which made of 20 combined-function magnets. The phase advance of a doublet cell.5.e. The phase advance of each FODO cell is about 52. Example 2: Doublet cells The values of the horizontal and vertical betatron functions in FODO cells alternate in magnitude.5 show the betatron amplitude functions /3x(s) and fiz(s) for the AGS. The lower plot shows schematically the placement of combined-function magnets. The middle plot shows the dispersion function D(s).sin $/2 . we consider a doublet beam line. to be discussed in Sec. 1 . The AGS lattice has 12 superperiods. (2. IV.726 m for a complete circumference of 807. and a half-cell length of L\ = 6. Note that the superperiod can be well approximated by five regular FODO cells. I~^J ' jinn -— ft ~ l .8. and Ll and L2 are the lengths . Some examples of paraxial beam transport beam lines are the doublet. each composed of 20 combined-function dipoles. is sinf = ^ . The middle plot shows the dispersion function Dx. In some applications. shown schematically in the bottom plot of Fig. 2. in thin-lens approximation. the triplet.8°.8° for a betatron tune of 8. The beam size variation increases with the phase advance of the FODO cell. The upper plot shows fix (solid line) and @z (dashed line). a paraxial beam transport system provides a simpler geometrical beam matching solution. 2.5: The betatron amplitude functions for one superperiod of the AGS lattice. / is the focal length of the quadrupoles.77) where we have assumed equal focusing strength for the focusing and the defocussing quadrupoles. 2.s i n $ / 2 ' l + sin$/2' at the focusing and defocussing quadrupoles respectively.56 CHAPTER 2. TRANSVERSE MOTION Figure 2.12 m. In the following example. shown schematically in Fig. and the solenoidal transport systems.6.
Thus we obtain y' = -^(tanV-f). ' quadrupoles can be filled with Ll dipoles. the horizontal and vertical betatron amplitude functions are nearly C identical along the transport line.6. (2.79) If Li < ^2. of t h e drift spaces shown in Fig. y" + K{s)y = 0. (2.2. II. we find the new Hamiltonian *=*+lK- (-4 28 ) . LINEAR BETATRON MOTION DOUBLET CELLS Q D Q Q f | | <® W T~| Q] i 1 L2 57 Figure 2.82) 3= ~ f r = tp se°2 * = h[y2 + {N+ayn (2'83) Applying the canonical transformation and using Eq. y') are conjugate phase-space coordinates. provided that P satisfies Eq. Thus the doublet can be considered as an example of the paraxial transport system. (2. can be derived from a pseudo-Hamiltonian where (y.81) where ip is the phase factor.6: A schematic plot of a doublet transport line. (2.12).^ $ . (2. .66).y ) . where < > Q two quadrupoles a r e separated K F T~] by a distance L\. and the conjugate action variable is (2.II. 2. where y' = dFi/dy is verified easily.80) The Hill equation.4 Action-Angle Variable and Floquet Transformation H=l-y'2+1-K(s)y2. We observe that Eq. and the P] ^ long drift space Li between two ' . (2. Other paraxial transport systems are triplets and solenoidal focusing channels (see Exercise 2.13) ~ ~ sin* / U t ( 2 7 8 ) Anin = 7 .66).2. This suggests a generating function F ^ V) = [y'dy = -|g(tanV> .70) is a solution of Hill's equation. T h e maximum and minimum values of t h e betatron amplitude function are (see Exercise 2.
58
CHAPTER 2. TRANSVERSE
MOTION
Hamilton's equation gives if)' = dH/dJ = l//3(s), which recovers Eq. (2.61). Since the new Hamiltonian is independent of the phase coordinate ip, the action J is invariant, T--%-*• ds dip Using Eq. (2.83), we obtain / y = \l2f3J cos-0, /2T y'=-J-— [smip + acosi>], <285>
(2.86)
where a = —/3'/2- Now it is easy to verify that the action J is16
J=^[
Z7T ./torus
dy'dy=±<fy'dy.
Z7T J
(2.87)
The phase space area enclosed by the invariant torus is equal to 2n J. Figure 2.7: The horizontal and vertical betatron ellipses for a particle with actions Jx = Jz = 0.57T mm-mrad at the end of the first dipole (left plots) and the end of the fourth dipole of the AGS lattice (see Fig. 2.5). The scale for the ordinate x or z is in mm, and that for the coordinate x' or z' is in mrad. For the left plots, the betatron amplitude functions are Px = 17.0 m, ax = 2.02, A = 14.7 m, and az = -1.84. For the right plots they are /3X = 21.7 m, ax = -0.33, fiz = 10.9 m, and az = 0.29. Figure 2.7 shows the phase-space ellipses (x, x') and (z, z') for a particle with actions Jx = Jz = 0.5TT mm-mrad at the ends of the first and the fourth dipoles of the AGS lattice (see Fig. 2.5). Such a phase-space ellipse is also called the Poincare map, where the particle phase-space coordinates are plotted in each revolution. The consecutive phase-space points can be obtained by multiplying the transfer matrices,
16The
Jacobian of the transformation from (y,y') to {J,ip) is equal to 1.
II. LINEAR BETATRON MOTION
59
where M x and M z are the transfer matrices of one complete revolution. The Poincare map of betatron motion at a fixed azimuth s is also called the Poincare surface of section. If the betatron tune is not a rational number, the consecutive phase-space points of the particle trajectory will trace out the entire ellipse. The areas enclosed by the horizontal and vertical ellipses are equal to 2-irJx and 2-KJZ respectively. As the particle travels in the accelerator, the shape of the phase-space ellipse may vary but the area enclosed by the ellipse is invariant. A. Normalized phase space coordinates We define the normalized conjugate phase-space coordinate Vy as
Vy = py' + ay = -JzpJs\ni>.
(2.89)
A particle trajectory in the normalized phase-space coordinates (y, — Vy) is a circle with radius \/2/3J. The shape of the normalized phase-space ellipse is independent of the location s. In terms of the betatron amplitude matrix of Eq. (2.68), the normalized phase space coordinates are expressed as
B. Using the orbital angle 9 as the independent variable The Hamiltonian H of Eq. (2.84) depends on the independent variable s. Because /3(s) is not a constant, the phase advance is modulated along the accelerator orbital trajectory. Sometimes it is useful to obtain a global Fourier expansion of particle motion by using the generating function
F2(r/,,J)=(^-^j
+ u9JJ
(2.91)
to compensate the modulated phase-advance function. Here 6 — s/R is the orbiting angle of the reference orbit. The new conjugate coordinates (T/S, J) are
$ = if>- f ' ^ + v6, Jo p J = J, (2.92)
and the new Hamiltonian becomes H = vJ/R. Changing the time coordinate from s to 9, the new Hamiltonian is re-scaled and becomes H = RH = vJ. (2.93)
60
CHAPTER 2. TRANSVERSE
MOTION
The transformation from betatron phase-space coordinates to action-angle variables is y= fifij cos (i> + x{s)-vO), Vv = py' + ay= - ^ S J s i n ( ^ + x(s) - vff), (2.94) (2.95)
where x = /oS ds/0 and (V>, J) are conjugate phase-space coordinates. The transformation is useful in expressing a general betatron Hamiltonian in action-angle variables for obtaining a global Fourier expansion in the nonlinear resonance analysis. Hereafter, the notation (•ip, J) will be simplified to (ip, J).
II. 5
Courant-Snyder Invariant and Emittance
Py' + ay= -a/31/2(s) sin (i/0(s) + 6). (2.96)
Using the general solution y(s) of Eq. (2.70), we obtain
The Courant-Snyder invariant defined by
C(y, y') = ^[v2 + H + Py')2] = iv2 + 2 W + Py'2
(2.97)
is equal to twice the action, which is independent of s. The trajectory of particle motion with initial condition (yo, y'o) follows an ellipse described by C(y, y') = e. The phase space enclosed by (y, y') of Eq. (2.97) is equal to 7re (see Fig. 2.8).
Figure 2.8: The Courant-Snyder invariant ellipse. The area enclosed by the ellipse is equal to 7re, where e is twice the betatron action; a,/3 and 7 are betatron amplitude functions. The maximum amplitude of betatron motion is i/Pe, and the maximum divergence (angle) of the betatron motion is y/ye.
A. The emittance of a beam A beam is usually composed of particles distributed in the phase space. Depending on the initial beam preparation, we approximate a realistic beam distribution function
II. LINEAR BETATRON MOTION
61
by some simple analytic formula. Neglecting dissipation and diffusion processes, each particle in the distribution function has its invariant Courant-Snyder ellipse. Given a normalized distribution function p(y,y') with / p(y,y')dydy' = 1, the moments of the beam distribution are
(y) = I Vp(y, y')dydy',
(y1) = J y'p(y, y')dydy', <# = /(</'- {y')?p{y, yVydy',
(2.98) (2.99) ( 2 - 10 °)
°l = f(y - (v))2p(y, vVydy1,
°m/ = J(y - (y)W - (y'))p(y> y')dydv' = r w ,
where ay and ayi are the rms beam widths, oyyi is the correlation, and r is the correlation coefficient. The rms beam emittance is then defined as €rms = \jo2yO2y, _
a2yyl
= OyOy, Vl ~ r2.
(2.101)
If the accelerator is composed of linear elements such as dipoles and quadrupoles, the emittance defined in Eq. (2.101) is invariant. The rms emittance is equal to the phase-space area enclosed by the Courant-Snyder ellipse of the rms particle (see Exercise 2.2.14). Although incorrect, the term "emittance" is often loosely used as twice the action variable of betatron oscillations. The betatron oscillations of "a particle" with an "emittance" e is y(s) = JJe cos [v^){s) + 8}. (2.102) Figure 2.8 shows a Courant-Snyder invariant ellipse for a given emittance of a beam. For a beam with rms emittance 7re,17 the rms beam width is y/3(s)e, and the beam rms divergence y' is ^Jry(s)e. Since 7 = (1 + a2)/j3, the transverse beam divergence is smaller at a location with a large /3(s) value, i.e. all particles travel in parallel paths. In accelerator design, a proper f3(s) value is therefore important for achieving many desirable properties. B. The cr-matrix The a-matnx of a beam distribution is defined as
"ill
ZXt
:f) = «y-W»-M)').
(2,03)
where y is the betatron state-vector of Eq. (2.36), y+ — {y,y') is the transpose of y, and (y) is the first moment. The rms emittance denned by Eq. (2.101) is the
17The accelerator scientists commonly use 7r-mm-mrad for the unit of emittance. However, the factor 7 is often omitted. In beam width calculation, we get cry = ^KCy/ly/ir. The synchrotron T light source community also uses nano-meter (nm) as the unit for emittance. In fact, the factor n is implied and omitted in the literature.
62
CHAPTER 2. TRANSVERSE
MOTION
determinant of the cr-matrix, i.e. erms = \/det<7 (see also Exercise 2.2.14). Using the transfer matrix of Eq. (2.37), we obtain a(s2) = M(s2\s1)a{s1)M(s2\siy. (2.104)
It is easy to verify that y^(J~1y is invariant under linear betatron motion, thus the invariant beam distribution is p(y,y') = piv^-'y)C. Emittance measurement The emittance can be obtained by measuring the cr-matrix. The beam profile of protons and ions is usually measured by using wire scanners or ionization profile monitors. Synchrotron light monitors are commonly used in electron storage rings. More recently, laser light has been used to measure electron beam size in the submicron range. Using the rms beam size and Courant-Snyder parameters, we can deduce the emittance of the beam. Two methods commonly used to measure the rms emittance are discussed below. C l . Quadrupole tuning method Using Eq. (2.104), we find the rms beam radius R2 at a drift-distance L downstream of a quadrupole:18 an(s2) = R22 = an(s1)(l + ^ ^ - - L g ] V cm(si) / +^-L2, o-ii(si) (2.106) (2.105)
where g = Bi£q/Bp is the effective quadrupole field strength, L is the distance between the quadrupole and the beam profile monitor, and <7y(si)'s are elements of the a matrix at the entrance of the quadrupole with ej?ms = (Ji\O22 — a\2, and crn(s2) is the 11-element of the cr-matrix at the profile monitor location s2 (see Exercise 2.2.14(d) for an equation with thick quadrupole lens). The R\ data measured with varying quadrupole strength g can be used to fit a parabola. The rms emittance erms can be obtained from the fitted parameters. This method is commonly used at the end of a transport line, where a fluorescence screen or a wire detector (harp) is used to measure the rms beam size.
18If the transfer matrix between the tuning quadrupole at si and the profile monitor at S2 is m, we obtain cru = an [mu + (cumu/iTu) - "Ji2ff]2 + (7ni2erms)/crii> where <Jn is the 11-element of the cr-matrix at s2 , oy's are elements of the cr-matrix at si, m y 's are elements of the transfer matrix, and g = BiEq/Bp is the effective focusing strength of the quadrupole.
II. LINEAR BETATRON MOTION C2. Moving screen method
63
Using a movable fluorescence screen, the beam size at three spots can be used to determine the emittance. Employing the transfer matrix of drift space, the rms beam radii at the second and third positions are [ i?2 = an + 2L1<7i2 + L-^a^, \ R2 = an + 2{U + L2)a12 + (L, + L2)2a22, /r, i n 7 \ {Z'W'>
where an = R\, on and 022 are elements of the a matrix at the first screen location, and L\ and L2 are respectively drift distances between screens 1 and 2 and between screens 2 and 3. The solution an and <722 of Eq. (2.107) can be used to obtain the rms beam emittance: erms = yan<?22 ~ a\iIf screen 2 is located at the waist, i.e. dR\jdLx = 0, then the emittance can be determined from rms beam size measurements of screens 1 and 2 alone. The resulting emittance is (2.108) e2 = (R\Rl - Rl) /L\. This method is commonly used to measure the electron emittance in a transfer line. D. The Gaussian distribution function The equilibrium beam distribution in the linearized betatron phase space may be any function of the invariant action. However, the Gaussian distribution function (2.109) P{y,v') =-^exp(——-(<T 222/2 -2(Ti22/2/'+ crU2/'2)) \ z det a / is commonly used to evaluate the beam properties. Expressing the normalized Gaussian distribution in the normalized phase space, we obtain p(y^y) = ^e-(y2+^2"2y, (2.110)
where (y2) = (p2) = a* = f3yerms with an rms emittance erms. Transforming (y, Vv) into the action-angle variables (J, ip) with y = ^2/3yJcos^, Vy = -sj2^Jsmi), (2.111)
where the Jacobian of the transformation is
the distribution function becomes p{J) = —e-J'*-,
'rms
p(e) = -^—e-^™,
£€rms
(2.113)
64
CHAPTER 2. TRANSVERSE
MOTION
Table 2.1: Percentage of particles in the confined phase-space volume e/erms 12 14 I 6 I 8 Percentage in ID [%] 63 86 95 98 Percentage in 2D [%] 40 74 90 96
where e = 2J. The percentage of particles contained within e = ne rms is 1 - e""/2, shown in Table 2.1. The maximum phase-space area that particles can survive in an accelerator is called the admittance, or the dynamical aperture. The admittance is determined by the vacuum chamber size, the kicker aperture, and nonlinear magnetic fields. To achieve good performance of an accelerator, the emittance should be kept much smaller than the admittance. Note that some publications assume 95% emittance, i.e. the phase-space area contains 95% of the beam particles, eg5% « 6e rms for a Gaussian distribution. For superconducting accelerators, a dynamical aperture of 6<r or more is normally assumed for magnet quench protection. For electron storage rings, quantum fluctuations due to synchrotron radiation are important; the machine acceptance usually requires about 10cr for good quantum lifetime. Accelerator scientists in Europe use e = 4erm3 to define the beam emittance. This convention arises from the KV distribution, where the rms beam emittance is equal to 1/4 of the total emittance [see Eq. (2.131)].
E. Adiabatic damping and the normalized emittance
The Courant-Snyder invariant of Eq. (2.97), derived from the phase-space coordinate y, y', is not invariant when the energy is changed. To obtain the Liouville invariant phase-space area, we should use the conjugate phase-space coordinates {y,py) of the Hamiltonian in Eq. (2.18). Since py = py' = mcP'yy', where m is the particle's mass, p is its momentum, and Pj is the Lorentz relativistic factor, the normalized emittance defined by en = $fe (2.114) is invariant. Thus the beam emittance decreases with increasing beam momentum, i.e. e = €n//?7- This is called adiabatic damping. The adiabatic phase-space damping of the beam can be visualized as follows. Because the transverse velocity of a particle does not change during acceleration, the transverse angle y' = py/p becomes smaller as the momentum of the particle increases, and the beam emittance e — en//?7 becomes smaller. It is worth pointing out that the beam emittance in electron storage rings increases with energy as j 2 because of the quantum fluctuation to be discussed in Chap. 4. The
II. LINEAR BETATRON MOTION
65
corresponding normalized emittance is proportional to 7 3 , where 7 is the relativistic Lorentz factor. On the other hand, the beam emittance in electron linac will be adiabatically damped at high energies.
II.6
Stability of Betatron Motion: A FODO Cell Example
In this section, we illustrate the stability of betatron motion using a FODO cell example. We consider a FODO cell with quadrupole focal length /1 and - / 2 , where the ± signs designates the focusing and defocussing quadrupoles respectively. The transfer matrix of {§QFi O QD2 O |QF X } is _ _ / ( 1
1+
OWl
LA/1
(A / I
Lt\(
1 \
0\
^-7^-2&
2L l ( l + ^ )
+
\ h
h
hh
+
2/f + i!ih>
h
h
V2 I
where L\ is the drift length between quadrupoles. Identifying the transfer matrix with the Courant-Snyder parametrization, we obtain
co8«, = l + £ - £ - - £ y , C0S$z = 1 _ ^ + ^ l _ J L .
(2-116) (2 . 117 )
The stability condition, Eq. (2.52), of the betatron motion is equivalent to the following conditions: |1+2X2-2X1-2X1X2| <1 and |1 - 2X2 + 2XX - 2X^X2\ < 1, (2.118)
where Xx = Z-i/2/i and X2 = Li/2/ 2 . The solution of Eq. (2.118) is shown in Fig. 2.9, which is usually called the necktie diagram. The lower and the upper boundaries of the shaded area correspond to $ x , z = 0 or -K respectively. Since the stable region is limited by X1]2 < 1, the focal length should be larger than one-fourth of the full cell length. The stability condition of the above FODO cell example seems to suggest that the phase advances $x and $ z of a repetitive module should be less than TT.19 However, this is not a necessary condition. The phase advances of a complex repetitive latticemodule can be larger than TT. For example, the phase advance of a flexible momentum compaction (FMC) module is about 3TT/2 (see Sec. IV.8 and Exercise 2.4.17) and the phase advance of a minimum emittance double-bend achromat module is about 2.4?r
19The phase advance $ x of a double-bend achromat is larger than 7r (see Sec. IV.5). Thus a simple FODO cell working as double-bend achromat is unstable.
66
CHAPTER 2. TRANSVERSE
MOTION
(see Sec. III.l; Chap. 4). In general, the stability of betatron motion is described by ICOS^JI < 1 and |cos$ 2 | < 1 for any type of accelerator lattice or repetitive transport line.
Figure 2.9: Stability diagram of a FODO cell lattice. The lower and upper boundaries correspond to <&I]Z = 0 or 180° respectively.
II.7
Symplectic Condition
_ J. In general, the transfer matrix of a
The 2x2 transfer matrix M with detM = 1 satisfies MJM = J, where M is the transpose of the matrix M, and J = I Hamiltonian flow of n degrees of freedom satisfies MJM = J, where M is the transpose of the matrix M, and
J =
(2.119)
(-I
o)'
With
j2 =
"7'
J = ~J<
J~l = -J
(2-120)
with / as the n x n unit matrix. A 2n x 2n matrix, M, is said to be symplectic if it satisfies Eq. (2.119). The matrices / and J are symplectic. If the matrix M is symplectic, then M~l is also symplectic and detM = 1 . If M and ./V are symplectic, then MN is also symplectic. Since the set of symplectic matrices satisfies the properties that (1) the unit matrix I is symplectic, (2) if M is symplectic then M~x is symplectic, and (3) if M and iV are symplectic, then MN is also symplectic, the set of symplectic matrices form a group denoted by Sp(2n). The properties of real symplectic matrices are described below.
II. LINEAR BETATRON MOTION
67
• The eigenvalues of symplectic matrix M must be real or must occur in complex conjugate pairs, i.e. A and A*. The eigenvalues of a real matrix M or the roots of the characteristic polynomial P(X) = \M — \I\ = 0 have real coefficients. • Since \M\ = 1, zero can not be an eigenvalue of a symplectic matrix. • If A is an eigenvalue of a real symplectic matrix M, then I/A must also be an eigenvalue. They should occur at the same multiplicity. Thus eigenvalues of a symplectic matrix are pairs of reciprocal numbers. For a symplectic matrix, we have K~\M or P(A) = X2nP{\) If we define Q(X) = X~nP{X), then Q(X) = Q(\). (2.123)
A
- XI) K = M~x -XI=
-XM~X{M - A"1/)
(2.121)
(2.122)
II.8
Effect of Space-Charge Force on Betatron Motion
The betatron amplitude function w — Jpy of the Floquet transformation satisfies Eq. (2.60). Defining the envelope radius of a beam as
Ry = yffay,
where ty is the emittance, the envelope equation becomes ^' + ^ - - ^ = 0,
(2.124)
(2.125)
where the prime corresponds to the derivative with respect to s. Based on the Floquet theorem, if Ky is a periodic function of s, i.e. Ky(s) = Ky(s + L), where L is the length of a repetitive period, the solution of the envelope equation can be imposed with a periodic condition, Ry(s) = Ry(s + L). The periodic envelope solution, aside from a multiplicative constant, is equal to the betatron amplitude function. The envelope function of an emittance dominated beam is equal to \lpyty. What happens to the beam envelope when the space-charge force dominates the beam dynamics? Here we discuss some effects of the space-charge force on betatron motion.
68
CHAPTER 2. TRANSVERSE MOTION
A. The Kapchinskij-Vladimirskij Distribution It is known that the Coulomb mean-field from an arbitrary beam distribution is likely to be nonlinear. In 1959, Kapchinskij and Vladimirskij (KV) discovered an ellipsoid beam distribution that leads to a perfect linear space-charge force within the beam radius. This distribution function is called the KV distribution.20 Particles, in the KV distribution, are uniformly distributed on a constant total emittance surface of the 4-dimensional phase space, i.e.
**> V~ * ?-) = J^5 G? (*2 + ^ ) + h 0 2 + *?) - l) . •
(2-126)
where N is the number of particles per unit length, e is the particle's charge, a and b are envelope radii of the beam, x and z are the transverse phase-space coordinates, and Vx — R'x, and Vz = R'z are the corresponding normalized conjugate phase-space coordinates. Some properties of the KV distribution are as follows. 1. With the phase-space coordinates transformed into action-angle variables, the KV distribution function becomes rfJ,,7,) = ^ ( ^
+
^ - l )
(2.127)
Thus beam particles are uniformly distributed along an action line
3j-+Jy
f-x
€z
=\
^
(2.128)
where ex and ez are the horizontal and vertical emittances. The envelope radii are
a = y[KZ, b = JpJ;.
(2.129)
2. Integrating the conjugate momenta, the distribution function becomes
^-sH'-S-if)
3. The rms emittances of the KV beam are _(x^_e _<f!)_!i
(2i3o)
where the 9(^) function is equal to 1 if f > 0, and 0 if £ < 0. In fact, the KV particles are uniformly distributed in any two-dimensional projection of the four-dimensional phase space.
(2m)
Thus the rms envelope radii are equal to half of the beam radii in the KV beam.
20I.M. Kapchinskij and V.V. Vladimirskij, Proc. Int. Conf. on High Energy Accelerators, p. 274 (CERN, Geneva, 1959).
(2. = Q' ('3) 214 ( 2 . w2 v x (2-138) (2. beam particles can be viewed as a charge distribution in an infinite long wire with a line-charge density given by Eq. Including the mean-magnetic-field. A noteworthy feature of the KV distribution function is that the resulting mean-field inside the beam envelope radii is linear! If the external focusing force is also linear.z) = ^-(-~^—-x+—^-rz). Neglecting the longitudinal variations. and N is the number of particles per unit length.130). and Kx is the "normalized" space-charge perveance parameter given by (2. LINEAR BETATRON MOTION B.139) . Thus Hill's equations of motion become H*.133) ' b(a + b) J v where 7 is the relativistic energy factor. z) is i?/ A Ne ffj-j^n x'2 z'2(x-x')x + (z-z')z + E{x>z) = 2^abJJdxdz 2ne0 \a(a + b) @{l-^-¥\x-xiy {z-z>y v .+ A = 0. (2. Performing Floquet transformation of the linear KV-Hill equation x = wxe?*' and z = wzeji>'.137) we obtain < + (K* ~ " T ^ M ) W.135 > where the prime is a derivative with respect to the longitudinal coordinate s.136) where r 0 = e2/4-n:eomc2 is the classical radius of the particle.II. the force on the particle at (x. b(a + b) ) where eo is the vacuum permittivity. the KV distribution is a self-consistent distribution function. The electric field at the spatial point (x. z) is F(x. <+ \ a(a + b)J w% (K> ~ 7T^) Wz + —3=Q. v ' 27reo72 \a(a + b) (2. \ b(a + b)J w* <= 4w2 i>l = —. The Coulomb mean-field due to all beam particles 69 The next task is to calculate the effect of the average space-charge force.W -^) I=0' z" + {K^-wfvyjz *« = ^ f .
the space-charge parameter. i. The usefulness of the KV equation has been further extended to arbitrary ellipsoid distribution functions provided that the envelope functions a and b are equal to twice the rms envelope radii. and the emittances ex and ez are equal to four times the rms emittances.140) and (2. (2. b) = ~(Kxa2 + Kzb2) .2KSC ln(a + b) + ^ +^ .J. 7. (2. (2. (2. Sacherer. To understand the physics of the mismatched envelope. and R. Lee and R.143) we can derive the KV equations (2. it is advantageous to extend the envelope equation to Hamiltonian dynamics as discussed below. For space-charge dominated beams. Nncl. we obtain the KV envelope equations. or simply the KV equations: a!' + Kxa-^--% a + b a6 OK c2 OK f2 = Q.K.70 CHAPTER 2. b{s)=b{s + L).142). IEEE Trans. 1101 (1971).139) by ^ e j . (2. Part. J. (2. (2. The matched beam envelope solution can be obtained by a proper closed orbit condition of Eq. ibid.145) 21 P. Lapostolle. For beams with an initial mismatched envelope. E. and the beam emittance. Pb = b'. Kx(s) = Kx(s + L). Gluckstern.142) A numerical integrator or differential equation solvers can be used to find the envelope function of the space-charge dominated beams. 5. P. the KV equation can be solved by imposing the periodic boundary (closed orbit) condition (Floquet theorem) a(s) = a(s + L). Accel. Sci. (2.L. 1105 (1971). (2.D. the envelope solution can vary widely depending on the external focusing function.141) from the envelope Hamiltonian: ffenv = \(pl+pl + Kxa2 + Kzb2) .140) b" + Kzb-^-% = Q.M. the envelope equation can be solved by using the initial value problem to find the behavior of the mismatched beams. NS-18. 61 (1973).138) by JTX and Eq. TRANSVERSE MOTION Multiplying Eq.e. Lapostolle.P.M. F. and identifying a = wxJTx and b = wzy/e^. C. . 83 (1976). Lawson.141) Solving the KV envelope equation is equivalent to finding the betatron amplitude function in the presence of the space-charge force. ibid.144) With the envelope potential defined as Vem(a.21 If the external force is periodic. Cooper. Hamiltonian formalism of the envelope equation Introducing the pseudo-envelope momenta as Pa = a'.2KSC ln(o + 6) + ^ + ^ .
i. .150) (9 Tin _ -ft^tot _ .C Kenv / .^sclna+ A = \V\ + Venv(a). we can obtain the tune of the envelope oscillation. where _ K^L (2. V 1 0 K e nv / \o . we consider the effect of space charge on the envelope function.146) where am and bm are the matched envelope radii.e. For example. a2m=(^)[K + V^l\.( a m . (2.^ . With a = b in Eq. Now. the matched envelope solution is amo = \JtxL/2-K = ^expx. where the focusing function is Kx = (2TT/L) 2 .15) independent of the envelope-oscillation amplitude. bm) = .II. if we start from the condition with envelope momenta pa = pb = 0. (2. LINEAR BETATRON MOTION 71 the matched beam envelope can be easily understood as the equilibrium solution of the envelope Hamiltonian.( a m . bm) = 0. L .148) When the space-charge force is negligible.e. the envelope Hamiltonian is #env = \vl + \ ( f ) 2 « 2 . The matched envelope radius is obtained from the solution of dVem/da = 0. The second-order derivative at the matched radius becomes The tune of the mismatched envelope oscillation is twice the tune of betatron motion (see also Exercise 2. The envelope oscillations of a mismatched beam can be determined by the perturbation around the matched solution env = 2~d^T^ ~ ^ + 2 ~ 9 6 ^ ( " m ) + ' ' ' • ( ^ Using the second-order derivatives. and the betatron amplitude function is equal to L/2-K. D. the matched envelope radii are located at the minimum potential energy location. i. .^ . (2.140). \9 • rn -t A>-J\ Here L is the betatron wavelength. An example of a uniform focusing paraxial system First we consider a beam in a uniform paraxial focusing system.2.
Phys. Lee and A.C.exL) = 1. Rev. See Eq. 1609 (1995). There is a large envelope detuning from 2/z to \/2/i. Rev. Chen and R.150) for the matched envelope radius. When the space-charge perveance parameter is zero. Phys. and L tot and $tot are the total length and total phase advance of a transport system. is the betatron phase advance. the envelope tune approaches 22The Laslett (linear) space-charge tune shift is related to the space-charge perveance parameter by £sc = Ai/sc = KscLtot/4iWex = KV./2ir for the unbetatron tune) as a function of the maximum amplitude of the envelope amplitude. where /j. E 51. Lett. A nonlinear envelope resonance can be excited when perturbation exists and a resonance condition is satisfied. and obtain which is the phase advance per unit length of small amplitude envelope oscillation in the presence of the Coulomb potential. 2195 (1994). C.4199 in this example.72 CHAPTER 2. See also Ref. Rev.150) indicates that the betatron amplitude function increases by a factor K + %/«. the phase advance of > the small-amplitude envelope oscillations can maximally be depressed to 2\/2 TT/L. [4] for an exploration of the space-charge dynamics.23 Figure 2.2 + 1 due to the space-charge force. Phys. TRANSVERSE MOTION is the effective space-charge parameter. At a large envelope amplitude. 72. where v is the tune. the phase advance of the envelope oscillation is twice of that of the betatron oscillation. n = 2.28175. Riabko.2817 radian (or v = fj. Davidson. E49. Riabko et al. 3529 (1995). 5679 (1994). The matched radius is RQ — am^/2Tr/(fj.10: The phase advance of the envelope oscillations divided by the original betatron phase advance for a high space charge beam with Ksc = 10. . Phys.22 Equation (2. The ordinate R is the normalized maximum envelope radius of the beam. Figure Ksc = 10 perturbed oscillation 2. Next we evaluate the second-order derivative of the potential at the matched radius. A. (2.Y. Rev. 23S. as K — oo. and when the space-charge force is large.10 shows the envelope tune of a space charge dominated beam with and a phase advance of /x = 2.. E 51.
in the thin-lens approximation. of Michigan Press. When the space charge parameter K is large. Show that the mapping matrix M for a short quadrupole of length i. 2. / > 0. i. 1971). (2. is -(-}:) where / = l i m ^ o ^ ^ ) " 1 ! is the focal length of a quadrupole. The focusing function K(s) for most accelerator magnets can be assumed to be piecewise constant. When a particle enters a dipole at an angle S with respect to the normal edge of a dipole (see drawing below).s\. (2. Show that the transfer matrices for the horizontal and vertical betatron motion due to the edge focusing are 24Using edge focusing.5 GeV. See L. The ZGS was made of 8 dipoles with a circumference of 172 m attaining the energy of 12. ( K(s)=K<0. Greenbaum. For a focusing quad. Exercise 2. 18. the betatron tune can be depressed to zero.e. 1963. _ \J\K\smhyf\K\s V^F Zcosh^\K\s with s = S2 . . This phenomenon is usually referred to as edge focusing.2 1. (2.150) into Eq. M(S2\Sl)=(l J)./sc = fsc = KV. there is a quadrupole effect.EXERCISE 2. Effect of space charge force on particle motion The single particle betatron phase advance per unit length is obtained by substituting Eq. Ann Arbor. Show that K(s) = 0. ) cos VKs . Near the matched envelope radius (or small amplitude envelope oscillations). where v = $tot/(27r) is the tune of the accelerator. the envelope tune approaches y/2 times the unperturbed betatron tune. Its first proton beam was commissioned on Sept. the zero-gradient synchrotron (ZGS) was designed and constructed in the 1960's at Argonne National Laboratory.K). / < 0. $* = -J-(VK2 Lt 2TT + 1 .135). M( S2 | Sl )= cos \fRs -VKsmvKs -4T sin \/TCs \ ) ).24 We use the convention that 5 > 0 if the particle trajectory is closer to the center of the bending radius.2 73 twice the unperturbed betatron tune.153) When the space charge parameter n is small. and for a defocussing quad. the incoherent space-charge (Laslett) tune shift is equal to A. A Special Interest (Univ.
dBz/dx = 0. where 9 is the bending angle. calculate the mapping matrix for the basic period and discuss the stability condition. T h u s t h e A*z = I tan* i M* = tani5 / ^ \ v ^ .2b). p is the bending radius.74 CHAPTER 2."i / zontal defocussing and vertical focusing. (a) Show that the horizontal and vertical transfer matrices are (p/Vl — n) sin(-\/l — n s/p) \ yr _ ( cos(\/l — n s/p) x \ —(%/! ~ n/p) sin(\/l — n s/p) cos(\/l — n s/p) ) ' M _ ( cos(Vn s/p) (p/Vn) sin(^/n s/p) \ Z V —(y/n/p) sin(Vl — n s/p) cos(-v/n s/p) ) ' (b) Show that the betatron tunes are vx = (1 —n)1//2 and vz = n1/2. 2. The particle orbit enters and exits a sector dipole magnet perpendicular to the dipole edges. Note that a sector magnet gives rise to horizontal focusing. The entrance and exit edge angles of a rectangular dipole are 5\ = 0/2 and 82 = 6/2.1. Kz{s) = n/p2 = constant and Kx = (1 — n)/p2.0) dx x=o' ( where we have chosen the coordinate system shown in Fig. and the stability condition is 0 < n < 1. is the length of the dipole.' / \ / ' ^ \ 7 ^ ^ \ / \ ~ - 3. with Kx = Kz = 0. 4.^ ^^~ ^ \ "~~\^ V j \^ \ / ^__ . The focusing index n is ' p(s) dBz(s. Find the horizontal and vertical transfer matrices for a rectangular dipole (Fig.e. and (.x. TRANSVERSE MOTION \~J~ 1 / V—— lJ where 8 is the entrance or the exit angle edge effect with S > 0 gives rise to hori. Solve the following problems by using the uniform focusing approximation with constant n. where p is the radius of the accelerator.. are introduced into the accelerator lattice adjacent to each combined-function dipole. fl i\ where 0 is the bending angle. i. For a weak-focusing accelerator. .. Assuming that the gradient function of the dipole is zero. 6. The path length for a particle orbit in an accelerator is C = j ^[l + {x/p)f + xl2 + z^ds. 2..0) Bz{s. /cos0 psin0\ .Q. (c) If N equally spaced straight sections. 5. show that the transfer matrix is . / of the particle with respect to the normal direction of t h e dipole edge.
In a strong-focusing synchrotron. and QD is a defocussing quadrupole.25 (d) Find the phase advance $ that minimizes the betatron amplitude function at the focusing quadrupole location. I /9 = acosh2^\K\s + bsmh. where there are no quadrupoles.As and s? = s0 + As. Show that the average orbit length of a particle executing betatron oscillations is longer by C \R? ' Thus the orbit length depends quadratically on the betatron amplitude. show that the betatron amplitude function is 25Find /?'s at Si = So . (a) Express a. /?o and 70 at the beginning of the element. In the smooth approximation. Using Eq. OO represents either a drift space or bending dipoles of length L\. show that p'" + 4/3'K + 2/3K' = 0.EXERCISE 2. Solve this equation for a drift space and a quadrupole respectively. Using the thin-lens approximation. focusing quadrupole < fi = a cos 2y/l(s + b sm2^/Ks + c. a at the quadrupoles and at the center of the drift space as a function of L\ and $. . defocussing quadrupole. vz and z are the average radius. and the betatron oscillations can be expressed as where R. the vertical betatron tune. (2. and calculate the derivative from these numbers. (a) Find the mapping matrix and the phase advance of the FODO cell and discuss the stability condition.2^/\K\s + c. A FODO cell is composed of QF 0 0 QD 0 0 . the art (or science) of magnet arrangement is called lattice design. The length of a FODO cell is L = 1L\.2 75 Show that the average orbit length of the particle with a vertical betatron action Jz is longer by A C _ 1 A + a2 where az and j3z are betatron amplitude functions. where QF is a focusing quadrupole. and c in terms of parameters c*o. 7. and the vertical betatron amplitude respectively. and Xz is an arbitrary betatron phase angle of the particle. the betatron amplitude function is approximated by (f3z) = R/vz. 6. and show that the solution of this equation must be one of the following forms: drift space ( 0 = a + bs + es 2 .66). The basic building blocks of a lattice are usually FODO cells. (b) Find the parameters /3. 8. (b) In a drift space. (c) Verify that /3' = — la numerically at the center of the drift space.
the injection or extraction kickers are located at a high /9 locations with a 90° phase advance. TRANSVERSE MOTION where P* is the betatron function at the symmetry point s = s* with P' = 0. (2. . 11.72 at s2 are related to ai.67) becomes M(s2\si) = I^MBj" 1 .e. Show also that 7 = (1 + Q2)/P is equal to 1/P*. Mf2 / \71/ where My are the matrix elements of M(s2\si).76 CHAPTER 2. Use the transfer matrix M(s2\si) of Eq. Use these equations to verify 9. i. i. the displacement at a downstream location is Ax2 = dy/Pifhsmij). (2. your solution to part (a). sin^N . and if> = ip(s2) — ip(si) is the betatron phase advance between s\ and S2.80) into Eq. when a particle is kicked at si by an angle 9. We consider a FOFO focusing channel where the focusing elements are separated by a distance L. 10.1. where B 2 and Bi are the betatron amplitude matrices at s = s2 and s\ respectively.67) to show that. 12.4). 7 is constant in a drift space. where fii and p2 are values of betatron functions at si and s2 respectively. Transforming the betatron phase-space coordinates onto the normalized coordinates with Y= or TPV' v^TP{ay+fi^ show that the betatron transfer matrix in normalized coordinates becomes Cri 1 M(s2 \si)N= I cosV".48).93). .A>7i at s\ by fp2\ I M\x -2MnM12 M11M22 + M12M21 -2M 2 1 M 2 2 M\2 WAX \ a2 = -M11M21 V72/ V M22! -M12M22 I I a i .e. p2. (c) Using the similarity transformation Eq. Show that the Floquet transformation of Eq. (2. The focusing channel can be considered as a focusing-focusing (FOFO) channel. (2. Use the thin-lens approximation to evaluate beam transport properties of a periodic FOFO channel. . Often a solenoidal field has been used to provide both the horizontal and the vertical beam focusing for the production of secondary beams from a target (see Exercise 2.94) transforms the Hamiltonian of Eq. Show that the transfer matrix of Eq. (2. the betatron transfer matrix becomes coordinate rotation with rotation angle equal to the betatron phase advance. show that the Courant-Snyder parameters a2. (2. To minimize the kicker magnet strength 9.The quantity ^PiP2sim/> is usually called the kicker arm.
xi = j xp(x. Nucl. These quadrupole doublets can be used to maintain round beam configuration during beam transport.(x1)) = roxax. Lapostolle.6). The doublet pairs are repeated at intervals L2 2> L\ for beam transport (Fig. (c) Show that the minimum betatron amplitude function is |8* = ^/ii(4/2-LiLa)/4L 2 .x')dxdx' = l.2 (a) Show that the phase advance of a FOFO cell is Sin 2=2V7' 77 $ 1 [I where / is the focal length given by f~l = g2i = ®2/£. 30 (1991). The first and second moments of beam distribution are 1 r I r. (a) Show that the betatron phase advance in a doublet cell is •0 = i>x. (d) Sketch the betatron amplitude functions and compare your results with that of the FODO cell transport line. IEEE Trans. 2. Sci. Oxx' = jf £ ( z i .. . g = Bu/2Bp is the effective solenoid strength.x')dxdx'. B\\ is the solenoid field. describe the properties of betatron motion in a doublet transport line. where / is the focal length of the quadrupoles. Buon. (x1) = -fiY.x')dxdx'. CERN 91-04. The statistical definition of beam emittance is applicable to all phase space coordinates. ^ = JfY.x'). °l = jf £ t e . The doublet configuration consists of a focusing and defocussing quadrupole pair separated by a small distance L\ as a beam focusing unit. .x'i = J x'p(x.x') be the distribution function with fp{x.{x))(x'i . (b) Show that the maximum and minimum values of the betatron amplitude function are Anax = i/sin $.<*'»2.z = arcsin (yfLiLz/Zf] . Statistical definition of beam emittance:26 We consider a statistical distribution of N non-interacting particles in phase space (x. 14.(*»2> 4 = }f £(*. Let p{x. /3min = / sin $. 26See P. 13. 1101 (1971). NS-18. and @ = g£ is the solenoid rotation angle. £ is the length of the solenoid.EXERCISE 2. and J. (b) Show that the maximum betatron amplitude function is approximately /?max = (£l +L2 + LiL2/f)/smif). Using the thin-lens approximation with equal focal length for the focusing and defocussing quadrupoles.
Ly/KsinVKlq + ga f (ai) f-j= sinV#l q . show that the total phase-space area is A = nab = 47rerms. particles are distributed in the Courant-Snyder ellipse: I(x. Use this result to show that x ^ r ^ x of Eq. (b) Show that the rms emittance defined above is invariant under a coordinate rotation X = a: cos 0 +a. Use the coordinate rotation to show that 9 9 trms — ai Q — at.r2.\_ (7X2 + 2axx' + ftx12). i. and show that the correlation coefficient R = aYV. Show that ax and ax. and r is the correlation coefficient. to ensure that the phase-space area of such an ellipse is Tre. (a) Assuming that particles are uniformly distributed in an ellipse x2/a2 + xl2/b2 = l..106) becomes \ axx' ax' / 2 \ axx' ax' / 1 a2x(s2) = ox(Sl) (cos VK£q . according {?'. is zero if we choose X tan 2 0 = . For a thick quadrupole lens.'sin 0.I r ^ r [-4= sin \fiCL + L cos -JKI} . The rms emittance is defined as £rms = PxVx' Vl ./ara the rotation angle to be AA ' A . reach extrema at this rotation angle.78 CHAPTER 2. in the linear betatron motion.* % . (2. where M+ is the transpose of the matrix M.e. X' = -x sin 0 + x' cos 0. TRANSVERSE MOTION Here ax and ax> are rms beam widths. The transport equation for the amatrix can be used to measure the cr-matrix elements and derive the rms beam emittance. ft. y) =MM«)(f*. (c) In accelerators. +L cos VKia) )2 + . 7 1 ' — /75—5 a 0 or Show that x}<7~lx = erms VPi ( 13 -a\ ( a2x axx. (d) Show that the a matrix is transformed.105) is invariant under betatron motion and thus an invariant beam distribution function is a function of xla~lx. x') = jx'2 + 2axx' + fix2. y) ^(-si-i)*. where a. (2. 7 are betatron amplitude functions. The factor 4 has often been used in the definition of the full emittance. e = 4e rms . show that Eq.
where the particle betatron coordinate obeys Hill's equation y" + Ky(s)y = 0. i. E51.Y. where R is the average radius. and L is the length of the drift space between the quadrupole and the profile monitor. we have (Ky) = (2nQy/C)2 obtained from Floquet transformation to Hill's equation. Rev.dH.' « * e* >" <*><&•»• For a linear Hamiltonian.e. Rev. Riabko et al. (a) Show that the envelope equation of motion is Y" + Ky(s)Y-^ = 0. Show that the betatron motion is Le 2-KS . Riabko. 3529 (1995). 27See S. where L is the wavelength of the betatron oscillations. . i. Show that the rms emittance is conserved. Consider a beam of noninteracting particles in an accelerator with focusing function Ky(s).EXERCISE 2. Y) are conjugate envelope phase-space coordinates with P = Y'.K. 28Using the smooth approximation. Let Y be the envelope radius of the beam with emittance e.dH... The "potential energy" of the envelope Hamiltonian is V — 1g AK rY 2 +4. Ym = \jLej2n. _ dx dx' _ da ' ds Show that de2 n dH dx „ .e. E51. Phys. Lee and A. where K(s) is the focusing function. . where (P. dH. . and Qy is the betatron tune.28 The equivalent betatron amplitude function is Py = L/2TT. (e) Particle motion in synchrotrons obeys Hamiltonian dynamics with . . where C is the circumference. 1609 (1995). (b) Show that the envelope equation can be derived from the envelope Hamiltonian27 tfenv = \P2 + \Ky{s)Y2 + ~ . Y(s) = ^/3(s)e. .. .2 79 where K = B\/Bp and tq and the focusing function and the length of the quadrupole. Phys. What would your conclusion be if the Hamiltonian were nonlinear? 15. Ky(s) = (2n/L)2. . The matched beam radius is given by dVenv/dY = 0.dHxs •dJ = -2o^x &F>" ^ X a* » + 2 " . The corresponding average betatron wavelength is C/Qy.) = R/Qy.2Y3' t venv V In a smooth focusing approximation. we have dH/dx = Kx. . . A. and the average betatron amplitude function is (/?j.
The Courant-Snyder phase-space ellipse of a synchrotron is yy2 + 2ayy' + j3y'2 = e. 16. Show that the normalized envelope R satisfies the equation: Using (R. . where a. in fact. The envelope Hamiltonian is. 29The easiest way to estimate the emittance growth is to transform the injection ellipse into the normalized coordinates of the ring optics. Show that the exact solution of the envelope equation is R2 = y/l +a2 +acos{2i/(f> + x). (c) Let us make Floquet transformation to the envelope equation in part (a) with B. where a is the envelope mismatch amplitude. The deviation of the injection ellipse from a circle in the normalized phase space corresponds to the emittance growth. and show that the injection ellipse becomes (P where U+ (axp-fila)2\ M ) 2 arf-aP! + 0 ft YP + T ~e' 2 _ Y = Tpy' P = j?to + M.-v R + — . linear. the resulting oscillation will be sinusoidal. and v is the betatron tune. If the injection optics is mis-matched with 71J/2 + 2ot\yy' + /3\y'2 = e.29 (a) Transform the injection ellipse into the normalized coordinates of the ring lattice. Thus the envelope of a mis-injected beam bunch will oscillate at twice the betatron oscillation frequency (the quadrupole mode).J l •_ 1 f ds where /? is the betatron amplitude function. TRANSVERSE MOTION and the solution of the envelope equation is y2 = /^Ii7 +Acos(2? F +x) ' where the parameters A and x Sire determined by the initial beam conditions.80 CHAPTER 2. Note: if the square of the rms beam width is plotted as a function of revolution turns. fi and 7 are the Courant—Snyder parameters. PR = dR/d(f>) as the conjugate phase space coordinates. we obtain the envelope Hamiltonian as H = \P^ + Venv(R). where the envelope potential is Venv . find the emittance growth factor.
the lattice betatron functions are usually designed to an appropriate (3* z value with symmetry condition: axz = 0 .0 m and ax = 2. The luminosity.s2)dxdzdsd(fict). <*s are respectively the rms beam sizes in x.Pet and s2 = s — Pet. F-=\Xam-y/Xlm-l) / . show that the luminosity. K bvoxo*z where R is the reduction factor.14) *mm = I (7i/3 + 017 ~ 2aia) = —!— {/3a2x.15). oz = VPz^z. \l/2 . in a short bunch condition with as <S (3XZ.z.00 mm and 6 = 1. iS C = 2fNlN2 f I pi(x. nonlinear betatron detuning arises from space-charge forces. etc.si)p2(x. the phase-space area of the mis-injected beam will decohere and grow. Because the betatron tune depends on the betatron amplitude. where s\ = s 4. where a = 5. 17. + -ya2x + 2aaxx. or at a symmetry point in a storage ring. nonlinear magnetic fields. (a) Assuming Gaussian bunch distribution with P[X'Z' i S> ~ ^- 1 (2*)V2axoz*s 6XP / \ *2 *2 s2 I 2^ " 2^ " 2^/ ' where ax = VPx^x.02. .2.z. What happens to the beam if the beam is injected into a perfect linear machine where there is no betatron tune spread? Show that the tune of the envelope oscillations is twice the betatron tune (see Exercise 2. and ax = \/P%ex and a* = v //3je 2 are rms beam size at the IP.2.).2 81 (b) Transform the ellipse to the upright orientation.2. Find the final beam emittance after nonlinear decoherence. Show that the emittance growth factor is Fi=(xmm+y/x^iy (d) Let the betatron amplitude function at the injection point be fix = 17. chromaticities.EXERCISE 2. Note that the rms quantities ax. The injection ellipse of a beam with emittance 5TT mm-mrad is given by x2fa2 + x'2/b2 = 1.00 mrad. and show that the major and minor axes of the ellipse are F+={Xmm + JX2im-l) / . At an interaction point (IP) of a collider. C. z. measuring the probability of particle encounters in a head on collision of two beams. The resulting betatron amplitude functions in the straight section become f)XtZ = (3* z + s2/0x>z (see Exercise 2. s directions. where the mismatch factor Xmm is (see Exercise 2.ax> and axx> can be measured from the injected beam. (c) In general.8). \l/2 .
17. Bennewitz and W. 2 18. 38. Haberli. W. with 100 us duration and 5 Hz repetition rate. (c) For a round beam with A = Ax = Az. Paul. show that the luminosity reduction factor for two identical Gaussian distributions is R(A H{Ax.82 CHAPTER 2.47047^)3 ' R(A) = ^AeA where the latter approximate identity is valid up to about A < 2. A ^ y/ZA(l+ 0. 139. Most colliders operate at a condition Ax. Ann. Focusing of atomic beams: 30 There are now two types of polarized ion sources: the atomic-beam polarized ion source (ABS). Plot R(A) as a function of A and show > that the actual luminosity is C = R(A)C0 = {NlN2 v^V 2 erfc(A) 47re^<rs for a given as. ABS has produced polarized H~ ions with about 75% polarization at a peak current of 150 fik. 159 (1951). Naturwiss. which is a quadrupole or a sextupole. show that (see Section 7.G.2836. In a short bunch approximation with Ax ^> 1 and Az 3> 1.. Paul.Az) ^]- 2 ^J f A l + {C2/Ai)){1 ^ + {C2/Ai]) where AXtZ = /?* z/crs is a measure of the betatron amplitude variation at the interaction point. The luminosity reduction due to finite bunch-length is called the hour-glass effect. 32H. [26]) C = R(AZ)CO = ™ 4^Vpxex€zpz V7r * VlA0(f). 373 (1967). i.AZ) ss 1. Nucl. 31The 30See . Ax > 1. where ej_ = ex = ez. show that the reduction factor becomes R=2Azre^£=A^e4A1 where KQ is the modified Bessel function.z « 1. in Ref. Asymptotically. we have R{A) —• 1 for A —)• oo. Sri.1. and the optically pumped polarized ion source (OPPIS) producing mainly hydrogen and deuterium ions. [25]) D/^ i-A A' C .. Similarly. Priedburg. Does the luminosity decrease at A < 1? (d) For a flat beam with [5% > as. Rev.e.31 The principle of the ABS is to form atomic beams in a discharge tube called a dissociator. H.07703A2) erfc(A) » ( 1 + 0. As the beam travels through the beam tube. TRANSVERSE MOTION (b) Because of finite bunch-length as. and W. Z. Calculate the reduction factor as a function of Az and show that the luminosity is (use 3. This exercise illustrates e.364.32 The non-uniform magnetic field preferentially selects one spin state (Stern-Gerlach effect).5. the spin states of the atoms are selected in a separation magnet.g.4 + 0. we obtain R(AX.3 of Ref.3. Phys. 489 (1954). Plot £ as a function of A. OPPIS has been able to produce a polarized H~ ion source up to 400 /iA with 80% polarization at a normalized emittance near 1 7r mm-mrad.
F. and the polarized ions are drawn by the electric field to form a polarized ion beam. (a) Show that the sextupole field focuses the spin state of the atomic beam with lower magnetic dipole energy. it defocuses the spin state with higher magnetic dipole energy. Let ft = gfj. What is the focal length? 33 B.EXERCISE 2. A paraxial focusing system (lithium lens): A strong paraxial focusing system can greatly increase the yield of the secondary beams. the polarized ions are formed by the bombardment of electron beams. where g is the Lande ^-factor. The selected atoms. ro = 10 mm. which have a preferential one-spin state. ro is the radius of the Li conductor. w no = 4TT X 10~7 Tm/A is the permeability. (c) If the temperature of the dissociator is 60 K. The Li lens was first used at Novosibirsk for focusing the e + e" beams. et al.a « \iB for the hydrogen-like atom. The electron spin is quantized with respect to the magnetic field.e.788 x 10~ 5 eV/T is the Bohr magneton. The magnetic flux density is where / is the current.B J be the magnetic moment of the atomic beam. i. and /j.33 A cylindrical lithium rod carrying a uniform current pulse can create a large magnetic field. where in the high-field regime the nuclear spin can be flipped by rf field. the lithium lens or a strong solenoid has been used. /j. The atoms not contained in the beam pipe will be pumped away. 19. Here the the magnetic field is slowly changed to align all atomic polarization into the uniform field ionizer region. and JJ. Bayanov.B = 5. Thus the force acting on the hydrogen atom is F = V(jl-B) = ±^aV\B\ for two quantized spin 1/2 states of the hydrogen atom. It is worth pointing out that there is no preferred direction of the spin projection inside the sextupole. (a) Find the focusing function for the 8-GeV kinetic energy antiprotons if / = 500 kA. Methods. in other words. r is the distance from the center of the rod. will pass through the transition region. the electron spin is quantized along the B direction. Nucl. Inst. and / is the angular momentum of the atom. 190.2 83 the focusing effect due to a sextupole field. and the length is 15 cm. what is the velocity spread of the atomic beam? Discuss the effect of velocity spread of the atomic beam. (b) When a quadrupole is used to replace the sextupole magnet. The magnetic energy of the atomic beam in the magnetic field B is W = -p-B. It became the essential tool for anti-proton collection at Fermilab. To this end. show that the effective force on the atom is a dipole field. 9 (1981). .
OOdegDIP)" ! CIS =1/5 of Cooler circumference =86.E2=EANG.3 x A1!3 fm.364m/4 Ll:= 2. The atomic weight is 6.TAPE STOP . f o r edge a n g l e ANG := TWOPI/4 00 : DRIFT.L=L1."CIS BOOSTER (1/5 Cooler).DELTAP=0.0. Low energy synchrotrons often rely on the bending radius Kx = 1/p2 for horizontal focusing and edge angles in dipoles for vertical focusing.SUP. choose the length of the Li lens to be less than 10% of the nuclear reaction length.341 ! c e l l length 17. e e LCELL:=4. SUP: LINE=(BD. What is the effects of changing the edge angle and dipole length? Discuss the stability limit of the lattice.82m / 5 =17. E1=EANG.*TW0PI/360 ! u s e r a d .84 CHAPTER 2.00) ! a superperiod USE.013 x 105 N/m).941 g. CTPIA = vr(rp + R\).27324 EANG:=12. ANGLE=ANG.#S/E TWISS. JRA = 1. and A is the atomic mass number. Find the lattice property of the low energy synchrotron described by the following input data file (MAD). where rp = 0. TRANSVERSE MOTION (b) The total nuclear reaction cross-section between the antiprotons and the Li nucleus is given by the geometric cross-section. TITLE. show that the nuclear reaction length is about 1 m. 20. (c) Find the magnetic pressure P = B2/2fio that acts to compress the Li cylinder in units of atmospheric pressure (1 atm = 1. and the density is 0.SUPER=4 PRINT.8 fm.0 ! dipole length L2:=LCELL-L1 ! s t r a i g h t section length RH0:=1. To minimize the beam loss.5 g/cm 3 .L=L2 BD : SBEND.364m ! I t accelerates protons from 7 M V to 200 M V in 1-5 Hz. i.e. K2=0.
and feed-down from higher-order multipoles. Let v _ ( W A > v _ (Vo\ y+~{y'o) y-~\y'o-o)' be the phase-space coordinates of the closed orbit just before and just after the kick element located at s0. can be represented by oo ABZ +jABx = Bo £ > „ +jan) (x+jz)n. III. The effect of linear betatron coupling due to the skew quadrupole term. This section addresses the linear betatron perturbations resulting from the dipole and quadrupole field errors. dipole field errors may arise from errors in dipole length or power supply. where ABdt is the integrated dipole field error and Bp = po/e is the momentum rigidity of the beam. etc. VI. A.^ .. (2.154) where the perturbing fields ABZ and ABX. The perturbed closed orbit and Green's function First. (2. dipole roll giving rise to a horizontal dipole field. EFFECT OF LINEAR MAGNET IMPERFECTIONS 85 III Effect of Linear Magnet Imperfections In the presence of magnetic field errors.25). Bo is the main dipole field.)• <2155) . z" + Kz(s)z = . we will show that linear magnet imperfections have two major effects: (1) closed-orbit distortion due to dipole field error.The closed-orbit condition becomes M (5)-(«-. ai. and illustrates possible beam manipulation by using the perturbing fields.l Closed-Orbit Distortion due to Dipole Field Errors Up to now. and (2) betatron amplitude function distortion due to quadrupole field error. Based on our study of the betatron motion in Sec. we have assumed perfect dipole magnets with an ideal reference closed orbit that passes through the center of all quadrupoles. Hill's equations are x" + Kx(s)x = ^ . hi is the sextupole field error. we consider a single thin dipole field error at a location s = So with a kick-angle 8 = ABdt/Bp in an otherwise ideal accelerator. b0 and bx are respectively the dipole and quadrupole field errors. The a's are skew magnetic field errors. II. similar to Eq. and the solenoid will be discussed in Sec. In reality. n=0 Here j is an imaginary number.III. a closed orbit not centered in the quadrupoles.
82. the .^(s o )|) 2 sin TTU (2. the values of the betatron amplitude Figure 2. the closed orbit is dominated by the fifth error harmonic. (2.s0)9(s0).11 shows the closed-orbit perturbation in the AGS booster due to a dipole field error of 6. Po functions at kick dipole location s 0 . Since the betatron tune of the AGS booster is 4.158) (2. The right plot shows the same closed orbit as a function of the longitudinal distance.11: The left plot shows schematically the closed-orbit error of the AGS booster resulting from a horizontal kicker with kick-angle 9 = 6.\iP(s) . where G(s. The orbit response arising from a dipole field error is given by the product of the Green function and the kick angle. Since the betatron tune of 4.e. TRANSVERSE MOTION where M is the one-turn transfer matrix of Eq.82 is close to the integer 5.a ° c o s ™ ) ' are ( 2 . (sin7ri/ .COS7ny' y'°= 2iirT^. s0) = V S ) / ? ( S o ) cos( W .156 ) where v is the betatron tune and ao.86 CHAPTER 2.67). we obtain yco(s)=G(s. The closed orbit at other location s in the accelerator can be obtained from the propagation of betatron oscillations.159) is the Green function of Hill's equation. (2. The right plot of Fig. The resulting closed orbit at SQ is on a yo = 2^.82 mr.53) for an ideal accelerator. 2. The left plot is a schematic drawing of the resulting closed orbit around an ideal orbit. Using Eq. i.82 mr at the location marked by a straight vertical line.
12: Left. a schematic plot of the closed-orbit perturbation due to an error dipole kick when the betatron tune is an integer. B. if the betatron tune is a half-integer.III. y') in the presence of a dipole error when the betatron tune is an integer. 2. Here Ay' = 8.12). Since Hill's equation with dipole field errors. 2. the closed orbit can be obtained by a linear superposition of dipole kicks. A9(t) = (AB(t)/Bp)dt. AB(t) .159) shows that the closed orbit becomes infinite when the condition SHITTY = 0 is encountered. showing 5 complete oscillations in Fig. dipole field errors are distributed around the accelerator. JP(s) rs+c . the angular kicks of two consecutive revolutions cancel each other (see right plot of Fig. Right. The orbit kicks in every turn due to a dipole error coherently add up. The left plot of Fig. Figure 2. 2. However. Distributed dipole field error In reality. is in the same direction in each revolution. i. Since the angular kick Ay' = 9. where 6 is the dipole kick angle. the closed orbit becomes very sensitive to dipole field error.e. Thus the betatron tunes should also avoid half integers. Equation (2. the closed orbit does not exist. In other words. a schematic plot of the particle trajectory resulting from a dipole kick when the betatron tune is a halfinteger. making the closed orbit unstable. For the closed orbit. This is why the betatron tunes are designed to avoid an integer value.11. if the betatron tune is near an integer. is linear. we will show later that the quadrupole field error will produce betatron amplitude instability at a half integer tune. On the other hand. it is better to choose a betatron tune closer to a half-integer. here the angular kicks from two consecutive orbital revolutions cancel each other. EFFECT OF LINEAR MAGNET IMPERFECTIONS 87 closed-orbit perturbation is dominated by the n = 5 harmonic.12 shows schematically the evolution of a phase-space trajectory (y. where 9 is the kick angle of the error dipole.
"P k=-oo (2.165) which has simple poles at all integer harmonics.159).160) shows that the closed orbit may not exist at all if the betatron tune is an integer. Bp (2. and ip(s) = v<j>{s). The resulting closed orbit is usually dominated by a few harmonics near [u]. Js t) ^ | ^ d t . The orbit response of the inhomogeneous Hill equation is yco(s) = fS+CG(s.160) is the closed-orbit solution of the inhomogeneous Hill equation where A S = ABZ for horizontal motion and AB — —ABX for vertical motion. (2. the closed-orbit displacement yco(s) becomes Vcois) = y/W) £ -P^e**.160) is a periodic function of 2n. The integer stopband integrals Since square bracketed term in the integrand of Eq. (2. The simple pole structure in Eq.88 CHAPTER 2. we expand it in a Fourier series: f(<l>)=f?l\4>)^®= £ fke^. (2. (2. C. TRANSVERSE MOTION where <j>(s) = (l/i/) /05 dt//3(t). In Fourier harmonics.163) where the Fourier amplitude /& is the integer stopband integral given by with /_* = f%. It is easy to verify that Eq. which is an integer nearest to the betatron tune. (2. In a single stopband approximation. The presence of sin -KV in the denominator of Eq.162) where the Green function is given by Eq. the closed orbit can be approximated by y/ffOQH/Ml COs([t/]0 + x) 2 [y .165) indicates that the closed orbit is most sensitive to the error harmonics closest to the betatron tune. (2.[„]) Vco{S) " .
Closed-orbit correction Closed-orbit correction is an important task in accelerator commissioning. the effective angular kick is e = l£Ay = T> (2167) where B\ = dBz/dx is the quadrupole gradient. N. is not known a priori. E. EFFECT OF LINEAR MAGNET IMPERFECTIONS D. For example. the perturbing field error AB/Bp. and the rms angular kick angle. (2. and / is the focal length. Now we consider the dipole field error generated by quadrupole misalignment. . a statistical argument is usually used to estimate the rms closed orbit. the harmonic correction scheme. The remaining closed orbit can generally be corrected by the stopband correction scheme. Substituting Eq. If the closed orbit is large.1 mm will result in a rms closed-orbit distortion of 2 mm. The coefficient in curly brackets is called a sensitivity factor for quadrupole misalignment.169 ) where 0t is the angular kick of the zth corrector. and 0ims are respectively the average ^-function.III.166) where /?av. or the x2-minimization method. any major known source of dipole error should be corrected. we obtain Wms « ( 9 ^ / " TV^Q} A2/"ns. the stopband near k = [v] is / = 2^E^e-'W<. Statistical estimation of closed-orbit errors 89 In practice. (2. The sensitivity factor increases with the size of an accelerator.rms * ^-J^ 2v2| SHITTY VNOm*.166). ?/co.167) into Eq. due mainly to random construction errors in the dipole magnets and misalignment errors in the quadrupoles. M ( 2 . one can adjust the real and imaginary parts independently. (2. the number of dipoles with field errors. (2.168) |k2v/2/av|sin7rz/| v J where Nq is the number of quadrupoles and / a v is the average focal length. When quadrupole magnets are misaligned by a distance Ay. First. With a few dipole correctors. Placing these correctors at high-/? locations with a phase advance between correctors of [v\<t>i « n/2. the beam lifetime and dynamical aperture can be severely reduced. if the sensitivity factor is 20. an rms quadrupole misalignment of 0. During the design stage of an accelerator.
manipulation with an internal target. of Nc correctors. (2.. and higher order terms associated with betatron motion are neglected. Possible schemes of local orbit bumps are the "four-bump method" discussed in Sec. VPi (i = 1 . . The BPM resolution for proton storage rings is about 10 to 100 /im.170) where Co is the orbit length of the unperturbed orbit. Effects of dipole field error on orbit length The path length of a circulating particle is C = j y/(l + x/pf + x'2 + z'2 ds « Co + j . N C ) . F.. 34The BPM resolution depends on the stability of the machine and on the number of bits and the effective width of the pickup electrode (PUE). Let yi<co and A* be the closed-orbit deviation and BPM resolution of the ith BPM. Since a dipole field error gives rise to a closed-orbit distortion. .d s + ---. extraction.3.34 The aim is to minimize x ~k N-> hi. the resolution is reduced by a factor of 16.62.I 2 A? by varying 61.. = — w ( a k c o s kcj>i + bk s i n kfa). In many beam manipulation applications such as injection.For example... For example. etc. Because the closed orbit is not sensitive to errors in harmonics far from the betatron tune. III. the fcth stopband can be corrected by adjusting the ak and bk coefficients. these harmonics can hardly be changed by closed-orbit correction schemes. Let Nm be the number of BPMs and Nc the number of correctors. where ft and <f>i are the betatron amplitude function and the betatron phase at the ith kicker location. the circumference of the closed orbit may be changed as well. if Nc dipole correctors are powered with 9..3 and the "three-bump method" (see Exercise 2. the BPM resolution for the data acquisition system with a 12-bit ADC and a 40-mm effective width PUE is about 10 fim.90 CHAPTER 2. If an 8-bit ADC is used. TRANSVERSE MOTION The harmonic closed-orbit correction method uses distributed dipole correctors powered with a few harmonics nearest the betatron tune to minimize a set of stopband integrals fk.4). These orbit correction schemes minimize only the errors in harmonics nearest the betatron tune. Another orbit correction method is the ^-minimization procedure. A few harmonics can be superimposed to eliminate all dangerous stopbands.. local closed-orbit bumps are often used.
etc. tidal action. EFFECT OF LINEAR MAGNET IMPERFECTIONS 91 We consider the closed-orbit change due to a single dipole kick at s = s0 with kick angle 90. Thus the change in orbit length due to a dipole field error is equal to the dispersion function times the orbital kick angle. traffic and mechanical vibration. However.III. J p (2.174) 36The FFT spectra of a transverse phase-space coordinate display rotational harmonics at integer multiples of the revolution frequency and the betatron lines next to the rotation harmonics. This method can be used to measure the betatron tune. The modulation frequency from ground vibration is typically less than 10 Hz. particle motion in an accelerator will not be affected by a small-amplitude modulation provided that the modulation frequencies do not induce betatron or synchrotron resonances. III.|V. an rf dipole field operating at a betatron sideband35 can kick the beam out of the vacuum chamber. . the power supply ripple can produce modulation frequency at some harmonics of 50 or 60 Hz. the change in the total path length becomes AC = <£ D(s)^%^-ds.(a) . the dipole field errors are generated by power supply ripple. These betatron frequency lines are called the betatron sidebands.7 for details. Bp (2. Using Eq. this is called rf knock-out. For example.162). the equation of motion for a dipole field error in a constant-focusing quadrupole is x" + Kx = ^ .. and thus the circumference is modulated at some modulation frequencies. particle motion will be strongly perturbed. .171) where D(8o) = J f^lfAds P = 2 sin TT^J.^(so)|)<fa (2. IV). When dipole field errors are distributed in a ring. we find the change in circumference as AC = C-C0 = 80 <f G*(s>s°) ds = D(s0) 0o. if the modulation frequency is equal to the betatron or synchrotron frequency. (2. Normally. For example. See Sec. III.173) Bp J In many cases. J yliS0) / ^ p ^ cos (Try.154) for the closed orbit of the betatron oscillation can be solved by the extended 3x3 transfer matrix method. ground vibration. and the frequency generated by mechanical vibrations is usually of the order of kHz.2 Extended Matrix Method for the Closed Orbit The inhomogeneous differential equation (2.172) is the value of the dispersion function at s0 (see Sec. (2.
(2. . Proc.1 / / 1 Ayjf \ .155) is equivalent to /j/b\ \y'o = (I 0 0 \ /Afn 0 1 9\\M21 Mi2 0 \ (yo\ M22 0 ] \ y ' o \.178) \ i/ Vo o i ) \ o o i)\ \ ) where the M's are matrix elements of the 2x2 one-turn transfer matrix for an ideal machine. TRANSVERSE MOTION The betatron phase-space coordinates before and after the focusing quadrupole can be obtained from the extended transfer matrix by /x\ \x'\ W2 / cosVKe jg sin VKI %ff?(l-cosVKe)\ =\-y/K sin y/Kl cosVKt £%sany/Ke V 0 0 ^ 1 AW: /x\ U ' > (2175) where I = s2 — s\. (2. Examples are the local-orbit bump. 36S. Let Aj/q be the quadrupole misalignment. The resulting extended transfer matrix in the thin-lens approximation is Mquad = / 1 0 0 . In thin lens approximation. etc.175) becomes M(s 2 | S l ) = /I 0 0\ -1// 1 d .J. Similarly. For example. (2.. 1991). rf knock-out. the closed-orbit equation (2.176) V o oiy where 6 = ABZ£/Bp and / = 1/JW are respectively the dipole kick angle and the focal length of the perturbing element.177) V 0 0 1 ) The 3x3 extended transfer matrix can be used to obtain the closed orbit of betatron motion.36 III.3 Application of Dipole Field Error Sometime. Lee. one-turn kicker for fast extraction. and 9 is the dipole kick angle. Piscataway. the 3x3 extended transfer matrix can be used to analyze the sensitivity of the closed orbit to quadrupole misalignment by multiplying the extended matrices along the transport line. (2.92 CHAPTER 2. Eq.. IEEE PAC Con}. 1639. S.Y. (IEEE. N. we create imperfections in an otherwise perfect accelerator for beam manipulation. The dipole field error can also arise from quadrupole misalignments. Tepikian. p.
the two-bump method has been used at favorable phase-advance locations in accelerators. or i/9i#i cosliru-ipn] + \fW162 c o s ^ i / . EFFECT OF LINEAR MAGNET IMPERFECTIONS A. For example. Using four bumps. we obtain Vco(s) = ^ f ^ .4). and to avoid the limiting-aperture in the accelerator. we obtain / \ / M s = -{\[K. Figure 2. Orbit bumps 93 To facilitate injection. to Sj.^ ] + \fW%®% coslnv—ipte] + \fW$n COSTTJ/ — 0. V^^isinfTr^-^i] + i / S ^ s i n ^ .4) has also been used for local orbit bumps.III.^ ] + v^^sinTrv = 0.0\ sinipn + \JJ182 sin^42)/ sin^43. the middle bump dipole has negligible field strength.179) where 9t = (ABAs)i/Bp and (ABAs). The three-bump method (see Exercise 2. Expressing 63 and 64 in terms of 6\ and 62. B.3. avoiding unwanted collisions in colliders.E JK 0i cosfri/ .^ | ) . Although the slope of the bumped particle orbit can not be controlled in the three-bump method. y'co(si) = 0. we discuss the four-bump method facilitated by four thin dipoles with kick angles Q{ (i = 1. are the kick-angle and the integrated dipole field strength of the i-th kicker. Occasionally. or special-purpose beam manipulation.37 the orbit of the beam can be bumped to a desired transverse position at specified locations.. where xpji = ipj—ifii is the phase advance from s. extraction.i / ^ ] + V ^ ^ s i n ^ .2. etc. (2. The conditions that the closed orbit is zero outside these four dipoles are VCO{SA) = 0. . Using Eq.\i> .160). this method is usually used for the local orbit correction because of its simplicity. internal target area. In this example. a fast kicker magnet is usually powered in about 20-100 ns rise and fall times in order to bump beam bunches into the ex37Other examples are orbit bump at the aperture restricted area.3. Fast kick for beam extraction To extract a beam bunch from the accelerator. to avoid unwanted collisions. the counter-circulating e+ and e~ beams. I I I I \ (0 1 s n ^ *-**J) [ sjPtfi = {yjPxOiSYMpn + y'&^sin^M/sinvW The orbit displacement inside the region of the orbit bump can be obtained by applying the transfer matrix to the initial coordinates. we can adjust the orbit displacement and the orbit angle to facilitate ease of injection and extraction. Since the two outer bumps happen to be nearly 180° apart in the betatron phase advance.13 shows an example of a local orbit bump using three dipoles. or the p and p beams in a collider can be made to avoid crossing each other in a common vacuum chamber with electrostatic separators. 2 sin 7 v ~[ T v (2.
flx(s) is the amplitude function at location s. B^ is the kicker dipole field. a kicker kicks the beam from the bumped orbit to the the extraction channel at x\.14 shows a schematic drawing of the cross-section of a Lambertson septum magnet. The magnetic kicker employs ferrite material to minimize eddy-current effects. The rise and fall times of the kickers range from 10 ns to 100's ns. where a septum is located. etc.38 With the transfer matrix of Eq. current sheet septum.181) where 6y = f B^ds/Bp is the kicker strength (angle). To achieve a minimum kicker angle. where the former will not affect the circulating beams. Depending on the application. In this example. where the uniform dipole field bends the beam into the extraction channel. the septum is located about 90° phase advance from the kicker. such as wire septum. . 38The kicker is an electric or magnetic device that provides an angular deflection to the charged particle beam in fast rise and fall times so that it can selectively deflect beam bunches. The septum is a device with an aperture divided into afield-freeregion and a uniformfield region.13: A simple orbit bump in the AGS booster lattice.67). (2. The iron in the Lambertson magnet is shaped to minimize the field leakage into the field-free region and the septum thickness. Figure 2. that is of the order of 4-10 mm depending on the required magnetic field strength. (2. The quantity in curly brackets in Eq. the kicker array for stochastic cooling. Since the first and third kickers are nearly 180° apart in the betatron phase advance. the local orbit bump is essentially accomplished with these outer two kickers. Similar constraints apply to the kicker in the transverse feedback system. there are 3 focusing and 2 defocussing quadrupoles between two outer bump dipoles. A beam is bumped from the center orbit xc to a bumped orbit x^. The symbol X marks the three dipole kicker locations. and the latter can direct the beam into an extraction or injection channels.94 CHAPTER 2. The electric kicker applies the traveling wave to a stripline type waveguide. TRANSVERSE MOTION Figure 2. At the time of fast extraction. and A<f>x(s) is the phase advance from s^ of the kicker to location s. Px{sy) is the betatron amplitude function evaluated at the kicker location. Lambertson septum.181) is called the kicker lever arm. and the values of the betatron amplitude function at the septum and kicker locations are also optimized to obtain the largest kicker lever arm. the transverse displacement of the beam is AzCo(s) = ypx{sk)/3x(s)sm(A<t>x(s))}ek. (2. etc. one can choose among different types of septum. traction channel.
/30 is the value of the betatron amplitude function at the rf dipole location. and x^.o o .8. C is the circumference.14: A schematic drawing of the central orbit xc. if the betatron tune is 8. and Wo is the orbital angular frequency.182) with y VPo Hill's equation becomes 1 r» ds v Jo P where vm = w m /w 0 is the modulation tune. Hill's equation is cPv °° -r^ + K{s)y = 6asinumt £ 6(s-nC). The arrows indicated a possible magnetic field direction for directing the kicked beams downward or upward. rf knock-out In the presence of a localized rf dipole. and the particular solution rjco is the coherent time dependent closed orbit. "S n=-oo (2. oo). bumped orbit x\>. large betatron . Xf. The solution of the inhomogeneous Hill's equation is r] = Acosi>(j) + Bsinis(j) + r}co.182) where 9a = AB£/Bp and uim are respectively the kick angle and the angular frequency of the rf dipole. and t = s//3c is the time coordinate. The periodic delta function reflects the fact that the beam particles encounter the kicker field only once per revolution.. The blocks marked with X are conductor-coils. and kicked orbit x^ in a Lambertson septum magnet. C. (2. Performing the Floquet transformation to Eq. ^ = J L 2*R[v>-\n'+Vm)*) °° v2B3^9 Sln(n + ^" (2"185) Note that the discrete nature of the localized kicker generates error harmonics n + vm for all n € ( . For example. (2. The ellipses marked beam ellipses with closed orbits xc.III.184) where A and B are the amplitude of betatron motion determined by the initial conditions. EFFECT OF LINEAR MAGNET IMPERFECTIONS 95 Figure 2. Effects of rf dipole field.
v(n + i/m) sin v<j>\ where the last approximate identity is obtained by expanding the term in the sum with n + vm sa u. shown in the upper trace.41 39It is worth pointing out that the coherent growth time of the betatron oscillation is inversely proportional to \vm . Now we examine the coherent betatron motion of the beam in the presence of an rf dipole at i/m « v (modulo 1) with initial condition y — y' = 0.D." The fractional betatron tune. ^2 r Sln(n + ^rn)0 . Rev.40 The rf dipole can be adiabatically turned on to induce coherent betatron oscillations for betatron tune measurement without causing serious emittance dilution. The rf dipole was on from 1024 to 1536 revolutions starting from the triggering time. 4051 (1994).186) indicates that the beam is driven coherently by the rf dipole. Lett. To measure this small effect in the environment of the existing power supply ripple.. The solution is y(S> = —9^R— Z7r-K n=-oo " ~ \n + ^W ^ 1A—(„. is equal to the knockout tune. Ph. is measured by averaging the phase advance from the Poincare map (see Sec. the two-kick method was used to measure the instantaneous betatron tune change at the moment of the second kick. Beyond the coherent time. 4673 (1998).1.8. .15 shows the measured betatron coordinate (lower curve) at a beam position monitor (BPM) after applying rf knock-out kicks to the beam in the IUCF Cooler Ring. This two-kick method can be used to provide a more accurate measurement of the dependence of the betatron tune on the betatron amplitude. This process is related to the Landau damping to be discussed in Sec.. the beam would have been driven out of the vacuum chamber. Ellison et a/. where data from two BPMs are used. At revolution number 2048. III. £ 5 0 .1. Rev. Phys. Equation (2. 41M. Thus the method is called the "rf knock out. the beam was imparted a transverse kick. Phys. that. Note the linear growth of the betatron amplitude during the rf dipole-on time. Rev. and the amplitude of betatron motion grows linearly with time.0. Phys..4. See M. VIII. E56. the beam motion is out of phase with the external force and leads to damping.39 Figure 2. Bai et al.96 CHAPTER 2.2. 40The power supply ripple at the IUCF cooler ring gives rise to a betatron tune modulation of the order of 2 x 10~3 at 60 Hz and its harmonics.u\ (mod 1). and retaining only the dominant term. and the fractional part of the betatron tune (upper curve). 80. TRANSVERSE MOTION oscillations can be generated by an rf dipole at any of the following modulation tunes: vm — 0. 6002 (1997).8. in this experiment.2.— The localized repetitive kicks generate sidebands around the revolution lines. Had the rf dipole stayed on longer. On the other hand. the dependence of the betatron tune on the betatron action is typically 10~4 per lir mm-mrad. Thesis. Indiana University (1999).5).
This method is usually referred to as the beam transfer function (BTF). Figure 2. the beam profile restored back to its original shape. VIII). the beam was imparted by a one-turn kicker. After another 512 revolutions. The rf dipole was turned on for 512 revolutions. Furthermore. . the beam profile became larger because the beam was executing coherent betatron oscillations. EFFECT OF LINEAR MAGNET IMPERFECTIONS 97 Figure 2. the measurement of the coherent betatron tune shift as a function of the beam current can be used to measure the real and imaginary parts of the transverse impedance (see Sec. the beam profile restored to its original shape.15: The lower curve shows the measured vertical betatron oscillations of the beam of one BPM at the IUCF cooler ring resulting from an rf dipole kicker at the betatron frequency. Note the linear growth of the betatron amplitude during the rf knockouton time. After the rf dipole was adiabatically turned off. where data from two BPMs are used.III. The beam profile appeared to be much larger during the time that the rf dipole was on because the profile was an integration of many coherent synchrotron oscillations. As the rf dipole is adiabatically turned off. Figure 2. and the profile was obtained from the integration of many coherent betatron oscillations. The upper curve shows the fractional part of the betatron tune obtained by counting the phase advance in the phase-space map.16: The beam profile measured from an ionization profile monitor (IPM) at the AGS during the adiabatic turn-on/off of an rf dipole. When the rf dipole was on.16 shows the vertical beam profile measured at the AGS during the adiabatic turn-on/off of an rf dipole. The induced coherent betatron motion can be used to overcome the intrinsic spin resonances during polarized beam acceleration.
Con}. i = 1. The ORM method minimizes the difference between the measured and model matrices Rexp a n d Rmodei. 128 (1994). • • •.. sextupole field strength.98 CHAPTER 2. is the rms error of ith measurements.. iVm) vs the dipole kick at Oj (j = 1. etc. where iVj. Proc.. sextupole misalignment. Nb). 1994 European Part. TRANSVERSE MOTION D. The measured response matrix needs calibration in the kicker angle and BPM gain. and the machine stability during the experimental measurement..42 We consider a set of small dipole perturbation given by Oj.Nh i = l. quadrupole roll. Accel. If the closed-orbit response to a small dipole field perturbation can be accurately measured. Nm.. Con}. i. j = l. AIP Conf. The outcome of response matrix modeling depends on the BPM resolution. Sj) of the actual machine.162) shows that the beam closed orbit in a synchrotron is equal to the propagation of the dipole field error through the Green's function that is an intrinsic property of the betatron motion. KeXP«- fj9i ' 42 See J. etc. Proc.. Here the number of index k is Nh x Nm.Nm. Proc. Experimentally. Safranek.. Lee.. Orbit Correction and Analysis in Circular Accelerators. where <7. The response matrix R. N^. we measure Ry (i = 1. . It is worth mentioning that iVb is not necessarily equal to Nm. defined as yi = R t j 9 j .. is the number of dipole kickers. the calibration of the BPM gain factor. 315. where JVm is the number of beam position monitors. The resulting response functions can be used to calibrate quadrupole strengths.. and the model response matrix can be calculated from MAD[19]. The full set of the measured response matrix R can be employed to model the dipole and quadrupole field errors. • • •. j = 1. The ORM method has been successfully used to model many electron storage rings..J. where y stands for either x or z.. Accel. J. quadrupole misalignments. 1027 (1997). The measured closed orbit from the dipole perturbation is yi. No. BPM gains. Safranek and M.. J. SYNCH[20]. Orbit response matrix for accelerator modeling Equation (2. 1995 IEEE Part.Let Wk = I R ™»M«..e.J. Safranek and M.187) is equal to Green's function Ry = Gy(si. Proc. Lee. dipole field integral. (2.B «P«I / 2 _ 18g ) be the difference between the closed-orbit data measured and those derived from a model. The orbit response matrix (ORM) method measures the closedorbit response induced by a known dipole field perturbation. the Green's function of Hill's equation can be modeled.. 2817 (1995). or C0MF0RT[21] programs.. the number of BPMs and kickers..
The singular value decomposition (SVD) algorithm decomposes the matrix W into w = ovVk dw m = U A v T (2192) where V T is a real orthonormal Np x Np matrix with V V T = V T V = 1. and A i s a m x n diagonal matrix. and gt is the gain factor of the ith BPM.190).e. the quadrupole strength and roll. and V is composed of orthonormal eigenvectors of * WTW. the BPM gain factor. A is a diagonal Np x Np matrix with elements An = \f\l > A22 = y/X^--. i. (2.(VA. Once the SVD of matrix W is obtained. and U = AVA" 1 is a {Nm • Nb) x Np matrix with U T U = I. 43The SVD decomposition ofamxn matrix W in Eq. Np is the number of parameters.1 = l/\fK and 0 for all remaining diagonal elements with i > r. The ORM accelerator modeling is to minimize the error of the vector W by minimizing the %-square (x2) defined as ^=5vnr£w2.e. etc. A2. The iterative procedure continues until I Aw m | or the change of x 2 are small. WTW = VA 2 V T . Some of these parameters are kicker angle calibration factor. In our application to accelerator physics. (2.1 ^) W(wn). Wk(wm + Awm) « Wk(wm) + ^ A w m = 0.> 0. The ORM modeling is to find a new set of ium-parameters such that ||W(«»m)|| = 0. = 0 (i > r) is equivalent setting Aw* = 0 for i > r.191) To evaluate Awm. EFFECT OF LINEAR MAGNET IMPERFECTIONS 99 where / . sextupole strength. This means that these dynamical parameters have no relevance to the measured data.190) First. . A^. (2-189) We consider sets of parameters w m 's that are relevant to accelerator model and orbit measurement. (2. Here.193) where A " 1 is a diagonal matrix with AJ"/ = l/\f\[.III. The SVD-method sets all eigenvalues A < Ac. = 0.192) can also be carried out in such a way that U and V are respectively orthonormal real mxm and nxn matrices with U T U = UU T = 1 and V T V = W T = 1. we invert matrix W = ^ t . (i > r). one finds Awm as Awm = . (2. The idea is to find a new set of parameters wm + Awm that satisfies Eq. (2. (i > r) to A. i. the dipole angle and dipole roll. • • • are eigenvalues of the matrix WTVV. which has the dimension of is (Nb • Nm) x Np. is the calibration factor of the j t h kicker. where Ac is called the tolerance level and r is called the rank of the matrix W. Setting all A. {Nb • Nm) » Np. we begin with parameters wm and evaluate W(iu m ). 43 Here Ai. • • •.
the dimension of the matrix W. (eq23green) at a calibrated vertical steerer angle. For example.17: Left. (2) BPM gain <?. the proton storage ring (PSR) at Los Alamos National Laboratory accumulates protons for 3000 turns and the beam bunch is extracted after accumulation for high-intensity short-pulse neutron production.. 2.g. (4) dipole angle calibration. digitized betatron oscillation data of one BPM are used to derive betatron amplitude. . 1481 (1997). Right. TRANSVERSE MOTION The response matrix modeling has been successfully implemented in many electron storage rings.17). "First Test of Orbit Response Matrix in Proton Storage Ring".. top plot shows the closed orbit data compared with Green's function of Eq. For high-power synchrotrons. Technote: PSR03-001 (2003).44 In accelerator modeling.. beam particles are injected. The bottom right plot shows a similar comparison after ORM modeling.100 CHAPTER 2. et al.45 The right plots of Fig. The betatron oscillations of each BPM can be used to obtain the betatron amplitude. 4 5 X. phase and tune. Huang et al. e. These steps are sometimes essential in attaining a reliable set of model parameters. (1) kicker angle calibration fj. p. etc. dipole and quadrupole power supplies. The closed orbit data can be obtained by averaging betatron oscillations in a single turn injection. Chu.17 shows an example of typical fit in ORM modeling. phase and tune. accelerated and extracted in a short time duration. BPM gain.M. Proceedings of PAC 1997. and closed orbit offset. and the closed orbit (see the left plot of Fig. (5) dipole roll. sextupole misalignment. It is advantageous to model accelerator parameters in sequences. These information can be used in the ORM analysis for accelerator modeling. quadrupole strength and roll. 44 C. where the BPM resolution is about l~10 /zm. where the BPM resolution is usually of the order of 100 fim. etc. can be large. 2. The inversion of a very large matrix may become time consuming. The method has been used to calibrate kicker angle. (3) quadrupole strength AKi. Analysis of the Orbit Response Matrix Measurement for PSR. The method is also applicable to proton synchrotrons. (Nm • Nb) x Np. Figure 2.
Rev. Rev. 1684 (1999).25). Vadim Sajaev. Why don't we choose a half-integer betatron tune? This section addresses the effect of quadrupole field errors that can arise from variation in the lengths of quadrupoles. Thesis. 82. III. from the horizontal closed-orbit deviation in sextupoles. II. C. What happens to the betatron motion if some quadrupole strengths deviate from their ideal design values? We found in Sec.4 Quadrupole Field (Gradient) Errors The betatron amplitude function discussed in Sec. Stanford University (1999).194) where K0(s) is the focusing function of the ideal machine discussed in Sec.3C. Betatron tune shift Including the gradient error. Ph. one uses an rf dipole pinger to excite coherent betatron oscillation and measures the response function with turn-by-turn BPM digitizing system (See Sec.X. II depends on the distribution of quadrupole strengths. PEP-II and Advanced Photon Source.X. EFFECT OF LINEAR MAGNET IMPERFECTIONS 101 The success of accelerator modeling depends critically on the orbit and tune stability. III. . Model Independent Analysis Using turn-by-turn BPM data excited by resonant pinger discussed in Sec. This method has been successfully applied to SLC linac. and Y. ABX = B2(xcoz0 + x0zg). and C. (2. Yan. E. (2. These errors correspond to the bi term in Eq.Y. Beams 6.D. where B 2 = d2Bz/dx2. C.co.X. This process is called feed-down. in Appendix B).46 For the application of MIA in a storage ring.l that the effect of dipole field error on the closed orbit would be minimized if the betatron tune was a half-integer. II. III. proper set of experimental data for attaining relevant parameters. Hill's equation for the perturbed betatron motion about a closed orbit is 1 l + [K0(s) + k(s)}y = 0. Phys.47 etc. the number of BPMs and orbit steerers.III. Wang. and a quadrupole field gradient B2a. The perturbed focusing function K(s) = K0(s)+k(s) satisfies 4 6 J. Wang. we obtain ABZ = -B 2 (xeo + 2zCoZ/3 + x% . Phys. 104001 (2003). Irwin. C. Wang.T. Lett. ST Accel. J.T. Yao. Irwin and Y.25). called Model Independent Analysis (MIA). (2. A. 151 (2000). one can also carry out response matrix analysis for accelerator modeling. Proceedings of EPAC 2000. and k(s) is a small perturbation. Yan. from errors in the quadrupole power supply. Thus an off-center horizontal orbit in a sextupole generates a dipole field ^B2xl0.z}). p. 47 Substituting x = xco + x@ and z = zp into the sextupole field of Eq.
196) The betatron tunes are particularly sensitive to gradient errors at high-/3 locations. where C is the circumference. (2. and negative for a defocussing quadrupole. Let Mo be the one-turn transfer matrix of the ideal machine. M 0 (s) = / c o s $ 0 + J s i n $ 0 . The one-turn transfer matrix at s2 is M(sj) = M{s2 +C|5i) m(«i) M(Sl\s2). and the betatron tune shift is Az^ = -^f3(si)k(sx)dsi. TRANSVERSE MOTION a weaker superperiod condition K(s + C) — K(s). A = P(si). z where A$ = $ — $ 0 . / is the 2x2 unit matrix. . The transfer matrix of this infinitesimal localized perturbing quadrupole error is The one-turn transfer matrix M(si) = Mo(si)m(si) becomes A/re \—( c o s ^ o + Qisin$ 0 -/?i^(si)rfsisin$ 0 \— ji sin$ 0 — [cos$o + aisin$ 0 ]^( s i)^ s i /?isin$ 0 \ cos $o — ai sin $ 0 / ' where ot\ = a(si).102 CHAPTER 2. and \-7(s) -a(s)J Here a(s). cos<3> — cos$o = —y8(si)fc(si)dsisin$0) z or A$ «-/3(s1)A. Thus the power supply for high-/3 quadrupoles should be properly regulated in high energy colliders. (2. where $o = 27r^o is the unperturbed betatron phase advance in one complete revolution. The phase advance of the perturbed machine can be obtained from the trace of M. and 7(s) are betatron amplitude functions of the unperturbed machine. we again consider an infinitesimal quadrupole kick at s\ of Eq.(si)rfs1. the tune shift is Au = ~ f p(Sl)k(Sl)dSl. /3(s). it is positive for a focusing quadrupole.e. v0 is the unperturbed betatron tune. For a distributed gradient error. Here the betatron tune shift depends on the product of the gradient error and the betatron amplitude function at the error quadrupole. i. i.e. We consider now the gradient perturbation with an infinitesimal length ds\ at Si.195). B. and 71 = 7(si). and high-brightness storage rings. Betatron amplitude function modulation (beta-beat) To evaluate the effect of the gradient error on the betatron amplitude function.
the gradient error function i/o/32k(s). which is a periodic function of s. (2.197) and integrating over the distributed gradient errors.& + &)].67).3.198) = -TT^f- where (j> = (l/^o) Jo ds/p.$ 0 Removing the subscript 2 in Eq./32 = /2(s2) fa = V)(si)/t'o> a n dfa= ^(^V^o are the values of the unperturbed betatron functions. wherefi2= P{S2) is the value of the perturbed betatron function and $ is the perturbed betatron phase advance. The half-integer stopband integrals In a manner similar to the closed-orbit analysis.10) C. (2.200) where JP = 7T'1>P 2TT J Hs) er^ ds (2.199) becomes WW "A f V K. (2. It is easy to verify that Ap/p satisfies (see Exercise 2.196) is equal to the zero harmonic of the stopband integral. (2. we obtain llr = -^r^ms^os^+^fa)]^ k(fa)p2(fa)cos[2v0(n + <f>-fa)}dfa. where ft = /?(si)./32 and A $ = $ .) -'2j^^-(p/2r (2-202) f 2 2 0 2) . (2. we obtain (A/?2) sin $ 0 = AM12 .fa)]. (2. Since M i 2 = J32 sin $.Ill EFFECT OF LINEAR MAGNET IMPERFECTIONS 103 Using Eq.e. We note that the tune shift of Eq. The solution of Eq.201) is the pth harmonic half-integer stopband integral. (2.^ M s i A f t c o s p i ^ T r . i.197) where A/32 = ft . Av = Jo/2. we find the change of the off-diagonal matrix element as A[M(s2)]i2 = -Msi/Sift s\n[vo(<j>i -fa)}sin[zvo(27r +fa./?2 cos $ 0 A $ = . can be expanded in a Fourier series vof32k(s)= £ p=—oo Jpe^.
199) is JW (2. Figure 2. The change of the slope y' is proportional to the displacement y. This will lead to an ever increasing betatron amplitude. This means that the betatron tune should differ from a half-integer by at least the stopband width. (2. . Thus an integer betatron tune is also a half-integer resonance. Thus the half-integer stopband gives rise to unstable betatron motion.18 shows the behavior of a quadrupole kick at a half-integer tune. (2. and p is the integer nearest 2^o.12. quadrupole kicks will resemble the left plot in Fig. 0 -p) > (2-203) where \ ls a phase angle.Since the quadrupole kick is proportional to the displacement y.195)] Ay = 0 and Ay' = -k(si)ydsl = -y/f. The right plot shows the effect of zero tune shift 7r-doublets. The "closed orbit" of the betatron amplitude function will cease to exist.104 CHAPTER 2. The left plot of Fig. 2. Therefore the betatron tune should not be a half-integer. as shown in the left plot of Fig. that produce a local perturbation to betatron motion. The right plot shows the effect of zero tune shift 7r-doublets. and beam loss may occur. this is called a half-integer resonance. and y is the displacement from the center of the closed orbit.18. The amplitude function becomes infinite when 2v0 approaches an integer. The evolution of phase-space coordinates resulting from a quadrupole kick is [using Eq. the coherent addition of the kick angle in each revolution gives rise to the unstable particle motion. which give rise only to local betatron perturbation. which changes sign in each consecutive revolution at a half-integer betatron tune. When the betatron tune is an integer. The leading term of Eq. The stopband width is defined by 5vp ~ \JP\ such that |A/3(s)//?(s)|max « 1 at v0 ss | ± \5vp. 2. TRANSVERSE MOTION This indicates that the betatron amplitude function is most sensitive to those error harmonics of P2k(s) nearest 2v0. where the quadrupole kicks are coherently additive. a quadrupole error can generate coherent additive phase-space kicks every revolution. the beam size will increase by at least a factor of \/2.18: Left. where / = l / ( M s i ) is the focal length of the error quadrupole. 2. schematic plot of a particle trajectory at a half-integer betatron tune resulting from a defocussing error quadrupole kick Ay' = —y/f. When the betatron tune is a half-integer. When the betatron tunes are inside the stopband.
Pellegrin. H. R. 48 48R.205) where /3ir2 are betatron amplitude functions at quadrupole pair locations. Boer. IEEE Trans.L. 136 (1991). M.18. the average focal length. 63 (1989). Employing such modules. IV. p. Further detailed discussions can be found in the literature. Statistical estimation of stopband integrals 105 Again. Proc. we obtain AAtfiALi + /32AK2AL2 = 0. CERN 84-15. Using the zero tune shift condition. Sci. Strehl. p. SLAC PUB-2522 (1980). and (AK/K)ims are respectively the average /3 value. i. (2.205) also produces a zero stopband integral at p = [2v]. the stopband integral can be estimated by statistical argument as 47TJav \ -K /rms where P&v. p. and Proc. 1933 (1985). NS32. 105. p. if we do not know a priori the gradient error. the number of quadrupoles. J[2v] — 0- Since the stopband integral J[2v] of a zero tune shift 7r-doublet is zero. CERN 89-05. 869 (1983). EFFECT OF LINEAR MAGNET IMPERFECTIONS D. in the design stage of an accelerator. on High Energy Accelerators. 385 (1984). 2. a zero tune shift quarter-wave quadrupole pair produces a maximum contribution to the half-integer stopband. the doublet has little effect on the global betatron perturbation shown in the right plot of Fig. Zero tune shift 7r-doublets can be used to change the dispersion function and the transition energy (to be discussed in Sec. Effect of a zero tune shift 7r-doublet quadrupole pair A zero tune shift 7r-doublet (or the zero tune shift half-wave doublet) is composed of two quadrupoles separated by 180° in betatron phase advance with zero tune shift. AIP Conf. 99 (1987). where the betatron perturbation due to the first quadrupole is canceled by the second quadrupole. p. CERN 91-04. In this section we discuss some basic beam diagnosis tools. CERN 87-10. . and the rms relative gradient error. R. (2. Jung. Shafer.e. and AKiALi is the integrated field strength of the iih quadrupole. J. On the other hand.III.fsv.5 Basic Beam Observation of Transverse Motion Measurements of beam properties are important in improving the performance of a synchrotron. F. Littauer. Koziol. we can correct half-integer betatron stopbands. E. J. Serio. Conf. III.8). 11th Int. Zero tune shift half-integer stopband correctors We find that the zero tune shift ?r-doublet produces a zero stopband width.Nq. The zero tune shift condition of Eq. P. Nucl. 459 (1980).
split electrodes and buttons.g. E = U+ + [/_ is the sum signal. the beam position is y * 2 WTTT w U+-U= 2 E' wA (2-206) where U+ and C/_ are either the current or the voltage signals from the right (up) and left (down) plates.106 CHAPTER 2. which is the self-inductance of the loop.19: A schematic drawing of electric beam position monitors. Similarly.206) may require nonlinear calibration. we can obtain the closed-orbit information from the DC component.g. (2. we can measure the betatron motion. The button BPMs are used mainly in electron storage rings. where the bunch length is small. Measurements of the normalized difference signal with proper calibration provide information about the beam transverse coordinates. e. sampling the position data at a slower rate. configurations. the induced image electric charges on the plates can be transmitted into a low impedance circuit. the relation Eq. A. The voltage is proportional to the rate of variation of the magnetic flux associated with the beam current linked to the loop. If we digitize beam centroid positions turn by turn. Figure 2. An electrostatic monitor is equivalent to a current generator. As the beam passes by. On the other hand. The BPM can have an electrostatic. Beam position monitor (BPM) Transverse beam position monitors (BPMs) or pickup electrodes (PUEs) are usually composed of two or four conductor plates or various button-like geometries. small secondary loop winding. the strip-line type has a larger transfer function. or the induced voltage can be measured on a high impedance port such as the capacitance between the electrode and the surrounding vacuum chamber. e.is called the difference signal or the A-signal. A = U+ . In general. where the image charge is detected by the shunt capacitance of the electrode to ground. . Depending on the geometry of the PUE. TRANSVERSE MOTION Figure 2.19 shows a sketch of some simple electric BPM geometries used mainly in proton synchrotrons. The split-can type BPM has the advantage of linear response. a magnetic loop monitor is equivalent to a voltage generator with a series inductor.U. and w/2 is the effective width of the PUE. or a magneto-static.
Dots in the left plot of Fig. B. The fractional part of the horizontal betatron tune is ux = 0. EFFECT OF LINEAR MAGNET IMPERFECTIONS 107 Figure 2.i) ellipse. . /3i and p2 are the values of betatron amplitude function at two BPMs. From the FFT spectrum. (2. (2. The invariant phase-space ellipse becomes x\+ o ( IK «/£• esc VV P 2 fci2- cot V>2i Zi \2 j =2AJ. we find that the horizontal and vertical tunes of this experiment were ux = 3.20: The measured betatron coordinates at two horizontal BPMs. where the solid line is obtained from Eq. Figure 2. where tp21 = "4>2 — ipi is the betatron phase advance between two BPMs. The solid line is drawn to guide the eye. The observed vertical betatron tune at vz = 0.208) where the area enclosed by the (z 2> zi) ellipse is 27iV/?i/32 |sin^2i|<A and J is the betatron action.21 shows the measured (x2. The phase-space trajectory can be optimally derived from the measured betatron coordinates at two locations with a phase advance of an odd multiple of 90°.III.758 and vz = 4.a.20 shows the data for the horizontal betatron oscillation of a beam after a transverse kick at the IUCF cooler ring. the betatron tune can be determined from the FFT of the transverse oscillations (see Appendix B).208) by fitting y/Si/ft and ip2i parameters . (2. Measurements of betatron tune and phase-space ellipse If the betatron oscillations from the BPM systems can be digitized turn by turn. and a\ = —P[/2 at the first BPM. 2. The top plot shows the digitized data at two BPM positions (xi and x2).002.683 respectively. we obtain . Using Eq.242 ± 0.62).317 may result from linear coupling or from a tilted horizontal kicker._csc^2i l~vmX2~ (coty>2i+Qi) A Xu (2-207) . The FFT spectrum of the BPM data (middle plot) shows the fractional part of the horizontal betatron tune. The lower plot shows the FFT spectrum of the Xi data. vs the revolution number. after the beam is imparted a magnetic kick. Here a total of 385 data points are used in the FFT calculation.
Because the horizontal tune in this example is 3. 2.£i. and 2ft J = 8 x 10"6 m2. IV. we can derive the betatron amplitude function by measuring the betatron tune as a function of the quadrupole strength. (2. the phase-space ellipse of (a:i. for the orientation. ihi = 80°.n+i vs ii i B . Other applications. Because the betatron tune is nearly 3. If ft is independently measured.20. The turn by turn digitized data require a high bandwidth digitizer and a large memory transient recorder.196).21: The left plot shows the phase-space ellipse (x2. 2. The right plot of Fig. will be discussed in Sec. The area enclosed by this nearly circular ellipse is 27rft| sin2irux\J.x{) of Fig. A.20). Two BPMs separated by about 90° in phase advance are useful for obtaining a nearly upright transverse phase-space ellipse. ft-Function measurement Using Eq. the action of the ellipse can be determined.6 Application of quadrupole field error By using the quadrupole field error. measured. the phase space is an upright circle.n+i) is nearly a circle. The area enclosed is 27rft| sm2ni/x\J. obtained by plotting betatron coordinates of successive revolutions of single digitized BPM data.21 shows ii. and ft ^ for the size of the ellipse.8. (2. TRANSVERSE MOTION Figure 2. such as ?r-doublets for dispersion function manipulation. If the betatron amplitude function ft is independently measured.n. The right plot shows a poor man's phasespace ellipse.108 CHAPTER 2.208) with y/falPi = 1-4.758. The area enclosed by the ellipse is 27iVft/?2 I sin •jfel | J. if available hardware is limited. However. the optical properties of the lattice can be altered. Examples of ^-function measurement and the betatron tune jump are described below. or manipulated. 2. III. the action of the betatron orbit can be obtained. the phase-space ellipse can be obtained by using digitized data of successive turns of a single BPM.75 (see Fig. The solid line shows the ellipse of Eq. The average betatron ampli- .
Tune jump The vector polarization of a polarized beam is defined as the percent of particles whose spins lie along a quantization axis. Figure 2. the fractional horizontal tune is seen to increase with the strength of the horizontal defocussing quadrupole.22 shows an example of the measured fractional part of the betatron tune vs the strength of a quadrupole at the IUCF cooler ring. The "average" betatron amplitude function at the quadrupole can be derived from the slopes of the betatron tunes.HI. B. the actual horizontal tune is below an integer. The slope of the betatron tune vs the quadrupole field variation is used to determine the betatron amplitude functions.79284739 for protons. Since the fractional part of the horizontal tune increases with the defocussing quadrupole strength. Because the fractional parts of betatron tunes are qx — 4 — vx and qz = 5 — uz. In this example. acceleration of a polarized beam may encounter spin depolarization resonances [22]. where iV± are the numbers of particles with their spin projection lying along and against the quantization axis.0011596522 for electrons.N-)/(N+ + AL). where the horizontal and vertical tunes are determined from the FFT spectrum of the betatron oscillations. where qx and qz are the fractional parts of the betatron tunes. For polarized beams in a planar accelerator. and 0.49 Thus G7 is called the spin tune. . Since the spin tune increases with the beam energy. the polarization of a proton beam is P = (N+ .g.z) at a quadrupole becomes where AKl is the change in the integrated quadrupole strength. For the IUCF cooler ring. EFFECT OF LINEAR MAGNET IMPERFECTIONS 109 Figure 2. According to the Thomas-BMT equation. e. the polarization vector precesses about the vertical axis at Gj turns per revolution. where the "imperfection resonance" 49G = 1.22: An example of betatron amplitude function measurements. and thus the horizontal betatron function is larger than the vertical one. tude function (px.2)/2 is the anomalous gfactor and 7 is the Lorentz relativistic factor. the quantization axis can be conveniently chosen to lie along the vertical direction that coincides with the vertical guide field. the slope of the horizontal betatron tune is larger than that of the vertical. we have i/x = 4 — qx and vz = 5 — qz. where G = (g .
The AGS had 96 closed-orbit correctors for imperfection resonance harmonics. 51 An rf dipole has recently been used to overcome these intrinsic spin resonances. Similarly. Because of the integer and half-integer stopbands. the magnitude of tune jump is limited to about Avz « 0. a 5% partial snake has recently been used to overcome all imperfection resonances.3.7 Transverse Spectra A. —00 (2. Lett. TRANSVERSE MOTION arises from the vertical closed-orbit error.g. Transverse spectra of a particle A circulating particle passes through the pickup electrode (PUE) at fixed time intervals To. Huang et al. where To = 2-KR/jic is the revolution period.210) 50 At AGS. M. When the G7 value reaches an intrinsic spin resonance.8. Phys. nonlinear resonances. 73. 80. Phys.50 The intrinsic resonance in low/medium energy synchrotrons can be overcome by the tune jump method. the bandwidth of PUEs is normally from 100's MHz to a few GHz. The amount of tune change is Al/* = h f ^ds> (-0) 2 29 where ABi is the quadrupole gradient of tune jump quadrupoles. The imperfection resonance can be corrected by vertical orbit correctors to achieve proper spin harmonic matching. Rev.51 III. See. Lett. etc. The AGS had 10 fast ferrite quadrupoles to produce a tune jump of about 0. Rev. should be carefully evaluated. .110 CHAPTER 2. and @c is the speed. the betatron tune is suddenly changed to avoid the resonance.3 in about 2. Placement of tune jump quadrupoles to minimize the stopband integral can reduce non-adiabatic perturbation to the betatron motion. 4673 (1998). With a large tune jump. beam dynamics issues such as non-adiabatic betatron amplitude function mismatch. A 20 G-m rf dipole was used to replace 10 ferrite quadrupoles with an integrated field strength of f Bids = 15 T.5 jus.g. the important half-integer stopbands are located at p = 17 and 18. This betatron tune jump can be achieved by using a set of ferrite quadrupoles with a very fast rise time. Bai et al. e. linear betatron coupling. 52 We assume that the bandwidth of PUEs is much larger than the revolution frequency.. R is the average radius. See.. Since the betatron tune of AGS is about 8. and the "intrinsic resonance" is produced by the vertical betatron motion.. e. non-adiabatic closed-orbit distortion. In fact. H. the non-adiabatic closed-orbit perturbation due to the misalignment of tune jump quadrupoles can also be analyzed. The current of the orbiting charged particle observed at the PUE52 is 00 /(t) = e£<J(t-nT 0 ). 2982 (1994).
Figure 2. The rf current is twice the DC current because negative frequency components are added to their corresponding positive frequency components. and S(t) is the Dirac 5-function. (d(t)) = (I(t))y0.212) d{t) = I(t)y{t) = I(t) [y0 + ycosuj?t}. (2. shown in the bottom plot. If we apply a transverse impulse (kick) to the beam bunch. we obtain I(t) = f £ e***' = ^ + 2 f £ cosnWoi. and observed in a spectrum analyzer (bottom plot).23 shows the periodic time domain current pulses.Because the negative frequency components are added to their corresponding positive frequency components. The top plot of Fig.211) where j is the complex number. where y0 is the offset due to the closed-orbit error or the BPM misalignment.e." Passing the signal into a spectrum analyzer for fast Fourier transform (FFT). we observe a series of power spectra at integral multiples of the revolution frequency nfo. The BPM measures the transverse coordinates of the centroid of the beam charge distribution (dipole moment). The DC current is e/T0. y is the amplitude of the betatron oscillation. J 0 n=-oo 1f> i0 n=i (2.23: A schematic drawing of current pulses in the time domain (upper plot). and W = f5c/R = 2ftfo is the angular frequency. The DC component of the dipole moment can be obtained by applying a low-pass filter to the measured BPM signal. Expressing the periodic delta function in Fourier series. 2. and up = Qyuio is the betatron angular frequency with betatron tune Qy. o Note that the periodic occurrence of current pulses is equivalent to equally spaced Fourier harmonics. and the rf current is 2e/To.III.213) . the rf current is twice the DC current. i. The middle plot shows the frequency spectra of the particles occurring at all "rotation harmonics. given by (2. in the frequency domain (middle plot). the beam will begin betatron oscillations about the closed orbit. EFFECT OF LINEAR MAGNET IMPERFECTIONS 111 where e is the charge of the particle.
n=—oo (2. the betatron tune can be measured by measuring the frequency of betatron sidebands. The Fourier transform of the rectangular current pulse becomes !(«>) = f" / 1 r°° l~K J-oo We-**dt sidebands are classified into fast wave.112 CHAPTER 2. the betatron oscillations obtained from the BPM signals contain sidebands around the revolution frequency lines. the distribution can be a cosine-like function. This topic is important to collective instabilities.215) where the density distribution is normalized according to / /•To/2 J-To/2 p(t . v ' where A is the bunch width in time. (-1) 228 . 10 otherwise. We discuss two simple examples as follows. and slow wave. 1. We ask what happens if the beam distribution has a finite time span with 00 I{t) = Nae Y. (2.e. 53The = Hr-^-\^J^-n^- [ALewosinwAl ^2. / = (n ± Qj. backward wave. Expanding the dipole moment in Fourier harmonics.53 B.nT0)dt = I. to be discussed briefly in Sec. the betatron oscillation can be measured. VIII. If the beam is confined by a barrier rf wave or a double rf system. Naturally.)/o with integer n. On the other hand. TRANSVERSE MOTION where the betatron oscillation can effectively be removed. by employing a band-pass filter. i. Fourier spectra of a single beam with finite time span We note that a periodic 5-function current pulse in time gives rise to equally spaced Fourier spectra at all revolution harmonics./2A if-A<*-nT0<A. If the beam is confined by a sinusoidal rf cavity to form a bunch. we obtain dp = ~ y T (e>(»-+Qv)»ot + ei(n-Q. p(t-nT0).216) There are many possible forms of beam distribution.)uot\ ( 2 2 1 4 ) In the frequency domain. the beam distribution can be approximated by the rectangular distribution: p(t-nT0) = {.
' 0 n=—oo .The frequency spectra of a long bunch. In the frequency domain. Since all particles in the bunch are assumed to have an identical revolution frequency. The form factor serves as the envelope of the revolution comb shown in Fig.«*)• (2-220) Figure 2." T ° ) 2 / 2 " ' . (2.219) The Fourier transform of the current pulse can be carried out easily to obtain / H = [^e. e. 2. (2. In general.e . the Fourier spectra can extend to about l/at.218) and (2. the 5-function pulses are replaced by pulses with finite frequency width. (2. the Fourier spectra of Eqs.III.( ' . Figure 2. EFFECT OF LINEAR MAGNET IMPERFECTIONS 113 2.nT0) = _ L .24: The form factors for the Fourier spectra of a Gaussian bunch and a rectangular bunch with rms bunch length at = 1 ns.221) n=-oo . The beam distribution for electrons in storage rings is usually described by a Gaussian distribution due to the quantum fluctuation p(t . If there is a revolution frequency spread.24 shows the envelope factor for Gaussian and rectangular beam distributions with an rms bunch length of 1 ns. will have coherent spectra limited by a few hundred MHz. The beam current observed at a PUE is I(t)=e £ °O 5{t-n^) 71 •'" =^ AT- OO £ <**"**». if the beam has a time width at. Note that the coherent signal of a rectangular bunch can extend beyond the Gaussian cut-off frequency. Fourier spectra of many particles and Schottky noise We consider N charged particles evenly distributed in the ring.g.220) are (^-function pulses bounded by the envelope factors. 1 m bunch length (3.23.w2 *< 2/2 ] £ *(« . the spectrum of the beam pulse is truncated by a form factor that depends on the time domain distribution function.3 ns). C.
(2. the first coherent Fourier harmonic is Bu0. However.g. N > 108.223) d(*) = E ^ T «*(<"/«*+ *) £ e ^ . the frequency spectrum is practically outside the bandwidth of PUEs. and the spectrum is simply invisible. e." Similarly. the average power of the dipole moment can be measured.114 CHAPTER 2. If the particles are randomly distributed.225) 5 4 The analysis of equally spaced short bunches in the ring has identical Fourier spectra. the coherent betatron sidebands of a nearly uniform distribution are beyond the bandwidth of PUEs. and the spacing of Fourier harmonics is also Nco0. the frequency spectra of the transverse dipole moment of N equally spaced particles give rise to a betatron sideband around the coherent orbital harmonics Nui0 ± uip. This means that the beam appears to have no rf signal.224) Normally. if there are B bunches in the ring. When N is a very large number. The beam that fills the accelerator is called a "DC beam. i. Similarly. It is important to realize that particles are not uniformly distributed in a circular accelerator.e. the average power of the dipole moment is P^ = ^[T\d2{t)\dt. . e.g. n=lt=l (2. the coherent betatron frequency becomes too high to be visible to PUEs. TRANSVERSE MOTION Note that the first Fourier harmonic is located at Nw0.54 If the number of particles is large.W ." or a "coasting beam. i=l 1* n=-oo (2.222) The beam signal arising from random phase in charged particle distribution is called the Schottky noise. This is called the Schottky noise signal. o i + A0i(i)).f " > . The power spectrum at each revolution harmonic from a low noise PUE is proportional to the number of particles. the dipole moment of the «th particle is oo di(t) = ej)i cos(u0it + Xi) E n——oo pit 1i S(t ~ nTi ~ *oi) °° = ^cos(cj0it + Xi) E e ^ ( . The longitudinal signal of N particles in a PUE is I(t) = eJ2 £ Sit-U-nT. N > 108. The dipole moment of the beam becomes n=-oo (2.) = 2ixe E i=\ n=-oo oo N Z>*eWt~ei) cc N n=-ooi=l « Are/o + 2 e / o E E c o s ( n a .
Beam injection and extraction Electrons generated from a thermionic gun or photocathode are accelerated by a high voltage gap to form a beam. The charge exchange injection involves H~ or H^ ions. this means that dipole moments of particles with frequencies within T~l m 10~2 Hz may interfere with one another.3.III. e. T is of the order of minutes. a duoplasmatron. 55 The chicane magnet may sometimes be replaced by punching a hole through the iron of a main dipole magnet provided that the saturation effect at high field is properly compensated.5S Since the injection orbit coincides with the closed orbit of the circulating protons without violating Liouville's theorem. and extracted by a voltage gap to form a beam.25a. The resulting Schottky power can be contaminated by particle-to-particle correlation. The Schottky signal can be used to monitor betatron and synchrotron tunes. as shown in Fig.226) The power spectrum resembles the single-particle frequency spectra located at nuo ± up.g. The injection procedure is as follows. frequency and phase space distributions. i. III. The beam is accelerated by a DC accelerator or an RFQ for injection into a linac (DTL). i. The closed orbit of the circulating beam is bumped onto the injection orbit of the H~ or Hj beam by a closed-orbit bump and a set of chicane magnets. Al. ions are produced from a source.12). the resulting phase-space area will be minimized.8 Beam Injection and Extraction A. except that we must take into account the effect of emittance blow-up through multiple Coulomb scattering due to the stripping foil (see Exercise 2.e. The strip or charge-exchange injection scheme There are many schemes for beam injection into a synchrotron. The beam is captured in a linac or a microtron and accelerated to a higher energy for injection into other machines. . pav = E «=i ^ 4Jt at u = n(uo) ± (w/j).e. EFFECT OF LINEAR MAGNET IMPERFECTIONS 115 where 2T is the sampling time. where a stripping foil with a thickness of a few /zg/cm2 to a few mg/cm2 is used to strip electrons. The injection efficiency for this injection scheme is high. It is the essential tool used for stochastic beam cooling. betatron sidebands around all rotation harmonics. (2. 2. the Schottky power is proportional to the number of particles. The medium energy beam is then injected into various stage of synchrotrons. For practical consideration. Measurements with varying sampling times can be used to minimize the effect of particle correlation. Since the phases u)itOi and xi a r e random and uncorrelated. etc. The injected beam can be painted in phase space by changing the closed orbit during the injection. Similarly.
116 CHAPTER 2. the closed orbit is bumped near the septum (dashed ellipse) so that the injected beam marked (1) is captured within the dynamical aperture. The efficiency may be enhanced by employing betatron resonances. TRANSVERSE MOTION Although the intensity of the H~ source is an order of magnitude lower than that of the H + source. Injection of the electron beam is similar to that of proton or ion beams except that the injected electrons damp to the center of the phase space because of the synchrotron radiation damping (see Chap. a higher capture efficiency and a simpler injection scenario more than compensate the loss in source intensity. The procedure is to bump the closed orbit of the circulating beam near the injection septum. and the injected beamlet will damp and merge with the circulating beam bunch. Figure 2. The injection efficiency is usually lower.7 eV binding energy. the particle distribution in betatron phase space can be optimized. cooling. Betatron phase-space painting. the closed-orbit of circulating beams is bumped (kicked) close to a septum magnet so that the injection beam bunch is within the dynamical aperture of the synchrotron. As the bumped orbit is moved during the injection time. Most modern booster synchrotrons and some cyclotrons employ a H~ source. the injected beam can avoid the septum in the succeeding revolutions marked (2) and (3).25b. 2. A2. At the time of injection pulse. radiation damping The injection of protons or heavy ions into a synchrotron needs careful phase-space manipulation. since the last electron in H~ has only about 0. The stable phase-space ellipse is shown as the dashed line in Fig. At the completion of the injection procedure. the bump is removed. The combination of phase-space painting . the phase space is painted and the injected beam is accumulated. However. This procedure is called phase-space painting. (b) The process of betatron phase-space accumulation. 4). If the betatron tune and the orbit bump amplitude are properly adjusted.25: (a) A schematic drawing of a chicane magnet that merges the H~ and H + orbits onto the stripper. Because of the betatron motion. During the injection. it can easily be stripped by a strong magnetic field at high energy. etc.
and of rf phase displacement acceleration. etc. and stacking accumulation of proton or polarized proton beams. The method will be discussed in Chap.9 Mechanisms of emittance dilution and diffusion A. Slow extraction employs nonlinear magnets to drive a small fraction of the beam particles onto a betatron resonance. residual gas scattering. III. The extracted beam can be delivered to experimental areas. intrabeam scattering. noise may arise from various sources such as power supply ripple. III. the value of the betatron amplitude function at the septum location. this is called stochastic slow extraction. A fast kicker is fired to take the beam into the extraction channel of a septum magnet (see Sec.3). Other injection methods A method that has been successfully applied at the ISR is momentum phase-space stacking. 3. etc. medical treatment. This method is also commonly used in low energy cooler rings for cooling. orbit bump is usually excited. Fast single turn extraction and box-car injection When a beam bunch is ready for extraction. B. The efficiency depends on the thin-septum thickness.Ill EFFECT OF LINEAR MAGNET IMPERFECTIONS 117 and damping accumulation can be used to provide high-brightness electron beams in storage rings. ground vibration.3). More recently. betatron phase advance between the nonlinear magnet and the septum location. Beam extraction Bl. Emittance diffusion resulting from random scattering processes In actual accelerators. . VII. called the box-car injection scheme. B2. A3. etc.1. efforts have been made to improve the uniformity of the extracted beam by stochastic excitation of the beam with noise. The slow extraction using the third order resonance will be discussed in Sec. beam particles can be slowly extracted by employing the half integer resonance (see Exercise 3. or be transferred into a another synchrotrons.3. Slow extraction Slow (beam) extraction by peeling-off high intensity beams can provide a higher duty factor56 for many applications such as high reaction rate nuclear and particle physics experiments. This requires an understanding of the momentum closed orbit or the dispersion function. This 56The duty factor is defined as the ratio of beam usage time to cycle time. Similarly. Large-amplitude particles moving along the separatrix are intercepted by a thin (wire) septum that takes the particles to another septum on the extraction channel.
particularly at high /3x-function locations. nonresonant and non-adiabatic ground vibration. The incoherent space-charge . and multiple Coulomb scattering from gas molecules. multiple scattering on the residual gas. Other effects are due to the angular kicks from synchrotron radiation. Al. VII). (2. the resulting change in the betatron action is A / = I(y. 3 and 4.8). lifetime effect due to nonlinear resonances (see Sec. and the beam is composed of particles with many different betatron phases. intrabeam Coulomb scattering. beam lifetime is further reduced by beam-beam effects. B.8). etc. i.3. intrabeam Coulomb scattering. injection and extraction kicker noises.. TRANSVERSE MOTION can induce emittance dilution and beam lifetime degradation. these will be addressed in Chaps. This effect can also be important in the strip-injection of the H" and Hj ion sources from the stripping foil. II. etc. Touschek effect (to be discussed in Chap.227) If the angular kicks are uncorrelated. The space-charge effect is characterized by an incoherent Laslett tune shift parameter £sc = Avsc (see Exercise 2.e. i. The emittance growth rate can be obtained from the well-known multiple Coulomb scattering. etc. Beam Lifetime The single beam lifetime is determined by nuclear scattering on residual gas in the beam pipe. (2. ion or electron trapping due to residual gas scattering. y' + O).4 II. diffusion processes caused by rf noise. Our understanding of betatron motion provides us with a tool to evaluate the effect of noise on emittance dilution.118 CHAPTER 2.12 gives an example of estimating the emittance growth rate. Exercise 2. Aerms = 2(A/) = {pe2) « (/3X)(92). photo desorption. Space charge effects The repulsive Coulomb mean-field field of a beam can generate defocussing force to reduce the effective external focusing. Multiple scattering from gas molecules inside the vacuum chamber can cause beam emittance dilution. If the betatron angle y' is instantaneously changed by an angular kick 9. y') = 0{ay + (3y') + ^B2. the increase in emittance due to the random scattering processes is obtained by averaging betatron oscillations and kick angles.2).228) Random angular kicks to the beam particles arise from dipole field errors. particle loss due to beam-beam collisions. In a collider. quantum fluctuation resulting from energy loss.3. The tune shift parameter for low energy linacs at the ion source can be large. the betatron tune can be detuned to a value nearly 0 (see Sec.e.I(y. beam aperture limitation.
where Hill's and the envelope equations are \y"+(k(s)-4r))y V p(s)/ I y" + k(s)y . II. and /3(s) is the betatron amplitude function. For synchrotrons.Ill EFFECT OF LINEAR MAGNET IMPERFECTIONS 119 tune shift for low energy synchrotron has a typical value of 0. e = 4erms is the KV beam emittance. and the over-dots are derivative with respect to the independent variable (time-coordinate) 4>. the space-charge terms in Hill's and envelope equations can be considered as a small perturbation unless a resonance condition is encountered.' 7 / 2 ^% =0 (y<Rb). For a KV beam. Making Floquet transformation with we transform Hill's and envelope equations into J +A .2 . where A is a ^-independent constant shift in the equilibrium radius and r is the independent term depending on the dynamics of the machine. We expand the envelope radius around the unperturbed closed orbit with R = 1 + r + A. Bl.^ (2. = 0. all particles are within the envelope radius.8.i l .6.136). Ksc is the space-charge perveance parameter. Rb = J/3(s)e is the KV beam envelope radius. The coherent envelope oscillations due to space-charge force We consider a simple KV model of ID paraxial system (see Sec. We try to illustrate possible mechanisms.0. = 0. (2. We expand the spacecharge factor: vP{a)KK = k / + g ^CQSM + A (2234) . Yet.230) Here y stands for either the particle's horizontal or vertical betatron coordinate. Rb + k(s)Rb . (2.232) (2. k(s) is the focusing function. which is about 10% or less of the betatron tunes. \y\<Rb(s) (2.^ *• y = o. defined in Eq.229) \y\> Rh(s) = 0. almost all low energy synchrotrons suffer space-charge induced emittance growth.233) R + SR-^-^ii^ where v is the betatron tune.
19. and it generates a perturbation term.232). vx = 3. obtained from a PIC simulation calculation for the Proton Storage Ring (PSR) at Los Alamos National Laboratory.234) into Hill's equation (2.£sc. Cousineau. The envelope radius.120 in Fourier series. The reduced envelope radius R shown in Fig. we obtain V+A - 2jRr- U + E In cos(n^ + xn) J T) = 0. n=l (2.4i/fsc)r « 2 ^ s c E In cos{n<j) + Xn). we obtain A = £sc/2i/ and OO r + {4v2 . after a closer inspection by substituting R = 1 + A + r into Eq.Rightfully. The parameter £sc is the Laslett (incoherent) linear space-charge tune shift parameter and £Sc<7n and Xn a r e the Fourier amplitude and phase of the n-th harmonic. (2.26 m circumference. the original betatron amplitude function (dashed line). It serves as a compressor to compress 1.26 clearly shows 4 oscillations in one circumference. fsc is called the linear space-charge tune shift parameter. (2.237) The space-charge force plays two roles in the envelope equation.238) may cause a large particle oscillation at n — 2{v — £sc) for the Mathieu instability. TRANSVERSE MOTION U~^t ZscQn = . Ph. 5 7 S. where the Fourier harmonic in the intrinsic betatron amplitude function serves as a harmonic perturbation to the envelope equation. . Indiana University.57 The PSR is a fixed energy synchrotron with 90. where CHAPTER 2.19 and vz = 2.233).19.234) into Eq. thesis. One speculates that a large envelope oscillation shown in Eq.239) The particle tune is vp « v . Since the vertical betatron tune of the PSR is about 2. (2. (2.16 ms (3214 turns in PSR) of proton pulse from the 800 MeV Linac into a high intensity proton pulse of about 180 ns. 2002. (2.D. (2. However.^ T ~ # =^t \MsWds' ^| sc (2'235) (2. It decreases the envelope tune from j / e n v = 2v to venv = 2v — £sc.236) cos{n<j> + Xn)d<t>.j . Substituting Eq.26 shows the space-charge perturbed vertical betatron amplitude function (solid line). Substituting Eq. or the perturbed betatron amplitude function. the dominant perturbing harmonic in the envelope equation is 4. and the normalized envelope radius R (dotted line). is resonantly excited by the harmonic n « vem with ^-n^l^^rs^+Xn)- (-3) 228 Figure 2. 2.239).
37 x 1013 particles) in the PSR at LANL. However. In reality. this difficult experiment has not been successfully demonstrated.e. we find that the resonance strength is actually zero. 6. The Fourier components of its betatron amplitude functions will be zero except harmonics 0. If particle motion inside the beam core is not affected by the envelope oscillation. its stopbands will only occur at the betatron tune values of 0. the harmonic content of the betatron amplitude function arises from the distribution of the focusing function. If the > stopband width fscgn is not zero. The ratio of these two betatron amplitude function. 18. 12. .26: The square root of the perturbed vertical betatron amplitude function (solid line).238). Detailed theoretical and numerical nalyses of 2D Hill's and envelope equations (including the effect of off-momentum particles) would be very valuable. (2. we illustrate a possible emittance dilution mechanism. We consider a stable beam orbiting in a synchrotron with space-charge tune shift parameter £sc at an equilibrium beam radius Rb{s). the envelope oscillation of a beam can not affect particle motion inside the envelope. shown as dotted line. No artificial quadrupole error is needed in generating the envelope stopband. (2.EXERCISE 2. 12.3 121 Figure 2. For example. is compared with the square root of the intrinsic betatron amplitude function (dashed line). 6. the envelope radius will be resonantly excited as shown in Eq. This causes a mismatch in the betatron phase-space ellipses for all particles inside and near the beam envelope radius and results in emittance dilution due to phase space mismatch. the envelope equation of Eq. We note that the envelope stopband can arise from the harmonic content of the intrinsic betatron amplitude function. 18. for a beam with high intensity (4. if an accelerator has a 12-superperiod symmetry in its focusing function.238) will not be resonantly excited if the envelope tune is chosen to be far away from these stopbands. • • •. Note that the average of R is slightly larger than 1. We speculate that the emittance dilution for space charge dominated beams can be minimized by correcting some half-integer harmonics of betatron amplitude functions. (2. When new particles are injected into the beam core.231). i. what is the mechanism for emittance dilution? In the following. is the reduced envelope radius R defined in Eq. the envelope tune is pushed toward an integer stopband venv —• n. the space-charge parameter £sc increases. Likewise. • • -.
3. i t where fk are integer stopband integrals. where NB is the number of particles per bunch and crs is the bunch length.160) is a solution of the above equation. we find that a particle at a distance r from a uniformly distributed paraxial beam bunch experiences a space-charge defocussing force ~ 2mc2Nr0 _ a 2 7 2 r' where 7 is the relativistic Lorentz factor.<l>x) = S{<j>-<!>{) is G(<j>. a is the radius of the beam bunch.B for vertical and radial betatron motion is given. (b) Show that the Green function G(4>. we should replace N by N = JVB/-V/27T<TS. (c) Expanding /33/2AB/Bp in Fourier series ^ = l j ^ wh A = . and f = xx + zz. (2. show that the equation of motion becomes Show that Eq. Use the Green function to verify the solution given by Eq.<j>i) in i ~ + u2\G{<t>. 2. show that the integer stopband width !?[„] is given by r ^ ] w 5v\f[v}\/V€r™s< w n e r e fy\ is the integer nearest the betatron tune.2) where the error field A. and limiting the closed-orbit deviation to less than 20% of the rms beam size. (a) Defining a new coordinate r\ = y/y/fi with <p = {1/v) /os ds//3 as the independent variable. TRANSVERSE MOTION Exercise 2. N is the number of particles per unit length. From Exercise 1. Particle motion in the presence of dipole errors is (Sect. In a Gaussian bunch.3 1. respectively. II.160).(j>i) = [COSI^(TT — \(f> — 0i|)]/2^sin7ri/. ro is the classical radius of the particle.^ . by AB = -ABX and A S = ABZ. .122 CHAPTER 2. show that the closed orbit arising from the dipole error is yco(s) = y/m £ k—-oo ^*»- (d) Using a single stopband approximation.L / ^ e . (2.
we have F G a u s s . 3. . the fraction of particles within la of a round Gaussian beam is 1 .161) can be derived from the 58This formula is derived on the basis of uniform beam distribution. show that Eq.e . where the beam distribution is not uniform. i. show that the space-charge force is equivalent to a defocussing quadrupole with strength R7.2 m.632. i. This is called the Laslett space-charge tune shift.EXERCISE 2. Thus the Laslett space-charge tune shift is also called the incoherent space-charge tune shift. For a round Gaussian distribution. a factor that depends on the distribution function should be used to estimate the space-charge tune shift [see part (c) of this Exercise]. Using r] = yJsfWy and p .4. Find the space-charge tune shift by using the data shown in the figure below. It is in fact a tune spread.3. = (1 . Draw a line in the figure for emittance vs the number of particles per bunch for a space-charge tune shift of 0. where {/3y) is the average betatron amplitude function and eN is the rms normalized emittance.*« 9 > where ATSC = 2Nro/(l32j3) is the normalized space-charge perveance parameter used frequently in the transport of space-charge-dominated beams in linacs.e" 1 ) « 0.e. 1. (b) The rms beam radius is a2 = (py)eN/p''y. Show that the betatron (Laslett) tune shift induced by the space-charge force is given by58 __ FBNBro ^ 2irRKsc "sc ~ 27reNj872 ~ 47re ' where F& = Jjp* is the bunching factor and e = eN //3*y is the emittance of the beam. and /3 and 7 are Lorentz's relativistic factors.\ \ f 2Nr° 9 00 ^ . The beam intensity in low energy synchrotrons is usually limited by the space-charge tune shift. (c) The Fermilab booster synchrotron is operating at 15 Hz with a circumference of 474. In estimating the space-charge tune shift for an actual accelerators. Particles with large betatron amplitudes have a small space-charge tune shift. = dr]/d(j> with <j> = {l/fy) /os ds//3y as conjugate phase-space coordinates. The rms bunch length at injection is about 1 m.1 .e. The Laslett tune shift is the betatron tune shift for particles with small betatron amplitudes. and <j> as time variable. the formula for the space-charge tune shift should be adjusted by a beam distribution form factor Fdjst. When you are applying this formula to an actual accelerator.3 123 (a) Using the result of Sec. (2.
A commonly used algorithm is based on the "three-bumps" method. it can be considered as a lattice made of 60 FODO cells with betatron tunes vz = 8.tf))* = ~f* {£P3/29(v')dv'] di>.(AH(J. and the orbit distortion is localized between the first and third steering magnets. Jo g(r.62. op (a) Letting r) = y/2J/u cos tp and dtp/d<j> = v. and 63 be the three bump angles. Let 61.124 Hamiltonian CHAPTER 2. 5.e. The AGS is composed of 12 superperiods with 5 nearly identical FODO cells per superperiod. Show that these angles must be related by 0 --6 / ^ ~ s i n ^ 3 1 Y /?2 Sin ^32 ' 6-6 / ^ ~ s i n ^ 2 1 V ^ 3 S m ^32 ' where ft is the ^-function at the ith steering magnet. where <Aff(J. 4. i.^))^ + [AH . + viTi2)+AH(T.')dr. Assuming as 3> o>. 2X<7? pis) = -jL-e^M.tf)). where three steering dipoles are used to adjust local-orbit distortion. show that the Hamiltonian becomes H = vJ+ (AHiJ. and P(r) = ^e-(*2+*W. a local orbit bump can be attained by two steering dipoles 6\ and 63 if and only if ^31 = nv.) = ^-. Show that the betatron tune is shifted by the perturbation Av — d(AH)^.). Obviously. where N& is the number of particles in a bunch. . evaluate the space-charge tune shift as a function of the amplitude r.12 m. (b) We consider a cylindrical Gaussian bunch distribution p(x.z) = NBp(r)p(s). The circumference is 807. AH = -S r^g(r.s./dJ.'. ijjji = ipj . where the phase advance is an integer multiple of IT.>].8 and vx = 8. The closed orbit can be locally corrected by using steering dipoles. Replacing r by yjifijjv cos ip. V27T<7S are respectively the transverse and longitudinal Gaussian distributions with rms width aT and as.fi is the phase advance from the ith to the j t h steering dipoles.6. TRANSVERSE MOTION H=±<p*. where TQ = e2/A-Ke^rru? is the classical radius of the particle. show that the Lorentz force for a particle at distance r from the center of the bunch is ^s)^{l-e-^)p{s).
How far from the closed orbit of the circulating beam should the septum be located? What effect. We assume that the values of the betatron amplitude functions are fix = /3Z = 10 m.1 T.25 in about 2. Where should the stripper be located with respect to the center of the circulating beam? What is the minimum width of the stripper? Sketch a possible injection system scenario including local orbit bumps. In the H~ or H^ strip injection process. What are the stopband integrals due to these tune jump quadrupoles? iii.025. During the beam accumulation process. . The injection beam arrives through the center of a septum while the circulating beam closed orbit is bumped near the septum position. and a vertical one to horizontal dipole field error. the betatron amplitude functions are Ar = Pz = 10 m. the orbit bump is reduced to avoid beam loss through the septum.s. This means that each quadrupole changes the betatron tune by -0.202) for the AGS.5 fj.EXERCISE 2. the emittances are ex = ez = 2.3 125 (a) Estimate the closed orbit sensitivity factor of Eq. the closed orbit is bumped onto the stripper location during the injection pulse. where xc0 is the closed orbit and xp is the betatron displacement. At the septum location. What are the favorable configurations for these quadrupoles from the beam dynamics point of view? iv. what is the minimum length of the kicker? What advantage. if any.5TT mmmrad for the injection beam. The phase advance between the septum and the kicker is 60°. /3Z = 8 m. i. a set of 10 ferrite quadrupoles located at high-/^ locations are powered to change the vertical tune by At>z = —0. (2. Multi-turn injection of heavy ion beams requires intricate phase-space painting techniques. The extraction septum is located 40 mm from the center of the closed orbit of the circulating beam. The septum (current sheet) thickness is 7 mm. if any. The injection beam and the circulating beam merge at the same phase-space point. and ex = ez = 40TT mm-mrad for the circulating beam. the betatron functions are f}x = 10 m. At extraction. (c) During the polarized beam acceleration at AGS.168). What is the kicker angle required for single-turn extraction? Assuming that the maximum magnetic flux density for a kicker is 0.5 n mm-mrad for the injection beam. 7. A ferrite one-turn kicker is located upstream with $x = 10 m and pz = 8 m. does an orbit bump provide? 9. Discuss a scenario for efficient single-bunch extraction. (b) Estimate the the rms half-integer stopband width of Eq. the 95% emittance of the beam is adiabatically damped to 5 7r mmmrad at Bp = 10 Tm. does the betatron tune have on the beam-accumulation efficiency? 8. Particle motion in the presence of closed-orbit error is X = Xco + Xp. and the thickness of the wire septum is 1 mm. (a) Show that an off-center horizontal closed orbit in quadrupoles gives rise to vertical dipole field error. Are there advantages to installing 12 quadrupoles? What are they? 6. What is the effect of these tune jump quadrupoles on the horizontal tune? ii. (2. We assume that the 95% emittances are 50 ir mm-mrad for the stored beam and 2.
Zgngier. and oto and ai are related to the derivatives of the betatron amplitude functions. a'o = KopQ . (a) Show that where Aif = Kx . LAL report 77-35. 75-90 (1987). where B? = &iB2/dx2\x_0z_0. . TRANSVERSE (b) The magnetic field of a nonlinear sextupole is MOTION ABZ + jABx = Bf-(x2-z2 + 2jxz). 1977.2 t t l . (c) In thin-lens approximation.126 CHAPTER 2.apPx -/Mi ' „ _ ffi . where il>o and ipi are the unperturbed and the perturbed betatron phase functions. Thus Pa and fix satisfy the Floquet equation: P'o = . This exercise provides an alternative derivation of Eq. Show that the effective quadrupole gradient is dBz/dx\eS = xC0B210.59 We define the betatron amplitude deviation functions A and B as _ aiffp .W. (jE^As/Bp) is the integrated sextupole strength. Montague. In the presence of gradient error. the betatron amplitude functions and the betatron tunes are modified. P[ = . the phase-space trajectory of A vs B is a circle.Ko. CERN 87-03. d^/ds = l//3i. and (Po) is the averaged value of betatron function in the quadrupole. Show that a horizontal closed-orbit error in a normal sextupole produces quadrupole field error. (d) In thin-lens approximation. (b) In a region with no gradient error.e. show that the change of A in a sextupole is A A ss Pogeg. a i = Kxpx .199). and xco is the closed-orbit deviation from the center of the sextupole. (2.7 o . # 0 / d s = 1/A>.A) vm' where /3o and fi\ are respectively the unperturbed and the perturbed betatron amplitude functions associated with the gradient functions KQ and K\. where geff = {B2As/Bp)xC0 is the effective quadrupole strength.2 a 0 .7 l . B. 69See also H. show that A2 + B2 = constant. show that the change of A at a quadrupole with gradient error is AA = j VWi AX ds » (P0)g. i. where g = + / Aif ds is the integrated gradient strength of the error quadrupole.
8. where P is the pressure. T is the temperature. .3). Show that the emittance growth rate is 1 -2e»~\ ^ ) TO> re _ 1rfe _ o . and Ag is the gram molecular weight of a gas. Because the emittance growth is proportional to the betatron function.641 x Kr6j9-Pg[ntorr]4g [g/cm 2 /s]. velocity. Po + Pi Show that this equation reduces to Eq.4 p 2 ^A*. The radiation length is 716. /3c and zp are momentum. where /3c is the velocity of the beam. l J> where (/?j_) is the average transverse betatron amplitude function in the accelerator.4 . n is the number of moles. and p is the momentum of the beam.4. . XQ is the radiation length. particularly at high-/? locations. z p is the charge of the projectile. 2l where Z and A are the atomic charge and the mass number of the medium. [nTorr]. Xog is the radiation length of the gas. 12. This effect can also be important in the strip-injection process. P g is the equivalent partial pressure of a gas at room temperature T = 293 °K.3 127 (e) If we define the average betatron phase function as where 1 f* ( 1 1\ .A. Show that the half-integer stopband integral Jp is approximately zero at p = [2v] for two quadrupole kickers separated by 180° in betatron phase advance with zero betatron tune shift. (a) Using the ideal gas law. and R = 8.314 [J (°K mol)" 1 ]. This exercise estimates the emittance dilution rate based on the multiple scattering formula (see the particle properties data) for the rms scattering angle fl2_2g2^J13. IV. V is the volume. show that the equivalent target thickness in [g/cm 2 /s] at room temperature is x = 1. 11. PV = nRT.4g edt ' PeN [irmmmrad] \pc[GeV]J XOg [g/cm2] .199) in the limit of small gradient error. better vacuum at high-/3x location is useful in minimizing the multiple scattering effects.EXERCISE 2. Multiple scattering from gas molecules inside the vacuum chamber can cause beam emittance dilution. and x is the target thickness. and charge number of the beam particles.6[MeV]zp\2 x 6 where p. 7 is the Lorentz relativistic factor. Such a zero tune shift it-doublet can be used to change 7 T with minimum effects on betatron motion (see Sec. ^ M A 1 + AJ*1 n rsa+C / i show that the function B satisfies 0 d(j> 2 +4 ^ = . (2. 1 5 7(fli) M / zp yP.
. the H~ passes through a thin foil of thickness tfon [/ig/cm2].foji tf0ii[^g/cm2] A Ac = 117. the efficiency of charge exchange is small. /3c is the velocity of the beam.60 60If the stripping foil is too thin. Show that the emittance growth per passage is IT?O #i.foii is the betatron amplitude function at the stripper location. p is the momentum of the injected beam. P2{pc[MeV})2 X 0 [g/cm 2 ] L " where /3j_.128 CHAPTER 2. and Xg is the radiation length. and the proton yield is little. A compromise between various processes is needed in the design of accelerator components. Estimate the emittance growth rate per passage through carbon foil with H~ beams at an injection energy of 7 MeV if /3j_ fOii = 2 m and tfoii = 4 [^g/cm2].8 —T7— ' L —57Trmmmrad . If the foil is too thick. the beam emittance will increase because of multiple Coulomb scattering. TRANSVERSE MOTION (b) During the H~ strip-injection process.
we can study the motion of off-momentum particles perturbatively. Its effect on betatron motion will be addressed in Sec V. the dispersion action." and a particle with momentum po is called a synchronous particle. IV.6 we introduce the standard transport notation. 61 The revolution frequency of a synchronous particle is defined as the revolution frequency of the beam. . IV. where we introduce the phase focusing principle of synchrotron motion.2. For a particle with momentum p.What happens to particles with momenta different from p0? Here we study the effect of off-momentum on the closed orbit.g. we will find that the off-momentum closed orbit is proportional to 5 in the first-order approximation. IV. and the dispersion function is defined as the derivative of the off-momentum closed orbit with respect to 5. including dipole field errors and quadrupole misalignment. |<5| < 10"4 for SSC. Ill. In Sec.7 we describe methods of dispersion measurements and correction. we discussed the closed orbit for a reference particle with momentum Po.e. a beam is made of particles with momenta distributed around the synchronous momentum po. IV. and < 2 • 10"2 for typical electron storage rings. In Sec.240) for 5 = 0 were discussed in Sec.4. the momentum deviation is Ap ~ p — po and the fractional momentum deviation is 5 = Ap/po. OFF-MOMENTUM ORBIT 129 IV Off-Momentum Orbit In Sec. 1 Dispersion Function Expanding Eq. Solutions of Eq.IV.61 However. In Sec. The frequency of the radio-frequency (rf) cavities has to be an integer multiple of the revolution frequency of the beam. By using closed-orbit correctors. and in Sec. (2. a synchronous particle synchronizes with the rf electric field applied to the beam.8 methods of transition energy manipulation. IV. i. in particular. < 3-10"2 for anti-proton accumulators. e. the integral representation. We will discuss the properties of the dispersion function. In Sec.5 we discuss the achromat transport system. The momentum compaction factor and transition energy are discussed in Sec. we can achieve an optimized closed orbit that essentially passes through the center of all accelerator components. we obtain / X+{P>(I 1-5 K(. II. and the %-function will be introduced in Sec. and in Sec. IV. (2. we examine the method of dispersion suppression in a beam line. Since 5 is small.The fractional momentum deviation 6 = Ap/p is typically small. < 5-10"3 for RHIC. IV.)\ {i 6 + + 6) + 6))x-p(i 5y (2 . Minimum (H) lattices are discussed in Sec. IV.3. This closed orbit is called the "golden orbit.240) where K(s) = B\/Bp is the quadrupole gradient function with Bi = dBz/dx evaluated at the closed orbit. IV. IV. The name "synchrotron" for circular accelerators is derived from the synchronism between the orbiting particles and the rf field.9.29) to first order in x/p. < 10"4 for the IUCF Cooler Ring.1.
(2.240) can be expressed as a linear superposition of the particular solution and the solution of the homogeneous equation:62 x = xp(s) + D{s)6. (2. D" + (Kx{s)+AKx)D = .245) where L is the length of a repetitive period. The local closed-orbit condition of Eq. However.241) In this section. the closed-orbit condition is imposed on the dispersion function63 D(s + L) = D(s). To the lowest order in 5. the inhomogeneous equation can easily be solved by the matrix method. we will neglect the chromatic perturbation term AKx(s). this local periodic closed-orbit condition facilitates accelerator lattice design. where D(s)S is the off-momentum closed orbit Aside from the chromatic perturbation AKX. The solution of a linear inhomogeneous dispersion equation is a sum of the particular solution and the solution of the homogeneous equation: ( ^ ) = "<*>O + (i). . where C is the circumference. (2.245) for repetitive cells is not a necessary condition. with Kx = ±-K(s).130 CHAPTER 2. «. Since Kx{s) and p(s) are usually piecewise constant for accelerator components. TRANSVERSE MOTION For an off-momentum particle with 5 ^ 0. the solution of the linearized inhomogeneous equation (2. the solution of the homogeneous equation Xp is the betatron motion around the off-momentum closed orbit. the dispersion function obeys the inhomogeneous equation D" + Kx(s)D = l/p. AKx = [-^ + K(s)}5 + O(S2). The solution of the inhomogeneous equation is called the dispersion function. the displacement x is x = xco(s) + xp(s) + D(s)6.244) Since Kx(s) and p(s) are periodic functions of s. (2. 63The closed-orbit condition for the dispersion function is strictly required only for one complete revolution D(s) = D(s + C) and D'(s) = D'(s + C).m 62Including the dipole field error. D\s + L) = D\s). where xp(s) and D(s) satisfy the equations x"p + (Kx(s) + AKx)xfi = 0.242) (2.+ O(S).243) (2. where i c o is the closed-orbit error discussed in Sec. III.
and d and dl are the particular solution. OFF-MOMENTUM ORBIT 131 where the 2 x 2 matrix M(s2\si) is the transfer matrix for the homogeneous equation. and B represents bending dipole(s). and 9 is the bending angle. d'). is represented by C = {^QF B QD B ^QF}.IV. Example 1: Dispersion function of a FODO cell in thin-lens approximation A FODO cell with dipole. Using thin-lens approximation. 2. as shown in Fig. The transfer matrix in Eq. where Kx = 1/p2. where QF and QD are focusing and defocussing quadrupoles. we obtain V ^k s i n ^ s ) k ^ ^sinh^S \ /O-y'l-fCil v J / lf^<0- The transfer matrix for a pure sector dipole. the transfer matrix of a sector dipole becomes M= \M\ 9 \. (2. Let d be shorthand notation for the twocomponent dispersion vector with d) = (d.249) 0 0 /I t 0 1 1 J where p is the bending radius. Vo o i / \o o i / \o o i / \o o i / V° ° !/ . we obtain M= (I -i 0 0\ (I L \L9\ 1 0 0 1 9 (I U 0 0\ (I L \L0\ 1 0 0 1 9 ( 1 -£ 0 0\ 1 0 . (2.4.246) can be expressed by the 3 x 3 matrix For a magnet with constant dipole field and field gradient. In the small angle approximation. VO 0 1 J where £ = p9 is the length of the dipole. is ( cos0 -{l/p)sin6 psin9 cosfl p(l—cos#)\ sinl? .
The dispersion function at the defocussing quadrupole location is £g(l-l8in(*/2)) sin 2 ($/2) ' UD~ D°-°- (2-253) The middle plot of Fig. which can be approximated by a lattice made of 60 FODO cells. The dispersion function at the focusing quadrupole location becomes The dispersion function at other locations in the accelerator can be obtained by the matrix propagation method. we obtain *-A o _. We list here some characteristic properties of the dispersion function of FODO cells. The closed-orbit condition of Eq. (2. (2. (2. and it is smaller with shorter cell length and smaller bending angle.245) becomes (D\ {") = [-&+& l~fi 2 ^ . • The dispersion function at the focusing quadrupole is larger than that at the defocussing quadrupole by a factor (2+sin(§/2))/(2-sin($/2)). which is about 2 at $ = 90°.247).£ ) J m S i n ( 1-$ 21(1+ i ) 2L0(1 + ^ ) \(D\ (225o) Note that D and D' in Eq.5 shows the dispersion function of the AGS lattice.250) are values of the dispersion function and its derivative at the focusing quadrupole location. the product of the cell length and the bending angle of a FODO cell. Using the Courant-Snyder parameterization for the 2x2 matrix. and / is the focal length of the quadrupoles. • The dispersion function is proportional to L6. the dispersion function is proportional to the inverse quadratic power of the phase advance. 2. • When the phase advance is small. 6 is the bending angle of a half cell.132 CHAPTER 2.f . Eq. TRANSVERSE MOTION where L is the half cell length.2£(l + sm(g/2)) where $ is the phase advance per cell. .
OFF-MOMENTUM ORBIT 133 Example 2: Dispersion function in terms of transfer matrix In general.M22) + Mi2M23 ~ 2-Mu-M22 _ MnM2i + (1 .a s i n $ ) D .258) Since the dispersion function satisfies the homogeneous betatron equation of motion in regions with no dipole (1/p = 0). For a FODO cell.cos $ . (2.Afn)M23 ^ " 2-Mu-M22 u _ M13(l .a sin $) " 2(1-cos $) ./3sin$ D'\ IV. (2. but in regions with dipoles. it is not invariant. Px (2. the transfer matrix of a periodic cell can be expressed as (Mu M = Mu M22 M13\ M23 V 0 M21 0 1 ) . ( cos $ + a sin $ —7sin$ 0 /?sin<I> (1 .53). p and 7 = (l+a2)/f3 are the Courant-Snyder parameters for the horizontal betatron motion at a periodic-cell location s. (2.245). a.2 The dispersion %-function is defined as n(D. we obtain _ Mi 3 (l . Mu. Action.c o s $ + asin$) + M23. 'HF < 7iD. where _ ^ S i n $ ( l + Isinf)2 2(1 +sin | ) sin4 f ' _L02sincfr(l-Isinf)2 D~ 2(1 . the 3x3 transfer matrix is cos$ — asin<3> 7 s i n $ D + (1 — cos$ + asin<I>) D' \.257) This representation of the transfer matrix is sometimes useful in studying the general properties of repetitive accelerator sections.254) where Mu. [2-2i3b) l^WJ where $ is the horizontal betatron phase advance of the periodic cell. the 'H-function is invariant.flsin$ " 2(1-cos $) ' _ -M137 sin $ + M23(l . Solving M13 and M23 as functions of D and D'.e.sin f) sin4 f ' l ' .cos$ .IV. and Integral Representation + 2axDD' + /3XD'2 = -j-[D 2 + (&£>' + axD)2\. and D and D' are the value of the dispersion function and its derivative at the same location. D') = jxD2 ^-Function. Using the closed-orbit condition of Eq. M2i and M22 are given by Eq. i. 0 1 ) (2. the dispersion %-function at the defocussing quadrupole is larger than that at the focusing quadrupole.
and 3 dispersivesections for injection.261) In a straight section. J d is not constant. the normalized dispersion coordinate Xd is nearly constant. etc. D ~ \fWx. 2.= £ > = y ^ c o s S d . In a region with dipoles. is identical to the betatron phase advance. Figure 2.134 CHAPTER 2.28 shows the normalized dispersion coordinates for the IUCF Cooler Ring. The change of the dispersion function across a thin dipole is AD = 0 and AD1 = 6. AXd = 0. TRANSVERSE MOTION and the dispersion H-function is proportional to the inverse cubic power of the phase advance. (2. the normalized dispersion phase-space coordinates for the double-bend achromat (DBA) lattice (see Sec.1 Example 1. IV. Now we define the normalized dispersion phase-space coordinates as { Xd = .5. rf cavities. aside from a constant. In contrast.262) where 0 is the bending angle of the dipole. Note that Xd is indeed nearly constant. Figure 2.. which is composed of 3 achromat straight-sections for electron cooling.A) shows different behavior.5) that is approximately made of 5 FODO cells. PA = JPxD1 + -^D where the dispersion action is given by = -p Jd = ^n{D.e. Jd is invariant and $ d . and Pd is small.27: Left: Normalized dispersion phase-space coordinates Xd and Pd are plotted in a superperiod of the AGS lattice.27 shows the normalized dispersion phase-space coordinates in one superperiod of AGS lattice (see Fig. and (Pd. Right: the coordinates are shown in Xd vs Pd. (2.D'). The scales for both Xd and Pd are m1/2. IV. 2. i. momentum stacking.260) Jd sin $ d . Figure 2. etc.34).e. Xd) propagate in a very small region of the dispersion phase-space (see also Fig. APd = y[px AD' = Jfx9 AJ d = (PXD' + axD)0. The machine is made of six 60°-bends . i. Y* (2. and the change in dispersion action is For FODO-cell lattice shown in Sec.
39. With the substitutions AB Ap 1 n . Note that the achromat sections are described by a single point at origin with Xd = Pd = 0. OFF-MOMENTUM ORBIT 135 Figure 2.Ap .38 and 2.28: Left: Normalized dispersion phasespace coordinates X& and Pd of the IUCF Cooler lattice are plotted. the minimization of (H) plays no important role in beam dynamics. The resulting dispersion phase-space coordinates are much larger than those of minimum emittance DBA lattices shown in Fig. 2.38. a minimum fiz inside dipole will provide a criterion for the magnet gap g. 2. .263) Po P where p is the bending radius. Thus the corresponding (3X will be large in dipole. For an ion storage ring. 2. Integral representation of the dispersion function The dispersion function can also be derived from the dipole field error resulting from the momentum deviation. the normalized dispersion coordinates increase in magnitude. it is preferable to design a machine with a minimum j3z inside dipoles.31. 2.i and Pd are m1/2. and ds is the infinitesimal length of the dipole. forming a 3 similar double-bend achromat modules. the normalized dispersion coordinates are located on invariant circles. Since the power required in the operation of a storage ring is proportional to g2.IV. the horizontal betatron phase-advance is also nearly n. It is worth pointing out that the lattice function and the dispersion phase-space coordinates of the IUCF Cooler Ring differ substantially from the low emittance DBA lattice to be shown in Figs. The scales for both X. The angular kick due to the off-momentum deviation is given by 9= 45*.28. Inside dipoles. Thus the dispersion phase $d advances nearly n in the dispersion matching section. (2. that are nearly half-circles as shown in Fig. In dispersion matching sections. Right: The coordinates are shown in Xd vs Pd at the end of each lattice elements. Instead. Since the dispersion phase-advance is equal to the horizontal betatron phase-advance in a straight section. where the dispersion function is shown in Fig.
where / is the revolution frequency.29). Because a high energy particle travels faster. Transition energy and the phase-slip factor 137 The importance of the momentum compaction factor will be fully realized when we discuss synchrotron motion in Chap. and v is the speed of the circulating particle. we discuss the phase stability of synchrotron motion discovered by McMillan and Veksler [17]. OFF-MOMENTUM ORBIT A. and 7Tmc2 or simply 7T is the transition energy. . To = l / / 0 is the revolution period of a synchronous particle. (2.^ = ^ . the converse is true. Phase stability of the bunched beam acceleration Let V(t) = Vo sin(hojot + <f>) be the gap voltage of the rf cavity (see Fig. The acceleration voltage at the rf gap and the acceleration rate for a synchronous particle are respectively given by Vs = Vo sin fa. In the meantime. Eo = foeVo sin fa. 7T « vx. This is the isochronous condition. <j> is an arbitrary phase angle.Ap . Without a longitudinal electric field. its speed compensates its longer path length in the accelerator. h is an integer called the harmonic number.^ . with 7 > j T .IV. where Vo is the amplitude. a higher momentum particle will have a revolution period shorter than that of the synchronous particle. 3. the fractional difference of the revolution periods between the off-momentum and on-momentum particles is AT AC AD . Particles with different momenta travel along different paths in an accelerator. At 7 = 7T the revolution period is independent of the particle momentum. Below the transition energy.270) . Since the revolution period is T = C/v. A / / / o = -1)5. 2. W = 2TT/O is the angular revolution frequency. and 6 = Ap/p 0 is the fractional momentum deviation. and /o is the revolution o frequency of a synchronous particle. or equivalently. where fa is the synchronous phase angle. For FODO cell lattices. the time slippage between a higher or lower energy particle and a synchronous particle is TQT)5 per revolution. l. which is the operating principle of AVF isochronous cyclotrons.269) Here jT = J\/ac is called the transition-7. so that a higher energy particle will arrive at a fixed location earlier than a synchronous particle. A synchronous particle is denned as an ideal particle that arrives at the rf cavity at a constant phase angle <j> = fa. with 7 < 7T and 77 < 0. where C is the circumference. All particles at different momenta travel rigidly around the accelerator with equal revolution frequencies. (2. The phase-slip factor r) is ^ = Q c . Above the transition energy. B.
P d ( s ) = 2 l i n ^ I. Since the change in path length due to betatron motion is proportional to the square of the betatron amplitude [see Eq. (2.4. Since D(s) is normally positive. (2.iri/x)dt p \lPx{t) ^ 265) IV. and the last approximate identity uses thin-lens approximation.2). Bx is the betatron amplitude function. vx is the betatron tune. (2. p S i n ( ^ ( t ) ~ ^ ( S ) " *"')dtMomentum Compaction Factor Since the synchronization of particle motion in a synchrotron depends critically on the total path length. $ is the phase advance of a FODO cell.160).266) which depends linearly on the dispersion function D(s).4ix(s) . The normalized dispersion functions can then be expressed as 1 xd{s) rs+c JPx{t) = 7T-/ 2 sin rcvx Js 1 fs+c cos{tpx{t) . the momentum compaction factor for a FODO lattice is given by Qc~ (£>F + DD)8 62 l_ 2L ~sin 2 ($/2) ~ ^ 2 > where L and 9 are the length and the bending angle of one half-cell. it is important to evaluate the effect of the off-momentum closed orbit on path length.3 . the dispersion function becomes jBJs) rs+c \/Px(t) where C is the circumference. The momentum compaction factor is then denned by where {D)i and 6j are the average dispersion function and the bending angle of the ith dipole. On the other hand. For example. the effect is small. TRANSVERSE MOTION in Eq.t) is the Green function of the horizontal Hill equation. ipx is the betatron phase function. . the deviation of the total path length for an off-momentum particle from that of the on-momentum closed orbit is given by AC = j -ds = U ^-ds] 6.136 CHAPTER 2. and Gx(s.170)]. and vx is the betatron tune (see Exercise 2. the total path length for a higher momentum particle is longer.
the acceleration rate is E = feVo sin 4>. The rate of change of the energy deviation is (see Chap. P £>o UQ where AE = E — EQ is the energy difference between the non-synchronous and the synchronous particles. f 0 < 4>s < TT/2 if 7 < 7T or rj < 0. 7 0 < <j>s < TT/2 for 7 < 0. where / is the revolution frequency. and the rf phase angles of a synchronous particle. TRANSVERSE MOTION where e is the charge.138 CHAPTER 2.e. It is usually called synchrotron motion. the phase focusing principle requires for 7 > 0. = ^ at Jo ^ *M**. 3.272) Equations (2. I) l(^) = ^ ( s i n ^ S i n ^' ±U .This is the equation of motion for a biased physical pendulum system. and n/2 < (j>s < -K 7 A non-synchronous particle will arrive at the rf cavity at a phase angle <f> with respect to the rf field. LBNL). where 4> can vary with time. (Courtesy of D. Li.29: Schematic drawing of an rf wave.272) form the basic synchrotron equation of motion for conjugate phase-space coordinates <f> and AE/OJQ. Figure 2. and the higher and lower energy particles. The differential equation for the small amplitude phase oscillation is ~ ^ - = ^ ^ ( s m 0 - W s ) * toPE* (^"^ (2 ' 273) Thus the phase stability condition is given by T?COS0S < 0. where 0 is the actual angular position of the particle in a synchrotron. At phase angle (f>.*) = -hfiu. \ TT/2 < <t>s < -K if 7 > 7T or rj > 0. Sec.271) and (2. Eo is the energy of the synchronous particle. is = hV^ = Po (2. the equation of motion for the rf phase angle <fr = —h9. . For a stable synchrotron motion. i. Similarly. and the overdot indicates the derivative with respect to time t.
Eq. u)syn — 0 as 7 — 7 T . If the arc is composed of modular cells.rms is the rms emittance. However. thus the transition energy problems can be eliminated. The synchrotron frequency of small-amplitude phase oscillations is given by I heV0\rj cos <j)s q». 64The curved transport line is usually called the arc. offers an attractive solution to these problems. Thus the beam size of a collider at the interaction point can be minimized by designing a zero dispersion straight section. Such a lattice is called an imaginary 7T lattice. a lower energy particle arrives later and gains more energy from the cavity. OFF-MOMENTUM ORBIT 139 Below the transition energy.29). when the beam is accelerated through the transition energy. microwave instability due to wakefields. A sudden change > > in the synchronous phase angle of the rf wave will not cause much beam dilution. IV. (2. the dispersion function can not be zero there. Thus the energy of the particle will becomes smaller than that of the synchronous particle. etc. Methods of achieving a negative compaction lattice will be addressed in Sec. Similarly. where the transition 7T is an imaginary number. with 0 < 0S < TT/2.8. This process gives rise to the phase stability of synchrotron motion. rf cavities. . such as FODO cells. and the straight section that connects arcs is usually called the insertion. On the other hand. and interaction regions for colliders. If the betatron and synchrotron motions are independent of each other. internal targets. In many applications.e.274) Particles are accelerated through the transition energy in many medium energy synchrotrons such as the AGS. the CERN PS. A zero dispersion function in the rf cavity region can also be important to minimize the effect of synchro-betatron coupling resonances. i. Particle motion in an imaginary 7T lattice is always below transition energy. etc.. needed for injection.245). An accelerator lattice with a negative momentum compaction factor. the Fermilab booster and main injector. i. 2. where ex.i{D)i9i < 0.4 Dispersion Suppression and Dispersion Matching Since bending dipoles are needed for beam transport in arc sections. the dispersion function should be properly matched in straight sections for optimal operation. Attaining an imaginary 7T lattice requires a negative horizontal dispersion in most dipoles. synchrotron motion around the transition energy region is very slow. and the KEK PS.ms + £>2(s) ((Ap/po)2>. Fortunately. beam loss and serious beam phase-space dilution can result from space-charge-induced mismatch. extraction. IV. The synchronous angle has to be shifted from (j>s ton — (j>s across the transition energy within 10 to 100 fis./?^ • (2 . insertion devices.=<*V 2. which simplifies lattice design.e. a higher energy particle arrives at the rf gap earlier and receives less energy from the rf cavity (see Fig.IV. the rms horizontal beam size is given by CT2(S) = /3i(s)e:t)1. the synchronous phase angle should be TT/2 < <f>s < n at 7 > j r . nonlinear synchrotron motion. Y. the dispersion function is usually constrained by the periodicity condition.64 We discuss here the general strategy for dispersion suppression.
65 Here M is the 2 x 2 transfer matrix of each cell.245). a strategy for dispersion function suppression can be derived.' f)- (?)-(••)(. Brown and R Servranckx. the dispersion function of the repetitive half achromat is D = d/2. Dispersion suppression Applying the first-order achromat theorem. [12].+ . D' = d'/2. If the dipole bending strength of the adjoining —I section is halved. We consider a curved (dipole) achromatic section such that Mn = I. The transfer matrix of n cells is R l = ^ ( M . and d is the dispersion vector. i. and / is a 2 x 2 unit matrix. (2. p. Let the 3x3 transfer matrix of a basic cell be where M is the 2 x 2 transfer matrix for betatron motion. Thus the achromat condition w = 0 can be attained if and only if Mn = I or d = 0. (d/2\ !/0\ «» = (-. The proof of this theorem is given as follows. the transfer matrix becomes _ and the dispersion function will be matched to zero value in the straight section. Eq. A unit matrix achromat works like a transparent transport section for any dispersion functions. + l)J^M» wy (2276) where w = (Mn — I)(M — I)'1^. .+ M .e.)• 65 See K.140 First-order achromat theorem CHAPTER 2. We note that one half of this achromatic section can generally be expressed as Using the closed-orbit condition. 121 in Ref. TRANSVERSE MOTION The first-order achromat theorem states that a lattice of n repetitive cells is achromatic to first order if and only if Mn = I or each cell is achromatic. An achromat section matches any zero dispersion function modules.
the beam closed orbit depends on particle momentum.5 Achromat Transport Systems If the dispersion function is not zero in a transport line. A. The double-bend achromat A double-bend achromat (DBA) or Chasman-Green lattice is a basic lattice cell frequently used in the design of low emittance synchrotron radiation storage rings. Is the dispersion function unique? A trivial corollary of the first-order achromat theorem is that a dispersion function of arbitrary value can be transported through a unit achromat transfer matrix.4 offers an example of an achromat. IV.iy>dy (2278) where M is the transfer matrix of the basic module with dispersion vector d. Is the dispersion function obtained unique? This question is easily answered by the closed-orbit condition Eq. IV. the dispersion function of an accelerator lattice is uniquely determined. The transport matrix of n identical modules is R"=(M. the fitting procedure is straightforward. Since the machine tune can not be an integer because of the integer stopbands. This is usually called the missing dipole dispersion suppressor (see Exercise 2. (2. With use of computer programs such as MAD and SYNCH. Using the closed-orbit condition. i. However. Eq. (M» -D(M . it is possible to design a transport system such that the beam positions do not depend on beam momentum at both ends of the transport line. OFF-MOMENTUM ORBIT 141 Thus we reach the conclusion that the matched dispersion function is equal to the dispersion function of the matched arc.e. a small modification in the quadrupole strengths is needed for dispersion suppression.245). A possible variant uses —I sections with full bending angles for dispersion suppression by varying the quadrupole strengths in the —I sections. The reduced bending strength scheme for dispersion suppression is usually expensive because of the wasted space in the cells. a 3 x 3 unit matrix.e. (2. Now we consider the case of an accelerator or transport line with many repetitive modules. In the case of unit transport. Such a beam transport system is called an achromat. any arbitrary value of dispersion function can be matched in the unit achromat.IV. we easily find that the dispersion function of the transport channel is uniquely determined by the basic module unless the transport matrix is a unit matrix.245) for the entire ring. i. A . When edge focusing is included. The achromat theorem of Sec. which however do not form a unit transfer matrix.4. Mn = I.3c).
4. where O and 0 0 can contain doublets or triplets for optical match. II. It is represented schematically by [00] B {0 QF 0 } B [00]. Lower plot: triplet DBA. the dispersion matching condition is (see Exercise 2. (2.28 °) Note that the focal length needed in the dispersion function matching condition is independent of the dipole bending angle in thin-lens approximation. The zero dispersion value at the entrance to the dipole is matched to a symmetric condition D'c = 0 at the center of the focusing quadrupole. Upper plot: standard DBA cell. 9 and L are the bending angle and length of the dipole. 2. The required focal length and the resulting dispersion function become f= \{Ll + \L)' D<=(Li + \L)e- ( 2 .30 shows a basic DBA cell. The top plot of Fig. In thin-lens approximation.280) renders a horizontal betatron phase advance $ x larger than n in the dispersion matching section (from the beginning of the dipole to the other end of the other dipole).13) [Dc\ 0 ( = 1 -1/(2/) 0 OWl Lx 0\ (I L L9/2\ 1 0 0 1 0 0 1 0 /0\ 0 .30: Schematic plots of DBA cells. TRANSVERSE MOTION DBA cell consists of two dipoles and a dispersion-matching section such that the dispersion function outside the DBA cell is zero. and it can easily be obtained from the geometric argument.6) indicates that betatron function matching section [00] can not . the betatron function depends on the magnet arrangement in the [00] section. where the quadrupole triplet is arranged to attain betatron and dispersion function match of the entire module. The dispersion function at the symmetry point is proportional to the product of the effective length of the DBA cell and the bending angle. and L\ is the distance from the end of the dipole to the center of the quadrupole. and possible other quadrupoles in the dispersion matching section.279) Vi ) \ o o i A o o i/\o o i M i / where / is the focal length of the quadrupole. The dispersion matching condition of Eq.142 CHAPTER 2. (2. Figure 2. where [00] is the zero dispersion straight section and {0 QF 0 } is the dispersion matching section. We consider a simple DBA cell with a single quadrupole in the middle. The stability condition of betatron motion (see Sec. Although this simple example shows that a single focusing quadrupole can attain dispersion matching.
R24 elements describe the linear .6 Transport Notation In many applications. OFF-MOMENTUM ORBIT 143 be made of a simple defocussing quadrupole. The design strategy is to use achromatic subsystems. or a triplet.3. An example of achromatic subsystem is the unit matrix module (see Sec. where a quadrupole triplet is located symmetrically inside two dipoles. Some properties of the triplet DBA storage ring can be found in Exercise 4. R23 Ru. Such DBA lattice modules have been widely applied in the design of electron storage rings. Achromatic modules can be optically matched with straight sections to form an accelerator lattice. medical radiation treatment. The achromatic transport system find applications in high energy and nuclear physics experiments.282) Note that the 2x2 diagonal matrices for the indices 1. (2. IV. j=i ( M = 1. and 5 = Ap/p0 is the fractional momentum deviation of a particle. 2.6. . Other achromat modules The beam transport system in a synchrotron or a storage ring requires proper dispersion function matching.4 are respectively the horizontal and vertical M matrices.16). The achromatic transport modules are also important in the transport beamlines (see Exercises 2. The transport of the state vector in linear approximation is given by Wiis2) = '£Rij{82\a1)Wj{81). The Ru.2. A quadrupole doublet. A simple DBA cell is the triplet DBA (lower plot of Fig. is usually used in the [00] section.281) \wj \ 6J PcAt where /3c is the speed of the particle.---. /3cAi is the path length difference with respect to the reference orbit. B. and 3.13 to 2. (2.6). the particle coordinates in an accelerator can be characterized by a state vector fWA W2 W5 ( x \ x' W= Z\ = I.JV.30). A unit matrix module can be made of FODO or other basic cells such that the total phase advance of the entire module is equal to an integer multiple of 2TT.4 on the first order achromat theorem).4. and other beam delivering systems.4. This compact lattice was used for the SOR ring in Tokyo. IV.
(2. and we obtain R l (2.C. D. The program TRANSPORT 6 6 has often been used to calculate the transport coefficients in transport lines. . particle transport through a thin sextupole is given by AT' _ S (r2 „. Here we used the convention that 5 > 0 corresponds to a focusing sextupole.R26 elements are the dispersion vector dot Eq. FNAL Report TM-1046 (1981). 72\ A. Carey et al. we get the momentum compaction factor as ac = R56. 233 — X ) J . the nonlinear dependence of the state vector can be expanded as Wi(s2) = J2RijWj(s1) + 3=1 3=1 k=l 1=1 J:J2TijkWj(s1)Wk(sl) 3=1k=l + E E E ^yH^(ai)W*(«i)Wi(«i) + • • • • For example.C. Without synchrotron motion. 66K. D. Brown. Fermilab-Pub-98-310 (1998). Rothacker. . The corresponding transport matrix elements are Ti2 1 1 Q U rp J ^ c rp Q ——7T.i l i — i>. D. The Ri6. In general.283) x z z x z5 x5 zS2 xS2 T . CERN 80-04 (1980). Tracing the transport in one complete revolution.C. Carey. we have R55 = Re6 = 1. TRANSVERSE MOTION betatron coupling. Iselin and F.144 CHAPTER 2.+ 1 11 - l •n-21 — —~c. All other elements of the R matrix are zero.275). •••. ^436 = — T J (^2166 — ~ 7 i ^4366 = + T - Similarly.' S where 5 = —B^tjBp is the integrated sextupole strength.L. Ch. Carey. -^43 = +"7i -1216 — + 7 . SLAC-R-530. particle transport through a thin quadrupole is given by .
The slope of this measurement is used to obtain the "measured" dispersion function.co is the closed orbit. The lower plot compares the measured dispersion function (rectangles) with that obtained from the MAD program (solid line). The resulting closed orbit will have the characteristic modulation frequency. the fast betatron oscillations are averaged to zero. On the other hand. 2.31 shows the closed orbit at a BPM location vs the rf frequency at the IUCF Cooler Ring. In the lower plot of Fig. Fitting the resulting closed orbit with the known modulation frequency. (2. Using Eq. A high dispersion straight section is used for momentum-stacking injection and zero dispersion straight sections are used for rf and electron cooling.284).e. we can determine the dispersion function more accurately.13). Figure 2. we can deduce the dispersion function at the BPM location.31: The upper plot shows the closed orbit at a BPM vs the rf frequency for the IUCF Cooler Ring. The upper plot of Fig. and also on the effects of power supply ripple. The dispersion function can be measured from the derivative of the closed orbit with respect to the off-momentum of the beam.4. OFF-MOMENTUM ORBIT 145 IV. To improve the accuracy of the dispersion function measurement. 2. if the BPM signals are sampled at a longer time scale. . r\ is the phase-slip factor. / 0 is the revolution frequency. dxco D dxco OQA\ (2 ' 284) = d[K^)=~rik^ where a.IV.67 The accuracy of the dispersion function measurement depends on the precision of the BPM system. i. and the momentum of the beam is varied by changing the rf frequency. 67Note here that the IUCF Cooler Ring lattice belongs generally to the class of double-bend achromats (see Exercise 2. The DC output provides the closed orbit of the beam.7 Experimental Measurements of Dispersion Function Digitized BPM turn by turn data can be used to measure the betatron motion.31 the "measured" dispersion functions of the IUCF Cooler Ring is compared with that obtained from the MAD program [19]. we can induce frequency modulation to the rf frequency shift.
and the design principle of the imaginary 7T lattices. This is called the "negative momentum compaction" or the "imaginary j T " lattice. The revolution period deviation AT for an off-momentum particle Ap = p — p0 is given by Eq. To avoid all the above unfavorable effects. p. For example. IV). Here we examine the strategy of 7T jump schemes pioneered by the CERN PS group. We discuss below the methods of ac manipulation. These problems can be avoided by an accelerator having a negative momentum compaction factor. Risselada. The jT jump schemes have been used successfully to ease beam dynamics problems associated with the transition energy crossing. Proc. which leads to unstable longitudinal motion resulting in serious beam loss. 1991. Since the frequency spread of the beam Aw = —T]u)(Ap/p0) vanishes at the transition energy. 161. 1974). (2. Hardt. DC. causing beam loss (see Chap. particle acceleration through the transition energy is unavoidable. 3. on High Energy Accelerators (USAEC. Furthermore. The accelerator becomes isochronous at the transition energy (7 = 7 T ).68 6 8 W. it is appealing to eliminate transition crossing. 7T jump schemes In many existing low to medium energy synchrotrons. Proc. CERN Accelerator School. VII). there is little or no Landau damping of microwave instability near transition (see Chap. Alternatively. CERN-91-04.146 CHAPTER 2. Con}. Sec. A. 3. All modern medium energy synchrotrons can be designed this way to avoid transition energy. the bunch area may grow because of collective instabilities. such as longitudinal microwave instability and nonlinear synchrotron motion. particles with different momenta may cross transition at different times. one can design an accelerator lattice such that the momentum compaction factor ac is negative.8 Transition Energy Manipulation Medium energy accelerators often encounter problems during transition energy crossing. 9th Int. See also T. There are many unfavorable effects on the particle motion near the transition energy. As a result. the momentum spread of a bunch around transition can become so large that it exceeds the available momentum aperture. and thus the beam never encounters transition energy. TRANSVERSE MOTION IV.268). the transition energy jump scheme. Washington. . Sec. Finding a suitable 7T jump scheme can provide beam acceleration through transition energy without much emittance dilution and beam loss. This has become a routine operation at the CERN Proton Synchrotron (PS). in these schemes some quadrupoles are pulsed so that the transition energy is lowered or raised in order to enhance the acceleration rate at the transition energy crossing.
and D* is the perturbed dispersion function at s = Si.so)—dso « £G s (s. s i)Ki. we obtain C0Aac = -*£ KiD'Di. is the dipole angle. If N 7 T -jump quadrupoles are used to change the momentum compaction factor. (2-289) Thus we usually employ zero tune shift quadrupole pairs for the 7T jump. t (2.IV. An important constraint is that the betatron tunes should be maintained constant during the 7T jump in order to avoid nonlinear betatron resonances. the closed orbit is Axco(s) = Js rs+C 147 Gx(s. assumed positive for a focusing quadrupole. /\B (2-285) where 9^ is the dipole angular kick in thin-lens approximation. (2. A(2s = 7 .fe KiDtD^J 5.287) where A is the unperturbed dispersion function. From Hill's equation. Thus the change of the orbit length for the off-momentum particle is given by AC « £ DA « . N (2. = --?-][X i tf i = 0. the angular kick resulting from the ith 7T jump quadrupole is given by 9t = -Ki \xC0{Sl) + D*5]. i.288) Note that the change in momentum compaction (called jT jump) depends on the unperturbed and perturbed dispersion functions at kick-quadrupole locations. the dispersion function is given by D(s0) = [C Jo Gxi"'"o)ds p(s) « £ Gx(sh 30)9. and GX(S. (2. AQ.I The effect of quadrupole field errors on the closed orbit Consider T quadrupoles for the 7T jump.264) where 0. Similarly..159). Equation (2. A. (2. We would like to evaluate the change of V orbit length for off-momentum particles due to the 7T jump quadrupoles.287) indicates that quadrupoles at nonzero dispersion locations can be used to adjust the momentum compaction factor.e. Note here that the kick angle 9t from quadrupoles at nonzero-dispersion function locations can be used to perturb the dispersion function and change the orbit length for off-momentum particles. .SQ) is the Green's function of Eq.£ / M ^ = °. OFF-MOMENTUM ORBIT In the presence of dipole field error.286) where Ki = —Bii/Bp is the strength of the zth 7T jump quadrupole. and we neglect higher-order terms in 5.
285): [D*{s) ..£ KiD\ + £ KiKjGx(si. ..)D. The resulting change in momentum compaction becomes N (2.295) (2.F)~XQ = (1+ F + F2 + F3 + .. (2.294) This result can be easily proved by using the zero tune shift condition: /3XtkKk + Ar.. TRANSVERSE MOTION A. s^KiD* 6. Using the 7r-doublets.292) C0Aac = -*£Ki(l ij + F + F2 + .) y I>iA. sjDiDj. and the change in the momentum compaction factor is given by C0Aac = .3 7 T jump using zero tune shift 7r-doublets When zero tune shift pairs of quadrupoles separated by IT in the betatron phase advance are used to produce a jT jump. the matrix F satisfies Fn = 0 for n > 2. cos{nvx .D{s)} 5 = . The perturbed dispersion function at these quadrupole locations can be solved to obtain D* = (1 .cos(7T!/a. i (2-291) where Fji = —Gx(sj.ipk\) = . (2-293) A.2 The perturbed dispersion function The change in the closed orbit resulting from the quadrupole kicks can be obtained by substituting Eq.fc+ijKWi = 0 and the -K phase advance condition: COS(7TZ/X \tpk .\ipi . (2.290) Thus the closed orbit solution is Di=Dj + '£FjiB'i. (2.148 CHAPTER 2. the perturbed dispersion function becomes DT^il + F^Dj. i ij (2.\ipi - ipk+1\).C O S ^ \ipk+i 1pj\).1pj\) = .286) into Eq.296) Here three points are worth mentioning: .Si)Ki. i (2.£ Gx(s.
and thus £ 4 KiDf <x J \ Kifii = 0 because of the zero tune shift condition. thus making a negative momentum compaction factor. 2829 (1991). Teng proposed an innovative scheme using negative dispersion at dipole locations. Part. The change in the momentum compaction factor contains a linear and a quadratic term in K.e. Fermilab (1988). 3. the 7r-doublet does not produce a large perturbation in the betatron amplitude function. On the other hand. Thus if all quadrupoles used for 7T jump are located in FODO cells. 915 (1989). In 1972. the amount of tune jump is second order in the quadrupole strength.C. IEEE Trans. ) ^ % 149 2.71 In this method a systematic closed-orbit stopband is created near the betatron tune to induce dispersionwave oscillations resulting in a high 7T or an imaginary 7 T . Sci. 72 L. Garren. 1955). AA = D* . a lattice having a very small or even negative momentum compaction factor can also be designed. Technical Memo. s . Vladimirskij and Tarasov70 introduced reverse bends in an accelerator lattice and succeeded in getting a negative orbit-length increase with momentum. 71 R.A = -<?. the resulting lattice is less tunable and the dispersion functions can be large. (2. p. Since the stopband integral of Eq. where the dispersion function can be matched by a straight section with a phase advance of TT to yield little or no contribution to positive orbit-length increment. Another method of designing an FMC lattice is called the harmonic approach.M. If the zeroth harmonic term dominates. Accel. Tarasov. . Courant. Proc. Teng. 70 V.D. Wienands. Thus the dynamical aperture may be reduced accordingly. Vladimirski and E. NS-32. G. 81 (1972). 1991 IEEE PAC. 69 This statement can be expressed mathematically as follows. i. the term linear in Ki vanishes because of the zero tune shift condition.69 The resulting change in the momentum compaction factor is a quadratic function of Ki. Theoretical Problems of the Ring Accelerators (USSR Academy of Sciences. we have D\ oc ft. T.IV. p. 2308 (1985). OFF-MOMENTUM ORBIT 1.72 This concept is the basis for flexible momentum compaction (FMC) lattices. Botman. Proc. 1989 IEEE PAC. and U. The change in the dispersion function is linear in K. 4. Guignard.K. Gupta and J. Nucl. However. Moscow.(*. 7T jump using quadrupoles in straight sections can be made linear in quadrupole strength.I. Collins. If the 7T jump quadrupole pairs are located in the arc. E. Flexible momentum compaction (FMC) lattices Alternatively.201) at p = [2vx] due to the tune jump quadrupole pair is zero because of the zero tune shift condition. where the unperturbed dispersion function is dominated by the zeroth harmonic in the Fourier decomposition. A.V. Beta Theory.A. which require parts of the lattice to have negative dispersion functions. B.
Y. TRANSVERSE MOTION Recently.74 F D CL O O EL QF/2 B Q D B Dispersion Matching Section Q r l QD2 F D CL O O EL B i i QD B QF/2 ni i i I I i 11 l i i r n I n i i i m i i l l i i n i l in I Ma Mb Mc Figure 2. Trbojevic.260) are handy. Rev. the normalized dispersion vector changes by AP = \fp\B and AX = 0. Tepikian. the dispersion function satisfies the homogeneous equation. Outside the dipole (p = oo). Proc. For attaining proper dispersion function matching.e. D. 3040 (1993). S. and S. Ng. The module forms the basic building blocks for a ring with a negative momentum compaction factor or an imaginary j T . P = Jfciy +-?£=D =-yfiTiSiniii. K.32: A schematic drawing of a basic module made of two FODO cells and an optical matching section. D. 1991 PAC. the maximum value of the dispersion function can be optimized to less than that of the FODO lattice. K. This dispersion phase-space plot can be helpful in the design of lattices and beam-transfer lines.d. Lee. S. i. 168 (1993). Proc. Therefore. The dispersion phase-space maps are carefully matched to attain a lattice with a pre-assigned 7T value. 1990 EPAC. and S. In the thin-element approximation. K. p.Y. Trbojevic. i. E48. the normalized dispersion coordinates Xi and Pi of Eq. 74 D. B. Lee.i and X^ lie on a circle P2 + X2 = 2JdThe phase angle ipd of the normalized coordinates is equal to the betatron phase advance. Ng. . 159 (1991).244) indicates that AD = 0 and AD' = 6 in passing through a thin dipole with bending angle 9. Fermilab Internal Report FN-595 (1992).Y. X = -L. and S. and 73 D. 1993 IEEE Part. p.Y. (2. at the same time. and the dispersion action J^ is invariant. P. Conf.D = y2JdCos</. in normalized Pd-X^ space. Holmes. It has also been used to lower the dispersion excursion during a fast 7T jump at RHIC. 1536 (1990).150 CHAPTER 2. Peggs. S. Trbojevic.I The basic module and design strategy A basic FMC module has two parts: (1) the FODO or DOFO cell.Y. Phys. Proc.e. Trbojevic. Lee. and D. Gerig. Ng. Accel. Finley. R. Eq. (2.Y. Trbojevic et al. The module can be made very compact without much unwanted empty space and. and D. where the negative dispersion function in dipoles provides a negative momentum compaction factor.73 re-introduced a modular approach for the FMC lattice with a prescribed dispersion function. Trbojevic. p.
2.32: Ma j .IV. /3p and D? are respectively the betatron amplitude and dispersion functions at the center of the focusing quadrupole for the regular FODO cell. (2. the momentum compaction factor of the accelerator can be varied. the dispersion phasespace coordinates are located on a circle as shown in Fig. 2. 2. 75The packing factor is defined as the fraction of the circumference of an accelerator that is occupied by magnets. Although not strictly necessary. We also assume reflection symmetry for all Courant-Snyder functions at symmetric points of the module. The right plot shows a similar plot in thin-lens approximation. and S's stand for dipoles. The horizontal betatron transfer matrix of the FODO cell from the marker Ma to the marker Mb is given by [see Eq. Although they look slightly different. we have chosen <&x = $ z = $ for the betatron phase advance of the FODO cell. we consider a basic module composed of two FODO cells and a dispersion matching section shown schematically in Fig. Detailed matching process is given in following subsections.c are marker locations. O's are drift spaces.297) . Then. Q's are quadrupoles. (2. Figure 2.4. reflection symmetry considerably simplifies the analysis and optical matching procedure. Figure 2.34. the dispersion function is propagated through FODO cell to obtained a dispersion vector at the marker Mj. Adjusting the initial dispersion function value Da. Since there is no dipole in this example shown in Fig. First. for simplicity. For example. If the lattice has a reflection symmetry at the marker Mc.34 shows an example of dispersion function matching for an FMC module by plotting the normalized dispersion phase-space coordinates X& vsPj. the thin-element approximation can provide essential insight in the preliminary design where dispersion matching is required. (2.34. the desired value Da of the dispersion function at the marker Ma is chosen. The procedure of betatron amplitude function matching is given as follows. ( cos$ -^sin$ /3 F sin$ cos$ DF(l-cos$)\ | f sin $ . the dispersion function is matched in the matching section.Q F B QD B -QF j Mb {Q Fl Oi QD 2 O2} M C + reflection symmetry .32. the matched dispersion phase-space coordinate is Pd = 0. A negativemomentum-compaction module requires X& < 0 in dipoles as demonstrated in the left plot of Fig.3] 0 0 I ) where. 2. and a symmetry condition /?F = 0 and D'F = 0 is assumed to simplify our transfer matrix in Eq.297).75 Because the dispersion function inside dipoles in FODO cells is mostly negative. OFF-MOMENTUM ORBIT 151 (2) a matching section that matches the optical functions.33 shows the betatron amplitude functions for a matched FMC basic module with an added dipole in dispersion matching section in order to increase the packing factor.257) and Exercise 2. the resulting momentum compaction factor can become negative. where Majb.
b = \ ^ + foDb ] = Jdj?[l .2 Dispersion matching The dispersion function at the beginning of the FODO cell is prescribed to have a negative value of Z?a with D'& = 0. TRANSVERSE MOTION Figure 2.C) cos $ + (1 . B. D'h = DF~D* Pb sin <> .£>a) cos $ . In this example. and the dispersion action is invariant in this region. Jd.C)2] . Jd. (2. The overall compaction factor can still be adjusted by a properly chosen Da.35 shows \/Jdtb/Jd.2(1 . E (2. Now we assume that there is no dipole in the matching section.297). and it increases when the initial dispersion £>a at marker Ma is chosen to be more negative.299) where £ = L>a/Dp is the ratio of the desired dispersion at marker Ma to the dispersion function of the regular FODO cell. and J^p is the dispersion action of the regular FODO cell at the focusing quadrupole location. It is preferable to have a smaller dispersion action in the matching section in order to minimize the dispersion function of the module.33: The lattice function of an FMC basic module. (2. Using the transfer matrix in Eq. we find the dispersion function at marker Mb to be Db = DF~ (DF . . Although the dipole in the matching section will contribute a positive value to the momentum compaction.F as a function of ( for various values of phase advance per cell. The ratio of the dispersion action has a minimum at ( = 1 — cos $. i. given in thin-lens approximation by v4k c o 3 E:j s i 1fi2[ sin3 f (1 + sinf) J <2'»> Figure 2. a dipole is added in the middle of dispersion matching section in order to increase the machine packing factor. As we shall see.e.c = J*.c are dispersion actions at markers Mb and Mc. the choice of D a essentially determines the dispersion excursion and the 7T value of the module.152 CHAPTER 2. Jd.b.298) where /?b is the betatron amplitude function at marker Mb with /3b = /3F.
The dispersion matching condition at marker Mc is D'c = 0. The betatron transfer matrix for the matching section is / M6_>c= y^cos^ —ri=sinV> V^ScSinV ^/¥cosip 0\ 0 .IV. and we have assumed the symmetry conditions /3b = 0 and /3'c = 0 for the Courant-Snyder parameters.A compromise choice for the phase advance of the FODO cell is between 60° and 75°. (2.298). However. we obtain 1-(1-C)cos$ v ' .300) is inversely proportional to (sin($/2)) 3 / 2 . and thus we should choose a larger phase advance for the FODO cell in order to obtain a smaller overall v/2Jd. where the normalized dispersion phase-space coordinates X& = Z)/\/S v s Pd = {otx/VPx)D + yffi^D' are shown. where horizontal steps are associated with a dipole that is divided into three segments. ij. is the betatron phase advance between Mb and Mc. OFF-MOMENTUM ORBIT 153 Figure 2.c. (2. The normalized dispersion phase-space coordinates for periodic FODO cells are marked "FODO CELLS.34: Left: an example of dispersion matching for a basic FMC module. the dispersion amplitude i/2J d F in Eq.35 that a smaller phase advance in the FODO cell would be preferred. 2. Using Eq. The dispersion functions and other Courant-Snyder parameters are then matched at the symmetry point at marker Mc with a doublet (or triplet). There is no dipole in the matching section and thus the normalized phase-space contour is a perfect circle in the matching section." The corresponding thin-lens approximation for the FMC is shown in the right plot. One might conclude from Fig. (2. This can be true if we compare the dispersion of the basic module with that of the regular FODO lattice with the same phase advance.301) V o 0 1 / where /3b and /3C are values of the betatron amplitude function at markers Mb and Mc.
17). or a low-beta insertion with doublets or triplets for the matching section. (2.35: Ratio of dispersion actions Jd. Figure 2. Figure 2. the phase advance ip and the quadrupole strengths in the dispersion matching section are constrained by the stability condition of betatron motion (see Sec. TRANSVERSE MOTION Figure 2. Furthermore. C « -0.4. The total phase advance of the whole basic module is then given by 2($ + ip). Quadrupoles QFI and QD 2 m the matching section can be adjusted to attain the required phase advance if] given by Eq. This means that the phase advance of the matching section is not a free parameter.F as a function of £ = £>a/DF for various values of phase advance $ in the FODO cell. B. II.302) and to produce low betatron amplitude functions at marker Mc.6 and Exercise 2.b/Jd. the values of the dispersion function at the midpoints of dipoles in the FODO cell are given by . This condition is independent of whether we use a FODO-type insertion.36 shows the required betatron phase advance 2ip (in unit of 2n) in the matching section as a function of phase advance $ of the FODO cell for various values of C = D^/D^.3 ~ -0. which is a function only of the desired dispersion function at marker Ma and the phase advance $ in the FODO cell.36 shows the total phase advance of the whole module as a function of the phase advance of the FODO cell for £ = —0. but is determined completely by the initial dispersion value _Da at marker Ma and the phase advance of the FODO cell. To achieve a |TT phase advance for a quarter-wave module.6.3 Evaluation of momentum compaction factor In small-angle approximation.3 to —0.4 and a phase advance per FODO cell of $ = 60° to 75° can be used.154 CHAPTER 2.
the phase advance of the FODO cell. .^(y/Sl + 8S+ + SI) + j ( v t e + 8S+ .36: Left: Phase advance in the matching section as a function of phase advance $ in the FODO cell for various values of C = D&/DF.) .303) should be modified as follows: DBl = £>. we obtain qc _2LU-2S65 2 .2S3 5 2 (5 + 25) 1 C+ ^ ^ .306) +1* [| +1(^/5!+8S + -S_)]. Note that the momentum compaction factor of the module is determined entirely by the choice of £>a. (2.L^ [ 4-2S-S 2 4-2S-H ' (2-3°5) where S = sin($/2).IV. The momentum compaction factor should be modified accordingly. Eqs.|^+] l-L6. In comparison with the momentum compaction factor of a lattice made of conventional FODO cells. [l . The momentum compaction becomes where 9 is the bending angle of each dipole and L m is the length of the half-module. Right: The total phase advance of a FMC module as a function of the phase Advance $ in the FODO cell for various values of <: = DJDF.^(y/Sl+8S+ + S_)] + < DB2 = D* [l . the momentum compaction factor depends linearly on the initial dispersion function £>a. and the ratio of the lengths of the FODO cell and the module. (2. If the horizontal phase advance <&x of the FODO cell differs from its vertical phase advance <£z. where S± = sin2 ^$x ± sin2 | $ z . OFF-MOMENTUM ORBIT 155 Figure 2. When the length of the module is constant.S.
or a triplet. D. The dispersion function inside a sector dipole is given by D(s) = p(l . In general. and rf cavities.iAn\* . Other similar FMC modules CHAPTER 2. If the achromat condition is imposed. a doublet. The dispersion matching section on the right side of the dipole can be made of a single quadrupole. a slightly smaller |£| can be used to minimize the magnitude of the dispersion function in the module.e. j3D. D F . the module is called a double-bend achromat (DBA). . FMC in double-bend (DB) lattices A double-bend module (Fig. (2./fcosf* DF-DD^ cos^ -fl-ft-sinf* ' (2-307) V o o i ) where <> is the phase advance of a FODO cell. Because the dispersion value at the defocussing quadrupole location is smaller than that at the focusing quadrupole location.308) (2.4.30) is made of two dipoles located symmetrically with respect to the center of the basic module given by Ma / Triplet \ or B {dispersion matching section} Mc + {reflection symmetry}.156 C. The betatron transfer matrix in the DOFODO cell becomes ' V^ c o s f* Ma^b= _ i s i n | $ y[hh. V Doublet/ A triplet or doublet matching section on the left side of the dipole B is the betatron amplitude matching section. D'{s) = s i n < £ . DD are the betatron 3 amplitudes and dispersion values at the focusing and defocussing quadrupoles of the FODO cell. the result will be a larger total dispersion value. TRANSVERSE MOTION The above analysis can be applied to a basic FMC module composed of two DOFO cells and a dispersion matching section (see Exercise 2. The zero dispersion region is usually used for insertion devices such as the undulator. 2. three FODO cells instead of two are placed inside a basic module. A similar analysis with a different number of FODO cells can be easily done.17).309) 76 The packing factor of a lattice is defined as the ratio of the total dipole length to the circumference.cos <£) + Do cos <f> + pD'o sin 0. and /3F.76 one may use a DOFODO in place of the FODO cell. the wiggler. i. To design a lattice with a higher packing factor.— s i n <1> + D'O c o s <j>.
In this section. Finally. a reverse-bend dipole placed at the high dispersion straight section can also be used to adjust the momentum compaction factor of a DBA lattice. the strategy of minimizing {%} inside dipoles will be discussed.cosl?) J where Lm is the length of one half of the double-bend module.312) where R is the average radius of the storage ring. The dispersion function in the rest of the module can be matched by quadrupole settings.9 Minimum {H) Modules In electron storage rings.c o s 0 ) .313) . the momentum compaction in small dipole angle approximation becomes acDBA « ^ (2. Since the DBA module has Do = 0 and D'Q = 0.2a o psin0(l . In small-angle approximation. OFF-MOMENTUM ORBIT 157 where p is the bending radius of the dipole. 8 = L/p. the momentum compaction is given by ac = -f-\e-sin9+— Lm I p sin 8 + D'0{l.11) H = n0+2(a0D0+/3oD'Q)sin(f>-2(jQD0 + aoD'0)p(l-cos(l>) +A)Sin20 + 7op2(l -coscp)2 . For a matched double-bend module.IV. and Do a n d D'o are respectively the values of the dispersion function and its derivative at s = 0. (2. IV.l . The evolution of the "H-function in a sector dipole is given by (see Exercise 2. The momentum compaction factor of a DBA lattice is independent of the betatron tune. the natural (horizontal) emittance of the beam is determined by the average of the ^-function in the dipoles (see Chap. we will consider a single dipole lattice unit where the dispersion and betatron amplitude functions can be independently controlled. <t> = s/p is the bend angle. (2. Such a lattice can provide a small-emittance negative momentum compaction lattice for synchrotron radiation sources.4. To simplify our discussion. 4). and d'o = D'o/8. the condition for negative momentum compaction is given by 6do + 3 d ' o < .311) where d0 = D0/L0. and L is the length of the dipole. Note here that the momentum compaction factor depends on the initial dispersion function at the entrance of the dipole.
158 CHAPTER 2. TRANSVERSE MOTION where "Ho = jaD^ + 2a0D0D'0 + PoD'o> a0.E -> 1. With the normalized scaling parameters do = % d'o =^ . A = -S^P°3> 77 The (2-318) average of the ti function is given by (H) = j f n(4>)ds = \ j H(4>)d4>. (2. 7o = 7o^. (H) ~ p93. and <f> = s/p is the coordinate of the bending angle inside the dipole. we obtain (H) min . the average %-function becomes (-H) = p63i[jQdl + 2aodod'o + Pod2 + (aoE-^F)do +0OE . (2. +|cj .e.B -t 1.| F ) 4 + kA-^B Note that (H) obeys a scaling law. the average ^-function is {U) = p9*^A-^B + ^c}. and Fm 2(1-cos 0) 6-8cos0 + 2cos20 = gi ' 6(fl-sinfl) C 6fl-3sin2fl p • 30^ . (2.315) where L = p9 is the length of the dipole.40sin0 + 5sin20 W = B(9) In the small-angle limit. /?0. Li JO <> Jo . A ^ 1. The average H-function in the dipole becomes77 {%) = n0 + (a0D0 + poD'0)02E(e)-l-(y0D0 + a0D'0)pe2F(9) (2-314) +^<PA(0) . i. and F ->• 1.C -t 1.^ B ( J ) + ^ C ( » ) > where 6 is the bend angle of the dipole. j 0 . Minimum (^)-function with achromat condition In the special case with the achromat condition d0 = 0 and d'o — 0. Po = ^.316) A.317) Using the condition /3o7o = (1 + do). ao=ao. Do and D'o are the Courant-Snyder parameters and dispersion functions at s = 0.
the dispersion matching quadrupole at the center is also split into two in order to leave space for a sextupole. The evolution of the betatron amplitude function in the dipole can be obtained from Eq. 2. 2. The APS lattice has 40 superperiods so that the circumference is 1104 m. XA) in Fig. Figure 2. Px is minimum inside a dipole in order to attain a minimum (H). Note that (W) is slightly smaller in a long dipole because of the 1/p2 focusing effect of the sector dipole. we show the normalized dispersion coordinates (Fd.39.28 x 10~4 in agreement with that of Eq.15B2. The momentum compaction factor is QC = 2. The tunes of this lattice are Qx = 35. In the small-angle approximation.312).38: The low emittance lattice functions for a superperiod of APS. Here. The ME lattice data are for minimum (U) without the achromat constraint. the minimum betatron amplitude and its location are given by S--^-L 4v/6Q^' s* Smin.298.37: The minimum (H) factors G = V16AC .A - - -3L g ^- Figure 2.15B2_ for the DBA (lower curve) and G = VlSAC . The factor G = \/16AC — 15B2 (see Fig.37) decreases slowly with increasing dipole bending angle 6 because of the horizontal focusing of the bending radius.IV.56). In the APS lattice. /?0 = Vl2 CJy/EG and a0 = &B/G.38 shows the betatron amplitude functions of a low-emittance DBAlattice at the advanced photon source (APS) in Argonne National Laboratory.219. Qz = 14.A Pmin.15B2 for the ME (upper curve) lattices are plotted as a function of the bending angle 0. OFF-MOMENTUM ORBIT 159 Figure 2. where G = V16AC . (2. To study the behavior of the lattice dispersion function. where the dipole has been split into 10 . (2.
TRANSVERSE MOTION slices in order to show the propagation of the normalized dispersion coordinates inside a dipole. Since the lattice is designed to minimize (H) inside dipole. the details of emittance minimization procedure will be addressed in Chapter 4.38 for the corresponding lattice functions. (2. the normalized dispersion coordinates are small (to be compared with that shown in Fig. minimization of the ^-function can be achieved through the following steps.28).a0B + ^6) . employ low emittance DBA-lattice for their storage ring. (H) can be minimized by finding the optimal dispersion functions with dd0 ' dd'o to obtain dOMa = ^F.319) (H) = ^ (fa* . APS. Note that the achromat section of the DBA lattice is located at the origin X d = P d = 0. Since we emphasize the dispersion function in this section. etc.320) where A = 4A-3E2. we obtain the minimum (H) as Using the relation $. 2. 2. III. See Fig. B.160 CHAPTER 2. {nUn=iimp93' (2'321) . The resulting (H) becomes d'0. First.£ . JSRF.39: The normalized dispersion coordinates for the low emittance APS lattice is shown in one superperiod.B = W-2EF.C = \C-\F2.7o = 1+djj. In the dispersion matching straight section.min = . ELETTRA. Many third generation high-brilliance light sources such as the ESRF. the normalized dispersion phase-space coordinates are located on a circle with the center at the origin. Sec. Figure 2.. (2. Minimum (%) without achromat constraint Without the achromat constraint.
15B2 (see Fig. i. Exercise 2. 2. Show that the solution can be expressed as fD(s)\ (Do\ (?) ""(?)• where the transfer matrix is ( cos VKs -V^sinv^s -^ sin VKs cos y/Ks ^ (1 .4 161 where G = y/l6AC . Even though the minimum (7i) is one third of that with the achromat condition. Computer codes such as MAD [19] and SYNCH [20] can be used to optimize {%). i. In actual machine design. the required minimum betatron amplitude function is less stringent.37).4.cos VKs) \ ^sin^s . The corresponding minimum betatron amplitude function at the waist location is /^ i n = L/\/60 in small-angle approximation with 9 < 1. combined-function magnets with defocussing field may be used (see Exercise 2. Let DQ and D'Q be the dispersion function and its derivative at s = 0.EXERCISE 2.4 1. s* — L/2. The dispersion function in a combined-function dipole satisfies the equation D" + KXD = 1/p . (a) Show that the solution for constant Kx = K > 0 is D = a cos VKs + 6 sin VKs + ijpK. Thus the minimum (H) without achromatic constraint is a factor of 3 smaller than that with the achromat condition.e. I o o ) .18). where we will find that (H)min is actually larger than for a separate function lattice.e. R* "min = -/?* o^rnii^A" The corresponding maximum betatron amplitude function will be reduced accordingly. The betatron amplitude function at the minimum (%) is The waist of the optimal betatron amplitude function for the minimum (7i) is located at the middle of the dipole. We have discussed the minimum (H) only in sector dipoles.
2. show that the horizontal transfer matrix is (see Exercise 2. Each FODO cell is given by [iQF B QD B ±QF].3) /I M rectangu i ar dipoie = 1 0 \0 psinfl 1 0 p(l-cosfl)\ 2 tan(6>/2) . Use the thin-lens approximation to find the phase advance per cell and the betatron and dispersion functions at the focusing quadrupole.249).162 CHAPTER 2. and B is a dipoie with bending angle 9. 2. Ja(QD) as a function of the phase advance per cell < . The bending arc of an accelerator lattice is usually composed of FODO cells. (b) Simplify your result in part (a) with $ x = $ z = $ and calculate the dispersion actions Jd(QF). TRANSVERSE MOTION (b) Show that the transfer matrix for constant Kx = K < 0 is / coshv/JK|s -J=SmhJ\K\s cosh ^/\K~\s 0 ^(_l + C osh7iK| 5 )\ Af=L/[Ffsinh v PT'S V 0 —L. (a) Using thin-lens approximation. where QF and QD are the focusing and defocussing quadrupoles with focal length f\ and —farespectively. where / is the focal length. show that the dispersion function and the betatron amplitude functions are given by R Px'F L Z 1 ^ sin($x/2)Vl-T+' ft Px'D L l^-T+ sin($x/2) V 1 + T_ ' where 5± = sin 2 -^±sin 2 -^. . T± = ±(y/Sl+&S+±sS). and $ x and $ z are the horizontal and vertical betatron phase advance per cell. and £ and 9 are the length and bending angle of the dipoie. show that the transfer matrices M for quadrupoles and dipoles become / M q u a d i o o\ o 1/ Mdipoie= /i 0 e ee/2\ 1 8 = V o . (c) Part of the SYNCH program input deck for the TEVATRON (1988) is given below. Plot & Jd(QF)/J d (QD) as a function of $.I f f1 0 .sinh v/LKTs • 1 ) (c) Show that the transfer matrix of a sector magnet is given by Eq. (2. 1 / where p and 9 are the bending radius and the bending angle. Let L be the half cell length. Vo o i / . (d) For a rectangular magnet. (e) In thin-lens (small-angle) approximation.
702 BZ = 44. Estimate the momentum beam size vs the betatron beam size in the arc. The arc section is composed of regular FODO cells with bends. kG-m. a l l quads run a t same e x c i t a t i o n a s t h e C 35 t u r n .60038 C magnet d e c l a r e : length g r a d i e n t brho dipole type B MAG BL 0. kG/m.14028 00 000 DRF 0. I AGS Lceii (m) 13.4 163 TEV RUN DOUBLER LATTICE C DOUBLER l a t t i c e u s i n g two s h e l l normal quads and s p e c i a l C l e n g t h matching quads. RHIC and SSC lattices in thin-lens approximation. (2. V 0 0 1 / .45 $ (deg) 52.67894 0 DRF 0.EXERCISE 2.6 180 97.27664 GF = 760. and Ls and L a are the length of the straight section and the arc. 3.32056 BL = 6. Show that the 3x3 transfer matrix of a repetitive cell is generally given by Eq.001 | 0.m) 30 (Ap/p o ) rms I . Show that the transfer matrix of repetitive FODO cell is / cos* M = I -7Fsin$ /3 p sin$ cos$ 2£> p sin 2 ($/2)\ 7 F D F sin$ . and the straight insertion section is composed of quadrupoles without dipoles. kG.32056 GD = -760. 21 f o o t d i p o l e s .0001 (e) A collider lattice is usually made of arcs and insertions.257).5 Energy (GeV) 25 eN(w/j.2794 DRF 2.96 90 90 90 250 1000 20000 8000 30 30 10 15 I 0.1214 QL = 1. The dispersion suppressor matches the dispersion function in the arc to a zero dispersion value in the straight section. C A l l q u a n t i t i e s i n u n i t s of m. BRHO BZ $ QF MAG QL GF BRHO QD MAG QL GD BRHO C beam l i n e declaration f o r a CELL HC BML 00 B 0 B 0 B 0 B 000 CELL B L M Q D HC QF HC (d) Use the data in the table below to estimate the dispersion function of AGS.0001 | 0. Show that the momentum compaction factor of such a lattice is given by 1 aC^a2rc(l+£a/£a)' where 27ri>arc is the total accumulated phase advance in the arcs.003 | 0.005 I RHIC I Tevatron I SSC 1 LHC 29. BRHO = 33387.
and £>F is the dispersion function at the center of the quadrupole. the dispersion suppressor is composed of two reduced bending FODO cells. and $ is t h e phase advance of the F O D O cell.1) F O D O cells are [§QF B QD B | Q F ] with dipoles. (a) Show that /-I M| =90 o = 0 V0 0 -1 0 2DF\ 0 . Adjoining the regular arc./ unit.78 Show that the conditions for zero dispersion after the dispersion suppressor are j = W^ry and ei+d2 = e' where 6 is the bending angle of each dipole in t h e regular cell.4 is thus verified. (c) To match the dispersion function from a regular FODO cell in the arc to a zero value at the straight section._ 1 = sin$ . each with 90° phase advance. 0 1/ (b) Show that two FODO cells. 4. a n d t h e bending magnets in the last F O D O cell are replaced by drift spaces. show t h a t t h e dispersion function at t h e entrance of the first F O D O cell with a dipole is 1 — cos n<& + cos $ — cos(n — 1 ) $ 2(1-cos n$) FI 1 = .164 CHAPTER 2. show that the momentum compaction factor ac of an accelerator made of N FODO cells is given by 1 ac~2irRf 78A fDx ( 2TT \ 2 1 pdS-{2Nsin%) /SFsin* ~ vV reduced bending cell can be represented by the following matrix with fi = Q\jQ: ( cos$ £ I D F ( 1 . with bending angle #2 a n d 9\ for each dipole.s i n n $ + sin(n . (d) This exercise shows the effect of dispersion mismatch. we need a dispersion suppressor. ) . 1 / /I M| = 9 0 o = 0 \0 0 0\ 1 0 . TRANSVERSE MOTION where the symmetry conditions aF = 0 and D'F = 0 are used. At $ = TT/2. T h e theorem of dispersion suppression of Section IV. which is related to the integer stopband. The resulting mismatched dispersion function can be very large at n $ w 0 (mod 2TT). match a zero dispersion region to a final dispersion of D = 2Z)F and D' = 0.cos$)\ ~7j?sin$ 0 cos$ 0 SI7F£>Fsin* 1 I . $ is the phase advance per cell.1)$ 2(1-cos n$) 7 F' where DF is the dispersion function of the regular FODO cell at the center of the focusing quadrupole and $ is the phase advance per cell. these two F O D O cells form t h e . Assuming that the accelerator lattice is made of n F O D O cells. Using thin-lens approximation. j3F and 7 F are the Courant-Snyder parameters. where (n .
D = p/(l .5) with a constant focusing index 0 < n < 1. and Xd.244) can be transformed to d2jt +Sx-v2pm where X = D/y/fi. the ao harmonic dominates. p (V3) v 2TTP J Since v = f ds/27r/3 w fl/<^>. Show that the integral representation of the dispersion function in Eq.243). Consider a weak-focusing synchrotron (Exercise 2. show that Eq. (2.cos 2irvx)Xd + sin2irvxPd}P0 where Xp = x/V3i and Pp = (axx + f5xx')ly/]5x a r e normalized betatron coordinates. show that the path-length change due to the betatron motion is79 rs+C x AL = / -ds Js p = [sin 2irvxXd .4 165 where -R is the average radius of the accelerator. 79Use the integral representation of Eq. (2. 5.n). Assuming p w constant for all magnets.n.266). (b) Using Eq. where the zeroth harmonic ao dominates. (2.2. and vx is the horizontal betatron tune. the path length depends on the betatron amplitude quadratically. ^ k=-oo show that Note here that Z)(s) can be approximated by ao^/P{s) in a regular FODO lattice. Show that the lattice and dispersion functions are j3x = p/y/1 . show that i //J1/2. (Xp) = {Pp) = 0. Using the Floquet transformation. (2.264) satisfies Eq.(1 . show that a c « l/v2.EXERCISE 2. (2. $ is the phase advance per cell.265). and the transition energy is 7 T = VI —n. . Since the time average of the betatron motion is zero.265). (2. (2. 6.cos 2nux)Pd]Xp + [(1 . Substituting the betatron coordinate into Eq. show that A:=—oo where R = C/2-rr is the mean radius. (a) Using the Fourier expansion.266). Pz = p/y/n. 7. In most accelerator design.P<j are the normalized dispersion function phase-space coordinates of Eq. and <f> = /o ds/u/3.
2ao[Mi3M2i . In general.M23M12] + po[MuM2i .M 23 M 12 ] 2 . (2.166 CHAPTER 2.^(» 0 )|).M23Mu}2 +7o[Mi3M22 . The closed orbit of a horizontal dipole field kicker at location so in a synchrotron is given by (see Sec. 11. where #o is the kick angle. is the phase of /*• 10. etc. D'2 = M21Di + M22D[. 9. The values of the dispersion function at two locations in the beam line are related by D2 = AfnDi + M12D[. The change of orbit length due to a dipole error is the product of the dipole kick angle and the dispersion function at the kicker location. Show that the evolution of the 'H-function is U = Ho + 2(a0Do + /3oD'0)[M23Mn-M13M2i} +2(7oA) + a0D'0)[MuM22 . Show that the effect of the dipole kicker on the orbit length is AC = j> —ds = D{so)6Q.M23Mii][M\3M22 . Show that the vertical dispersion function k=—oo z where The vertical dispersion function can sometimes be approximated by a simple pole Dz « vzypz(s) .\i>x(s) . and Dx is the horizontal dispersion function at the skew quadrupole location. Vertical dispersion can also be induced by vertical closed-orbit error in quadrupoles. In a straight section of an accelerator. dipole rolls. Ill) xco(s) = Vy f l )&( 8 °) e0 cos (™s . In the presence of a skew quadrupole field with ABX = (dBx/dx)x. TRANSVERSE MOTION 8. for the vertical closed orbit is 80 z» Hill's equation + Kz(s)Z=-L^Dx6. Show that H = jD2 + 2aDD' + fiD12 is invariant in the straight section. feed-down from magnetic multipoles. and ipx is the phase advance function. M13 = 0 and M23 = 0. . where k = [vz] is the integer nearest the vertical betatron tune and (. Bp ox where Bp = po/e is the momentum rigidity.M23Mi2] 80This exercise demonstrates that residual vertical dispersion can be generated by skew quadrupoles. the dispersion function transfer matrix is given by Eq.254).
i. /o (MHz) 1 1. Double-Bend Achromat: Consider an achromatic bending system with two sector magnets and a focusing quadrupole midway between two dipoles. 0 .6 PHT 1.82 m.6c] O[l2] QF[K.6 -3. calculate the horizontal and vertical dispersion function at two horizontal and two vertical BPM locations.8 6. 1 .EXERCISE 2.9 0.03268 I 1.0 I I V.4.7 -5.03168 I 1. in thin-lens approximation. (2.po.249).6 -2.Jq] O[/2] B[-p.0] O[h] QF[JC.5 -5. (2.e. and BESSY (Berlin).-er] O\h] QF[JT. The parameters for this experiment were (1) proton kinetic energy = 45 MeV. (2) circumference = 86.4 I 0. and (b) the reverse-bend DBA B[p. and 70 are Courant-Snyder parameters at the initial location.3 -10.VKlq 2 -.5 PH24 I -0.2 2.0 3. Chasman-Green lattice cell.313). TLS (Taiwan).D0 + 1<XODQDQ +POD'Q\ Mij is a matrix element of the transfer matrix.9] where the reverse bend angle 9r < S can be used to adjust the desired momentum compaction factor.lq] O[l] B[p. KLS (Korea).6 PV12 PV14 PVT PV26 0. arranged to minimize {H) in the dipole. .BPM I 1. The double-bend in the design of low emittance storage rings. Here K and lq represent the focusing strength function and the length of the quadrupole.280).9]. Using the beam position data (in mm) in the table below at three different revolution frequencies (in MHz) at the IUCF cooler ring.f q ] O[h] B[p.03268 I 1.7 1.1 0. 12.03068 H.4 167 where %Q = 70.1).9] O[l] QF[K. Table: Some Beam Positions xco or zco (mm) vs /o (MHz) of the IUCF Cooler. Other (a) the triple-bend achromat (TBA) B[p.e0] which has been used in many synchrotron radiation light sources such as the ALS (Berkeley).8 | PV24 | 13. B[p.0 1.Iq] O[/] B[p.lq] O[/] B[p.6. the matching condition reduces to Eq.4 -12.03168 MHz.3 4.3 PH14 2.0o] O[ii] Q F [tf. show that % in a sector dipole is given by Eq.2 -4. This basic achromat is also called a achromat (DBA) is commonly used where quadrupole configurations are achromat modules are .03068 Zco Zco £co_ 0. and cto.3 PH12 -0.BPM Ico -Tco 3: co PHI 0.9 | 0.0 -2.4 | 1. Show that the dispersion matching condition is given by ptan —h I = —F= cot 2 JK and that.4 -1.9 -4. (3) reference orbit frequency = 1.7 8. (b) Find ~H in a rectangular dipole (use the result of Exercise 2.1 5. (a) Using the My of Eq. and (4) transition energy 7r=4. (2.03168 I 1.
.168 CHAPTER 2.Zq] O[h] B[-p.+ li = —== .-6] O[/a] B[-p. extraction.cos 9) cos <t> Pw { -[sin0 + 2 tan 0(1 . Assuming that DQ = D'D = 0. in small angle approximation.0] is achromatic if the following condition is satisfied: I _ 2cosS + l p sin# 16.= I (1 .0] O[l] B[p. /q <C(<1+*B) 4 + 24 + £ B ' where / q is the focal length of the quadrupole and £Q is the length of the dipole. etc. internal target operation. TRANSVERSE MOTION 14. It can be used as a beam translation (chicane) unit to facilitate injection. e) 0 Lw (.0] O[h] QF[K.-6] is achromatic if the following condition is satisfied:81 0 lc cos \fKlq + -L sin VKL psin. Show the three sector dipole system B[p. is Rm = 202(<?i + \p»)( p w . 0<s<Lw —i^. f-(l-cos</>).P w . VK -^^. sure to take the edge focusing into account.(1 .cos 0)] sin <f>.Q O[lc] QF[#. It can also be used as one unit of the wiggler magnet for modifying electron beam characteristics or for producing synchrotron radiation. show that the dispersion function created by the wiggler magnet is 82 .2 cos VKlq Show that.-26) ( 3LW Pw . (a) Show that the rectangular magnet beam translation unit is achromatic to all orders. in thin-lens approximation. . A set of four rectangular dipoles with zero net bending angle B[p. 2 lcy/K sin VKlq .e] O[k] B[-p. and show that the R^e element of the transport matrix. Lw < s < 2LW 82Be 81 At the symmetry point of the antisymmetric bending section D = 0. Achromatic translating system: Show that the transport line with two sector dipoles given by B[p. 2LW 4LW s (b) A simplified compact geometry with lx = l2 = 0 (shown in the figure above) is often used as a unit of the wiggler magnet in electron storage rings.0] O[l] B[p.cos (j>) . .-0\ O[h] B[p. 15.6] has many applications. e) .
Since D' = 0 at the symmetry point. 0 < s < iw V.cos6).cos 0)] cos 0. (a) Show that the phase advance of the dispersion matching section is determined completely by the prescribed dispersion function Z>a and the phase advance of the DOFO cell. / i : focal length of QDI.) = / -s 2 /2pw. I -(2Ll .(2LW . f2'.2tan0(l . In small bending-angle approximation. (1 . An FMC basic module can also be made of two DOFO cells with a dispersion matching section (shown schematically below).betatron phase advances of one half of the dispersion matching section.cos $ + C cos $ (b) In thin-lens approximation. and 169 { Show that .1~C°*e. 2L: length of the DOFO cell. DD dispersion function at the defocussing quadrupole.sin (j>. Lm: length of half a complete module. D(s = 2Lv. L w < s < 2LW. sin 0 + (1 .'( S N = { -s/Pw.) = 2pv.s) 2 )/2p w . the wiggler is an achromat. show that the dispersion function becomes D(.focal length of QF2I i'xi'i'z'.cos 0) sin 4> -[sin0 + 2tan0(l . £. DOFO CELL Dispersion Matching Section DOFO CELL v .s)/pw.EXERCISE 2. COS0 D'(s = 2K) = 0. 0<s<L . PD> 7D = 1 //^D : values of betatron functions at the center of QD. L w < s < 2LW.C ) s i n $ tan ibx = — 1 . 6: bending angle of a half DOFO cell.s i n # .L w ) / p w . \ -(2L W . -Da: prescribed dispersion function at marker M a with C = DA/DD. Lc: half length of the matching section from Mb to Mc.4 where <j> = s/pw and (j> = (s . s = iw+ LW < s < 2LW. 0 < s < Lw QD/2 i i in I B 11—11 II QF B I hn i i Qm Q F2 T i m i I i 11 1 B In I II QF B QD/2 I In Ma Mb Mo Use the following notations <&: phase advance of the FODO cell. 17. show that -M' + £)('-&)' »2*4-7f)(i+i)' .
g.' ic ^ /1 .a a o (1 + W / i ) 2 j o~i COS^ 1px Pz. TRANSVERSE MOTION Show that the stability of the betatron motion is a necktie region bounded by four lines: Lc < » 2/2 . ^ = 7r/4. e. Lc//2 and ^ are determined. " 1 . (c) Show that the values of the betatron amplitude functions at Mc are c Px. (2.170 CHAPTER 2. The dispersion function in the combined-function dipole satisfies D" + KXD = \/p.31). . Since V"i is determined by parameters $ and £.9—.g. To simplify the design of a DBA in a synchrotron storage ring. sin2f /5 1 * \ 1 18. where Kx = 1/p2 + (l/Bp)(dBz/dx) is the effective defocussing strength function and p is the bending radius of the dipole.2(1 . e. combined-function dipole magnets have often been used. in ELETTRA in Trieste and in the UVU and X-ray rings in the National Synchrotron Light Source (NSLS) at BNL. the parameter £ c //2 is a function of Lc//i> i-eLc _ /a ~ 2 cos2 Vx > 1 + ic//i' Draw the line Lc//2 vs Lcjf\ for constant ^ x . Furthermore.$\.Lc/2f2 ' where /J^D is the horizontal betatron amplitude function at the center of QD. 2• Lc/fl) COS 2 1pz (d) Show that the dispersion action in the matching section is Jb = Jc = JD (l .' LQ_ Lc/fi 2/2-1-Le//!1 Lc Lc/fi 2/2-l+Lc//i" Plot the necktie diagram of Lc/f2 vs Lc/f\. $ .c = Pz..83 83Because the electron has a negative charge.C)2) • (e) Show that the dispersion function at the middle of the dipole is / 1 *\ L6 Show that the momentum compaction is Doe\( . This means that the dispersion matching section is a one-parameter lattice.C) cos * + (1 . Once L c //i is chosen. the gradient term in Kx has a sign opposite that in Eq.c = Pi. show that the length of the matching section is _ /8IiDsini/'iCos^3.a a o (1 .
Kl=l.685 D3 :DRIFT.e.SYMM.D5.K2=0.4018946 Q4 :QUADRUPOLE.K2=0.L=.29943942 B : RBEND.. Plot G = V16AC . J30 = /30/L. 6 .4 (a) Show that 171 <W)=p0 3 [|^)-^B( g ) + gC(g)].L=0. TITLE.Q3. Note that the dipole is declared as RBEND for a rectangular magnet. however.L=.L=.L=..L=2.D6.45.HSUP.L=. and 70 = -y0L.4132.Kl=-1.Kl=-. "NSLS X-ray RING" Ql :QUADRUPOLE.70825 D5 :DRIFT.. .L=.026848954.L=0.. i. SD :SEXTUPOLE. discuss the effect of the combined-function dipole on (H). the combined-function DBA gives rise to a larger (H).8 cosh g + 2 cosh 2g ? ' = tf ' with q = y/\Kx\L.B.225.D4. we should take into account the edge focusing of the dipole magnet. (b) Show that the minimum of (H) is <W>min = 47l5^3' where G = V16AC .7.#S/E TWISS STOP .15B2 vs the quadrupole strength and show that V16AC — 15B2 > 1. Dl :DRIFT.SUPER=8 PRINT.D5. 3(sinh2g-2g) „.L=.EXERCISE 2.3484 D4 :DRIFT.L=. Neglecting the edge focusing.25 D2 :DRIFT.33731236 Q3 :QUADRUPOLE.ANGLE=.Q1. where in principle.L=2. (c) Use thin-lens approximation to verify the strength of matching quadrupole Q4 of the NSLS lattice input data (MAD) file (shown below) for the achromat condition. a0 = a 0 .25 HSUP :LINE=(D1. where A{q) = — v — ' (9) = _. In Chapter 4 the effect of damping partition number on the natural emittance of electron beams will be discussed.50186576 Q2 :QUADRUPOLE.8.SF.L=.Q4) USE.D2)Q2. .. 30g-40sinhg + 5sinh2<j C(9) .Kl=l.39269908 SF :SEXTUPOLE.SD.D3.15B2.9 D6 :DRIFT.Kl=-1.
g. CERN 91-04. the chromatic gradient error should include the effects of dispersion functions.Equation (2. (2323) where K = B^Bp and Bx = dBz/dx.I we define chromaticity and discuss its measurement and correction. 53.£ + *<•)] * + <>«•)—IM [ AKZ = -K(s)S + O(S2) « -KXS. that the chromatic gradient error is essentially equal to the product of the momentum deviation 5 and the main focusing functions —Kx and — Kz. S. TRANSVERSE MOTION V Chromatic Aberration A particle with momentum p executes betatron oscillations around an off-momentum closed orbit xco(s)+D(s)5. fringe fields. For details see. K. where xco is the closed orbit for the on-momentum particle. p. 1965).242) is Hill's equation of the horizontal betatron motion.[ . CERN Accelerator School. AKZ= ( ± ) ' D ' + 1 * . Note. Some of these terms are includes below: AKx = \ * + K + 2° (± . Note that the higher-order gradient error depends on the betatron amplitude and dispersion functions. (2. We will neglect all chromatic effects arising from the dispersion function and fringe fields of magnets.2 we examine the nonlinear perturbation due to chromatic sex84Including the effect of off-momentum orbits. the gradient error arising from the chromatic aberration is proportional to the designed focusing functions Kx and Kz. etc. The resulting gradient errors AKX and AKZ are given by84 | A * . Similar gradient error exists in the vertical betatron motion. New York. Steffen. and thus the chromatic gradient error is a "systematic" error that can cause major perturbation in the designed betatron amplitude functions and reduce the dynamical aperture for off-momentum particles. In Sec. The dependence of the focusing strength on the momentum of a circulating particle is called "chromatic aberration. the "beta-beat" associated with the half-integer stopbands. D is the dispersion function. a lower energy particle with d < 0 has a smaller momentum rigidity and a stronger effective focusing strength.172 CHAPTER 2. A higher energy particle with 5 > 0 has a larger momentum rigidity and thus a weaker effective focusing strength.(I)' [ p2 p \p2 ) \p) 1-K+-D+ D' + ^ D ] {8 -62 + •••) 0xp J v ' -••)+•••. in particular. V. High Energy Beam Optics (Wiley.242).. This is reflected in the gradient error AKX in Eq. Guiducci." Furthermore. 1991. . V. In this section we study the effects of systematic chromatic aberration and its correction.D \ {8-82 + where K = B\ jBp is the gradient function of quadrupoles. in Sec. The effects of chromatic aberration include the chromaticity. Proc. e. +•••.K ) . etc. and S = (p-po)/Po is the fractional momentum deviation from the on-momentum po.
1 for a FODO lattice. V. Since the chromatic effect of Eq. The "specific chromaticity. A beam is composed of particles with different momenta.4. and vy = N$y/2n is the betatron tune of the machine. V. (2. The natural chromaticity of a FODO lattice is given by (see Exercise 2. the betatron tune decreases with particle momentum. in Sec. the momentum spread gives 85In mathematical language.4 we outline basic machine design strategy. <£y is the phase advance per cell. and Cy < 0.V.326) Because the focusing function is weaker for higher energy particles. (2.196). since the betatron amplitude function is always larger at a focusing location where Ky > 0.85 The magnitude of the natural chromaticity Cy.324) \^ = VJ P*AK*dS * ( 4^ / t'K-*8) 6Cy = ^ . III. and the natural chromaticity is negative.3) f-rFODO 1 N (flnax Anin \ _ tan($ y /2) where N is the number of cells.3 we study systematic half-integer stopbands and their effects on higher-order chromaticity. defined as the derivative of the betatron tunes vs fractional momentum deviation. The chromaticity arising solely from quadrupoles is called the "natural chromaticity. On the other hand.nat depends on the lattice design. / is the focal length.y = Cy/vy. we find that the gradient error can induce betatron tune shift and betatron amplitude function perturbation. and in Sec. V." Cy^tK^fpyKvds.5. the resulting betatron tune shift. the integral § /3yKyds > 0. the specific natural chromaticity can be as large as —3. . Because of the chromaticity.325) The chromaticity. for a collider lattice or a low-emittance lattice. (2. is f Avx = -?.hxAKxds 47r/ « (^ l(5xKxds) 5. The momentum spread of the beam is typically of the order of as ~ 10~5 —10~2 depending on the application and the type of accelerator. CHROMATIC ABERRATION 173 tupoles. is nearly equal to ." defined as £. is where the subscript y stands for either x or z. Cx or Cz. (2.I Chromaticity Measurement and Correction In Sec.323) gives rise to a systematic gradient error. given by Eq. U n T ' (2.
E. Bleser. we find that 1 2 $ Figure 2. the growth of transverse head-tail instabilities depends on the sign of the chromaticity (see Sec. The dashed straight line shows the theoretical expected value. R. (2.40 shows the "measured specific" chromaticities of the AGS. 276 (1987). Auerbach. as discussed in subsection C. [3]). *-$—»•& <2-328> where r\ is the phase-slip factor.8). A. AGS Tech Note No. The solid curved line is obtained by modeling the sextupole field in the dipoles. .174 CHAPTER 2. Chromaticity measurement Machine chromaticities can be derived from measurements of betatron tunes vs beam momentum. but the horizontal chromaticity becomes more negative.40: The measured chromaticities divided by the betatron tunes of the AGS vs the beam momentum. 86E. VIII and Ref.e. particle loss may imminently occur.86 Note that the vertical chromaticity becomes positive above about 22 GeV. The dashed line shows the value of — ^ t a n * of Eq. TRANSVERSE MOTION rise to tune spread in the beam. From the experimental data. E. AGS Tech Note No. and wrf is the angular frequency of the rf system (see Exercise 2. 288 (1987). Since beam momentum is related to rf frequency. where $ as 53.5.8° is the phase advance of an AGS FODO cell. If the chromaticity and the momentum spread of the beam become large enough that the betatron tunes overlap a low-order nonlinear resonance. the chromaticity can be obtained from measurements of betatron tune vs rf frequency. Them.327). Furthermore. Bleser. i. Figure 2.
called geometric aberration. (2.333) (2.330) where xp is the betatron displacement and D(s)5 is the off-momentum closed orbit.331) can produce nonlinear perturbation in betatron motion.334) J 87It is also worth pointing out that the second term of Eq. AKZ = -S(s)D(s)S (2. Since a circulating beam with such a large tune spread does not have a long storage lifetime. Note that the first term of Eq. This requires a magnet whose focusing function increases linearly with momentum in order to compensate the loss of focusing in quadrupoles. and the resulting tune spread will be Av « 0.332) depend linearly on the off-momentum deviation. Chromatic correction The natural chromaticity of a high-luminosity collider with low-/?* insertions is usually large. the chromaticity becomes Cx = ^ f 4TT P*[K*(S) .V. we obtain \ZP 2 2 (2331) [ -^f = -[S(s)D(s)5]z0 .nat ~ -250. x= ~Z)> Xp{s) -W=BpXZ> Substituting the transverse displacement of an off+ D(s)S.329). (2. into Eq. pz[Kz(s) + S{s)D{s)}ds.87 Including the contribution of sextupoles. VII. the natural chromaticity for the RHIC injection lattice is about C^nat ~ —50. (2. Since the effective quadrupole focusing functions AKX = S(s)D(s)6. (2.1 for a beam with an rms spread of 8 = ±2 x 10~4. momentum particle. the natural chromaticity for the Superconducting Super Collider (SSC) was expected to be about Cy.S(s)D(s)]ds. sextupoles can be used for chromaticity correction. where we will find that the placement of sextupoles is important in minimizing nonlinear resonance strengths. which can lead to a natural tune spread of about Av « 0. CHROMATIC ABERRATION 175 B. where S(s) = —B2/Bp is the effective sextupole strength. The magnetic flux density of a sextupole magnet is ABZ B2 2 2 ABX B2 (2329) -W=2B-P{X where B2 = d2Bz/dx2\x=z=0. Similarly.331) depends linearly on the transverse betatron displacement. to be discussed in Sec. First we examine the possibility of using sextupole magnets for chromaticity correction.5 with a beam momentum spread of 6 = ±5 x 10~3.S(s)xpzp. chromatic correction is needed to ensure good performance of a storage ring. (2. Cz = ^ l . For example.
and 9 the bending angle per half-cell. where 4f. For example. we consider a lattice of N repetitive FODO cells.3) _ 1 5F~2/^(1 sinf + Isinf)' bD~ 1 sinf 2/20(1-I sinf)' [ } where / is the focal length. where (3XDX and /3ZDX are maximum. Nonlinear modeling from chromaticity measurement The measurements of chromaticities can be used to model nonlinear sextupole fields in an accelerator. strong sextupoles are needed to correct it. C.5. 4d. For colliders or low-emittance storage rings. • In order to minimize their strength. which consist mainly of FODO cells or DBA/TBA type cells. where sextupoles are located near the focusing and defocussing quadrupoles. The second-order chromaticity and the betabeat can be simultaneously corrected by a proper chromatic stopband correction. In Sec. Let Sp = —B2{F)la[/Bp and So = —i?2(D)4d/Sp be the integrated sextupole strengths at QF and QD respectively. the chromatic sextupoles should be located near quadrupoles. TRANSVERSE MOTION This shows that sextupoles located at nonzero dispersion function locations can be used to correct chromaticity. For example. 5 2 (D) are the length and the sextupole field strength at QF and QD. • A large ratio of px/pz for the focusing sextupole and a large ratio of /3z/f3x for the defocussing sextupole are needed for optimal independent chromaticity control. located in the arcs. the simple chromatic correction scheme using two families of sextupoles may not be sufficient to correct the higher-order chromatic effects. Since the low-/?* values in these lattices give rise to a large chromaticity. Figure 2.3. The sextupole strength needed to obtain zero chromaticity is (see Exercise 2. If the intrinsic systematic half-integer stopband widths are large. V.176 CHAPTER 2. • The families of sextupoles should be arranged to minimize the the systematic half-integer stopbands and the third-order betatron resonance strengths. and B2(F). Rules for their placement are as follows. we will show that the chromatic gradient error can also create a large betatron amplitude function modulation (betabeat). Generally. $ the phase advance per cell. which in turn induces a large second-order chromaticity.41 shows an example of chromatic correction with two families of sextupoles in RHIC. chromatic sextupoles are also arranged in families. two families of sextupoles are needed to correct horizontal and vertical chromaticities. we discuss the nonlinear sextupole modeling of the . they are called chromatic sextupoles. Note that the second-order chromaticity Afx>2 ~ C^2) S2 can cause substantial tune spread in a beam with a large momentum spread.
2 x 10~4 + 5.40 represent theoretical calculations with the integrated sextupole strengths 5b = 5e -5. and proportional to B. For the long magnets (2. . 5 e and the first term in 5b may be considered as the systematic error in dipoles. and 5 e is the integrated sextupole field distributed only at the end of each dipole. which has recently attained an intensity of 6 x 1013 protons per pulse. we assume that the sextupole fields arise from systematic error at the ends of each dipole. CHROMATIC ABERRATION 177 Figure 2.7.fodo. where px « fiz. Cz. the eddy current sextupole due to the vacuum chamber wall.0 x 1 0 . A chromaticity of about —Zvx does not appear to cause difficulties in the AGS operation.6 x 10~4p .fodo. Many low energy synchrotrons do not use chromatic correction sextupoles. To model the AGS.017 (nr 2 ). = -0. which is inversely proportional to the beam momentum. The saturation term is nonlinear with respect to the momentum p. The second term in 5b is due to the eddy current on the vacuum chamber wall. AGS based on the measured chromaticities shown in Fig. the horizontally defocussing sextupoles must be located in dipoles. where 5 = 2 T/s in this experiment.3876 m) in the AGS.41: Variation of the betatron tune vs Ap/p after chromatic correction with two and four families of sextupoles in RHIC.fodo. and the iron saturation sextupole at high field. and they are momentum independent.V + 2. chromaticity correction is absolutely essential in high energy synchrotrons and storage rings. 2. However. and C^data + C2]data = CXtfodo + Cz.8 x 10"V) (m" 2 ).8 x W~2/p -(3. 5b is the integrated sextupole field in each dipole distributed in the whole dipole.40.0066 m) respectively.data > Cz.V. and the saturation sextupole field depends on a higher power of the beam momentum. the eddy current sextupole field depends inversely on the beam momentum. The systematic error is independent of the beam momentum. for the body and the ends of the short AGS bending magnets (2. 2. the integrated sextupole strength of the 5b term is assumed to be proportional to their length. The solid lines in Fig. Since CX]data < Ci. Here p is the beam momentum in unit of (GeV/c).
we will show that if chromatic sextupoles are separated by an odd multiple of 180° in the betatron phase advance. their contributions to the third-order stopband width cancel each other in the first-order perturbation theory. TRANSVERSE MOTION V.178 CHAPTER 2. (2. the nonlinear resonance strength can be minimized by properly arranged sextupole families. Such arrangements can also be used to correct the systematic half-integer stopband discussed in the next section.336) The Hamiltonian including sextupole nonlinearity is This Hamiltonian can drive third-order and higher-order nonlinear resonances at 3ux = £. V. VII. drl>1/d8 = l/fa.337).A> we obtain where AK = K\— Ko is the gradient error. In Sec.10) .. Thus. the betatron amplitude functions /?o and Pi satisfy the Floquet equation P'Q = -2a0.3 s ^ ) .To. However.f t &ff — .2 Nonlinear Effects of Chromatic Sextupoles H = | (x'j + Kxxj + 4 + Kzz2) + ^ ( ^ . the change of A across a sextupole is given by Av AA= [Jp^AKds^-^-^-.. we find that A2 + B2 = constant in regions where AK = 0. From Eq. Defining the betatron amplitude difference functions A and B as (see Exercise 2.. In thin-lens approximation.aojdi B _ Pi . ai = ffi0i-7i. Po . and six families of sextupoles can be used in a lattice with 60° phase advance per cell. vx ± 2vz = £. (2. and ipo and ipi are the unperturbed and perturbed betatron phase functions.. _ aiPo .2 a 1 . Similarly.3. four families of sextupoles can be arranged in a lattice with 90° phase advance per cell. d^0/ds = 1/A» /3'1 = .3 Chromatic Aberration and Correction The systematic chromatic gradient error can produce a large perturbation in the betatron amplitude functions for all off-momentum particles. the change of A across a quadrupole is given by J v / Po where / is the focal length of the quadrupole. a'o = KoPo . A A « . where £ is an integer.
(2. (2. Systematic chromatic half-integer stopband width We have found that the perturbation of betatron function is most sensitive to stopband integrals near p ss [2v] harmonics (see Sec. Since the phase of A or B propagates at twice the betatron phase advance (see Exercise 2. At p — 0 (Mod P).3. Here we investigate the effect of systematic chromatic stopband integrals. two identical quadrupoles (sextupoles) separated by odd multiples of 90° in betatron phase advance cancel each other. Note that Jp<y = 0.201): \jp.338) We consider a lattice made of P superperiods. The integral of Eq. The treatment is identical to the stopband integral to be discussed next. i.z = —fpzAKze-^ds. where L is the length of a superperiod with K(s + L) = K(s).y = ~{^[PyKye-^ds\ = ~{^[PyKye-^ds^ [l + e-*¥ + e"^* + e^3p* + • • •] CP(js)e-j*pE^.4). and the diffracting function CP (u) is given by Note that the diffracting structure function £P -» P as u -> integer. CHROMATIC ABERRATION 179 where ge$ = (B2As/Bp)D is the effective gradient error. Let C = PL be the circumference of the accelerator.V. two identical quadrupoles (sextupoles) separated by an integer multiple of 180° in betatron phase advance will produce additive coherent kicks. unless p = 0 (Mod P). (B2As/Bp) is the integrated sextupole strength.x = ^-hxAKxe-^ds. Similarly. each superperiod contributes additively to the chromatic stopband integral. (2. I llX J [jp. 0(s + L) = /3(s).10). A. We will show that systematic stopbands can generate a sizable second-order chromaticity.e. the global chromatic perturbation function of the lattice can be minimized. and D is the dispersion function. The effect of systematic chromatic gradient error on betatron amplitude modulation can be analyzed by using the chromatic stopband integrals of Eq.338) becomes JP. the half-integer stopband integral increases by a factor of P. . (2. By using sextupole families. III.339) where y stands for either x or z.
which is composed of JV FODO cells.341 where $ is the phase advance per cell. the AGS lattice has P = 12. the AGS lattice can be approximated by a lattice made of 60 FODO cells. In particular.Cw(f—)e~J—or-. TRANSVERSE MOTION Since the perturbation of betatron functions is most sensitive to the chromatic stopbands near p w [2ux] and [2vz]./V FODO cells is small. /3 max and /3m.88 Generally. and P = 22 for the SPRING-8 at JSRF.340). it is beneficial to design an accelerator with high super-periodicity so that the betatron tunes can be located far from the important chromatic stopbands. 18. i. and the diffracting function (N(u) is given by Eq. the chromatic stopband of the arc adds up to zero at harmonics p w 2u. Similarly. and the resulting chromatic perturbation is small. P = 40 for the APS.^ ) [l + e-** + e-^i + e-t*>i + • • •] = y ( s i n .90 • • •. the chromatic stopband integral at p s» 2v due to . The actual betatron tunes at vx/z = 8. For example.60.e. This can be achieved by choosing the betatron tunes such that [2vx] and [2vz] are not divisible by the superperiod P. If p^/2iri/ = 0 (Mod N). Trcosf \ 2 4u \. The chromatic stopband integral in thin-lens approximation is given by Jp = ~ ( £ p . or the stopband integrals of two modules cancel each other.v I 2-nv 2. B. / is the focal length of each quadrupole. which are far from the betatron tunes. 30. if N<& = integer XTT. In fact.8 are indeed far from systematic half-integer stopbands at p = 6 and 12. the diffracting function is equal to N. Thus the goal is to design an accelerator such that the chromatic stopband integral of each module is zero. 12. a basic design principle of strong-focusing synchrotrons is to avoid important systematic chromatic stopbands. a high energy accelerator or storage ring with large super-periodicity is costly. 24. 88The stopbands in a collider can also be minimized by local cancellation of various beam line modules. (2. Fortunately. the TEVATRON has a super-periodicity of P = 6.180 CHAPTER 2. etc.^ p e . since $/27r is normally about 1/4 (90° phase advance) so that p<&/2-Ki> « p/4v ss 1/2.n are values of the betatron amplitude function at the focusing and defocussing quadrupoles respectively. Chromatic stopband integrals of FODO cells Now we examine the chromatic stopband integral of the arc. etc. However. . and the betatron tune should avoid a value of 6. the stopband integrals a t p « [2i/] resulting from iV FODO cells in the arcs is small if the total phase advance of these FODO cells is iV$ = integer x 7r.+ j s i n ^ .c o s y . P = 16 for the ESRF. The important stopbands are located at p = 30. This means that each FODO cell contributes additively to the stopband integral. Some examples of high superperiod machines are P = 12 for the ALS. to be discussed in the next subsection. and the betatron tune should avoid 18.
91 A. G. J.89 cancellation of the chromatic stopband integrals between two adjacent insertions would be desirable. particularly when the beam momentum spread is large.V. 1626 (1985). . IEEE Trans. Substituting /3 = A>(1 + A/3/A0 into Eq. Thus. the chromatic stopband integrals of two adjacent insertions cancel each other. and is proportional to 5. high-/? triplets or doublets on both sides of the IP contribute additively to the systematic half-integer stopband near p « 2vx/z. .338).D. (2. Hahn. Effect of the chromatic stopbands on chromaticity The chromatic stopband integrals for large colliders. (2. private communications. Lee. the insertion may contribute a substantial amount to the chromatic stopband integral. This cancellation principle remains valid when two insertions are separated by a unit transfer matrix. The chromatic stopband integral of insertions Because of its small /?* value. Claus. Since it is difficult to design an insertion with zero chromatic half-integer stopband width. remain important even after careful manipulation of piecewise cancellation.Y. Such a procedure was extensively used in the design of the RHIC lattice90 and the SSC lattice.324). we obtain Auy = C^5 + C^52 + ---. Let 3>lns and J™s be respectively the phase advance and the chromatic stopband integral of an insertion.344) 89In fact. E. we obtain Jp = 0 if $ lns = (2n+l)ir/2. Parzen. The betatron modulation of the lattice is given by A/3_ T |JPlcos(p0 + x) 2(u-p/2) ' . 90S. CHROMATIC ABERRATION 181 where the transfer matrix of the arc becomes a unit matrix / o r a half-unit matrix -I. See also the SSC report. H. Nud.342) At the harmonic p « [2v]. called betabeat. C. NS-32. Garren. n s [l + e x p ( j ^ ) ] . such as the SSC and RHIC.91 D. Sci. The following example illustrates the effect of betatron amplitude function modulation on chromaticity. if the insertion is a quarter-wave module. (2. (2'343) where the chromatic stopband integral Jp is given by Eq. and second-order chromaticity for off-momentum particles. The total contribution of two adjacent insertions becomes Jp = j. Courant. We consider a lattice dominated by a single p harmonic half-integer chromatic stopband. They give rise to a large betatron amplitude modulation. (2.
To obtain a nonzero chromatic stopband integral.41 shows an example of the second-order chromatic tune shift with 8. Effect of sextupoles on the chromatic stopband integrals The chromatic sextupoles also contribute to the systematic chromatic stopbands. that is commonly used in FODO cells with 90° phase advance.e. Hahn. The remaining second-order tune shift C^62 can arise from the chromatic stopband integral. (1987). E. G. Conf. Here we present an example of chromatic correction for a collider lattice. the chromatic sextupole does not contribute significantly to the chromatic stopband integral if the transfer matrix of the arc is / or —/.347) where N is the number of cells.D K r W .348) Lee. the chromatic stopband integrals due to the parameters Ap and AD are given by AJp. D^ = Su — AD}.F. Sox = SQ + AD. 1328. sextupoles are organized in families. (2.W-Dp*/2".\) 92S.182 CHAPTER 2. (2. Dell.^ . and C^ and C£2) are the first. G.and second-order chromaticities c»1} = ~h / &(*» ~5^)rfSi (-4) 2 35 If the first-order chromaticity is corrected.340). then C^1^ = 0.sext = ^ C v ( | ^ . p. First we evaluate the stopband integral due to the chromatic sextupoles.339). (2. and the diffraction function £N is given by Eq.sext = £. Here the parameters 5 F and So are determined from the first-order chromaticity correction. i. H.C {Jr-) [fcSFDF + pDSDDDe-^2"} e-. However. A D will not affect the first-order chromaticity. Let S? and SD be the integrated sextupole strength at QF and QD of FODO cells in the arc. the stopband integral is zero or small if N$/n = integer. Parzen.a / ^ . We consider an example of a four-family scheme with {SFI = Sp + Ap. the parameters A F . which is proportional to the zeroth harmonic of the stopband integral. Since /3(s) and D{s) are periodic functions of s in the repetitive FODO cells. (2. We next discuss the half-integer chromatic stopband correction using sextupole families. Proc 1987 Part.92 The stopband correction that minimizes the /3-modulation also minimizes the second-order chromaticity. . The p-th harmonic stopband integral from these chromatic sextupoles is JP. Accel. SF2 = Sp — Ap. As in Eq. [/3FAFZ?P +/?DADZW*/4"] e . Figure 2.. TRANSVERSE MOTION where y stands for either x or z.Y.
. To improve the slow extraction efficiency. S F3 . particularly in the strip injection scheme. where the second-order chromaticity and the betatron amplitude modulation can be simultaneously corrected. • The betatron tunes should be chosen to avoid systematic integer and half-integer stopbands and systematic low-order nonlinear resonances. 2. • The chromatic sextupoles should be located at high dispersion function locations. the lattice design of accelerator can be summarized as follows. 5 F2 . Fig. • The betatron amplitude function and the betatron phase advance between the kicker and the septum should be optimized to minimize the kicker angle and maximize the injection or extraction efficiency. we have (w -> JV.41 shows an example of chromatic correction with four families of sextupoles in RHIC.V. Local orbit bumps can be used to alleviate the demand for a large kicker angle. The scheme works best for a nearly 90° phase advance per cell with N$ — integer x TT.349) V. the six-family sextupole scheme works for 60° phase advance FODO cells. The focusing and defocussing sextupole families should be located in regions where /3X 3> /3Z. every FODO cell contributes additively to the chromatic stopband. the stopband width should be corrected. Dm. i. and low-emittance lattice storage rings. The lattice is generally classified into three categories: low energy booster. The /3X and j3z values at the injection area.e. the j3 value at the (wire) septum location should be optimized. By adjusting Ap and AD parameters.5 D3 } has two additional parameters. and px <C Pz respectively in order to gain independent control of the chromaticities.4 Lattice Design Strategy Based on our study of linear betatron motion. CHROMATIC ABERRATION 183 At p « [2i/] and $/2TT W 1/4 (90° phase advance). the betabeat and the second-order chromaticity can be minimized. the injection line and the synchrotron optics should be properly "matched" or "mismatched" to optimize the emittance control. should be adjusted to minimize emittance blow-up due to multiple Coulomb scattering. The resulting stopband width is proportional to Ap and A D parameters. SDI. where the third-order resonance-driving term vanishes also for the four-family sextupole scheme. otherwise. where the six-family scheme {Spi. Similarly. The local vacuum pressure at the high-/? value locations should be minimized to minimize the effect of beam gas scattering. Furthermore. collider lattice. (2.
. and /3 max is the maximum betatron amplitude function at the triplet. and $ is the phase advance of the FODO cell. beam lifetime. 4. TRANSVERSE MOTION • It is advisable to avoid the transition energy for low to medium energy synchrotrons in order to minimize the beam dynamics problems during acceleration. nonlinear betatron detuning. Some of these issues will be addressed in this introductory textbook. A set of three quadrupoles ({QFI QD2 QF3} or {QDI QF2 QD3}). Exercise 2..184 CHAPTER 2. Sec. Besides these design issues. is commonly used in insertion regions to provide horizontal and vertical low-/3 squeeze. show that the betatron phase advance between the triplet and IP is 7r/2.3 (see Exercise 2. should be addressed. vacuum requirement. etc.5 1. problems regarding the dynamical aperture.3. Note that the required sextupole strength is larger at the defocussing quadrupole.2). 9 is the dipole bending angle of a half FODO cell. This criterion usually determines beam emittance and intensity. called a low-/3 triplet. (c) Show that the triplets on both sides of IP contribute additively to the stopband integral at p w 2u. (a) Show that the low-beta triplets contribute about __2As___J_ //3 max 4TT/8* ~ 2n\j /3* units of natural chromaticity. (b) If /9max > jS*. 3. where $ is the phase advance per cell and v = N$/2n is the betatron tune. Show that the strengths of two sextupole families used to correct the chromaticities of FODO cells are F 1 sin($/2) 2/ 2 0(l + isin($/2))' = D 1 sin($/2) 2/ 2 6>(l-I sin($/2))' where / is the focal length of the quadrupole in the FODO cell. where v is the betatron tune. 2. • Experience with low energy synchrotrons indicates that the Laslett space-charge tune shift should be limited to about 0. where As is the effective distance between the triplet and the interaction point (IP). rf system. /3* is the value of the betatron amplitude function at IP. III. collective beam instabilities. Show that the chromaticity of an accelerator consisting of N FODO cells in thin-lens approximation is F0D0 _ tan($/2) Onat ^ — ^ . The design of minimum emittance electron storage rings will be discussed in Chap.
( ^ 1 . (2.340). (2.0542203 ANGLE = 0.6 and C = 86.N{u) is given by Eq. and vx. where 7 T = 4.889612 Kl = 0. $ z . Show that the chromatic stopband integrals for a lattice made of JV FODO cells in thin-lens approximation are JPiX = -i.030680 Qx 3.7243 3. FNALBSTCELL : LINE = (BF S120 BF S050 BD S600 BD S050) BF : SBEND L = 2.7364 1 4. and the diffraction function C.5 185 4.0577073 ANGLE = 0.82 m. show that the chromatic stopband integral is j" . The AGS is composed of 12 superperiods with 5 nearly identical FODO cells per superperiod.889612 Kl = -0. 6.060157561 Sabc : DRIFT L = a.M E l e . Verify Eq.W * ) ^(JLje-W-i)/^ where $ x . Calculate the systematic stopband widths for harmonics 17 and 18 respectively.bc Find the systematic stopband width and discuss the choice of the betatron tunes. The Fermilab booster is a combined function synchrotron. 8.w 1 " " . (2.8 and vx = 8. The betatron tunes are vz = 8.347) and Eq. The lattice is made of 24 cells.Pz axe betatron amplitude functions.031680 I 1.EXERCISE 2. Betatron tunes vs revolution frequencies of the cooler Frequency [MHz] I 1." 5.-Jit h ?cos s + ' si ° 5} f .032680 I 1. / F and / D are focal lengths for focusing and defocussing quadrupoles.348). vz are the phase advances per cell and the betatron tunes. Assuming / F = fD with $ T = $ z = $ = 2nu/N. Use the experimental data below to calculate the chromaticity of the IUCF cooler ring.070742407 BD : SBEND L = 2.7.7080 _Qz | 4. What region of betatron tunes should be avoided to minimize the effect of systematic stopbands? 7. Px.6790 .7156 3.6913 | 4. as shown below. at 45 MeV proton kinetic energy.
(2. Here we find that the linear coupling can induce amplitude exchange between horizontal and vertical betatron motions.93 Measurement and correction of linear coupling will also be discussed. for solenoids. . (2. As = 0. 1 The Linear Coupling Hamiltonian The vector potentials for skew quadrupoles and solenoids are given by Ax = Az = 0. vertical closed-orbit error in sextupoles or horizontal closed-orbit error in skew sextupoles. 94 The skew quadrupole can also arise from "feed-down" of an off-centered vertical closed orbit in sextupoles.4. VI.350) Ax = ^Bl\(s)z. + 2gx' -(q + g')x = 0. TRANSVERSE MOTION VI Linear Coupling We have discussed uncoupled linear betatron motion.19). Substituting the components of the vector potential in Eq. IV.351) 93In Sec.—zr—) x z . The skew-quadrupole field arises from quadrupole rolls. Let zco be the closed orbit at a sextupole with sextupole strength B? = d2Bz/dx2.6. The solenoidal field exists in electron cooling storage rings. 21dz dx f° r skew quadrupoles.10). (2. and feed-downs from higher-order multipoles.g')z = 0.3): x" + Kx(s)x z" + Kz{s)z + 2gz' -(q. we show that a skew quadrupole at a high horizontal dispersion location can produce vertical dispersion.— ^-f) and B\\(s) are skew-quadrupole gradient94 and solenoid field strength. fringe field of a Lambertson septum. Linear betatron coupling is both a nuisance and a benefit in the operation of synchrotrons: the available dynamical aperture for particle motion may be reduced. but in reality betatron motions are coupled through solenoidal and skew-quadrupole fields. The effective linear coupling Hamiltonian and resonance strength will be derived based on perturbation approximation. but the vertical emittance of electron beams in storage rings can be adjusted. (2.186 CHAPTER 2. where \ir§£. which can generate vertical emittance for electron beams and result in lower luminosityforcolliders (see Exercise 2. Here we discuss the beam dynamics associated with linear betatron coupling arising from skew quadrupoles and solenoids. and in high-energy detectors at the interaction point (IP). Ag = --B\\(s)x. we obtain the linearized Hamiltonian for particle motion in accelerators as (see Exercise 2. and the Touschek lifetime limitation can be alleviated by linear coupling. x As = -(-^. The effective skew quadrupole strength becomes q = B2Zco/Bp.350) into the Hamiltonian in Eq.
351) can be derived from the following linearized Hamiltonian: -q{s)xz .356) where R is the average radius of the accelerator. and are effective solenoid and skew quadrupole strengths. (2. <j>z) are pairs of conjugate phase-space coordinates..c) + ( G l .px/p.* " . Kx and Kz are quadrupole-like focusing functions. and (Jx. $z = <i>z+ Xz (s) . (2.) 1 / 2 |[-Q + i fffe-^][cos(^ + $ 2 )+cos($ x -$ z )] (2. <j>x) and (Jz. Since V\c{s) is a periodic function of s. _ M e ^ . Xx= JO Px ^-. Xz= Jo j .g{s) \^z . it can be expanded in Fourier harmonics as VXc{9) = ^ 5 £ { ( G l .*. (2. are given by Gl'™ *** = h f V ^ ^ s ) eSbc^X'-f^-Wda. where rs f^Q ®x = <t>x+ Xx{s) ~ VXB. we obtain the coupling-potential: Vc = (^ 2 JxJ. be the conjugate phase space coordinates.^ + * .s i " .* 1 • PJ [P (2-354) Using Floquet transformation of Eq.^ J . (2.pz/p) motion of Eq. G\ ^neJX~ and G\\ie3XJr. The Fourier coefficients of the difference and sum resonances.355) +9 (jx ~ j ^ sin($x + $.+ j^j sin(*s . The betatron Let (x.> + c. (2.) J .c)} .357) . w e**-"--"^ + c.z.VI.353) Here the linear coupling potential is Vlc = -qxz .vz9. £ is an integer.) + g (J.94) for the uncoupled Hamiltonian. LINEAR COUPLING 187 where the primes are derivatives with respect to the independent variable s.
and the resonance strength is usually small. TRANSVERSE MOTION Here vx. Thus the effective Hamiltonian for betatron tunes near an isolated coupling resonance will be discussed in the following sections.358) obtained from the linear coupling potential of Eq. (2.^ + g(s)(f . P Px Pz Px Pz (2. Thus the linear-coupling resonance-strength should be minimized. The coupling resonance can cause beam size increase and decrease the beam lifetime.188 CHAPTER 2.2: Linear coupling resonances and their driving terms Resonance Driving phase AmplitudeClassification dependent factor vx + Vi=l ($ x + $ z ) ji/2ji/2 sum resonance vx . the horizontal and vertical betatron motions are coupled. • • -. vz are betatron tunes. Both skew quadrupoles and solenoids can drive the sum and difference linear coupling resonances. 16. Table 2. to minimize the effect of the systematic linear coupling resonance. each superperiod contributes additively to the linear coupling resonance strength.vz = £'.355). 95We will show. The strength of the linear coupling resonance due to random errors such as quadrupole roll and vertical closed orbit in sextupoles is smaller. %z = So ds/Pz are betatron phases. the difference between the integer part of the horizontal and vertical betatron tunes should not be 0. It occurs at all integer £. In general. If the linear coupling kernel A\CT satisfies a periodic condition similar to that in a synchrotron with P superperiods. where £ and £' are integers. Table VI. 8. Near a difference linear coupling resonance. the resonance coupling coefficient Gi iT i^ will be zero unless £ is an integer multiple of P. If £ is an integer multiple of P. in Sec. since the superperiodicity of the LEP lattice is 8. Xx = So ds/@x. and the linear coupling kernel ^4ic^(s) are A^{s) = .95 the optics of the betatron motion is normally designed to avoid sum resonances.$ z ) J]j2 J\l2 difference resonance The linear coupling potential has been decomposed into terms of the difference and sum resonances located respectively at vx — vz = £ and vx -\.v2 = £ ($ x . the coupling betatron sum-resonances are dangerous to the stable betatron motion. VII. 1 lists the corresponding driving terms. that the horizontal and vertical betatron amplitudes can grow without bound near a betatron sum resonance. This is called the systematic linear coupling resonance. For example. .Hi) + jg(s)(~ ± h .
£ and the phase factor \._i. 2 Effects of an isolated Linear Coupling Resonance Since the betatron tunes are normally near the linear coupling line. (2.353).£) ±-X (2. |(?i.£| as demonstrated in Fig. The Hamiltonian Eq.359) corresponds to two coupled linear oscillators. (2.If + |Gi. LINEAR COUPLING 189 VI.± = l£yx + vz + l)±-^\. (2.vz = I. and provide linear coupling correction. and the horizontal axis is the digital to analog conversion (DAC) unit of a COMBO power supply for a set of horizontally focusing quadrupoles. showing that the horizontal and vertical motion are coupled. in action-angle phase space coordinates.360) .a r e given by Eq.359) where the Fourier amplitude Gi. The vertical axis is the fractional part of the betatron tunes. The minimum distance between two normal modes is equal to the coupling coefficient jd?iT_i^|. Figure 2. Figure 2. (2. this section studies the effects of an isolated coupling resonance on betatron motion. the Hamiltonian Eq.VI. reaching a minimum value of tune separation.42. As the strength of a quadrupole is varied across the linear coupling resonance vx — vz + 1 « 0 (I = — 1 for the IUCF Cooler). 2.± =-(vx + vz .357).361) This means that the betatron tunes are separated by A. can be approximated by H a* vxjx + i>zJz + Gi-lttJj^Jzcos{<l>x -<pz-ie + x). u2.42 shows an example of measured betatron tunes vs quadrupole strength at the IUCF cooler ring. the betatron tunes of normal modes approach each other. This method has been commonly applied to measure the linear coupling strength. Effective Hamiltonian for a Single Linear Coupling Resonance Near an isolated coupling resonance vx . (2.42: The measured betatron normal mode tunes vs the strength of an IUCF cooler quadrupole.--i._ M | 2 . where A = yl(vx -v. A. which can be expanded in terms of two normal modes with tunes (see Exercise 2.5) V\. and the minimum separation between the normal mode tunes is |Glj_lj^|.6.
we obtain Jx + Jz = J2 = constant. where Si =vx — vz—l'vs the resonance proximity parameter. J\ = Jx. J i = Jx + Jz+ X)J\ + <t>zJ2.W J i ( J 2 . _ v > / J i ( J 2 . C. J\. (2. <t>z. H2(J2) = vzj2. (2. which corresponds to an initial horizontal betatron oscillation with Ji imax = J2. all tori can be described by a single parameter Ei that is determined from the initial condition.364 ) (2. TRANSVERSE MOTION B. 2 l cos0 x .190 CHAPTER 2. The particle trajectory that satisfies Hi = 61J2 is P2 + Q2 = 2J2. h) = ((t>x -<t>z-£0 where the new action-angle variables are </>l = <t>x . (2. ' '2y/Ji(J2-Ji) ( 2 .26 + X. Initial horizontal orbit We first consider the simple orbit with "energy" E\ = SiJ2.365) For a given J2. Since J2 is invariant.<t>z .359) into the "resonant precessing frame" by using the generating function F2{<j)x. Resonance precessing frame and Poincare surface of section We transform the Hamiltonian Eq.J i ) s i n < ^ 0! = 5 ! + G i _ 1 £ — .Ji) cos <fc. . Hamilton's equations of motion are Ji = G i . The particle motion in the resonant precessing frame is determined completely by the condition of a constant J2 and a constant Hamiltonian value Hi(Ju <j>u J2) = Ex. Hx = 6^ + G i .366) Q^ + | F 2 = 26p2.362) 02 = 4>z. J2) + H2{J2). The new Hamiltonian is H = HiiJufa.363) The horizontal and vertical betatron motions exchange their actions while the sum of actions is conserved. (2. The system is integrable with two invariants J2 and H\ = E±. (2.367) .
_i^|.367).-M /2~2Jl = 0. This means that the horizontal action can be fully converted to vertical action and vice versa. where Ji = J2. the particle inside the Courant-Snyder circle. the phase (f>i rapidly varies on the Courant-Snyder circle (see the top right plot of Fig. If there is no other noise source. If 6i = 0. The size of the ellipses depends on the initial condition. moves along the Courant-Snyder circle shown in very rapidly.-!^! 2 . 2/MJ2-. Figure 2. (2. (2. When the particle trajectory Eq.366). They are located at fa = 0 or T with T S1 ± Gx. LINEAR COUPLING where A = JS{ + IGI. (2.365).368) Figure 2.366) and (2. 191 and the normalized coordinates Q.367). (2.370) . P^-^/zhsinfa. P are Q = fehcosfa.VI. (2. As the betatron oscillation reaches follows the coupling ellipse. the coupling ellipse becomes a straight line cutting through the origin Q = 0 and P = 0.P = sfiT-i.47).369) If S\ 3> |Gi. Based on the equations of motion (2./1) (2.43: Schematic drawing of the CourantSnyder circle of Eq.365) changes rapidly on the Courant-Snyder circle. D. which is The minimum horizontal amplitude is Qmin = %fih.366) and the coupling ellipse of (2. A (2. Eq.43 shows a schematic plot of the Courant-Snyder circle and the coupling ellipse of Eqs (2. particle motion will follow the path of solid (or dashed) lines. 2.364) and (2. The phase coordinate fa of Eq. the phase fa varies Q = 0. General linear coupling solution The fixed points of the Hamiltonian are determined by the conditions j \ = 0 and fa = 0. then Qmm ~ V^h and the betatron coupling is negligible.367) with 5i = X/s/2.
where the betatron tunes are vx = 4.00628 m" 1 .364) and (2. The results are obtained from simple tracking calculations of particle motion in a synchrotron with perfect linear decoupled betatron motion everywhere except a localized skew quadrupole kick. Thus the effective resonance strength is about G\t-ifi = 0. Thus the evolution of the action coordinate at a linear coupling resonance is given by h = /7 2 -(£/A) 2 cos[A0 + <p] + J. Using Hamilton's equations [Eqs.372) J = (2Ji£ + Gl_litJ2)/2\2 with a Hamiltonian value E = 5\J\ + Gi^iti^Ji(J2 . (2. n At SFPs. The values of the betatron amplitude functions at the skew quadrupole location is fix = 10 m.44 shows 6 Poincare surfaces of section in the resonance rotating frame with a given value of J2 = Jx + Jz.368) in the resonance rotating frame obtained from numerical simulations of particle motion in a synchrotron with linear betatron motion and a localized skew quadrupole kick. Figure 2. we obtain Ji + X2Ji = A2 J.43 and 2. (2.01.44: Phase space ellipses of P vs Q given by Eq. and j3z = 10 m.366) is divided into two halves (see Figs.825 and the strength of the skew quadrupole is a\/p = 0. (2. (2. (0i = TT) -fr . the Courant-Snyder ellipse Eq. the skew quadrupole strength is a\/p = 0.192 CHAPTER 2. Figure 2. (2.00628 m"1. vz = 4. where (2. The values of betatron amplitude functions are /3X = 10 m and f}z = 10 m at the skew quadrupole location. the betatron tunes of the machine are vx = 4. Note that the structure of the phase space ellipses remains the same if J2 is varied.820.825. TRANSVERSE MOTION The stable fixed points (SFPs) of the Hamiltonian are J (2 "" °i/AA)J2' (01-0) [ \ (5 + <*i/2A) J 2 .367) rewritten as G\t-\/ \fT\ cos 4>\ — &\y/7^—~J[. With the coupling ellipse Eq. These ellipses correspond to various initial J\ and (pi values with J2 = 90TT mm-mrad.373) . 2.82 and vz = 4. the horizontal and vertical betatron motions are correlated in phase without exchange in betatron amplitudes.365)].44).Ji) cos</>i.
VI. (2.82 m. they will orbit around different fixed points at different island tunes. and the betatron tunes for this experiment were chosen to be vx = 3. we discuss an experimental study of linear coupling at the IUCF cooler ring. But." Here we find that the island tune of coupling motion around SFPs is equal to A. The cooler is a proton storage ring with electron cooling.*|2. vz = 4. The beat period were measured to be about 120 revolutions. VI. The tune of beating is equal to A = yj(vx . the bunch will resume its original shape after A"1 revolutions. The number of complete island motions in one revolution is called the "island tune. LINEAR COUPLING 193 where \E\ < XJ. The linear coupling gives rise to beating between the horizontal and vertical betatron oscillations. Note that the tune of the linear coupling motion is independent of betatron amplitude. In the following. The experiment started with a single bunch of about 5 x 108 protons with kinetic energy of 45 MeV at the Indiana University Cyclotron Facility cooler ring.96 If particles in a given bunch distribution have identical betatron tunes. However. which is independent of the betatron amplitude.45: The measured coherent betatron oscillations excited by a horizontal kicker. The SFPs of Eq. Stable islands are separated by the separatrix orbit that passes through unstablefixedpoints (UFPs).0083. and the motion will decohere after some oscillation periods. The circumference is about 86.362). . if particles have different betatron tunes. which corresponds to A ss 0.817 with ux — vz ss —1.371) correspond to the orbit with E — ±AJ = i A J ^ p . and the injected beam was electron-cooled for about 3 s before the measurement. there is no UFP for the linear coupling Hamiltonian Eq.uz)2 + |Gi. Figure 2. the horizontal and vertical betatron tunes are tuned to the linear coupling resonance line at vx — vz = t.826. and tp is an initial phase factor._i.3 Experimental Measurement of Linear Coupling To measure the effect of linear coupling. (2. linear coupling can cause bunch shape oscillations. The cycle time was 10 s. producing a full-width at half-maximum bunch length of about 9 m 96The motion about SFPs of a nonlinear Hamiltonian resembles islands in the phase space and is thus called island motion.
Figure 2.0309 MHz. The Lambertson septum magnet at the injection area also contributed a certain amount of skew quadrupole field. The linear coupling in the IUCF cooler ring arose mainly from the solenoid at the electron cooling section.45 are transformed to the Poincare map in the normalized coordinates (x. The tune separation between these two normal modes is equal to A of Eq.05 7r-mm-mrad). Note that the betatron beating between the x and z betatron motion gives rise to energy (action) exchange between the horizontal and vertical betatron oscillations. we used a kicker with rise and fall times at 100 ns and a 600 ns flat top. . the motion of the beam can be visualized as a macro-particle. The subsequent bunch transverse oscillations from a BPM are detected and recorded. TRANSVERSE MOTION Figure 2. The beat period were measured to be about 120 revolutions. The rf system used in the experiment was operating at harmonic number h = 1 with frequency 1.0083. (or 100 ns) depending on the rf voltage. For the IUCF cooler ring. which corresponds to A « 0.Vz) is out of phase with that of the horizontal map.46: The betatron oscillations of Fig.0309 MHz revolution frequency.97 The minimum tune splitting of these two normal modes is equal to the magnitude of the linear coupling constant. Figure 2. which was locally corrected. In the presence of linear coupling. the measured betatron tunes correspond to normal modes of the betatron oscillations. The vertical map (z.42 shows the normal-mode tune vs quadrupole combo. The coherent betatron oscillation of the beam was excited by a single-turn transverse dipole kicker.Vx)The amplitude modulation of betatron motion is translated into breathing motion in the Poincare map. Since the emittance of the beam in the cooler is small (0. and possibly also from quadrupole roll and vertical closed-orbit deviations in sextupoles. (2. IGi^j^.45 shows a typical example of the beating oscillations due to the linear betatron coupling following a horizontal kick.360). 97 A tune combo is a combination of power supply to a set of quadrupoles for achieving independent horizontal or vertical tune change. 2. This is sufficient for a single bunch with a bunch length less than 100 ns at 1.194 CHAPTER 2.
where the relative betatron phase advances at the locations of the horizontal and vertical BPMs were included. The solid line in the bottom right plot shows a fit by using Eq. Transforming the phase space into the resonant precessing frame. and f)x = 7.43.55 m. 2. where the particle motion follows the solid line of the Courant-Snyder invariant circle and the coupling ellipse shown in Fig.46 shows the normalized phase space x. the horizontal and vertical phase-space maps were completely smeared.z') is shown in the top right plot.364) to obtain the coupling strength Git-ite = 0. dJ\/dN (right) in [7r-mmmrad/turn].47: The top left shows the actions Jz vs Jx near a linear betatron resonance. The solid line in the bottom left plot shows a five-point running average. The Poincare surface of section in the resonant processing frame derived from (x. LINEAR COUPLING 195 Figure 2. Measurement of linear coupling phase To measure the linear coupling phase x. Vx (a similar plot can be obtained for z.0078 and the coupling phase x = 1-59 rad. II. the torus of the 2D Hamiltonian is shown in the upper right plot in Fig. (2. 2.VI. . we can transform the horizontal and the vertical Poincare maps into the resonant precessing frame discussed in Sec.45. x') and (z.J2Ji(}xsm<l>i. The orientation of the resonant line was used to determine the coupling phase x = 1-59 rad. Vz) of the data shown in Fig. P = -. Because of linear coupling.47. Figure 2. The resonance phase was fitted to obtain an upright torus. The bottom plots show the action Ji (left) in [Tr-mm-mrad] and its time derivative. where Q = yJ2J\Pxcos(j>i. 2.
2. "The difference signal or a A-signal from BPMs carries the information of betatron oscillations around the closed orbit.5 ms before the beam was coherently excited by a horizontal kicker. where the vertical betatron tune jump method is used to overcome intrinsic depolarizing resonances.48 shows the output from a spectrum analyzer using the Asignal of a horizontal beam position monitor (BPM) as the input.196 CHAPTER 2.98 The Poincare map derived from experimental data at a 2D linear coupling resonance shows invariant tori of the Hamiltonian flow (see Fig. A spectrum analyzer operating at zero span mode is a tuned receiver that measures the power of betatron motion. VI. we can obtain the magnitude and phase of the linear coupling. of skew quadrupoles. Figure 2.45 corresponds to the time interval between the dips of Fig. we can determine the magnitude and the phase of the linear betatron coupling. Such a correction method can be used for on-line diagnosis to make the choice of skew quadrupole correction families more efficient. The beat period shown in Fig. where a five-point moving average of Ji is used to obtain a better behaved time derivative of the action Ji.48. 2. 2. The data of the time derivative dJi/dN are fitted with Eq. This implies a smaller nonlinear betatron detuning for the IUCF cooler ring. The magnitude of the linear coupling obtained from the invariant tori agrees well with that obtained by the traditional method of finding the minimum separation of the betatron tunes with combos of quadrupole strengths.47 has a small curvature.4 Linear Coupling Correction with Skew Quadrupoles The linear coupling resonance is usually corrected by maximizing the beat period of the transverse betatron oscillations using a pair. The procedure for linear coupling correction is as follows 98Note that the coupling line shown in the Poincare surface section (upper left) plot of Fig.43). shown as a solid line in the lower graph of Fig.47. 2.364) to obtain Gh-he = 0. 2. 2.0006 and x — 1-59 rad. TRANSVERSE MOTION Measurement of coupling strength Git-ij The measured action J\ as a function of time and its time derivative dJi/dN = 2irJi are plotted in the bottom plots of Fig. Using these invariant tori and Hamilton's equations of motion. Knowing the dynamics of the linear coupling of a single-particle motion may also help unravel questions concerning the dynamical evolution of the bunch distribution when the betatron tunes ramp through a coupling resonance." The spectrum analyzer was tuned to a horizontal betatron sideband and was triggered 1. 2. top right plot and the solid line in Fig.47. . the increase in vertical emittance due to linear coupling may cause difficulty in later stages of polarized proton acceleration. When the betatron tunes cross each other adiabatically after the tune jump. In a single digitized measurement. Such a problem is important for polarized proton acceleration in a low to medium energy synchrotron.47.0078 ±0. or at least two families. (2.
F. Sci.. and (3) the characteristic change in features at a 17 ms interval corresponded to a strong 60 Hz ripple. which altered betatron tunes. NS20. which is evident in Fig. Nucl.6. 1990 EPAC.6.2). II can be expanded into 4x4 matrix by using transfer matrices for skew quadrupoles (Exercise 2. This reduces the coupling strength Gi.6. This procedure is however hindered by the betatron decoherence and by the 60 Hz power supply ripple. 1429 (1990).1) and solenoids (Exercise 2. the most important issue is that there is no guarantee a priori that the set of skew quadrupoles can properly correct the magnitude and phase of the linear coupling. Guignard. (2) the decay of the power spectrum corresponded to betatron decoherence.6).5 ms before a coherent horizontal kick. 100D. p. et o(. 1432 (1990). 2. The 4x4 transfer matrix in one complete revolution can be diagonalized to obtain normal-mode betatron amplitude functions. 2. Repeated iteration of the above steps can efficiently correct the linear coupling provided that the skew quadrupole families have proper phase relations. IEEE Trans. Other possible complications are closed-orbit changes due to off-center orbits in the quadrupoles and skew quadrupoles. The transfer matrix method of Sec. Figure 2. Maximize the time interval between dips (or peaks) of the spectrum by using families of skew quadrupoles. Maximize the peak to valley ratio in the spectrum by using quadrupole combos. 2. G.A.-i/. . Note that (1) the time interval between these dips corresponded to the beat period of Fig.VI.C. ibid.45. Teng. Gourber et al. Proc.48: The spectrum of the A-signal from a horizontal BPM from a spectrum analyzer tuned to a betatron sideband frequency with resolution bandwidth 30 kHz and video bandwidth 30 kHz triggered 1.48. VI. p. LINEAR COUPLING 197 1. 758 in Ref.5 Linear Coupling Using Transfer Matrix Formalism So far. Edwards and L. Willeke and G. our analysis of linear coupling has been based on single-resonance approximation in perturbation approach. [11] (1988).100 This procedure has been implemented in MAD [19] and SYNCH [20] programs (see Exercise 2. Thus measurement of the coupling phase is also important.P. J. and the coupling angle at each position in the ring. This is equivalent to setting Si = 0 for attaining 100% coupling. However. Ripken. p. 855 (1973).
where Mqua<j is the transfer matrix of a quadrupole.d »)• " < ' 2)- .—^ Bp dz (b) Show that the transfer matrix of a skew quadrupole is C+ -JqSC_ \-y/qS+ where C+= 5 + = —. where q= .6 1. z) by an angle tj> is ( i \ / a: \ / cos ( ^ 0 sin (j> 0 \ £' I p/j. z" + qx = 0. p / S+/Jq C_ C+ -JqS+ 5_/V? C+ C_ -y/qS- 5_/V9\ C_ S+/^q\ C+ I cos 6 + cosh 6 _ s i n # + sinh# = 2 ' 2 ' °-= 5 cos 6 — cosh 0 - = sin^ — sinhS 2 ' 2 ^ ' 0 = ^fqL. > > (d) In the thin-lens limit. show that the 4x4 coupling transfer matrix reduces to "-1 + T»- v . Az = 0.198 CHAPTER 2. and £ is the length of the skew quadrupole. AX = 0. i. This exercise derives the linear transfer matrix for a skew quadrupole. Bs = 0.25). z) to (x. (a) Show that the equation of motion in a skew quadrupole is x" + qz = 0. This means that a skew quadrupole is equivalent to a quadrupole rotated by 45°.~ ) 2 \ dx dz Jx=z=0 where Bo is the main dipole field strength.\ I ^ . L — 0 and qL — 1 / / . p/j-v f RW=\ 0 sin(j) C0Sl ^ 0 0 cos sin0 I • ^ 0 V 0 -sin^ 0 cos(f>J Show that the transfer matrix of a skew quadrupole is M skew quad = -R(-45°)M quad i?(45°). Bx = BoalX. where the magnetic field is with B0oi = \ (^ . where / is the focal length. (c) The coordinate rotation from {x. the skew quadrupole field satisfies Maxwell's equation dBz/dz + dBx/dx = 0. Apparently. TRANSVERSE MOTION Exercise 2.e. =W) ^ 5'/ \z'/ . The vector potential is Bl = -Boalz. As = -BQCLIXZ. and oi is the skew quadrupole coefficient in multipole expansion of Eq. (2.
y = e? y. where L is the length of the solenoid.jg'y = o. and the equation of motion becomes y" + g2y = 0. i. show that the transfer matrix for the solenoid becomes cos 2 0 isinflcosfl -sin0cos6> -isin20 \ —g sin 9 cos 9 cos2 9 gs'm92 — sin 9 cos 9 s'm9 cos 0 isin20 cos 2 0 isin^cos^ —psin2^ sin 9 cos 9 —gsin9cos9 cos2 9 ) 3. Thus both horizontal and vertical planes are focused by the solenoid. .6 199 2. the corresponding focal length is f~x = g2L = 0 2 / I . and 0 = gL is the rotating angle of the solenoid. where the solenoidal field strength is g = —2p • (a) Show that the coupled equation of motion becomes y" .353) in the presence of skew quadrupoles and solenoids are ( I01Note here that the solenoid. (b) Transforming coordinates into rotating frame with 9 = 1 gds. x" + Kx(s)x + 2gz'-(q-g')z = 0. Jo show that the system is decoupled. The focusing function is equal to g2. and j is the complex imaginary number.e.jtgy' . Linear transfer Matrix of a Solenoid: The particle equation of motion in an ideal solenoidal field is x" + 2gz' + g'z . z" . in the rotating frame. (c) Show that the transfer matrix in the rotating frame is y =ye~^"\ where ( cosS jsin0 0 0 \ -gsmO 0 0 cos0 0 0 0 cos6> -gsin9 0 | isintfl' cosfl / where 9 = gs.101 (d) Transforming the coordinate system back to the original frame. In small rotating angle approximation.g'x = 0. z" + Kz(s)z + 2gx'-(q + g')x = 0. where g = B\\(s)/2Bp and q = -{dBz/dz)/Bp = ax/p.EXERCISE 2. Show that Hamilton's equations of motion for the Hamiltonian (2. where y = x + jz.2gx' .0. acts as a quadrupole in both planes.
TRANSVERSE MOTION (a) Show that the perturbation potential due to skew quadrupoles and solenoids is V]c = -^Xz P + \P g{s)(^x-^z).Y. and Ei = <5i/i + G\t-\tiy/I\{l2 — Ii) cosrj)i is a constant of motion.359). (a) Show that the new conjugate phase-space variables are h = Jx. show that the linear coupling equation of motion for the Hamiltonian (2.<f>zJi. . Liu et al. 4.102 5.h) = (<£* -4>z-id + X)h + 4>zh.i for the ^-th harmonic is given by Eq. see J. Rev. Px =-V^sin((j)x+Xx). A = JS\ + G\ _x e. \Z = v / 2 ^ c o s ( ^ z + Xz). 102 For a general discussion on linear coupling with nonlinear detuning. Using the generating function F2(<t>x.362) in resonance rotating frame. The Hamiltonian H = uxjx + vzjz + Git-ite\/JxJzcos((t>x ~4>z + x) for a single linear coupling resonance can be transformed to the normalized phasespace coordinates by (X = %/2Jx~cos(<l>x + Xx). Pz = -^/2Tzsm{j>z + Xz). fa = <t>x ~ 4>z ~ 10 + x. 8\ = vx — vz — t is the resonance proximity parameter. (d) Discuss the solution in the resonance rotating frame. (a) Show that the Hamiltonian in the new phase-space coordinates is H = \vx(X2 + Pi) + \vz{Z2 + P2Z) + \GX^{XZ + PXPZ). 2347 (1994). h = Jx + Jz.357). Phys.200 CHAPTER 2.359) can be transformed into the Hamiltonian (2. <h = 4>z- (b) Find the invariants of the Hamiltonian (2. E 49. where the overdot corresponds to the derivative with respect to orbiting angle 6.. (c) If the accelerator lattice has P superperiods. where Xx ~ Xz = X 1S a constant linear coupling phase (Mod 2TT) that depends on the location in the ring. show that G\ _i i = 0 unless ( = 0 (Mod P). P ) (b) Expand the perturbation potential in Fourier series and show that the coupling coefficient Gi:-i. (c) Show that the equation of motion for I\ is /i + A271 = S 1 5 1 + 7 2 G ? j _ M / 2 . (2.
sin $ z I ' ]j | sin^sin^zl j ' f ~ I V where / is the focal length of the skew quadrupole. we note that the "horizontal" and "vertical" betatron oscillations carry both normalmode frequencies. 2. the particle motion in a synchrotron with linear betatron motion and a localized skew quadrupole kick. Show that the condition of linear stability for betatron motion is VM~* < M i n ( 2 /(I + " » * » ) ( ! + « » $ . i.EXERCISE 2. can you find the stability limit of a linearly coupled machine with superperiod P? . 6.6 (b) Show that the eigen-frequency of the Hamiltonian is v± = \{vx + vt)±^\ A = y/(ux . /3X and /3Z are values of betatron amplitude functions at the skew quadrupole location.) 1 I sin $3.44. ) 2 /(l-C06& a )(l-C0Bg. Based on your study of this problem. Analyze the linear stability of the simple tracking model shown in Fig. T^]f\A+ cos(l/+f + *+) + A~ ""("-V + ?-)- where ^4±.e.v2f + |G x . 201 (c) Solve X and Z in terms of the normal modes. and §x and $ 2 are betatron phase advances of the machine without the skew quadrupole. and show that { X = A+ cos(v+ip + £+) ~ J^T£AZ = COS(I/_<^ + £_).^± are obtained from the initial conditions. Particularly._ w p.
The changes of phase space . the betatron Hamiltonian [x12 + Kxx2 + z12 + Kzz2\ + V3(x. the nonlinear magnetic field can give rise to geometric aberration in the beam ellipse if a resonance condition is encountered. z. they are an integral part of accelerator lattice design.z. Including the sextupole field. Since the sextupole magnets used in accelerator are usually short. More generally. (2.202 CHAPTER 2. V shows that chromaticity correction in particle accelerators is essential for attaining particle beam stability.376) The evolution of phase space coordinates of orbiting particles can be obtained by tracking the equation of motion. s). modern high energy storage rings usually use high field (superconducting) magnets that inherently possess systematic and random multipole fields. TRANSVERSE MOTION VII Nonlinear Resonances Our discussion in Sec. For off-momentum particles. 0 (2.374) . Let S = J S(s)ds be the integrated sextupole strength. and thus the nonlinear geometric aberration due to sextupoles and higher order multipoles needs to be addressed. the sextupole strength S(s) should be replaced by B2/KI + S)Bp].375) where Vz(x.s) = ^S(s)(x3 — 3xz2) is the nonlinear perturbation potential with S(s) = —B2/BP. z" + Kz(s)z = +S{s)xz. This section provides an introduction to this important subject. Hill's equation of motion becomes x" + Kx{s)x = -^S{s)(x2 .3xz2). Careful analysis of the nonlinear beam dynamics is instrumental in determining the dynamical aperture. (2. Tracking methods In the presence of sextupole magnetic field. where B2 = d2Bz/dx2\x_z_0 is H=lAs = § ( x 3 . 1 Nonlinear Resonances Driven by Sextupoles The vector potential for a sextupole magnet is Ax = Az = 0. but is limited to first-order perturbation treatment. Since sextupole and higher order multipole magnets are needed in chromaticity correction. thin lens approximation has often be used in particle tracking.z2). where 5 — Ap/po- A. VII. Although the nonlinearity is normally of the order of 10~3 — 10~4 relative to that of the linear component.
s) becomes Vs = -^Ji / 2 J z /3y 2 ^5( S )[2cos$ I + cos($:c + 2$ 2 )+cos($ I -2$ z )] +^Jll2Pl'2S{s)[cos 3$x + 3 cos $x].49: The Poincare maps for the betatron motion perturbed by a single sextupole magnet at a tune below (left) and above (right) a third order resonance. The topology of the phase space maps rotates 120° when the tune moves across the third integer resonance. B. With Eq. z.378) 103In this mapping equation for betatron motion.49 shows the Poincare maps with one sextupole in an otherwise perfectly linear accelerator near a third order resonance. Figure 2. NONLINEAR RESONANCES coordinates at the sextupole magnet are103 Ax' = -\§(x2 .94) for coordinate transformation. (2.377) The propagation of phase space coordinates outside the sextupole magnet is given by the mapping equation (2. we disregard the effect of sextupoles on orbit length. we perform Floquet transformation to the Hamiltonian (2. The integrated sextupole strength is S = 0. (2. The region of stability decreases as the tune approaches the third order resonance. Az' = Sxz. we find AC = (xAx' + zAz').45).z2).170). Figure 2.375). .VII. The leading order resonances driven by sextupoles In order to analyze the third order resonance analytically.5 m~2. 203 (2. (2. the nonlinear perturbing potential V3(x. Using Eq.
Jl12 cos 3$x Pl/2 Jjj/z driving terms Classification sum resonance difference resonance parametric resonance parametric resonance C. .i drive vxJr2vz — £ and ux—2uz = £ resonances. <j)x) and (J 2 .^i. Table Resonance vx + 2i/z = £ ux -2vz=£ ux = £ 3vx = £ 2.£ are Fourier amplitudes. Gi.^ I1/ V. ^i.379) 1 where £ is an integer. Since V3 is a periodic function of s.i.i) + £ GwHwJl'2J. . xx= -5-.i and G\. G3. 1 lists nonlinear resonances that can be excited by sextupoles in firstorder perturbation theory._2. + J2 Gi. and • • • describes the remaining resonance driving terms at vx = integers. Third order resonance at 3^x = £ Near a third-order resonance at 2>yx = £.vxe.379) can be approximated by H w vxjx + G3fiil fj2 cos (30X -£9 + 0.-2.. the Hamiltonian (2.104 The Hamiltonian (2. (2.£ are the phase of the Fourier components.o.-2. . Jo pz Here (Jx. G\2.iJl'2 cos(30x . G\^.0. The Fourier amplitude Gz$.o. We discuss below a ID third-order resonance at 2>vx = £. Guignard. 008(0. can also be excited by strong sextupole fields through second..2$ z ) Pl/2p~z Jx/2Jz cos$ x Pl/2PZ] P'^2 Jx^2Jz.«.id + &.or higher-order perturbation expansion.0 2 ) are pairs of conjugate phase-space coordinates.£) e cos(0s + 2cj>z -M + 6.2 .-2.i drives the third order resonance at 3 ^ = £. Table VII.3: Resonances due to sextupoles and their Driving term Lattice Amplitude cos($ I + 2$ z ) Pll2Pz Jx/2Jz cos($j.£. p.20.«. etc.. [10] (1988)._w) + • • •. .375) expressed in action-angle variables becomes H = vxJx + VzJz + J2 G3.2. (1976). Other higher-order resonances. §z = <l>z + Xz{s)-Vz6. .o. Guignard. CERN 76-06. ^3.204 where CHAPTER 2. such as 4vx = £. and similarly. it can be expanded in Fourier harmonics. 822 in Ref.£6 + £3. G. G. .2. (2-380) 104 G. TRANSVERSE MOTION $x = <l>x + xx{s) . . 2vx±2vz = £. Jo p x f ds Xz= -5-. .
381) The betatron phase space of the Hamiltonian (2.M-(3*-Mds. Since the chromatic sextupoles are usually arranged according to the superperiod of the machine. (f>x are conjugate phase-space coordinates.384) 0 = 5 +\G3.eWe note that if the accelerator has a superperiod P and the sextupole field satisfies a similar periodic condition. 9 is the orbiting angle serving the time coordinate.382) the Hamiltonian Eq. Using the generating function F2 = (4>x-i-e+^)J.o.380) becomes H = 5J + G3. the resonance strength Gz$.24.VII. one should pay great attention to the systematic sextupolar nonlinear resonances.e.o. (2. (2.1). the sextupole can cause "geometric aberration" to the betatron motion. Since the Hamiltonian (2. where the new phase-space coordinates are (2.380) is distorted by the nonlinear resonance. and the Fourier amplitude G3.o. and their resonance strengths are usually weak. the systematic third-order resonance strength for the AGS will be zero except for £ = 12.i is zero unless £ is an integer multiple of P (see Exercise 2.383) Here S — vx — £/3 is the resonance proximity parameter. For example. Particle motion in the phase space follows the contour of a constant Hamiltonian.< are G3i0/ & = ^ f Pi'2 S(s) e*Px. the contribution of each superperiod is coherently additive to the resonance strength.7. Using Hamilton's equations of motion cos 30. At a systematic resonance.« and the phase f = £3io. etc. vx is the horizontal betatron tune.385) . NONLINEAR RESONANCES 205 where Jx. the "Hamiltonian" is invariant. Thus the nonlinear resonances are classified into systematic and random resonances. (2. J = 3G3. The magnitude of the geometric aberration is proportional to the resonance strength G3. the betatron tunes should avoid low-order nonlinear resonances. (2.383) is autonomous. Random sextupole fields induce nonlinear resonances at all integer £.eJ3/2 cos 30.o. Systematic nonlinear resonances are located at £ = Px integer. (2. Nevertheless. i.Q/J112 we obtain 3 + 9623 YG10/32 = 96E.£J3/2sin30.
388) These unstable fixed points can be easily verified as follows. The solid line shows aJ^/Gzja^i vs aS/G^0<l for the case a = axx > 0 and 03. When the amplitude is small. the UFP. the tune. TT. Thus a particle can stay indefinitely at a fixed point.50: The dashed line shows the third-order betatron resonance in the zero detuning limit. the Hamiltonian assumes the value *--!(«£. Figure 2. The fixed points are characterized as stable or elliptical fixed points (SFPs) and unstable or hyperbolic fixed points (UFPs). . Small-amplitude motion around a SFP is a bounded ellipse. Bifurcation of the third-order resonance occurs at a8/G\Ql = 9/16 marked by the rectangular symbol.206 CHAPTER 2.)'• K . (2. The equation of motion becomes 105Fixed points of a Hamiltonian are phase-space loci with zero velocity field.6-^—K2 = 0.383) has three unstable fixed points (UFPs)105 with de These UFPs are located at ji/2__2S_ UFP " 3G3. <2-» (2. ±2^/3. (2"386) At the fixed point. where FP stands for both stable and unstable fixed points. The SFP section and the UFP section are marked. of Stable and unstable fixed points The Hamiltonian Eq. J^l/G^i vs 6/GJM.o. if S/GW > 0. of the third-order resonance is 35 because the betatron amplitude repeats three times in every revolution.352K . U F P = 0. around an UFP it is hyperbolic. Let K = J — JUFP and E = EUFP. in the resonance rotating frame. and the overdot indicates the derivative with respect to the orbiting angle 9.0/ > 0. I 0FP = dbr/3.* with ' de~ if«5/Gw<0. TRANSVERSE MOTION where E is the Hamiltonian value.
the third-order resonance appears at all values of S.391) for the case of 5/Gz.1] [P . 2. With X and P defined as X = J-—cos(/>. the betatron tunes depend on the betatron actions. Three straight lines X = 1/2. the separatrix can be obtained from Eq.389) Separatrix The separatrix is the Hamiltonian torus that passes through the UFP. Note that the stable phase-space area is proportional to the resonance proximity parameter <52 (see Eq. the stable phase-space area in (x. The stable motion is bounded by the curve of J^P(S) shown in Fig. Without a nonlinear detuning term. and P = -^{X + 1) divide the phase space into stable region and unstable regions. beam particles can be slowly squeezed out of the stable area and extracted to achieve high duty cycle for nuclear and high energy physics experiments. V "MJFP P = -J-—sin<t>. Near a thirdorder resonance.o. i\. (i^). P)VFP is given by the intersection of these three lines: (X. Including the effect of nonlinear .390) the equation for the separatrix orbit becomes [2X .383) with the condition H = EVFP. NONLINEAR RESONANCES 207 Thus the motion near the fixed point is hyperbolic. (2. For the thirdorder resonance in the zero detuning limit. The third-order resonance can be applied to extract beam particles slowly from a synchrotron.386)). i.P)UFP = (-l. For a given aperture J. (2. nonlinear magnetic multipoles also generate nonlinear betatron detuning. Thus the separatrix is given by three intersecting straight lines.50. V "AjFP (2.~).VII. the width of the third-order betatron resonance is then Hwidth = 3G3.±(X + 1)] [p + -^(X + 1)] = 0 (2. x') is equal to %/3<J/2|G3io.e.^|. Because of the nonlinear term in Eq. the amplitude is seen to grow faster than an exponential. P = ±(X + 1). and (X.0).388).£J1/2/2(2. Beam loss may occur when particles wander beyond the separatrix.o.i > 0. If the betatron tune vx ramps slowly through a third-order resonance. The dynamical aperture is defined as the maximum phase-space area for stable betatron motion. Effect of nonlinear detuning In fact. (2.
Measurements of Poincare maps near a third-order resonance have been successful at SPEAR. (2. 7942 (1992).106 E. ±TT/3 6 < 9G^/16a 0 < 5 < 9G§p(W/16or ' (2.e < 0.= I +3/4 + (3/4) y/l . stable fixed points appear.393) The bifurcation of third-order resonance islands occurs at I6a5 < §G\ 0 1 . we can model sextupole strengths of the storage ring.51 shows a Poincare map obtained from a nonlinear beam dynamics experiment at the IUCF cooler ring.0.D. Figure 2. [ + 3 / 4 .378). Ellison et al.« J 3 / 2 cos 3<£. experimental measurements are generally difficult. D.±27r/3 A 5<0 J ^ . 572 (1996) for the vx +2vz= t resonance at the IUCF cooler ring.392) to obtain parameters G^o^ and £.(I6a5/9G2M).50 shows aJ^F2p/\G3fi/\ vs a5/G\fil for the bifurcation of third-order resonance. . 107 See 106 D.208 CHAPTER 2. Aladdin.±ir/3 cj> = TT.(3/4) y/1 . Converting into action-angle variables. and the IUCF cooler ring. Phys. Figure 2. et at. sextupoles contribute importantly to the nonlinear coupling resonances at vx ± 2vz = t with integer Lim The third-order resonance strength can generally be obtained by taking the Fourier transform of Eq.2vz = I induce betatron coupling. I i < = 0.2vz = I resonance. Budnick et al. we can fit these data by the Hamiltonian (2. Methods A368.3 / 4 + (3/4) 0 : ^ ( 1 6 ^ 7 9 0 1 ^ ) . Inst. Nucl. TRANSVERSE MOTION betatron detuning. Rev.(16aaS/9Gjji(W). It is easy to observe degradation of beam intensity and lifetime near a resonance. TEVATRON. and obtain the parameter S by measuring the betatron tune at a small betatron amplitude.392) where a = axx is the nonlinear detuning parameter. Rev. Caussyn. 4> = w. M. Using these measured nonlinear resonance parameters. Experimental measurements of nonlinear resonances are usually difficult because of short lifetime at the resonance condition. Experimental measurement of a Zvx = £ resonance Because beam particles may be unstable at a nonlinear resonance. and J. 4051 (1994) for the vx . the Hamiltonian for the third-order resonance is H = SJ+ -aj2 + G3.c f .t > 0 are aJi/2 ^-^3. Phys.0. The difference resonance at vx . A 46. The fixed points of the Hamiltonian for a > 0 and G3fi.. A similar analysis can be carried out for a < 0 or Gsfi. while the sum resonance can cause beam emittance blow-up in both horizontal and vertical planes and leads to beam loss. With nonlinear detuning. (2. Other 3rd-order resonances driven by sextupoles Besides the third-order integer resonance. E50.
Tori for particles inside the separatrix are distorted by the third order resonance. The solid lines are Hamiltonian tori of Eq. etc. Here we give an example of the fourth-order parametric resonance at 4vx = 15. Y. 33 (1992). Avz. 292. Phys. 1838 (1992). (2. et al.108 Similarly. Nonlinear beam dynamics is beyond the scope of this book. Proc. Lett. 2i/x ± 1vz. nonlinear beam dynamics studies at the IUCF cooler ring show the importance of nonlinear resonances. Rev. and dynamical aperture. Wang. 2752 (1988). 6 1 . <j>). 67. EPAC p. T. No. 170 (1992).7496. Lett. However.109 108 A. Figure 2.Y. E 4 9 . et al. 5697 (1994). The concatenation of strong sextupoles can generate high-order resonances such as \vx. 68. rotates at a rate of betatron phase advance along the ring.378) that sextupoles will not produce resonances higher than the third order ones listed in Table VII.52 shows the Poincare maps of the single sextupole model of Fig. Phys.392). T.px) of betatron motion near a third-order resonance 3wx = 11 at the IUCF cooler ring... Satogata. 5vx. Phys. The right plot shows the Poincare map in action-angle variables (J. et al. 2.1. M. Lett.. nonlinear beam dynamics experiments at Fermilab Tevatron were used to study the concept of smear. NONLINEAR RESONANCES 209 Figure 2. nonlinear detuning. Rev. N. 791 (1988). strong sextupoles are usually needed to correct chromatic aberration. Rev. Employing strong sextupoles. 3768 (1991). Lee. et al.VII. AIP Conf. 68.. decoherence. Phys. . Chen et al.49 at vx = 3. Rev. (2. Rev. VII. Proc. Phys. determined by sextupoles. The orientation of the Poincare map. Note that a single sextupole can also drive the fourth and higher order resonances.2 Higher-Order Resonances It appears from Eq. Chao. et al. Merminga... p. Lett.51: Left: The measured Poincare map of the normalized phase-space coordinates (x.. Note that particles outside the separatrix survive only about 100 turns. 109 S. Ellison et al.
The Poincare map near a fourth-order resonance Avx = 15 measured at the IUCF cooler ring is shown in Fig. Systematic experimental measurements of nonlinear resonances can be used to derive the resonance parameters. In order to overcome nonlinear resonances. In this example. Accelerator operators are keen to avoid low order strong resonances because of visibly short beam lifetime. 2.53. the fourth-order resonance islands are enclosed by stable invariant tori. (2.49 at vx = 3. 2. a few nonlinear magnets (usually up to octupole) are powered to eliminate the Fourier components of the nonlinear resonance near the machine operation condition. The solid lines shows the Hamiltonian tori of Eq. Note that when the betatron tune is exactly 15/4.53./ can be obtained from the Fourier transformation of the effective particle Hamiltonian in the synchrotron. the betatron motion will be located at fixed points of the fourth-order resonance island.394). The tune of motion around SFP of an island is called island tune.210 CHAPTER 2. Ps) phase space and the right plot shows the Poincare map in action-angle variables. Near a fourth-order ID resonance. The topic is beyond this introductory text.52: The Poincare maps for the same sextupole model shown in Fig. (2-394) where the resonance strength G^o. The chromatic sextupoles located in the ring can also be powered to eliminate the un-wanted nonlinear resonance Fourier components. Accelerator physicists are eager to apply their skill to correct or compensate the resonances for minimizing their effects on the beams. 2. and thus the Hamiltonian for particle motion in the accelerator can be modeled. .7496 show the effect of the fourth order resonance. Small deviations from the fixed points will execute motion around the stable fixed points (SFP) shown in Fig. the Hamiltonian can be approximated by H = vx3x + ±axxJ2x + GWJ2X cos{4i>x -M + X). where the left plot shows the Poincare map in the normalized (x. TRANSVERSE MOTION Figure 2.
vx) J . The solid lines are the Hamiltonian tori of Eq. SiS&j PX:j PzJ — - j.| ^ | ) ] sin -KVX J 64?r ~ .| ^ . n l ax* ~ ^\IJS^P^P*JP^J[ i V<? < B^B^R 7 R l"cos[2(7rt/z .[ ) ' '' [ sin ZTTVX cos(7ri/g .53: Left: The measured betatron Poincare map (surface of section) (x.VII. Px) of normalized phase space near a fourth-order resonance 4ux = 15 at the IUCF cooler ring. NONLINEAR RESONANCES 211 Figure 2. the sextupoles will not. concatenation of sextupole perturbation to the betatron motion can induce substantial nonlinear betatron detuning. These coefficients are „ _ 1 V o o q3/2o3/2 [cos3(7ri/J .axz. VII.ijD]! sin7r(2j/2 .<j> = ipx). Note that the phase-space ellipse is distorted into four island when the betatron tune sits exactly on resonance.394). Qz = vz + axzJx + azzjz. 3 Nonlinear Detuning from Sextupoles Because the potential resulting from sextupole fields is an odd function of the betatron coordinates.\1>x#\] S i n 7 r(2^ +^) COS[2(7TI^ . (2. Because sextupole strengths are large in high energy collider and storage rings. . in linear approximation.396) The detuning coefficients axx.2 1 .395) (2. and azz can be obtained from the phase average of the concatenated one-turn Hamiltonian in a storage ring. The dependence of the betatron tunes on the betatron amplitude can be approximated by Qx = vx + axxJx + axzjz. contribute to the betatron amplitude detuning.\ipZtjj\) .(KVX ~ IV'x. The right plot shows the Poincare map in action-angle variables (J = Jx.\$tM\) + nux . (2.
Similarly.i ~ Ad are betatron phase advances from Sj to s. where mxvx +mzuz = I with \mx\ < 1 and \mz\ < 1 and £ is an integer.212 n a" CHAPTER 2. the betatron tunes should avoid linear coupling resonances at vx ± vz = £ due to skew quadrupoles and solenoids. III. The solid lines corresponds to resonance lines associated with normal multipoles.i . 4>Z. Unfortunately.54: Left: the linear resonance lines. TRANSVERSE MOTION _ ! V ? ? /91/2/91/2/9 ft [cos[2(7r^ . The left plot of Fig.}ijjXiij\] ~ 64^ jj SiS'P" P'* P'>iP*<* [ sin7r(2i/. and the dashed lines are those associated with skew multipoles. Since the tune depends on the zeroth harmonic of a perturbed quadrupole field.. V. n are integers. higher order multipoles can drive higher order . where \mx\ + \mz\ < 4.Ipxj.e mxvx + mzvz = £.\tpXij - ip^D'i sinir(2i/z-vx) sin in>x J' where il>X. and half-integer integer betatron resonances at 2vx = m o r 2vz — n due to the linear imperfections discussed in Sec.ij = il>X. + ^ ) | COS[2(TT^ - \jiz.54 shows linear betatron resonances for the fractional parts of betatron tunes. We have shown that sextupoles and higher multipoles are important to beam stability in Sec. Figure 2. i. Right: the resonance lines up to the fourth order coupling resonances.1 ^ 1 ) + nvx . The symbol qx and qz are the fractional parts of betatron tunes vx and vz. 2. the nonlinear detuning parameter is proportional to the superperiod of the accelerator. VII.jj\) - {TTVX - \ipx. These coefficients can be evaluated from sextupole strengths distributed in one superperiod.4 Betatron Tunes and Nonlinear Resonances The betatron tunes should avoid the linear betatron resonances at vx = m or vz = n.jj\)] ^COS(TTVX . where m.ij = tl>2.
55 shows betatron resonances up to the 8th order. where P is the superperiodicity of the machine. where the solid lines correspond to resonances due to normal multipoles.110 resonance (stopband) correction becomes important for attaining beam stability.7 213 resonances discussed in this section. (2. CERN 84-15 (1985). m Figure 2. Betatron tune stability has becomes an important issue for successful operation of storage rings. where higher order betatron resonances can decrease the beam lifetime. betatron amplitude detuning. beam-beam interaction. L. in the Proceedings of the CERN Accelerator School on Antiprotons For Colliding Beam Facility. 2. Resonancefree tune space becomes very small in storage rings. 110The betatron tune spread of a beam may arise from the incoherent space charge (Laslett) tune shift. chromaticity. The solid lines corresponds to resonance lines associated with normal multipoles.o/ = 0 if (• ^ 0 (Mod P). with \mx\ + \mz\ < 8 and integer £. Koop and G. 319. .3 x 10~3 per crossing (see Eq. for systematic resonances. p. Note that the available resonance free tune space becomes small. and the dashed lines are those associated with skew multipoles. Exercise 2. When the betatron tune spread of the beam becomes large. the beam-beam interaction can cause higher order_ resonance observed very early on at the SPPS. Evans. Lifetime degradation has been observed near the 7th order resonance at the SPPS driven by beam-beam interaction with linear beam-beam tune shift parameter of ^ = 3. The lifetime of beams in many storage rings and colliders may suffer if the betatron tunes sit near a higher order betatron resonance. (4.R. while the dashed lines arise from skew multipoles. Show that the 3vx = I resonance strength is given by Eq.7 1. (a) Show that.381) in the first-order perturbation approximation. Figure 2. 4 ) .EXERCISE 2.55: Resonance lines up to the 8th order. where mxvx + mzvz = (. edited by I.g. The right plot of Fig.54 shows the betatron resonances up to the 4th order. see also the Proceedings of the third ICFA Beam Dynamics Workshop on Beam-Beam Effects in Circular Colliders.10) in Chap. Tumaikin (Novosibirsk. are shown in this figure. 1989). and many e+e~ colliders. G3. In particular. etc. 111 See e. The tune space that is free from high order resonances becomes very small.
the "geometric aberrations" of these two sextupoles cancel each other if ip2l — T and \px(Sl)f2 [S{sx)As] = [&(s 2 )] 3 / 2 [S{s2)As]. where £ is an integer. vz are the betatron tunes. g = Gi]+2. and the stable fixed points are located at for cf>i = 0 or 7 respectively. the Hamiltonian can be approximated by H = vxjx + uzJz + gJll2Jz cos{(j>x + 24>z .<h)> and show that the new Hamiltonian is H = H\ + H2. Show also that 2Jx + Jz is invariant. Near a third-order coupling difference resonance at vx — 2vz = £.J2. <j>z.ufp = "^» and <j>i = ± arccos ( * ). show that the unstable fixed points of the Hamiltonian are located at •A. AO = (s2 . where ux. Vzh. where Hi{Juh) = H2{J2. show that the geometric aberration of two chromatic sextupoles located in the arc of FODO cells separated by 180° in phase advance cancel each other.*2 ds/px is the betatron phase advance.vz are betatron tunes.-(3^-0A»i ) where ip2i = X.<t>i. and (Jxi 4>x-> Jz) 4>z) are the horizontal and vertical action-angle phase-space coordinates. the Hamiltonian can be approximated by H = vxjx + vzJz + gJll2Jz cos(0x . and 81 = vx — 2vz — £ is the resonance proximity parameter. 2. and (Jx.). (b) For a given J2.SI)/RQ. <j>x. at the 3ux = £ resonance. Discuss the difference between the sum and the difference resonances. Near a sum resonance at ux + 2vz = £. . Ju J 2 ) = ( ^ .. TRANSVERSE MOTION (b) Show that the resonance strength of the third-order resonance at 3i/x = £ due to two sextupoles at si and s2 is proportional to Wx(si)f2 [S(Si)As] + [J3x(s2)f2 [S{s2)As\ e >P*. and Ro is the average radius of the accelerator.(j>2) = <5iJi+9J 1 1 / 2 (J2-2Ji)cos«^i.2<6Z -19 + £ ) J i + <j>zJ2.f is the effective resonance strength. (c) Based on the above result. (a) Using the generating function F2{4>x.2(j>z -£9 + 0 . 4>z) are horizontal and vertical action-angle phase-space coordinates. where vx. transform the phase-space coordinates from {JxAxiJz-i^z) to (Ji. g = G\t-2.£0 + (. Show that. T 3.214 CHAPTER 2.i is the eifective resonance strength. Jz.
e. (c) Show that the action J2 is invariant. h) = W > * + n<j>z -10 + OJi + 4>zJ*. In general. (b) Show that the new Hamiltonian is invariant. Normally only low-order resonances are important. If the betatron tune of the machine is chosen such that mvx + nvz ~ I. are integers.<f>l. i. betatron motion in storage rings can encounter many nonlinear resonances.7 215 4.J2.J\. and (. n. 4>z. (a) Transform the phase-space coordinates from {Jx. This is called a sum resonance if mn > 0. Discuss the difference between the sum and the difference resonances. Neglecting the perturbing term AH that includes contributions from other resonances.EXERCISE 2.<t>x.<l>z) to (Jl. derive the invariants of the approximated Hamiltonian. njx — mJz = constant. and find the new Hamiltonian. the Hamiltonian can be approximated by H = HO(JX. . where m > 0. and a difference resonance if ran < 0. Jz) + ff4m|/24n|/2 cos(m^ + n<f>z -W + O + Atf.Jz.(fa) by using the generating function F2{<t>x.
TRANSVERSE MOTION VIII Collective Instabilities and Landau Damping So far we have discussed only single-particle motion in synchrotrons. In Sec. Since particle motion in an accelerator is classified as transverse betatron motion or longitudinal synchrotron motion.216 CHAPTER 2. which is the electromagnetic waves induced by a passing charged particle beam. vacuum ports. impart a force on the motion of each individual particle. where each particle can be described by a simple harmonic oscillator. VII. in turn. 3. Here. and narrow-band impedance due to high-Q resonance modes in rf cavities. backward. we list these impedances as follows. some properties of impedance are listed. and BPMs. septum and kicker tanks. the impedance of an accelerator is related to the voltage drop with respect to the motion of the charged particle beams. Likewise. or slow waves. the impedances are classified as longitudinal or transverse. see Ref. Sec. In Section VIII. For beams.4. VIII. The longitudinal impedance has the dimension ohm. broad-band impedance due to bellows. A self-consistent distribution function may be obtained by solving the Poisson-Vlasov equation. there are transverse and longitudinal impedances. VIII.1. where the impedance plays an important role in determining the circulating current. . Without deriving them. single-particle motion is governed by the external focusing force and the wakefield generated by the beams. The transverse impedance is related to the transverse force on betatron motion. [3]. where the waves are classified as fast. Landau damping and dispersion relation will be discussed in Sec. The induced electromagnetic field can. Thus. etc. In reality.2 we discuss transverse wave modes. and the beam distribution is determined by the motion of each particle. and has the dimension ohm/meter. space charge. In Sec. VIII. and by definition is equal to the energy loss per revolution in a unit beam current. 1 Impedance The impedance that a charged-particle beam experiences inside a vacuum chamber resembles the impedance in a transmission wire. a circulating charged particle beam resembles an electric circuit. Likewise.3. image charge on the vacuum chamber. VIII. we will show that a slow wave can become unstable in a simple impedance model. The effect of longitudinal impedances will be discussed in Chap. wakefields are classified as having transverse or longitudinal modes. The impedance is more generally defined as the Fourier transform of the wakefield. For a complete treatment of the subject. we discuss some basic aspects of transverse collective beam instabilities and Landau damping. The transverse impedance arises from accelerator components such as the resistive wall of vacuum chamber.
where c is the speed of light. the impedance per unit length becomes X'mag _ JcABz _ . Here.oIoXo/2-Kb2. . we find the induced dipole field inside the beam cross section to be Ai3Z]b = ij. the transverse impedance is related to the longitudinal impedance by 7 _ 2cZ||irw 02 LJ . Using the result of Exercise 1. fic is the permittivity in metal. (2. and 6(x) is the Dirac 5-function. (2. Resistive wall impedance AND LANDAU DAMPING 217 The resistive wall impedance is given by112 T>i7 2x.16) Jw = -(IOXQCOS<f)K/nb2)6(r . is the skin depth of the electromagnetic wave in metal. b is the vacuum chamber radius.6). The resulting beam current density is i(r. The total induced vertical dipole field due to the beam displacement becomes By definition. Let XQ be an infinitesimal displacement from the center of the cylindrical vacuum chamber. The perturbing current is a circular current sheet with cosine-theta current distribution.VIII.397) where R is the mean radius of the accelerator.9. *) = A 9 (a irar . ZQ = fioc = 377 ohm is the vacuum impedance. For resistive wall impedance. Similarly the induced image current is (see Exercise 1.399) where Q(x) = 1 if x > 0 and 0 otherwise. B. . ac is the conductivity. and the induced dipole field due to the image wall current is ABZ:VI — —/j. and the second term arises from an infinitesimal horizontal beam displacement. Space-charge impedance Let o be the radius of a uniformly distributed beam in a circular cylinder. the first term corresponds to the unperturbed beam current. (5Skjn = y 2/<7c//ca. COLLECTIVE INSTABILITIES A.a).rwH = (l+j)£^4kin. and u is the wave frequency. Here.olQXo/2Tra2.r) + I^^5(r 7ror . the resistive wall impedance consists of a resistive and an inductive component.Zo / J L _ M ~J ploxo " J 2 7 r W b V ' 112The imaginary number j = —i of engineering convention is used throughout this textbook.
bb = T T — 75—. the perturbation current of Eq. [3].399) is invalid. . when the oscillatory amplitude XQ is large. . (2. etc. The remaining space charge impedance is the image current term.. (2. The formula that takes into account the shape of the vacuum chamber can be found in Ref. Rs is the shunt resistance. R is the average radius of the accelerator. b2 UJ b2U> 1 + jQ(LJ/U)r TT» .—-. and 6 is the beam pipe radius. Note that the space charge is capacitive because the beam radius a is less than the vacuum chamber radius b.oc is the vacuum impedance. Similarly. Narrow-band impedance Narrow-band impedances are usually represented by a sum of Eq. TRANSVERSE MOTION where j3c is the velocity of the beam. b is the beam-pipe radius. • „. bellows. where the corresponding Q-factor is usually large.218 CHAPTER 2. BPMs. the space-charge impedance is important for low energy beams. and the self space-charge force term may disappear. and Zo = fj. which is inductive. can be lumped into a term called the broad-band impedance. vacuum ports. Broad-band impedance All vacuum chamber gaps and breaks. the impedance due to the electric field is 7 • Zo (l M Thus the transverse impedance due to space charge in one complete revolution is113 * ~ ~ ^ (?-?)• (2-400) where a is the beam transverse radius. septum and kicker tanks. 113Note here that the derivation of the space charge impedance assumes a uniform circular beam distribution for the direct term and a circular vacuum chamber geometry for the induced charge term.. C. D. Because of the f32j2 factor in the denominator.401) where Q « 1 is the quality factor. which is usually assumed to take the form of a RLC circuit: 2c%bb 2c Rs OAm\ ^±. However. R is the average radius of the accelerator.(*>r/U) (2. Narrow-band impedances may arise from parasitic rf cavity modes.401). and 7 is the Lorentz relativistic factor. The space-charge impedance can be considered as a broad-band impedance because it is independent of wave frequency. etc. OJT « (R/b)u>0 is the cut-off frequency of the vacuum chamber.
f°° Z^Y^du 2?r J-OO (2.56. The factor /? in the denominator is included by convention. Properties of the transverse impedance When the beam centroid is displaced from the closed orbit. The dipole current will set up a wakefield that acts on the beam. V . du' 1 W ' . For example.e.407) or ReZj_(-w) = -ReZ ± (w). and the imaginary part is an even function. COLLECTIVE INSTABILITIES AND LANDAU DAMPING 219 E. Thus. the impedance of RLC resonator circuit in Eq. (2. where P.404) (2.VIII. it may have poles in the upper half plane. Since the wake function is real. This occurs because the driving force is leading the dipole current by a phase of ir/2. means taking the principal value integral. the real and imaginary parts are related by a Hilbert transform ReZ±^) = --f 7T J P . the motion can be expressed as a dipole current.U> ^^!. Thus the real part of the transverse impedance is negative at negative frequency.405) lmZ±(uj) = -[ do/ReZl(u/). To summarize. 2.V. the impedance at a negative frequency is related to that at a positive frequency by ZL(-W) = ~Zl(u). where the real part of the impedance is an odd function of ui.403) with the causality condition W±(t) = 0 (t < 0). the impedance can not have singularities in the lower half of the complex u plane. ImZL{-uj) = +ImZ L (w). (y) is the centroid of the beam in the betatron motion. The imaginary number j included in the definition of the impedance is needed to conform a real loss for a real positive resistance. The analytic properties of impedances provide us with the Kramer-Kronig relation. The transverse impedance of the ring is defined by Z±M = Tffiv) f F^ds = ife /(^ + ^ x S)±ds = T i W±{T) e^T dT' (2'402) where I\ = Io(y) is the dipole current. and C is the circumference of the accelerator.406) (2. (2.401) has two poles located at u> =uv [±v/l-(l/2Q) 2 +j(l/2Q)] . i. (2. . various components of the transverse impedance ZJ_(CJ) are schematically shown in Fig. however. The wake function is then related to the impedance by WL{t) = -3J.
410) where Q is the betatron tune.411) There are three possible transverse wave modes: the fast wave. (2.w=(l + . A broad-band and a narrow-band impedance are represented by peaks in the real parts. ifn>0: fast wave backward wave slow wave. the betatron oscillation of the transverse motion is oo V(t. the nth mode of transverse motion is y(t. The corresponding angular phase velocity is (1 H a =)—{-. U4Another IV M y .T—r I w0.9o)= n=—oo E ynej{Q"ot-ne°\ (2. TRANSVERSE MOTION Figure 2. i. The resistive wall impedance is important in the low-frequency region. Its Fourier harmonic contains all modes with equal amplitude (see Sec. the transverse coordinate at any instant of time is given by 114 y(tO. and n is the mode number. VIII.409) Since (2. 9) = ynej[ (»+«-»'-»»]. The real paxts are shown as solid lines and the imaginary parts as dashed lines.W (2. and the slow wave.408) where 0 is the orbiting angle.56: A schematic drawing of the transverse broad-band and narrow-band impedances. yn = constant.7). At a fixed azimuth angle 9Q. (2 412) if n < 0 and In < Q : if n < 0 and In > Q : extreme case is a beam with a delta-function pulse. 1 I wo.220 CHAPTER 2.2 Transverse Wave Modes oo For a coasting (DC) beam.e.0)= n=—oo E Vne'jn9. and W is the angular revolution frequency. and the spacecharge impedance is independent of frequency. III. where particles continuously fill the accelerator. I 1 . o 9 — 80 + uot. jwo. where the angular phase velocity is 0n. the backward wave.
(2. (2. 7 is the Lorentz relativistic factor. that of a slow wave is slower than the particle velocity. and F± is the time-dependent transverse force resulting from the wakefield.nu)0)2yk. (2-414) where R is the mean radius of the accelerator.3 Effect of Wakefield on Transverse Wave Let yk be the horizontal or vertical transverse betatron displacement of thefcthparticle. The equation of motion in the presence of a wakefield can be expressed as a force oscillator equation115 Vk + (QkUofyk = ^ p (2. If beam particles encounter collective instability of mode n. We will show later that the characteristic responses of these waves to wakefields are different.VIII. they execute collective motion with a coherent frequency w: yk = Yke^t~ne\ (2. and a backward wave travels in the backward direction.413) where the overdot corresponds to the derivative with respect to time t. the betatron motion is well approximated by simple harmonic motion.417) (2. VIII. we obtain 115In a global sense. Using the relation Vk = ^+O^=j(uj-nLJo)yk. which is a sideband at rotation harmonic nu)Q. we obtain yk =-(u . COLLECTIVE INSTABILITIES AND LANDAU DAMPING 221 The phase velocity of a fast wave is higher than the particle velocity. The EM force on a charged particle [see Eq.415) where n is the mode number.413). m is the mass. (2. The signal picked up in a transverse beam position monitor (BPM) will have a single frequency located at \n + Q\uj0. and let Qkuo be the corresponding angular frequency of betatron motion. and Yk is the amplitude of collective motion for the kth particle.416) Substituting into Eq.402)] resulting from a broad-band impedance is *l(t) = -J6-§^ (V). .
sextupoles. One can also use a positive frequency approach to express the slow wave. nw (2. Now we discuss coherent frequency spread vs off-momentum variable 5. the mode number n0 of Eq. the betatron amplitude can serve as a £ parameter. (2. from Eq. .422) is a slow wave. Here. Since betatron tunes depend on betatron amplitudes due to space-charge force. then the resulting dispersion relation changes sign. and AQ = CyS. Q is betatron tune. where ui0 is the angular revolution frequency of the beam. O + [Cy ~ mj\ W0 S. we obtain the collective wave frequency as Wn.415). TRANSVERSE MOTION ^-^^iJ^M' {y) = j PiOvkdti (2'418) is the centroid of the beam. (2.422) Thus if Cy/rj < 0. It is worth noting that. r] is the phase-slip factor. Using Awo/wo = —T)6. Since Q and u>0 depend on the off-momentum parameter 6 = Ap/p.419) and we have used the relation W — TW + Qwo « Wn. |n| < Q backward wave. |n| > Q slow wave.116 Averaging over the beam distribution. the wave frequency spread vanishes at mode number n0 = (^L. (2. discussed as follows. fast wave. we obtain a dispersion relation for the collective frequency u> epiZL f PJQ dc (2420) The set of parameters f represents any variables that wn>w and the beam distribution function depend on.222 or where CHAPTER 2. u)n)W is the wave frequency given by ( n> 0 n < 0. The beam may become unstable against transverse collective instability. and Cy is chromaticity.421) where S = Ap/p0 is the fractional off-momentum coordinate. 116When the transverse coordinate of collective motion is represented by Eq.421).w — "Wo + Qwo — 2QwoJ o Note that the real part of the slow wave frequency wniW is negative. n < 0. (2.w = W . the slow wave frequency is negative. (2. 6 can also be chosen as a possible £ parameter. we have assigned the fractional off-momentum coordinate as a £ parameter. p(f) is the normalized beam distribution function with f p(£)d£ ~ 1J ? represents a set of parameters that describe the dependence of the betatron tune on its amplitude. and other higher-order magnetic multipoles.
56). the imaginary part of the impedance gives rise to a frequency shift.424) where V is related to growth rate. The remarkable thing is that there are solutions of real u> even when — U + jV is complex.o of a slow wave is negative. In general. and there is no growth of collective instability. If the distribution function . The threshold of collective instability can be obtained by finding the solution with ui = ui — j\0+\. If the imaginary part of the coherent frequency is negative.VIII. and the resistive part generates an imaginary coherent frequency ui. Since the imaginary part of the collective frequency is negative. (2. coherent oscillation is damped.U.423) Thus. (2. wniWo is positive. the dispersion relation provides a relation between U(LO) VS V(LJ). On the other hand. Defining U and V parameters as V + jU=A e%IZLn . Beam with zero frequency spread For a beam with zero frequency spread. for a given growth rate. Beam with finite frequency spread With parameters U and V. B. On the other hand. Im [wcon] = V. the collective frequency uin>v. n • (2. if the imaginary part of each eigenmodes is positive. we obtain Re [wCou] = wn. p(£) = 5(£ — £o). For fast and backward waves. i. the betatron amplitude grows exponentially with time. the growth rate can be solved from the dispersion integral with known impedance and distribution function.w0 + j 6 223 ' . thus the imaginary part of the coherent frequency is positive. If the imaginary part of the coherent frequency is negative.w0 . the dispersion relation for coherent dipole mode frequency w becomes (-U + jVV = j P{0 dg. we obtain w = wn. where the real part of the transverse impedance is negative. 2. Similarly. The real part of the impedance ZJ_(OJ) is positive (see Fig. a beam with zero frequency spread can suffer slow wave collective instability. and U is related to collective frequency shift.e. and the beam encounters collective instability. the amplitude of the coherent motion grows with time.425) The solution of the dispersion relation corresponds to a coherent eigenmode of collective motion. COLLECTIVE INSTABILITIES AND LANDAU DAMPING A. where 0 + is an infinitesimal positive number.
(2. (2. In general. TRANSVERSE MOTION is symmetric in betatron frequency. We consider the frequency spread model w». A model of collective motion We consider a macro-particle model of a beam with (Y) = YlPkYk. (2.Thus any amount of a negative real part of the impedance can produce a negative imaginary collective frequency and lead to collective instability. the collective mode disappears.w(*)n = wB|WOn + Mi{Yk .w(fc)] Yk = WYt i PiYi.427) which is identical to the solution of Eq. The requirement of a large frequency spread for Landau damping is a necessary condition but not a sufficient one. i. Eq. (2.wo is independent of k. In nuclear physics. where Afl is a constant that determines the frequency spread of the beam.425). C.224 CHAPTER 2. The corresponding eigenvector for collective mode is Yjt)COii — PkYh. the coupling between external force and beam particles is completely absorbed by the collective mode.418) becomes [w . For any beam distribution p(£) that does not have infinite tails. the collective frequency is trivially given by117 wcoii = wn. In fact. The disappearance of the collective mode due to tune spread is called Landau damping. no frequency spread. If wn>w(fc) = wn.426). This means that if the coherent frequency shift is beyond the distribution tails. if there is a frequency spread between different particles.w0 + W. (2.423). the giant dipole resonance where protons oscillate coherently against neutrons presents a similar physical picture. and there is no coherent motion.In matrix form. This is equivalent to solve the collective mode frequency from the dispersion relation of Eq. In this model. the threshold curve contains two straight vertical lines lying on the U axis. the frequency shift of a particle is proportional to the local density of the U7 The collective mode occurs frequently in almost all many-body systems.e. if the frequency spread Aw nw among beam particles is larger than the coherent frequency shift parameter W. Now. unstable against collective instability. but may not necessarily be. where Pk is the distribution function with Y*Pk = 1. All other incoherent solutions have random phase with eigenvalue wn>w0.wn. and the growth rate is proportional to the real part of the impedance. we have to diagonalize the matrix of Eq. the U vs V contour plot will have reflection symmetry with respect to the V axis.426) where W = —U + jV for a broad-band impedance.( y » . . (2. the beam can be.
the space-charge tune shift alone can not provide Landau damping against transverse collective instability. 2. CJ@ = 0. This is the essence of Landau damping. COLLECTIVE INSTABILITIES AND LANDAU DAMPING 225 beam. we see that a slow wave can suffer transverse collective instability for a beam with zero frequency spread. A. The resulting collective mode frequency is (2. Up P (2. The particle motion will be out of phase with the external force sooner or later. We are interested in the response of the particle under external force. The lower plot of Fig.VIII. Landau damping The equation of collective motion (2.76 (line) under the action of an external force w = 0. 2. The solution is v(t) — H—5 o \s\aut Up sinugt I +y0cosuist+ P — sinujgt. and ojp = Qw0 is the betatron frequency.428) Wcoiia = wn. A smaller w — wg results in a longer in-phase time.57 shows y{t) for three particles with u$ = 0.429) where w is the collective frequency. What is the effect of frequency spread on collective instabilities? The key is the Landau damping mechanism discussed below. and the energy will be transferred back to the external force.413) can be represented by a forced oscillator: y + oj20y = Fsinujt. F = 0. as shown in the lower plot of Fig. Note particularly that if up differs substantially from the driving frequency w. and the coherent motion is relative to the closed orbit of the machine. which describe unperturbed particle motion.430) LJJ-LJ2 \ J where y0.75.85 (dash-dots). This is equivalent to the argument that the space-charge tune shift can not damp the transverse collective instability.423).57. This model of tune spread resembles space-charge tune shift.8 (dashes).4 Frequency Spread and Landau Damping From Eq. Since the second and third terms. (2. y0 are initial values at t = 0. (2. . the number of particles (oscillators) that remain in phase with the external force becomes smaller and smaller. and u)g = 0. Since the space-charge tune shift is a tune shift relative to the center of a bunch. the external force can not deliver energy to the system forever.w0 + W. As time goes on. This means that the frequency spread that is proportional to the distribution function can not damp the collective motion. VIII. The examples illustrate the essential physics of Landau damping. are of little interest here. we set yo = 0 and y0 = 0.01.
85 ( d a s h dots) . Thus the average power is given by Eq. 0 • . I • • . 118In general. .431) where £ — |(w . • I • • • • I . fewer and fewer oscillators will be affected by the external force. TRANSVERSE MOTION i r l ^sin2(f)/f3 / \ _ j i .57 shows the coherent functions (sin2 () / (2.e. . the coherent frequency window decreases. and if u is in 106 rad/s.76 p i n e ) 0. = 0 5 I I I ! I I I I I ' I I / \ r\ ! ! I ^ I I ^ 10 I |_ I ! I : CJ = 0 . PT> (2.80 ( d a s h e s ) A A A : A~ ~ : OJ = 0 . 20 • I . 7 5 0^=0.432) or equivalently. i. 40 . (2. where H is the Hamiltonian of the system. 7 5 CJ ( S =0. |w-w/8|~l/T. i . This means that the external force can not coherently act on a particle if (up — u)T becomes large. t is in s. \ . (2. When the external force can not pump power into a beam with a finite frequency spread.\ / i . . 60 80 • • • : 100 t Figure 2. Here the units of w and t are related: if u is in rad/s. we are interested in the average power that the external force exerts on the particle:118 < ( ) = i f yFrin^= [ i ^ y ^ ] r + . collective instability essentially disappears.^ /-^ o8 -10 1 . then t is in /is. where V is the potential energy.0. 7 5 co0=O. i V /. .05.e.As time T increases. The lower plot shows the response of three particles vs time t to an external sinusoidal driving force F(t) = Fsinut. Here we retain only the leading term that is proportional to time T. .Note that the function becomes smaller as the £ variable increases./ . 0 ^ A -5 I I I I = . and 0. .01. the system is Landau damped.1 shown respectively as solid line. The frequency difference of these three particles is Au = 0. The upper plot of Fig.5 — CJ = 0 . 2.wp)T. the total energy the external force delivered to the system after time T is AH = JQ yF(t)dt. \ / . In fact. o F • . and dots. dashes.226 CHAPTER 2.431). when an external force F(t) is applied to a Hamiltonian system with y+dV/dy = F(t). . 1 / .57: The upper plot shows the coherent function (sin2 C)/C2. i.i . . Note that the particle with a large frequency difference will fall out of coherence with the external force.
8. 2. v= .434) (2. where the rectangular symbols in each curve represent coherent frequency shifts at Re(ui — wn)Wo) = ±CTU (inner ones) and ±2au (outer ones)./"°° —dt. 119The complex error function is w(z) = e-*2erfc(-jz) = . we observe that if the frequency of the coherent mode is within the width of the spectrum. and o& is the rms momentum width of the beam. Using Eq. . Thus the collective beam motion is damped. or phase space decoherence due to tune spread (see Exercise 2. then induction of collective beam instability requires a finite resistive impedance. Landau damping differs in essence from phase-space damping due to beam cooling. the dispersion relation of Eq. B.435) is the rms frequency spread of the beam for mode n. The curves tivsn for Gaussian distribution for Im(w/crw) = 0 and —0.425) becomes -u + jv = j[w(^^-)]~\ where <ra = y/2 \Cy . which will absorb energy from the external force and lead to collective instability.431) comes entirely from the second term in parentheses in Eq. the term y(t) that is in phase with the force is actually a reactive term.421). COLLECTIVE INSTABILITIES AND LANDAU DAMPING 227 It is worth noting that the power dissipation to the oscillator in Eq. The term that will absorb power from the external force is the second term in parentheses in Eq.5 are shown in Fig. 2.58. That is to say. (2.119 and u= .430). From Fig. which does not dissipate energy. (2.5).VIII. (2. and most of the beam particles are off resonance. (2.nrj\ ujoas (2. (2. Solutions of dispersion integral with Gaussian distribution We consider a beam with Gaussian distribution given by ^ ^ <2-433) where S = Ap/po is the fractional off-momentum coordinate. This is because the coherent mode excites only a small fraction of the particles in the beam. This corresponds to a resistive term.430). w(z) is the complex error function.58.
y = —s T sinwi u} ~ w2 \ w .Wo) = icr^ and ±2frw.426). \ smwat . TRANSVERSE MOTION Figure 2. F = 0. (2.58: The normalized u vs v for Gaussian distribution is plotted with two different growth rates with Im(u. The rectan- gular symbols represents the coherent frequency shifts at Re(w — wn. and backward waves travel faster. 120For bunched beams. Because such modes have vanishing frequency spread.8 1. . (2. then mode no with vanishing frequency spread is a fast wave.423) for the dispersion relation at zero frequency spread is identical to the collective frequency solution by matrix diagonalization of Eq. (2. p. and backward relative to particle angular velocity. slow.434). Since the real part of a fast wave is positive. Treatment of head-tail instability is beyond the scope of this book. and thus there is no collective instability.) = 0 and —0.5CTW. and 0.01 with three particles at up = 0. The solution of Eq. 2. [14]). "IS ) (a) Plot y(t) as a function of t for w = 1. 0.228 CHAPTER 2.Coii = PkYk3. (2. respectively. and show that the eigenvector of collective motion is Yjfc. We note particularly that the frequency spread can vanish for mode number n0 of Eq.422). (2.8.120 Exercise 2.433) to show that the dispersion relation becomes an algebraic equation. Using the Gaussian distribution of Eq. (2. the imaginary part of collective frequency is positive. 134 in Ref.429) with initial condition j/o = Vo = 0 is F ( . However.9.99. if chromaticity Cy is negative below transition energy or if Cy is positive above transition energy. Verify the wave angular velocity of Eq. 4. Eq. This has been commonly employed to overcome transverse collective instabilities. the head-tail instability has been observed in SPS and Fermilab Main Ring above transition energy if the chromaticity is negative (see J. and show that fast. Gareyte. Show that the solution given by Eq. (2. slower.411). collective instabilities will not be Landau damped.
A beam is usually composed of particles with different frequencies. particles are not damped to the center of phase space. otherwise.e.2 U / ( « W ) _ 2e -«/(« 2 +« 2 ) cos[t)/(u2 + v20]' ' Show that the condition that Imw = 0~ is U2 + (V + . 121This exercise illustrates the difference between Landau damping and beam decoherence (or filamentation). Note that coherent beam motion will decohere within a time range At ~ 1/(7. See also Fig. 2.58. v = V/2aw. i. 229 Show that the first term in square brackets does not absorb energy from the external force but the second term can. where a is the rms frequency spread. where |e| is a small frequency deviation.8 (b) Let u)p = iij + e. Show that F ri-cos(et) . 5. and compare your result with that shown in Fig. otherwise. i. The first term corresponds to a reactive coupling and the second term is related to a resistive coupling. and 0. As the coherent motion is damped. . Consider a beam with uniform momentum distribution ( J ) fl/(2A) \0 if|5|<A. (b) Show that the imaginary part of the coherent frequency is T ..121 Let p(up) be the frequency distribution of the beam with J p(u)p)dwfj = 1. find the centroid of beam motion as a function of time with the following frequency distribution functions. and begin coherent betatron motion. we choose £ = e and p(e) = 1/2A. and aw = \Cy — nr)\uit)A. (y(t)} = fy(t)p(£)d£. 2. where a is the rms frequency spread of the beam. 1 ) 2 2TT = JL. (a) Show that the dispersion relation Eq. For example. .e.15 for coherent betatron oscillation induced by an rf dipole kicker. (c) If a beam has a distribution function given by p(£) with J p(£)d£ = 1.. . if |e| < A.EXERCISE 2. 4TT2 Plot u vs v. y{t) = jlcosu^t. If initially all particles are located at y = y = 0. { n w e-"sinfr/(«2+^)1 1 + e . where u = U/2aw. discuss the centroid of beam motion.425) becomes (—u+jv) = In • . show that (y) = AeT" * I2 cos uiot. (a) If the frequency distribution of the beam is p(W/J) = -J=^ c -<"*-o) i /*' 2 . 6. and at time t = 0 all particles are kicked to an amplitude A. . (2. y(t) as — ^-^-sinurt sin(ei) 1 —-cosurf .
ifcjo-r<w0<uJo otherwise. TRANSVERSE (b) If the frequency distribution is a one-sided exponential P(UR) p/ = MOTION / (l/ff)c-to-"»>/*. otherwise. PK 0> •.230 CHAPTER 2. show that . where F = \f%o and cr is the rms width. where Jo a n d Ji are Bessel functions. + T. otherwise.r < w / 8 < w o + r. (0.sinFt (e) If the frequency distribution is parabolic with piijff) = {( 3 /( 4r )) I1 ~«w/>-^)/r)2]. . ifw O -r<w / . where F = 2<r and a is the rms width.w o )a + r2]' where F is the width.wo)/rf. otherwise.<« o + r.((up . show that (y) = 2 2 [cos wi . = / i / ( 2 r ) . . show that {y) = A [Jo (Ft) + J2(Fi)] coswoi. where <x is the rms frequency spread. show that . (d) If the frequency distribution is uniform with n(u. i f w O . where F = y/ia and cr is the rms width. and (cup) = u)g + a. . /sinrt cosFA <2/> = M W .T r 7 F J C O S W 0 < (f) If the frequency distribution is quadratic with p(Up) = I (2/TTF) y/l . . \ 0. \0 if W / J >wo.o-tsinwt]. [ 0. (c) If the frequency distribution is a Lorentzian p(w'} = »[( W / J . show that (y) = Ae~vt cos wi.
/V I!\\ / : \\ 1 1 .—•—i—i—i—•—i—i—•—•—'—. . and A = 1.—i—.EXERCISE 2. 1 1 1 r- A o n e —side e x p o n e n t i a l : Gaussian : d o t s uniform: d a s h e s line -i.—. 1 . .1.—i—. Compare your result with the Gaussian.—iO 1O 2O 3O 4O cot . a = 0. 1. and uniform distribution results shown in the plot below.—.o L—J—. 1 . . 1 1 .—. .0 r i — j -i -| . one-sided exponential. 1 .8 231 (g) Plot (y(t)) vs t for the parabolic and Lorentzian distribution functions with wo = 1.
Thus the rf accelerating field can be represented by ^.px.sk) sin(wrf* + fok).437) where 6p(s — s^) = Yin <HS ~ s * ~ 2nnR) is a periodic delta function with period 2nR.pz. The terminology of synchrotron motion is derived from the synchronization of particle motion with rf electric field. —H) or (t.px) phase-space coordinates. The name "synchrotron" has been broadly used for all circular accelerators that employ rf electric field for beam acceleration. This unified description has the advantage of treating synchrotron motion and betatron motion on an equal footing. (2. Lett. we disregard vertical betatron coordinates (z. Vk is the rf voltage. 5133 (1998) for the effects of space charge dominated beams. —E). (2. As is the longitudinal vector potential.rf = — E W w rf k s " sk) cos(wrft + <j>Qk). z. Suzuki. The static transverse magnetic field is 1 dAs x 1 8AS 1 + (x/p) dx' 1 + [x/p) Dz ' and the longitudinal varying electric field can be obtained from r)A Es = —gf = Yl W 5 . Rev. $ is the sealer potential.122 To simplify algebra. Here we will study the "synchrotron" equation of motion for phase-space coordinates (t.Y.438) 122 See T. wrf is the angular frequency of the rf field. we have discussed particle motion only in (x.232 CHAPTER 2. (2. p = ^J(E/c)2 — (me)2 is the momentum of a particle. and <j>ok is the initial phase of the /cth cavity.px. TRANSVERSE MOTION IX Synchro-Betatron Hamiltonian So far.) U „ x. Part. 115 (1985). the Hamiltonian is [see Eq. —E) have not been mentioned.—E) are canonical phase-space coordinates.pz) and consider only a planar synchrotron. \/E-e$\2 . 18. p is the bending radius of the Frenet-Serret coordinate system. see also S. Lee and H. Okamoto. . Neglecting vertical betatron phase-space coordinates.-<4H) +(1+ .z. Accel. and (x. The remaining phase-space coordinates (t. It is particularly useful in the study of synchrobetatron coupling resonances.18)] Ho = .>(^H-' <» "> o __ z J -m2c2-p2-p2 22 2 211/2 -eAs where the orbital length s is used as an independent variable. Phys. 80.t.( 1 + .
we obtain „ AE 1 . P (2. (2.* . and the dispersion function D satisfies (^. 2 AE x (2 4 4 1 ) Ho = .ft_|i)> D" + KXD = -. . Using the generating function F2{x. = Box + | V + iBi(x 2 . — + „ . Expanding the dipole field 5 Z in power series with Bz = Bo + B\X + • • •.438) stands for the vector potential of rf cavities. _ ( _ ) -Po^+PI+PI + P±{KXX2 + Kzz2) _ eAsT{ zp0 z up to second order in phase-space coordinates. (2. Substituting the sealer and vector potentials into the Hamiltonian.440) where AStIi given by Eq.* . SYNCHRO-BETATRON HAMILTONIAN 233 The Hamiltonian is an implicit function of energy E. The next step is to transform the coordinate system onto the closed orbit for a particle with off-energy AE. where Si = dBz/dx. This procedure cancels the cross-term proportional to (AE/P2E0) • x in the Hamiltonian.D*Hr f=t+ AE = E-E0.442) .z2) + • • • + As. Let E = EQ + AE and p = p0 4.Ap. which signifies the expansion of x around the closed orbit at the reference energy.£>— r )p s . AE . that can be represented by a sealer and vector potentials $ = Vsc and ASiSC with J4SJSC = P2Vsc/pc. The space charge force of the beam particles gives rise to a mean field. where Eg and po a r e the energy and momentum of the reference particle.ri + AIJK. and we used the identity condition BQ = —Po/ep. We obtain then PO ~ ^ 2 s 0 27* > V • P2E{i ~ po + 2 7 2i Po) • ^-«».-AE) = (x .(E + AE)t P -bo where the new phase-space coordinates are PX=PX-D'^ -x = x. we obtain ^ . where Kx = 1/p2 — B\/Bp is the focusing function for the horizontal plane.IX.pX:t.
px.448) Making a scale change to canonical phase-space coordinates with {x. Using the corresponding function hs F2 = xfx + (wrff .s*) cos(wrf£ + (j>ok) = -^—j^ cos(wrft .W) -+ (x. (2. i. W = Ulrf (2.447) . <Sp(s-s*)cos(wrf«-|-0o*) = 7 .—)W. (2. 4>.—).{ i .hs <5P(s .444) Now we expand the standing wave of the rf field into a traveling wave.234 we obtain a new Hamiltonian.$. we obtain the Hamiltonian x = x. H (2.p E [e J ( n e + W r f ' + ^-^) + e j ( n e . TRANSVERSE MOTION 1\(AE\2 px2 p- 2 . Wf V r L V P &o Pc I J (2-443) Note that x is the betatron phase-space coordinate around the off-momentum closed orbit. AE 1 (D CHAPTER 2.445) ^ti n-_oo Keeping only terms that synchronize the beam arrival time with n = ±h.x' = Po —. where Px=Px.^ + Tc")-eA^ eASid = — ]T eVk Sp(s .sk) cos L r f ( i .-^zrPx + -^-x) + ^ok \.W r f '-^.446) 1 °° - where <j>ok + h9k should be an integer multiple of 2?r.^ .d S . </> = w r f i .n f l t )]. and the rf vector potential is (2..— + 4>0k + h0k). Po . we obtain 1 .e.
it is called synchro-betatron resonance (SBR). Jta where E and B are electromagnetic fields. can generally be expressed as a function of 6D phase-space coordinates. sj are the entrance and exit azimuthal coordinates of the kicker. Proc. then the energy gain depends on the transverse coordinates. The synchrotron phase-space coordinates are chosen naturally to be (R(f>/h. 249.A. Lambertson. x') are coupled through dispersion function (D. If a resonance condition is encountered. No. Consider a particle of charge e and velocity v = ds/dt experiencing a kick from a component in an accelerator. 537 (1992). . and Vj_ is the transverse gradient. D') in rf cavities. E-ds. AIP Con}. SYNCHRO-BETATRON we obtain the Hamiltonian HAMILTONIAN 235 -Ssk? rti ~(*-5 I * + jH Since < and (a. R(j>/h is the longitudinal phase-space coordinate of the particle. which relates the transverse kicks to the longitudinal energy gain.L. the SBC potential must satisfy the Panofsky-Wenzel theorem. The total transverse momentum change is rh Ap± = e / (E + v x B)i_dt.IX. syn> / chrotron and betatron motions are coupled. p. (2. The total energy change will be AE = e rsb -. which satisfies the Panofsky-Wenzel theorem Eq. This synchro-betatron coupling potential. This is called synchro-betatron coupling (SBC). Thus if the transverse kick depends on the longitudinal coordinates. and 4 — ta is the transit time of the kicker component.449). where sa. Then the Panofsky-Wenzel theorem yields a relation between the transverse kick and the energy gain123 AAfA^vJ-^) Rd4>[po ) H W ' (2 449) ( ' where Apx/p 0 is the transverse kick. Goldberg and G. In general. and the Hamiltonian in 6D phase-space coordinates becomes 123D. — Ap/po)..
4 lists some properties of electron storage rings. Neglecting synchro-betatron coupling.452) = ^ i .W-9k).^ ) s i n ^ ] ' lh\r)\eV Vs"i2*P2EQ (2-454) where rj is the phase slip factor. TRANSVERSE MOTION - | ^ E ^ - ^ + ^ ) . the phase factor -Dx' + D'x will be the same for all cavities (see Exercise 2. (2. Thus it is beneficial to put rf cavities in dispersion free regions. the Hamiltonian for canonical phase-space variables (x.T ) ( — ) 2 " £ lS^[ C 0 S ^+(^. (2. z'.453) where rf cavities are assumed to be at dispersion free locations.450) It is worth noting that if RF cavities are located in a straight section. and is the synchrotron tune of the stationary bucket with <f>s = 0. The action of the synchrotron oscillations and the linearized betatron oscillations can be defined on an equal footing as 7» = A / — W' Ix = ^-fx'dx.1). .*') sin 4>. R<j>/h.) = . The driving terms for the synchro-betatron coupling in Eq. -Ap/p0) is H = H±(x.z') with HL H° + Hs(^^) h p0 (2.^I { — ? ~ 0 l o 2 EJQ I c o s ^ ~ cos<f>*+ {<!>.9.455) Table 2. Z7T/1 J Po Z7T 7 Iz = ^-fz'dz. where the transverse emittances and the longitudinal phase-space area are determined by the equilibrium between the quantum fluctuation of photon emission and the phase-space damping due to beam acceleration to compensate energy loss in the longitudinal direction.236 CHAPTER 2. x'. the Hamiltonian for synchrotron motion becomes (H. Z7T J (2. Averaging over one revolution around the ring.451) = ^{x12 + Kxx2 + z12 + Kzz2) + • • • (2.450) coherently add up in all cavities arranged in one straight section.<t>s) sin<f>s\ p po Zixhp 1 / \ 27 j/2 = -2 7 7 (~) 2 -/^l[ C 0 S < ? ! > ~ C 0 S ^ + W . (2.x\z. z.
51 0. Show that rf cavities located in a straight section contribute coherently to SBC if the dispersion function is not zero.6 -11.7 ^ 34 48 ass [m-1] -3.0 eV-s.28 76.8 98 127 267 699 -6.96 0.3 -25. and the primes are derivative with respect to the longitudinal coordinate s. x is the horizontal betatron function.0 6.35 60 a[xHT4] 400 152 C [m] 240.064 (AE/Eo) [xlO" 4 ] 4.6 3. Table 2.5 6.18 24.2 -0. the corresponding longitudinal action is 100-1000 times as large as the transverse action. —Ap/po). it satisfies the Panofsky-Wenzel theorem.28 25.8 9.1 9 55 7 32.9 237 The synchrotron action Is (Tr-mm-mrad) is related to the commonly used phase area A (eV-s) of the phase-space coordinates {<j>.65 0.4 574 -0.18 70.2x10^ M - (2-456) Since the typical longitudinal phase-space area is about 0.8 0.3 A [xlO" 4 eV-s] 3.7 3.61 Exercise 2.0522 0.5 7.36 ex [nm] 450 240 ez [nm] 35 8 p [m] 10.4 9.5 -10.7 78.6 165.3 196.8 328 499. .2 14.z'.0082 7.38 vz 6.4: Parameters BEPC CESR E [GeV] 2.86 1.1.48 4. AE/huo) by is = ^ A = 3. LER HER LEP APS 3.3 96 48 51 8 3.9 1.18 4. Show that if the SBC potential is an analytic function of 6D phase space coordinates (x.5 of some electron storage rings.8 2.016 0.3 26658.085 0.x'.08 30.z.22 35.4 h 160 1281 / rf [MHz] 199.27 ALS 1.96 14.5 14. This result has important implications for the synchro-betatron coupling resonances.7 5.0498 0.5 499. where D is the dispersion function.4 3.1 . 4.EXERCISE 2.2 38.0061 9.43 1.9 1104 3492 3492 31320 1296 476 476 352.1 5. 2.2 6 ux 5.3 2199.866 2.8 9.9 24.1 4.8 vs 0.2 35.4 768.1 8. Show that the function -Dx' + D'x in the Hamiltonian H4 is invariant in a straight section.0 3096.2 352.R<j>/h.01 14.374 2199.93 0.1 0.0 6.28 8.2 Is [103 nm] 7.
.
particles gain energy from the electric field in the longitudinal direction. 2. Alternatively. what happens to a particle with a slightly different momentum when the synchronous particle is accelerated? 1This statement also applies to beam acceleration in the betatron and the induction linac. Particles with different betatron amplitudes execute betatron motion around this ideal closed orbit. for simplicity.1 Since the electric field strength of an electrostatic accelerator is limited by field breakdown and by the length of the acceleration column. Since the energy gain depends sensitively on the synchronization of rf field and particle arrival time. D5. A synchronous particle will gain or lose energy. In this chapter we study particle dynamics in the presence of rf accelerating voltage waves. A particle with momentum p has its own off-momentum closed orbit. A particle synchronized with rf phase <f> = <j>a at revolution period To and momentum po is called a synchronous particle. 239 . where D is the dispersion function and 5 = (p — po)/po is the fractional momentum deviation. we will derive the synchrotron Hamiltonian based only on the revolution frequency and energy gain relations. electrostatic accelerators have been used mainly for low energy acceleration. <ps is a phase factor. A beam bunch consists of particles with slightly different momenta. eVsin(f>s. Sec. This formalism lacks the essential connection between synchrotron and betatron motions. here. a radio-frequency (rf) cavity operating in a resonance condition can be used to provide accelerating voltage with V sm(4>s + uijft).Chapter 3 Synchrotron Motion In general. IX). in which the induced electromotive force is given by the time derivative of the magnetic flux. per passage through the rf cavity. and wrf is the angular frequency synchronized with the arrival time of beam particles. but it simplifies the choice of synchrotron phase-space coordinates. Normally the magnetic field is ideally arranged in such a way that the synchronous particle moves on a closed orbit that passes through the center of all magnets. Although we can derive a 6D Hamiltonian for both synchrotron and betatron oscillations (see Chap. where V is the amplitude of the rf voltage.
Particle acceleration without phase stability is limited to low energy accelerators. I. In Sec. bunched beams can be shortened. In Sec. etc. bunch rotation. we study beam injection. In the case of df/d5 < 0. Section II deals with adiabatic synchrotron motion. cf>d = hcjot. etc. etc. VIII. h is an integer called the harmonic number.240 CHAPTER 3. we derive the synchrotron equation of motion in various phase-space coordinates.e. df/dS > 0. Section VI treats fundamental aspects of rf cavity design. called "synchrotrons. higher energy particles will receive less energy gain from the rf gap. Cockcroft-Walton. If the revolution frequency / is higher for a higher momentum particle. it remains the cornerstone of modern accelerators. i." and after half a century of research and development. we introduce collective longitudinal instabilities. where the Hamiltonian is not invariant. extraction.g/2l3c) (n = integer). Therefore if the rf wave synchronous phase is chosen such that 0 < <> < TT/2. (3. Ill. or stacked to achieve many advanced applications by using rf manipulation schemes. beam manipulations with double rf systems and barrier rf systems. (j> < <j>s. ground vibration. In Sec. In Sec. where g is the rf cavity gap width. We assume that the reference particle passes through the cavity gap in time t € nT0 + {-g/2pc. /s Similarly. combined.e. and 4>s is the phase angle for a synchronous particle with respect to the rf wave. elongated. the higher energy particle will arrive at the rf gap earlier. lower energy particles will arrive at the same rf gap later and gain more energy than the synchronous particle. The discovery of phase stability paved the way for all modern high energy accelerators. stacking.g.1) We assume that the longitudinal electric field at an rf gap is where wo = PQC/RO is the angular revolution frequency of the reference (synchronous) particle. we study the perturbation of synchrotron motion resulting from rf phase and amplitude modulation. Furthermore. . e. In Sec. I Longitudinal Equation of Motion £ = £0 sin(<?!>rf (t) + & ) . phase stability requires TT/2 < cj>s < TT. Van de Graaff. In this chapter we study the dynamics of synchrotron motion. we provide an introduction to the linac. phase displacement acceleration. V. VII. Phase-space gymnastics have become essential tools in the operation of high energy storage rings. £0 is the amplitude of the electric field. we treat non-adiabatic synchrotron motion near transition energy. synchro-betatron coupling through dipole field error. /30c and Ro are respectively the speed and the average radius of the reference orbiting particle. In Sec. i. This process provides the phase stability of synchrotron motion. betatron. SYNCHROTRON MOTION The key answer is the discovery of the phase stability of synchrotron motion by McMillan and Veksler [17]. where an invariant torus corresponds to a constant Hamiltonian value. IV.
(j> = <f>s + A<f>.ujo. ( w = wo + Aw. E = Eo + AE.cj. However. and T is the transit time factor: _ sin(/ig/2fio) . and the energy of the synchronous particle. where <f> is the rf phase angle. i. Here (j)s. it encounters the rf voltage at the same phase angle 4>s every revolution. If the gap length is small. the azimuthal orbital angle. the momentum. Thus the acceleration rate of a non-synchronous particle is E=~eVsin(t>. The acceleration rate for this synchronous particle is £0 = ^ s i n i .p.1).6s.E are the corresponding parameters for an off-momentum particle.(hg/2RQ) • (3-3) 1 The effective voltage seen by the orbiting particle is V — SogT.e. a high electric field associated with a small gap may cause sparking and electric field breakdown.6) .9. The phase coordinate is related to the orbital angle by A / = <f> — <f>s = —hA9. the angular revolution frequency. (3.I LONGITUDINAL EQUATION OF MOTION The energy gain for the reference particle per passage is AE = eSofic / /•9/2/Soc 241 sm(huot + <j>s)dt = e£ogT sin 0S. (3. or <> Au = ±A9 = -l±A^=J-dA.po. (3.2) J-g/2poc where e is the charge of the circulating particles. Since a synchronous particle synchronizes with the rf wave with a frequency of Uri = hu>o. I p = po + Ap. where u>0 = pQc/R0 is the revolution frequency and h is an integer. Now we consider a non-synchronous particle with small deviations of rf parameters from the synchronous particle. the transit time factor is approximately equal to 1.Eo are respectively the synchronous phase angle.5) dt hdt v hdt y ' The energy gain per revolution for this non-synchronous particle is eV sin <j>. 2TT (3.4) where the dot indicates the derivative with respect to time t. e = 9s + A0. The transit time factor arises from the fact that a particle passes through the rf gap within a finite time interval so that the energy gain is the time average of the electric field in the gap during the transit time (see also Exercise 3. and <f>.
where the momentum compaction factor is3 a c = . Sec. is called the transition energy. up to first order. 2. (3. Most accelerator lattices have Qo > 0 a n d the closed-orbit length for a higher energy particle is longer than the reference orbit. the mean radius of a circular accelerator is R = RO{1 + a o 6 + a x 5 2 + a 2 6 3 + •••). is independent of particle momentum.8). SYNCHROTRON MOTION and the equation of motion for the energy difference is2 d {AE\ 1 Using the fractional off-momentum variable d-^~ Ap _ u0 AE PE~W' (3-8) we obtain S=^^eV(smct>-smcl>s). 2.12) and 7Tmc2.w0) = -hAoj. (3.£ = a o + 2 a x 5 + 3a262 + ••• = —. where. 2 We use the relation u UJQ Uo UQ WO L A£> J at \ OJO / 3Typically. .5).J T . Sec. The orbit length in a negative compaction lattice is shorter for a higher energy particle. using Eq.242 CHAPTER 3. IV. we have 4> = -h(u . (3. medium energy proton synchrotrons have been designed to have an imaginary j r or a negative momentum compaction (see Chap.9) The next task is to find the time evolution of the phase angle variable 0. The ai term depends on the sextupole field in the accelerator. we obtain — " ^ . (3. Some specially designed synchrotrons can achieve the condition a0 = 0. Recently.10) Using the relation LUR/LJQRQ = /3/Po. we have Qi72 ss -^-^f =s 1 for accelerators without chromatic corrections. or simply 7 T .1 (3 11) Following the result in Chap. where the circumference.13) (3. IV.
I. (3. IV. i.21) form the "synchrotron equation of motion. 7o /7o y9o(5/8n . a higher energy particle with 5 > 0 has a higher revolution frequency. LONGITUDINAL EQUATION OF MOTION 243 Let p — mcP^f = po + Ap be the momentum of a non-synchronous particle.18) (3-19) (3. (3. with 7 > 7 T .1 . we obtain 2. the particle appears to have a "negative mass.7) and (3.11) and (3. The AVF cyclotron operates in this isochronous condition.17) j)." . % = ~ + ai . Above the transition energy. The nonlinear term in Eq. S) are pairs of conjugate phase-space coordinates.17). Equations (3.(5)5 = . (3. (3. the revolution frequency is independent of particle momentum.17) becomes important near transition energy.15) A> yji + 2ffi6 + /?0252 To 27o2 27o2 Combining Eqs. AE/u>0) or equivalently (4>.a0r/o.10) and (3.^ r i + Q 2 ~ 2 a ° a i + " I + "o7?" ~ -TT•^7o 7o ^7o In the linear approximation.20) Below the transition energy. The speed of the higher energy particle compensates more than the difference in path length. and (3. r)0 = (a0 1 3/32 (3. we have Aw = -T)OUJO6 = ( — .— )wod. At the transition energy.e.( % + ViS + V262 + • • -)6. a higher energy particle with 6 > 0 has a smaller revolution frequency.12). the phase equation becomes where ((/>." With Eqs.= Jl+ 20$6 +ffiP. we obtain — where = -r. (3. with 7 < 7 T .1 ) Qi 2 3^o Q 0 %= . The fractional off-momentum coordinate 5 is 8=^ =^ . to be addressed in Sec.14) Expressing /? and 7 in terms of the off-momentum coordinate 5.
although legitimate. AE/LOO) or H = -hujor]o52 + 2 "°f 2 _g[cos (j> .c o s & + (<£-&) sin &] (3. Phys. SYNCHROTRON MOTION I.I The Synchrotron Hamiltonian The synchrotron equations of motion (3. the synchronous phase angle should be 0 < fa < TT/2. 5 This Lee. E49.7) and (3. Below the transition energy. . This Hamiltonian. The synchrotron tune. To simplify our discussion. we now discuss the stability condition for small amplitude oscillations. 4 S. can be accomplished by a phase shift of TT — 2<j>s to the rf wave.5 The angular synchrotron frequency is [heV\rfycosfa\ Ws c IheV\r]cosfa\ =i?V = WoV WE 2*E ' (3-26) where c is the speed of light and R is the average radius of the synchrotron. where the linearized equation of motion is The stability condition for synchrotron oscillation is r]0cosfa<0 (3. where s is the independent coordinate. with 7 < 7 T or 70 < 0. A fully consistent treatment is needed in the study of synchro-betatron coupling resonances. is inconsistent with the Hamiltonian for transverse betatron oscillations.25) discovered by McMillan and Veksler [17]. Rev. Similarly the 7 synchronous phase angle should be shifted to n — fa above the transition energy. we will disregard the inconsistency and study only the synchrotron motion.cos fa+ (</>-fa)sin fa] (3.22) for phase-space coordinates (</>.244 CHAPTER 3.4 With this simplified Hamiltonian. defined as the number of synchrotron oscillations per revolution. 6) with time t as an independent variable. is UJS Qs = ^0=i lheV\r]0cosfa] 2K(PE • (3 ' 27) Typically the synchrotron tune is of the order of < 10~3 for proton synchrotrons and 10"1 for electron storage rings.21) can be derived from a "Hamiltonian" H=lj^E{w) + ^ : [ c o s ^ . 5706 (1994).23) for phase-space coordinates (<fr.Y.
2 The Synchrotron Mapping Equation In Hamiltonian formalism. It is no surprise that Eq. where the rf potentials for (f>s = 0 and cj>s = TT/6 are shown. then the rf phase 0 n + 1 depends on the new off-momentum coordinate <5n+1. (3. The potential well near the synchronous phase angle provides restoring force for quasiharmonic oscillations. Figure 3. the rf electric field is considered to be uniformly distributed in an accelerator.1: The left plot shows schematically the rf potential for (f>s = 0 and vr/6. 3. and therefore synchrotron motion is more realistically described by the symplectic mapping equation ( I Sn+l =5n+ eV o^g (sin (j>n .Esx vs cf>. The right plot shows the corresponding separatrix orbits in {ixh\r)\leV02E)1l2di. 1.28) . The dashed line shows the maximum "energy" for stable synchrotron motion. 2nhr}(6n+i)6n+i.I LONGITUDINAL EQUATION OF MOTION 245 The stability of particle motion in the rf force potential can be understood from the left plot of Fig.g 2g.1. The corresponding stable phase-space (bucket) area is shown in the right plots. . First. The horizontal dashed line shows the maximum Hamiltonian value for a stable synchrotron orbit. The phase (f>u is the turning point of the separatrix orbit. In reality. I 4>n+i = K + The physics of the mapping equation can be visualized as follows. rf cavities are localized in a short section of a synchrotron.sin <j)s). the particle gains or loses energy at its nth passage through the rf cavity.
During beam acceleration. Figure 3. AE/u>0) is invariant.30) (3.28) is independent of energy. AE//32E) with parameters V = 100 kV.<5n+i) preserves phase-space area. 3.1 is a closed curve. When the acceleration rate is high. they are usually used in particle tracking calculations. AE/LUQ) should be used. The phase-space tori change from a fish-like to a golf-club-like shape.6 Note that the separatrix is not a closed curve when the acceleration rate is high. tori of the synchrotron mapping equations are not closed curves. In a rapid cycling synchrotron or electron linac where the acceleration gradient is high. (3.n + eV sin fa. and the separatrix orbit shown in Fig.5). Eq. Hamiltonian formalism and mapping equations are equivalent.246 satisfies the symplectic condition: CHAPTER 3.n+i = £o. Since the acceleration rate for proton (ion) beams is normally low. (3. the separatrix torus shown 6The actual rf voltage V is about 200 V in a low energy proton synchrotron. h = 1. It is worth pointing out that Eq. If the acceleration rate is low. AE) are AEn+l = AEn + eV(sin <f>n . 1.04340. 6) obtained from Eq. Because synchrotron motion is usually slow. Therefore. j = E/mc2.I/7 2 . In reality.2 shows two tori in phase-space coordinates (cj). (3.30) depends on the acceleration rate according to E = £0. the rf cavities may be distributed non-uniformly. 3.1 can be considered as a closed curve. a c = 0.3 Evolution of Synchrotron Phase-Space Ellipse The phase-space area enclosed by a trajectory (</>. The rf phase change between different cavities may not be uniform. (3. /3 = y/l . AE/LJ0) to {(j). The adiabatic damping of phase-space area can be obtained by transforming phase-space coordinates (<j>.I/7 2 . the phase-space area in (4>. SYNCHROTRON MOTION Jacobian= 9(w^ = 1 (329) Thus the mapping from {cj>n.28) can not be used in tracking simulations of beam acceleration. the separatrix is not a closed curve.sin fa). The mapping equations for synchrotron phase-space coordinates (<j).31) 0n+l = <t>n + 2^AEn+u where the quantity rj//32E in Eq. the factor hr]/{32E is nearly constant. This is equivalent to the adiabatic damping of phase-space area discussed earlier.28) treats the rf cavity as a single lumped element in an accelerator. . 5n) to (<^n+i. and r) = ac . (3. fa = 30° at 45 MeV proton kinetic energy. The separatrix for the rf bucket shown in Fig. Because of the simplicity of the mapping equations. The phase-space mapping equation for phase-space coordinates {<f>.
3.I LONGITUDINAL EQUATION OF MOTION 247 in Fig. The voltage requirement becomes Fsin0 9 = 1.30) and (3. Similarly.04340. where p « 2. ac = 0. 1.31) with parameters V = 100 kV.1 is a good approximation. the tori near the separatrix may resemble those in Fig. = 30° at 45 MeV proton kinetic energy. . we obtain V sin <j>s ss 240 Volts.4 m.6 Tesla/s.2MV. which is independent of the harmonic number used. 3. The circumference is 3319. (3.2: Two tori in phasespace coordinates ((f>. e.4 m with p = 235 m.g. and &. proton acceleration in the IUCF cooler ring from 45 MeV to 500 MeV in one second requires B = M ^ l „ l. in many electron accelerators. When the acceleration rate is high. h = 1. Figure 3.2. AE//32E) obtained from mapping equations (3. acceleration of protons from 9 GeV to 120 GeV in 1 s at the Fermilab Main Injector would require B « 1.4 Some Practical Examples Using the basic relations e we find a basic rf cavity requirement: Vsm(j)s = 27rRpB.l Tesla/sec. Using R ss 14 m.32) pc 2nR For example.
7 . where 7 > 0. . .34) • Using (<f>. —Ap/p0) as phase-space coordinates. Using t as independent variable Using time t as an independent variable. 6) as phase-space coordinates: d(j> Tt=huoV6. (3.5 CHAPTER 3./iwor) . V = — {h\r)\/vs)5) as the normalized phase-space coordinates: — = uavj>.40) The corresponding normalized phase space is (T.38) ^ I7?! • Using ( r = (0 — (j>s)/hwo. AE/UIQ) as phase-space coordinates: d<p hLoZn fAE\ H=l^(—) d(AE/u0) 1 .-W)--«./IW0T sin <£s]. the negative sign in the first term corresponds to negative mass above the transition energy.sin^ s ). — = —7W0^s(sini/> . .<£s) sin <j>s]. In particular. (3. • Using {4>.cos 4>s + {4>.41) where ua = Jh\r]\eV/2irf32Eo is the synchrotron tune at <j>s = 0. This synchrotron Hamiltonian is on an equal footing with the transverse betatron motion. d5 ojoeV .T>\—) ^ \Po / -T571[cos^-cos& + (^-&)sin&]) M \V\ (3.35) (3. 2 J^ 6 (3-39) [cos(0s . B. (3. .248 1. f/w s ). the Hamiltonian is H = -T. Using longitudinal distance s as independent variable • Using (R<f>/h. + ^[cos0-cos0s + (0-0s)sin0s]. • Using (<f>. (3.t) as phase-space coordinates: I"* H =-i2+ 5-^"-<*.37) 1 Tj H = -ZOJQI/SV2 + ~UJ0^S[COS (/> . .cos 0S . .„ ocx _ = 5-^(sin0-sm0s).36) H = -huj0r]62 + ^ [cos <(> . (3. the equations of motion and the Hamiltonian are listed as follows.<t>s) sin 0 S ]. SYNCHROTRON Summary of Synchrotron Equations of Motion MOTION A.cos 4>s + {<(> .
e. Calculate synchrotron tunes for the proton synchrotrons listed in the following table with <f>s = 0.5 24. (3.E.1 249 1. 2.12 3833. e and m are the charge and mass of the particle.6 86. Thus the transit time factor T is the same for all particles.8 5.446 C [m] 807. An rf cavity consists of an insulating gap g across which the rf voltage is applied. and x = 0/2TT. (Mod 1). The total energy gain of a particle passing through the gap is the time average of the rf voltage during the transit time. 4. Redefine y = h\r)\8.95 h 12 342 588 84 7r 8.2 K.8 ^s 1 1 1 1 I I ~ 3. RF parameters of some synchrotrons P-synchrotron I AGS I RHIC I FNAL-MI 1 FNAL-BST 28 8 0. Show that the effective voltage is V _ V T sin(hg/2R) where R is the mean radius of the accelerator. xn+i = xn + yn+\ where ws is the synchrotron tune.28) of the symplectic mapping equation for a stationary bucket synchrotron motion can be transformed into the standard map: 2M+1 = Vn .0001 1 4.2 Vrf [MV] 0.3 2 0.4 474.5 21. The gap length is finite and the rf field changes with time during transit time At. .84 3319. and c is the speed of light.045 0.3 0. [GeV/u] 0.EXERCISE 3. i. and <j> the rf phase of the particle. _ hi \ g2w 1/2 (a) Show that Eq.1 Exercise 3. p is the bending radius of the dipoles. RQ is the mean radius of the accelerator. At J-At/2 e fA*/2 V(t) = Vg sm(<j> + huot) where Vs is the peak gap voltage. Show that the relation between the rf frequency of an accelerator and the magnetic flux density B(t) during particle acceleration at a constant radius is given by " r f ~ Ro [B2(t) + (mc2/ecp)2 where h is the harmonic number. AE= — V(t)dt.2 I SSC 2000 10 17424 140 87120 I Cooler 0.IKVI sin27rzn.
62 4>s [deg] I BEPC 240.12 I TRISTAN 3018 30.2. The energy loss per turn is given by UQ = Cj^Et/p.35 0.81 ux j^ 70.8 160 5.8 38.4 2.39324366 [2ws2c = 0.2 7.y) such that x e [—1.5 10 1. (c) Explore the phase-space evolution at us > i/SjC.91 46. explore the dependence of the separatrix on the acceleration rate.1].98 p [m] 3096.28 35.18 7. /3c is the beam velocity. Uo = eVTfSm<j>s.3 8. 2/£[-1. and C 7 = 8.8 1060 223 Energy [GeV] 50 1.85 x 10" 5 m/(GeV) 3 . where the critical synchrotron tune is i/SiC = 0.5 400 5120 25.44 64.1 76. I LEP I ALS I APS 1 NLC P R ? H 26658.2 4.01 38. The energy loss due to synchrotron radiation is compensated by the rf accelerating field.86 26.35 Vrf [MV] 400 1.2 8. SYNCHROTRON MOTION (b) Write a program to track the phase-space points (x.18 14. where Eo is the beam energy.0 1.0 6.1]. i.9 196.2 14.7 _& 1 1 1 1 1 I . 6.22 23.96 4.971635406]. Write a computer program to track synchrotron motion near the separatrix. Calculate synchrotron tunes for the electron storage rings listed in the following table. p is the bending radius of dipoles. and verify the golf-club-like tori in Fig.2 10. 246.e. Electrons in storage rings emit synchrotron radiation. 5. 3.0 h 31320 328 1248 531 7r 50.5 36.250 CHAPTER 3.
The typical synchrotron tune in electron storage rings is of the order of 10"1.§ « 1. when a^ < 0." For simplicity in notation. i. Typically. (3.„ (3 ' 27) . ADIABATIC SYNCHROTRON MOTION 251 II Adiabatic Synchrotron Motion With time t as an independent variable. 6= " (sin <j> .05. the subscript of the energy Eo of the beam has been neglected.</>s)sinc/>s]. =V'fi™**1 ~ .coscj>s + {(j>. This corresponds to adiabatic synchrotron motion. if the acceleration rate is low. During beam acceleration. The synchrotron period is TS = TO/QS! where To is the revolution period. 6) is H = ^hu0r]52 + ^^[cos<f> . where parameters in the synchrotron Hamiltonian change slowly so that the particle orbit is a torus of constant Hamiltonian value. the small amplitude synchrotron tune is ^ Qs = lheV\ricos(/>s\ r. However. The typical synchrotron tune in proton synchrotrons is of the order of 10~3. the Hamiltonian (3.II.s u n f e ) . the Hamiltonian is time independent or nearly time independent. If }rj\ ^ 0. If the rf parameters V and 4>s vary only slowly with time so that the gain in beam energy in each revolution 7 is small. Figure 3. the synchrotron Hamiltonian for phase-space coordinates (<j>. (3. aa = \*£ = i.23) generally depends on time. The condition for adiabatic synchrotron motion is wj dt 2?r dt where a/s is the angular synchrotron frequency and a ^ is called the adiabaticity coefficient. V 2*fPE where "s-y2nP*E \h\q\eV is the synchrotron tune at j cos0 s | = 1. a (3. the Hamiltonian can be considered as quasistatic. and 7 differs substantially from 0.42) where the over-dots indicate derivatives with respect to time t. it takes about 1000 revolutions to complete one synchrotron oscillation. Hamilton's equations of motion are 4> = hr)bjQ5.e.23) where the first term can be considered as "kinetic energy" and the second as "potential energy.43) .1 illustrates schematically the potential energy as a function of cj> for <f>s = 0 and </>a = TT/6. hereafter. the time variation of synchrotron period is small and the trajectories of particle motion can be approximately described by tori of constant Hamiltonian values.
Small amplitude phase-space trajectories around the stable fixed point are ellipses.7r/6. The phasespace area enclosed by a Hamiltonian torus is A = J8{<t>)dct>. 5TT/6.252 CHAPTER 3. Particles outside the rf bucket drift along the longitudinal direction. and only particles in the stable region can be accelerated to high energy. the phase-space trajectories near the unstable fixed point (UFP) (ir . . Thus the UFP is also called a hyperbolic fixed point. and particles inside the rf bucket execute quasi-harmonic motion within the bucket. The synchrotron phase space is divided into stable and unstable regions.7r/3 and for r] > 0 with (f>s = 2?r/3.4>s. Figure 3. A beam in which particles are grouped together forming bunches is called a bunched beam.4>s. 1 Fixed Points The Hamiltonian for adiabatic synchrotron motion has two fixed points (<^s. TT.0) and (TT . The stationary buckets that have largest phase space areas correspond to cj>s = 0 and n respectively. which is also a contour (a torus) of constant Hamiltonian value. where 0 = 0 and 5 = 0. The phase space area enclosed by the separatrix is called the bucket area. it separates phase space into regions of bound and unbound oscillations.7T. and for r\ < 0 with <j>3 = 0.7r/6. The torus that passes through the UFP is called the separatrix. SYNCHROTRON MOTION II. Therefore the SFP is also called an elliptical fixed point. Thus particles in synchrotrons are naturally bunched.57r/6. Figure 3. 0) is the stable fixed point (SFP). particle motion adiabatically follows a phase-space ellipse. The maximum momentum deviation of the separatrix orbit is called the bucket height.3: The separatrix orbits for r) > 0 with <j)s = 2?r/3. The phase-space point (cf>s. For a slowly time-varying Hamiltonian.7r/3. 0).3 shows the separatrix orbit for r) < 0 with <f>s = 0. 0) are hyperbola. On the other hand. The phase-space area enclosed by the separatrix orbit is called the bucket area.
e.1 6 v S £ « ' * » = ^ = 3 »<«• (3-47) where the factor ab(</!|s) is the ratio of the bucket area between a running bucket (4>s ^ 0) and a stationary bucket (</>s = 0).1 lists Qb((/>s) as a function of the synchronous phase angle cj>s. (3. 1 /•*-«.49) The corresponding invariant bucket area in (</>.(?r . Table 3.^ .46) A . AE/UJ0) phase-space variables. The phase-space area enclosed by the separatrix is called the bucket area. i.2 lists some relevant formulas for rf bucket properties. where <fiu is c o s (j>u + <j>n s i n 4>s = — c o s <^>s + (n — (j>s) s i n 4>s. [cos0 + cos <f>s . AE is the bucket energy height (eV). and Qb(7r/2) = 0.<j>a) sin0 S ] = 0.45) The separatrix has two turning points. (3. Therefore the Hamiltonian value of the separatrix is Hsx = ^—^ [-2 cos <j>s + (TT . i. (3.44) The phase-space trajectory of the separatrix is H = Hsx.e. ADIABATIC SYNCHROTRON MOTION 253 II.50) W o is the phase-space area of h buckets in the entire accelerator. where At is the bucket width in time (s). or *« + rKpitihr\ eV « n . the bucket area vanishes at 90° synchronous phase angle./ « • ) * .II. 1 + sin <> /s (3. B2E AB = -—. Note that Qb(0s) can be approximated by a simple function aM « £?£. Naturally ab(0) = 1. . and the resulting bucket phase-space area is in eV-s.e.2&) sin 0J. 0). For </)s = 0. i.4B « hAtAE. (3. the turning points are — ir and ir. 2 Bucket Area The separatrix passes through the unstable fixed point (TT — </>s.48) [ *7 J Table 3. f In I 11/2 ah{<ps) = -r7= \—^ [cos0 + cos(/> s -(7r-0-(k)sin0 s ] df 4 v ^ '^u (3. <fiu and TT — <fis.
4286 0.45 0.1429 0.75 0.2903 0.00 -136.37 168. 1 Bucket Area (Affi 1 (<P.00 I 0. and the bucket height or the maximum momentum width is s-'{^mfY^'mtiU (351) . 1 0.8888 0.00 [ 90.6729 0.4832 0.2919 0. SYNCHROTRON MOTION Table 3.7992 0.0408 0.8182 0.4815 0.7577 0.2: Formula for bucket area in conjugate phase space variables.4459 0.3806 0.46 165.80 0.6611 0.48 4.6667 0.19 1.51 156.1765 0.9048 0.0526 0.4305 0.3793 0. bucket height and bucket area factors.79 115.54 159.2058 0.42 180.2885 0.85 0.1731 0.00 0.10 0.0000 0.3967 0.S) a 1 (4.84 108.1: Bucket length.5852 0.1111 0.26 171.25 0.2349 0.95 4>u 1 7T .88 -13.90 0.0000 0.3333 0.35 0.8402 0.38 37.9208 0. Table 3.0170 1.0256 1.26 150.0811 0.15 0.7391 0.& I y ( & ) I qb(<fe) I jgjffi -180.5385 0.1323 0.11 -38.5399 0.05 0.00 | 90.47 -118. | 0.59 25.2500 0.254 CHAPTER 3.1679 0.5388 0.9606 0.59 -64.90 -105.8041 0.^6) ^ 16 Q b ^> 16 (£§f^) V * Qb(&) 16 ( a f e f f ) 1 " Bucket Height 1 2 ( g g j ^ y f o ) [ ^^J)1''^^) | 2 YQfeT The bucket length is \(n — <j>s) — <f>u\.7294 0.70 0.55 0.13 174.50 0.45 -55.32 -93.6000 0.69 -30.66 -47.87 121.7156 0.3333 0.77 53.75 14.5980 0.0000 0.8807 0.1028 1.63 143.00 177.3455 0.46 135.31 -4.20 0. sin& I 0.2460 0.41 126.31 -21.71 -83.26 -73.30 0.0685 0.52 162.40 0.65 0.42 153.2121 0.13 139.60 0.6295 0.00 146.57 131.4936 0.0991 0.
e. The corresponding rms phase-space area is . Gaussian beam distribution The equilibrium beam distribution is a function of the invariant ellipse of Eq. In many beam applications.53) where ip = 6 — 6S. The phase-space area that contains 95% of the particles in a Gaussian beam distribution is 6-4rms. (3.52) Table 3. The phase-space ellipse of a particle /^V+M 2 -! * __(eV\cos6s\\1/2_ Qs [dj + U J ~ ' 4>-WpEh\v\) -h\n\' (3'55) where 5 and 6 are maximum amplitudes of the phase-space ellipse. Y{6S) = 1 n -26 ^ 1/2 tan 6S .Arms = naga^.26 1/2 ^ sin 6S . Y{6S) = cos 6S . (3. II. and the bucket height factor.55). .27).4 7 r / g 2 g V?2. (3.1 lists the turning points.II. where UJS = becomes QSLJ0 5= -~-J>sH^ h\r]\ + X). (3-54) is the angular synchrotron tune. we use the normalized Gaussian distribution given by ***>-5^-H[$ + £]}-495% = (-6 35 ) where as and o"^ are rms momentum spread and bunch length respectively. Y(6S). ADIABATIC SYNCHROTRON MOTION 255 Here the bucket height factor Y((j)s) and Y(6S) are the ratios of the maximum momentum height to the height of the stationary bucket. A. where the factor 6 depends on the distribution function.3 Small-Amplitude Oscillations and Bunch Area 2 w0eVcos6s 2 1 H = -h^rjS2 . The phase-space area of the ellipse is ir5(f>. of an rf bucket. and (p = (f>cos(ujst + x). i. The linearized synchrotron Hamiltonian around the SFP is (3. The synchrotron frequency is given by Eq.
i.58) become S~ ^ 1 /2yl/4 fe l/4| r? |-l/4 7 -3/4 ! fl~>tVV-l/4/l-1/4|r?|l/47-l/4) (3 6 Q ) where the adiabatic damping is also shown.J-fr where 5 and 9 are maximum amplitudes of the phase-space ellipse.57) S = AW (j±. Thus the phase-space area is commonly defined as phase-space area per amu expressed as [eV-s/u] for heavy ion beams. It will be discussed in Sec.5) space becomes 7Since the energy of a heavy ion beam is usually expressed as [MeV/u] or [GeV/u]. e -> Ze.. the E in the denominator of Eq.\V2 \*PEJ (heV\coS(f>s\\1/4 { 2TT/32E\V\ ) ' h \np2EJ \heV\ cos <f>s\J Qs 5_(heV\coscl>s\y/2 Note that here the phase-space area A is the invariant phase-space area for one bunch in eV-s. Similarly. where Zis the charge number of the ion beam. and 8 —> 0. and u = 0. (E/A). As the energy approaches the transition energy with rj — 0. SYNCHROTRON MOTION Since the synchrotron phase-space area A.7 it is related to A by A = *W = hA(j^y Using Eq. The scaling properties of the bunch length and bunch height of Eq. the invariant phase-space ellipse in (9. (3. we expect that 5 —> oo.55). where A is the atomic mass number or the number of nucleons in a nucleus. The factor eV/E in this chapter should be modified by a charge-to-mass ratio of Z/A for heavy ion beams. (3.57) can be expressed as A x (E/A). IV. is defined as the area in the phase space (c/>/h. and E -^ Ay. E/A = juc2. (3. S) phase space is W .e. The normalized Gaussian distribution in (9. usually measured in eV-s. This is not true because the > synchrotron motion around the transition energy is non-adiabatic.931494 GeV/c2 is the atomic mass unit. . AE/u0) for one bunch. the maximum momentum width and the bunch length are (3.256 CHAPTER 3.
y/2-Kag (3.e -*/*} V27T(T^ o r m = -T=-e-"»i. where R is the average radius of the accelerator. or at = crg/uio in s. = fsini/>. See Eq. the synchrotron Hamiltonian becomes (see Exercise 3. i.II. and the solution can be expressed as r = fcos?/). Now we consider NB particles distributed in a bunch.68) where f and ip are respectively the synchrotron amplitude and phase.333) for its application.| tan <^s ^ . (3. Synchrotron motion in reference time coordinates In the discussion of collective beam instabilities.67 ) The equation of motion is f 4.63) The peak current (in Amperes) of the bunch is ~ = NBe = NBeuj0 = f 2ir \ NBe \p2mat y/^ag \\f2KOg) To B. ADIABATIC SYNCHROTRON MOTION 257 Here og and as are respectively the rms bunch angular width and the rms fractional momentum spread.e.65) The linearized synchrotron Hamiltonian becomes where uis is the angular synchrotron frequency shown in Eq. The phase-space ellipse that corresponds to a constant Hamiltonian is T' + ~2 = f^ ( 3 .69) . (3. The line distribution is p(fl =-*l. ip = ip0 + ujst (3.2. it is sometimes useful to use the particle arrival time r and its time derivative f for the synchrotron phase-space coordinates.52 + ~^Ql [v>2 .-^ p* + • • •] . r = -lzlli and r = — =+tf. The bunch length is as = Rag in meters. where JVB may vary from 108 to 1013 particles. Approximate action-angle variables Expanding the phase coordinate around the SFP with <j> = <f>s + <p.26). (3. C.w|r = 0. (3.11) H = -hu)0r.
w e o b t a i n • = u)0eVcos<i>s 2TT/32E J = w2<5. With normalized coordinates . 5 8In reality. V Vs V nv (3.258 CHAPTER 3. V 0 = -2^O¥>2tanV>. If we use the approximate action-angle variables. the beam does not move in the phase space. tp) are approximate action-angle variables of the Hamiltonian in (<f>. the Hamiltonian for synchrotron motion becomes H = UJOQSJ + CJ0^2yB 12 tan4>s J3'2 [cos3</> + 3cosV>] . the averaged synchrotron Hamiltonian becomes H = uj0QsJ . <P' . (3. Using the generating function for linearized synchrotron motion ^ . we assume r\ > 0 in this section.11).73) (3. 6) phase space. the phase of the rf wave is being shifted so that the UFP is located at the center of the bunch. ^ = VU)° ^ ^ or ^5 = waV(3. we study the evolution of an elliptical torus of Eq.74) QS(J) * Qs [l . 6 = -J^-^i>.^ II. Now.55) at the UFP.uj—^cos^</>• 6 (3.71) where the conjugate variables (J. (j> x o = S-.4 Small-Amplitude Synchrotron Motion at the UFP Small amplitude synchrotron motion around the unstable fixed point (UFP) is also of interest in accelerator physics.2. We would like to find the evolution of bunch shape when the center of the beam bunch is instantaneously kicked8 onto the UFP at time t = 0.72) If we apply the canonical perturbation method (see Exercise 3. SYNCHROTRON MOTION where Qs = ij heV\r] cos <j>s\/2nft2E = vs^j\ cos</is| is the small amplitude synchrotron tune. For simplicity.. Expanding the Hamiltonian around the UFP. ip = (j> — (TT — <f>s). (l + | tan2 0S) j ] . .V ip = —. (3. instead. i.^ Thus the synchrotron tune becomes ( l + jj tan 2 ^ J 2 + • • •.76) Thus the particle motion is hyperbolic around the UFP. the synchrotron phase-space coordinates are transformed according to (fi= (3.e.70) /2§ZcosV.
tanh 2uist ) <p6 + 52 = (cosh 2ujst)-1.II. we find the synchrotron oscillation period as T = j \2tiLJoV \Ho .&) sin 0 j j j #.be'"3''. . The width and height of the phase-space ellipse increase or decrease at a rate e±u>st.79) where Ho is the Hamiltonian value of a torus.6) is the synchrotron Hamiltonian in Eq. 6 = ae"'1 .78) \\v\ ) Thus the upright phase-space ellipse will become a tilted phase-space ellipse encompassing the same phase-space area.S) = Ho. (3. where H(4>.23) and the constant Hamiltonian value Ho is Ho = -hu}Or/S2 = 2n32E^C°S ^ ~ C ° S ^+ ^ ~ ^ Sm^' Here 0 and <5 are respectively the maximum phase coordinate and fractional momentum deviation of synchrotron motion.76) are <p = ae1"*' + be-Ust. This scheme of bunch deformation can be used for bunch rotation or bunch compression.77) where a and b are determined from the initial condition. where t is the length of time the bunch stays at the UFP (see Exercise 3. The action of the torus is J=hi[h^[Ho~S^E{COS*~cos0s+{<t>~0s)sin^s)]) #. With the constants a and 6 eliminated. II. At ust 3> 1.cos & + {</.(3-80) The synchrotron period of Eq.| ^ [ « > s <f> .2.5 Synchrotron Motion for Large-Amplitude Particles The phase space trajectory of adiabatic synchrotron motion follows a Hamiltonian torus H(cj). Using Hamilton's equation 0 = huiorj8. the ellipse becomes a line (p ± 5 — 0. 259 (3.. ADIABATIC SYNCHROTRON MOTION the solutions of Eq.80) with respect to J. (3. However.5).79) can also be derived by differentiating Eq. (3. The angular synchrotron frequency is 2TT/T. (3. the evolution of the bunch shape ellipse is (p1 -2\rL. (3. (3. and using dH0/dJ = UJ(J) to find the synchrotron frequency. the nonlinear part of the synchrotron Hamiltonian will distort the ellipse.
.74) at <f>s . When the value of the Hamiltonian Ho approaches that of the separatrix Hsx of Eq. .85) Figure 3. where 5{<f>) = ^ . (3.81) (3-82) (3. Stationary synchrotron motion CHAPTER 3.85) with a measured synchrotron tune at the IUCF Cooler. we find Qs(4>) « (1 .2. In the small angle approximation. Synchrotron tune I-K/2 //.. where the modulus of these integrals k = sin(</>/2) and .4 compares the theoretical curve of Eq. ±6((j>)). Since the synchrotron tune is nonlinear.P s i n io •'0 are the complete elliptic integrals of the first and second kind. fit/2 1 (3.k2) K{k)] . _ .[-B(fc) .83) The Hamiltonian torus is the phase space trajectory given by ((/>. If the bunch area is . or the action J enclosed by the Hamiltonian torus is A = 2TT J = 2 / 0 5{<t>)d4> = 1 6 ^ .44). the synchrotron tune becomes zero and the synchrotron period becomes infinite. Note that the maximum off-momentum coordinate 5 is related to the maximum phase coordinate (j> a Hamiltonian torus by *-*4 (. which is identical to Eq. we consider the stationary synchrotron motion above the transition energy with 7 > 0. (3. SYNCHROTRON MOTION For simplicity.(1 . •/o VI .cos0). particles having different synchrotron amplitudes in a beam bunch can have different synchrotron tunes.8) Q8(0) = 7r*V2#(sin(^/2)) (3. or <f>s = n.260 A. The Hamiltonian value for a torus with a maximum ? phase coordinate 4> (or maximum off-momentum coordinate 5) is Ho = ihuovS2 = % s 2 ( l . E{k)= Jl-k2sin2wdw..V ' 2 ( C 0 S ( ? i .84) The synchrotron tune of the Hamiltonian torus with maximum phase amplitude 4> becomes (see Exercise 3.C 0 S ^ ) The phase space area A. K{k)= B.YQ4>2)US.0. (3.
synchrotron tune spread is useful in providing Landau damping for collective beam instabilities. For a mismatched beam bunch. The final bunch area is determined by the initial beam distribution and parameters of the rf system (see Fig. The zero amplitude synchrotron tune was ua = 5. or rf voltage and phase modulations. Since synchrotron oscillation is rela- . Beam filamentation causes a mismatched beam bunch to evolve into spirals bounded by a Hamiltonian torus. In this section we discuss the methods of measuring the off-momentum and rf phase coordinates of a beam. The fractional off-momentum coordinate of a beam can be derived by measuring the closed orbit of transverse displacement Axco at a high dispersion function location. V). the synchrotron tune spread may be large. 3.II. The solid line shows the theoretical prediction of Eq. Filamentation can dilute the phase-space density of the beam. a phase detector is needed in implementing a phase feedback loop to damp dipole or higher-order synchrotron modes.4: The measured synchrotron tune obtained by taking the FFT of the synchrotron phase coordinate is plotted as a function of the maximum phase amplitude of the synchrotron oscillations. When the beam encounters longitudinal collective beam instability. and the corresponding FFT spectrum. The off-momentum coordinate is Ap Axco T = "#' (3-86) where D is the horizontal dispersion function. The inset shows an example of the synchrotron phase-space map measured at the IUCF Cooler.6 Experimental Tracking of Synchrotron Motion Experimental measurements of synchrotron phase-space coordinates are important in improving the performance of synchrotrons.2 x 10-4. or mis-injection in the rf bucket. a filamentation process. where beam particles spread out in the synchrotron phase space. synchrotron tune spread can cause beam decoherence. ADIABATIC SYNCHROTRON MOTION 261 Figure 3. etc. This process is important to rf capture in low energy synchrotrons during injection. a substantial fraction of the bucket area. For example.. (3.85). II. On the other hand.19 in Sec. the mismatched phase-space distribution will decohere and result in beam dilution.
and the horizontal dispersion function D is about 4. Equation (3. the signal from a beam position monitor (BPM) or a wall gap monitor (WGM)9 is OO 00 I(t.4 shows a synchrotron phase space ellipse measured at the IUCF Cooler Ring.262 CHAPTER 3. The BPM system had an rms position resolution of about 0.87) shows that the periodic delta-function pulse. The wall current that flows through a resistor. To measure the phase coordinate or equivalently the relative arrival time r. is equivalent to sinusoidal waves at all integer harmonics of the revolution frequency. the type III utilizes the edge triggered JK-master-slaveflip-flopcircuit. The 10 See Roland E. The position signals from the BPM were passed through a 3 kHz low-pass filter before digitization to remove effects due to coherent betatron oscillations and high frequency noise. we examine the characteristics of beam current signal from a beam position monitor. We assume that the bunch length is much shorter than the circumference of an accelerator. To is the revolution period. or we select the fundamental harmonic with a low-pass filter including only the fundamental harmonic. can then be measured. typically about 50 Ohms with a stray capacitance of about 30 pF. and the fractional off-momentum coordinate is obtained from the displacement of the beam centroid measured with a beam position monitor (BPM). The synchrotron phase coordinate can be measured by comparing the bunch arrival time with the rf cavity wave. the signal-to-noise ratio can be enhanced by using a low-pass filter at a frequency slightly higher than the synchrotron frequency.0 m at a high-dispersion location. The bandwidth is about 100 MHz. The type II phase detector utilizes XOR logic. and the phase between the beam and the reference rf wave can be obtained by using phase detectors. With the beam bunch approximated by an ideal 5-function pulse. 7-9 (McGraw- . By averaging the position measurements the stability of the horizontal closed orbit was measured to be within 0. Hill. Phase Locked Loops. pp. Design. by Aa. The momentum deviation is related to the off-momentum closed orbit. r) = NBe £ fc-oo 5{t + r . and Applications. Axco. The phase coordinate is obtained by a phase detector. we first select a sinusoidal wave by using the band-pass filter. a 3 kHz low-pass filter could be used to average out betatron oscillations of a few hundred kHz. The sinusoidal signal is compared with the rf wave. Best. the 9A wall gap monitor consists of a break in the vacuum chamber. Since the synchrotron frequency at the IUCF Cooler in this experiment was less than 1 kHz for an rf system with h = 1. SYNCHROTRON MOTION tively slow in proton synchrotrons. u>0 = 2TT/T0 is the angular revolution frequency. 3. Theory.87) where NB is the number of particles in a bunch. and has a range of ±180°.1 mm.co = D5. The inset in Fig. 1984). in time domain. where 5 = Ap/po is the fractional momentum deviation.02 mm. and r = (8 — OS)/UIQ is the arrival time relative to the synchronous particle. and has a range of ±90°.10 Normally. First.ITO) = NBe £ n=-oo ein^t+T\ (3. New York.
(b) The bunch area is determined by several factors. Phys. 4051 (1994).5 GeV? (d) How does the rf bucket area change during the acceleration process? 3. the acceleration time is 160 ms. Rotate the phase-space ellipse of Eq. where t is the time the bunch stays at the UFP. the transition energy is ~fT = 4. what is the minimum rf voltage needed? (c) What is the rf frequency swing needed to accelerate protons from 200 MeV to 1. Rev.5 GeV kinetic energy.2 263 BPM sum signal or the WGM signal can be used to measure the relative phase of the beam.The top inset in Fig. To extend the range of beam phase detection. etc. show that the width and height of the bunch change by a factor e±Ust. show that the rf bucket area in the (AE/UJQ.2 1. and estimate the time needed to double the bunch height. Verify Eq. the synchrotron motion can be tracked at N revolution intervals. such as line charge density. the extraction energy is 1. If we need a bunch area of about 1 eV-s per bunch in (AE/uiQ. 4>/h) phase space has a minimum at 7 = \ / 3 7 r . Exercise 3. the type II can be used.5.<f>/h) phase space. 4.EXERCISE 3. the bottom inset shows the FFT of the phase data. (3. This exercise concerns the acceleration of protons in the AGS booster. 3. and the harmonic number is h = 3. transition crossing in the AGS. (3. The resulting synchrotron tune as a function of peak phase amplitude is compared with the theoretical prediction in Fig. but can adequately measure the synchrotron tune. Ellison et al.78 m.78) into the upright position. n M . where N -C l/vs. Particle acceleration at a constant bucket is a possible "rf program" in synchrotrons.4 MHz low-pass filter to eliminate high harmonics noise before it was compared with an rf signal in a phase detector. Find the relation between rf voltage and beam energy. For more accurate measurement of phase amplitude response.03 MHz for the 45 MeV protons in this measurement at the IUCF Cooler. a type IV phase detector with a range of ±360° can be used. The phase-space map of synchrotron oscillations can be obtained by plotting Ap/po vs <j> in each revolution.76). Write a simple program to calculate a^((j>o)2. the BPM signal was passed through a 1. . For a constant rf voltage and synchronous phase angle. microwave instabilities. 3. and the bucket area is about 1.4.11 Since the rf frequency was 1. E 50. (a) Find the rf voltage needed for acceleration of a proton bunch in the booster. Since the synchrotron tune of a proton synchrotron is small.4 shows the Poincare map of the longitudinal phase space at 10 turn intervals. The circumference of the booster ring is 201. type III has a phase error of about ±10° near 0°.2 times as large as the bunch area. 5. The injection kinetic energy is 200 MeV from the linac.
7.V. (b) At 1/4 of the synchrotron period after antiproton injection.4 474.5 0. and R = 83 m. Dugan.045 Vrf [MV] 0. [13] (1983). Show that the final rf voltage V2 is related to the initial voltage V\ by Find the final matched rf voltage for the Debuncher.0001 h 12 342 588 84 1 7T 8. (3. SYNCHROTRON MOTION 6.84 3319.95 0. The anti-protons produced from the Main Injector (Main Ring) pulses have the following characteristics: p 0 = 8. 9.84).5 0. Assuming stationary bucket.3 0. Tollestrup and G. aE = 180 MeV.2 86.15 ns. The antiprotons are captured in the Debuncher into the 53. or Ap/p 0 = ±2%.6 C [m] 807. 954 in Ref.E. Define p^ = hur]5. . P0 = o w 2 ( s i n ^ . and show that the synchrotron equations of motion become <I> = P4>. and synchrotron period of the Debuncher ring for the rf system.s i n ^ s ) .446 4. 12 (a) Find the bucket height.5 21.8 A [eV-s] 1. 7 T = 7.0001 aE [MeV] <Jt [ns] I I I I I 8. 12See A. P-synchrotron I AGS I RHIC I FNAL-MI I FNAL-BST I Cooler K. fill out the beam properties of the proton synchrotrons in the table below. Note that 5 MV is the maximum voltage that the Debuncher rf system can deliver. synchrotron tune. at = 0.264 CHAPTER 3.1 MHz (h = 90) rf bucket with V = 5 MV.5 24.12 3833.8 5. (c) Show that the final energy spread in this debunching process is Find the final energy spread of the antiproton beams. the rf voltage is lowered suddenly to match the bunch shape. p. [GeV] 25 250 120 8 0.3 2 0.15 0JJ5 0.9 GeV/c. Show that the synchrotron tune of a particle with phase amplitude <j> in a stationary bucket is where K(x) is the complete elliptical integral of the first kind given in Eq.7.
w o Q 2 p . r —- . Let (j> be the maximum synchrotron phase amplitude.8. Show that the Hamiltonian below the transition energy becomes H = usJ + w2 1 cos 2 tb .EXERCISE 3.. where //tey|T?cos^sJ For simplicity. + ^s2(cos^-l). and the overdot indicates the derivative with respect to time t. Expanding the phase coordinate around the SFP with (j) = <j>s + ip. the synchrotron Hamiltonian becomes H = -hw0r. show that the synchrotron tune is approximately given by [2 where J\ (w) is the Bessel function. we assume r\ > 0 in this exercise.82 + ^ . V<S> = —\/2Jussm4>. w J V ws (c) Compare the accuracy of the above approximated synchrotron tune to that of the exact formula given by Exercise 3.tan fa <pz . Show that the maximum offmomentum deviation is 11.2 265 where us = w$y/h\q\eV/2-Kp1E. where J and ip are action-angle coordinates.—<pA + • • -j . L ws Vv w s j \ (b) Using the phase averaging method. 10.2. The Hamiltonian for a stationary rf system with fa becomes ff=^ (a) Using the generating function i^-y^tan^ show that phase-space coordinates are <j> = \J2Jjus cos-0.cos I A — cos ip I .
the rms fractional momentum spread of the electron beam is ag = 0. Compare your result with that of Eq. show that terms proportional to J 3 / 2 in the Hamiltonian can be canceled if Gz and G\ are chosen to be G3 = ^ t a n ^ / 3 / 2 i G l = ^ t a n ^ s 7 3/2. p is the bending radius. (> where <p is the maximum synchrotron amplitude in the quasi-harmonic approximation. (c) Show that the new Hamiltonian is H = u0QsI uiohrj —I* cos4 ip 6 tan 2 4 .266 (a) Using the generating function CHAPTER 3. where Cq = 3. . 12 Un ^ j3/2 [CQS ^ + 3 CQS ^ _ "skn ji 6 C0S4 ^ (b) Using the generating function F2(ip.."frv^Qa 8 0 s /i/2[ c o s 3 ^ + 3cos ^][3Gr3 c o s 3^.3. 8— — y2QsJ/hijsinip.. + G l CDS ^]_ Now the perturbation in the new action variable is proportional to 7 2 .. 12. (d) Show that the average Hamiltonian is <tf>="oQs/-^(l + ^tan^s)/2 + .85) for <ps = 0. I)=ipl + G3(I) sin 3^ + Gi(J) sin V. SYNCHROTRON MOTION show that the phase-space coordinates are related to action angle (J. Show that the synchrotron tune for a particle with a synchrotron amplitude (p is Q¥ ) = Q s [ l .83 x 10~13 m. The natural rms fractional momentum spread of electron beams in a storage ring is OE/E = JCq~f2/JEP. and the Hamiltonian in action-angle coordinates is H = u^j _" o v y .1. Find the bunch length and rms phase-space area in eV-s. and JE ~ 2 is the damping partition.000813. In the NLC damping ring (DR) parameter list shown in Exercise 3. Finding new canonical variables to cancel low-order perturbation terms is called the canonical perturbation technique.^ ( l + 5tan 2 <^ 2 ]. ip) by ip = J2hr] J/Qs cos ip. (3.
EXERCISE 3. the resulting coherent beam motion is called the quadrupole synchrotron mode. Make coordinate transformation into the synchrotron rotating frame. .61). AV is the mismatched voltage. show that a2e « al{\ .—^ H 5. Because the bunch tumbles at twice the synchrotron frequency. When a mismatched Gaussian beam p(5. Show that the peak current for the weakly mismatched beam is Discuss your result. where 6 = \r)\6/uB. The nonlinear synchrotron tune will cause the mismatched injection to filament and the resulting phase-space area will be larger. (b) For a weakly mismatched beam. whereCTO= Jag + {r]as/i/s)2 is the matched rms beam width. (3. The equilibrium distribution in linearized synchrotron phase space is a function of the invariant ellipse given by Eq.p)dp. t) = J^Le-8*l2*2 V27TCT ~a2 = CT| CQS2 ^ + fl^/^2 gin 2 ^ Show that the peak current is I(t) = N^euol{\p2/na•. The beam profile in the x plane is equal to p{x) — J p(x. and the mismatch condition for the linearized synchrotron motion is given by ag / \r)\as/vs(a) Show that the projection of the beam distribution function onto the 0 axis is 13 p(0..> ' 27r<T5CT9 F \ 2 [o-92 as2\ J is injected into the synchrotron at time t = 0.2 267 13. (va5/us)2 « «rg(l + AV/2V). and V is the voltage for the matched beam profile. ^Transform the (9.AV/2V).8) coordinate system into the normalized coordinate system (x = 9 and P — M^/"«)> where the matched beam profile is a circle.0) = exp < . what is the time evolution of the beam? Here ag and ag are respectively the initial rms bunch angular width and fractional momentum spread.
In the normalized phase-space coordinates.l Normalized Phase-Space Coordinates Using normalized momentum deviation coordinate V = —(/i|7?|/^s)(Ap/p). The synchrotron Hamiltonian is autonomous (time independent).2).90) where the complete elliptical function integrals are [25] E{k) = [n/2 Jl-k25m2w Jo dw. (3. (3. we study the effects of a single frequency sinusoidal rf phase and voltage modulation on particle motion and beam distribution. The understanding of the beam response to a single frequency modulation can be applied to the analysis of more complicated situations. V) are normalized conjugate phase-space coordinates.88) where i/s = *Jh\r)\eV/2n/32E is the synchrotron tune at |cos^>s| = 1.COSUJ. and the maximum bucket area is A — 27rJmax = 16 (see Table 3.. and medium frequency from mechanical vibration etc. .(1 . Expressing the synchrotron coordinates in parameters k and w as d> sin— = ksinw. the orbital angle 9 is the independent variable. The action is J^~ivd4>=[E(k) . power supply ripple. III. (3. where k = 0 corresponds to the SFP and k = 1 corresponds to the separatrix orbit that passes through the UFP. s i n 2 ^ . the Hamiltonian for a stationary synchrotron motion is #o = ^ P 2 + 2 M . In this section. SYNCHROTRON MOTION III RF Phase and Voltage Modulations Particle motion in accelerators experiences perturbations from rf phase and amplitude noise.89) we obtain Ho = 2i/sk2.k2)K(k)}. wakefields.0) and (<fr. = dw.O). These perturbation sources cause rf phase or voltage modulations. etc. low frequency from power supply ripple and ground motion. the frequency spectrum of rf noise may contain high frequency arising from random thermal (white) noise. and (<fi. V — = A. In general.V)UFP = (TT. and thus the Hamiltonian value is a constant of motion.k2 sin w . The Hamiltonian has fixed points at ( ^ ) S F P = (0. the maximum action (k = 1) is J max = 8/TT. K(k) = r / 2 Jo l VI .268 CHAPTER 3.
can be obtained simply by integrating Eq. in Fourier harmonics of the conjugate angle parameter ip. (3. ^W ~ 2[1"(2j T"(2-4j 3 (2-4. which is conjugate to the action J.6} 5" J" Thus the action is related to the parameter k by J = 2k2(l + l-k2 + ^ + • • •). RF PHASE AND VOLTAGE MODULATIONS 269 For synchrotron motion with a small action. (3. Jo we obtain the angle coordinate ^ v = 4G7W*Jt. using Hamilton's equation 4> = vaV.94) Using the generating function Fa{<l>. (3. (3. we can relate the orbital angle 0 to the w parameter of Eq. .93). the power series expansions of elliptical integrals are K(k) = \ 1 + (\?e + ( I ^ | ) V + ( ^ | ) 2 * 6 + • • • ] . The synchrotron tune becomes 9 J ~ 2K(k) ~Ml ys(<7) where we have used the identities 2k^ = E(k) -K(k).e.91) 2fc2 = J^-TeJ-iej2 -•)• 8 256 }' ^ (3-93) In terms of the action. ^dJ§t = ^m-K(k). vs k V((/>) dJ The angle variable ip. and the synchrotron phase coordinate <j>.III.89) as vs{0 . First. i.e0) = f* § = u .96) The next task is to express the normalized off-momentum coordinate V.u0. V> = ^ 0 + ift>(3.J)= [*V($) dj>. the Hamiltonian is Ho{J).
dn2(w|A. u0 = I . v = 2toH. n=—oo (3.100) Gn(J) = ^. en and sn.98) Thus the expansion of V and sin(0/2) in Fourier harmonics of ijj is equivalent to the expansion of cn(u\k) and sn(u\k) in V = vu/2K.97) and the synchrotron phase-space coordinates are related to the Jacobian elliptical function by V = 2k cn(u\k). Sum rule theorem The solutions of many dynamical systems can be obtained by expanding the perturbation potential in action angle variables.cos^e-^di/j. sin | = k sn(u\k). (3. [25]. SYNCHROTRON . are then defined as sinw = sn(u|fc).cos 5V + ---.k2).e.102) . Jo VI — k2sin w Jo v l — k2sin w The Jacobian elliptical functions.c o s 2 V . The expansion of normalized coordinates in action-angle variables is useful for evaluating the effect of perturbation on synchrotron motion. aw. aw. i. For the case of rf phase modulation.— c o s # + • • •.99) where ip is the synchrotron phase with the q parameter given by with K' = K(\/l . This can be achieved by using Eq. (3. (3.2) in Ref. (3.u>o 1 MOTION .) = _v_^_^__ c o s ( 2 n + 1)^ (oj)3/2 cos3V' « (2J) 1 / 2 cosV + ^ — + (2J)5/2 i ^ . .23. (16. we <h 2sin2r= °° 1 J2 J2 Gn{J)e>n* « .[2n{l . (3.101) 2?r JO where G_n = G*. Gn = 0 for odd n.270 where u= rw I CHAPTER 3..). using the identity k2sn2(u\k) obtain = 1 . discussed below. . cosw = cn(u\k). Similarly. the expansion of the normalized off-momentum coordinate is oo ?= E W)eini>. Because 1 — cos<f> is an even function.
719 (1993). from Eq. Rev. RF PHASE AND VOLTAGE MODULATIONS where /_„ = f* and. Phys. Furthermore. the sum of all strength functions is (see Exercise 3. The resulting rf phase difference in every revolution is Aip = 2TTi/macos{vm9 + xo)For simplicity. In this section. we consider the case of a stationary bucket with 4>s = 0 for r\ < 0. Rev. the strength functions /„ are hm+1~ 271 2nVkqm+^ K(k)(i + q*"+iy _ hm~ Because V is an odd function. and xo is an arbitrary phase factor. / > where vm is the modulation tune. where 9 = u>ot is the orbiting angle serving as time coordinate. M. H. (3. only odd harmonics exist.107) 14 M. (3. 4678 (1993). 70. E 4 8 . 71.103) We observe that the strength functions are zero at the center of the rf bucket where J — 0 and at the separatrix where Qs(JSx) = 0.3. Using the normalized off-momentum coordinate V = — {h\rj\/vs)8. E 4 9 . Phys.2) E \fn\2 = ^~J^s n=-oo (3. Rev. 591 (1993). 1610 (1994). Ellison et al. eV 5n+1 = 5n + —(sm4>n+1-sixi(t>s). the synchrotron mapping equation is <l>n+l = <Pn + 27ThVSn + Aip(e). we consider only a sinusoidal rf phase modulation with14 < = <zsin(j/m0 + Xo). (3.2 RF Phase Modulation and Parametric Resonances If the phase of the rf wave changes by an amount <p(6). . Wang et al. Lett.106) where the perturbation potential of rf phase modulation is Hi = vmaV cos(i/m0 + xo).99).105) where A(p(9) = ip(9n + 2TT) — ip(9n) is the difference in rf phase error between successive turns in the accelerator.104) (3. Huang et al. a is the modulation amplitude. Rev. Phys.III. Y. Phys. III. we obtain the perturbed Hamiltonian H^H0 + Hl = -vj>2 + 2iss sin2 ^ + vmaV cos(t<m0 + Xo). Syphers et al. (3.. Lett.
$•$ — a/32\/2.n.I) = (Tl>-vm0-xo-n)IThe new phase-space coordinates become X = 1> . In the following. SYNCHROTRON MOTION Expressing the phase-space coordinate V in action-angle coordinates with Eq.vme . we consider only the dominant dipole mode below. B. In this section. Dipole mode If the phase modulation amplitude is small.1H) . particularly the 1:1 dipole mode. (3. A. vm = (2m + l)fs. Near the first-order synchrotron sideband with vm sa vs.xo)] (2J)3/2 +v™a IOQ [C0S(3^ + vm0 + Xo) + cos(3V> .110) The Hamiltonian can be transformed into the resonance rotating frame by using the generating function F2{il>.99). etc. However. VII. (3.xo . For example.108) where J and ip are conjugate action-angle variables. The rf phase error generates only odd order parametric resonances because V is an odd function.vm6 . i.109) where / i = a/y/2. Chap. we can expand the perturbation in action-angle variables Hi = vmcn/j/2 [cos(V> + vm6 + Xo) + cos(^ . This primary parametric resonance is called (2m +1):1 resonance. stationary phase condition exists for a parametric resonance term.e. two nearby strong parametric resonances can drive secondary and tertiary resonances. The effect of rf phase modulation on phase-space distortion can be solved by using the effective parametric resonance Hamiltonian. (3. the 1:1 and 3:1 parametric resonances driving by a strong phase modulation can produce a secondary 4:2 resonance at vm ~ 2vs. We neglect all non-resonance terms in Hi to obtain an approximate synchrotron Hamiltonian HKVSJ^ysJ2 + vmf2m+xJm+1'2 cos ((2m + l)tf . (3.272 CHAPTER 3.xo)] + • • •.vmd Xo). I = J. we discuss only the primary parametric resonances. 2. that resembles the Hamiltonian for 1-D betatron resonances discussed in Sec. (3.112) (3. the Hamiltonian for the dipole mode is HKVJ±-VSJ2 ID + ^J1'2 V2 cos(V .vm6 - Xo). Effective Hamiltonian near a parametric resonance When the modulation tune is near an odd multiple of synchrotron sideband.vm6 . the dominant contribution arises from the m = 0 sideband.
115).1 .III.115) \ vs J When the modulation tune is below the bifurcation tune i/\.1/2. with x = 0 or 7T. 273 (3.. which characterize the structure of resonant islands. where x = l-vm/vs. Eq. xbif = l-uhi{/vs.^ I 1 / 2 cosx. solid lines) and UFP (\gc\.114) The fixed points of the Hamiltonian.^( 4 «) 2 / 3 ] . 16 3 V VZbif/ Here ga and gt. The reason that ga and gt. 15Find the root of the discriminant of the cubic equation (3. RF PHASE AND VOLTAGE MODULATIONS and the new Hamiltonian is H=(vsvm)I . x bif = — (4o) 2 / 3 . where Hamilton's equations of motion are X = vs-vm--vsl-vs—j==cosx. and gb -)• 0.\f given by15 vw = *. we have f -> 7r/2. [l . are respectively the outer and the inner stable fixed points (SFPs) and gc is the unstable fixed point (UFP). In the limit vm <C vbif. (V = 0) [7~~x~\^ .±vj2 .113) Since the new Hamiltonian is time independent in the resonance rotating frame. Using g = %/2Jcosx. x = 0./ = x1'2 cos . dashed line) shown in the left plot of Fig. • gb(x) = ^=x"2 sin(^ . are given by the solution of 7 = 0.5 vs the modulation frequency is a characteristic property of the dipole mode excitation with nonlinear detuning. . 3. we obtain the equation for g as g3-ie(l-—)g + 8a = 0. Particle motion in the phase space can be described by tori of constant Hamiltonian around SFPs. to represent the phase coordinate of a fixed point.. are SFPs and gc is the UFP will be discussed shortly. thus ga -> -4x 1 / 2 . The lambda-shaped phase amplitudes of the SFPs (\ga\ and \gb\. (3. gc ->• 4a. i=-vs-V2Isinx(3.115) has three solutions: 8 £ (ip = ir) (V = 0) (3-116) 9a(x) = . ^ = arctanW (3.117) ^ ( x H ^ a ^ s m ^ + i). (3.| ) . a torus of particle motion will follow a constant Hamiltonian contour.
and they disappear together.-(jL)+ij -^-(JL). and ga = — 2(4a) x / 3 at x = lyfThe characteristics of bifurcation appear in all orders of resonances with nonlinear detuning. i. the UFP and the outer SFP move in and the inner SFP moves out. the phase space ellipses return to this structure in l/ivm revolutions. SYNCHROTRON MOTION The Hamiltonian tori in phase space coordinates V — — %/2/sin x vs X = %/2/cos x are shown in the right plot of Fig.r^/. and the unstable fixed point is gc. As the modulation tune approaches the bifurcation tune. (3.02. vm > z/bjf (x < Xbif). The intercept of the the separatrix with the phase axis is denoted by g\ and <2 ?When the modulation frequency approaches the bifurcation frequency from below. and right plot: Poincare surfaces of section for fm = 245 Hz and / s = 262 Hz at a = 0. resonance islands can be created or annihilated.i8) In particular.5: Left plot: fixed point amplitudes |ga|.115): / / 3 \ 1 / 3 / / 3 \ 1 / 3 fcW-(<. Figure 3..py be the local coordinates about a fixed point of the Hamiltonian.e. (3. y = V2IcosX-g. The stable fixed points are ga and <?(. The actual Hamiltonian tori rotate about the center of the phase space at the modulation tune vm. the UFP collides with the inner SFP with 9b — 9c = (4a) 1 / 3 . \gi. The torus passing through the UFP is the separatrix. C. Island tune Let y. which separates the phase space into two stable islands. ga = —(8a)1/3 at x — 0 (vm = vs). py = -V2IsmX. 3.119) . At the bifurcation frequency. i.) j . there is only one real solution to Eq.274 CHAPTER 3. (3.\.5.e. where x = rcbif and f = 0.. Beyond the bifurcation frequency. and \gc\ (in unit of (4a)1/3).
are useful in determining the maximum 16 M. These intercepts. (3. The equilibrium beam distribution (see Appendix A.122) where x — 1 — vmjv&.4). When the modulation frequency becomes larger than the bifurcation frequency so that [1 — (p3/4o)]1/2 -¥ 1.5 and 3. we obtain again ^isiand — K ( l .) = us \±xgl .113). Because gl/Aa < 0 and 0 < gl/Aa < 1. With a local coordinate expansion.(1 — j^g2) — vm\.jj-g2) . the Hamiltonian (3.120) can also provide information on the local distortion of the bunch profile. the linear superposition principle fails. 3. RF PHASE AND VOLTAGE MODULATIONS 275 where g is a fixed point of the Hamiltonian. In this region of the modulation frequency. When the modulation tune vm approaches fbif.a)xl2 —¥ 0. Sec.\ag^ . (3. gc is the UFP. at vm -C Vbu is approximately given by island ~ |fs(l —-j^ff2) —"m|.This means that the solution of the equations of motion can be approximated by a linear combination of the solution of the homogeneous equation with tune f s (l — j^g2) and the particular solution with tune ^m. With the UFP gc substitutes into the Hamiltonian (3.±g*c . the separatrix torus is H{J. (3.16 Thus the island tune is the beat frequency between these two solutions. Ellison et al. and the linear superposition principle is again applicable. which satisfies the Fokker-Planck-Vlasov equation. D. II. . Rev. Eq. shown in Figs. is generally a function of the local Hamiltonian.III. Since g\jAa > 1. ga and g^ are SFPs. 591 (1993). Lett. The separatrix orbit intersects the phase axis at g\ and g2. The island tune for large-amplitude motion about a SFP can be obtained by integrating the equation of motion along the corresponding torus of the Hamiltonian in Eq. 70.£)V2 + 7 ^ + • • • • Ag 4a Ag y (3-120) Therefore the fixed point g is a stable fixed point if (1 — g3/4a) > 0. Phys.113) becomes island = ^ ( 1 . Separatrix of resonant islands The Hamiltonian torus that passes through the UFP is the separatrix.6. The island tune for the small-amplitude oscillations is ( 2\ / 3 \ ^/^ '-fej-M'-y • (3-m) The island tune around the inner SFP given by gi. with (1 — gl/4. i.113). the island tune for small-amplitude oscillation about the inner SFP approaches 0 and the small-amplitude island tune for the outer SFP at vm = i^jf is i^and = 3|K.vm\.
hi and hi. = g. satisfies the equation H(J. h2 = -he + —==. At x = x0. and hc are shown in 3. (3.6: Thefixedpoints in units of (4a)1/3 are plotted as a function of the modulation frequency in x/xbn. This means that there are two non-intersecting tori with the same zero Hamiltonian value. hi. E.276 CHAPTER 3.123) besides the solution <j>0 = 0. and other tori orbit about the outer SFP.6.-hc 2 2 •==.123) is Uxo) = -2 5 / 3 (4a) 1 / 3 . The torus passing through the origin For a beam with small bunch area. which is the torus-O. With the notation h. (3. if)) = 0. there are three solutions to Eq.21/3:Cbif). Figure 3. two solutions of Eq. called the torus-O.123) where x = 1 . This means that the torus-O is also the separatrix of islands. The SFPs are K = ffa/(4a)1/3 and hb = ff6/(4a)1/3 and the UFP is hc = pe/^a) 1 / 3 . When the separatrix passes through the origin. or vm < v0 = K. SYNCHROTRON MOTION phase amplitude of synchrotron motion with external phase modulation. where x = 1 — vmlvs and Zbif = ^(4a) 2 / 3 with a as the amplitude of the phase modulation. (3.124) .{vm/vs).(1 . ha. The Hamiltonian torus passing through the origin.When x > x0 = 21/3Zbif. (3. the intercepts of the separatrix are hi . the phase axis intercept of Eq. The intercepts of the separatrix with the phase axis are shown as hi = ffl/(4a)1/3and/l2=fl2/(4a)1/3. all particles can be approximately described as having initial phase-space coordinates at the origin. The intercepts (j>0 of the torus-0 with the phase axis are then 4>0{<j>l .32x(j>0 + 3 2 a ) = 0. (3. One of the tori orbits about the inner SFP. and the fixed points. The intercepts of the separatrix with the phase axis. /(4a) 1 / 3 .123) become degenerate.
5. A separate function generator produces two modulating voltages. A. The intercept is then ^'--("•qK'-SE) III. The corresponding revolution period was 969 ns with an rf frequency of 1. initially at 0. or about 1910 revolutions (turns) in the accelerator.m0.4 m (or 60 ns). II. resulting in an rf phase shift ymod in the rf wave.123) besides <j>0 = 0. experiences the rf phase sinusoidal modulation with ipmod = asinz. 3.6. The phase lock feedback loop was switched off in our experiment. RF PHASE AND VOLTAGE MODULATIONS 277 At a higher modulation frequency with a. At 1 MHz. The low-frequency rf system of the IUCF Cooler at h = 1 was used in this experiment. Measurements of subsequent beam-centroid displacements have been discussed in Chap. The torus-0 orbits around the outer SFP. = 0.III. The experimental procedure started with a single bunch of about 3 x 108 protons with kinetic energy 45 MeV. The principle of the phase shifter used is as follows.= 0. Sinusoidal rf phase modulation When the bunch. resulting in a half-power bandwidth of about 25 kHz.3 U/ x* \"' +1J l"s -[('-££) "'] )• <3'125> \i x> v" 1"*] Measurements of Synchrotron Phase Modulation Here we discuss an example of experimental measurements of rf phase modulation at the IUCF Cooler. the synchrotron oscillation frequency was chosen to be about 540 Hz. the beam was kicked longitudinally by a phase shifter and the data acquisition system was started 2000 turns before the phase kick. The corresponding response time for a step rf phase shift was about 40~50 revolutions. These two modulated signals were added. each proportional to the sine and cosine of the intended phase shift <pmod. Both the phase error due to control nonlinearity and the parasitic amplitude modulation of the IUCF Cooler rf systems were controlled to less than 10%.. The control voltage versus actual phase shift linearity was experimentally calibrated. The cycle time was 10 s. the two rf channels are multiplied by sin (pmod and cos tpmOd respectively. using an rf power combiner.03148 MHz. The injected beam was electron-cooled for about 3 s. Sec.As a result of the amplitude modulation. the quality factor Q of the rf cavity was about 40. The full width at half maximum bunch length was about 5. < x0. In this experiment. where um is the modulation tune and a the modulation . there is only one real root to Eq. For the longitudinal rf phase shift. The response time of the step phase shift was limited primarily by the inertia of the resonant cavity. The rf signal from an rf source is split into a 90° phase shifted channel and a non-phase shifted channel. (3.
The modulation amplitude was a = 1. Thus the synchrotron equation of motion becomes (j> H LOQ (j> + v l s i n 4> = . and the initial phase kick amplitude was 45°. and A is the damping decrement due to electron cooling.7 show examples of measured <j) and V = ^-^ vs turn number at 10-turn intervals for an rf phase modulation amplitude of 1. (3.126) where <f> is the particle phase angle relative to the modulated rf phase. Since the measurement time was typically within 150 ms after the phase kick or the start of rf phase modulation. Figure 3. 3. the effect of electron cooling was not important in these measurements.278 CHAPTER 3. The synchrotron motion. The corresponding Poincare surfaces of section are shown in the right plots. 5 = sin</>. The upper and lower plots correspond to fm = 490 and 520 Hz respectively.127) The measured damping coefficient a at the IUCF Cooler was a = uj0X/4n « 3 ± 1 s"1.a v 2 m s i n v m 6 H UJQ vma cos vm6. is eV <f> = hr]d + uma cos vm6. (3.45° after an initial phase kick of 42° at modulation frequencies of 490 Hz (upper) and 520 . The subsequent beam centroid phase-space coordinates are tracked at 10 revolution intervals. in terms of a differential equation. The left plots of Fig. SYNCHROTRON MOTION amplitude with a -C 1.110).7: The left plots show the normalized off-momentum coordinate V and the phase 0 as functions of revolutions at 10-turn intervals. The solid line shows the Hamiltonian torus of Eq.45°. the overdot indicates the derivative with respect to the variable 9.X5. (3.
This procedure can improve the accuracy of data analysis. V) space by a constant factor h\q\l{ys^J\ cos0s|).129) is used to calculate k.^ 0 (3. . 1. (3.e.130). (3.E(k) and q functions in order to obtain the action J and ip. the action J is obtained from Eq. 2 tan^ = . Poincare surface of section The Poincare map in the resonance frame is then formed by phase-space points in (^/2Jcos(•0 . -V2Jsm{tjj .vm6)). B. and finally.128) in the {<j>. S) phase space is related to the action in the (0. can be obtained from the expansion i£i = £ tan( f " *>" 1 1 T T ^ s i n ^ (3-130) For synchrotron motion with relatively large k. Eq.90) or Eq.V). i.34) and (17. Eq. 2.36) of Ref. C.vm9).III.129) The action can be obtained from Eq. (17. [25] to evaluate K(k).91).3. V) phase space. (3. (3. (3.71) can be used to deduce the action and angle variables. The resulting response can be characterized by the beating amplitude and period. (3. The k value at the phase-space coordinates {<t>. and the beating amplitude is equal to the maximum intercept of Poincare surface of section with the phase axis.V) is *2 = ^ + sin2|. (3.3. The beating period is equal to To/VjSiand> where To is the revolution period and z/jSiand is the island tune. RF PHASE AND VOLTAGE MODULATIONS 279 Hz (lower). a better approximation for data analysis can be obtained through the polynomial approximation of Eqs. 17Note that the action in the (<j>.90).17 J = I ( 0 2 + p 2 ). Action angle derived from measurements For small-amplitude synchrotron motion. For large-amplitude synchrotron motion. we need to use the following procedure to deduce the action-angle variables from the measured synchrotron phase-space coordinates. For each data point {(j>. tjj. The synchrotron phase. The corresponding angle variable ip is obtained from Eq.
SYNCHROTRON MOTION The resulting invariant tori are shown in the right plots in Fig.113).858 to avoid nonlinear betatron resonances. Equation (2. The trajectory of a beam bunch in the presence of external rf phase modulation traces out a torus determined by the initial phase-space coordinates of the bunch.03168 MHz at 45 MeV proton kinetic energy. Sec.173) in Chap. (3. Sec. the phase slip factor was r) « —0.7 shows invariant tori deduced from experimental data. where the synchrotron frequency was fitted to be about 535±3 Hz. The change in the circumference is AC = D6(t) = D§ sin(wmi + xo). if the dispersion function at the modulating dipole location is not zero. (3. III. depends on the rf phase modulation frequency. 3. and the revolution frequency was /o = 1. the stable phase angle was 4>0 = 0.7.<f>x(s0)\). the horizontal closed-orbit deviation xco(t) becomes (see Chap. This effect is equivalent to rf phase modulation. 0 = Bm£/Bp. The solid lines are invariant tori of the Hamiltonian in Eq. and the response amplitude is the intercept of the invariant torus with the phase axis. the path length and thus the arrival time at rf cavities of the reference (synchronous) particle are also modulated. shows that the path length of a reference orbit is changed by dipole field errors at nonzero dispersion function locations. With horizontal dipole (vertical field) modulation at location s0. which passes through fixed initial phase-space coordinates. The synchrotron tune was vs = u>s/u)0 = 2.131) . 2. If the dipole field is modulated.280 CHAPTER 3. The rf voltage was chosen to be 41 V to obtain a synchrotron frequency of / s = WS/2TT = 262 Hz in order to avoid harmonics of the 60 Hz ripple. Here we discuss experimental measurements of dipole field modulation at the IUCF Cooler.4 Effects of Dipole Field Modulation Ground motion of quadrupoles and power supply ripple in dipoles can cause dipole field modulation.86.| ^ ( s ) . 2. the path length is also modulated. which gives rise to parametric resonances in synchrotron motion. and Bm is the peak modulation dipole field. Figure 3. The effect is a special type of "synchro-betatron coupling" that may limit the performance of high energy colliders. where 9{t) = 0sin(wm£ + xo). For this experiment. Since the torus. The corresponding smallest horizontal and vertical betatron sideband frequencies were 177 and 146 kHz respectively. It becomes clear that the measured response period corresponds to the period of island motion around a SFP. vz = 4. We chose vx = 3. Ill) ico(<) = VP*{s)Px{So)9(t) 2 sin •KVX c o s ( ^ . Furthermore.54 x 10~4. the harmonic number was h = 1. the measured tori depend on the driven frequency. Ill.828.
Expanding the term sin</> in Eq. the damping time for the 45 MeV protons was measured to be about 0. which was indeed small compared with us = 1646 s .134) where the damping coefficient is a = \u)a/kn. (3.132) where the fractional momentum deviation of particles (Ap/po) is the conjugate coordinate to synchrotron phase angle <j>.33 ± 0. where we measured the transient solutions. Eq.1 .82 m is the circumference of the IUCF Cooler. Because the synchrotron frequency is much smaller than the revolution frequency in proton storage rings. i. (3. where C = 86.134). We therefore measured the steady state solution. we obtain the equation for the modulation amplitude g as [-u2mg + 2ujJ1(g)]2 + [2aumgf = [wmw8a]2 + [2awsa]2 (3. Let the steady state solution of the nonlinear parametric dissipative resonant system.75 A. (3. the effective phase modulation amplitude parameter a is « = ^ = ^ A 0 . (3. where the magnetic field Bm is in Gauss.135) Although the cooling was weak. the transient solution of Eq. Thus the synchrotron equation of motion. Ap/po) at the nth and the (n + l)th revolutions are transformed according to the mapping equations <£ n+1 = 4>n + 2-Khr] ( ^ J +Acf>.136) where we used the approximation of a single harmonic.134) was damped out by the time of measurement. The longitudinal phase-space coordinates (0. in the presence of transverse dipole field modulation.1 s or a = 3 ± 1 s""1. — g (XL (XL (3.e. (3.134) up to the first harmonic. The equivalent phase modulation amplitude is enhanced by a factor wo/27rwm. With an electron current of 0.78 x 10~5i?m radians. (3. the maximum rf phase shift per turn A~4> was 0. In our experiment. be </>xgsin(Ljmt-x). becomes — + 2a— + W sin</> = w^a coscomt + 2aojsasinujmt. The corresponding rf phase difference becomes A<j> = 2TTII(AC/C).III. the phase errors of each turn accumulate. RF PHASE AND VOLTAGE MODULATIONS 281 where D is the dispersion function at the modulation dipole location. and A is the phase-space damping parameter related to electron cooling. in contrast to the experiment discussed in the previous section.137) .
When the modulation frequency is larger than the bifurcation frequency. with Xb w —TT/2 is the inner attractor. Xc) approach each other. only the outer attractor solution exists. ( ( W ) 2 + (2aa. they collide and disappear. i.s)2 \1/2 A. while the attractors rotate about the center of the bucket at the modulation frequency.137). Particles in the phase space are damped incoherently toward these attractors. At a large damping parameter. T h e stable solution at a smaller phase amplitude <?(. (3. T h e existence of a unique phase factor x f ° r solutions of the dissipative pararrietric resonant equation implies that the attractor is a single phase-space point rotating at modulation frequency w m . these fixed points of the Hamiltonian become attractors.137) are called attractors for t h e dissipative system. Eq. Xa) and the unstable solution (gc. (3. When the modulation frequency is far from the bifurcation frequency. 3. A stable solution with a large phase amplitude ga and phase factor Xa ~ T / 2 is the outer attractor. A weak damping force does not destroy the resonance island created by external rf phase modulation.e. or for the outer attractor at uim S> wt>if. as shown in Fig. the response amplitude for the inner attractor at ujm -C oJuf. can be approximated by solving the linearized equation (3. (3. Chaotic nature of parametric resonances In the presence of a weak damping force. the outer SFP and the UFP may collide and disappear. T h e third solution gc with Xc ~ —TT/2 corresponds to the unstable (hyperbolic) solution. When the damping parameter a is small. fixed points of the time-averaged Hamiltonian become attractors. Wbif. given by the condition OUm =0. Because of phase-space damping.e. i. the outer attractor solution disappears. They rotate about t h e origin at the modulation frequency [see Eq. these two stable solutions are nearly equal to the SFPs of the effective Hamiltonian.137) has three solutions. which is associated with the U F P of the effective non-dissipative Hamiltonian.5. When the modulation frequency is below t h e bifurcation frequency. and are almost opposite to each other in the synchrotron phase space. When the damping parameter a is increased. Steady state solutions of Eq. . the stable solution (flo. SYNCHROTRON MOTION l 9 ^i + ^)-2^mJl{g)l where J\ is the Bessel function [25] of order 1. As the damping force becomes larger.282 with the phase x given by = arctan CHAPTER 3.136)].
(3. Numerical simulations indicate that all particles located initially inside the rf bucket will converge either to the inner or to the outer attractor. . especially for particles outside the bucket. 250. Observation of attractors Since the injected beam from the IUCF K200 AVF cyclotron is uniformly distributed in the synchrotron phase space within a momentum spread of about (Ap/p) w ±3 x 10~~4. 3. where each black dot corresponds to initial phase-space coordinates that converge toward the outer attractor. (3. Figure 3. it also shows the rf waveform for reference.8. However.133). 240. 220. which converge to the outer attractor are shown for Bm = 4 Gauss and / m = 230 Hz. The synchrotron frequency is 262 Hz. Complementary phase-space coordinates converge mostly to the inner attractor except for a small patch of phase-space coordinates located on the boundary of the separatrix. The number of phase-space points that converge to the inner or the outer attractors can be used to determine the beamlet intensity.131). RF PHASE AND VOLTAGE MODULATIONS 283 Numerical simulations based on Eq. obtained from a numerical simulation of Eq. B. To which attractor a particle will converge depends sensitively on the initial phase-space coordinates.133) were done to demonstrate the coherent and incoherent nature of the single particle dynamics of the parametric resonance system. The orientation of initial phase-space coordinates converging toward the inner or the outer attractor depends on the initial driving phase xo of the dipole field in Eq.9 shows the longitudinal beam profile accumulated through many synchrotron periods with modulation field Bm — 4 G for modulation frequencies of 210. Figure 3. initial phase-space coordinates in a small patch located at the separatrix of the rf bucket converge toward two attractors moving along the separatrix. One of the results is shown in Fig. and 260 Hz.III. which will converge toward two attractors located near the separatrix. all attractors can be populated. (3. 230. The phase coordinates of these attractors could be measured by observing the longitudinal beam profile from BPM sum signals on an oscilloscope.8: Initial normalized phase-space coordinates. The basin of attraction for the inner and the outer attractors forms non-intersecting intervolving spiral rings.
as if there were no synchrotron motion for the beam bunch located at a relatively large phase amplitude. we found that the beam profile was not made of particles distributed in a ring of large synchrotron amplitude. The sine waves are the rf waveform. The modulation amplitude was Bm = 4 G. using a fast sampling digital oscilloscope (HP54510A) for a single trace. The relative populations of the inner and outer attractors can be understood qualitatively from numerical simulations of the attractor basin. which measured the peak current of the beam. 14 o) V27TCT2 where pi and p% represent the populations of the two beamlets with px + p 2 = 1. Both beamlets rotated in the synchrotron phase space at the modulating frequency. then the sum signal. the beam profile became flat with a smaller peak current. would show a large signal at both extremes of its phase coordinate. the current density distribution function becomes p^t\ = fj V27T<Ti e-[4>-Mt)?l2°l + P^e-[*-Mt)?lz°^ ( 3 . It was puzzling at first why the longitudinal profile exhibited gaps in time domain. If the equilibrium distribution of the beamlet was elongated. Therefore the profile observed with the oscilloscope offered an opportunity to study the equilibrium distribution of charges in these attractors.9: Oscilloscope traces of accumulated BPM sum signals showing the splitting of a beam bunch into beamlets below the bifurcation frequency. When the beamlet rotated to the central position in the phase coordinate.Since each particle in the two beamlets rotates in the phase space at modulating frequency .284 CHAPTER 3. If we assume an equilibrium elliptical beamlet profile with Gaussian distribution. However. as measured from the fast Fourier transform (FFT) of the phase signal. SYNCHROTRON MOTION Figure 3. where the peak current was large. but was composed of two beamlets.
the hysteresis depended also on the dissipative force. the parameters </>i]2 and <Tii2 are <j>\(t)=gasin(umt . For example. these profiles were not sensitive to the relative positions of the two beamlets. obtained by solving Eqs. Since the profile observed on the oscilloscope was obtained by accumulation through many synchrotron periods. .x 6 ).III. the center peak disappeared (see 260 Hz data of Fig. if the modulation frequency. where the amplitudes of the coherent 7r-mode oscillations showed hysteretic phenomena. On the other hand. 3. given by 1 : 1 + r\ of the outer beamlet at modulation frequency 220 Hz was found to be about 1:3 from the profile in Fig. At a modulation frequency near the bifurcation frequency. RF PHASE AND VOLTAGE MODULATIONS u)m. obtained by fitting the data. (3. cr2. the phase amplitude jumped from the outer attractor to the inner attractor solution. The hysteretic phenomena of attractors The phase amplitudes of attractors shown in Fig.137). Hirata.9. The relative populations of the two beamlets was about 75% for the inner and 25% for the outer.Xa).137) and (3.138). i-e. 3. was ramped downward. Accel. Similar hysteretic phenomena have been observed in electron-positron colliders. the phase amplitude of the synchrotron oscillations increased along the outer attractor solution. This means that the peak current for the outer beamlet was reduced by a factor of 3 when this beamlet rotated to the center of the phase coordinate.i>. p.9). and <7io and <72Q represent the average rms bunch length. Since a large damping parameter could destroy the outer attractor.18 At a large beam18See T.10 also exhibited hysteresis phenomena. the amplitude of the synchrotron oscillations jumped from the inner to the outer attractor solution. When the modulating frequency was higher than the bifurcation frequency w^f. 4>2(*) = 56sin(wmt . 3. As the modulating frequency increased toward the synchrotron frequency. related to beam-beam interactions.b are the amplitudes and phases of the two beamlets. 285 Here <7aii) and Xa. (3. the phase amplitude of the outer beamlet became smaller and its population increased. The eccentricity parameters r\ and r2 signify the aspect ratio of the two beamlets. which was initially above the bifurcation frequency. the amplitude of the phase oscillations followed the inner attractor solution. When the modulation frequency. Ieiri and K. Conf. When it reached a frequency far below the bifurcation frequency. 1989). 926 (IEEE. = cr20 (1 + r2 sin2 wm£). Proc. The observed phase amplitudes were found to agree well with the solutions of Eq. it did not depend on the parameters Xo. the aspect ratio. New York. was ramped up toward the bifurcation frequency. 1989 Part. The hysteresis depended on beam current and modulation amplitude a. originally far below the bifurcation frequency. and CT? = <7io (1 + r i sin2 wmi). C.
The solid lines show the synchrotron tune and its third harmonic. On the basis of the KAM theorem. Systematic property of parametric resonances The formalism discussed so far seems complicated by the transformation of phasespace coordinates into action-angle variables. In this section. The circles in Fig. the essential physics is rather simple. 1987 Part. 3580 (1979).R. Thus the external perturbation excites only particles locally in the phase space where the amplitude dependent synchrotron tune falls exactly at the modulation tune. are compared with the theoretical synchrotron tune. 3. the perturbed Hamiltonian contains a perturbing term similar to that in Eq.M.P. . Proc. and the measured third order 3:1 resonance islands fall on the curve of the third harmonic of the synchrotron tune. However. measured from the oscilloscope trace.19 D. IEEE Trans.108). Accel. New York. Sci.H. most of the Hamiltonian tori are not perturbed except those encountering a resonance condition. When an external time dependence perturbation is applied to a Hamiltonian system. The third order resonance island falls also on the third harmonic of the synchrotron tune. Jackson and R.286 CHAPTER 3. Because the rf phase modulation does not excite 2:1 resonance. 1987). Paterson. NS-26. Con}. The sideband around the first order synchrotron tune corresponds to the 60 Hz power supply ripple. Donald and J. The bifurcation of the resonance islands follows the unperturbed tune of the synchrotron Hamiltonian. 3. (3. G. Siemann. SYNCHROTRON MOTION beam tune shift. shown as the lower solid line (see also Fig. the vertical beam size exhibited a flip-flop effect with respect to the relative horizontal displacement of two colliding beams.10: The phase amplitudes of beamlets excited by rf phase modulation. we will show that the global property of parametric resonances can be understood simply from Hamiltonian dynamics. 1011 (IEEE. where the particle 19See M.10 show a compilation of beamlet phase amplitude vs modulation frequency for four different experimental phase modulation amplitudes. We note that the bifurcation of the 1:1 resonance islands follows the tune of the unperturbed Hamiltonian system.H. p. Figure 3. we did not find parametric resonances at the second synchrotron harmonic.5 on the bifurcation of 1:1 parametric resonance). Nucl.
An important implication of the above parametric excitation theorem is that chaos at the separatrix orbit is induced by overlapping parametric resonances. can be excited by time dependent perturbation.109). ground vibration. and the local potential well becomes the basin for stable particle motion. However. 3. rf phase error. we do not observe a 2:1 attractor in Fig. Now. where higher order nonlinear resonances serve as the source of time dependent modulation. In reality. however. Thus a beam inside an rf bucket can split into beamlets. a perturbation with low frequency modulation can produce many overlapping parametric resonances near the separatrix and lead to local chaos. In fact. . 3.III. a stronger phase modulation is applied to the dynamical system. forming islands within the bucket. If the beam size is relatively small. as clearly seen in Fig. i. the perturbation arising from wakefields. This result can be applied to synchrotron motion as well as to betatron motion. Let Q(J) be the tune of a dynamical system. If. particle orbits near the center of the bucket will be strongly perturbed. The 20The remaining terms play the role of time dependent perturbations to the effective Hamiltonian of Eq.. a 2:l-like (4:2) parametric resonance can be formed by 1:1 and 3:1 resonances through second order perturbation. Now a time dependent perturbation can induce a series of parametric resonances in the perturbed Hamiltonian. when the modulation frequency approaches the tune of particles at the center of the bucket. These parametric resonances. dipole field error. This can be understood as follows. When the modulation frequency is varied. SFPs (attractors) are formed along the tune of the unperturbed Hamiltonian. Q(JSx) = 0. etc. we apply this result to evaluate the effect of low frequency modulations on particle motion. where the tune is zero at the separatrix. the SFP becomes an attractor. When a weak damping force is applied to the dynamical system. Since nQ(Jsx) ~ 0 for all n near the separatrix.10. Since the rf phase modulation does not excite even synchrotron harmonics. vm = n&(J S F P ). located at nQ(J) with integer n.109). it will induce overlapping parametric resonances only near the separatrix. If the amplitude of low frequency modulation is not large. i.10. a n d the amplitude of perturbation.141) The measurement of attractor amplitude vs modulation tune is equivalent to the measurement of synchrotron tune vs synchrotron amplitude. the external perturbation creates a local minimum in the potential energy at the SFP locations. consists of a spectrum of frequency distributions. the strength function gn(J).e. RF PHASE AND VOLTAGE MODULATIONS 287 motion can be described by the effective parametric resonance Hamiltonian (3. the stochasticity at the separatrix will do little harm to the beam motion.20 The size of the resonance island depends on the slope of tune vs amplitude. (3. (3.e. The KAM theorem produces a hierarchy of higher order resonance islands within parametric resonance islands.
N. et al. For details see M. Shih and A. Byrd. Part. Instru. 11th Int. S. there has been some interest in employing rf voltage modulation to induce super slow extraction through a bent crystal for very high energy beams. power supply ripple. (1997). SYNCHROTRON MOTION mean field of the perturbation gives rise to the effect called potential well distortion. 92. The complicated collective instability phenomenon is in fact closely related to nonlinear beam dynamics. Accel 42. Caussyn et al. Li et al. (3. 107 (1982). 1980).J. 3484 (1979). Li et al. Conf. the synchrotron equations of motion are (/>n+1 = </>n-2vvaj^Pn. M. 620 (Birkhauser.21 III.. The remaining time dependent perturbation can generate further bunch deformation. Proc. 25 M. Lee. bunch splitting.. W.22 Recently. (1997). 235 (1993). Sweeping the rf phase modulation frequency and measuring the response by measuring either the centroid of the beam.g. Boussard. Rosenzweig. Since the rf voltage modulation may be used for enhancing a desired beam quality. Dome.G. 1993). 555 (2002). modifies the unperturbed tune of the system. Accel. NS-26. depending on its frequency spectrum. Phys.143) a series of beam transfer function measurements were made at electron storage rings.M. SSCL-389 (1991). Rice. Nucl. Kick. solved self-consistently in the Vlasov equation. etc. p. Basel. Conf. (1997). 2 4 D. et al. J. Minty et al. CERN 87-03. and S.23 rf voltage modulation to stabilize collective beam instabilities. R. Wang. Ace. . Peggs. Part. ibid. 5 RF Voltage Modulation The beam lifetime limitation due to rf noise has been observed in many synchrotrons. E 48. Piscataway. etc. the super proton synchrotron (SPS) in CER.M.24 The rf voltage modulation has been implemented to stabilize coupled bunch instabilities induced by parasitic rf cavity modes with high brightness beams at the Taiwan Light Source. Krinsky and J. 205 (1995). on High Energy Accelerators. rf voltage modulation for extracting beam with a short bunch length. (3. Accel 12. Methods A 364. Part. 370 (1987). D.142) Vn+i 21Recently. ibid. p.288 CHAPTER 3.Y. Boussard. D. wakefields. IEEE Trans. et al. D. 29 (IEEE. Gabella. 2 2 D. Con}. Wang. etc. 2 3 H. the response of the beam to external rf phase modulation can be obtained. J. G. Nucl. Proc.H. Sci. and S. The equation of motion with rf voltage modulation In the presence of rf voltage modulation. NJ. D.25 A. p. R1638 (1993). Beam response to externally applied rf voltage modulation has been measured at the IUCF Cooler. 1997 Part. hysteresis. that may arise from rf noise.D. we will study the physics of synchrotron motion with rf voltage modulation. Rev. e. = Pn-2irvs[l + bsm{vm9n+1+X)}sm<l>n+1-—Vn. private communications. or the beam profile from a synchrotron light monitor using a streak camera.H. Wang. Journal of Applied Physics. Proc. Taratin. which.
. W = 2TT/O is the angular revolution frequency. equivalently. 2i/«(l . we need to consider only the lowest order Mathieu instability.III. i. r\ < 0. (3.146) Similarly. In other words. 7 is the phase slip factor. b = AV/V is the fractional rf voltage modulation strength (b > 0).D. Thus stable solutions of Mathieu's equation are obtained with the condition that the parameter p is bounded by the characteristic roots aT(q) and bT+i(q). the phase-space damping rate was measured to be about a « 3. vs = Jh\r]\eV/2Tr/32Eo is the synchrotron tune at zero 7 amplitude. 9 is the orbital angle used as time variable. Eq. Neglecting the damping term.1. and q = 2fo/ s2 /^. Without loss of generality.M.0 ± 1.147) where the second order Mathieu resonance can be obtained from second order perturbation theory.26 The width of the instability decreases rapidly with increasing order for small b. the second order unstable region is ". Eo is the beam energy. o and a is the phase-space damping factor resulting from phase-space cooling. (3. In our application.144) where the overdot indicates the time derivative with respect to 9. which is much smaller than wo^si typically about 1500 s" 1 for the h = 1 harmonic system.(1 . p and q are real with 5 < 1. Landau and E. Oxford.2. • • •. where r = 1. (3.144) reduces to Mathieu's equation. 8 = Ap/po is the fractional momentum deviation from the synchronous particle. we can linearize Eq. 1976). • • •. ed. x is a phase factor. a = 0.145) In accelerator physics applications. the equation of motion for phase variable (f> is ij> + v2s{\ + bsm{vm0 + x)] sin<£ = 0. 26L. 3rd. (3.144) into Mathieu's equation [25] ^ 4 + (p . we discuss the case for a particle energy below the transition energy. i.2q cos 2z)(j> = 0. Lifschitz.e.2. By choosing X = -TT/2 and z = \vm9. vm is the rf voltage modulation tune.. In linear approximation with sin<jf> « <j>. (Pergamon Press.(l + ^& 2 ). p = 4^/j/^. At the IUCF Cooler. RF PHASE AND VOLTAGE MODULATIONS 289 where V = -h\ri\5/vs is the normalized off-momentum coordinate conjugate to <> /. where r = 0. Since synchrotron motion is nonlinear.\b) <vm< 2PS{1 + hb).e.0 s"1. the linear Mathieu instability analysis should be extended to nonlinear synchrotron motion as follows. (3. (3. Z Thus the first unstable region is obtained from 61 (q) < p < < i (q) or. unstable solutions are in the region br(q) < p < ar(q). Mechanics.^& 2 ) < ^m < «/.
cos <t>]. (3.n]. induced by the external harmonic modulation of the rf voltage.150) where we choose x — 0 for simplicity. and |G n (J)| is the Fourier amplitude of the factor (1 — cos</>) with 7 n its phase. (3.101). particle motion is coherently perturbed by the rf voltage modulation resulting from a resonance driving term (stationary phase condition). defined in Eq. vm fa nQs (n = even integers). (3. SYNCHROTRON MOTION The synchrotron equation of motion with rf voltage modulation can be derived from the Hamiltonian H = Ho + Hi with Ho = ^usV2 + vs{l-cos<f>).n^ 7n).149) where Ho is the unperturbed Hamiltonian and Hi the perturbation.101) is zero except for n even with G_n = G*n. The resonances.148) (3. Since (1 — cos(j>) is an even function of T/J in [—ir. are called parametric resonances. The perturbed Hamiltonian CHAPTER 3. i.151) . Using the generating function we obtain the Hamiltonian in the resonance rotating frame as H = E{J) . the Fourier integral for Gn from Eq. we expand Hi in action-angle coordinates of the unperturbed Hamiltonian Hi = vjb £ \Gn{J)\ sm(i/m0 . we obtain U0 ~ 2 J + 2048J + ' "" ' U 2 ~ ~ 4J + 128J + ' U i 64J + 2048 J ° 6 4096J +"""- The GQ(J) term in the perturbation can contribute to synchrotron tune modulation with a modulation depth AQS « -J/s6sinfm^.290 B. Expanding Gn(J) in power series. 6). Hi = psb sin(z/m0 + x) [1 . For a weakly perturbed Hamiltonian system. $. C. (3. Thus rf voltage modulation generates only even-order synchrotron harmonics in H\.e. n=—oo (3.—J + vsb\Gn{J)\cosn4> + AH(J. Parametric resonances When the modulation frequency is near an even harmonic of the synchrotron frequency.
158) vm = 2i/. Note here that \Gn+2/Gn\ ~ J for n > 0. •••.11. RF PHASE AND VOLTAGE MODULATIONS 291 where the remaining small time dependent perturbation term AH oscillates at frequencies um. 0. if i/m < 21/. .153) is autonomous. (3.155) o 4 j> = us-^f-^J+^bcos2ip.^ L ) .154) (3. 2vm.s + I^ (3-15?) with ip = 7r/2 and 3TT/2.III. particle motion is governed by the n = 2 parametric resonance Hamiltonian (H) = (!/„ -V-f)J . according to (3. Thus the time averaged Hamiltonian (H) for the nth order parametric resonance becomes (H) = E{J) . Quadrupole mode When the rf voltage modulation frequency is near the second harmonic of the synchrotron frequency.146).s-I^<. For simplicity. We note that the second harmonic rf voltage modulation can induce an instability at J UFP = 0 in the frequency domain 2us . Nonlinear synchrotron motion extends the instability to lower modulation frequency at larger synchrotron amplitude.^ J 2 + £&Jcos2tf Z ID 4 (3.\vtb. Tori of the Hamiltonian flow around SFPs are shown in Fig. This is the first order Mathieu resonance of Eq. In the time average.| 0. (3. The system is most sensitive to the rf voltage modulation at the second synchrotron harmonic. Since the Hamiltonian (3. we drop the tilde notations.— J + vsb\Gn{J)\cosni>. . The unstable fixed points (UFPs) are located at j J U F P /8(l-£)-2&. we have (AH) « 0. the Hamiltonian is a constant of motion.i&i/. The resonance strength is greatest at the lowest harmonic for particles with small phase amplitude.(l . D.152) n The phase-space contour may be strongly perturbed by the parametric resonance. Li (3.153) in the resonance rotating frame. if2. o z .\bvs < vm < 2vs + \bvs. 3. tp = 0. Hamilton's equations are j = ^-bJsm2if).m<2. if vm > 2vs + ~bvs with tp = 0 and TT. Zi The fixed points that determine the locations of the islands and separatrix of the Hamiltonian are obtained from J = 0. The stable fixed points (SFPs) are (.
To obtain the island tune. rotating about the longitudinal phase space at half the modulation frequency. Proc. Since electrons are damped incoherently into the SFP by the synchrotron radiation damping. European Part. Island tune and equilibrium beamlet profile The island tune i/isiand. p. The synchrotron frequency is / s = 263 Hz. where /iSiand is the frequency with which a particle rotates around a SFP in the resonant precessing frame. the Mathieu resonance gives rise to an UFP at the origin of the phase space and the SFP is displaced to JSFP = 26. Accel. Con}.D. 1992). The damping mechanism may be understood as follows. Py = — v2JsinV> + y2Josim/>oj 27J. Fox and P. Modulation of the rf voltage at the second harmonic of the synchrotron tune has been found useful in damping the multi-bunch instabilities for the damping ring of the Stanford linear collider (SLC). defined by /isiand//o. the beam distribution becomes dumbbell-shaped in phase space.153) in the resonance rotating frame. the collective instability of high brightness electron beams in the SLC damping ring can be controlled. SYNCHROTRON MOTION Figure 3. 1079 (Springer-Verlag. and the modulation frequencies are / m = 526 Hz (left plot) and fm = 490 Hz (right plot).292 CHAPTER 3. Corredoura. with y = \/2J cosij) — y2J 0 cosi/'o. Heidelberg. which is a nonlinear extension of Mathieu instability. the voltage modulation amplitude is b = 0. we expand the phase-space coordinates around a fixed point of the Hamiltonian. The size and orientation of the dumbbell can be controlled by parameter b and phase xE. . or equivalently the synchrotron frequency.05. When the voltage modulation at vm = 2v& is applied.27 By adjusting the amplitude and phase of the rf voltage modulation.11: The separatrix and tori of the Hamiltonian (3. is an important property of a resonant system.
which satisfies the Vlasov equation. as shown in Fig. (3. it is the line density of the bunch or the projection of the density distribution function onto the phase coordinate P(y) = I p(y.161) are ay = <TQ/yJ\B\.163) (3. The small amplitude island tune is inland = \/AB. Eq. the beam profile will retain its shape except for exchange of its local coordinates. the . Since the rms widths of the distribution function (3. In terms of the local coordinates py and y. aPy = ao/y/\A\. For b > 0.-vaJo sin2 Vo .y .153).159) T ^ O COS2 Vo + -Ms ~ -l/aJ04 4 o It is clear that the fixed point is stable if the parameters A and B satisfy AB > 0. and Jo = JSFP — 8(1 — vm/2vs) + 2b are stable because A = -\vsb and B — —\VSJSFP SO that AB > 0.^ K . RF PHASE AND VOLTAGE MODULATIONS 293 where (v^^JoCosip0.162) the aspect ratio of the phase-space distribution <JPy/oy is ^J\B/A\ evaluated at the SFP.III. The longitudinal profile monitor measures the image current on a wall gap monitor. TT/2.. Since the resonance rotating frame rotates in the phase space at half the modulation frequency. n. the fixed points associated with i/i = 0.g^s Jo. Assuming a Gaussian distribution. the Hamiltonian. becomes H =\A with A = vs .J Z ^ J U F P and B = \bvs. where nal/VAB is the rms phase-space area of the beamlet. we obtain *y^»1BM-^-^M (-6) 3 11 in the resonance precessing frame. When the beamlet rotates to the phase coordinate. (3. The small amplitude island tune at the SFP becomes v^BA = y/AB = va^^-. and so AB < 0. (3.11.159).Py)dpy. is a function of the Hamiltonian (3.3IT/2.160) JUFP and Jo = are unstable since The equilibrium beam profile. The fixed points associated with tp = A = . -^/2Josin^o) are the phase-space coordinates of a fixed point of the Hamiltonian in the resonance precessing frame. B = l/s--^Z V \ + l-By2 + ••• (3. 3.
/max = (1 + \fl-x)JS¥V.VFP). which passes through the UFPs. G. F. SYNCHROTRON MOTION aspect ratio of the beamlet becomes yjJSFP/26.\bvs if 2vs . and the peak current will be large. is given by H(J.11 shows also the intercepts of separatrix with phase axis. The intercepts can be used to determine the maximum synchrotron phase oscillation due to rf voltage modulation.n and J max given by i n = (1 . Figure 3. On the other hand.E). The separatrix intersects the phase axis at the actions Ji and J 2 given by j and J.164) = l JSFP + \/JIFP ~ JUFP \ 2JSFP ^ ^m < 2vs .\bvs <vm< ^ 2vs + \bvs ^ ^m < 2i-s . The island size A</>jSiand is \f2J[ — y/2J2.^UFP if (3. the Hamiltonian is a constant of motion.\bvs . = ] ^ S F P ~ V^SFP . the action J is limited by Jm. with x € [^UFP/^SFP > !]• Note that JSFP = |(^min + Jmrn). Using Hamilton's equations of motion. where x = E/Es. the aspect ratio becomes y26/JsFP and the line density becomes small. when the beamlet rotates to a position 90° from that of Fig. The Hamiltonian value is Es = ^ ^ S J | F P at SFP.153). and Eu = J^S-'UFP a^ UFP.294 CHAPTER 3. \ 0 if 2vs .The island tune becomes .3 16g. . which is normally much larger than 1.iP) = H(JVFP.i.11. The amplitude dependent island tune of 2:1 parametric resonance For an autonomous dynamical system governed by the Hamiltonian (3. 3.\bvs <vm< 2vs + \bvs. where For a given Hamiltonian value E.X) JSFP.Vl . The separatrix The separatrix torus. we obtain J = f(J.
with a non-vanishing perturbation strength function Gn(J). The . where J is the invariant action of the particle motion. producing a full width at half maximum bunch length of about 9 m (or 100 ns) depending on rf voltage. the perturbation creates n resonance islands in the longitudinal phase space around J = J r . Near the resonance island.160) at x = 1. the island tune of the separatrix orbit is zero. the island tune is zero at the separatrix with x = JUFP/^SFPH.03168 MHz. (3. Voltage modulation control loop The voltage control feedback of the IUCF Cooler rf system works as follows. The cavity rf voltage is picked up and rectified into DC via synchronous detection. RF PHASE AND VOLTAGE MODULATIONS where K(k) is the complete elliptical integral of the first kind [25] with . where J r is obtained from the resonance condition: vm — nQs(JT). Physical interpretation In the longitudinal phase space. (3. This oscillation tune is equal to the island tune. These islands precess in the phase space at 1/n of the modulation tune.168) reduces to Eq. the action J is no longer invariant and the synchrotron tune is likewise perturbed. The experiment started with a single bunch of about 5 x 108 protons with kinetic energy 45 MeV. Particles located far from resonance islands experience little effect on their synchrotron motion if the voltage modulation amplitude is small. In other words. For particles located at the "separatrix" of the parametric resonance (not the separatrix of the rf bucket) the period of this amplitude oscillation becomes infinite. The synchrotron tune of a particle on the separatrix is exactly vm/n. The low frequency rf system used in the experiment was operating at harmonic number h = 1 with frequency 1.6 Measurement of RF Voltage Modulation We describe here an rf voltage modulation measurement at the IUCF Cooler. The cycle time was 10 s. When the rf system is perturbed by a harmonic voltage modulation at vm. Similarly. _ 1 / % JSFP — JUFP 295 It is easy to verify that Eq. or equivalently the synchrotron tune at the resonance action J r . The synchrotron tune for particles at or near SFP is also vm/n with an amplitude modulation whose tune is equal to the island tune.III. A. particles execute synchrotron motion with an amplitude dependent tune QS(J). III. with the injected beam electron-cooled for about 3 s. A particle executing synchrotron motion within the nth order resonance island will have a characteristic tune f m /n with a regular amplitude oscillation due to the island motion.
Then the steady state bunch distribution was measured. The error found goes through a nearly ideal integrator that has very high DC gain.296 CHAPTER 3. A fast 1 x 109 sample per second oscilloscope was used to measure the profile of the beam in a single pass.2. i. the effect of its inertia can be ignored if the loop gain is rolled off to unity well before /o/2Q. The amplitude modulation is summed with the reference and compared to the cavity sample signal. The maximum modulation rate is limited by the loop response time of about 10 kHz. The overall loop response exhibits the exponential behavior prescribed by a first order differential equation. the rf voltage was modulated. The beam was injected.05 at modulation frequency fm = 480 Hz with synchrotron tune / s = 263 Hz.75 A. and the beam was cooled with electron current 0. The modulation amplitude was measured and calibrated. s. The modulation rates in our experiments are well within this limit. Thus the phase .200 fj.12 shows that the sum signals from a beam position monitor (BPM) on a fast oscilloscope triggered at the rf frequency exhibited two peaks around a central peak. Note that the outer two beamlets rotated around the center beamlet at a frequency equal to half the modulation frequency. SYNCHROTRON MOTION rectified DC signal is compared to a preset voltage. Thus. The voltage modulation amplitude is 6 = 0. Because of the relatively low Q of the cavity at the IUCF Cooler. The beam particles were damped to attractors of the dissipative parametric resonant system. we first measured the phase oscillation amplitude of the steady state solution by using the oscilloscope. dV/dt = —V/T. Figure 3. The modulation causes a change in the error voltage sensed by the control loop and results in modulation of the attenuator around a preset cavity voltage. Figure 3.12 indicated that there were three beamlets in the h = 1 rf bucket. where V is the rf voltage and the characteristic relaxation time r is about 10 .12: The beam bunch was observed to split into three beamlets in a single rf bucket measured from a fast sampling scope. 3. Observations of the island structure Knowing that the beam bunch will be split into beamlets.e. B. The profile shown in Fig. no proportional error feedback is needed to stabilize the loop. as shown in Sec. where /o is the resonant frequency of the rf cavity and Q ~ 50 is the cavity Q value. III. The integrated signal is then used to control an attenuator regulating the level of rf signal being fed to rf amplifiers.
A possible explanation is that the actual beam size was larger than the separation of islands. (3. the observed beam profile in an oscilloscope is a time average of the BPM sum signal. the resulting beam profile will exhibit two peaks at the maximum phase amplitude. Experimentally. Once fm reached 2/ a . where we did not observe beam splitting. On the other hand.EXERCISE 3.13. Figure 3.3 1. .90). where JUFP = 0. The actions of UFP J UFP and intercepts J\ and J2 of the separatrix with the phase axis are also shown. Since the attractors (or islands) rotate around the origin of the rf bucket with half the modulation frequency. the synchrotron frequency was determined more accurately to be about 263±1 Hz for this run. JSFP is also a linear function of modulation frequency. 3. It was also clearly observed that all parametric resonance islands ceased to exist at / m = 2/ s + | 6 / s « 532 Hz. Exercise 3. when a beamlet rotates to the flat position.153) is also shown for comparison.156) fits data with /„ = 263 Hz. 3. Using this sensitivity. resembling that in Fig. The measured action J of the outer beamlets as a function of modulation frequency is shown in Fig. Here J ~ j ^ 2 with 0 as the peak phase amplitude of attractors. where J SFP of the Hamiltonian (3.3 297 amplitude of the outer peaks measured from the oscilloscope can be identified as the phase amplitude of the SFP. a larger peak current can be observed. The solid line for JSFP obtained from Eq.\bfs « 520 Hz. the aspect ratio becomes small and the line density is also small. where the slope depends sensitively on synchrotron frequency.520] Hz. This implies that when a beamlet rotates to the upright position in the phase coordinate. where the SFPs are located on the V axis. Different symbols correspond to measurements at different times for an almost identical rf voltage. Because the equilibrium beamlet distribution in a resonance island has a large aspect ratio in the local phase-space coordinates. In this case. Prove the identity of the action integral in Eq. (3. Similarly.12. we found that the action of the outer attractor varied linearly with modulation frequency. the beam was observed to split into only two beamlets. the SFPs were about 100 ns from the center of the bucket. Our experimental results agreed well with the theoretical prediction except in the region / m € [510.13: The measured action J of outer beamlets as a function of modulation frequency.
Jo show that the coordinate transformation between phase variable ip and coordinate (/> where ip is the conjugate phase variable to the action J. n=—oo 00 prove the sum rule theorem n=-oo "» 3. where D(SQ) is the dispersion function at the dipole location. Prom Exercise 2. m t + xo). Expanding V in action-angle variables with P = £ fnein*.4. The modulating tune is um = cjm/u)Q. Give a physical argument that the amplitude of the equivalent rf wave phase error a is amplified as t h e modulation t u n e vm becomes smaller. we find that the change of orbit length due to a modulating dipole kicker is given by AC = D{s0) 6(t) = D{sQ) 6 sm{umt + X o). However. (b) Show that the amplitude of the equivalent rf wave phase error is o = A(/)/2in/m. where wo is the angular revolution frequency. and h is the harmonic number. fs is the small amplitude synchrotron tune. . (a) Show that the modulating dipole field produces an equivalent rf phase error A0 = cS° sin(cjmt + xo) = A>sin(o. 28 In linear approximation. small amplitude behavior of the potential is not a necessary condition for the sum rule theorem stated in this exercise. Using the generating function F2 = / Vd<t>. and V(<j>) is the potential. 9 is the maximum dipole kick angle. where C is the circumference of the synchrotron.298 2. uim is the modulating angular frequency. V) are conjugate phase-space variables with orbiting angle 8 as time variable. where ((j>. and xo is an arbitrary initial phase. the potential can be expressed as V(cj>) = \vs<j>2 + •••. We consider a general Hamiltonian CHAPTER 3. 28 The action is J = (l/2ir) §Vd4>. SYNCHROTRON MOTION H = \vsV2 + V(<j>).8.
and octupoles are used to provide nonlinear detuning otxx. B% is the octupole strength.{vm/2) and. Show that the separatrix for vm 5: 2vs — Vsb/2 is given by two circles (Q_Q c )2 with Qc = \/46. The resulting effective Hamiltonian is 1 £ -Heff = vxjx + -axxJ% + bJx cos(tl>x .4 1 1 1 1 262 60 60 4 4 1 1 1 1. PUFP = 0 (2J/S .8 3319.4 3319. where axx = (1/WnBp) § 0^. (3. 2vs + usb/2) PUFP = ^/l6(l .5 1 342 588 1 4. + vab/2) QUFP = 0. C (m) ABl (Gm) / m o d (Hz) D (m) 7 h.3 299 (c) Evaluate the effective rf modulation amplitude a for the accelerators listed in the table below. Quadrupoles are used to provide resonance driving term b. P= -V2Jsm(ip--vm9).EXERCISE 3. The separatrix in the betatron phase space for slow beam extraction that employs a half integer stopband is identical to that given in this exercise.8 3833. + p2=r2. D is the dispersion function at the dipole.157). Using the conjugate phase space coordinates Q = V2Jcos(i>--vme).vj2vs) .46 Compare this result with Eqs. AB£ is the integrated dipole field error. without loss of generality. show that the Hamiltonian (3.04796 24 21. Show that the fixed points of the Hamiltonian are located at -PSFP = 0.-0). / mo d is the modulation frequency. 7 is the Lorentz relativistic factor. r = yfl66/vs.um/2us)+4b (i/m > 2M. and h is the harmonic number. QUFP = 0. a 1 IUCF Cooler I RHIC [ MI I Recycler 86.153) for the quadrupole mode is H=\{5+ f)Q> + I(« . we assume b > 0.vsb/2 <um< (um < 2vs -wsb). QSFP = 0 (vm> 2us + uab/2) PSFP = 0.156) and (3. QSFP = ^16{1 .B^ds is the detuning parameter. where C is the circumference. (Q + Qc) 2+p2=r2 .8 9. and 6 is the half integer stopband width.f)P> " g(O2 + P2)\ where 8 = vs.
182) near a betatron sideband can be casted into an effective Hamiltonian HeS = uJ+ -aJ2 + gjll2 cos(V> . and a. <f>). and i/m is the rf dipole modulation tune. (2. Show that the equation of motion for rf dipole on betatron motion in Eq. the action-angle coordinates. Find the fixed points of the Hamiltonian and discuss the dependence of the fixed point on parameters vm — v.300 CHAPTER 3. SYNCHROTRON MOTION 5. where v.vm0 + x). . (J. g is proportional to the rf dipole field strength. a are the tune. and the detuning parameter of the betatron motion.
g. and in Sec. 29Since the bunch width becomes very short and the momentum spread becomes large at transition energy. IV. IV. . when the phase slip factor % of Eq. The integral of the linearized Hamiltonian is also an ellipse. and the circulating beams can suffer microwave instabilities and other collective instabilities for lack of Landau damping.4 we study the effects of nonlinear phase slip factor and examine the properties of the so-called a-bucket. Oxygen and sulfur ions have been filtered at transition energy in the CERN PS.e. Although the action of a Hamiltonian flow is invariant. Sci. to be discussed in Sec. NS-28. In Sec. If the phase slip factor is independent of the off-momentum variable. 2389 (1981). The linearized rf potential is a good approximation. We will discuss the scaling properties of the beam at the transition energy crossing. J. VII.H.P. we will obtain analytic solutions for the linearized synchrotron motion near transition energy in Sec. i. This results in non-adiabatic synchrotron motion. the adiabaticity condition (3. NONADIABATIC AND NONLINEAR SYNCHROTRON MOTION 301 IV Nonadiabatic and Nonlinear Synchrotron Motion Transition energy has been both a nuisance in machine operation and a possible blessing for attaining beam bunches with some desired properties. and K. parts of a beam bunch can encounter a defocussing force during transition energy crossing. IV. See e. Near the transition energy region. 1. (3. which may provide beam bunches with ultra-short bunch length. the synchrotron frequency spread vanishes at transition energy. where the bucket area increases dramatically. the Hamiltonian is time dependent and is not a constant of motion. Delahye.18) becomes small. and the action is a constant of motion.29 However. such as enhanced beam separation for filtering ion beams having nearly equal charge to mass ratios. Using the sensitivity of the closed orbit to beam momentum at transition energy. IV. IEEE Trans.IV.3 we examine beam manipulation techniques for particle acceleration through transition energy. the torus is highly distorted and particles in a beam may be driven out of the rf bucket after crossing the transition energy. i. Nucl. This again raises another nonlinear prob7 lem in synchrotron motion.5 we study problems associated with quasi-isochronous (QI) storage rings. In Sec. the nonlinear phase slip factor term 7 1 can be important. However. one can filter beam momentum from nearly identical Z/A (charge to mass ratio) ion beams.2 we study nonlinear synchrotron motion due to nonlinearity in phase slip factor. In Sec. transition energy may be used to generate short bunches. IV. R.e.. and the phase-space area occupied by the beam bunch is a small fraction of the bucket area. Reich. Cappi.43) is not satisfied. and beam bunches with ultra-small beam width.
(3.7 4.5 Tad (ms) 02 JTO I AGS I RHIC I KEKPS I CPS 339. 1 Linear Synchrotron Motion Near Transition Energy Since the energy gain per revolution in rf cavities is small.4 20.5 30When \t\ > 4raa the adiabatic condition is approximately fulfilled because aad = IdC^f 1 )/^! = |(rad/l*l) 3/2 « 0.3: The adiabatic and nonlinear times of some proton synchrotrons.5 2. 31 Note that the beam parameters for RHIC correspond to those of a typical gold beam injected from the AGS with charge number Z = 79.30 Table 3. and assume that all particles in a bunch pass through transition energy at the same time. The injection energy for proton beams in RHIC is above transition energy.3 lists the adiabatic time for some proton synchrotrons.12 3833. .302 CHAPTER 3.19 | 0.27).06.2 3319.169 ) Here we have neglected the dependence of the phase slip factor on the off-momentum coordinate 5. 0.4 T8 628. r ad (3-170) where r ^ is the adiabatic time given by T a d = Uo 2 ^|cos0 s |J • (3-171) At |i| S> Tacj.32 200 6-20 6.5 70 1.6 L5 r nl (ms) I 0.29 90 9 6.4 7 (s" 1 ) 200 190 A (eVs/u) 0.4 V (kV) 950 4000 h 84 588 7T 5. SYNCHROTRON MOTION IV.2 «^r7T ( 3 .5 22.61 807.4 2.43) is satisfied. Substituting Eq.5 60 0. I FNAL I FNAL Booster MI C (m) 474.8 300 300 12 360 8. Table 3.3 5. and atomic mass number A = 197.5 6. where j = d^/dt is the acceleration rate.3 6.13 | 0.5 36 [ 63 | 0.76 40 0. we obtain Ws2 = 4 .6 1. The phase slip factor becomes % = a o . the adiabaticity condition (3. 31 Typically r ad is about 1-10 ms.04 0. we assume 7 = 7T + jt. (3.169) into Eq.04 5 (xlO~ 3 ) 6.7 | 0.7 . and t is the time coordinate.
177) = g^2 [(|^5/3 . • 2hoJojt A<f> bx2?3 ( [2J 2 / 3 1 [2iV2/3 }\ Combining this with Eq. ^ = £ {^r) M~962 K.176).175) can be written readily as32 A<f> = bx [cosx J2/3(y) + sinxN 2/3 (yj\ ./.175) where <p = y~2'3A<f>. (3.2^/3) . (3.^^-)<p y y = 0.^/a (2j2/3 .6A(/)5 + assS2 = 1. (3. The offmomentum coordinate 5 can be obtained from Eq. The notation used for Nu{z) is Yu(z) in Ref.172). the synchrotron equations of motion near the transition energy region become where the overdot indicates the derivative with respect to time t.IV. i./-^(zJJ/sinTri/. It is also called the Bessel function of the second kind. NONADIABATIC AND NONLINEAR SYNCHROTRON MOTION 303 In linear approximation. (3. . and the primes indicate derivatives with respect to time variable y.\y^)].173) can be transformed into Bessel's equation of order 2/3.e. Taking into account the synchronous phase change from <j>a to IT — <j>s across transition energy. (3. /3 2/sJ" V 7^ J 32 The Neumann function is defined as JV^(z) = [J r (z)cosTTI/. where au (3. and 6 = Ap/po and A</> = <f> — 4>s are the fractional off-momentum and phase coordinates of a particle.174) Eq. . </ + V + (1 . we obtain the constant of motion a 0 0 (A0) 2 + 2a<j. (3. we obtain Defining a new time variable y as Jo £(i|| A ') + A ' = 03 (3173) r^ y= fx x ' 2 dx=\x % l 2 with x=$-. [25].2^2/3) + (2J2/3 .\yJ^) ] .(|^.176) where \ a n d b are constants to be determined from the initial condition. The solution of Eq. (3.
183) atjuj.177) is a constant of motion given by Ja^ass . SYNCHROTRON MOTION There is no surprise that the constant of motion for a time dependent linear Hamiltonian is an ellipse. (3.1/a 7T~ 1/3 - (3-186) .7-*.184). /?27Tmc2 where A is the phase-space area of the bunch in eV-s.ofa 2/1704. the maximum momentum width of the beam will be smaller. The asymptotic properties of the phase space ellipse The phase-space ellipse is tilted in the transition energy region. we obtain 7T2 4 a ^ = 9^3V3[r(§)]2> (3'180) ^ = -gj2 {—^—) V (3 ' 181) aw = 9^l^T"J ^ ^ ~ ' . (3 8) The tilt angle. In (0. Using a Taylor series expansion around y = 0. Thus the parameter b is (2AhMirlV12 b ~ \ 3 m c ^ ) • (3-179) A. we obtain the following scaling property: 5 7=7T ~ /i 1 ' 3 V 1 / ! U 1/2 7. At a higher acceleration rate. — ass i^^f(f)(3^J .T -v / 2A V2 v ( A \1/2 - / a« _32/3r(|)/2^^7^d\1/2 ~ y <*„<*„-<% ~ ~r~ \ zmtp-t) • (3-185j Note that 6 is finite at 7 = 7T for a nonzero acceleration rate.a502 ^(^j ' (3^ X 0 7=.171) into Eq. the maximum momentum spread. The phase-space area enclosed in the ellipse of Eq. (3.304 CHAPTER 3. the shape of the ellipse changes with time. S) phase-space coordinates. Substituting the adiabatic time r ^ of Eq. (3. and the maximum bunch width of the ellipse are ^=^tan-1 2 2a** (3.
and.17) becomes quite important.JA4>)2+2a^6(A4. we can evaluate the evolution of the peak <> current at the transition energy crossing. 1. the synchrotron equations of motion become A> = h. This is not true. all particles were assumed to cross transition energy at the same time.3 ( a » Q W . NONADIABATIC AND NONLINEAR SYNCHROTRON MOTION 305 The scaling property is important in the choice of operational conditions. and the normalized distribution functions Gi(A(f>) and C?2(<5) are Gl(A fl = i 3(°»"« ~ als) exp{. the nonlinear phase slip factor of Eq. 2 Nonlinear Synchrotron Motion at 7 fa 7T In Sec.IV. (3. (3. (3. At time . (3. the phase slip factor has been truncated to second order in 6. Near the transition energy region. where NB is the number of particles in the bunch.o ( ^ + V1S) 5. we can use asymptotic expansion of Bessel functions to obtain "•2 1/9 „ ft2 (2/*7^o'T?d\ 1/2 The phase-space ellipse is restored to the upright position. B.O ftW} \| nagg ass V 7T a Ss G2{6) = J**H exp{-3ass(5 + ^A<^) 2 }. IV.178) corresponds to 95% of the beam particles. we obtain #0(A<M) = = 3NB(Oi4"i'aS6 ~ als)1/2 c-3\ad. 6 = ^ g g ^ (A*). the factor 3 is chosen to ensure that the phase-space area A of Eq. Expanding the phase slip factor up to first order in 5. to a good approximation.187) NBG1{Ac/>)G2(6). and the peak current is still located at A / = 0. IV. because the phase slip factor depends on the off-momentum coordinate 5.188) where the synchronous particle crosses transition energy at time t = 0.177). Note here that Gi(A(j>) is the line charge density.)+ali/i62] (3. Using the ellipse of Eq. The equilibrium Gaussian distribution function at transition energy The distribution function that satisfies the Vlasov equation is a function of the invariant ellipse (3. Using the Gaussian distribution function model.177). In the adiabatic region where x 3> 1.
Note that the nonlinear time for RHIC is particularly long because superconducting magnets can tolerate only a slow acceleration rate.17). 7 1 is obtained from 7 Eq. we hope that the unstable motion does not give rise to too much bunch distortion before particles are recaptured into a stable bucket. (3. and the a\ term can be adjusted by sextupoles.14. A beam bunch is represented by a line of r](5) vs S.306 CHAPTER 3. which is below the transition energy of 5. some portions of the beam could experience unstable synchrotron motion. particles at 5 > 0.e. 7?c*i = 0. At the beam synchronous energy of E = 5. a portion of the beam particles can cross transition energy and this leads to unstable synchrotron motion. SYNCHROTRON MOTION Figure 3. particles are projected onto the off-momentum axis represented by this line. The synchrotron motion corresponds to particle motion along this line.446. rjo + Vi$ = — (2771. i. Table 3. or where 8 is the maximum fractional momentum spread of the beam.14: Schematic plot of n vs 5 near the transition energy region for the Fermilab Booster. A beam bunch with momentum width ±6 is represented by a short tilted line. 3. Note that the nonlinear time depends on the off-momentum width of the beam. At a given time (or beam energy). where 7T = 5.05 eV-s are used to calculate TJ(S) for the beam. To characterize nonlinear synchrotron motion.11 GeV. the synchronous phase is also shifted from <f>s to w — (j>s in order to achieve stable synchrotron motion. For a lattice without sextupole correction.14 shows the phase slip factor 7 vs the fractional off-momentum coor7 dinate 5 near transition energy for a beam in the Fermilab Booster. as shown in the example at 5. Figure 3. When the beam is accelerated (or decelerated) toward transition energy. Since the phase slip factor is nonlinear. the line is tilted. we typically have 7^«i ~ 1 (see footnote 3). where ct\ = 0 is assumed. Since the synchrotron motion is slow.1/7') + Vi$ = 0.3 lists the nonlinear time of some accelerators.1 GeV. Within the nonlinear time ±r n i.0018 will experience unstable synchrotron motion due to the nonlinear phase slip factor. .1 GeV beam energy in Fig.5. we define the nonlinear time rn\ as the time when the phase slip factor changes sign for the particle at the maximum momentum width 5 of the beam. t = 0. and a phasespace area 01 0.
IV. 1. Since the solution of the nonlinear equation is not available. When the bunch is 33 The microwave instability will be discussed in Sec.188). The relative importance of non-adiabatic and nonlinear synchrotron motions depends on the adiabatic time of Eq. we estimate the growth of momentum width by integrating the unstable exponent. Note that when the nonlinear time rni vanishes. However. Depending on the adiabatic and nonlinear times. Using Eq. The problem is most severe for accelerators with a slow acceleration rate.171) that governs the adiabaticity of the synchrotron motion. Tad 5 (3. the solution of Eq. the effects of nonlinear synchrotron motion and of microwave instability can be analyzed. Therefore these particles experience defocussing synchrotron motion. (3-192) where r)0 = 2-yt/j^.33 We have seen that the momentum width will increase due to the nonlinear phase slip factor. Therefore the area of the phase-space ellipse of each particle is conserved. The growth factor is for a particle with 5 = 5.190) is an Airy function. NONADIABATIC AND NONLINEAR SYNCHROTRON MOTION When the beam is accelerated toward transition energy to within the range 7 T . The action integral is a distorted curve in phase-space coordinates. discussed in Sec. lower momentum portions of the bunch will experience defocussing synchrotron motion. we can easily prove that the Jacobian is 1. within which some portion of the beam particles experiences unstable synchrotron motion. (3. After the synchronous energy of the bunch reaches transition energy and the synchronous phase has also been shifted from </>„ to IT — 4>s. we obtain S" = -X5 + ^C. we should bear in mind that the synchrotron motion can be derived from a Hamiltonian H = iha. The maximum momentum height is increased by the growth factor G. IV. (3. Expressing Hamilton's equation as a difference mapping equation. which depends exponentially on T^/T^. VII. 307 the phase equation begins to change sign for particles at higher momenta while the phase angle (j>s has not yet been shifted. (3. and the nonlinear time rnl. and the ID dynamical system is integrable."Km < 7 < 7 T + 7Tm.£ J | ^ cos U^)2.0 [% + | m< j] <52 . .190) where the primes indicate derivatives with respect to x = |t|/r a( j.
if j r is changed by one unit in 1 ms. For a modern high intensity hadron facility. The 5% beam loss at transition energy found for proton synchrotrons built in the 60's and 70's may arise mainly from this nonlinear effect.34 the effective transition energy crossing rate is 1000 s~1. the KEK PS. Bunched beam manipulation are usually needed to minimize beam loss and uncontrollable emittance growth.308 CHAPTER 3. Minimizing both Tad and TD\ provides cleaner beam acceleration through the transition energy. Transition energy jump By applying a set of quadrupoles. . The effective 7T crossing rate is jes = 7 — j r . The scheme has also been studied in the Fermilab Booster and Main Injector. which is much larger than the beam acceleration rates listed in Table 3. Use of momentum aperture for attaining faster beam acceleration The synchronization of dipole field with synchronous energy is usually accomplished by a "radial loop. The tolerance of microwave instability near transition energy will be discussed in Sec. IV. Since there is no frequency spread for Landau damping. The growth of the bunch area is approximately G2 = exp{|(r n i/r ad ) 3 '' 2 } shown in Eq. Transition jT jump has been employed routinely in the CERN PS. (3. However. the revolution frequencies of all particles are nearly identical.3 Beam Manipulation Near Transition Energy Near the transition energy.193) B. therefore efforts to eliminate transition energy loss are important. i. the beam is isochronous or quasi-isochronous.e. They may be captured by other empty buckets of the rf system.3. The nonlinear phase slip factor can cause defocussing synchrotron motion for a portion of the bunch. the beam can suffer microwave instability. SYNCHROTRON MOTION accelerated through transition energy.r n . VII. and the AGS. In most accelerators. The minimum 7T jump width is A 7 T = 2 7 x Max(r ad . some portions of the phase-space torus may lie outside the stable ellipse of the synchrotron Hamiltonian. the maximum B is usually limited. Sec. IV.191). the time scale can be considered as adiabatic in betatron motion so that particles adiabatically follow the new betatron orbit. but the rf voltage and synchronous phase angle can be adjusted to move the beam across the 34The 7T jump time scale is non-adiabatic with respect to synchrotron motion. (3. or may be lost because of the aperture limitation. A.)." which provides a feedback loop for rf voltage and synchronous phase angle.8). the loss would cause radiation problems. For example. 2. transition energy can be changed suddenly in order to attain fast transition energy crossing (see Chap.
M. Phys.t\) + Vlhco052 (t . u0 = 4. E54. C.<t>\. (3. all particles gain an equal amount of energy each turn. Rev. {/S. CM. Inst. Bhat et al. have many applications such as time resolved experiments with synchrotron light sources. Flatten the rf wave near transition energy Near transition energy. The radial loop can be programmed to keep the beam closed orbit inside the nominal closed orbit below transition energy. Phys. Nucl. 36 A. and thus 5 of each particle is approximately constant in a small energy range. This concept was patented by G. very short proton bunches are needed for attaining small emittance. Note that the ellipse evolves into a boomerang shaped distribution function with an equal phase-space area.194) 7T where t\ is the rf flattening period. partial loss of focusing force in synchrotron motion can be alleviated by flattening the rf wave.5. Figure 3. U. 35see e.4 Synchrotron Motion with Nonlinear Phase Slip Factor In the production of secondary beams. and 7^771 « 2. or to reduce the momentum compaction factor for electron storage rings.15 shows the evolution of the phase-space torus when the rf wave is flattened across the transition energy region.36 employed this method for beam acceleration. j . Very short electron bunches. The rf flattening scheme is commonly employed in isochronous cyclotrons. the parameters used in this calculations are 7T = 22. D.35 In the flattened rf wave. Because of its potential benefit of the low r\ condition.IV. (3.g. For an experienced machine operator to minimize the beam loss with a radial loop. E55. we carefully study the physics of the QI dynamical system. and damping rings for the next linear colliders. Jeon et al. Bai et al. A 301. sub-millimeter in bunch length. h = 360. 3493 (1997).188) with 5 = 0 is A<t> = A0! + ^ ^ ( i 2 . and 8 — Si. E54..917 x 105 rad/s. This can be done by choosing <f>s = n/2 or employing a second or third harmonic cavity.h). IV. Phys. 815 (1996). E55. the essential trick is to attain a faster transition energy crossing rate. ti = —63 ms. Pellegrini and D. coherent synchrotron radiation. e.1. Riabko et al. Methods.B. Patent 2778937 (1954). Rev. Rossi. Rev. Since the ratio of bunch length to bunch height is proportional to J\ri\. Rev. NONADIABATIC AND NONLINEAR SYNCHROTRON MOTION 309 momentum aperture. The solution of Eq. and to attain faster acceleration across transition energy so that the beam closed orbit is outside the nominal closed orbit above transition energy. 4192 (1996). C.6 s"1. a possible method of producing short bunches is to operate the accelerator in an isochronous condition for proton synchrotrons. The AVF cyclotron has routinely . Robin.S. 1028 (1997).g. Phys.5\) are the initial phase-space coordinates of the particle.
we obtain the Hamiltonian for synchrotron motion as H=\h (r]0 + ^ms"j S2 + ^ S ^ [ c o s 0 . We define vs = Jh\rio\eV/2-KJ32E for small amplitude synchrotron tune.2 and Eq. Proc. LBL-37758 (1995). The fixed points with 5pp = 0 are the nominal fixed points. 9 (1993). Robin.0S. D.V ? i ) . 0). <5)UFP = (JT . Expanding the phase slip factor as r\ = r)0 + rjiS H and using the orbiting angle 6 as the independent variable. <5)SFP = (0s. 822 (1973). Brack et al. (3. H. Takano and B. (3-196) (0. Note that the off-momentum coordinates of each particle are unchanged. Takano. . Appl.0s)sin0s]. 0). and use the normalized phase space coordinates 0 and V = (hrjo/i/s)6. A. . 29 (1993)..60) show that the synchrotron bucket height and momentum spread become very large when |7y| is small. Hama. (3. Robin. while the bunch length elongates along the tj> axis. Isoyama. A329. 32. NS20. Phys. The synchrotron Hamiltonian needs to take into account the effects of nonlinear phase slip factor. et. Nucl. 128 (1994). 1285 (1993).310 CHAPTER 3. Nadji.197) Note that the nonlinear phase slip factor introduces another set of fixed points in the phase space. Methods. Japan J. H. The fixed points of the nonlinear synchrotron Hamiltonian are (0. EPAC94 p. Table 3. (0S. E48. L. and A. Hama and G. Sci. Nadji et al. Hama. Liu et al. H. SYNCHROTRON MOTION Figure 3. (TT . H. The fixed points with (5pp = — ^o/^i arising from the nonlinear-phase-slip factor are called nonlinear-phase-slip-factor (NPSF) fixed points. Methods.15: The evolution of a phase-space ellipse in the flattened rf wave near the transition energy region. -Tfy/rn). These fixed points play important role in determining the dynamics of synchrotron motion. The Hamiltonian of 27 (1991). S.195) where we have truncated the phase slip factor to the second order in 5. al.0s. Phys. IEEE Trans. D. S.cos0s + (0 . (3. A329. its dependence on the fractional momentum deviation 5 becomes important. Rev. Nucl. Isoyama. Instru. 2149 (1993). This requires careful examination because when the phase slip factor T) is small. Nucl. Instru.
The separatrix that passes through the nominal fixed points are nominal separatrix. Particle motion can be well described by neglecting the V3 term in the Hamiltonian. Figure 3.200) For y . In this example. (3. the phase space tori will be deformed. Right: Separatrix with parameters <f>s = 180° and y = 8 (top).1962 (middle). Note the dependence of the Hamiltonian tori on the parameter y.cos &].198) 2/ = 3 H 2 / 2 % ^ (3. the stable buckets of the upper and lower branches are separated by a distance of AV = 2y/3.4. we have assumed r/o > 0 and T?I > 0.4>s) sin fa . the nonlinear phase slip factor is not important.16 shows the separatrix of the nonlinear Hamiltonian in normalized phase space coordinates for <> = 150° and 180° respectively. and if \y\ is small.IV. given by 2/cr = v/27[(?r/2 .0406 (middle) and 1 (bottom). where. P = V) for the synchrotron Hamiltonian with parameters tps = 150° and y = 5 (top). and 3 (bottom).16 and Exercise 3.199) signifies the relative importance of the linear and nonlinear parts of the phase slip factor. For y < yCI. 311 (3. They are called "a-bucket.</>s) sin <f>s}. y = yCT = 3. 3. the separatrix of two branches will become one (see the middle plots of Fig. If \y\ » 1." Since the a-bucket is limited in a small region . we assume T)Q > 0 and ?7i > 0. the separatrix ("fish") is deformed into up-down shape (see lower plots).cos 4>s+ ((/>. This condition occurs at y = yCI.16: Left: Separatrix in the normalized phase space ((/).6). Figure 3. When the nominal separatrix crosses the unstable NPSF fixed point. without loss of gener/s ality.§> ycr. y = ycr = 5. NONADIABATIC AND NONLINEAR SYNCHROTRON MOTION synchrotron motion becomes H = \vsT2 z The parameter + ^-vsV3 Zy + ua[coa cf> .
202) where % and r]i are the first order and second order phase slip factors. the equation of motion for the fractional off-momentum deviation is i -5^^'* + «. (3.204) the synchrotron Hamiltonian for particle motion in QI storage rings becomes H0 = \p2 + \x2-l-x\ (3. truncation of the phase slip factor at the ??i term is a good approximation. (^r) =4(^-ei)(p-e2)(P-e3). IV.312 CHAPTER 3. With t = vs6 as the time variable. and r\ is the phase slip factor given by V = Vo + ViS + • • •. The particle motion inside such a quasi-isochronous (QI) dynamical system can be analytically solved as follows. (3. \] for particles inside the bucket. In many storage rings.206) .5 The QI Dynamical Systems 4> = hrjd.205) This universal Hamiltonian is autonomous and the Hamiltonian value E is a constant of motion with E € [0.16). the overdot indicates the derivative with respect to the orbiting angle 0 = s/Ro. and Eo is the energy of the beam. Similarly. where * =^ . /3c is the speed. 3.201) The synchrotron equation of motion for the rf phase coordinate 0 of a particle is where h is the harmonic number. (3. where vs = JheV0\r]0 cos <j>s\/2-nP2Ea is the small amplitude synchrotron tune.203) is a good approximation because the (up-down) synchrotron bucket is limited in a small range of the phase coordinate (see Fig. and with (x. SYNCHROTRON MOTION of the phase coordinate <j>. Here.p) as conjugate phase-space coordinates. (3. small angle expansion is valid. The equation of motion for the QI Hamiltonian with Hg = E is the standard Weierstrass equation.t a *"-W* (3-203) where Vo and <j>B are the rf voltage and synchronous phase angle. 5 = Ap/p0 is the fractional momentum deviation from a synchronous particle. (3. the linearized phase coordinate in Eq. P = ^ .
is ^ ( t ) = 1 -^h7TT' p^ = ( i h W The tune of the QI Hamiltonian is < 3 . e2 = ^ + cos(£-120°). 3. The separatrix of the QI bucket is one of the separatrix. and the Weierstrass p function can be expressed in terms of the Jacobian elliptic function [25] x(t) = e3 + (e2 .16. the discriminant A = 648^(1 — 6E) is positive. The Weierstrass elliptic p-function is a single valued doubly periodic function of a single complex variable. Figure 3. Figure 3.^ * M m = .17: Schematic plots of the QI bucket (left) and the QI potential (right). The separatrix orbit. The turning points e\. NONADIABATIC AND NONLINEAR SYNCHROTRON MOTION where u = t/y/6.IV. where e2 and e3 are turning points for stable particle motion. p = x.e3 sin(f + 60°) v . The £ parameter for particles inside the bucket varies from 0 to TT/3.17 shows the separatrix of the QI bucket QI potential. and the turning points. and the turning points are ei = ^ + cos(0. shown in Fig. (3-207) e2_-es= sine ei .209 ) qw-"*•%* r r ) r V6K(m) (3^o) .e3) sn2 ( \ p . plotted sideway. e3 . For particle motion inside the separatrix. and e3 are also shown.\ + cos(£ + 120°) 313 with £ = |arccos(l — 12E). which corresponds to m = 1. e2.
Wang. A364. M. E49. et al. 3. Here.18: The synchrotron tune of the QI dynamical system (upper curve) is compared with that of a single rf potential (lower curve). Methods.18. 591 (1993). et al. we note that the synchrotron tune decreases to zero very sharply near the separatrix.314 CHAPTER 3. M. Phys. 70. Phys. D. The resulting Hamiltonian is H0(J)*J-^J2 + ---. the equation of motion for QI electron storage rings is x" + Ax' + x . 4678 (1993). Phys. (3. Rev.e3)^F ( j . Y. Note that the sharp drop of the QI synchrotron tune at the separatrix can cause chaotic motion for particles with large synchrotron amplitudes under the influence of the lowfrequency time-dependent perturbation. 7 1 . (3. E48. The action of the separatrix orbit is Jsx = 3/5?r. Huang. Ellison. Lett. E48.m) . J)= f p dx. R1638 (1993).x2 = 0. et al. Syphers. SYNCHROTRON MOTION Figure 3. Li.211) where F is the hypergeometric function [25]. et al. Rev. Using the generating function F2(x. D. et al.212) the angle variable is ip = dFz/dJ = Qt.213) 3 7 H. 205 (1995). Because of the synchrotron radiation damping. Nud. Rev. Lett. 719 (1993). et al. Inst.37 The action of a torus is J = ^fpdx = | y | ( e 2 . Rev. Rev. (3. Phys. . -^3. Li. or equivalently the bucket area id 6/5. The tune of the QI Hamiltonian is compared with that of the normal synchrotron Hamiltonian in Fig. time dependent perturbation will cause overlapping parametric resonances and chaos near the separatrix. Phys. Because of the sharp decrease in synchrotron tune. 1610 (1994).e3)2(ei .
wm = vm/i>B is the normalized modulation tune.4 1. the Hamiltonian in normalized phase-space coordinates is H = j + -x2 . Rev.5.4 where the effective damping coefficient is 315 A = A = 3lE_. 38A. the nonlinear time. where B =— (3. and vm is the modulation tune of the original accelerator coordinate system. Jeon et al. E55. Show that Eq. (a) Express the solution in terms of Airy functions and find the equation for the invariant torus. 815 (1996). (3. Rev.216) is the effective modulation amplitude. Exercises 3.215) The stochasticity of such a dynamical system has been extensively studied. Detailed discussions of this topic is beyond this introductory textbook. 2. Verify the adiabatic time. 4192 (1996).EXERCISE 3. where T ^ is the adiabatic time of Eq.. i.e.e. Rev. . and the momentum spread of the beam 8 at 7 = 7 r for the accelerators listed in Table 3. B ~ |T?I|/|T?O|3''2Including the damping force.171). M. E54. (3.3.j. (3. Phys.38 Experimental verification of the QI dynamical system has not been fully explored. Note that the effective modulation amplitude B is greatly enhanced for QI storage rings by the smallness of ?j0. the equation of motion becomes x" + Ax'+ x-x2 = -um B cos umt. Bai et al. Phys. Riabko et al. (3.217) (3. 3493 (1997). Uo is the energy loss per revolution.-x3 + ujmBx cos ojmt. E54. Including the rf phase noise. i. D. the effective damping coefficient is enhanced by a corresponding decrease in synchrotron tune. A ~ |J7O|~1/'2J where the value of A can vary from 0 to 0. a is the rf phase modulation amplitude. Phys.214) Here A is the damping decrement. In QI storage rings. and JE is the damping partition number.172) can be reduced to 6" + x5 = 0 where the primes indicate derivatives with respect to the variable x = |t|/Ta.
Show that when y = ycr of Eq. Show that the QI Hamiltonian can be reduced to Eq. calculate the characteristic time and the maximum momentum spread for a phase space area of 0.5) of Eq.177).<fe) sin 4>s] . (3. (3.04 eV-s. SYNCHROTRON MOTION 3. (3.200) the separatrix of the upper branch passes through the UFP of the lower branch. Si) of the initial ellipse. Assuming 7 T = 20.4. (3. 7. Show that T^/T^ OC 7~ 5 / 6 7~ 2 / 3 . .n) sin 4>s) = 0. show that the Hamiltonian (3. Using the normalized phase space coordinates <f> and V. Show that the phase space area enclosed by (A<f>. Discuss the effects of high vs low yT lattices on the dynamics of synchrotron motion near the transition energy.—y3 = 0. vsV* + yV2 + 1y[cos <t> .cos <f>s+ {(}>.316 (b) Verify Eq. 6.205) and that the solution is given by the Weierstrass elliptical function. Show that the separatrices of the Hamiltonian are vsV% + yV2 + 2j/[cos 4> + cos </>s + ((f> + <f>s .195) with nonlinear phase slip factor depends only on a single parameter y = 3hrjQ/2usr)i. 4. The Fermilab Main Injector accelerates protons from 8.9 GeV to 120 GeV in 1 s. 5.194) is equal to the phase space area enclosed by (A^i. CHAPTER 3.
the fractional change of beam velocity in low energy boosters can be large. The beam is accumulated. electrons are almost relativistic at energies above 10 MeV. etc. and the energy compensation of the rf field is along the longitudinal direction. The synchrotron radiation emitted by a relativistic electron is essentially concentrated in a cone with an angular divergence of I/7 along its path. The effects of synchrotron radiation must be taken into account in beam manipulation. where the space-charge tune shift. The mean-field Coulomb force can also have a large effect on the stability of low energy beams in boosters. phase-space painted. is limited to about 0. called booster synchrotrons or boosters. During beam acceleration. For acceleration of ion beams. The resulting momentum spread is independent of the rf voltage. However. phase-space stacking. the range of beam energy for a synchrotron is limited. innovative bunched . electrons emit synchrotron radiation. pre-accelerated by an electrostatic Cockcroft-Walton or an RFQ. and the mean energy loss of a beam is compensated by the rf field. and the required range of rf frequency change is small. Careful consideration is thus needed to optimize the operation and construction costs of accelerators. Equilibrium is reached when the quantum fluctuation due to the emission of photons and the synchrotron radiation damping are balanced. particle motion in synchrotron phase-space is damped. including phase displacement acceleration. that have often been applied in the space charge dominated beams and high brilliance electron storage rings for providing a larger tune spread for Landau damping. The reasons for this complicated scheme are economics and beam dynamics issues. Since dipole and quadrupole magnets have low and high field operational limits. BEAM MANIPULATION IN SYNCHROTRON PHASE SPACE 317 V Beam Manipulation in Synchrotron Phase Space A charged particle beam is usually produced by an intense ion source.. adiabatic capture. Since synchrotron radiation power depends on particle energy. and debunching. which must be compensated by the longitudinal rf electric field in a storage ring. and accelerated toward higher energies by a chain of synchrotrons of various sizes. and the transverse emittance depends essentially on the lattice arrangement. and the beam dynamics issues of minimum momentum aperture and phase-space area. accordingly. We also study the barrier rf systems that have been proposed for low energy proton synchrotrons. rf frequency for a low energy booster has to be tuned in a wide range. In this section we examine applications of the rf systems in the bunched beam manipulations.3-0. prebunched and injected into a linac to reach an injection energy for low energy synchrotrons.4. stacked in a low energy booster.V. the betatron motion is also damped. bunch rotation. proportional to circumference of the synchrotron. bucket to bucket transfer. rf power source. The rf voltage requirement is determined by technical issues such as rf cavity design. In general. The beam distribution function can thus be manipulated to attain desirable properties for experiments. phase-space area is normally conserved. We carefully study the double rf systems. On the other hand.
electrons are nearly relativistic at all energies. K. the rf system is usually limited by the range of required frequency swing. [GeV] / r f [MHz] Av.30 7x84 Kf [kV] |_90 I 300 1 300 j_950 | 4000 In some applications. and the angular revolution frequency UJQ is a function of the magnetic field B and the average radius of the synchrotron RQ. On the other hand. Thus the rf frequency is an integer multiple of the revolution frequency ui^ = hLjo(B. High frequency pill-box-like cavities are usually used. and e is the particle's charge. with ramping frequency w/2?r varying from 1 Hz to 50 Hz.Rags 6x60 I FNALBST 0.E. Normally the .4-4.218).001703/p[m] Tesla for electrons. Rate [GeV/s] Max.2(0.E. SYNCHROTRON MOTION beam manipulation schemes can enhance beam quality for experiments.1273/p[m] Tesla for protons. or resonantly as B = (B/2)(l — cosu)t) = Bsin2(cut/2). The momentum po of a particle is related to the magnetic field by po = epB. Radius [m] h I AGS BST 1 AGS 0.1 2. [GeV/u] Ace. K. (3. The rf frequency is a function of the dipole magnetic field. In low to medium energy synchrotrons.47 84 1 FNALMI 8. the magnetic field can be ramped linearly as B = a + bt.68-26. V. for which cavities with ferrite tuners are usually used.4) 200 8 30. Table 3. where h is the harmonic number.5 30 0. the rf frequency should follow the magnetic field ramp according to Eq.6 128. \A-iVi) rf frequency ramping is particularly important for low energy proton or ion accelerators.8-53.74 (19/4).4: RF parameters of some proton synchrotrons Inj.7 250 26.I lists parameters of some proton synchrotrons. where p is the bending radius. and the rf frequency swing is small.8 75.2 0.0-52. Since rru?_ _ f 3.Ro).001/0.I RF Frequency Requirements Particle acceleration in synchrotrons requires synchronism between rf frequency and particle revolution frequency.2(1. Thus the rf frequency is Pc _ hepB _ he [ B*{t) |1/2 where m is the particle's mass.318 CHAPTER 3. Table V.18-4.5) 100 60 1.457 (l/4)-Rags 1-3 (2) 12 (8) I RHIC 12 3. ~^p~~\ 0.1 528.0 100 500 52.
The choice of harmonic number for high energy electron storage rings is determined mainly by the availability of the rf power source. and the ratio of harmonic numbers is 4. 350. Since the damping time of electron beams in electron storage rings (see Table 1. acceleration rate is less important in storage rings used for internal target experiments. a large angle Coulomb scattering process converting the horizontal momenta of two electrons into longitudinal momenta. Similar reasoning applies to the chain of accelerators. 1. 350.4) is short. the injection scheme of damping accumulation at full energy is usually employed in high performance electron storage rings. and 700 MHz regions. most of the rf cavities of electron storage rings are operating at these frequencies. Requirements of rf systems depend on their applications. efficient high quality cavity design. In recent years. B. BEAM MANIPULATION IN SYNCHROTRON PHASE SPACE 319 frequency range can be in the 200. 4. the choice of rf voltage is important in determining the beam lifetime because of quantum fluctuation and Touschek scattering. the average radius of the AGS Booster is 1/4 that of the AGS. New methods of beam manipulation can be employed. 40A box-car injection scheme is equivalent to bucket to bucket transfer from one accelerator to another accelerator. the rf voltage is limited by the rf power source and the Kilpatrick limit of sparking at the rf gap. Chap.4. 500. The total rf voltage of synchrotrons and storage rings is 39The ISIS at the Rutherford Appleton Laboratory has a 50 Hz ramp rate. Since the rf bucket area and height are proportional to \A^f. where rf power sources are readily available. 500. In electron storage rings. To achieve high beam power in meson factories and proton drivers for spallation neutron sources. . 700 MHz regions. The choice of rf voltage High intensity beams usually require a larger bunch area to control beam instabilities. which can be important for colliding beam facilities. whereas the rf systems in the Spallation Neutron Source (SNS) provide only beam capture.V. In general. A. and the size of the machine.39 On the other hand.40 For example. a minimum voltage is needed to capture and accelerate charged particles efficiently. The choice of harmonic number The harmonic number determines the bunch spacing and the maximum number of particles per bunch obtainable from a given source. a fast acceleration rate is important. Sec. The harmonic number is then determined by the rf frequency and circumference of the storage ring. The harmonic numbers are related by the mean radii of the chain of accelerators needed to reach an efficient box-car injection scheme. wideband solid state rf power sources and narrowband klystron power sources have been steadily improved. Since rf power sources are available at 200.
5% instead of 0. .2 Capture and Acceleration of Proton and Ion Beams At low energy. intrabeam scattering. The right plots. (e) to (h). A possible solution is to install a debuncher in the injection transfer line for lowering the momentum spread of the injected beam. the intensity and brightness of an injected beam are usually limited by space-charge forces. very little beam loss in the synchrotron phase-space can theoretically be achieved by adiabatically ramping the rf voltage with <j>a = 0. the initial rf voltage should have a small finite initial voltage Vo. phase-space painting for beam distribution manipulation can be used to alleviate some of these problems (see Chap.6%.320 CHAPTER 3.1). After beam capture.. SYNCHROTRON MOTION usually limited by the available space for the installation of rf cavities. for transverse phase-space painting). A. The maximum voltage is only barely able to hold the momentum spread of the injected beam from linac. The actual capture efficiency is much lower. microwave instability. 41 The peak voltage is usually limited by the power supply and electric field breakdown at the rf cavity gap. The proton beam was accelerated from 7 to 200 MeV at 1 Hz repetition rate. the synchronous phase was ramped adiabatically to attain a desired acceleration rate. III.41 The resulting captured beam brightness depends on the rf voltage manipulation. we find that the capture efficiency is about 99. Sec. In order to satisfy the adiabatic condition. The following example illustrates the difference between adiabatic capture and non-adiabatic capture processes. and the rf voltage is ramped to a final voltage smoothly (see also Exercise 3. Good acceleration efficiency requires adiabatic ramping of V and 4>s while providing enough bucket area during beam acceleration.1% shown in this example. V. the momentum spread of the injected beam is about 0. while the synchronous phase was kept at zero. of Fig.5.43) becomes Ts dVd_ Ts dAB (3 ' 220) a a d -«^T-2^^T' where Ts is the synchrotron period and AB is the bucket area. (3.8.19 show an example of adiabatic capture in the IUCF cooler injector synchrotron (CIS). Since the injected beam from a linac normally has a large energy spread. the rf voltage requirement in booster synchrotrons needs enough bucket height for beam injection. A debuncher or a bunch rotator in the transfer line can be used to lower the momentum width of injected beams. Adiabatic capture During multi-turn injection (transverse or longitudinal phase-space painting or charge exchange strip injection). The adiabaticity coefficient of Eq. 3. In reality. 2. and the rf voltage VTi(t) was increased from a small value to 240 V adiabatically. etc. In this numerical example. plots (e) and (f).
1%. Indiana University. and thus the actual adiabatic capture efficiency is substantially lower. The actual momentum spread of the injected beam is about ±0. (e) to (h). Spacecharge force and microwave instability are not included in the calculation. . 1998). The rf synchronous phase is then ramped adiabatically to achieve the required acceleration rate.19: The left plots. show adiabatic capture of the injected beam: the rf voltage is ramped from 0 to 240 V adiabatically to capture the injected beam with a momentum spread of 0.5%. BEAM MANIPULATION IN SYNCHROTRON PHASE SPACE 321 Figure 3. Kang (Ph. The right plots. (a) to (d). This calculation was done by X. Thesis. show non-adiabatic beam capture during injection and acceleration.D.V.
As seen in plots (b) and (f). The decoherence results in emittance growth. When the beam is transferred from one accelerator to another. the bunch length of a beam may need to be shortened in many applications. the peak voltage of an rf system is limited by the breakdown of electric field at the acceleration gap. However. 3. of Fig. Similarly. the rf frequency / [MHz] is related to the peak electric field gradient EK [MV/m] by f = 1.223) l*v¥LrL*v¥L- _ [ i [W] (-2) 322 . In this case.l L-R^Jacc. Non-adiabatic capture CHAPTER 3. According to the empirical Kilpatrick criterion. located at the source. Beam loss occurs during acceleration. a beam chopper consisting of mechanical or electromagnetic deflecting devices. the injected beam particles decohere and fill up the entire bucket area because of synchrotron tune spread.64 El e-8-5/EK. and the capture efficiency is low. (3. (3-221) fi [W] This matching condition may be higher than the limit of a low frequency rf system. Chopped beam at the source Many fast cycling synchrotrons require nonzero rf voltage and nonzero rf synchronous phase (j>s > 0 to achieve the desired acceleration rate.3 Bunch Compression and Rotation When a bunch is accelerated to its final energy.2 or equivalently. the beam profile matching condition is L-RflJacc. V. C. A simple approach is to raise the voltage of the accelerator rf system. capture efficiency is reduced by the nonadiabatic capture process. To circumvent low efficiency. (a) to (d). the capture efficiency may be even lower. SYNCHROTRON MOTION The left plots. it may be transferred to another accelerator or used for research. When the if voltage is set to 240 V to capture the injected beam. can be used to paint the phase-space of the injected beam and eliminate beam loss at high energy. the beam fills up the entire phase-space. as shown in plot (b). the final phase-space area is larger. the rf parameter matching condition is \l] =\l] .19 show an example of non-adiabatic capture with nonzero initial rf voltage.322 B. With microwave instability and space-charge effects included.
etc. defined as the ratio of the bunch lengths at (Vo = V2) -> Vi ->• V2.3. the longitudinal emittance of the secondary antiproton beam becomes smaller.3). the bunch height will become bunch width according to Eq. Generally.g. The antiproton beam can be further debunched through phase-space rotation in a debuncher by converting momentum spread to phase spread. the emittance of secondary beams is equal to the product of the momentum aperture of the secondary-beam capture channel and the bunch length of the primary beam. the rms bunch width and height are obtained from Eq. becomes " where we have used the properties that the bunch area supposedly fills up the bucket area at Vxi = V\. e. and the final antiproton beam is transported to an accumulator for cooling accumulation (see Exercise 3. VIII). A few techniques of bunch compression are described below. For a given bunch area.5. BEAM MANIPULATION IN SYNCHROTRON PHASE SPACE 323 Because of this limitation. the maximum attainable rf voltage is limited. Vo -* V1. . we have to use different beam manipulation techniques such as bunch compression by rf gymnastics. or a kicker is fired to extract beams out of the synchrotron.A Bunch compression by rf voltage manipulation The first step it to lower the rf voltage adiabatically.58) during the adiabatic rf voltage compression from Vo to Vx. Figure 3. and the fact that the bucket area is 16 (see Table 3.20 shows schematic phase-space ellipses during the bunch compression process. Beam bunch compression is also important in shortening the electron bunch in order to minimize the beam breakup head-tail instabilities in a linac (see Sec. and the bunch area containing 95% of the beam is 6TT(T^ in the normalized synchrotron phase space coordinates. The lower-left plot shows the final phase-space ellipse in an idealized linear synchrotron motion. At 1/4 or 3/4 of the synchrotron period. Bunched beam gymnastics are particularly important for shortening the proton bunch before the protons hit their target in antiproton or secondary beam production.The unmatched beam bunch rotates in synchrotron phase-space. so that the bucket area is about the same as the bunch area. The maximum bunch compression ratio.2). and the final phase-space ellipse is distorted by the nonlinear synchrotron motion that causes emittance dilution. (3.59). (3. After the rf voltage is jumped to V"2. When the bunch length of a primary proton beam is shortened. In reality. Then the rf voltage is increased non-adiabatically from VI to Vi. V. a second rf system at a higher harmonic number is excited to capture the bunch.V.
As the voltage is nonadiabatically raised to four times the original rf voltage.88) can be approximated by two straight lines crossing at 45° angles with the horizontal axis cj>.3. The rate of growth is equal to exp(wsiufP)The maximum rf phase coordinate 0 max that a bunch width can increase and still stay . II.324 CHAPTER 3. The bunch area is initially assumed to be about 1/5 of the bucket area (top-left). (3.5). When the SFP of the rf potential is shifted back to the center of the bunch. V. In the normalized phase-space coordinates. the bunch can be captured by a matched high frequency rf system or kicked out of the accelerator by fast extraction.B Bunch compression using unstable fixed point If the rf phase is shifted so that the unstable fixed point (UFP) is located at the center of the bunch. where ws is the small amplitude synchrotron angular frequency. a kicker can be fired to extract the beam. the mismatched bunch begins to rotate. Ts is the synchrotron period.20: Schematic drawings (clockwise) of bunch compression scheme using rf voltage manipulation. When the bunch length is shortened (lower-left) at 1/4 of the synchrotron period. When the rf phase is shifted so that the beam sits on the UFP. the bunch width and height will stretch and compress along the separatrix. the bunch length and bunch height change according to exp{±wsiUfp} = exp{±27rtufp/Ts}. At 3/8 of the synchrotron period. Near the UFP. SYNCHROTRON MOTION Figure 3. The length of stay at the UFP can be adjusted to attain a required aspect ratio of the beam ellipse. the Hamiltonian for stationary synchrotron motion is given by Eq.4 and Exercise 3. the separatrix of the Hamiltonian in Eq. (3. In linear approximation.2. the bunch will begin compressing in one direction and stretching in the other direction along the separatrix orbit (see Sec.88). <j> and V = — (h\ri\/vs)(Ap/p). We now derive the ultimate bunch compression ratio for the rf phase shift method as follows. The voltage is adiabatically reduced by 16 times so that the bunch is almost fill the bucket area (topright). and iufp is the time-duration that the bunch stays at the UFP. The mis-matched bunch profile will begin to execute synchrotron motion.
the beam is kicked out of the synchrotron and the R^ transport matrix element will compress bunch. By employing a cavity to accelerate and decelerate parts of the beam bunch. The difficulty of nonlinear synchrotron motion in the final stage of bunch rotation can be solved by using the buncher in the transport line.3.ZZI) The time needed to reach this maximum compression ratio is ujsiufp = In — . lower energy particles travel shorter path. conservation of phase-space area.228) A difficulty associated with bunch compression using rf phase-shift is that the rf voltage may remain at a relatively low value during the bunch rotation stage.max — —„ ~ /» > (6. However. BEAM MANIPULATION IN SYNCHROTRON PHASE SPACE 325 within the bucket after the rf phase is shifted back to SFP is given approximately by I ^ + 2sin2(^)«2. (3.\ = 7rc7-p.0. First. V. we find / mx ^a\. This method is commonly used in the beam transfer line. Thus we obtain <> a ~ V%. let the beam drift a distance L so that higher energy particles are ahead of lower .' (3.203. i.C Bunch rotation using buncher/debuncher cavity The principle of bunch rotation by using a buncher/debuncher cavity is based on the correlation of the time and off-momentum coordinates (the transport element R$&).Since there is no constraint that the final bunch size should fit into the bucket. and the higher energy particle travel a longer path. a simple debuncher used to decrease the energy spread of a non-relativistic beam out of a linac can function as follows. After proper bunch compression.e.Using Liouville's theorem. one can regain the factor of y/2 in staying longer at the UFP.226) Assuming that 95% of the beam particles reach 0 max = y/2 so that a-p.225) where we assume linear approximation for particle motion near SFP. The effect of non-linear synchrotron motion will be more important because the ratio of bucket-area to the bunch-area is small. = a4>.i — r^max — y/2/3.fcr0. the bunch length and the momentum spread can be adjusted.V.f(3. the resulting compression ratio is reduced by a factor of l/\/2. For example. we find the compression ratio as r c.
Note that the momentum spread of the entire beam remains the same in this non-adiabatic debunching process. It requires bending magnets for generating local dispersion functions so that the path length is correlated with the off-momentum coordinate. 58 (CERN. 1956. In a successful example of beam stacking in the ISR pp collider. 635 (1993). V.g. which increases the density and the collision rate. . therefore particles outside the bucket can not be captured during acceleration. the momentum spread will not change. of Int. For relativistic particles. L. Neglecting synchrotron radiation loss. p. 44.42 A buncher/debuncher cavity can then be used to shorten or lengthen the bunch. A cavity that decelerates leading particles and accelerates trailing particles can effectively decrease the energy spread of the beam. and subsequent groups are accelerated and deposited adjacent to each other. a single beam current of 57.5 Beam Stacking and Phase Displacement Acceleration The concept of beam stacking is that groups of particles are accelerated to a desired energy and left to circulate in a fixed magnetic field. p. The accumulated beam will overlap in physical space at special locations. (3. C. the resulting debunched beam has a smaller momentum spread. In this case. Methods of radio-frequency acceleration in fixed field accelerators with applications to high current and intersecting beam accelerators. Since the magnetic field 42 See e. a drift space can not provide the correlation for the transport element R^ because all particles travel at almost the same speed. we can adiabatically lower the rf voltage. Proc. 1993 Part. 43 K. T. Symon and A. Terwilliger. and S. SYNCHROTRON MOTION energy particles. Raubenheimer. Jones. The phase-space area remains the same if we can avoid collective beam instability. Emma. particles drift and fill up the entire ring because the rotation frequency depends on the off-momentum variable.229) where 5 is the maximum momentum spread of a beam. P. The debunching rate is <j> = huior]S. Con]. Accel.R. in Proc. V. e. p. Conf.g. Kheifets. Sessler. Pruett. small ft and zero D(s) locations.M.M.R. particles can not cross the separatrix.H.W.326 CHAPTER 3.43 In a Hamiltonian system.. To reduce the momentum spread in the debunching process. phase displacement acceleration is usually employed. 1959).5 A was attained. K. on High-Energy Accelerators and Instrumentation. CERN Symp. Symon and K. To accomplish phase-space stacking.. The bunch shape will be distorted because particles of higher and lower momenta drift in different directions. The debunching time can be expressed as T d b = 2Tr/hLj0r]5.4 Debunching When rf systems are non-adiabatically turned off.
giving its way to a fully operational SPPS. 8th Int. which may lower the thresholds for transverse and longitudinal collective instabilities. The machine stopped operation in December 1983.4 GeV without loss of luminosity. Space charge induces potential well distortion and generates coherent and incoherent betatron tune shifts. Proc. V. Averill et al.D. This method has been successfully used to accumulate polarized protons at low energy cooling storage rings. The installation of low-/? superconducting quadrupoles in 1981 brought a record luminosity of 1. a double rf system has often been used to increase the synchrotron frequency spread. As early as 1971. the cooling stacking method can enhance polarized proton intensity by a factor of 1000 in the IUCF Cooler. p.4 x 1032 cm 2 s -1 .6 Double rf Systems Space charge has been an important limitation to beam intensity in many low energy proton synchrotrons. a newly injected beam accelerated by phase displacement can be moved toward the cooling stack to achieve a high cooling rate. 301 (CERN 1971). only particles inside the stable rf bucket are accelerated toward high energy. which enhances Landau damping in collective beam instabilities. Particlesflowalong lines of constant action. and their energies are lowered. that observed its first pp collision at the center of mass energy of 540 GeV on July 10. the circulating beams in ISR were accelerated from 26 GeV to 31.45 Similarly. BEAM MANIPULATION IN SYNCHROTRON PHASE SPACE 327 depends on rf frequency. the beam energy will be displaced upward in phase-space. In a storage rings with electron cooling or stochastic cooling. Conf. Thesis. antiprotons can be moved to the cooling stack for cooling accumulation. The change in energy is AE = LJoA/2n. To increase the threshold beam intensity. when a bucket is decelerated toward lower energy. Fast beam loss may occur during accumulation and storage when the peak beam current exceeds a threshold value. Particles outside the rf bucket are lost in the vacuum chamber because of the finite magnet aperture. Pei. For example. that can be handled by a low power rf system in the ISR. it may not be captured into the bucket if the rf bucket acceleration is adiabatic. Ph.46 This technique was also successfully applied to cure coupled bunch mode instabilities at ISR.V. 45A. with phase displacement acceleration. 1981. accelerated. . Indiana University (1993). By employing the phase displacement acceleration. and to accumulate antiprotons at antiproton accumulators. where 44A high current stack at the ISR has a momentum spread of about 3%. Phase displacement acceleration has been used to accelerate coasting beams in the Intersecting Storage Ring (ISR) at CERN44 and to compensate synchrotron radiation loss in electron storage rings. on High Energy Accelerators. an attempt was made to increase Landau damping by installing a cavity operating at the third harmonic of the accelerating frequency in the Cambridge Electron Accelerator (CEA) . Similarly.e. i. 46 R. What happens to the unbunched coasting beam outside the separatrix when an empty moving bucket is accelerated through the beam? Since the beam is outside the separatrix.
defined as the fraction of the circumference occupied by a beam or the ratio of average current to peak current.sin^ ls + ^ fsin L s + ^ ( 0 . 49 See S. on High Energy Accel. Baillod et al. p. E50. (3. IEEE Trans. and hi is the harmonic number for the primary rf system.230) where < is the phase coordinate relative to the primary rf cavity. Bramham et al. a double rf system with harmonics 5 and 10 was successfully used in the Proton Synchrotron Booster (PSB) at CERN to increase the beam intensity by 25 — 30% when the coherent longitudinal sextupole and decapole mode instabilities were suppressed by beam feedback systems. 221-251 (1995).M. Nucl. Rev. Lee et al.232) are Hamilton's equations of motion for a double rf system. and V\ and V2 are the voltages of the rf cavities. 5717 (1994). Conf. 9th Int. For example. Part. NS-30. 1974). Liu et al. PAC. 3499 (1983). Accel. Synchrotron equation of motion in a double rf system For a given particle at angular position 9 relative to the synchronous angle 9S. the peak current and consequently the incoherent space-charge tune shift are reduced.328 CHAPTER 3. .232) where the overdot is the derivative with respect to orbiting angle 9. Bramham et al.Y.231) where h2 is the harmonic number for the second rf system and <j>2S is the corresponding synchronous phase angle. 1490 (1977). R3349 (1994).sin02sj j . The equation of motion becomes 5 = ^ | jsin<£ . (CERN. the rf phase angle for the second rf system is 02 = fas -h2(69S) = <t>2s + ^ .47 Adding a higher harmonic rf voltage to the main rf voltage can flatten the potential well. Phys. J.0ls).48 At the Indiana University Cyclotron Facility (IUCF). P. Galato et al. the phase angle of the primary rf system can be expressed as 4> = <t>is-h1(6-6s). Phys. Therefore.49 A. Proc. Nucl. a recent beam dynamics experiment showed that with optimized electron cooling the beam intensity in the cooler ring was quadrupled when two rf cavities were used. than that of a single rf system. Liu et al. for a given DC beam current in a synchrotron. Since the equilibrium beam profile follows the shape of the potential well. (3. Equations (3. NS-24.Y..0ls)l . (3. (pis is the phase > / angle for the synchronous particle. SYNCHROTRON MOTION an additional cavity was operated at the sixth harmonic of the primary rf frequency. Sci. Similarly. a double rf system can provide a larger bunching factor. 47 P. IEEE Trans. Sci. E49. Rev. 1298 (1987). Proc.21) and (3.Y. J. G. 48 see J. 49.
cos(02s + h{(f> .V. the method presented in this section can be extended to more general cases with 0i s ^ 0 and 02S ^ 0. However.0). there are two inner buckets on the <j> axis. we study the double rf system with ft = 2.O) \<r | (±arccos(j).236) .^Vd<t>. Table 3.T.0 ls )) . r = -V2/Vu and <j)ls and (j>2s are the corresponding rf phase angles of a synchronous particle.cos 4>) + (<f>is .0) sin 0 l s -T-r [cos02s . the net acceleration is zero and the Hamiltonian becomes H = ^V2 + vs [(1 .233) + V(cf>)> where the potential V(<f>) is V{4>) = ^{(cos (j>is . The fixed points (0FP.235) are listed in Table V. The effective acceleration rate for the beam is AE = eVi(sincj)is — r sin02a) per revolution.cos 20)1 .h((j> .0) | (0. ft = ft2/fti.0) I UFP (TT.(1 . ISFP 0<r < i (0. Here.5: SFP and UFP of a double rf system. The action is J{E) = . 7T J-cj> (3. we study a stationary bucket with 0is = 02s = 0°. (3. To simplify our discussion. tonian is H=1-psV2 329 the Hamil(3.234) ft Here i/s = ^hleVi\T]\/2K/32Eo is the synchrotron tune at zero amplitude for the primary rf system.0) Since the Hamiltonian is autonomous. For r > I/ft. Action and synchrotron tune When the synchrotron is operating at 0 l s = 0 2s = 0.6.2].4>ls)sin02s]}. the Hamiltonian value E is a constant of motion with E/vs G [0. the conditions r = I/ft and ft sin 02s = sin</>is are needed to obtain a flattened potential well. BEAM MANIPULATION IN SYNCHROTRON PHASE SPACE Using the normalized momentum coordinate V = -(hi\r)\/vs)(Ap/p0). B. (±7r. Because the rf bucket is largest at the lowest harmonic ratio.^FP) (3.cos 0) .
the phase-space area is 2irJ. this formula is also valid for r > 0. C. ( l-2r + tl YT1* Thus the synchrotron tune becomes [26] Qs__^(l-2r) + 2tl + (l + 2r)tt vs 2(1+tl)K(k1) ' where K(k\) is the complete elliptic integral of the first kind with modulus [6-2M) 1 /(l-2r) + 2(g + (l+2r)«J In fact. The value E is related to 4> by E = 2vs(l . we obtain 9J 2(1+^) ri[ 2 d<j) = —-dt. The inner separatrix.2r cos2(</>/2)) sin 2 (0/2). which passes through the origin. r = —.. and the synchrotron tune is Qs = (dJ/dE)"1. intersects the phase axis at ±(j)h with cos(0b/2) = l/-v/2r. A given torus inside the inner bucket corresponds to a Hamiltonian flow of constant Hamiltonian value.5 case Changing the variables with t = tan .2). t0 = tan ..5 case For r > 0. L V2r J (3. The r < 0. The r > 0. where 0b is the intercept of the inner separatrix with the phase axis. the origin of phase-space V = <j> = 0 becomes a UFP of the unperturbed Hamiltonian. Let <j>\ and 0U be the lower and upper intercepts of a torus with the .330 CHAPTER 3.237) which is a monotonic increasing function of the ratio r. Two SFPs are located at V — 0 and 0 = ±<fo.5. SYNCHROTRON MOTION where 0 is the maximum phase angle for a given Hamiltonian torus. where cos(0f/2) = l/2r.5 and 4> > 0b. The bucket area «4b is A = 27rJ = 8k/rT2r-|--i=ln(\/rT2f+\/2r)l . The corresponding bucket area for the single rf system is Ab(r -» 0) = 16 (see Table 3. D.
and # = 2dt/(l +1 2 ).5.057^). BEAM MANIPULATION IN SYNCHROTRON PHASE SPACE 331 phase axis. Figure 3. and two small potential wells are formed inside the inner separatrix.5. dE nvsy/2f h dt ^(*5-t2)(t2-t?)' where tu = tan(0 u /2). the synchrotron tune becomes Qs = nt0 ^2{1+t20)K{k) = 7r(g/2i/ 5 ) 1 / 4 V2K{k) V* with modulus where to = tan(</>/2). For small amplitude synchrotron motion.21 shows the synchrotron tune as a function of the amplitude of synchrotron oscillation for various voltage ratios. Thus the synchrotron tune is Qs "= V277Ttu 1 ^/(l + ig) (1 + if) ^( fc 2> ' where modulus hi = \Jt\ — t2/tn.V. are valid only for the case with r = 0. In this case. Jtp (3. The derivative of the action with respect to the energy for the torus becomes 8J_ = V ( l + <g)(l + <?) rt.244) . where the synchrotron tune spread of the beam is maximized for a given bunch area. located at 0 = 117° (or E = 1.7786i/s. Action-angle coordinates Although analytic solutions for action-angle variables. the maximum synchrotron tune is Qs = 0.sin2(</>u/2). i = tan(<£/2). As r increases. = tan(^/2). the derivative of synchrotron tune vs action becomes large near the origin. a dip in QS(J) appears at the inner separatrix of inner buckets. where </>u = 0 and sin(<fo/2) = ^/sin2((/>b/2) . t. t0 = 0 and k0 = l/%/2. presented in this section. Since large tune spread of the beam is essential for Landau damping of collective beam instabilities. At r = 0.5. the system reduces to a single primary rf cavity. E. dQs/d<j) is very small or zero. an optimal rf voltage ratio is r = 0.5. the method can be extended to obtain similar solutions for other voltage ratios. When the voltage ratio is r > 0. At r = 0. where the synchrotron tune is Qs/vs = 1 at zero amplitude. Using the generating function F2(<M)= fvWW. Near this region.
dj-^JU r*ffP Q.. we obtain the angle coordinate as . and two SPPs are produced.21: The normalized synchrotron tune as a function of the peak phase <j> = 0 for various values of voltage ratio r. V ( W > the angle coordinate becomes (3-246) * ~ dJ ~~dJk BET ~ vJi'V _ dF2 _dE r*dV. Using the generating function ^(<M) = / .5._dF±_dE v.. SYNCHROTRON MOTION Figure 3. the center of the bucket becomes an UPP. (3. Note that when r > 0.236)._Qs [*d<t> where and the Jacobian elliptical function cnw is .332 CHAPTER 3.r+W dEd<p ~ us h V { ' where the action variable is given in Eq.
The formulas for small amplitude approximation are summarized as follows: elli cnu V . F. (3.8541. K' = A ^ / T ^ F ) . 2 50) \2J \2J 1 + [tan (0/2) cn«]2 V .250) remain valid provided that the modulus is replaced by kx of Eq. Small amplitude approximation A tightly bunched beam occupies a small phase-space area. we obtain </> = 2 arctan I tan . (3251) "s-^-fy. V) to the action-angle variables (J. (3. BEAM MANIPULATION IN SYNCHROTRON PHASE SPACE with q = e-«K'lK.249) V = . and a-p and a^ the rms conjugate phase-space coordinates.249) and (3..240) or k2 of Eq. We then obtain . or tan — = tan -cnu. (3 .^- T-^'-d-^^y J~^rte! -^r~ sin 2' + (3-252) ^^EoTT?^cos(2n l^ ^ ..250) or equivalently <j> where i = E/2vs. \ 2 ) II and from Hamilton's equation of motion. and q « e~*. I cn% . and 333 ^wir^wy' From Eq. Let A be the rms phase-space area of the bunch. Eqs. %))) can be accomplished by using Eqs.^ S ^ ^ " 1 ' 2 " ^ (-5) 32 3 where k ss l/%/2. Thus the transformation of the phase-space coordinates (<f>.cnu .248) to (3. (3.5. When the voltage ratio is not 0. K = K{k) « 1.242).2 v ^ s i n (+) tan (+) ^ ^ . we get (3-248) (3.247).V. (3. (3.
Harding. The beam may be susceptible to collective instabilities. E55. V.7 The Barrier RF Bucket Bunch beam gymnastics have been important in antiproton production.A. The demand for higher beam brightness in storage rings and higher luminosity in high energy colliders requires intricate beam manipulations at various stages of beam acceleration.Y. Nucl Sci.J. A most critical situation arises when the synchrotron amplitude of the beam reaches the region where Qs is maximum or near the rf bucket boundary. NS-34. The sum rule can be used to identify the region of phase-space that is sensitive to rf phase modulation (see Exercise 3. and A. particle motion near the center of the bucket may become chaotic because of overlapping resonances.1). IEEE Trans. the chaotic region is bounded by invariant tori.103). the Recycler would also accumulate newly produced. 1025 (1987). V. NS30. Ng. Sci. Phys. The extreme of the flattened rf wave form is the barrier bucket. accumulation. and J.E. a Recycler has been built.A. it may be of concern that large amplitude particles can become unstable against collective instabilities. Griffin. a flattened rf wave form can be employed to shape the bunch distribution in order to alleviate space-charge problems in low energy proton synchrotrons and to increase the tune spread in electron storage rings. Lee and K. and the effect on beam dilution may not be important. 5992 (1997). S. However. J. To maintain the antiproton bunch structure. Expanding V in action-angle coordinates as V = En fn{J)ejnt.Y. Ankenbrandt. Rev.334 CHAPTER 3. When an rf phase or voltage noise is applied to beams in a double rf system. and feedback systems may be needed for a high intensity beam that occupies a sizable phase-space area. phasespace painting. MacLachlan. multi-turn injection. SYNCHROTRON MOTION The rms tune spread of the beam is then AQ'7^{^T»G. IEEE Trans.3. where the tune spread is small. which would recycle unused antiprotons from the Tevatron.50 For achieving high luminosity in the Fermilab TeV collider Tevatron. Nucl. a barrier rf wave form can be used to confine the 50See J. we find that the strength functions fn(J) satisfy the sum rule shown in Eq. beam coalescence for attaining high bunch intensity. Bharadwaj. Griffin. (3. J.250). D. . In particular. At the same time. etc. cooled antiprotons from the antiproton Accumulator. Since dQ/dJ = 0 occurs inside the bucket. MacLachlan. The recycled antiprotons can be cooled by stochastic cooling or electron cooling to attain high phase-space density. Sum rule theorem and collective instabilities (3255) The perturbing potential due to rf phase modulation is linearly proportional to V of Eq. (3. C.K. 3502 (1983). Moretti.
For example. and a /"\ The barrier rf wave is normally generated by a solid state power amplifier. The rf wave form is applied to a wideband cavity with frequency hf0. we . which has intrinsic wide bandwidth characteristics. /3c and Eo are the speed and the energy of a synchronous particle. Acceleration or deceleration of the beam can be achieved by employing a biased voltage wave in addition to the bunchconfining positive and negative voltage pulses. a pulse width To. BEAM MANIPULATION IN SYNCHROTRON PHASE SPACE 335 beam bunch and shape the bunch distribution waiting for the next collider refill. its energy can increase or decrease depending on the sign of the voltage it encounters. and / 0 is the revolution frequency of synchronous particles. and To is its revolution period. Equation of motion in a barrier bucket For a particle with energy deviation AE.22 shows some possible barrier rf waves with half sine. Thus the wide bandwidth rf wave can create a barrier bucket to confine orbiting particles. A. The required bunch length and the momentum spread of the beam can be adjusted more easily by gymnastics with barrier rf waves than with the usual rf cavities. and square function forms. the fractional change of the orbiting time AT/To is — To ~ V i V -n— f3 256) ( 56) where rj is the phase slip factor.T. orbiting particles see no cavity field in passing through the cavity gap. When a particle travels in the time range where the rf voltage is not zero. Most of the time.. Without loss of generality. the accelerator is divided into stable and unstable regions. A . and integrated pulse strength / V(r)d. rf wave is characterized by a voltage height Vo. These wave forms are characterized by voltage amplitude V(r). triangular.22: Possible wave forms for the barrier bucket. An arbitrary voltage wave form can be generated across a wideband cavity gap. pulse gap T2 between positive and negative voltage pulses. The barrier pulse gap Ti.V. the integrated pulse strength for a square wave form is VoTi. Figure 3. pulse duration 7\. Figure 3. where h is an integer. The effect on the beam depends mainly on the integrated voltage of the rf pulse.. In this way.
„ 1 fT-2/2+W ^=r{AE)2 = -f eV(r)dr. Since the barrier rf Hamiltonian is time independent.257) and (3. the wave form of the barrier bucket is reversed. an invariant torus has a constant Hamiltonian value. The equation of motion for the phase-space coordinate r is Passing through a barrier wave. For T] > 0. . all physical quantities depend essentially on the integral / V(r)dT. dJ^r B. The time coordinate for an off-momentum particle —r is given by the difference between the arrival time of this particle and that of a synchronous particle at the center of the bucket. the particle gains energy at a rate of .258). SYNCHROTRON MOTION consider here synchrotron motion with r\ < 0. We define the W parameter for a torus from the equation below: hi . Thus.336 CHAPTER 3.2— (^A where Tc is + 4T (3 262) Clearly. the essential physics is independent of the exact shape of the barrier rf wave.257) and (3. Synchrotron Hamiltonian for general rf wave form From the equations of motion (3. (3.258). we obtain the general synchrotron Hamiltonian for an arbitrary barrier rf wave form: H=-2h^2-T-SeV{T)dTThus the maximum off-energy bucket height can be easily derived: (2B2En rT2/2+Ti \1/2 (3-259) where 7\ is the width of the barrier rf wave form.^ • <3-258> at l0 The equations of particle motion in a barrier rf wave are governed by Eqs. (3.261) The synchrotron period of a Hamiltonian torus becomes T .
^ where u>0 = 2TT/0 is the angular revolution frequency of the beam.T2/2<lr\<{T. The mathematical minimum synchrotron period of Eq. we consider only the square wave forms with voltage heights ±V0 and pulse width Ti in time. and To is the revolution period of the beam. it gains (loses) an equal amount of energy eVQ. separated by a gap of T2.V.264) Thus the phase-space trajectory for a particle with maximum off-energy AE is f (AE)2 if \T\ < T 2 /2 ^ 2 = {{AEf-(\r\-T{)^^ . d(AE)/dt = ±eV0/TQ every turn. The phase-space area of the invariant phase-space ellipse is ^ = 2 T 2 A ^+3^^(A^3- (3-266) The maximum energy deviation or the barrier height that a barrier rf wave can provide is where 7\ is the pulse width of the rf voltage wave. When the particle passes through the cavity gap at voltage ±V0. The bucket height depends on VQTJ. which is the integrated rf voltage strength / V(T)CLT./2)+Tl. (3. The number of cavity passages before the particle loses all its off-energy value AE is JV=^L (3. The synchrotron period is A£b=hrTj (eV0T12pE0V/2 ' (3-267) for particles inside the bucket. The phase-space ellipse is composed of a straight line in the rf gap region and a parabola in the square rf wave region.e. BEAM MANIPULATION IN SYNCHROTRON PHASE SPACE C. Square wave barrier bucket 337 Since the effect of the barrier rf wave on particle motion depends essentially on the integrated rf voltage wave.268) is S'min=l T =2 w l ^ J + 4 ^ T o s \v\eV0 ) ' T2(p*E0\ \AE\ (-6) 328 (3'269) and the corresponding maximum synchrotron tune is _(T1WV^V" \l2 6lfi'-tiQ ) . i.
TuT2). Hamiltonian formalism The Hamiltonian for the phase-space coordinates (r. Note that if T2 > 4Ti.3 Hz.23 shows va vs AE with Fermilab Recycler parameters Eo = 8. This feature is similar to that of a double rf system. SYNCHROTRON MOTION Note here that TTTO/(16T2) plays the role of harmonic number h of a regular rf system.^)0(r .. Lee et al. the synchrotron tune is peaked at an off-energy AE smaller than the bucket height AE\. D. The synchrotron tune is a function of the off-energy parameter AE given by *-**-i/i||(1+« [Ill's)"'- w Note that when the rf pulse gap width decreases to T2/T1 < 4. -yT = 20. AE) is Ho = ^ r ( A £ ) where MT.338 CHAPTER 3.2.| ) + ( r Tl + '^) (3.5 us.. . Parameters used are EQ = 8. (3.7 x 10"5 for T2 = Tu i. the synchrotron frequency is 3.51 Figure 3. and Ti = 0. For example. J.9 GeV.8 kHz. the synchrotron tune is a monotonic function of AE. Liu et al. 7\ = 0.e. Rev.23: Synchrotron tune vs off-energy parameter AE.TUT2) 2 + ^^fO(T.Y.4.Y. Phys.| ) ] . the synchrotron tune becomes peaked at an amplitude within the bucket height. /o = 89.8 kHz. 5717 (1994). On the other hand. Figure 3. and 8. and T2/Ti = 1. E50. if T2 < 4Ti. /„ = 89.5 /JS.272) = -l + Yi[(r + Ti + ~)e(r + T1 + ^)-(r+^)9(r _ ( r _ Tl)0{T .9 GeV. E49. -yT = 20. i/s>niax = 3. Phys. Vo = 2 kV.7. Vo = 2 kV.Tx . 51 S. R3349 (1994).273) .7. Rev.
B = 2nJ = (2T2 + ^Ti) AEh. AE) to the actionangle variable can be achieved by using the generating function F2(J. J—t (3. and W = 7\ is associated with particles on the bucket boundary. For a constant Ti.e. W has the physical meaning that it is equal to the maximum phase excursion \T\ in the rf wave region.TuT2)dr.T)= fT AEdr.274) The parameter PV with a dimension of time is related to the Hamiltonian value by *-f»^K' <3-275> For a given Hamiltonian torus.277) V(T)CIT Again. E./ AEdr = i R p 27T J 2ir \ 7r|r?| / /W + Mr. Action-angle coordinates = Canonical transformation from the phase-space coordinates (r. i. The action of a Hamiltonian torus is J = i. \ o / (3. Therefore W = 0 corresponds to an on-momentum particle. T2 and Vo. J " (3. the bucket area depends only on the integrated rf voltage strength / VQTX.V. BEAM MANIPULATION IN SYNCHROTRON PHASE SPACE 339 Here 9(x) is the standard step function with 9(x) = 1 for x > 0 and 9(x) = 0 for x <0. the Hamiltonian Ho is a constant of motion. The action for a particle torus inside the bucket is The bucket area is related to the maximum action with W = 7\. The angle variable ip is .278) where f = W + (T 2 /2).
340 CHAPTER 3. AE < 0 2ir\/W / 1 4Vc + 2V. The momentum compaction factor is ac = 0. (a) Assuming that the rf voltage is ramped according to Vrf (i) . SYNCHROTRON MOTION The integral can be evaluated easily to obtain ^mJW A + + \T* + T \1-W-\T2<T<-\T2. and that the motion of a stable particle orbit in the barrier bucket with 7 < 0 is clockwise. We choose the convention of ip > 0 corresponding to ? a clockwise motion in synchrotron phase-space. The resonance strength function decreases slowly with mode number. Active compensation may be used to compensate the effect of rf phase modulation. .W . . stable bucket area may be reduced. The resonance strength functions and their associated sum rules can be derived analytically.V0 + {V.V0) U^ 52 See . Lee and K. T!]. The rf system operates at h = 1 with a maximum voltage 240 V.5 1. Note that 2ipc + ips = n for one half of the synchrotron orbit.52 Exercise 3.6191. 5992 (1997). if 2 c + A .^ 7 w iW V I 2^ A£>0 1-K\fW 3A + A + I 1 + ^ + T2 + 4W\]W+2T2 2T2 < r <W+±T2: AE < 0 nTtW {lT2 ~ T) -5 T 2 < ^ < \T2. it is important to avoid a large reduction of stable phase-space area. The rf phase and voltage modulation can severely dilute bunch area if the modulation frequency is near the top of the synchrotron tune and its harmonics.Y.T2 + 4W\]W + -T2 + r if . such as rf noise. Phys. Rev. S.AE>0 T^hw(T+lT2) + if-|T 2 <r<lT 2 . where ^ = l^w> ^ = T7^W <3-280) are respectively the synchrotron phase advances for a half orbit in the rf wave region and in the region between two rf pulses. AE < 0. The rf phase modulation due to orbit length modulation resulting from ground vibration can be important. . The circumference is 17. When a perturbation. t e [0. The Cooler Injector Synchrotron (CIS) accelerates protons from 7 MeV to 200 MeV in 1. The momentum spread of the injection linac is about ±5.AS>0 lT2~T ~T if if l T 2<r<W+iT 2 . Because the solid state amplifier is a low power device.\T2 < T < -\T2.Y.0 x 10~3.0 Hz. is applied to the barrier rf system.2^) .364 m. E55. Ng.
show that the bunch length in the final step is where initial is the initial bunch length in orbital angle variable.2. it is given by (E] -C<JsP> where Js is the damping partition number with Js w 2 for separate function machines.4 m. the rf gymnastics for bunch rotation is performed by adiabatically lowering the voltage from Vi to V2 and suddenly raising the voltage from V2 to V\ (see also Exercise 3.EXERCISE 3.5 341 where VQ and V\ = 240 V are the initial and the maximum final rf voltages. and find the maximum B. find the frequency ramping relation of the rf cavity. 2. the harmonic number is h = 588.15 ns with an initial voltage V\ = 4 MV. Using Eq. and the phase-space area is A = 0.4. (3.1. and vs\ and uS2 are the synchrotron tune at voltages V\ and V2.05 eV-s for 6 x 1010 protons. Neglecting wakefield and other diffusion mechanisms.43). (b) If the magnetic field of a proton synchrotron is ramped according to B(t) = B0+ (£ . -Bo).58) and conservation of phase-space area. (3. Calculate the adiabaticity coefficient of Eq.8. In proton accelerators. Ti is the voltage ramp time. For a flattened potential well in the double rf system with (6ls = <j>2S = 0.83xl0-i3m . where the circumference is 3319. For an isomagnetic ring. and c 4mc 32V3 me Using the electron storage ring parameters listed in Exercise 3. and the rf bucket height during the rf voltage ramping as functions of time t with VQ = 10 V and T\ = 10 ms. calculate the phasespace area in eV-s. show that the Hamiltonian for small amplitude synchrotron motion is 3Cy» = J5 A = 3. Apply the bunch rotation scheme to proton beams at E = 120 GeV in the Fermilab Main Injector.5). 4. The energy of the secondary antiprotons is 8.2~\ (B. the transition energy is yT = 21.9 GeV. Find the voltage V2 such that the final bunch length is 0. h] where Bo and B\ are magnetic field at the injection and at the flat top. Change these parameters to see the variation of the adiabaticity coefficient. If the acceptance of the antiproton beam is ±3%. what is the phase-space density of the antiproton beams? 3. Verify Eq. and t = 0 and t = ti are the time at the beginning of ramp and at the flat top. te [0.232) and derive the Hamiltonian for the double rf system. what is the phase-space area of the antiproton beams? If the antiproton production efficiency is 10~5. the momentum spread of an electron beam in a storage ring is determined mainly by the equilibrium between the quantum fluctuation of photon emission and the radiation damping. (3.
We solve the synchrotron motion for the quartic potential below.-V»-(^)d.j .85407468 is the complete elliptical integral with modulus k = l/v/2. h is the ratio of the harmonic numbers.342 CHAPTER 3. Compare your results with that of Eq. the Hamiltonian value E is a constant of motion. 41 is the amplitude of the phase oscillation.253) for the h = 2 case.J)= ( Td<t>. Show that the action variable is related to the Hamiltonian value by where K = K{J\) = 1. sn. . (b) Show that the synchrotron tune is (c) Define the generating function F2{<I>. and the independent "time" variable is the orbital angle 6. (3.(^Hi). SYNCHROTRON MOTION where b = (h2 — l)/24. (a) Since the Hamiltonian is time independent. where en. and dn are elliptical functions with modulus k = l/\/2. Jo and show that the solution of the synchrotron motion is given by (IK 1\ <t> = 4> en ( — ip\. .
defined as the ratio of the square of the rf voltage seen by the beam to the dissipated power. Some fundamental parameters of cavities are transit time factor. V-E = 0. but a smaller gap can cause electric field breakdown due to the Kilpatrick limit (see Sec. Beam loading and Robinson dipole-mode instability will be addressed. The transit time factor reduces the effective voltage seen by passing particles.VI FUNDAMENTALS OF RF SYSTEMS 343 VI Fundamentals of RF Systems The basic function of rf cavities is to provide a source of electric field for beam acceleration.3) reflects the finite passage time for a particle to traverse the rf cavity. Maxwell's equations (see Appendix B Sec. Properties of pillbox and coaxial-geometry cavities will be discussed. We may reduce the accelerating voltage gap to increase the transit time factor.281) where e and \i are dielectric permittivity and permeability of the medium. The longitudinal electric field must be synchronized with the particle arrival time. Further properties of high frequency cavities used in linacs will be discussed in Sec. VI. Thus a cavity with a higher Q-factor has a higher shunt impedance. V. coaxial geometry is commonly employed. Generally. VIII. 1 Pillbox Cavity We first consider a cylindrically symmetric pillbox cavity [18] of radius b and length I (left plot of Fig. of a resonance cavity will be defined and discussed. In this section we examine some basic principles in cavity design. and the filling time. VxB =^ . V) for electromagnetic fields inside the cavity are V . The quality factor (Q-factor) depends on the resistance of the cavity wall and the characteristic impedance of the rf cavity structure. The EM waves in the cavity can conveniently be classified into transverse magnetic (TM) . shunt impedance. 3. the shunt impedance. At lower frequencies. is an important figure of merit in cavity design. pillbox cavities with nose-cone or disk loaded geometry can be used. (3. Vxfi = ~ (3. and quality factor. For cavities operating at a few hundred MHz or higher. Some fundamental characteristic parameters. where only electromagnetic fields at resonance frequencies can propagate. the Q-factor. while the accelerating field varies with time. At a given resonance frequency.B = 0. the ratio of shunt impedance to Q-factor depends only on the geometry of the cavity and the characteristic impedance. It is defined as the ratio of the rf power stored in the cavity to the power dissipated on the cavity wall.24). Cavities are classified according to their operational frequencies. Resonance cavities.3). The shunt impedance. are a natural choice in rf cavity design. we will show that a resonance cavity can be well approximated by an equivalent RLC circuit. The transit time factor of Eq.
ks.344 CHAPTER 3. the TM standing wave modes in cylindrical coordinates (r.283) Similarly the radial wave number is determined by the boundary condition with Es = 0 and E. for which the longitudinal electric field is zero.f. the electromagnetic fields satisfy the boundary condition: n x E = 0. Assuming a time dependence factor e?"* for electric and magnetic fields. h • H = 0. The longitudinal wave number k is determined by the boundary condition that Er = 0 and £ 0 = 0 at s = 0 and t. V) 53 Es = A k2 Jm{krr) cos rruj)cos ks Er = — AkkT J'm{kTr) cosm(t>sinks E.284) standing wave can be decomposed into traveling waves in the +s and -s directions. There is no tangential component of electric field.l.mn = 3jy. (3. Left: pill-box cavity with disk load. are zeros of Bessel functions Jm(jmn) = 0.P = Y> P = 0. . i. The TM modes are of interest for beam acceleration in the rf cavity. <j>. Figure 3. SYNCHROTRON MOTION mode. ' Bs = 0 (3'282) BT = -jA(mui/c2r) Jm{krr) sin mcj) cos ks .p — A (mk/r)Jm{kTr) sinm(j>sinks . and UJ/C = Jk2 + k2.24: Schematic drawings of high frequency cavities.2. m is the azimuthal mode number. where j m n . kr are wave numbers in the longitudinal and radial modes. i.---. k. listed in Table V. and no normal component of magnetic field. kr.2. = 0 at r = b.e. . these high frequency cavities have similar basic features. 53A (3. right: nosecone cavity. for which the longitudinal magnetic field is zero. and transverse electric (TE) mode.e. In an ideal acceleration cavity. B$ = -jA (bjkr/c2) J'm{krr) cos m<f> cos ks where A is a constant. Although their names and shapes axe different. s = 0 and I correspond to the beginning and end of the pillbox cavity. s) are (see the Appendix B Sec. where h is the vector normal to the conducting surface.
To slow down the phase velocity. fcoio = ^ . p) is 345 kmnp = ^mn + k?. (3.25 shows an example of a coaxial cavity. VIII. it requires a very small amount of ferrite for tuning. the cavity is loaded with one beam hole with an array of cavity geometries and shapes. The EM field of the lowest mode TMoio (kSiP = 0) is Es = EoJo(kr). All cavities convert TEM wave energy into TM mode to attain a longitudinal electric field. VI. FUNDAMENTALS OF RF SYSTEMS The resonance wave number k for mode number (m.285) The lowest frequency mode is usually called the fundamental mode.25: Schematic drawing of a low frequency coaxial cavity. The TEM wave in the coaxial wave guide section is converted to the TM mode at the cavity gap through the capacitive load. B* = j ^ J i ( f c r ) . The material is made of double oxide spinel Fe2O3MO. = J%" + P~ = ^ = ^L.24 shows high frequency cavities with disk and nose-cone loaded geometries.8 cm. The phase velocity. where M can . Other resonance frequencies are called high order modes (HOM). Note that the TEM wave is matched to a TM wave at the capacitive loaded gap for the acceleration electric field. n. where the length is much larger than the width. We will return to this subject in Sec. (3. Thus beam particles traveling at speed v < c do not synchronize with the electromagnetic wave. Many different geometric shapes are used in the design of high frequency cavities. Figure 3. Figure 3.2 Low Frequency Coaxial Cavities Lower frequency rf systems usually resemble coaxial wave guides. for the traveling wave component of the TMOio mode with kSiP = 0 is infinite. a 3 GHz structure corresponds to A = 10 cm and b — 3. A= ^ . Such a structure is usually used for high frequency cavities.286) For example. w//cSlP. When the cavity is operating in 50 to 200 MHz range. The art (science) of cavity design is to damp HOMs without affecting the fundamental mode. Figure 3. but their function and analysis are quite similar.54 When the cavity 54Ferrite is magnetic ceramic material that combines the property of high magnetic permeability and high electric resistivity.VI.
Touch-Tone telephone.3) I(s. At lower rf frequency. and £ is the length of the structure. Neglecting the flux penetration in the conductor.346 CHAPTER 3. 2173 (1983). Assuming a time dependent factor e?ui. Ferrites are commonly used in frequency synthesis devices. the rf cavities must be ferrite loaded in order to fit into the available free space in an accelerator. V{s. kickers. + 2?r ^ 1 + i TX 4?r V I r2 C=^-y ln^/n) (3. ferrite rings in the cavity are needed to slow down EM waves. Let ri and r-i be the inner and outer radii of a wave guide. the TEM wave guide is usually ferrite loaded with magnetic dipole or quadrupole fields for bias frequency tuning. Cr.291) be Mn.6. The characteristic impedance of a wave guide is Zc = Rc = JL/C = LjL»-l-<[^\n-. To understand the capacitive loading that converts the TEM wave into the TM wave at the cavity gap. we consider an ideal lossless transmission line. we study the rf electromagnetic wave in the wave guide. Application in accelerator can be found in induction linac. Smythe. t) = Io cos ks + j(V0/Rc) sin ks. frequency tuning for rf cavities. the resonating frequency is w= Vrc = ijw * Tfifo' 47"7" • /[MHz]0i//* o (3'288) where e = e0 is assumed for the dielectric permittivity.Vo cos ks + jI0Rc sin ks.290) Now.ca is the skin depth of flux penetration.289) For a cavity operating beyond 20 MHz. Thus the required cavity length for the fundamental mode is t = . t) . ferrite can be used only for tuning purposes. etc. IEEE Trans. NS-30. Ni..When a biased field is applied to the ferrite core. Sci. the magnetic permeability can be tuned to match the change of the particle revolution frequency. The inductance and the capacitance of the concentric coaxial wave guides are L = ^ l n r. (3.55 Using the wave guide transmission line theory. low loss microwave devices. where the electromagnetic field has no longitudinal component. 55 W. 5skin = ^2/ujfj.^ = = ^V^/Mo (3.287) where /ic is the permeability of the conductor. etc. the current and voltage across the rf structure are (see Exercise 3. characteristic properties of rf systems can be analyzed. (3. At frequencies below tens of MHz. etc. . Zn. Typically the magnetic permeability of ferrite is about 1500/io. Nucl.R. SYNCHROTRON MOTION is operating at a few MHz range.
£T = A/4: the length of the coaxial cavity is equal to 1/4 of the wavelength of the TEM wave in the coaxial wave guide.e.293) V(s.294). For example. and I is the length. (3. and C gap .294) becomes k£T = TT/2.e. Shunt impedance and Q-factor (3. for a given £T:RC. Thus the quality factor becomes Q = £ = !£„ * ™ _ £ h I*. a total capacitance of 10 pF implies that C gap = 20 pF.t) = I0{t)cosks. I{s. FUNDAMENTALS OF RF SYSTEMS 347 where s is the distance from one end of the transmission line. and the wave number of the line is 2TT _ w For a standing wave. ri and r-i are the inner and outer radii of the transmission line. (3. i. the boundary condition at the shorted side is V = 0 at s = 0. where the end of the transmission line is shorted.VI.t) = +jI0(t)Rcsinks. VQ and IQ are the voltage and current at the end of the line where s = 0. The gap voltage of the coaxial cavity is Zin + Zgap = 0. In principle. The lowest frequency is called the fundamental TEM mode. tan kl (3. the resonance condition of Eq. and Cgap is the capacitance of a half gap. The length of the line is chosen to match the gap capacitance at a required resonance frequency: = -. Z gap = — j/(wC gap ) is the gap impedance. The line input impedance becomes Zin = j ^ . The length £T of one-half cavity.297) . there are many resonance frequencies that satisfy Eq. Thus such a structure is also called a quarter-wave cavity. (3.= +JR. or tan Uv = Vrt = +jI(0)Rc sin k£r = + j 4 = f t vl + g A. (3. u> is the rf frequency. (3. i. the gap capacitance.294) w/i c c gap g where g is the geometry factor of the cavity.295) The surface resistivity Rs of the conductor and the resistance R of a transmission line are ^ = V!7' R = ~2^in+72)> (3 ' 296) where a is the conductivity of the material.292) The line impedance is inductive if kl < ir/2. the biased current. and the external loading capacitance can be designed to attain a resonance condition for a given frequency range. If the loading capacitance is small.
The total power of dissipation P& is ^ = IH^R JK cog2 x dx = J ! i ^ _ [ ( 1 + f) ^ .e. 0.05 11000 An important quantity in the design and operation of rf cavities is the shunt impedance. The input impedance of the wave guide is represented by an equivalent inductance.Bottom: Plot of the impedance of Eq. The wave guide is loaded with capacitive cavity-gap and real shunt impedance. 298) Table 3. As the gap capacitance increases.i g + g]_ (3 . This is the resistance presented by the structure to the beam current at the resonance condition. i. If Cgap = 0.300) •K L(l + ff2)cot 1g + g\ where the expression in brackets is a shunt impedance reduction factor due to the gap capacitance loading. Figure 3. i. the shunt impedance becomes (3. and <rcu ~ 5.e. .348 CHAPTER 3. 5 = 0.2 lists typical Q-factors for a copper cavity as a function of cavity frequency. where we have used In fo/ri) ~ 1 a n d r\ « 0.05 m.301). The resonance frequency and the Q-factor of the equivalent RLC-circuit are UJT = 1/VLeqCeq and Q = iish^Ceq/ieq.8 x 107 [flm]"1 at room temperature.05 3500 I 100 6.05 _Q 1100 I 10 21. The solid lines are the real and the imaginary impedances for Q=l. n 0.6: Some characteristic properties of copper RF cavities / [MHz] 11 <5skin H 66.26: Top: Schematic drawing of an equivalent circuit of a cavity. the shunt impedance decreases.6 0.299) #sh = . tf* = ~fFor a transmission line cavity. (3. (3.M • 2 ^ !-i _L ^ Q . the capacitance loading factor is 1. and the dashed lines are the corresponding impedances for Q=30. SYNCHROTRON MOTION Table VI.
becomes Z=(~+JuCeq + -±-) = .VI.' Ws = WsOe-"^. we obtain ^JT = .304) The time for the electric field or voltage to decay to 1/e of its original value is equal to the unloaded filling time 2Q Tm = — .294) implies that the reactance of the cavity is zero on resonance. B. represented by a parallel RLC circuit. where Ws is the stored energy. ^ --^hCosVe"^.305) . Q = Rsh^/Ceq/Leq.301) for Q = l and Q=30. Accelerator cavities usually contain also many parasitic HOMs.297) is equal to the ratio of the stored power P s t to the dissipated power P^. i. (3.301) h where Leq and Ceq are the equivalent inductance and capacitance.p o = . The right plot of Fig. the cavity gap presents a capacitance and resistive load shown in Fig. uiT = (L^C^)" 1 / 2 .. At the resonance frequency wr particles see a pure resistive load with an effective resistance Rgt. and ^ = tan _ 1 2QK-a^) (3302) Here tp is the cavity detuning angle. Each HOM has its shunt impedance and Q-value. 3.The rf system becomes capacitive at w > w n and inductive at w < wr. where Z-lTi = jwL eq .e. and the effective impedance is R^.^ W . (3. (3. and lowering the Q-factor of these sidebands are very important in rf cavity design and operation. (3. The impedance of the rf system. detuning.. and Ceq = Cgap.26. Using energy conservation. Correction. If the frequency of one of the HOMs is equal to that of a synchrotron or betatron sideband.26 shows the real and imaginary parts of the impedance of Eq. Filling time The quality factor defined in Eq.The matching condition of Eq. the beam can be strongly affected by the parasitic rf driven resonance. (3. 3. (3. FUNDAMENTALS OF RF SYSTEMS 349 From the transmission-line point of view.
.300. the rf voltage is the time derivative of the total magnetic flux linking orbit (Faraday's law of induction). The dissipation power q. By adjusting the bias current and the bias field direction.306) where A = lr\ In(r2/ri) « £(r2 — ri) is the effective area of the ferrite core and Bi is the peak magnetic flux at r = r x . At an rf frequency above tens of MHz. The peak magnetic flux in Eq. The shunt impedance of an rf structure is the resistance presented to the beam current at the resonance condition.e. where A is the effective area of the ferrite core. Frequency tuning can be achieved by inducing a DC magnetic field in the ferrite core. Assuming that the magnetic flux density varies as \/r in a coaxial structure and assuming a sinusoidal time dependent magnetic flux density. ^b ~ T P ~ ^^d p \Vrt\ = ~ 5 ~ ~ ~ KcQ' ^d RcPst r> n (3. Since the Q-value of ferrite is relatively low. SYNCHROTRON MOTION C. (3.308) which alone is not adequate for the required frequency tuning range. Qferrite « 50 . (3. power dissipation in ferrite is an important consideration. i. Note that increasing the outer radius of the ferrite core is an inefficient way of increasing the rf voltage.350 CHAPTER 3.rfBM „ Vr] in a cavity should be efficiently removed by cooling methods. Qualitative feature of rf cavities Qualitatively.307) /q on^l where Pst is the power stored in the cavity and Pj is the dissipated power. The quality factor Q of the ferrite loaded accelerating cavity is dominated by the Q value of the ferrite material itself. i. the effective permeability for rf field can be changed. using an external magnet or bias current to encircle the ferrite without contributing a net rf flux. we need a large volume of ferrite to decrease the flux density in order to minimize energy loss. the cavity size (normally 1/2 or 1/4 wavelength) becomes small enough that a resonant structure containing little or no ferrite may be built with significantly lower power loss at Q « 104 with a narrower bandwidth. we obtain Kf = wrf^ / 2 Jri B{r)dr = uJlf£B1rl In — « UJV(BIA. 7"i (3.e.306) depends on the ferrite material. To obtain high rf voltage at low frequencies.
It accelerates protons (or light ions) from 7 MeV to 225 MeV. . where / is the surface current and R of Eq. The cavity is a quarter-wave coaxial cavity with heavy capacitance loading. The fi of the ferrite material is changed by a superimposed DC magnetic field provided by an external quadrupole magnet.290) is about 60 fi. The external quadrupole magnet provides biased field in ferrite rings to change the effective permeability. ten Phillips 4C12 type ferrite rings are used. Example: The rf cavity of the IUCF cooler injector synchrotron The IUCF cooler injector synchrotron (CIS) is a low energy booster for the IUCF cooler ring.296) is the surface resistance of the structure. resonance frequency can be tuned only by a slotted tuner or by physically changing the size of the cavity. 3.27). Analysis of such a field shows that the field direction is mostly parallel to the rf field. The cavity can still be considered as a coaxial wave guide. i. the main portion of the rf cavity can be made of copper or aluminum with a small amount of ferrite used for tuning.56 To make the cavity length reasonably short and to achieve rapid tuning. The stored power is I2RC and the power dissipation is I2R. Figure 3. where the biased fields in the ferrite rings are perpendicular to the rf field.287) to (3. D. At frequencies above a few hundred MHz.e. (3. The ferrite rings return the magnet flux between the two adjacent quadrupole tips (Fig. required for synchrotron acceleration. FUNDAMENTALS OF RF SYSTEMS 351 At frequencies of a few hundred MHz. private communications. Pei. except near the tips of the quadrupole.306) remain valid. (3. where adequate and efficient rf power sources are commercially available. The characteristic impedance Rc of Eq. In the working 56A. and Eqs. (3.27: The cross section (left) and the longitudinal view of the CIS rf cavity. along the azimuthal direction.VI.
the number of windings is usually limited to no more than a few turns because of possible resonance and arcing. The CIS cavity is thus able to operate with a 10:1 frequency ratio with high efficiency. rather than B/H. The phenomenon of gyromagnetic resonance associated with perpendicular biasing. It usually takes 1000 A or more to bias such a cavity. the energy loss due to the passage of an rf gap. needs to be considered and avoided in the design of the cavity. is At/ = 11 J(w) \2Z(oj)dtJ = 2krq2. E. is determined by dB/dH. it has been difficult to feed the rf generator power to the cavity efficiently because of the high voltage standing wave ratio (VSWR) caused by impedance mismatch (see Appendix B. The advantages of using an external biasing magnet include making it possible to separate the rf field from the biasing elements.5 MHz or 1 . the power loss in ferrite material varies (usually increasing as frequency increases). as in perpendicular analysis.10 MHz by varying its loading capacitor. (3. and the rf field in the cavity will not be affected by the biasing structure. As a result. to first order in wave propagation. For example. the strength of the biasing magnet in each section can be adjusted by the coupling loop.352 CHAPTER 3. and the input impedance can be maintained constant to match the transmission line impedance of the rf amplifier. The loading capacitor reduces the length requirement of coaxial cavities and can also be used conveniently to switch frequency bands. . SYNCHROTRON MOTION region of the ferrite biasing strength. As the frequency changes. represented by an RLC resonator model. The coupling coefficient can be used to compensate the change in the gap impedance.310) where is the loss factor of the impedance at frequency wr. Wake-function and impedance of an RLC resonator model If we represent a charged particle of charge q by I(t) = qS(t) = (1/2TT) / qe?utdu). This means that the passing particle loses energy and induces a wakefield in the cavity.V. In the CIS cavity this problem was solved by dividing the ferrite rings into two sections. the effect of the perpendicular component on ferrite rf-fi is small.3). however. the bias supplies for these external quadrupole biasing magnet type cavities are rated at only 20 A. If the biasing field is to be produced only by a bias winding threaded through the rf cavity.5 . In CIS and the IUCF cooler ring. the CIS cavity can be operated at 0. due to the higher impedance of a resonant structure and optimized amplifier coupling. as in parallel biasing analysis. As many windings of the bias coils as practical can be used — resulting in a smaller amperage requirement for the bias supply. The effective rf-/i.
oscillating at frequency uvf. If the filling time is long. The effective voltage at the rf gap is a superposition of voltage due to generator current and induced voltage due to induced rf current. the resulting rf voltage acting on the passing beam may cause beam deceleration in an uncontrollable manner. Thus beam loading needs to be considered in the operation of rf cavities. i. and 0 if t < 0. where </)s is the synchronous phase angle. (3. The representation of sinusoidal waves in a rotating frame is called a phasor diagram and is particularly useful in analyzing beam loading compensation problems. Z{u) = / fOO W{t)e-jutdt = / roo W(t)e~jutdt.3 Beam Loading A passing beam charge can induce wakefields in an rf cavity.e. By definition. (3. The magnitude of the vector is equal to the amplitude of the rf voltage. When beams pass repetitively through the cavity. 2ir J L wrJfo J (3.305). given by the inverse Fourier transform of the impedance. can be considered as a vector rotating in the complex plane at an angular frequency u>rf. The rf voltage.311) JO J-oo the wake function.312) where 0(i) = 1 if t > 0. we have V0cos6 = Vosin^s. and thus the rf voltage is stationary in this rotating coordinate system. for the RLC resonator model becomes W(t) = •£. W(t) « 2kTe-t/T{0 coswrt. the effective voltage is the sum of the voltage supplied by the generator current and the wakefields of all beams. Now. then the wake potential is a sinusoidal function with angular frequency u>T.^ r sinwril e-t/Tf° Q(t). . and the rf voltage seen by the beam is the projection of the rotating vector on the real axis.(1/4Q 2 )) 1/2 . Beam loading is important in the design and operation of rf cavities. Let Vo and 6 be respectively the amplitude and the angle with respect to the real axis of the rf voltage vector. Thus the filling time corresponds also to the wakefield decay time. Tf0 = 2Q/wr is unloaded filling time denned in Eq. Without proper compensation.VI FUNDAMENTALS OF RF SYSTEMS 353 Since the longitudinal impedance is defined as the Fourier transform of the wake function. VI.[ Z{u)e>utdu) = 2kT fcoswTt . we choose a coordinate system that rotates with the rf frequency. and wr = wr (1 .
passing through the cavity. . 87. the voltage is expressed as a phasor V = Veje.354 A. we obtain X = 0. (3.. V* = \V*' f = \- ( 3 .313) Phasors are manipulated by using usual rules of complex vector algebra. SYNCHROTRON MOTION The electromagnetic fields and voltages in a standing wave rf structure are normally expressed as complex quantities. The total energy deposited in the cavity is Wc = a|H(l) + Kb(2)|2 = af2V b cos-J The energy loss by these two particles is AU = [qVe] + [qVe + qVh cos(x + 9)]. (3. 5 7 P. Proc. we assume that the stored energy in a cavity in any given mode is W = aV2. Phasor CHAPTER 3. From the conservation of energy. Now. We assume further that the induced voltage lies at phase angle \ with respect to the inducing current or charge. V = Vej(-ut+e\ where u is the frequency and 9 is a phase angle.317 ) The result can be summarized as follows: B. In the rotating coordinate system. Vh = ±.316) = 2aVb2(l + cosfl). and the effective voltage is Ve = /VJ. 452 (1981). The properties of rf fields can be studied by using graphic reconstruction in phasor diagrams. when a charged particle passes through the cavity. separated by phase angle 9.314) We assume that a fraction / of the induced voltage is seen by the inducing particle. (3. the image current on the cavity wall creates an electric field that opposes the particle motion. Fundamental theorem of beam loading The cavity provides a longitudinal electric field for particle acceleration. To prove this fundamental theorem. B. Wilson. (3. AU = Wc. is the induced voltage in each passage. where V}. AIP Con}. The question arises: what fraction of the electric field or voltage created by the beam affects the beam motion? The question can be addressed by the fundamental theorem of beam loading due to Wilson. However.315) where the first and second brackets are the energy losses due to the first and second particles respectively. we consider two identical charged particles of charge q.57 Theorem: A charged particle sees exactly | of its own induced voltage.
the rf phase shift is > <j>-{u. the phase angle \ = 02. and the term . The induced voltage of a beam must have a phase maximally opposite the motion of the charge. Steady state solution of multiple bunch passage Consider an infinite train of bunches. and T[ = 2Qi. (3./k>r is the cavity time constant or the cavity filling time. is the rf image current.^ (A->0). passing through an rf cavity gap.1 / 2 is neglected. separated by time Tb. When the cavity is on resonance.0)) « J i ^ ^ c o s ^ .e.321) For rf cavities used in accelerators.l pQL(^-^r)l = t a n _i [(w _ Wf)Tf] ^ (3 320) where to is the cavity operation frequency. When the cavity is detuned by a detuning angle rp. we have A = Tb/T{ = wrTb/2QL <C 1. 3. Ve = 14/2. k = Vb2/(4W/C). and the induced voltage seen by the beam is Vb = IAhX(-l + 1 _ g_1(A+. <P = t a n . FUNDAMENTALS OF RF SYSTEMS 355 1. where k is the loss factor. Vb = 2kq or Ve = kq. The particle sees exactly 1/2 of its own induced voltage. Vbo = IiR^hTb/T{. (3. i. 4.e. QL-(RA + Rs)Rc-lTd' d " V (3 . Wc = aV£ = q2/4a = kq2. and A = T\.cor)Tb = +(T b /T f ) tan ip = +A tan V ./Tf is the decay factor of the induced voltage between successive bunch passages. wr is the resonance frequency of the rf cavity. . taking into account the generator resistance Rs in parallel with the RLC circuit of the cavity. C. Here QL is the loaded cavity quality factor.319) The filling time of the loaded cavity is reduced by a factor 1/(1 + d). the induced voltage seen by the particle is Vb = \vb0 + Vb0(e-^ +e" 2 ^ + •••) = VM(~ + 1_e_(A+J>)).322) where I. The beam induced voltage across the rf gap at the steady state is exactly the rf image current times the impedance of the rf system.VI. i. (3-318) where 0 = — (u — wr)Tb [Mod 2?r] is the relative bunch arrival phase with respect to the cavity phase at the rf gap.
Right: When the cavity is detuned to a detuning angle ip. The combination of generator voltage Vg and induced voltage V\ gives rise to a decelerating field Vo. The voltage seen by the beam is the sum of the voltage produced by the generator current and the beam induced current. AIP Conf. p. It appears that the rf system would be optimally tuned if it were tuned to on-resonance so that it had a resistive load with Vg = IoRsh. generated by the beam is twice the DC current. The beam will induce I\Rsh across the voltage gap (see dashed line in Fig. When a short beam bunch passes through the rf system. 3. we will find shortly that the effect of beam loading would render such a scheme unusable.58 The detuning angle and the generator current are adjusted so that the resultant voltage has a correct 58J. Such a large rf generator current at a phase angle other than that of the rf acceleration voltage is costly and unnecessary. One way to compensate the image current is to superimpose. F. IEEE Tran.E. and results in deceleration of the beam. (2. we need a generator rf current IQ = Ioe>e with phase angle 9 so that the voltage acting on the beam is Vacc = Vg cos 9 = Vg sin <j>s.28).211).28 (left). Sci.However. Left: The beam loading voltage for a cavity tuned on resonance. This is shown schematically in Fig. 2138 (1985). where the required gap voltage IoRsh and the synchronous phase angle 4>s are altered by the voltage induced by the image current. Boussard. the image rf current /.4 Beam Loading Compensation and Robinson Instability To provide particle acceleration in a cavity. An alternative solution is to detune the accelerating structure. 3. VI. . current directly opposite to the image current. Nucl. CERN 91-04. the superposition of the generator voltage Vs and the beam loading voltage V\ gives a proper cavity voltage Vo for beam acceleration. where (j>s is the synchronous phase angle. Proc. Griffin. 294 (1991). The projection of the resultant vector Vo on the real axis is negative.28: Phasor diagrams for beam loading compensation.356 CHAPTER 3. D. SYNCHROTRON MOTION Figure 3. as shown in Eq. 87. 564 (1981). on the generator current. Pedersen. NS-32. Thus the stable phase angle 4>s of the synchrotron motion will be changed by the induced voltage.
mis-injection. mismatched beam profile. we obtain tanfl g = s tan ip .]iU costfe " * . cos(9g . we discuss only the dipole mode stability condition related to beam loading. FUNDAMENTALS OF RF SYSTEMS 357 magnitude and phase for beam acceleration. = — 7b Ve = Vge?e rf beam image current.£) = VQ cos 9 + £VQ sin 9 = Vo sin <ps + £Vo cos <f>s.324) where 9% is the phase angle of the generator current relative to the ideal To. We define the following phasor currents and voltages for the analysis of this problem. and Eq. 1 + Fcos# 7g = 70 s T 1 + Y cos 6 .e. This scheme will minimize the generator current. i. /„ = 7oe3' Ig = Ige^B+9^ generator current necessary for accelerating voltage in the absence of beam required generator current with beam < /. The optimal operating condition normally corresponds to 9S = 0. Vacc = Vo cos(0 . The accelerating rf voltage will be perturbed by the same phase factor.325) Figure 3. A. (3. rf noise. By equating the real and imaginary parts. (3.W.323) Here the induced voltage is derived from the steady state beam loading. Here.Y sin 0 y —. studied by Robinson in 1964.7. Robinson dipole mode instability In accelerators. CEA report CEAL-1010 (1964). (3. ' (3. voltage error. the generator current is optimally chosen to be parallel to 70. . which minimizes 7g.326) Robinson. The resultant vector of the generator voltage and the image current voltage is the effective accelerating voltage for the beam.324) reduces to 7g = 7O(1 + Fsin0 s ). (3.59 We consider a small perturbation by shifting the arrival time of all bunches by a phase factor f. 7. Beam stability may sometimes need sophisticated active feedback systems. = —7. The topic of control and feedback is beyond the scope of this textbook. beams experience many sources of perturbation such as power supply ripple. 59 K.28 (right) shows the beam loading phasor diagram with a detuned cavity angle ifi. tan-0 = Ycosfc.VI. is a positive quantity required rf accelerating voltage I/J = tan"12Q(^~"r) Y = 7j//o detuning angle ratio of image current to unloaded generator current The equation for a proper accelerating voltage is % = 7 0 7 W = [IgeW+*> . etc.
60 60See D.Y—^-r1. instability is a self-adjusting process. Since the stability condition is a function of bunch intensity. Boussard. the cavity frequency is detuned with u < ur.^ ° or * TT ^ °3-332) cos <ps cos 2 <pB This means that Robinson stability requires ip < 9 = \^TT-(/>S\. 626 (1987). the bunches in the accelerator will execute synchrotron motion.# / j .332) is applicable to all higher order modes. with cos</>s < 0. p. Robinson stability can be described as follows. sin ib cos ib sin2 ib . (3. . Active feedback systems are used to enhance the stability of bunched beam acceleration. (3. Thus the equation of motion for the phasor error £ is (see Exercise 3. In general.328) (3. Eq. Kc (3.e.325). 294 (1991).330) A small perturbation in arrival time causes a perturbation in acceleration voltage proportional to the phase shift. For those modes. and its induced rf voltage is AVg = -j£IAh cos </>e-**.f rv 0 cos V sin ip. p. CERN 91-04.329) The net change in accelerating voltage seen by the bunch becomes A c = ^ocos0s[l-F^^]. Above transition energy.327) The induced accelerating voltage is equal to the projection of the phasor voltage onto the real axis: AV0 = . The wrong arrival time shifts the image beam current by a phase angle f. . CERN 87-03. SYNCHROTRON MOTION where the first term is the intended accelerating voltage and the second term is the effect of phase perturbation due to an error in arrival time. Robinson stability can be attained by choosing s i n ^ < 0. = j£ii = . i. with cos 0 S > 0. If the voltage induced by the image charge is not significant.6. (3. the cavity should be detuned so that sin ip > 0 or UJ > Ljr in order to gain Robinson stability. Below transition energy. (3. we find that the Robinson stability condition becomes 1 . Beam loss will appear until the Robinson stability condition can be achieved.358 CHAPTER 3.7) Using Eq. The perturbation to the image rf current is A7.
Robinson stability will be attained below transition energy. Exercise 3. (a) Show that the surface resistivity defined as Rs = l/o"5skin [in Ohm] is given by Rs = \l2cT- . if the cavity is detuned such that hoJo < wr. \ y<yT : III CO L_l_l : CO Figure 3. cor hcoo hw 0 coT y>yT / : i \J I i . where the impedance of the cavity is assumed to be real. If the cavity is detuned so that HLOQ > wr. Qualitative feature of Robinson instability Robinson instability can be qualitatively understood as follows.29: A schematic drawing of the real part of impedance arising from a wakefield induced by the circulating beam. Thus the centroid of the beam bunch will damp in the presence of beam loading. and the beam bunch at lower beam energy sees a lower shunt impedance and loses less energy. The wakefield produced in a cavity by a circulating bunch is represented qualitatively in Fig. higher energy particles have a smaller revolution frequency and thus lose more energy if the cavity detuning is huio > uiT. A similar argument applies to rf cavities operating below transition energy. 3. 3. left). where wr is the resonance frequency of the cavity (Fig.29. the beam bunch at higher energy sees a higher shunt impedance and loses more energy.29.EXERCISE 3. Since the revolution frequency is related to the fractional momentum spread by Aw _ AE a higher beam energy has a smaller revolution frequency above the transition energy.6 359 B. Similarly. Above transition energy. where \i is the permeability. and the dipole mode of beam motion is Robinson damped. To avoid Robinson instability.6 1. > ur above transition energy and huo < wr below transition energy. the cavity should be detuned to h<jj(. The skin depth <5skin of an AC current with angular frequency w traveling on a conductor of bulk conductivity a is <5skjn = I/2/^CTW.
(3.e. Use the following steps to derive Eq. (3. t) = [Vo cosks + satisfies the TEM wave equation. (3.282). SYNCHROTRON MOTION Note that the surface resistivity does not depend on the geometry of the conductor.t) = [Io COS ks + j{V0/Rc) sinks]ejut I V(s. (a) Show that the general solution of the right/left traveling TEM wave is given by V = f(t^sVW).291) (I{s. Q = 104. 2. Show that the solution of Maxwell's equation in the cylindrical coordinate is given by Eq.322) 7. and wT is the resonance frequency.310) and show that the loss factor of a parallel RLC resonator is given by61 _ t^r-Rsh 47rQ where R^ is the shunt resistance. (3. •n-c where Rc = \JLjC is the characteristic impedance of the line. 6. Verify Eq. Verify the Fourier integral of Eq. the characteristic impedance is the impedance seen by traveling waves with V = IRc(b) Show that the current and voltage of Eq.331). (3. (b) Show that the resistance of a coaxial structure is given by Eq.360 CHAPTER 3. 3. Verify Eqs. 5. In a lossless transverse electromagnetic (TEM) wave transmission line.1/x)2]"1 yi-(l/4Q2)±j(l/2Q). Q is the Q-factor. I=±^-f(tTsVLC). (3.312).296) with where i is the length of the structure and ri. 61Use the identity [l + Q2(x .301) and plot Z vs UJ for wr = 200 MHz. i. (3. jIoRcsinks]^1 4. (3. ri are the inner and outer radii of the coaxial wave guide. = x2 [Q2{x2-r21+)(x2-rj_)]~\ where r 1 ± = . and i U = 25 Mfi. the equation for the current and voltage is dV_ !te~ 5/ 3? dl__ BV ~d~s~~ ~dt' where L and C are respectively the inductance and capacitance per unit length. Evaluate the integral of Eq.
EXERCISE 3. in {Y. where the overdot indicates the derivative with respect to orbiting angle 0. and 5/. 1 > (sin 2^/2 cos (j>s)Y.6O°.331). (c) Draw the Robinson stability region. Show that £ = hrt&b. (3.3O°. is the momentum error of the beam centroid. 180°.e.ip) for 0S = O°. 120°. . i.6 361 (a) Let £ be the rf phase associated with the error in beam arrival time. 150°. (b) Show that " i _ eV0 cos <fe I _ b~ 2-K^E [ sin 2^ 1 2cos4>s\^ Thus you have arrived at Eq.
4. we discuss only single bunch effects without mode coupling.63 Longitudinal collective instabilities have many modes. coherent and incoherent tune shift. 1st EPAC. 273 (Edition Frontiere. luminosity degradation. Ill. VII. 1988). Mode coupling and coupled bunch collective instabilities and other advanced topics can be found in a specialized advanced textbooks [3]. The results of collective instabilities are bunch lengthening. the physics of collective instabilities becomes more important. and T. In Sec. since the growth rate of the microwave instability is very large. Zotter.2. and discuss the Keil-Schnell criterion and the turbulent bunch lengthening. and problems in machine operation. Ref. p. This causes a beam bunch to form microbunches. This section provides an introduction to the collective instability in synchrotron motion induced by the wakefield. similar to the transverse collective dipole mode instability discussed in Chap. which is the Fourier transform of the wakefield. the collective motion is governed by the impedance. The impedance responsible for collective instabilities can be experimentally derived from beam transfer function measurements. and equilibrium momentum spread and emittance.362 CHAPTER 3.62 or from passive measurements of beam loss. Chin and K. In this introduction to the collective beam instability. Part. Suzuki. we list possible sources of longitudinal impedances. we study the linearized Vlasov equation with a coasting beam.3. In Sec. 179 (1983). Sec. An experimental measurement of coherent synchrotron mode will be discussed. as discussed in Sec. VIII. VII. where the phase space are split into resonance islands. beam brightness dilution. beam loss. Gif-sur-Yvette Cedex. p. 3rd EPAC. Knowledge of coherent synchrotron modes provides useful information about possible sources. Detecting the onset of instabilities and measuring coherent synchrotron modes can help us understand the mechanism of collective instabilities. The collective synchrotron motion can be classified according to synchrotron modes. 2. and about the signature at onset. Proc. Hofmann. 181 (World Scientific. VII. Proc. 1. B. SYNCHROTRON MOTION VII Longitudinal Collective Instabilities As the demand for beam brightness increases. In Sec. we examine the microwave instability for a beam with zero momentum spread and for a beam with Gaussian momentum spread. Y. [3]. VII. we discuss the coherent frequency spectra of beams in a synchrotron. On the other hand. it can be classified according to the longitudinal mode with density fluctuation. Indeed. The wakefield generated by the beam bunch can further induce collective motion of beam particles. Singapore. In the frequency domain. 13. 1992). Accel. of collective instabilities. almost all accelerators and storage rings have suffered some type of collective instability that limits beam intensity. and derive a dispersion relation for the collective frequency in single mode approximation. and decoherence due to nonlinear synchrotron motion generates emittance dilution. . 63 See 62 A. In Sec. Satoh.
Coherent synchrotron modes The synchrotron motion of beam particles introduces a modulation in the periodic arrival time. For B equally spaced short bunches.211). The amplitude of the mth synchrotron sideband is proportional to the Bessel function Jm. the coherent rf signal is invisible. Such a beam is called a coasting or DC beam because only the DC signal is visible. To is the revolution period. (3. for the effect of a finite bunch length.e. there are synchrotron sidebands around each orbital harmonic n. This analysis is applicable to a single short bunch or equally spaced short bunches. where TVB is the number of particles in a bunch. and the corresponding frequency spectra occur at all harmonics of the revolution frequency fa. (2.Similarly. The resulting spectra of the particle motion are classified into synchrotron modes. For a •^-independent particle distribution function p(f. Ie(t) = e Y.VII. We expand the current Eq. the beam current becomes Ia{t)=jle{t)Pa{T)TdfdiP = Im f ) V ™ * ' . Nf0 is well above the bandwidths of BPMs and detection instruments. i. LONGITUDINAL COLLECTIVE INSTABILITIES 363 VII. S(t-fcos(u}st + rP)-£T0) fc-oo oo oo oo = Y £ £ j-mJm(™of)e>Kn*>+m*»+m*\ (3. A bunch is made of particles with different synchrotron amplitudes and phases.333) where e is the charge. The frequency spectra of a single short bunch occur at all harmonics of the revolution frequency /o. f and tp are the synchrotron amplitude and phase of the particle. u>s — u>0^heV\r]cos(t>s\/2n/32E is the synchrotron angular frequency with 4>s as the rf phase of the synchronous particle. where the Fourier spectra are separated by Nf0. Since N ~ 108 -10 1 3 .tp) = PO(T). 1 Longitudinal Spectra The current observed at a wall gap monitor or a BPM from a circulating charged particle is represented by a periodic 5-function in Eq. n=—oo 64 The power of a coherent signal is proportional to . (2. the coherent synchrotron modes of the bunch can be obtained by averaging the synchrotron mode over the bunch distribution.215). (2. the current of N equally spaced circulating particles is described by Eq./Vg. (3-334) .221). and Jm is the Bessel function of order m. the coherent frequency spectra are located at harmonics of BfoM A. see Eq.87) of an orbiting particle with a linear synchrotron motion in Fourier series.
and Anfi is the Hankel transformation of Po.336) (3. we can deduce the beam distribution function from the amplitudes of coherent modes An.e. (3.m. Nucl. IEEE Trans. we measure the power of a synchrotron mode of a longitudinally kicked beam. 6 5 F. Note also that po can be obtained from the inverse Hankel transformation. As an illustrative example. p(f. all synchrotron sidebands of individual particles are averaged to zero. where fic is the coherent frequency. p. ibid NS-24.e. An.65 The coherent synchrotron sidebands can be measured by taking the fast Fourier transform (FFT) spectrum of the longitudinal beam profile digitized at fixed times during the onset of coherent mode instability. e. the coherent current signal becomes / Ie{t)Ap{f. However. Sci. (3.m = 2TT J™ Jm{nuj0T)pm(f)fdT. i>) with Ap(f.L. see also J. whose power is about 1/iV of the coherent ones. These coherent mode integrals form the kernel for the Sacherer integral equation in determining the longitudinal collective instability. although one can detect incoherent synchrotron sidebands from the Schottky signal. (1973). i. p. NS-20.^)=pm(f)e^t-m*). the inverse Hankel transformation can be used to reconstruct the coherent longitudinal distribution p m . Jackson. a spectrum analyzer (SA). IEEE PAC. (1977).66 This requires a digital oscilloscope with a sizable memory. can also measure beam power arising from the coherent synchrotron mode excitation. Using the inverse Hankel transformation. Piscataway. i. which is important in identifying the source of coherent excitations.meXn"°+r™°+n^. Sacherer. if there is a coherent synchrotron mode in the bunch distribution. Proc. It is a coherent synchrotron mode. NJ. SYNCHROTRON MOTION where / av = iVBe/0 is the average current. 1993). |>ln)m|2.337) where j4n>m is the mth order Hankel transformation. n=-oo oo (3. 264 (1987). 4>) = po(f) + Ap(f.335) Note that Eq. Anfi = 2nJ Jo{nuof)po{f)fdf. Now. Laclare.334) contains only orbital harmonics nu>o. CERN 87-03.338) The mth order synchrotron sideband appears around all coherent revolution harmonics. With the power spectrum of the the mth synchrotron mode known. 66 X. Lu and G. . tuned to a synchrotron sideband.ij)fdfdij = I0{t) + Iav J2 An.364 CHAPTER 3.g. 3366 (IEEE. (3.
which could be adjusted by varying the rf voltage. [26] . Measurements of coherent synchrotron modes The experiment started with a single bunched beam of about 5 x 108 protons at a kinetic energy of 45 MeV and harmonic number h = l. was about 4. The resulting phase oscillations of the bunch relative to the rf wave form were measured by a phase detector.VII. III).2 ^ . which normally locks the rf cavity to the beam.S f ) 7 " ^ ' An. The typical bunch length. The cycle time was 5 s.338) becomes67 (3. i.633. which was used to 67See e. The rf phase lock feedback loop. while the injected beam was electron-cooled for about 3 s.^ r ^ Sj-irimQym*' where /_ m = Im. Coherent synchrotron modes of a kicked beam 365 For simplicity.342) The power of the mth sideband of a kicked beam is proportional to the square of the mth order Bessel function. 6. the initial beam distribution becomes f2 TTk = ^ ( .03168 MHz and the phase slip factor was rj = -0. We describe below an experiment measuring the coherent mode power at the IUCF Cooler. The revolution frequency was /o = 1. (3.86.e. Thus the coherent distribution is ( — A\m (-4) 330 (3"341) T2 f2 TTi ^ =1 ^ . (3. A function generator was used to generate a 0 to 10 V square wave to control the phase kick.^ . For non-Gaussian beams. (3.4 of Ref. T 1 / Tk < 3 ^ When the beam is phase kicked by T^. LONGITUDINAL COLLECTIVE INSTABILITIES B.40) for the phase space coordinates): »te)-5=?->P^). the power spectrum is a weighted average of Bessel functions in Eq. C.g. was switched off. we assume an initial Gaussian equilibrium beam distribution (see Eq.5 m (50 ns) FWHM. The bunched beam was kicked longitudinally by phase-shifting the rf cavity wave form (see Sec.338). and the coherent mode integral of Eq. the rms bunch length oy was about 20 ns.m = e'^OTk)HV2Jm(nuj0Tk).
On the other hand. video bandwidth 100 Hz.^). 3.03168 MHz.58 and uT = 20 ns for the case shown in Fig. The magnitude of the phase shift was varied by the size of the applied step voltage.30: The synchrotron sideband power of a kicked beam observed from a spectrum analyzer tuned to the first revolution sideband (upper trace) and the 6th revolution sideband (lower trace) as a function of time. SYNCHROTRON MOTION calibrate the control voltage for the phase shifters versus the actual phase shift. the spectrum analyzer (SA) was triggered about 5 ms before the phase shift.30. 3. Ji(6woTa) increases. The setting of the SA was resolution bandwidth 100 Hz. The vertical axis is coherent synchrotron power in dB. where ra is the synchrotron amplitude.58 rad. The kicked amplitude was 90 ns. A6tl ~ e-0-299. The sideband power shown in Fig. or equivalently w0Tk = 0. Since UJQT^ « 0. The response time of the step phase shifts was limited primarily by the inertia of the rf cavities. . thus the measurement of the sideband power was taken at 10 ms after the phase kick. 3. and frequency span 0 Hz. Figure 3.366 CHAPTER 3. probably because of electron cooling in the IUCF Cooler. and the horizontal axis is time at 10 ms per division. The power observed at a synchrotron sideband from the SA is shown in Fig.30 was proportional to |^4i.30 increases with time. Therefore the power spectrum shown in the lower plot of Fig. Note that the sideband power decreased with time for the first harmonic and increased for the 6th harmonic. which had a quality factor Q of about 40. The revolution frequency was 1.30. where the top and bottom traces show the SA responses at the sidebands of the first harmonic f0 — fs and the sixth harmonic 6/o — fs vs time. Both the phase error due to control nonlinearity and the parasitic amplitude modulation of the IUCF Cooler rf systems were kept to less than 10%.i|2. Thus the initial power at the fundamental harmonic sideband. as 6cooTa decreases./!^. The resolution bandwidth of SA was 100 Hz. To measure the FFT spectrum of the coherent signal.i| 2 for the lower trace. we obtain Altl ~ e-00083^^). after the phase kick will be a factor of 6 larger than that of the 6th orbital harmonic. the power Aiti decreases because Ji(woTa) decreases with decreasing ujQTa.i|2 for the upper trace and |^6. which is proportional to |^4i. 3. As the synchrotron phase amplitude decreases because of electron cooling.
(3. 100 and 150 ns. For a kicked Gaussian beam.31 shows the power of the m = 1 sideband.343) normalized to the peak. Similarly. the power P n l is proportional to |^4n. Figure 3. These data were normalized to the peak. LONGITUDINAL COLLECTIVE INSTABILITIES 367 Figure 3.VII.343) Because the actual power depends on the beam intensity.i ~ \AnA\2 = e . The curves were theoretical predictions with no adjustable parameter except the normalization constant. which in turn perturb particle motion. 3. Measurement of AUtl for all orbital harmonics can be used to obtain the coherent mode distribution function.< " ^ ) 2 ^ ^ ) 2 | J i ( « ^ o r k ) | 2 . Because of the impedance of the ring. Plots from top to bottom correspond to a kicking amplitude (time) of 53. Let ^o(5) be the normalized distribution function with f^od5= 1. A self-consistent distribution function obeys the Vlasov equation d* d$ -a* -a* . setting up the central frequency at the second synchrotron harmonic.i|2: Pn.31. (3. we can measure the m = 2 synchrotron modes for the kicked beam. there is no rf cavity and the unperturbed distribution function is a function only of the off-momentum coordinate 5 = Ap/p0. where n is the revolution harmonic. as a function of UIT ~ WJJQTY.2 Collective Microwave Instability in Coasting Beams For coasting beams. When a bunched beam encounters collective instability. for various kicking times. Solid curves are obtained from Eq. 90. VII.31: Measured m = 1 synchrotron sideband power vs frequency for different phase kicked amplitudes is compared with theory based on a Gaussian beam distribution.8. (3. The effect of finite bunch length is visible in Fig. all data are normalized at the first peak around nw0Ty « 1. the beam generates wakefields.342). the observed sideband power \AnX\2 is proportional to the weighted average of the coherent mode density p(r) shown in Eq.
Im fl < 0. If the imaginary part of the coherent mode frequency is negative.e.e. the energy gain/loss per revolution due to the wakefield is equal to the current times the longitudinal impedance: AE per turn = Z« (eIQ I AVnd5) \ J ) e^nt-nB\ where the impedance is evaluated at the collective frequency Q. . i. (3. The perturbation causes density fluctuation along the machine. ~J 1*PE J Q^^dd ~3 2^E J ({l-ruo)*d6 ' (3'3 8) where partial integration has been carried out in the second equality. i.e/OTi(Jo(Z||/n) r dVp/dd JX _ . the perturbing distribution function should be written as a linear superposition of all possible modes.345) where < > is the unperturbed distribution. First we examine possible sources of longitudinal impedance. and A\Pn(<5) is the perturbation amplitude for the longitudinal mode n.eI0n2ujQ{Z^n) f % du JS. the time derivative of the 5 coordinate in a coasting beam becomes 6=^ (e/o^i / A*nd5) e* 0 *-*'. SYNCHROTRON MOTION where the overdot is the derivative with respect to time t. the collective instability of mode number n can cause a coasting beam to split into n microbunches. With the reo lation (j = W — u)oT]S. The terminology is derived from the fact that the coherent frequency observed is in the microwave frequency range. Q is the coherent frequency. In general. By definition. The eigenfrequency fl of the collective motion is given by the solution of the dispersion relation. 68 Here we assume a single longitudinal mode. we obtain the dispersion relation 1 _ . the perturbation amplitude grows exponentially.346) Since |A$ n | -C \l/o at the onset threshold of collective instability. In the presence of a wakefield. and the beam encounters the collective microwave instability. (3. we assume that the distribution function is approximated by68 tf = tf 0 (g) + A<bnej{Qt-n^. we linearize the Vlasov equation to obtain Using 0 = u) and integrating Eq. The frequencies of the collective motion are eigenfrequencies of the coupled system.368 CHAPTER 3. Thus. the dispersion integral can be analytically obtained for some distribution functions of the beam.347). 9 is the or30 biting angle. (3.
(3. we list below some sources of commonly used impedance models.|( ) e U =. the impedance has the symmetry property Zn{-u) = Z.i / do/^M.354) ! 2-Ktr l. LONGITUDINAL COLLECTIVE INSTABILITIES 369 VII.32). the wake function is related to the impedance by Wn(t) = — 1 r00 Z7T J— oo Z^e^du. Now we consider a small fluctuation in the line density and current with A = Ao + Axe*"*-"*).353) Thus the real part of the longitudinal impedance is positive and is a symmetric function of the frequency. e is the charge.Y. p.3 Longitudinal Impedance Z. 2TIT where A is the particle's line density.69 and the real and imaginary parts of the impedance are related by the Hilbert transform R Z. Space-charge impedance Let a be the radius of a uniformly distributed coasting beam. [12].352) where P. In fact. (3. and e0 and Ho are the permittivity and permeability of the vacuum.V. 3.fieis the speed. The electromagnetic fields of the coasting beam are eXr 2-Kta2 \ R B<t>-\ ( fj. (3.350) Since the wakefield obeys the causality principle. (3. . 472 in Ref. stands for the principal value integral.351) I Z( ) = +-/" m |W d^Z^'\ (3. 89See / = 70 + Iie^nt-n6\ K. and let b be the radius of a beam pipe (Fig.349) and similarly. see also Appendix 2.|H = r J-oo The impedance of an accelerator is related to the wake function by Wn(t)e-jutdLj. the property of Z\\(u))/u is similar to that of Z±(u). Ng. A. the impedance must not have singularities in the lower complex plane. (3. Without making the effort to derive them.VII.(u>). Because the wake function is real.QeXl3cr J 2na2 xa ~ r >a . .
dX/dt = —j3c(d\/ds). SYNCHROTRON MOTION Figure 3. 3. we obtain (E. if the perturbation is on the surface of the beam. For most accelerators. where Es and Ev are the electric fields at the center of the beam pipe and at the vacuum chamber wall. the geometric factor becomes go = I + 2 In (b/a). The perturbation generates an electric field on the beam.AW] = - A s ^ § . On the other hand. the vacuum chamber wall is inductive at low and medium frequency range. and the geometry factor g0 = 1 + 2 ln(6/a) is obtained from the integral along the radial paths from the beam center to the vacuum chamber wall. The induced electric fields that arise from impedance are shown schematically.370 CHAPTER 3.e. where Io = e/3cA0 and 7i = e/3cAi.F eg° dX (1W\ t. — r—. 70If [47r£o72 . (6. .s — hy. Let L/2-KR be the inductance per unit length.Ew)As + f*L[\{8 + As) . then the induced wall electric field is L dIw_ep<?Ld\ Thus we have K-2^Rlf- 47reO7 as arises from cancellation between the electric and magnetic ^rTTd? 27ri? J 9 s ' (3'356) _ [ g _ 0W\ d\ o 6 the impedance is averaged over the beam cross section.32: The geometry of a uniformly distributed beam with radius a in a beam pipe of radius b.600) where the factor I/7 2 fields. where da is the surface integral.70 Assuming that the disturbance is propagating at the same speed as the orbiting beam particles. i.32. Using Faraday's law £ Ed£=J — fB-da at J along the loop shown in Fig. The rectangular loop is used for the path integral of Faraday's law. the geometry factor becomes go = 21n(fc/a). the electric field acting on the circulating beam becomes W .
Typical values of the space-charge impedance at transition energy are listed in Table VII. (3. microwave frequency.7 22. (3. the vacuum chamber wall is not perfectly conducting. the displacement current contribution to Maxwell's equation is small. . . B.e / 3 c / ? S[l7. 7T I AGS I RHIC I Fermilab BST [ Fermilab MI I KEKPS" 8. Penetration of electromagnetic wave into the vacuum chamber can be described by Maxwell's equations O 77 VxE = -(jt-—. part of the wakefield can penetrate the vacuum chamber and cause energy loss to the beam. and Ew has a resistive contribution that depends on the conductivity.4 20. as Z.5 5.358) is the space-charge impedance and the second term is the inductance of the vacuum chamber wall.3.VII. and Zo = l/eoc = 377 ohms is the vacuum impedance. Here we have used Ohm's law. The first term in Eq. Table 3. and neglected the contribution of the displacement current for electromagnetic wave with not so high frequencies. we find V2E = fiac^.7: Typical space-charge impedance at 7 = 7 T . we obtain the impedance.71 From Eq. LONGITUDINAL COLLECTIVE INSTABILITIES The total voltage drop in one revolution on the beam is 371 A[/ = . (3.5 I 30 [23 | 20 In fact.359) whereCTCis the conductivity and /J.8 |Z||.4 6. Using R(d\/ds) = (dX/d6).| At/ \g0Z0 1 . Resistive wall impedance Because the resistivity of the vacuum chamber wall is finite. and skin depth. defined as the voltage drop per unit current.scl/rc [ft] 1 13 1 1.W o L ]' ('5) 33 7 where /3c = us0R is the speed of the orbiting particles.360) 71 For frequencies OJ <C <rc/e fa <rcZoc « 10 19 Hz.359). (3. V x H = J = acE. is the permeability. where e is the permittivity. and ej3c\\ = I\.
Since the magnetic energy is equal to the electric energy. (3. SYNCHROTRON MOTION Substituting the ansatz of the electric field E = s Eo exp{j(ujt — kx)} into Eq.360). i^h is the shunt impedance. and the resonance frequency to be the cut-off frequency w r . The longitudinal narrowband and broadband impedances can conveniently be represented by an equivalent RLC circuit Z(w) = 7" ^. ZO \w0/ (3. The imaginary part of the wave number is the inverse of the penetration depth. we obtain the wave number k = (1 . the magnitude of the reactance is equal to the resistance.362) where the sign function.372 CHAPTER 3. <5Skin. is added so that the impedance satisfies the symmetry property. /3 is Lorentz's relativistic velocity factor. The high order mode (HOM) of rf cavities is a major source of narrowband impedances. sgn(w) = +1 if UJ > 0 and — 1 if u < 0. and Q is the quality factor.j)y/\u\acn/2. the Q-factor is usually taken to be 1. bb = LOoR/b = Pc/b. Narrowband and broadband impedances Narrowband impedances arise from parasitic modes in rf cavities and cavity-like structures in accelerators. and other discontinuities in accelerator components. The electromagnetic fields penetrate a skin depth inside the vacuum chamber wall.361) where Zo is the vacuum impedance. The resistance due to the electric field becomes ZH X2^^- = ^{-0) *"»•»' (3 . For a broadband impedance.363) where cuT is the resonance frequency. The resistive wall impedance becomes Z||(W) = ( l + j s g n H ) ^ (M^ 5skin0 . Parameters for narrowband impedances depend on the geometry and material of cavity-like structures.364) . C. where x is the distance in the vacuum chamber wall. (3. the skin depth is Ss^n = ^J2/iJ. or equivalently. (3. Broadband impedances arise from vacuum chamber breaks.acLO. and ac is the conductivity of the vacuum chamber. bellows. b is the vacuum chamber radius.o = ^2/nacu>o is the skin depth at frequency uio. H is the permeability.
The magnitude of the broadband shunt impedance can range from 50 ohms for machines constructed in the 60's and 70's to less than 1 ohm for recently constructed machines. Figure 3. In the absence of momentum spread with \&o(<5) = 5A{5).VII. and space-charge impedances. LONGITUDINAL COLLECTIVE INSTABILITIES 373 where LJO is the revolution frequency.33: Schematic of a longitudinal impedance that includes broadband. VII. Experimental observations were obtained in the intersecting storage rings (ISR). where 5 = Ap/po and Sd(x) is the Dirac 5-function. where the solid and dashed lines correspond to the real and imaginary parts respectively. To summarize. The symmetry of the impedance as a function of w is also shown.4 Microwave Single Bunch Instability The negative mass instability was predicted in 1960's. we consider negative mass instability. and b is the vacuum chamber size.348) is / fi \ 2 eI0Zn/n U) =-'iyK (-6) 335 The condition for having a real fi is -j(Z^/n)rj > 0.33. or an indue- . R is the average radius of the accelerator. 3. This condition is only satisfied for a space-charge (capacitive) impedance below the transition energy. In this section. A. the solution of Eq. it was observed in almost all existing high intensity accelerators. we discuss the single bunch microwave instability. we find that |Re(Z||/o. where microwave signal was detected in the beam debunching process. where the vacuum chamber is carefully smoothed. Subsequently. the longitudinal impedances Z\\(UJ)/U> or Z\\/n are schematically shown in Fig. Including the resistive wall impedance in the longitudinal impedances. narrowband. (3.)| becomes large at u « 0. Negative mass instability without momentum spread First.
the coherent mode frequency 7 can be obtained by solving the dispersion relation. A higher energy particle takes 7 longer to complete one revolution. Vaccaro. Sec.72 72A. the threshold impedance for microwave instability is reflectively symmetric with respect to the real part of the impedance. On the other hand. the collective frequency becomes a complex number below the transition energy.&) S i n *J> ( 3 . it is also called negative mass instability. . in the longitudinal Hamiltonian (see Chap. a beam with a small 7 frequency spread can also encounter microwave instability at 7 < j r if the impedance is inductive.374 CHAPTER 3. CERN ISR TH/68-33 (1968). or resistive. see also Ref. and collective motion is Landau damped. e. Ruggiero and V. and the solution with a negative imaginary part gives rise to collective instability. Since the "microwave instability" resulting from the space-charge impedance occurs when 7 > 0. the threshold of collective instability can be estimated from the dispersion relation. The mass. SYNCHROTRON MOTION tive impedance above the transition energy. 2. If the distribution function is a symmetric function of momentum deviation 5. For resistive impedance. space-charge impedance. In this case. This results in a collective frequency shift without producing collective insta7 bilities. [3].g. Table VII.366 ) H C0S is negative above the transition energy with 7 > 0. there is a finite region of impedance value where the growth rate of collective instability is zero. Depending on the actual distribution function. Landau damping with finite frequency spread For a beam with a finite momentum spread with 7 ^ 0. Table 3. B. the beam with a zero momentum spread is unstable.G. —77. However. the collective frequency is a real number below the transition energy with 7 < 0. or it appears to have a negative mass.G.o7? " O UP2J? tC0S ^ * « + ( * .8: Characteristic behavior of collective instability without Landau damping. if the impedance is inductive. If Z\\/n is capacitive.4 shows the characteristic behavior of microwave collective instability. Below transition Above transition Z\\/n capacitive r\ < 0 stable 7 > 0 unstable 7 inductive unstable stable resistive unstable unstable The terminology of negative mass instability is derived from a pure space charge effect. IX) 1 /Az>\ 2 eV = .
except the Gaussian distribution.VII.4. C. or U' and V parameters as For the Gaussian beam. a simplified estimation of the stability condition is to draw a circle around the origin in the impedance plane Z. In the limit of small frequency spread. Note that a distribution function with a softer tail. The rms frequency spread of the beam becomes au = tJor/as. Eq. (3.367) reduces to Eq. All distribution functions. for the normalized distribution functions ^o(x) = 3(1 — £ 2 )/4./ V 7r J-oo x + il/(nujo'r]as) —rKTf \dx = 2[1 + J^*vwW> (3-368) fi = CI — nu>o. Eq. the distribution becomes the Dirac ^-function.z 2 ) 2 /16.0.34 shows the threshold V vs U' parameters. i.x2f'2/2. and the dashed lines outside the threshold curve are unstable with growth rates — (lmQ. we find <5FWHM = \/8 In 2 ag. Thus in the limit of zero detuning (or > zero frequency spread). 8(1 .5 respectively. 15(1 . f ? \ I 2cr <S J where 5 = Ap/po and as is the rms momentum spread.367) becomes -j(U + jV)JG/2 = 1.2.0. The dispersion relation can be integrated to obtain where JG [o r°° re~x2l2 =V.z 2 ) 4 /32. Keil-Schnell criterion Figure 3.3. Based on experimental observations and numerical calculations of the dispersion relation.365). gives a larger stability region in the parametric space. a less sudden cutoff. 3. we have JQ — y~2 as y —> oo. (3.0.34 shows the threshold V vs U' parameters of collective microwave instability with Im(fi) = 0. n < 2^Ea2MF elo v . Dashed lines inside the threshold curve correspond to stable motion.)/y/2 In2wor?aj = 0. In terms of U and V parameters.e. The right plot of Fig. (3. from inside outward. The solid line in the left plot of Fig. 3. we consider a Gaussian beam model of a coasting beam given by 1 V27TCT.34 show that the stability region depends on beam distribution.1. We usually define the effective U and V parameters.-K. LONGITUDINAL COLLECTIVE INSTABILITIES 375 For example. are limited to x < 1. and (l/V2^)exp(-a: 2 /2).. 315(1 . . and w(y) is the complex error function with y = —Q/(y/2nuioT](7s)Asymptotically. and 0.
Dashed lines outside the threshold curve have growth rates —lmQ/(V2 ln2uoT]as) = 0.2.2. where F is a form factor that depends on the distribution function. J.G. A.1. and 0. the total longitudinal energy drop from impedance. They correspond to -Ima/(V2 In2 W0T)OS) = -0.0. Right: The threshold V vs U' parameters for various beam distributions. z-± < **PWW eI n where / = FQIQ. and -0.e. Ruggiero and V.0. per unit frequency spread n\r]\\/2Tras for mode number n should be less than the total energy spread y/2^P2Eas of the beam. For a Gaussian beam. Pellegrini.M.-0. Keil and W.5 respectively. F = 1. and for a tri-elliptical distribution with ^o(^) = 8(1 .5. This Boussard conjecture has been well tested in the Intersecting Storage Ring (ISR).376 CHAPTER 3.94 [3]. Since the microwave growth rate is usually fast. the threshold condition can be obtained from the local peak current of the beam.-0. Dashed lines inside the threshold curve are stable. is the bunching factor. i. 554 (1980).3. and the the wavelength of the coherent wave is usually small compared with the bunch length.3.G. See e. e/0|Z|||. SYNCHROTRON MOTION Figure 3. CERN ISR TH/68-33 (1968). Schnell. Vaccaro.74 73 E. the Keil-Schnell criterion can be applied to the bunched beam by replacing the average current Io by the peak current /. and -FB = 27r/v/27rcr^.34: Left: The solid line shows the parameters V vs U' for a Gaussian beam distribution at a zero growth rate.-0. . Proc. This is the Keil-Schnell criterion.4. Wang and C. 74Since the growth rate of the microwave instability is normally very fast.1.g.4.0. CERN-ISR-TH-RF/69-48 (July 1969). F « 0. 11th HEACC. p.73 The Keil-Schnell criterion states that if the beam is stable.X2)3/2/3TT.
For a pure inductance impedance. Landau damping for microwave single bunch instability vanishes because of a small synchrotron frequency spread. Microwave instability below transition may arise from the real impedance.75 Landau damping plays an important role in damping collective instability. (3.j(Z^:SC/n) ohms was used to study the growth rate around the transition energy for RHIC.372) 1 = 1O\\ \ 3 ( a 0 0 q w . determination of microwave instability needs careful evaluation of the dispersion integral. Since the beam distribution function is nonadiabatic in the transition energy region. we assume a Gaussian beam model with the threshold impedance determined by the peak current.g. and the distribution function is therefore given by (see Sec. instability exists only below transition.374) shows that the growth rate near the transition energy is nearly equal to the growth rate without Landau damping. Furthermore. This is easy to understand: 75see e.348). Wang.374).Y. Nucl. (3. LONGITUDINAL COLLECTIVE INSTABILITIES D. T h e p e a k c u r r e n t is f (3. We assume a model of collective microwave instability such that the longitudinal modes are nearly decoupled and thus the coherent growth rate can be obtained by solving the dispersion relation Eq. The dispersion integral can be integrated to obtain the coherent mode frequency given by _ 1 3e/0 (Zy/n) 7 r V 3 ^ A t G > ( } ~3 2**/*FEv where JG = 2[l+jy/nyw(y)]. . The Keil-Schnell criterion is not applicable in this region. e. Sci. A ^ (6. we can find the eigenvalue of the growth rate Im (fi(t)) by solving Eq. The solution of Eq. (3.616) where Io is the average current and A is the rms phase-space area of the beam. 2323 (1985).VII. y = nujori %/6a M . 1) <jro(<5) = J^ie-3°ui\ V 7 T w h e r e a^ is given by E q .177). space-charge impedance. Because of a large space-charge impedance. IEEE Trans.g. Lee and J.M.a2^) irass = la y ^ 7 . (3. For a given broadband impedance model with constant Z\\/n. The region of collective instability can be estimated by using the Keil-Schnell criterion. The impedance model Z\\/n = 5 . IV. . Microwave instability near transition energy 377 Near the transition energy. The peak current is located at the center of the bunch A<j> = 0. For a pure capacitive impedance. the growth rate appears to be larger above the transition energy. NS-32. instability occurs when 7 > 7 T . S.
378
CHAPTER 3. SYNCHROTRON MOTION
at 7 = 7 T , the frequency spread of the beam becomes zero, and Landau damping vanishes. Fortunately, the growth rate is also small at 7 ss 7 T . The total growth factor across the transition energy region can be estimated by
G = exp j/(-Imfi) un8table d*j .
(3.375)
The total growth factor is a function of the scaling variable \Z\\/n\Nb/A. Note that the growth factor is much smaller if the initial phase-space area is increased. Phasespace dilution below transition energy has become a useful strategy in accelerating high intensity proton beams through transition energy. The CERN PS and the AGS employ this method for high intensity beam acceleration. Bunched beam dilution can be achieved either by using a high frequency cavity as noise source or by mismatched injection at the beginning of the cycle. The distribution function model Eq. (3.372) does not take into account nonlinear synchrotron motion near the transition energy. For a complete account of microwave instability, numerical simulation is an important tool near transition energy.76 A possible cure for microwave instability is to pass through transition energy fast with a transition energy jump. Furthermore, blow-up of phase-space area before transition energy crossing can also alleviate the microwave growth rate. We have discussed microwave instabilities induced by a broadband impedance. In fact, it can also be generated by a narrowband impedance. Longitudinal bunch shapes in the KEK proton synchrotron (PS) were measured by a fast bunch-monitor system, which showed the rapid growth of the microwave instability at the frequency of 1 GHz and significant beam loss just after transition energy (see Fig. 3.35).77 Temporal evolution of the microwave instability is explained with a proton-klystron model. The narrowband impedance of the BPM system causes micro-bunching in the beam that further induces wakefield. The beam-cavity interaction produces the rapid growth of the microwave instability. This effect is particularly important near the transition energy, where the frequency spread of the beam vanishes, and the Landau damping mechanism disappears. E. Microwave instability and bunch lengthening When the current is above the microwave instability threshold, the instability can cause micro-bunching. The energy spread of the beam will increase until the stability condition is satisfied. For proton or hadron accelerators, the final momentum spread of the beam may be larger than that threshold value caused by decoherence of the synchrotron motion.
76 W.W. Lee and L.C. Teng, Proc. 8th Int. Conf. on High Energy Accelerators, CERN, p. 327 (1971); J. Wei and S.Y. Lee, Part. Accel. 28, 77-82 (1990); S.Y. Lee and J. Wei, Proc. EPAC, p. 764 (1989); J. McLachlan, private communications on ESME Program. 77 K. Takayama et al., Phys. Rev. Lett, 78, 871 (1997).
VII. LONGITUDINAL COLLECTIVE INSTABILITIES
379
Figure 3.35: The longitudinal beam profiles observed at KEK PS revealing microwave bunching in the tail of the bunch. The bottom figure shows the longitudinal bunch profile before the transition energy, the middle figure at 1 ms after the transition energy, and the top figure at 2 ms after the transition energy. The microwave instability occurs near the transition energy for lack of Landau damping. The instability was found to be driven by a narrowband impedance caused by the BPM system. [Courtesy of K. Takayama, KEK]
For electron storage rings, the final momentum spread is equal to the microwave instability threshold due to synchrotron radiation damping. Using the Keil-SchnellBoussard condition of Eq. (3.371), we find
where vs is the synchrotron tune. Note that the bunch length depends only on the parameter f = {IQ\T]\IV1P2E) provided that the impedance does not depend on the bunch length. Chao and Gareyte showed that the bunch lengths of many electron storage rings scaled as a,~e1/(2+a)(3.377) This is called Chao-Gareyte scaling law. For a broadband impedance, we have a = 1. The scaling law is not applicable if the impedance depends on the beam current and bunch length. F. Microwave instability induced by narrowband resonances At low energy, the longitudinal space charge potential, shown as the first term in Eq. (3.357), can be large for high intensity beam bunch. It requires a costly large rf cavity potential to keep beam particles bunched inside the rf bucket. In particular,
380
CHAPTER 3. SYNCHROTRON MOTION
if it requires a beam gap for a clean extraction, and for minimizing the effect of the electron-cloud instability. The longitudinal space charge potential can be compensated by the inductive impedance shown in the second term of Eq. (3.357). We consider a cavity with ferrite ring filling a pillbox. The inductance is
L "~l^ l n iV (3'378)
where fj,' is the real part of the ferrite permittivity, i?i and R2 are the inner and outer radii of the ferrite rings, and I is the length of the pillbox cavity. The inductive inserts carried out at PSR experiment employs coaxial pillbox cavity with 30 ferrite rings each with width 2.54 cm, 12.7 cm inner diameter (id), and 20.3 cm outer diameter (od). The Proton Storage Ring (PSR) at Los Alamos National Laboratory compresses high intensity proton beam from the 800 MeV linac into a bunch of the order of 250 ns. The parameters for PSR are C = 90.2 m, 7 T = 3.1, vx = 3.2, vz = 2.2, vs = 0.00042, and /o = 2.8 MHz. To cancel the space charge impedance at 800 MeV for PSR at the harmonic h = 1, one requires about 3 pillbox cavities. The experimental test for this experiment was indeed successful.78 Unfortunately, the beam also encounters collective microwave beam instability at high intensity. The left plot of Fig. 3.36 shows the initial bunched coasting beam, and the right plot shows the microbunching of the beam under the action of three ferrite inserts.
Figure 3.36: The longitudinal beam profiles observed at PSR the bunched coasting beam in the presence of inductive inserts, where three 1-m long ferrite ring cavities were installed in the PSR ring. [Courtesy of R. Macek, LANL] The microwave instability is induced by a narrowband impedance with Q w 1 at the center frequency of / res « 27/o.79 Although the inductive inserts can be used
78M.A. Plum, et at, Phys. Rev. Special Topics, Accelerators 79see C. Beltran, Ph.D. thesis, Indiana University (2003).
and Beams, 2, 064201 (1999).
EXERCISE 3.7
381
to cancel the space charge impedance, the pillbox cavity can generate a narrowband impedance to cause microwave instability of the beam at higher harmonics. In order to alleviate this problem, it is necessary to broaden the narrowband impedance by either choosing different design geometries for different ferrite inserts, or by heating the ferrite so that the imaginary part (//') of the permittivity is larger at the cavity resonance frequency. At PSR, the cavities was heated to 125-150° C, so that the beam is below the microwave instability threshold.
Exercise 3.7
1. In synchrotrons, beam bunches are filled with a gap for ion-clearing, abort, extraction kicker rise time, etc. Show that the frequency spectra observed from a BPM for short bunches filled with a gap have a diffraction-pattern-like structure. Specifically, find the frequency spectra for 10 buckets filled with 9 equal intensity short bunches. The revolution frequency is assumed to be 1 MHz. 2. Show that the impedance of Eq. (3.363) has two poles in the upper half of the u plane, and find their loci. Use the inverse Fourier transformation to show that the wake function of the RLC resonator circuit is
W = nT^-"rt/2Q c o s ^ - ^ ^ s i n J , |
where £>r = o)r^/l — 1/4Q2. 3. The parameters of the SLC damping ring are E = 1.15 GeV, vx = 8.2, uz = 3.2, a c = 0.0147, -yex<z = 15 7 mm-mrad, aAp/p = 7.1 x 10" 4 , Vrf = 800 kV, C = 35.270 T m, h = 84, /,f = 714 MHz, p = 2.0372 m, and the energy loss per revolution is f0 = 93.1 keV. If the threshold of bunch lengthening is JVB = 1.5 x 1010, use the Keil-Schnell formula to estimate the impedance of the SLC damping ring.80 4. We assume that the growth rate of microwave instability in a quasi-isochronous electron storage ring can be obtained from Eq. (3.365). For electron beams, synchrotron motion is also damped because of the energy dependence of synchrotron radiation energy loss. The damping rate is given by TS = 2ETo/JsUo, where E is the energy of the particle, TQ is the revolution period, the damping partition Js ~ 2, UQ = C1E4/p, C 7 = 8.85 x 10~5 m/(GeV 3 ), and p is the bending radius. Assuming that the growth rate is equal to the damping rate at equilibrium, find the tolerable impedance as a function of the machine parameters. Discuss an example of an electron storage ring at E = 2 GeV. 5. Consider a pillbox-like cavity with length I (see Sec. VII.4). The cavity is filled with ferrite rings with inner and outer radii a and 6 respectively. Show that the longitudinal
80G.E. Fisher et al, Proc. 12th HEACC, p. 37 (1983); L. Rivkin, et al, Proc. 1988 EPAC, p. 634 (1988); see also P. Krejcik, et a!., Proc. 199S PAC, p. 3240 (1993). The authors of the last paper observed sawtooth instability at the threshold current JV B =3x 1010.
382
impedance for TMoio mode is 81 Z1=.ZS_ I
J2na\
CHAPTER 3. SYNCHROTRON MOTION
U'-jy," H^jk^H^jkcb) er
H[l\kca)42)(kcb)
- H^(kcb)H^(kca) - H^(kcb)H[2\kca)'
where Hm are Hankel functions which represent incoming and outgoing waves, ZQ = 377fi is the impedance of free space. kc = ui^/JIe = kJer{^i — j ^ " ) , k = ^ = wy'/ioeo in vacuum, tr is the relative permittivity and fx and n are the real and complex parts of the relative complex permeability.
81The general formula to calculate the shunt impedance is AV = —IZ\\ — —Esi, where Es is the longitudinal electric field, I is the total length, and / is obtained by Ampere's law: / = f Hdl =
VIII. INTRODUCTION TO LINEAR ACCELERATORS
383
VIII
Introduction to Linear Accelerators
By definition, any accelerator that accelerates charged particles in a straight line is a linear accelerator (linac).82 Linacs includes induction linacs; electrostatic accelerators such as the Cockcroft-Walton, Van de Graaff and Tandem; radio-frequency quadrupole (RFQ) linacs; drift-tube linacs (DTL); coupled cavity linacs (CCL); coupled cavity drift-tube linacs (CCDTL); high-energy electron linacs, etc. Modern linacs, almost exclusively, use rf cavities for particle acceleration in a straight line. For linacs, important research topics include the design of high gradient acceleration cavities, control of wakefields, rf power sources, rf superconductivity, and the beam dynamics of high brightness beams. Linacs evolved through the development of high power rf sources, rf engineering, superconductivity, ingenious designs for various accelerating structures, high brightness electron sources, and a better understanding of high intensity beam dynamics. Since electrons emit synchrotron radiation in synchrotron storage rings, high energy e+e~ colliders with energies larger than 200 GeV per beam can be attained only by high energy linacs. Current work on high energy linear colliders is divided into two camps, one using superconducting cavities and the other using conventional copper cavities. In conventional cavity design, the choice of rf frequency varies from S band to millimeter wavelength at 30 GHz in the two beam acceleration scheme. Research activity in this line is lively, as indicated by bi-annual linac, and annual linear collider conferences. Since the beam in a linac is adiabatically damped, an intense electron beam bunch from a high brightness source will provide a small emittance at high energy. The linac has also been considered as a candidate for generating coherent synchrotron light. Many interesting applications will be available if high brilliance photon beam experiments, such as LCLS, SASE, etc., are successful. This section provides an introduction to a highly technical and evolving branch of accelerator physics. In Sec. VIII. 1 we review some historical milestones. In Sec. VIII.2 we discuss fundamental properties of rf cavities. In Sec. VIII.3 we present the general properties of electromagnetic fields in accelerating cavity structures. In Sec. VIII.4 we address longitudinal particle dynamics and in Sec. VIII.5, transverse particle dynamics. Since the field is evolving, many advanced school lectures are available.
VIII. 1 Historical Milestones
In 1924 G. Ising published a first theoretical paper on the acceleration of ions by applying a time varying electric field to an array of drift tubes via transmission lines; subsequently, in 1928 R. Wideroe used a 1 MHz, 25 kV rf source to accelerate potas82 See G.A. Loew and R. Talman, AIP Conf. Proc. 105, 1 (1982); J. Le Duff, CERN 85-19, p. 144 (1985).
384
CHAPTER 3. SYNCHROTRON MOTION
sium ions up to 50 keV.83 The optimal choice of the distance between acceleration gaps is d = p\/2 = Pc/2f, (3.379) where d is the distance between drift tube gaps, pc is the velocity of the particle, and A and / are the wavelength and frequency of the rf wave. A Wideroe structure is shown in Fig. 3.37. Note that the drift tube distance could be minimized by using a high frequency rf source. In 1931-34 E.O. Lawrence, D. Sloan et al, at U.C. Berkeley, built a Wiederoe type linac to accelerate Hg ions to 1.26 MeV using an rf frequency of about 7 MHz.84 At the same time (1931-1935) K. Kingdon at the General Electric Company and L. Snoddy at the University of Virginia, and others, accelerated electrons from 28 keV to 2.5 MeV.
Figure 3.37: Top: Wideroe type linac structure. Bottom: Alvarez type structure. An Alvarez cavity has more than 50 cells. Here /3c is the speed of the accelerating particle, and X =
2TTC/CJ is the rf wave-
length.
To minimize the length of the drift region, which does not provide particle acceleration, a higher frequency rf source is desirable. For example, the velocity of a 1 MeV proton is v = Pc — 4.6 x 10~2c, and the length of drift space in a half cycle at rf frequency /rf = 7 MHz is \vf^1 « l m . As the energy increases, the drift length becomes too long. The solution is to use a higher frequency system, which became available from radar research during WWII. In 1937 the Varian brothers invented the klystron at Stanford. Similarly, high power magnetrons were developed in Great Britain.85
8 3 G. Ising, Arkiv fur Matematik o. Fisik 18, 1 (1924); R. Wideroe, Archiv fur Electrotechnik 2 1 , 387 (1928). 84 D.H. Sloan and E.O. Lawrence, Phys. Rev. 32, 2021 (1931); D.H. Sloan and W.M. Coate, Phys. Rev. 46, 539 (1934). 8 5 The power source of present day household microwave ovens is the magnetron.
VIII. INTRODUCTION TO LINEAR ACCELERATORS
385
However, the accelerator is almost capacitive at high frequency, and it radiates a large amount of power P = IV, where V is the accelerating voltage, / = OJCV is the displacement current, C is the capacitance between drift tubes, and w is the angular frequency. The solution is to enclose the gap between the drift tubes in a cavity that holds the the electromagnetic energy in the form of a magnetic field by introducing an inductive load to the system. To attain a high gradient, the cavity must be designed such that the resonant frequency is equal to the frequency of the accelerating field. A cavity is a structure in which electromagnetic energy can be resonantly stored. An acceleration cavity is a structure in which the longitudinal electric field can be stored at the gap for particle acceleration. A cavity or a series of cavities can be fed by an rf source, as shown in Fig. 3.38.
Figure 3.38: Left: Schematic of a single gap cavity fed by an rf source. The rf currents are indicated by j on the cavity wall. Middle: A two-gap cavity operating at vr-mode, where the electricfieldsat two gaps have opposite polarity. Right: A two-gap cavity operating at 0-mode, where the electricfieldsat all gaps have the same polarity. In 0-mode (or 27r-mode) operation, the rf currents on the common wall cancel, and the wall becomes unnecessary. The Alvarez structure shown in Fig. 3.37 operates at 0-mode. When two or more cavity gaps are adjacent to each other, the cavity can be operated at 7r-mode or 0-mode, as shown in Fig. 3.38. In 0-mode, the resulting current is zero at the common wall so that the common wall is useless. Thus a group of drift tubes can be placed in a single resonant tank, where the field has the same phase in all gaps.86 Such a structure (Fig. 3.37) was invented by L. Alvarez in 1945.87 In 1945-47 L. Alvarez, W.K.H. Panofsky, et al, built a 32 MeV, 200 MHz proton drift tube linac (DTL). Drift tubes in the Alvarez structure are in one large cylindrical tank and powered at the same phase. The distances between the drift tubes, d = /3A,88 are arranged so that the particles, when they are in the decelerating phase, are shielded
Alvarez, Phys. Rev. 70, 799 (1946). 88It appears that the distance between drift tubes for an Alvarez linac is twice that of a Wideroe linac, and thus less efficient. However, the use of a high frequency rf system in a resonance-cavity more than compensates the requirement of a longer distance between drift tubes.
86This
87L.
is the TMOio mode to be discussed in Sec. VIII.3.
386
CHAPTER 3. SYNCHROTRON MOTION
from the fields. In 1945 E.M. McMillan and V.I. Veksler discovered the phase focusing principle, and in 1952 J. Blewett invented electric quadrupoles for transverse focusing based on the alternating gradient focusing principle. These discoveries solved the 3D beam stability problem, at least for low intensity beams. Since then, Alvarez linacs has commonly been used to accelerate protons and ions up to 50-200 MeV kinetic energy. In the ultra relativistic regime with /3 —> 1, cavities designed for high frequency operation are usually used to achieve a high accelerating field.89 At high frequencies, the klystron, invented in 1937, becomes a powerful rf power source. In 1947-48 W. Hansen et al., at Stanford, built the MARK-I disk loaded linac yielding 4.5 MeV electrons in a 9 ft structure powered by a 0.75 MW, 2.856 GHz magnetron.90 On September 9, 1967, the linac at Stanford Linear Accelerator Center (SLAC) accelerated electrons to energies of 20 GeV. In 1973 P. Wilson, D. Farkas, and H. Hogg, at SLAC, invented the rf energy compression scheme SLED (SLAC Energy Development) that provided the rf source for the SLAC linac to reach 30 GeV. In 1990's, SLAC has achieved 50 GeV in the 3 km linac. Another important idea in high energy particle acceleration is acceleration by traveling waves.91 The standing wave cavity in a resonant structure can be decomposed into two traveling waves: one that travels in synchronism with the particle, and the backward wave that has no net effect on the particle. Thus the shunt impedance of a traveling wave structure is twice that of a standing wave structure except at the phase advances 0 or TT. TO regain the factor of two in the shunt impedance for standing wave operation, E. Knapp and D. Nagle invented the side coupled cavity in 1964.92 In 1972 E. Knapp et al. successfully operated the 800 MHz side coupled cavity linac (CCL) to produce 800 MeV energy at Los Alamos. In 1994 the last three tanks of the DTL linac at Fermilab were replaced by CCL to upgrade its proton energy to 400 MeV. Above j3 > 0.3, CCL has been widely used for proton beam acceleration. A combination of CCL with DTL produces the CCDTL structure suitable for high gradient proton acceleration. For the acceleration of ions, the Alvarez linac is efficient for /3 > 0.04. The acceleration of low energy protons and ions relies on DC accelerators such as the
89The linacs designed for relativistic particles are usually called high-/) linacs even though the maximum f) is 1. 90E.L. Ginzton, W.W. Hanson and W.R. Kennedy, Rev. Sci. lustrum. 19, 89 (1948); W.W. Hansen et al, Rev. Sci. lustrum. 26, 134 (1955). 91J.W. Beams at the University of Virginia in 1934 experimented with a traveling-wave accelerator for electrons using transmission lines of different lengths attached to a linear array of tubular electrodes and fed with potential surges generated by a capacitor-spark gap circuit, similar to the system proposed by Ising. Burst of electrons were occasionally accelerated to 1.3 MeV. See J.W. Beams and L.B. Snoddy, Phys. Rev. 44, 784 (1933); J.W. Beams and H. Trotter, Jr., Phys. Rev., 45,849 (1934). 92 E. Knapp et al., Proc. 1966 linac Con}., p. 83 (1966).
VIII. INTRODUCTION TO LINEAR ACCELERATORS
387
Cockcroft-Walton or Van de Graaff. In 1970 I. Kapchinskij and V. Teplyakov at ITEP Moscow invented the radio-frequency quadrupole (RFQ) accelerator. In 1980 R. Stokes et al. at Los Alamos succeeded in building an RFQ to accelerate protons to 3 MeV. Today RFQ is commonly used to accelerate protons and ions for injection into linacs or synchrotrons. Since the first experiment on a superconducting linear accelerator at SLAC in 1965, the superconducting (SC) cavity has become a major branch of accelerator physics research. In the 1970's, many SC post linear accelerators were constructed for the study of heavy ion collisions in nuclear physics.93 Recently, more than 180 m of superconducting cavities have been installed in CEBAF for the 4 GeV continuous electron beams used in nuclear physics research. More than 400 m of SC cavities at about 7 MV/m were installed in LEP energy upgrade, and reached 3.6 GV rf voltage for the operation of 104.5 GeV per beam in 2000.94 The TESLA project had also successfully achieved an acceleration gradient of 35 MV/m.
VIII.2
Fundamental Properties of Accelerating Structures
Fundamental properties of all accelerating structures are the transit time factor, shunt impedance, and Q-value. These quantities are discussed below. A. Transit time factor We consider a standing wave accelerating gap, e.g. the Alvarez structure, and assume that the electric field in the gap is independent of the longitudinal coordinate s. If £ is the maximum electric field at the acceleration gap, the accelerating field is Es=£ cos Lot. (3.380)
The total energy gain in traversing the accelerating gap is
AE = ejii£
cos f
ds = e£gTtr = eV0,
Ttr = ^
^
,
(3.381)
where Vo = £gTtv is the effective voltage of the gap, T tr is the transit time factor, A = 2TTC/CJ is the rf wavelength, and wg/PA is the rf phase shift across the gap. If the gap length of a standing wave structure is equal to the drift tube length, i.e. g = /3A/2, the transit time factor is T tr = sin(7r/2)/(7r/2) = 0.637. This means that only 63% of the rf voltage is used for particle acceleration. To improve the efficiency, the gap length g should be reduced. However, a small g can lead to sparking at the gap. Since
93See e.g., H. Piel, CERN 87-03, p. 376 (1987); CERN 89-04, p. 149 (1994), and references therein. The geometries of these low energy SC cavities are essentially the drift tube type operating at A/4 or A/2 modes. 94 P. Brown et al, Proceedings of PAC2001, p. 1059 (IEEE, 2001).
388
CHAPTER 3. SYNCHROTRON MOTION
there is relatively little gain for g < /JA/4, the gap g is designed to optimize linac performance. The overall transit time factor for standing wave structures in DTL is about 0.8. It is worth pointing out that the transit time factor of Eq. (3.381) is valid only for the standing wave structure. The transit time factor for particle acceleration by a guided wave differs from that of Eq. (3.381). An example is illustrated in Exercise 3.8.7. B. Shunt impedance Neglecting power loss to the transmission line and reflections between the source and the cavity, electromagnetic energy is consumed in the cavity wall and beam acceleration. The shunt impedance for an rf cavity is defined as Rsh = V02/Pd, (3.382)
where V is the effective acceleration voltage, and P<j is the dissipated power. For a o multi-cell cavity structure, it is also convenient to define the shunt impedance per unit length rSh as
r.-^-^•^cav
-Td/^cav
«
£--*,
US rsb
(3.383,
where £ is the effective longitudinal electric field that includes the transit time factor, and dP<i/ds is the fraction of input power loss per unit length in the wall. The power per unit length needed to maintain an accelerating field £ is P^/L = £2/rs^ and the accelerating gradient for low beam intensity is £ = yrShPd/£cav For a 200 MHz proton linac, we normally have rsj, ~ 15 — 50 Mfi/m, depending on the transit time factors. For an electron linac at 3 GHz, rsh « 100 Mfi/m. For high frequency cavities, the shunt impedance is generally proportional to a;1/2 (see Exercise 3.8.4). A high shunt impedance with low surface fields is an important guideline in rf cavity design. For example, using a 50 MW high peak power pulsed klystron, the accelerating gradient of a 3 GHz cavity can be as high as 70 MV/m. The working SLC S-band accelerating structure delivers about 20 MV/m.95 C. The quality factor Q The quality factor is defined by Q = oj\Vst/Pd, and thus we obtain dWJdt = -Pd = -LJWJQ,
95 P.
(3.384)
Raimondi, et al, Proceedings of the EPAC2000, (EPAC, 2000).
97 Alternatively. INTRODUCTION TO LINEAR ACCELERATORS 389 where Wst is the maximum stored energy. However.VIII. we define the stored energy per unit length as Wst = Wst/Lcav.387) where Lcav is the length of the cavity structure and v% is the velocity of the energy flow.tw = -kcav/^g.^ ' or Q = uwst -dPjdS- .. (3. For a traveling wave structure.385) where QL is the loaded Q-factor that includes the resistance of the power source.387). <F. the time for the field to decay to 1/e of its initial value is called the filling time of a standing wave cavity. (3. . (3386) The filling time for a traveling wave structure is96 *F. (3. VIII. it will quickly pass through the wave propagation region unless a wiggler field is employed to bend back the particle velocity vector. welds.3 Particle Acceleration by EM Waves Charged particles gain or lose energy when the velocity is parallel to the electric field. a wave guide designed to provide electric 96We will show that the velocity of the energy flow is equal to the group velocity. 97This scheme includes inverse free electron laser acceleration and inverse Cerenkov acceleration. In general. it can gain energy.385) is twice that of the traveling wave in Eq. On the other hand.SW = 2QL/o. (3. the Q-factor of an accelerating structure is independent of whether it operates in standing wave or traveling wave modes. A useful quantity is the ratio Rsh/Q'Q ^ ' Q u(Wst/Lcm) uwst(6-6m) which depends only on the cavity geometry and is independent of the wall material. A particle traveling in the same direction as the plane electromagnetic (EM) wave will not gain energy because the electric field is perpendicular to the particle velocity. if a particle moves along a path that is not parallel to the direction of an EM wave. and the power loss per unit length becomes dPd ~di = wwst . vt = Pd/wst. etc. For standing wave operation. The conventional definition of standing wave filling time in Eq.
the EM fields can be described by the traveling wave component in Eq. R. R. 1979 Part. We will discuss the choice of standing wave vs traveling wave operation.7. (r. The phase velocity of the EM waves can be slowed down by capacitive or inductive loading. (3. Hr = 0. In general. Miller. A. SYNCHROTRON MOTION field along the particle trajectory at a phase velocity equal to the particle velocity is the basic design principle of rf cavities. s is the longitudinal coordinate. = 0 listed in Table V. (3. . where ZQ = y/zoAo is the vacuum impedance. EM waves in a cylindrical wave guide First we consider the propagation of EM waves in a cylindrical wave guide. Early.k2T . (3. Its high duty factor can be used to accelerate long pulsed beams such as protons.390 CHAPTER 3. Con}.H. These waves are classified into transverse magnetic (TM) or transverse electric (TE) modes.A. 3701 (IEEE.w t l. VI. and k2 = {u/cf . In this section we study the properties of electromagnetic waves in cavities. at the pipe radius r = b.390) The propagation modes are determined by the boundary condition for Es = E$ = 0 . Bane. The standing wave can also accelerate oppositely charged beams traveling in opposite directions.A. On the other hand. traveling in the +s direction. rf cavities for particle acceleration can be operated in standing wave or traveling wave modes. Proc.H.282) in Sec. Kmn = jmn/b. and K.98 Standing wave cavities operating at steady state are usually used in synchrotrons and storage rings for beam acceleration or energy compensation of synchrotron radiation energy loss.391) where j m n are zeros of the Bessel functions Jm(jmn) pendix B Sec. employing high power pulsed rf sources. and continuous wave (CW) electron beams in the Continuous Electron Beam Accelerator Facility (CEBAF). <j>) is the cylindrical coordinate. i.e. V.. k is the propagation wave number in the +s direction. p. SLAC-PUB-3935 (1988). 1979). The EM fields of the lowest frequency TMoi mode. Hs = 0. Ace.2 in Ap- 98See G. are Es = Kr EoMkTr)e-X'a-ut\ (3. Since there is no ends for the cylindrical wave guide.389) Er = j^£oJi(fc r r)e-* s . Miller. the effect of shunt impedance. a traveling wave structure can attain a very high gradient for the acceleration of an intense electron beam pulse. R. Loew.1 (see Appendix B Sec. V). and the coupled cavity linac.8.L. see also Exercise 3. E# = 0.
However. We define wc = krc = 2.282)]. it is not useful for particle acceleration. the particle can not be synchronized with the EM wave during acceleration.405c/6. it becomes the transverse TEM wave. travels at a phase velocity of . Right: Dispersion curve (w/c)2 = fc2 + (2. At high frequency. (3. The phase velocity u/k for a wave without cavity load is always greater than the velocity of light. This mode is a free propagation mode along the longitudinal s direction. However. where kT -> 0. (LJC/LO)2]1/2 (3. 1 radial-node at the boundary of the cylinder [see Eq.405/6)2.211/2 > c.p ) 2 l c [ \OJ J \ V2 . the phase velocity approaches c. i. C. shown in Fig. The wave number of the TMOi wave and the corresponding phase velocity vp become k = ^\l.392) k [1- Unattenuated wave propagation at ui < uoc is not possible. the wave travels forward and backward with a very large phase velocity. the longitudinal component of the EM wave vanishes. Thus the frequency of the TMoi mode is LJ/C = \Jk2 + (2. = £ = . 3. Since the phase velocity propagates faster than the speed of light. The subscript 01 stands for m = 0 in ^-variation. INTRODUCTION TO LINEAR ACCELERATORS 391 Figure 3.39.VIII. v. At high frequencies. ET k ' ET ckZ0 Zo' J B.389) represents an infinitely long pulse of EM waves in the cylindrical wave guide. v .e. the electromagnetic field is transverse. The phase of the plane wave. the phase velocity approaches the speed of light.405/b)2 for the TMoi wave. . At low frequency. Phase velocity and group velocity Equation (3. ks — cut.39: Left: Schematic of a cylindrical cavity.
From Fig. we obtain E(t) = A(t . The power of the TM wave is P=\te[ 2 Js ErH.395) *-F-S| • wo < 3397 > Using Eq.395) into Eq. (3. (3. (3. and the amplitude function of the EM pulse propagates at the "group velocity" {ui-Ljo) = ko + k'(uj-uJo). v* = w = tc2=v*- (-0) 3 40 . (3.tte+wo41 dedw.39 we see that the group velocity is zero at k = 0. SYNCHROTRON MOTION vp = ds/dt = uj/k. In reality. we expand the dispersion wave number around Wo: k{u) = k(u0) + — aw Substituting Eq. we have to discuss a short pulse formed by a group of EM waves.399) where Wm is the magnetic energy. The velocity of the energy flow is Thus the velocity of energy flow is equal to the group velocity. (3.390) has been included.392 CHAPTER 3.396) Note that the phase of the pulse propagates at a "phase velocity" of vp = uo/ko. Since the Maxwell equation is linear. For a quasi-monochromatic wave at the angular frequency CJ0. the group velocity is equal to the velocity of energy flow in the wave guide.dS = \El^~ 2 CZQK^ JO f J!(krr)2nrdr. (3-394) where the dispersion of the wave number of Eq. (3. The propagation of the pulse inside a wave guide becomes E(t.394). (3.k's) ejiuot-kas\ (3.393) where A(t) is the amplitude with a short time duration. we obtain vg = kc2/uj. and the total energy per unit length stored is W = 2Wm = \E20J^-2 fQ J?(krr)2irrdr. s) = A{t)e^at-k^ = 7^fJ AiOeJ^-^-^+^dtdu. For a quasi-monochromatic pulse at frequency w0 in free space. In fact. (3.392) for single-mode wave propagation. s) = ^ff A(Oe J ' [llrt -* (w) . the electric field can be represented by E(t. or vpvg = c2. the pulse can be decomposed in linear superposition of Fourier series.398) where H^ is the complex conjugate of H^. 3.
•••.40: Left: Schematic of a cylindrical cavity.402) .282) in the closed cylindrical pillbox cavity is reproduced as follows: ( Es = Ck2r Jm{kTr) cosm<j>cos ks. The dispersion relation is UJ/C = ^Jk? + k2. p = 0 . 1 .VIII. Similarly. Figure 3. u is the angular frequency.40}. there are also TE modes where the longitudinal electric field is zero. where the longitudinal magnetic field is zero for TM modes. 2 . the TM mode solution of Eq. Right: Dispersion curve (w/c)2 = (pir/d)2 + (2. With proper design of pillbox geometry. We first discuss the standing wave solution of a closed pillbox cavity without beam holes. where d is the length of the pillbox. Here we discuss the standing wave solution of Maxwell's equation for a "closed pillbox cavity. The effect of a chain of cylindrical cells on the propagation of EM waves is discussed in the next section. ET = -CkK E. and kd is the phase advance of the EM wave in the cavity cell. The cylinder has a beam hole for the passage of particle beams (Fig. we obtain k d = PTT. and kr and k are wave numbers of the radial and longitudinal modes. ( Hs = 0. [ # 0 = -jCu>eokr J'm{krr) cos mcj) cos ks. Using the boundary conditions that Er = 0 and E$ = 0 at s = 0 and d." and the effect of beam holes.405/6)2 for TMoip resonance waves (marked as circles) for a closed cylindrical pillbox without beam holes. TM modes in a cylindrical pillbox cavity 393 Now we consider a cylindrical pillbox cavity. (3. J Hr = -jC^^I T Jm{krr) sin m0 cos ks. the phase velocity of the TMoio mode can be slowed to the particle speed for beam acceleration. we obtain kr. With a time dependent factor e7'"'*.p = Cnk -Jm(krr) sinm<f>sinks.mnb = jmn.401) 1 J'm{krr) cos m0 sin ks. 3. INTRODUCTION TO LINEAR ACCELERATORS C. (3. Using the boundary conditions Es = 0 and E^ = 0 at the pipe radius r = b. where both ends of the cylinder are nearly closed. (3.
027 mm. inner diameter of 26 = 83. The solid lines in Fig. we have Es = EoJo{krr).99 mm.793 mm. The circles in Fig. 021. SYNCHROTRON MOTION where b is the inner radius of the cylinder. At / = 2. and the phase velocity vp is equal to c. phase advance of 2TT/3. Medical Electron Accelerators. 1993). To lower the phase velocity. all mode frequencies become horizontal lines. disk diameter of 2a = 26. When the beam hole is completely closed. B^^j^-Jx{kTr). where the effective d parameter is reduced for a single cell structure. the phase shift per cell is about 120°. V).856 GHz. and d = 34.24 mm.842 mm.9 shows parametric dependence of a SLAC-like pillbox cavity at / = 2. Karzmark. When the beam hole radius decreases. it provides a continuous TM mode frequency as a function of wave number k." Because of the coupling between adjacent pillbox-cavities. The details of the TMOio mode are shown in the right plot.19. TMolo. The wall thickness chosen was 6. 020. 3. Increasing the size of the beam hole decreases the coupling capacitance and increases the TMOio mode frequency. 3. 011. 3.404) where LO/C = 2. 3. the discrete mode frequencies become a continuous function of the phase advance kd. Nunan. (McGraw-Hill.41. The EM wave modes can be calculated by finite element or finite difference EM codes with a periodic boundary (resonance) condition and a prescribed phase advance kd across the cavity gap.461 — 81. See also C. the circles in the left plot of Fig. D. Thus the resonance frequency w for the TM mnp mode is For the lowest mode.22 .394 CHAPTER 3.05 m. and the phase-velocity is effectively lowered.41 are the dispersion curves of frequency / vs phase shift kd for TMOnp modes of a SLAC-like pillbox cavity with a = 18 mm.405/6. (3. Xraig S. beam hole radius a and cylinder radius 6 are tailored to provide matched phase advance kd and phase velocity cj/k for the structure. New York. length of the structure of L = 3. and Eiji Tanabe.J. 030 for a closed cylindrical pillbox are shown as circles in the left plot of Fig. Table 3.41. Analytic solution of Maxwell's equations for an actual cavity geometry is difficult. and disk thickness of 5.2 (Appendix B Sec. . The dashed lines show the world line vp = c. the mode frequencies become discrete points. More importantly. Note that the shunt impedance per unit length is maximum at a phase advance " T h e calculation was done by Dr. The wall thickness slightly influences the mode frequencies of TM On i modes.40 (right) show the discrete mode frequencies of TMOIO and TM 0U on the dispersion curve. and j m n are zeros of the Bessel functions JmUmn) = 0 listed in Table V.856 GHz. Li using MAFIA in 2D monopole mode. Both these modes have phase velocities greater than c.856 GHz. The frequencies of the TM modes 010. The actual SLAC structure is a constant gradient structure with frequency of / = 2. b = 43 mm.
2 42. / vs kd. and thus we have b « 2.000 26. Alvarez structure The Alvarez linac cavity resembles the TMOio standing wave mode (see Table 3.405c/w.853 1. The phase advance per cell at a given frequency is mainly determined by the cell length.857 1.475 17.37 41. for TMoip modes for a pillbox cavity with a = 18 mm.5107 7713 29.9: Parametric dependence of the SLAC cavity geometry T(mm) I d (mm) I kd (deg) | / (GHz) I R& (10Bfl) I Q I rsh (10sfVnTr 42.99 120 2.580 39. Since fi increases .685 34.485 | 180 [ 2.8579 0.24 90 2.466 | 17646 | 46. and d = 34.56 41.79 41.10).290 [ 52. 6 = 43 mm. D.14 14848 54. Circles show the TMonp mode frequencies for a closed pillbox cavity.404) is independent of s.415 46.VIII. Right: Dispersion curve of TMoio mode. such as rods and slugs inside the cavity.98 of about 135°. Table 3.99 mm.2 10947 45. The dashed lines show the world line vp = c.653 160 2.416 16507 51.73 41.36 135 2.857 | 2.616 105 2.874 13700 53. are designed to obtain a proper resonance frequency for the TMOio mode. The tank radius and other coupling structures.857 2.805 30.559 12413 50. (3.41: Left: Dispersion curves. The total length is designed to have a distance /3\ between two adjacent drift tubes (cells).92 41. where fie is the speed of the accelerating particles.495 60 2.854 1. INTRODUCTION TO LINEAR ACCELERATORS 395 Figure 3. The resulting electric field of Eq.857 2.
vp w c. Loaded cavity cells can be joined together to form a cavity module. what happens to the EM wave in a chain of cavity cells? If the wave guide is loaded with wave reflecting structures such as iris. and the CEBAF cavity. The phase velocity must be brought to the level of the particle velocity. the phase advance kd = n. Figure 3. the SLAC cavity.42 (top). We observed in Sec. The dispersion relation in this case resembles that in Fig. b . When the a. At these frequencies. At some frequencies the reflected waves from successive irises are exactly in phase so that the irises force a standing wave pattern. The reflected waves for a band of frequencies interfere destructively so that there is no radial field at the irises. this gives rise to a minor perturbation in the propagating wave. frequency / vs phase advance kd of the loaded SLAC-like pillbox cavity. as an example.60 Fermilab (cavity2) 45 1902 59 2J)_ CEBAF SC cavity 1497 7. where .42 shows a slow wave structure. nosecone. D that the propagating wave in an unloaded cylindrical wave guide has phase velocity vp > c. the propagating EM waves can be reflected by obstruction disks.E-field is in the direction of beam momentum. unattenuated propagation is impossible. Opening a beam hole at the center of the cavity is equivalent to a capacitive loading for attaining continuous bands of resonance frequencies.e. For particle beam acceleration. or washers. SYNCHROTRON MOTION along the line. we consider the TM guided wave. The size of the beam hole determines the degree of coupling and the phase shift from one cavity to the next. i. Table 3.66 10.10 shows some properties of an Alvarez linac. Such a chain of loaded wave guides can be used to slow the phase velocity of EM waves. so that the EM wave becomes a standing wave and the group velocity again becomes zero.41 shows.. 3.396 CHAPTER 3.0 EiftA Fermilab (cavity 1) 47 744 55 1. the distance between drift tubes increases as well.39. etc.5 [ « 100 [ 20_ E. Figure 3. 5 5-10 SLAC linac | 2856 | 4. A simple method of reducing the phase velocity is to load the structure with disks. The question is. Loaded wave guide chain and the space harmonics In previous subsections.e.10: Some parameters of basic cylindrical cavity cells Machine I / (MHz) I b (cm) I d (cm) I JVcen I £ (MV/m) Alvarez linac 201. we find that the dispersion curve of a closed cylindrical pillbox cavity resembles that of a cylindrical wave guide except that there are infinite numbers of discrete resonance frequencies. i. 3. Since the irises play no role in wave propagation.2 | 3. shown in Fig. Table 3.25 57.
e.s).410) . 0. 4>. <l>. Es(r." These space harmonics are shown in Fig. the phase change from cavity to cavity along the accelerator gives an overall phase velocity that is equal to the particle velocity. where d is the period of the wave guide.J>. We note further that as kod — 0 or TT. parameters of the disk radii are tailored correctly.<t>. the electromagnetic field can be expanded in Fourier series (or Floquet series).408) (3. H^(r.q (3.42.s.406) With the Floquet theorem for the periodic wave guide: Es{r.409) = iEr£o. s). The solid line branches correspond to forward traveling waves and the dashed line branches are associated with backward traveling waves.<j>)e-^s'd = e^1 £ q=—oo g=—oo £s»)e-^s." andfeois the propagation factor of the "fundamental space harmonic. Bottom: Dispersion curve (tu/c) vs k. The field components of the lowest TMOn mode with cylindrical symmetry become Es = ^EOgJo(kriqr)e-^s-wt\ &r (3.t) = e-Xk°s-^ where g Es. 3. (q = integer) is the propagation wave number for the gth "space harmonic. #.VIII.S + d) = H^(r.t) = e-^s-^Es(r. q Kr. The EM wave of an infinitely long disk loaded wave guide is Es(r.407) 27rg kq = ko + —.s + d) = E3{r. <j>. s. etc. a.cj>. s).q V* = J^E^EoMkr^e-^-^.(3. 7r).405) (3.Ji(^/)e"3hs-ul1.^s). The phase velocity ui/k with a cavity load is equal to the speed of light at a specific point of the dispersion curve.q{r. shown as the intersection of the dashed diagonal line and the solid dispersion curve.t) = e'^-^H^r. The q = 0 space harmonic corresponds to kd £ (—IT.(r. (3.42: Top: Schematic of a chain of cylindrical cavities. forward and backward traveling > branches coincide and they will contribute to enhance the electric field.<f>. 37T). and the q = 1 space harmonic to kd £ (TT. i. INTRODUCTION TO LINEAR ACCELERATORS 397 Figure 3. •^0 q &r.
Each point corresponds to the propagation factor kq. At kod = ir. they must have zero slope at the lower frequency u>o/c. it represents a traveling wave or the maximum of a standing wave. and these curves must join.e. This indicates that the electric field of the qth space harmonic is independent of the transverse position. T h e statement t h a t t h e electric field is independent of transverse position is valid only near t h e center axis of loaded wave-guide structures. The extreme of the pass band is kod = 7T./c)2 . The arrows indicate the maximum electric field directions. i. or the propagation band.1 < cos kod < 1. (3. = V'- 100 One may wonder how t o reconcile t h e fact t h a t t h e tangential electric field component Es must be zero at r = b. .412) K —n. there are infinite numbers of crossings between the horizontal line and the dispersion curve. which has an identical slope in the u>/c vs k curve. where kod = T (see also T Fig.413) where the group velocity is zero. At a given frequency w.100 The dispersion curve of a periodic loaded wave-guide structure (or slow wave structure) is a typical Brillouin-like diagram shown in Fig. 3. Higher order space harmonics have no effect on a beam because they have very different phase velocity. 3. the cavity has lowest rf loss.A*.42. The lower plot shows a similar snapshot for kd = 0. The upper plot shows the snapshot of an electromagnetic wave. The electric field at a snapshot is shown schematically in Fig. where the branches with solid lines correspond to forward traveling wave. the phase velocity is vpq = -r = -.41).. The lengths of kd — n. an identical group velocity: doj duj (3-415) ^ = dk~g = Ik. The range of frequencies [u>o.414) If we draw a horizontal line in the dispersion curve within the pass band of the frequency. 3. Because the dispersion curve is a simple translation of 2ir/d.101 making this a favorable mode of operation for accelerator modules. p>* (3. These crossings are separated into space harmonics. 2TT/3. At an instant of time. SYNCHROTRON MOTION k\ = (o. kq ko + 2irq/d ' Note that kr>q = 0 and Jo(kr^r) = 1 for up>9 = c. TT/2. and at the upper frequency uv/c. 27r/3 and n cavities. ww] is called the pass band.398 with CHAPTER 3. and TT/2 cavities are also shown. (3. and the branches with dashed dots are backward traveling wave.411) (3. The condition for wave propagation is .43. 101 The rf loss is proportional t o \H$\2 on the cavity wall. where kod = 0.
i.e. and •K phase shift structures. The resulting shunt impedance is half of that in traveling wave operation. SUPERFISH. The actual electromagnetic fields must satisfy the periodic boundary conditions.27r/3. the resonance frequency of the electric coupled cavity is102 w m = u)0[l + «(1 . Since Jo(kTfir) = 1.417) where W is the resonance frequency without beam hole coupling. or krfi = 0 for the fundamental space harmonic [see Eq. Note that only half of the kd = TT/2 mode has longitudinal electric field in the standing wave mode. (3.cos k0md)]l/2 . This implies that the transverse force on the particle vanishes as well (see Sec. (3.VIII. For magnetically coupled cavity. (3. and 3D MAFIA.416) In the coupled RLC circuit model. The resonance frequency can be more accurately calculated from powerful finite difference. n/2. the resonance frequency is given by o o = > U[1 + K ( 1 . Bottom: Snapshot at the maximum electric field configuration across each cell for kd = 0. There are N + 1 resonances located at kOmd = miT/N {m = 0. VIII. 2TT/3.2.1. • • •. the energy gain of a charged particle is independent of its transverse position.C O S M ) ] 1 / 2 • . or finite element. and K is the couo pling coefficient. The operating condition vp = c is equivalent to kg = u>/c. 102See Exercise 3. N). and -K are shown. The snapshot represents the field pattern of a traveling wave guide or the maximum field pattern of a standing wave. INTRODUCTION TO LINEAR ACCELERATORS 399 Figure 3.8.411)].5).6. programs such as 2D URMEL. The phase advances kd = 7r/2. the longitudinal electric field of the fundamental space harmonic is independent of the radial position within the radius of the iris.43: Top: Snapshot of a sinusoidal wave. A module made of N cells resembles a chain of N weakly coupled oscillators. The size and the length of cavity cells are also tailored to actual rf sources for optimization. LALA.
because only half of the cavity cells are used for particle acceleration. The filling time of a standing wave structure is a few times the cavity filling time 2QL/W. For example. with drift tubes used to shield the electric field at the decelerating phase. The high-/5 linac can also be operated as a traveling wave guide. a wave guide accelerator. These field free cells are coupled to the main accelerating cavity in the high magnetic field region. e. SYNCHROTRON MOTION F.10). 3.44). e. Standing wave cavities are usually used to accelerate CW beams. the shunt impedance in kd = TT/2 mode operation is reduced by a factor of 2.3. if a cavity has 50 cells.45. In a storage ring. Standing wave operation of a module made of many cells may have a serious problem of many nearby resonances. a standing wave can be used to accelerate beams of oppositely charged particles moving in opposite directions.400 CHAPTER 3. Nagle in 1964. However. Similarly. There are two ways to operate high-/? cavities: standing wave or traveling wave. where the phase velocity is equal to the particle velocity. these empty cells can be shortened or moved outside. where dui/dk has its highest value. This problem can be minimized if the standing wave operates at the kd = n/2 condition. the resulting shunt impedance is 1/2 of that of a traveling wave structure except for the phase advance kd = 0 or n (see Fig.A 49 48 ^ = 7r'50?r'507r'--Since du/dk — 0 for a standing wave at fed = 0 or n.g. Since every other cavity cell has no electric fields in kd — TT/2 standing wave operation. the CEBAF rf cavity at the Jefferson Laboratory (see Table 3. This led to the invention of the coupled cavity linac (CCL) by E. can effectively accelerate particles in its entire length. The idea is schematically shown in Fig. it can have standing waves at I. where QL is the loaded Q-factor. and coupled cavity linacs We have shown that the Alvarez linac operates at the standing wave TMOio mode. and long pulse beams. The CCL cavities operate at TT/2 mode. A wave guide accelerator is usually more effective if the particle velocity is high. Knapp and D. traveling wave.g. to allow time to build up its electric field strength for beam acceleration. There are divided . A small shift of rf frequency will lead to a different standing wave mode. these resonances are located in a very narrow range of frequency. On the other hand. in the proton linacs and storage rings. The effective acceleration gradient is reduced by the transit time factor and the time the particle spends inside the drift tube. The electric field pattern of the main accelerating cavity cells looks like that of a w-mode cavity. 3. where field free cells are located outside the main cavity cells. the forward traveling wave component of a standing wave can accelerate particles. Such a design regains the other half of the shunt impedance and provides very efficient proton beam acceleration for /? > 0. Standing wave.
The filling time for a traveling wave guide is Lcav/vg.VIII.45: A schematic drawing of the 7r/2 phase shift cavity structure (top). Since only the forward traveling wave can accelerate the beam. Note that the particle riding on top of the rightgoing wave that has the phase velocity equal to the particle velocity will receive energy gain Figure 3.10 lists the properties of SLAC linac cavity. a traveling wave cavity can provide a high acceleration gradient for intense electron beams. that is a constant gradient structure operating at a phase advance of 2TT/3. the shunt impedance is 1/2 of that of the traveling wave structure except for kd = 0 and 7 standing wave modes. a standing wave (left) can be decomposed into forward and backward traveling waves (right). With a high peak power rf source. and moved outside to become a coupled cavity structure (bottom). .44: In general. Typical group velocity is about 0.8. where two T neighboring space harmonics contribute to regain the factor of two in the shunt impedance. into "constant gradient" and "constant impedance" structures (see Exercise 3. Table 3. The accelerating cavities of a constant impedance structure are identical and the power attenuation along the linac is held constant. where the field free regions are shortened (middle). INTRODUCTION TO LINEAR ACCELERATORS 401 Figure 3.05c. where Lcav is the length of a cavity and vg is the group velocity. On the other hand. the geometry of accelerating cavities of a constant gradient structure are tapered to maintain a constant accelerating field along the linac.8).
and W be the corresponding physical quantities for a non-synchronous particle. Since the momentum compaction in a linac is zero. and let t. These HOMs. or beam blow up) instabilities. (3. These instabilities are called BBU (beam break up. 9 (1965). A long range wake can affect trailing bunches. the beam in a linac is always below transition energy. and energy of a synchronous particle. Its threshold current can be increased by a quadrupole focusing system. When a beam is accelerated in cavities. AW//3%E is the fractional momentum spread. It also depends strongly on the misalignment of accelerating structure and rf noise.T. and —l/ja is the equivalent phase slip factor.103 The BBU is a transverse instability.R. 104See Jarvis. NS-112. This equation is in fact identical to Eq.21). The change of the phase coordinate is where v = ds/dt and vs = ds/dts are the velocities of a particle and a synchronous particle. Such efforts are instrumental for future linear colliders operating at high frequencies. p. higher order modes (HOMs) can be equally important in cavity design. G. and the subscript s is used for physical quantities associated with a synchronous particle. SYNCHROTRON MOTION So far we have discussed only the fundamental mode of a cavity. where u)/fisc is equivalent to the harmonic number per unit length. Nucl. AW = W-WS. Seeman. (3.104 VIII. HOMs CHAPTER 3. J. and a short range wake can cause a bunch tail to break up.419) where the coordinate s is chosen to coincide with the proper rf phase coordinate. [15]. IEEE Trans. We define the synchrotron phase space coordinates as At = t-ta.418) The accelerating electric field is £ = £0 sin u>t = £Q sin{ips + Atp). 255 in Ref. Let ts. particularly TMnp-like modes. Arp = tp-ipa=uj{t-ta). can affect the threshold current of a linac.C. In reality. (3. Efforts are being made to design or invent new cavity geometries with damped HOMs or detuned and damped HOMs. Crowley-Milling. and M. Sci. ip.4 Longitudinal Particle Dynamics in a Linac Phase focusing of charged particles by a sinusoidal rf wave is the essential core of longitudinal stability in a linac. . Saxon. Operation of the SLAC linac provides valuable information on transverse instability of intense linac beams.402 G. 103T. it also generates long range and short range wakefields. ^>s and Ws be the time. observed first in 1957. rf phase.
105Note that the convention of the rf phase used in the linac community differs from that of the storage ring community by a phase of 7r/2.„. the concept of synchrotron tune is not necessary.424) Since fcsyn ~ 1/I/T 5 . 403 (3. „ • (3. the longitudinal phase space will form islands as discussed in Sec. the wave number of synchrotron motion becomes very small for high energy electrons. In contrast to synchrotrons. i.sink's] « e£ 0 cos V>s A^>. (3. Parametric synchrotron resonances can occur if mvsyn = I is satisfied.422) Hereafter. . the Hamiltonian contour is not a constant of motion. FODO focusing systems. The beam will get the maximum acceleration and a minimum energy spread. if there is a quasiperiodic external focusing structures such as periodic solenoidal focusing systems. However. shown in Fig.e. etc. The linearized synchrotron equation of motion is simple harmonic. where m and i are integers. Tori of phase space ellipses form a golf-club-like shape. the synchrotron tune can be defined as the i/syn = ksynL/(2n). f ^ = -k%nAW. where L is the length of the periodic focusing system. This section will show that all captured particles ride on top of the rf wave. — = e£0 [sin(V>8 + Aip) . III. The beam moves rigidly in high energy electron linacs. Thus the synchronous phase angle is normally chosen as (f>s = | . 3. the linac usually do not have repetitive periodic structures. A. Near a parametric synchrotron resonance.2. The capture condition in an electron linac with vp = c Since (3S% changes rapidly in the first few sections of electron linac.VIII. electron bunches are riding on top of the crest of the rf wave.423) where the wave number of the synchrotron motion is ksyn = \ le£0u)cosips . we use the rf phase convention of the storage ring community. In this textbook.421) (3. INTRODUCTION TO LINEAR ACCELERATORS The energy gain from rf accelerating electric fields is105 dAW — . or periodic doublet focusing systems. as The Hamiltonian for the synchrotron motion becomes H = " JAW)2 2mcr)pJ7J + e£0 [cos(^s + AV>) + A^sinVs]. /3S and 7S are replaced by /? and 7 for simplicity..
428) ^ = _^sinV. and we have used /?2 = 1 and the relation tan (C/2) = ((1 . Let the electric field and the gap .> TT/2. which is usually about 80-150 kV.sin2C.^ .0)/(l + /?)]1/2 = 7 . Letting /3 = v/c. the electric field seen by the electron is fosin^. i. all particles within —IT/2 < fa < IT/2 will be captured into the region IT >fa.429) where the indices 1 and 2 specify the injection and the captured condition respectively.5. me dt Using the chain rule dtp/dt = (dtp/dQidC^/dt). we obtain (-2) 347 (3. (3. If the factor Ylnj = 1. A prebuncher is usually used to prebunch the electrons from a source.Since the phase velocity and the particle velocity are different. ^""sM^H-* Substituting f3 = cos£.A will be captured into the range TT/2 < fa < TT/2 + A 2 /2 (A <C 1).-cos^ = — t a n . For example.cos C)/(l + cos C))1/2 = [(1 .425) Z7T where A = 2nc/ui is the rf wavelength. particles distributed within the range A > fa > .5° in the capture process.\jl2 .429). Eq. we obtain The particle gains energy through the electric field. If Yinj = 1.1The capture condition. We assume a thermionic gun with a DC gun voltage Vo. we can integrate the equation of motion to obtain cosV. particles within an initial phase —TT/3 < fa < TT/3 will be captured inside the phase region IT >fa>> 27r/3. the path length difference between the EM wave and the particle in time interval dt is de={c. In particular.404 CHAPTER 3. favors a linac with a higher acceleration gradient £Q. and we use the fact that dl/\ = dip/2n. what happens to the injected electrons with velocities less than c? Let V be the phase angle between the wave and the particle.e. all injected beam with phase length 20° will be compressed to a beam with a phase length 3.— ( ^ — J =-Yiai. (3.v)dt = ^-dfa (3. The capture efficiency and energy spread of the electron beam can be optimized by a prebuncher. SYNCHROTRON MOTION In an electron linac operating at a phase velocity equal to c. Assuming constant gradient acceleration. which can be thermionic or rf gun.
Synchrotron motion in proton linacs Since the speed of protons in linacs is not highly relativistic. Until an equilibrium state is reached.13 %.11: Properties of rf bucket in conjugate phase space variables 1 (i>. Table 3.8. Electrons that arrive earlier are slowed and that arrive late are sped up. the faster electrons catch up the slower ones. (3. At a drift distance away from the prebuncher. at the same time.e. B. Thus electrons are prebunched into a smaller phase extension to be captured by the buncher and the main linac (see Exercise 3. the energies of individual beam bunches may vary.^) Bucket Area Te ("*'ff «*>)^ aM Bucket Height | 2 (rnc^feS^ Y{A) I hM) 16 ( ^ ) V ' ab(^s) | 2 (fa^go)1/2 y ( ^ ) ' .11 lists bucket area and bucket height for longitudinal motion in proton linacs (see also Table 3.2 for comparison). where a^ips) and F(V's) are running bucket factors shown in Eqs.1 rad will have an energy spread of about 0.48) and (3. individual adjustment of each klystron phase can be used to make a bunch with phase length A ride on top of the rf crest. etc. C. the wakefield induced by the beam travels along at the group velocity. INTRODUCTION TO LINEAR ACCELERATORS 405 width of the prebuncher be £ sin(wi) and g. All captured high energy electrons can ride on top of the crest of the rf wave in order to gain maximum energy from the rf electric field.VIII. Energy spread of the beam In a multi-section linac. The longitudinal particle motion follows a torus of the Hamiltonian flow of Eq. Other effects that can affect the beam energy are beam loading. The final energy spread of the beam becomes This means that a beam with a phase spread of 0.52). The synchrotron motion in ion linac is adiabatic. (3.422). i.1. The rf phase region for stable particle motion can be obtained from ipu and n — ips identical to those in the second the third columns of Table 3. ips = §. A train of beam bunches extracts energy from the linac structure and. wakefields. the synchronous phase angle ips can not be chosen as | . Thus the injection match is important in minimizing the final energy spread of the beam.9). Table 3.
46: A schematic drawing of electric field lines between electrodes of acceleration cavities. The screen produces a focusing force.10 respectively.. (-3) 34 1 (3.433) / H0 V e ^ocos% =\ [AZ(— . Q . Aifr) = <*!*>.However. the field at the exit end increases with time so that the defocussing effect due to the diverging field lines is larger than the focusing effect at the entrance end of the cavity gap. the Hamiltonian becomes H = . E.406 CHAPTER 3.The bunch length in r-coordinate is given by aT = a^jw. we find aAW ~ (w5 0 ) 1/4 (/?7) 3/4 .d w ( ^ ) 2 . -4 rms = TTCTAW/LJCA^. for a constant phase space area Ams. In small bunch approximation. where ^. p[H(AW/u>. the fractional momentum spread will decrease when the beam energy is increased: g ^ = V^r(m3C^7 J • (3-435^ Examples for beam properties in the Fermilab DTL linac and SNS linacs are available in Exercises 3. SYNCHROTRON MOTION The equilibrium beam distribution must be a function of the Hamiltonian. For rf accelerators.434) . i._. Note that the converging field lines contribute to a focusing effect in electrostatic accelerators. Figure 3. cosips) V /. Note that. . Aip)].8.8.\e£oCOS^ {^?p ( — .e.O. and aT ~ (wf o )" 1/4 (/37)" 3/4 . r m s is the rms phase space area in (eVs).e.432) A Gaussian beam distribution with small bunch area becomes where Ho is related to the thermal energy of the beam and the rms energy spread and bunch width are given by /ffomcSffV VAW/u.^. i.3 and 3. = \j ~3 aAt = \ —z fj^s fmc3/3373e£0cosAY/4 =V^ T { tf ) V 7 ym^p^^eto T ' (3 . ..4 (3... Lawrence placed a screen at the end of the cavity gap to straighten the electric field line. but unfortunately it also causes nuclear and Coulomb scattering.
!. Assuming a zero defocussing force. (3. (3.389). (3. we obtain dj-ymf) _ dt ~ euie0 sin ips 2/3-y2c T' ( • ) For a relativistic particle with 7 > 1 . the drift tubes of an Alvarez linac or the irises of a high-/? linac. The transverse force on particle motion is dt = ~eEr . Using Eq.VIII. INTRODUCTION TO LINEAR ACCELERATORS 407 VIII. Er = ~—£ocos > ij>. B& = —^£o cos tp.. e. phase stability requires TT/2 > ips > 0 (below transition energy).437) For a synchronous particle with v = vp. In reality quadrupoles are needed to focus the beam to achieve good transmission efficiency and emittance control in a linac. Thus the defocussing force experienced by the particle at the exit end of the gap is stronger than the focusing force at the entrance of the gap. (3.evB^ = — — (1 .46 shows the electric field lines between electrodes in an acceleration gap./ ) cos rp. if no other external force acts on the particle. where 7' = d'y/ds. the EM field of TMOio mode is Es = £0sin V .44I) Thus the orbit displacement increases only logarithmically with distance along a linac (Loreritz contraction). andfieldstrength increases with time during the passage of a particle. . the constant field strength gives rise to a global focusing effect because the particle at the end of the gap has more energy so that the defocussing force is weaker.440) (3.g.438) becomes Here we obtain 7— = constant = 70a. In an electrostatic accelerator. Eq. For rf linear accelerators. This has been exploited in the design of DC accelerators such as the Van de Graaff or Cockcroft-Walton accelerators.. the transverse defocussing force becomes negligible because the transverse electric force and the magnetic force cancel each other.436) where tp — (uit — w / ds/vp). 5 Transverse Beam Dynamics in a Linac Figure 3. ds Assuming 7 = 70 + j's.. we obtain X-Xo=(7±\nl)x< dx (3.
the transverse force is — * r J (3. the concept of betatron tune is not necessary. 562 in Ref.V ± £ s • LO cc (3. Lee. A mismatched linac will produce quadrupole mode oscillations along the linac structure. where I is also an integer. (3. 5706 (1994).107 106see e. one can define the betatron tune per period as vy = kyL/2n. and £ are integers. It should be designed from a known initial or desired betatron amplitude function and matched through the linac. Since there is no repetitive focusing elements.445) Thus the transverse force on a charged particle is related to the transverse dependence of the longitudinal electric field. This is the basic driving mechanism of synchro-betatron coupling resonances. E49. ^z{t.s) + Kz{s)z{t. Betatron resonances may occur when the condition mvx + nvz — £ is satisfied. Ruth. S. [15].s) = 0.g. Since there is no apparent periodic structure. many linacs employ periodic focusing systems.s)=O. it vanishes if the longitudinal electric field is independent of the transverse positions. p. However. In smooth approximation..443) where y is used to represent either x or z. VxfdsFn = -^Jd8F±.s) + Kx{s)x{t.106 Since TE modes have zero longitudinal electric field. Rev. SYNCHROTRON MOTION Transverse particle motion in the presence of quadrupole elements is identical to that of betatron motion.s) + k2y{s)y{t.s) = 0. Furthermore. In this case. Wakefleld and beam break up instabilities Applying the Panofsky-Wenzel theorem [24]. n. where L is the length of a period. 107See R. The design of cavities that minimize long range wakefields is an important task in NLC research. and ky is the wave number. where m. The linear betatron equation of motion is given by ^x{t.442) where Kx(s) and Kz{s) are focusing functions. the betatron motion in linac is an initial value problem. synchrobetatron resonances may occur when the condition mvx + nvz + li/syn = £ is satisfied.444) F±= ds Vx-Fjl = . These HOMs are also called wakefields. . the linear betatron motion can be described by —y{t. Phys.408 CHAPTER 3.Y. (3. its effect on the transverse motion vanishes as well. Thus we are most concerned with HOMs of the TM waves.
449) k2 — kx \ K2 / hi In t h e limit of equal focusing strength. p(t) is the density of particle distribution. 409 (3.>fci. s) = -j±rr ]t dtp(t)W±(i . x(t. as in Eq. INTRODUCTION TO LINEAR ACCELERATORS In the presence of a wakefield. (3. The motion of the trailing particle due to betatron oscillation of the leading particle becomes Gxi I k\ \ ki „ x2 = j-Xi sin k2s + -s T~2 sin Kis — — sin K2S .t)x(t.VIII. This is the essence of BBU instability. k(t.441) [3].447) X l = Gxu ( 3. If the beam bunch is subdivided into many macro-particles. s is the longitudinal coordinate along the accelerator. one would observe nonlinear growth for trailing particles. and kx and k2 are betatron wave numbers for these two macro-particles. They travel at the speed of light c. Each macro-particle represents half of the bunch charge. We divide an intense bunch into two macro-particles separated by a distance I = 2<rz. [3].we have / x2 —¥ xi sin kis + xi I Afc C \ — ) s cos kis. In the limit Ak — 0.108 108 Including beam acceleration. Detailed properties of the wake function and its relation to the impedance and the transverse force can be found in Ref. (3. and W±(t' — t) is the transverse wake function. If.4 4 8 ) ^^M where eN/2 is the charge of the leading macro-particle. i. s) + k\t. k2 .450) > where Ak = k2 — k\. 4 + k2X2 = (3. the trailing particle can be resonantly excited. s) is the transverse coordinate of the particle. The equation of motion in the smoothed focusing approximation is x'[ + k\xx = 0. s). The amplitude grows linearly with s. the equation of motion is [3] -^x(t. s)x(t. W±(£) is the wake function evaluated at the position of the trailing particle. the leading particle begins to perform betatron oscillation with X\ = Xisinkis. for some reason. .446) where t describes the longitudinal position of a particle. s) is the betatron wave number (also called the focusing function). the trailing macro-particle can be resonantly excited. x\ and x2 are transverse displacements. We will examine its implications on particle motion in a simple macro-particle model.e. the amplitude will grow logarithmically with energy (distance). (3.
Smirnov. Exercise 3. Lceii is the length of the drift tube cell. (3. In an Alvarez linac. AEn are the synchrotron phase space coordinates at the nth cell. Balakin. The SLC linac uses the latter method by accelerating the bunch behind the rf crest early in the linac. the energy spread is equivalent to a spread in focusing strength.11 are kd = n and 2TT/3 respectively. Show that the peak rf magnetic flux density on the inner surface of a pillbox cylindrical cavity in TMoio mode is B^K^-S or % [T] « 50 x 10"4 £ [MV/m].447) provides a good approximation for the description of particle motion in a linac. to restore the energy spread at the end of the linac. This method can also be used to provide BNS damping. SYNCHROTRON MOTION An interesting and effective method to alleviate the beam break up instabilities is BNS damping.8 1. (3. where Zo = fioc is the impedance of the vacuum. The bunch will perform rigid coherent betatron oscillations without altering its shape. where ipn. Show that the phase shifts per cell for the CEBAF and SLAC linac cavities listed in Table 3.451) can be achieved either by applying rf quadrupole field across the bunch length or by lowering the energy of trailing particles. A. It is also worth pointing out that the smooth focusing approximation of Eq.109 If the betatron wave number for the trailing particle is higher than that for the leading particle by the linear growth term in Eq. 109V. Proc.421) can be expressed as mapping equations: AEn+i = AEn + eVcosips Aif>n+i.450) vanishes. Note that BNS damping depends on the beam current. 12th HEACC. 2. and then ahead of the rf crest downstream. . Novokhatsky. p. 119 (1983).410 CHAPTER 3. and V. 3. (3. This means that the dipole kick due to the wakefield is exactly canceled by the extra focusing force. The BNS damping of Eq. and eV is the energy gain in this cell. the longitudinal equations of motion (3. Since the average focusing function is related to the energy spread by the chromaticity and the chromaticity Cx ~ — 1 for FODO cells.420) and (3.
See G. Estimate the total synchrotron phase advance in a cavity.H. .EXERCISE 3.0/6. Since the conductivity is proportional to the mean free path £.H. we can derive the amplitude function for synchrotron motion similar to that for betatron motion. There is little advantage to operating copper cavities at very low temperature.8 411 (a) Using the Courant-Snyder formalism. Soc. In a resonance circuit. 110In the limit that the mean free path I of conduction electrons is much larger than the skin depth (Sskini the surface resistance becomes Rs = (8/9)(\/3iilu}2£/16w<7)1^3.45 0. where Rs = l/o^skin is the surface resistance. Fermilab Alvarez linac Cavity Number Proton energy in (MeV) Proton energy out (MeV) Cavity length (m) Cell length (cm) (first/last) Average field gradient (MV/m) (first/last) Average gap field (MV/m) (first/last) Transit time factor (first/last) Number of cells 4. Pd = \ [ R*\H\2dS = ^ f ^ 2 Js 4 Js / \H\2dS.04/21.64/0. and is proportional to u2/3. wL R stored energy energy dissipation per period' 1 075 10.E.42 37.2/40.aui is the skin depth. £ av = V/Lce\\ is the average acceleration field. (b) Using the table below. calculate the synchrotron phase advance per cell for the first and last cells of cavities 1 and 2. and tps is the synchronous phase.8 2. and a is the conductivity.0 10.110 <5s](jn = y/2//j.30 7. Show that the synchrotron phase advance per cell is $ s y n = 2 arcsin ( ^ j .42 7. where the synchronous phase is chosen to be cos^ s = 1/2. the resulting surface resistance is independent of the mean free path.81 59 The energy stored in the cavity volume is The power loss in the wall is obtained from the wall current. A195. 336 (1984).86/0.54 19. The total energy loss in one period becomes AWd = 2JLPd = w !^Hi / 2 Js ]Hl2dS.8 1.81 55 2 10. 2 2 g where E — "fine2 is the beam energy.02 22. Reuter and E. A is the rf wave length. Proc.44 6. Q is expressed as 2&LI2 \RI2 where w = {LC)~ll2. Sonderheimer.45 0.60/2.62/7. Roy.
defined by ve = P/Wst. The average power flowing through a transverse cross-section of a wave guide is p = I [ E± x H±dS where only transverse components of the field contribute. For TM mode. Identical resonator LC circuits are coupled with disk or washer loading by parallel capacitors 2CP shown in the figure below.405.412 CHAPTER 3. Since <5skin ~ w~1/2.m = \ I \H±\2dS = ^ ^ Thus the total energy per unit length is j \£L\2dS Wst = Wst. (b) Show that the shunt impedance is D _ Zpd2 ^sh _ r 2u}fi . (a) Show that the energy flow. the diameter of the cavity will also be smaller. Us is the surface resistivity. (b) Verify that vg = du/d/3 = ve.856 GHz. ffI = ^°V £l- 7 A P - P-2Z-J^dS X [ k \ f 2WC The energy stored in the magnetic field is Wst. Note here that the shunt impedance behaves like rsh ~ wxl2.n 41 R^nb(b + d)J2{krb) Q ~ n{krb)2J2(krb) ~ ' "^ where kTb = 2. At higher frequencies.m + WKJ* = 2W st . The Q-factor depends essentially on geometry of the cavity. SYNCHROTRON MOTION (a) Using the identity /06 Jf(krr)2nrdr = Trb2J2(krb). the shunt impedance is more favorable.QC « 377f2. 6. m . Find the Q-value for the SLAC copper cavity at / = 2. . we find Q ~ w + 1 / 2 . however. show that the quality factor for a pillbox cavity at TMOio mode is = 2jv\H\2dV SSKafs\H\2dS = _d b_ = 2A05Z0 5skind + b 21^(1+ b/d)' where 6 and d are the radius and length of a cavity cell. is ve = fic/k. and ZQ = 1/fj. 5. which may limit the beam aperture.
(b) Show that the solution of the above equation is . where u>o = l/^/LCs is the natural frequency without coupling at kd = 0. Show that the frequency is u2 = WQ [1 + «(1 . r. Show that the dispersion curve of a magnetically coupled cavity is uil = J1 [1 + «(1 . — Q 1 9 • • • /t — u. these resonators are uncoupled.EXERCISE 3.2 cos(fcd) in + t n _! = 0.8 413 In the limit of large C p . The model describes only the qualitative narrowband properties of a loaded wave guide. (e) Cavities can also be magnetically coupled.cos kd)]. there are higher frequency modes. which give rise to another passband (see Fig. a small beam hole in a pillbox cavity corresponds to Cp > C s . 3.f . and k as the wave number. and K = C s /Cp is the coupling constant between neighboring cavities. Draw the dispersion curve of u vs k. ^.w 2 C p L. show that i n + i . (c) Show that the condition for an unattenuated traveling wave is LUQ < ui < uin. The magnetically coupled-cavity chain can be modeled by replacing 2CP in the LC circuit with £ p / 2 .cos kd)]. In a realistic cavity.. where ^="°( i+2 §) 1/2 ^°( i+ S) is the resonance frequency at phase advance kd — TT. or equivalently. We identify fed as the phase advance per cell. (d) Find k such that the phase velocity vp = c.-n _ p±j[nkd+xo] t — e . C cos(fcd) = 1 4. i. m (a) Applying Kirchoff's law. . m T h e equivalent circuit does not imply that a coupled resonator accurately represents a disk loaded structure. which corresponds to a pillbox without holes.41).
ceii> where J?sh. (a) For a particle traveling at velocity v. • • • . and K = Lp/L is the coupling constant between neighboring cavities. SYNCHROTRON MOTION where wo = 1/-\ZLCS is the natural frequency without coupling at kd = 0. We define the parameter a as 01 ~ 1 dPd 2P d ds ' 112The above calculation for voltage gain in the cavity structure is not applicable for an standing wave structure with kd = 0 and it. where two space harmonics contribute to the electric field so that £s = 2£0 cos ks cosut.1. For an rf structure composed of N cells.is equal to the particle velocity v. (b) For a sinusoidal electric field. i. and the shunt impedance is /2sh = NRa.e. 7. and to is the frequency. Nd] is the longitudinal coordinate.N. Using the definition of shunt impedance. d is the cell length of one period. This means that the voltage gain in the rf structure is AV = Nd£o. show that the shunt impedance of a standing wave rf structure is Thus the shunt impedance for a standing wave structure is equal to 1/2 that of an equivalent traveling wave structure. A constant impedance structure has a uniform multi-cell structure so that the impedance is constant and the power decays exponentially along the structure.408). the electric field of a standing wave rf cavity structure that consists of N cells is £s = £Q cos ks cos ut. where kd is the rf phase advance per cell. show that the total voltage gain in passing through the cavity is MT = -NdE f»fr(*-("/"))M* | sm(k + (U/v))Ndl 2 °[ (k-(ui/v))Nd {k + {u/v))Nd r m = 0. The resonance condition is kd = mir/N. Show that the energy gain is maximum when the phase velocityfc/o. A constant gradient structure is tapered so that the longitudinal electric field is kept constant.. There are two types of traveling wave structures. the power is Pd = N\£0d\2/2RshMl.414 CHAPTER 3. the energy gain of a standing wave structure is only 1/2 that of an equivalent traveling wave structure.ceii is t n e shunt impedance per cell for the traveling wave. (3. the power consumed in one cell is |M 2 /2iU. where s € [0. Show that the maximum voltage gain of the standing wave is (AV) m a x = Nd£o/2.cell- . Discuss the differences between the electric and magnetic coupled cavities. 112 8. Using Eq. k is the wave number.
386)] W g = u.2 T ))(Q(l-e. Calculate the longitudinal bucket and bunch areas in (eVs). The group velocity is equal to the velocity of energy flow. what is the longitudinal brightness of the beam in number of particles per (eVs)? . At a drift distance away from the prebuncher. Compare the rms bunch length in (ns) and in (m) with the rms transverse beam size at exit points of linacs.2 T ). the faster electrons catch up the slower electrons.e . Thus electrons are prebunched into a smaller phase extension to be captured by the buncher and the main linac. Jo (a) In a constant impedance structure. Each microbunch has about A^B = 8. show that the energy gain is AE(L) = eL(2r sh P o a) 1/21 ~ %" .383)] S2 = . show that Pd = P 0 ( l . The following table lists linac and beam parameters. (b) Assuming that rsh and Q are nearly constant in a constant gradient structure. DTL.findthe drift distance as a function of the Vo and Vi. Let the electricfieldand the gap width of the prebuncher be £ sin(wt) and g. CCL. RFQ.EXERCISE 3. where T = Jo a(s)ds. 9. as The total energy gain for an electron in a linac of length L is AE = e f £ds. We assume a thermionic gun with a DC gun voltage Vo.L(l-J(l-e. Electrons that arrive earlier are slowed and that arrive late are sped up. which is usually about 80-150 kV.£ ( l .8 415 the electricfieldis related to the shunt impedance per unit length by [see Eq. Show that the group velocity of a constant gradient structure is [see Eq. (3. An accumulator compresses the 1 ms linac pulse into a 695 ns high intensity beam pulse with 250 ns beam gap. Assuming a small prebuncher gap with Vi = £g -C Vo. Discuss the efficiency of prebunching as a function of relevant parameters. The design of the 2 MW spallation neutron source uses a chain of linacs composed of ion source.08 x 1014 particles per pulse at 60 Hz repetition rate.2 T ) ) . A prebuncher is usually used to prebunch the electrons from a source. (3. 10. which can be thermionic or rf gun.r s h ^ = 2a rsh Pd(s).70 x 108 protons. and SCL to accelerate 2.f\ and the energy gain is AE = e£L = e^P0rshL{l-e-2T). Cth where Po is the power at the input point.
SYNCHROTRON MOTION 1 RFQ 1 DTL L (m) length of the structure 3.8 185 185 1001.37 To. (MeV) •^bucket (eVs) at injection energy Ams (eVs) <yT (ns) I CCL I SRFL 55.5 0.45 ~5".2/0.065 2.12 206.5 402.108 e L (7r-mm-mrad) emittance at exit point _ 0.5 KEext (MeV) 2.2 | - | - | 10.6 86.3" .416 CHAPTER 3.33 fcsyn (m .0 " £0T (MV/m) KE inj (MeV) 0.812 805 805 60-62° 20° 3.1/5.60 0.5 86.21 "O0092~ " g A n.723 38.5 / r f (MHz) %j)s (differ from linac convention by -n/2) 60° 45-65° 3.1 ) /3x/z at exit (m) | 0.8 E|[ (7T-MeV-deg) emittance at exit point 0.7 402.
516 (1963). 52 (1948). The radiation is plane polarized on the plane of the electron's orbit. radiate electromagnetic energy. defined as T = ^hcjc/E. J. Rev. where UJP = c/p is the cyclotron frequency for electron moving at the speed of light.2 • Quantum mechanical correction becomes important only when the critical energy of the radiated photon. 40. Phys. 75. Proc. Acad. Rev. 102.Chapter 4 Physics of Electron Storage Rings Accelerated charged particles. 417 .L. • The radiation spans a continuous spectrum. 70. Schwinger. 74.P. Appl. Nat. Madden and K. Tomboulin and P. ibid. See Phys. 798 (1946). Phys. 10. 2D. 3F.3 applications of this radiation were contemplated. The power spectrum produced by a high energy electron extends to a critical frequency wc = 373wc/2. 810 (1947). its foundation was laid by J. Lett. in particular. and elliptically polarized outside this plane. As far back in 1898. Elder et al. 829 (1947). 18. Rev. The beamstrahlung parameter. Lienard derived an expression for electromagnetic radiation in a circular orbit. is a measure of the importance of quantum mechanical effects. Phys. is comparable to the electron beam energy. where 7 is the relativistic energy factor. E = •ymc2. 380 (1965).4 The 1J. Modern synchrotron radiation theory was formulated by many physicists. Appl. 4R.H. 36. particularly electrons in a circular orbit. This occurs when the electron energy reaches mc1(mcplfi)ll2 « 106 GeV. Phys. 1423 (1956). Codling at the National Bureau of Standards were the first to apply synchrotron radiation to the study of atomic physics. J. 71. Hartman experimentally verified that electrons at high energy (70 MeV then) could emit extreme ultraviolet (XUV) photons. Schwinger. Some of his many important results are summarized below:1 • The angular distribution of synchrotron radiation is sharply peaked in the direction of the electron's velocity vector within an angular width of I/7. Shortly after the first observation of synchrotron radiation at the General Electric 70 MeV synchrotron in 1947. 1912 (1949).R.. Phys. Rev. Sci. hioc = ^hcy3/p. 132 (1954).
and pM = (po.^ . etc. 1 dE . Today. p is the local radius of curvature.\=^\(dv\2 Zmc \dr dr J _l(dE\2} c2 \ dr j J ' . Applications of synchrotron radiation include surface physics.. condensed matter physics. i=l-\v\»-^ where w is the angular cyclotron frequency. For an isomagnetic ring with constant field strength in all dipoles.3 = \ 4. 1. The relativistic generalization of Larmor's formula (obtained by Lienard in 1898) is 2^ (dp. The radiation power arising from circular motion is (4.2 we will show that the power radiated from a circular orbit of a highly relativistic charged particle is much higher than that from a linear accelerator.e. i.418 CHAPTER 4.3) * = &**-&**-%*?• ("> where F± = u\p\ = evB is the transverse force.840 x If)"14 m/(GeV)3 for muons (4.P) is the 4-momentum vector. . medical research. biochemistry. dp. and . advanced manufacturing processes. was commissioned in 1968.846 x 10"5 m/(GeV)3 for electrons C7 = ^ 7 . A.5) 3 {me) [ ? 7 g 3 x 10_i8 m / ( G e V ) 3 for p r o tons. Basic properties of synchrotron radiation from electrons According to Larmor's theorem. K 3mc [{dr) ' ' where the proper-time element dr = dt/j.42. (F) _ _ _ _ _ . PHYSICS OF ELECTRON STORAGE RINGS first dedicated synchrotron radiation source. (4. dp . nearly a hundred light sources are distributed in almost all continents. The energy radiated from the particle with nominal energy EQ in one revolution is where R is the average radius. Tantalus at the University of Wisconsin. the instantaneous radiated power from an accelerated electron is p=J_?eW 47re0 3c 3 =2ro_(dp 3mc \dt &\ dt) ' X ' ' where v is the acceleration rate and r$ — e2/4ireomc2 is the classical radius of the electron.7) .. the energy loss per revolution and the average radiation power become Uo-C^EJp. v = /3c is the speed of the particle. C 8. In Sec.
Jx « 1 is a damping partition number. and the beam is compensated on average by the longitudinal electric field. whose applications include e+e~ colliders for nuclear and particle physics. and electron storage rings for generating synchrotron light and free electron lasers for research in condensed matter physics. II and III we will show that the natural emittance of an electron beam is enat = TCq^263/ Jx. A third generation light source employs high brightness electron beams and insertion devices such as wigglers or undulators to optimize photon brilliance.83 x 10~13 m. A second generation light source corresponds to a storage ring dedicated to synchrotron light production.1%bandwidth].1% of bandwidth). Using long undulators in long straight sections of a collider ring. Therefore a high brilliance photon source demands a high brightness electron beam with small electron beam emittances. one can obtain a wide frequency span tunable high brilliance monochromatic photon source.5 Synchrotron radiation sources are generally classified into generations. Murphy at BNL provides a list of beam properties of synchrotron light sources. and 0 is the bending angle of one half period. Neglecting the optical diffraction. or about ten order higher than the brilliance of X-ray tubes. mostly about 1020 photons/[s(mm-mrad)20. Furthermore. where the lattice design is optimized to achieve minimum emittance for high brightness beam operation. medicine and material applications.bnl. Some examples are SPEAR at SLAC. Using the synchrotron radiation generated from the storage rings. the product of the solid angle and the spot size dtldS is proportional to the product of electron beam emittances exez. and CHESS in CESR at Cornell University. A synchrotron radiation handbook edited by J. The factor T can be optimized in different lattice designs. In Sees. B.ELECTRON STORAGE RINGS 419 where To = 2nR//3c is the orbital revolution period. the longitudinal motion is damped.html . Table 4 lists some machine 5http://www. a beam with short bunch length can also be important in time resolved experiments. This natural damping produces high brightness electron beams. a few first generation light sources can provide photon beam brilliance equal to that of third generation light sources. Because the power of synchrotron radiation is proportional to E4/p2. biology. A first generation light source parasitically utilizes synchrotron radiation in an electron storage ring built mainly for high energy physics research. which is about five to six orders higher than that generated in dipoles.nsls.gov/AccPhys/hlights/dbook/Dbook. where Cq = 3.Menu. Synchrotron radiation sources The brilliance of the photon beam is defined as B = d4N dtdQdS(dX/X) ^ in units of photons/(s mm2-mrad2 0.
18 70. J. and LEP for CERN large electron-positron collider. we note that the emittances of third generation facilities.1 9 55 7 1.374 14.064 0.8 ez [nm] | 35 [8 [ 3.3 9. e+e~ colliders The development of electron and positron storage rings was driven by the needs of particle and nuclear physics research.3 8.1 5.36 35.s ] 3.4 2199. .1 0.0082 ^ [xlO. Fourth Generation Light Sources. are much smaller than those of their collider counterparts. 4.0 6.6 165.96 499.034 0.43 ex [nm] 450 240 64 48 51 8 4.4 768.1 8.2 35.8 h 160 1281 3492 3492 31320 1296 328 frf [MHz] 199. Colliders Light Sources BEPC I CESR 1 LER(e+) 1 HER(e~) I LEP ~APS I ALS E [GeV] 2.2 38.8 9.. APS and ALS. The widely discussed "fourth" generation light source is dedicated to the coherent production of X-rays and free electron lasers at a brilliance at least a few orders higher than that produced in third generation light sources.38 32. Proc.2 3.8 476 476 352.5 499.4 9. The reason is that colliders are optimized to attain a maximum luminosity given by 6M. Some of their properties are listed in Table 4.3 2199.2 14.3 26658.28 vx vz 6. where BEPC stands for Beijing electron positron collider.65 va 0.9 24. Proc.6 7.4 ] 4.96 4.006 0. ed.7 78.18 24. ESRF report (1996).35 60 30.2 352.4 3.2 6 3.9 1104 196.86 | 1.8 9.22 14. SSRL 92/02 (1992).. Fourth Generation Light Sources.51 | 0.016 0. CESR for Cornell electron storage ring.1: Properties of some electron storage rings.3 a[xlO"4] C [m] 240.28 25. PHYSICS OF ELECTRON STORAGE RINGS parameters of the advanced light source (ALS) at LBNL and the advanced photon source (APS) at ANL. eds.93 [ 0.5 6.5 7.6 Table 4.866 2.1 ^ ° [ x l o " 4 e V .48 C. Since 1960.420 CHAPTER 4. Cornacchia and H.18 p [m] 10.08 [ 0. LER and HER for low energy ring and high energy ring of the SLAC B-factory.01 400 152 14.0 3096. Laclare.085 0.5 5.28 76. many e+e~ colliders have served as important research tools for the particle physics.L. From Table 4. Winick.0522 0.
and f0 is the revolution frequency. The linear beam-beam tune shift of hadron colliders is independent of fi*. and eN is the normalized emittance.05 . Results of beam experiments at e+e" colliders show that the beam-beam tune shift is limited by £2 ~ 0. The resulting betatron tune shift is called the linear beam-beam tune shift7 ?z± — 7. /collision = /o-B is the beam encountering rate. the beambeam tune shift for hadron colliders is £ = Nro/iwje = Nro/AireN. r.1UJ 2njaz(ax + az) 2iryax(ax + az) where ro is the classical radius of electrons.10. If the luminosity of a machine is optimized. 7 . Anaxcrz is the cross section area at the interaction point (IP) of colliding beams. particles experience a strong Coulomb force of the opposite beam. ^4. we have £z ~S> £x.are the numbers of particles per bunch. (4. The electric and magnetic forces of the beam-beam interaction are coherently additive. \i __ sx± — NTrop: -. B is the number of bunches.ELECTRON STORAGE RINGS 421 where N+ and N.11) The luminosity expressed in terms of the tune shift parameter with N+ = 7V_ becomes *~ ~ 7Tj2 crxaz c2 2 fl*2~^z /collisionr0 Pz {^••i-^l Note that the luminosity is proportional to axaz. . /3* x are the values of the betatron function at the IP. Because of the nature of the Coulomb interaction. This design constraint for e+e~ colliders differ substantially from that for synchrotron light sources. in order to minimize the beam-beam tune shift the emittance of the beam can not be too small. then. 7Because the horizontal and vertical emittances of hadron beams are normally equal.0. Since ax ^> az for electron beams (see Sec. the beam-beam interaction for particles with a small betatron amplitude is characterized by a quadrupole-like force. During the crossing of the e + and e" beams. the beam-beam interaction for particles at a large betatron amplitude is highly nonlinear. . However. II). and 7 is the Lorentz relativistic factor. where r0 is the classical radius of the particle. _ NTrop.
The motion of the electron is specified by x'(t') with df' t=t. with .1: Schematic drawing of The retarded sealer and vector potentials (4-potential) due to a moving point charge are where J^(f .14) is needed to ensure the retarded condition. Here t' is the retarded time. With the identity /F6(f(t'))dt' = F/\df/dt\. (4.1).422 CHAPTER 4. A(x. will arrive at the observer at time c where R{t') = \x — x'\.t) = — K ' 4ire0c KR ^ . Figure 4. The electromagnetic signal. the scalar and vector potentials become $(£. and t is the observer time. ret (4-!5) . 4. The delta function in Eq.+m (413) _ a _ d^ the coordinates of synchrotron radiation emitted from a moving charge. emitted by the electron at time t' and traveling on a straight path. PHYSICS OF ELECTRON STORAGE RINGS I Fields of a Moving Charged Particle Let x'(t') be the position of an electron at time t' and let x be the position of the observer with R(t) = x — x'(t') (Fig. The unit vector along the line joining the point of emission and the observation point P is h = R{t')/R(t').t') = ec^6(x' — f(t')) is the current density of the point charge with Pfi = (P/c> l)i a n d r{t') is the orbiting path of the charge particle. t' is called the retarded time or the emitter time.*) = — — v ' 4ne0KRret .
t) = -^\^fM 47Te0 [7 2 « 3 i? 2 J 47T£oC [K3R +-J_[^x((n-^)x^)l J ret . defined as the energy passing through a unit area per unit time at the observer location. Using the relations we obtain the electric field as E{x. we obtain > E = JL. (4. (4. Using the identity V — V i ? ^ = n ^ .24) .I.dA/dt and B = V x A. is the Poynting vector S = —[E xB} = — \E\2n. J [*6V [ R2 Ane0 = e + 2-t) + ^ cRW + 2-t)]*> c c " ~^1 J ret \ L h i 1 d (4 17^ = _ £ _ [£^_ft 47re o c L 1 _d_£iinl CKdi' KR J ret f418l K Ki? 2 ' ' Since the time derivative of the vector n is equal to the ratio of the vector Vj_ to R dn _ n x (n x /?) _ (n CM" R ~ we obtain -P)h-0 R ' [ B(f rt _ _ ^ f ^ + A A J_ _ 1 ± A] 1 ' ' ~ 4ne0 « 2 i? 2 CK dt' K ^ c/c df KR \ J ret (A 20) ' [ I 47T€OC \ K2i?2 L\ CK dt' KR / J ret ' Note that the magnetic field is in fact related to the electric field by B = ( 1 / c ) h x E. The electric and magnetic fields are E = —V$ . Thus it suffices to calculate only the electric radiation field.23) The flux. FIELDS OF A MOVING CHARGED PARTICLE 423 where h = R/R = VR. a feature common to all electromagnetic radiation in free space.
which is proportional to 1/i?2. Hoc 16n2e0c 16nzeoc3 (4. dt .424 CHAPTER 4. which is proportional to 1/i?. The second term. n x /3 = |/3| sin0. This field can be transformed into an electrostatic electric field by performing a Lorentz transformation into a frame in which the charge is at rest.25) Note here that the electric field in Eq.e. Both E and B radiation fields are transverse to n and are proportional to 1/R.28) where 9 is the angle between vectors n and /?.27) L J ret and the Poynting's vector (energy flux) is 5 = — E xB = —\Ea\2h. The first term.1 Non-relativistic Reduction When the velocity of the particle is small. i. (4. the radiation field becomes ^ T ^c . PHYSICS OF ELECTRON STORAGE RINGS The total power radiated by the particle is g = (*•$)*£ = «rf|J|'. is a static field pointing away from the charge at time t. is the radiation field. dt' -. (4. Integration over all angles gives the same total radiated power as Larmor's formula: P= J_^ (41 l 47re0 3 c 3 ' ) ' 1. The total energy from this term is zero.M ^ l\ . dQ. 47re \ R 0 (4-26) (4.2 Radiation Field for Particles at Relativistic Velocities For particles at relativistic velocity.23) is composed of two terms. the Poynting's vector becomes ^•^^fei^^-^^^LThe total energy of radiation during the time between 7\ and T2 is W= /•T2+IR2/C) „ (2) 49 (4.^ — |n x (ft x /?)|2 = —f-^tfstfe. related to the acceleration of the charged particle. Mo Moc Thus the power radiated per unit solid angle is ^ = — \Ea\2R2 = .30) M+(Hl/c) (S-n)dt= rtl=T2 •/f=Ti (S-h)—d£. 1.
The integrated power is then T><^ fdP^ l 2e27S2 e2 fdpA2 .35 ) The rms of the angular distribution is also (0 2 ) 1 / 2 = 1/7. The first arises from the denominator with K = 1 — h-fi. The resulting wavelength of the observed radiation is shortened or. At relativistic energies. we have P = (1. the time interval of the electromagnetic radiation dt' of the electron appears to the observer squeezed into a much shorter time interval because a relativistic electron follows very closely behind the photons it emitted at an earlier time. where n = dt/dt' is the ratio of the observer's time to the electron's radiation time. the radiation from a relativistic particle is sharply peaked at the forward angle within an angular cone of 6 « I/7. j3 is parallel to 0.32 ) (433) where 6 is the angle between the radiation direction n and the velocity vector 0. y 'dt' v ' 4TT rjrnc\n*{{n-P)*h\ (l-n-Pf m ) There are two important relativistic effects on the the electromagnetic radiation.^)1/2«l . The angular distribution of the electromagnetic radiation is dPjt') _ remcv2 sin2 0 ( ' dn ~ 4TT ( l . When the observer is in the direction of the electron's velocity vector within an angle of 1/7.I. The second relativistic effect is the squeeze of the observer's time: dt — ndt' w dt'/j2.^ and K * (6* + l/ 7 2) ' • ( 4 . Since the angular distribution is proportional to 1/K 5 . Thus photons emitted at later times follow closely behind those emitted earlier. FIELDS OF A MOVING CHARGED PARTICLE Thus the power radiated per unit solid angle in retarded time is 425 ™£L = tf (S-ft)* = *#{§ • n) = dQ.1) -»• Y( 4 . Note that the instantaneous radiation power is proportional to 1/K 5 . The maximum of the angular distribution is located at e maj( = cos"1 \jg(y/l + 15/?2 . equivalently. Example 1: linac In a linear accelerator.^ c o s 6 ) 5 ' where 9 is the angle between n and /3. the energy of the photon is enhanced. Therefore it appears to the observer that the time is squeezed.
The total radiated power is obtained by integrating the power over the solid angle.2 shows the coordinate system. (4. AE is the energy gain per unit length. we find that the radiation from circular motion is at least a factor of 272 larger than that from longitudinal acceleration. / P x'(t') ^\^ ^v \ . PHYSICS OF ELECTRON STORAGE RINGS dpL 3.e. Therefore the radiation is also confined to a cone of angular width of (0 2 ) 1 / 2 ~ 1/7. Example 2: Radiation from circular motion When the charged particle is executing circular motion due to a transverse magnetic field. A. Ip ' " Figure 4.' .' . where dn B2r2 JpL = jmv = Jmti— = 299. Typically. at p Comparing Eq. i. The power per unit solid angle is then rfP _ dfl ~ e2v2 1 T sin2 0 cos3 $ 1 167r 2 e o c 3 (l-/?cos0) 3 [ ~ 7 2 ( l .426 where CHAPTER 4. -> ''' ] / ' 0/ N ' .2: The coordinate system for synchrotron radiation from the circular motion of a charged particle. (4.79/3B[T] [MeV/m].36). Figure 4.38) with Eq. and p is the bending radius. / 1 ./ 3 c o s 0 ) 2 J e2i.E/As is about 20 MeV/m in the SLAC linac.37) where v = /32c2/p. and 25 to 100 MV/m in future linear colliders.2 6 1 [ 47 2 6 2 cos 2 $] 7 ~ 2 ^ ? ( l + 7 2 6 2 ) 3 [ ~ (1 + 7202)2 J ' (4 . /? is perpendicular to /?.
and the charged particle illuminates the observer for a time interval cdt' « p0 rm s = p/7. the Fourier component has the property G(-LO) = G"(io). FIELDS OF A MOVING CHARGED PARTICLE 427 1. To the observer. i.I. Since the negative frequency is folded back to the positive frequency. however.26).= \G(t)\2. ^. (4. In this case. (4. Since the radiation from the parallel component has been shown to be I/7 2 smaller than that from the perpendicular component. %=r^ .3 Frequency and Angular Distribution The synchrotron radiation from an accelerated charged particle consists of contributions from the components of acceleration parallel and perpendicular to the velocity. The power radiated per unit solid angle is given by Eq. In other words. (Parseval's theorem). _.28). it can be neglected. we can define the energy radiation per unit solid angle per frequency interval as 8 The critical frequency is defined later to be uic = Z^UJP/2. 1 rOO —-= dil J-00 \G(t)\2dt = — \G{uj)\2du>.41) we obtain the total energy radiated per unit solid angle as (flilf TOO _. Using the Fourier transform G(w) = j G(t)ejutdt.31) has an angular width (6 2 ) 1 / 2 ~ 1/7. (4. the acceleration v± is related to the radius of curvature p by v± = v2/p « <? j p. the corresponding time interval At of the radiation is at 72 7dc Thus the frequency spectrum spans a broad continuous spectrum up to the critical frequency wc of order8 At ~ %At>« V = -r• W ~ c zb ~ 7 'p = j 3 u j p - (439) To obtain the frequency and angular distribution of the synchrotron radiation. the radiation emitted by a charged particle in an arbitrary extremely relativistic motion is about the same as that emitted by a particle moving instantaneously along the arc of a circular path. The angular distribution given by Eq. G(t) = (—Y' 2 [REU (4. we should study the time dependence of the angular distribution discussed in the last section.e. Git) = ^J G{w)e-jutdt.42) ZTT J—oo Since the function G(t) is real.40) with electric field E given by Eq. (4. (4.
(4. (4. the amplitude of the frequency distribution becomes 0/7T d eo c •'-oo K = M*T5— )V2 r ft x (ft x 327r J eo c •'-oo fief-V-Wde.44) The Fourier amplitude G(w) is 327r3e0c .49) The corresponding intensity spectrum becomes .[ d3xf(x. (4. i.e. The radiation amplitude is a linear combination of contributions from each charge.)| 2 = 2\G(OJ)\2.)|2 + |G(-u./ X ^ ^ ^ W . we have R=\xf{t')\ tzx-hr{t'). PHYSICS OF ELECTRON STORAGE RINGS ^ = |G(o.46) where x is the distance from the origin to the observer. where i? = \x — r(t')\ is the distance between the observer and the electron. (4./-oo «3 (4. Apart from a constant phase factor.47) where we use integration by parts and the relation K* dt< K ' l j We now consider a group of charged particles ej. ^ e " ^ " ^ . With the observer far away from the source.45) = (W^)1/2 / " " X ( ( " . e/^-jam-r7c _^ £ ej^-^^0 -> .428 with CHAPTER 4.
I. Let (4-51) n — (cos 6 sin $. (4.3." . FIELDS OF A MOVING CHARGED PARTICLE 429 L Z ^ \ a Figure 4. 0). 4. cos 9 cos $. Since the range of the t' integration is of the order of At? ~ p/cry. all horizontal angles are equivalent.^sin. r(t') / A. sinujpt'. (4. /3 = /3(sinujpt'./cose) « | [ ( 1 + e v +1^' 3 ] [i + o(l)] = f£(z + ^ 3 ) + . 0). The vector nx(nxJ3) can be decomposed into h x (n x /?) = p [—ey sin u>pt' + ej_ cos u>pt' sin 0j . where the trajectory is f(t') — p(l — cosojpt'.47) can be expanded as W(f - ±f) = W(f . (4. which is nearly perpendicular to the orbit plane. The radiation is beamed in a narrow cone in the forward direction of the velocity vector.52) where ey is the polarization vector along the plane of circular motion in the outward x direction and e± — h x ey is the orthogonal polarization vector.3: Coordinate system for circular trajectory of electrons. sin 6) be the direction of photon emission. cosujpt'. Because the particle is moving on a circular path.53) . the exponent of Eq.3 shows the coordinate system of a particle moving along a circular orbit. Figure 4. Frequency spectrum of synchrotron radiation The radiation emitted by an extremely relativistic particle subject to arbitrary acceleration arises mainly from the instantaneous motion of the particle along a circular path. The short pulse of radiation resembles a searchlight sweeping across the observer. as shown in Fig. where up = Pc/p is the cyclotron frequency and /3c = df(t')/dt' is the velocity vector. and it is sufficient to calculate the energy flux for the case $ = 0.
(4. the energy and angular distribution function of synchrotron radiation becomes where the amplitudes are Thus the energy radiated per unit frequency interval per unit solid angle becomes EK = T e S ^ O 2 ' 1 + X'f K K ) + TTX^w®] • (461> where the first term in the brackets arises from the polarization vector on the plane of the orbiting electron and the second from the polarization perpendicular to the orbital plane. . 18. 74. (4-56) J™ cos [ ^ (x + ^ 3 ) ] dx = ^ * i / 3 ( f l (4-57) for the modified Bessel function.53) are of the same order of magnitude. 829 (1947). 810 (1947). the radiation is purely plane polarized. 7 1 .9 On the orbital plane.R. The critical frequency wc has indeed the characteristic behavior of Eq. 9 F.55) Note that both terms in the expansion of Eq. With the identity jQ°° xsin [ ^ (x + \x3)] dx = ^ # 2 / 3 ( 0 . (4. The angular distribution has been verified experimentally. PHYSICS OF ELECTRON STORAGE RINGS and e=£-(i+xrj. Phys. Appl. Phys. Elder et al. J. (4. the radiation is elliptically polarized.39). Rev. where X = 0. Away from the orbital plane.430 where CHAPTER 4. 52 (1948). *-!•**-?£.
dfi = @=0 T^i—TH2{—). Figure 4. Thus the energy spectrum at 0 = 0 increases with frequency as 2.5 y=u/uc . and then drops to zero exponentially as e~u/"c above critical frequency. reaches a maximum near uic. We find w dl 3e2 2 where IF. 4.0 I ' 1 1 ' I 1 ' 1 1 I I ' ' 1 I 1 1 1 1 I 1 1 1 1 0 0. uc = Tiuc.64 with y = tu/u>c (Fig.I.91(W/UJC)2/3 for u> <C uic. Thus the synchrotron radiation is confined by W^O 1 ' 8 - (4-63) The synchrotron radiation spans a continuous spectrum up to UJC.5 1 1.4: The functions i?2(y) " and S(y) for synchrotron radiation 0. ^(I^P or if? »i.5 2 2. FIELDS OF A MOVING CHARGED PARTICLE B. 167T3£0C LJC 4. (4-62) we find that the radiation is negligible for £ > 1.where u = hco. Asymptotic property of the radiation Using the asymptotic relation of the Bessel functions 431 ^MvO^.4). The radiation at large angles is mostly low frequency. . Angular distribution in the orbital plane In the particle orbital plane with 0 = 0. C. • / ^ ^ ^ \ ^ H2(y) : o 5 -V I • / / ^^\ ---^^^^^ly) ^~^^^_^^ _ are shown as functions of y = u/uc. High frequency synchrotron light is confined in an angular cone 1/7. the radiation contains only the parallel polarization.
while the second term is the perpendicular component. we find that the parallel polarization carries seven times as much energy as does the perpendicular polarization. (4. . CC (4. Integrating over all angles. Phys. Rev. f .4. Angular distribution for the integrated energy spectrum When the energy flux is integrated over all frequency (see Section 6.67) where S(y) = 1 9-^-yf~K5/3(y')dy'. the flux is ^ dn 0=0 = <-i 4 7) m 3e2 Sm w LeJ 16n3e0hc w 2KuJ = 1. . we obtain the energy flux10 /H = ^7-/>V3(#^7^).J. (4. 1912 (1949). The instantaneous power spectrum becomes /» = ^-I(u) = ^S(-). This result was obtained by Lienard in 1898. The total instantaneous radiation power becomes r°° AP2 FA 2-Kp Jo 367re0p 2n pl where C 7 = 8.576 in Ref. 4.432 CHAPTER 4.85 x 10~5 meter/(GeV)3. 2iTp Ulc U)c PJ = ~ /Mdw =-p— 7 wc = ^ P % . [26]). 75.68) also shown in Fig. £°S{y) = l.61) over the entire angular range. we obtain f°° dP 7e2 -fue ( 5X2 \ Jo dudn ~ 967T£0C (1 + X2)5/2 ^ + 7(1 + X2)) ^' where the first term corresponds to the polarization vector parallel to the orbital plane. (4-69) (4. (4-72) v ywc' [s mr 2 0.33xl013£02^]^2(-) 0 l J 1 0 J. Frequency spectrum of radiated energy flux Integrating Eq. the photon flux density is i-[3i i ^^(S) 1 ' i + ^N'« + T^i«4 In the forward direction Q = 0. E.PtT5.1% bandwidth] ' ' Schwinger. PHYSICS OF ELECTRON STORAGE RINGS D.70) Since the energy of the photon is fuv.
.4. (4. . o The total number of photons emitted per second. du un(u)du = I(u))dw = I(LO)— n or (4.46xlO"£b[GeV]/[A]Gi(-) f uc where roo 2n [s mr2 0. we obtain dT r / 1 %/3e2 5u UJ r°° = 2.J (^) (4. is . The critical photon energy is uc [keV] = hu>c = 0. Thus the radiation due to the bending magnets has a smooth spectral distribution with a broad maximum at the critical frequency uc. 1. where h is Planck's constant. (4. Integrating Eq.665 E%[GeV] B[T] (4.I FIELDS OF A MOVING CHARGED PARTICLE 433 which peaks at y = 1 or u = u)c. we find that the spectral flux vanishes as (w/wc)2^3 for u <C u>c and as e~ulWc for w ~S> u>c.e.62).73) Using the asymptotic properties of the modified Bessel functions of Eq. Let n(u)du be the number of photons per unit time emitted in the frequency interval dui = du/h at frequency u). .1% bandwidth] ^T\ -.76) n{u)=^FO=^§ Uc where Uc O7T Uc r.4 Quantum Fluctuation Electromagnetic radiation is emitted in quanta of energy u — tuu.61) over the vertical angle 0 . 5ac 7 uc 2v^p (4. i.^Gx{y) is shown in Figure 4. Kv3{y)dy> Jujuc (-7 4?) (4.r f°° . we define 4wc as the upper limit for useful photon frequency from bending magnet radiation.78) F(y) = -S(y).79) V . Following the traditional convention. A/".75) Gi(y) = y Jy Ks/3(y')dy' The function S{y) . y Jo rFiy)^1-^. Vo W3P7 8 N= n(u)du=— •!-= —-rJ-.
Uo [MeV] 0.4.86 119. In Table 1.50 1. 19.0 77.0 x 10 9 uc [keV] 2.4 lists synchrotron radiation properties of some storage rings. E is t h e beam energy.5 55 7000 p [m] 10.434 CHAPTER 4.2 240.01 3096. (4.9 C [m] T o [//s] 0. r s and T± are radiation damping times of the longitudinal and transverse phase spaces (to be discussed in Sec.= -^Lory.3 1104 196.2 9 7 1.8 19.4 2199.00 0.6 165 38. 38.37 9. C is the circumference.66 89.0 x 10 9 7 i [ms] 18.28 7. PHYSICS OF ELECTRON STORAGE RINGS where a = e2/4Tre0hc is the fine structure constant.80 2. Note that the number of photons emitted per revolution is typically a few hundred t o a few thousand. II).34 3.80) Table 1. the quantum fluctuation varies as the seventh power of the energy. (482) Cu-^=. = ^u2c. 0.56 7.81) (u2) = ±fo°°u2n(«)du or N{u)-CuucP7-^—{mc2)3—.34 7.4 18.91 0.68 0. 89.52 5.45 0.35 60 30. Table 4.2 3096.7 8. p is t h e bending radius. UQ is the energy loss per revolution. 38. 16.040 | 285 | 777 I 415 | 1166 | 907 | 194 | 7125 |[ 494" iV7 The moments of energy distribution become {u) = 1 r°° 8 AfJo un(u)du = ^7=uc. 9.20 1. and JV7 is t h e average number of photons emitted per revolution. The average number of photons emitted per revolution becomes N7 = N2-K.78 19.3 2199.83) At a fixed bending radius. c Vo (4.9 26658. 2.30 3. .4 768. 155.2: Properties of some high energy storage rings I B E P C I CESR I L E R I H E R I A P S I ALS I LEP I LHC I E [GeV] 2.96 4. 4. (4. To is t h e revolution period.11 2 6 1 .00060 T|| [ms] 8.97 2.2 6 3.8 8. uc is t h e critical photon energy.8 26658. 1.
99. (4. .85 x 10" 5 [(£ [GeV]) 4 /p[m]] [GeV] ~\ 7.38). where K5/3 energy. Plot the angular distribution of synchrotron radiation shown in Eq..37) for /3 = 0.5 and P = 0. show that the number of primarily photons per unit energy interval in one revolution is ~r = -^—2 / K5/3(y)<iy. and show that the integrated power is given by Eq. (4. Find the angle of the maximum angular distribution. Express it in terms of the constants m. (4.5 T at 55 GeV beam energy? What will the energy loss per revolution be at 100 GeV? With the present LEP dipole magnets.0 0.5 5453 908 E [GeV] p [m] 7 uc [keV] Up [keV] N7 5. 3. A particle of mass m and charge e moves in a plane perpendicular to a uniform. 4. and show that the integrated power is given by Eq.28 0. the magnetic flux density in a LEP dipole is B = 592.99.78 x 1Q-6[(E [TeV]) 4 /p[m]] [GeV] <IN 9v^c/0 r ° „ . and 0 is the critical pnoton for electrons. _ 4nrpmp<?y4 ~ ~ 3p is the energy loss per revolution. uc = 3hcj3/2p _ f 8.5 G. (4. Find the maximum angular distribution of synchrotron radiation. 2.059 3246 123 10. At 55 GeV. du 8n ulc Ju/uc is the Bessel function of order 5/3. which will desorb the surface molecules.2 165 107632 17612 119 9.e.67).1 1.69). Show that the total number of primary photons in one revolution is given by 15V3Uo Verify 7V7 of the machines in the table below. Using Eq.5 and p = 0.96 13699 19.78 261495 3518 7136 Tl68 rings I APS 7 38. The synchrotron radiation generated by the circulating beam will liberate photo electrons from the chamber walls. (4.1 435 Exercise 4. The photon yields depend on the photon energy and the chamber wall material.61) for /? = 0.j and B. What happens if you design the LEP with a magnetic flux density of 0. static magnetic induction B.EXERCISE 4. (a) Calculate the total energy radiated per unit time.3 3530 1429 567 Electron storage LEP I HER(B) 55 9 3096. (b) Find the path of the electron.2 53289 21316 8526 3. Plot the angular distribution of synchrotron radiation shown in Eq. at what energy will the beam lose all its energy in one revolution? . for protons. Proton storage rings VLHC I SSC I LHC 50000 20000 8000 15000 10108 3096.
7 1 [A]. 11 The resulting pressure increase is given by kS ds where i) is the molecular desorption yield (molecules/photon). Grobner. (b) Show that the total number of photons per unit time (s) is given by M = 4 .60 x 1 0 1 6 4 1 * [ A ] as pl [photons/ml. 8. integrate the intensity over all angles. 5 is the pumping speed (liter/s).Od x 10 (^m])2 [W\.72) and (4. 454 in Ref.b. p. Verify Eqs. 1 4 x l O 1 7 . . (4. (4. and prove that the parallel polarization carries seven times as much energy as that of the perpendicular polarization. (a) For an accelerator with an average current / [A]. In designing a high energy collider. Verify Eq. 7.74). [15]. PHYSICS OF ELECTRON STORAGE RINGS 6. and k = 3. Show that the total number of photons per unit length in the dipole magnet is given by11 ^— = 6. .2 x 1019 (molecules/torr-liter) at room temperature. show that the total synchrotron radiation power is given by F. See 0. you need to take into account the problems associated with gas desorption due to synchrotron radiations.66).436 CHAPTER 4.
On the other hand. and R is the average radius of a storage ring. 3% of its total energy. The energy loss per revolution at 100 GeV is 2. and methods of manipulating the damping partition number. The balance between damping and excitation provides natural emittance or equilibrium beam size.096 km) will lose 0. p (4. electrons lose energy in a cone with an angle about 1/7 of their instantaneous velocity vector. In this section we discuss damping time. and C1 = 8. beam emittances. there is a damping-fluctuation partition between the longitudinal and transverse radial planes.84)] and the average beam energy is compensated by longitudinal electric field. The energy of circulating electrons is compensated by rf cavities with longitudinal electric field.e. Since higher energy electrons lose more energy than lower energy electrons [see Eq. (4. The vertical emittance is determined by the residual vertical dispersion function and linear betatron coupling. The damping (e-folding) time is generally equal to the time it takes for the beam to lose all of its energy.II. The balance between quantum fluctuation and phase-space damping provides natural momentum spread of the beam.18 GeV per turn.85 x 10~5 m/(GeV) 3 is given by Eq. p is the local radius of curvature. For example. an electron at 50 GeV in the LEP at CERN (p = 3.5). . i. (4. The total energy radiated in one revolution becomes Uo — ——f 2TT -r J p1 (= C 7 —for isomagnetic rings). synchrotron radiation is a quantum process. The photon emission is discrete and random. The longitudinal and transverse motions are coupled through the dispersion function. This mechanism provides transverse phase-space damping. damping partition. Furthermore. there is radiation damping (cooling) in the longitudinal phase space.6) Therefore the average radiation power for an isomagnetic ring is (P)-~cCjEA (4 7) where To = /3C/2TTJ? is the revolution period. RADIATION DAMPING AND EXCITATION 437 II Radiation Damping and Excitation The instantaneous power radiated by a relativistic electron at energy E is *-£7-•£*>**• < 484 ' where B is the magnetic field strength. and the quantum process causes diffusion and excitation. and gain energy through rf cavities in the longitudinal direction.9 GeV. quantum fluctuation.
C is the accelerator circumference. l3Here. V(T) = Vos\n(f> = Vosinwrf(r + r s ). (4. For simplicity. where the energy gain in the rf cavity is to compensate the energy loss in synchrotron radiation. EJ AF (4. if the field is linear with respect to displacement. since a particle having nonzero betatron amplitude moves through different regions of magnetic field. W =% . (4. and the difference in arrival time is13 (~* A p AT = ac Thus the time derivative of the r coordinate is C Ej — = acT0—. its rate of synchrotron radiation may differ from that of an electron with zero betatron amplitude.e. we obtain12 U(E) =U0 + WAE.89) where the rf frequency is wrf = hu>0 = h2ir/T0.85) at.438 CHAPTER 4. AE) be the longitudinal phase-space coordinates of a particle with energy deviation AE from the synchronous energy. Let (C(T + TS).90) 12In fact. (4. First. we assume a sinusoidal rf voltage wave in the cavity and expand the rf voltage around the synchronous phase angle (f>s = hu>oTs. i. w0 is the revolution frequency. and let (CTS. where a c is the momentum compaction factor. the phase slip factor is rj = ac — 1/y2 fa ac for high energy electrons. and h is the harmonic number. Now we consider the case of a storage mode without net acceleration. Thus the net energy change is d(AE) dt eV(T)-U(E)^ TQ where the radiation energy loss per revolution is U(E) = UQ + WAE. Thus Eq. However. PHYSICS OF ELECTRON STORAGE RINGS II. we consider the longitudinal equation of motion in the presence of energy dissipation. The path length difference between these two particles is AC = acC^r. the electron loses energy U(E) by radiation. E=E0 where Eo is the synchronous energy. and gains energy eV(r) from the rf system. We will show later that the coefficient W determines the damping rate of synchrotron motion.86) !=*¥• = During one revolution. [/rf = eV(r) = Uo + eVr (4.84) around synchronous energy. We assume that all particles travel at the speed of light. 0) be those of a synchronous particle. 1 Damping of Synchrotron Motion Expanding the synchrotron radiation power of Eq. the radiation power averaged over a betatron cycle is independent of betatron amplitude. . (4.85) does not depend explicitly on betatron amplitude.
V'= wrfVo cos(a>rfTs). Since the damping rate is normally small. Particle motion is damped toward the center of the bucket.96) . where W <*E = ^ . OE -C WS. (4-91) Thus.95) Figure 4. c J p c J p h/Q (4. aceV ws2 = .87).dt = fp^ds > i J J as = .4 lists the longitudinal and transverse damping times T\\ = 1/CXE and T± of some storage rings. i. (4.lp. we have dJ^l = at Jo Combining with Eq.5: A schematic drawing of damped synchrotron motion.00).e. the solution can be expressed as r{t) = Ae~aEt cos(wst . we need to evaluate W. (4. 1/e damping time is 103 — 104 revolutions. .92) g + 2« B f+u<?r = 0. (4.II. Typically. Table 1. in small amplitude approximation. Since the radiation energy loss per revolution is £ ™ = fP.94) This is the equation of a damped harmonic oscillator with synchrotron frequency ws and damping coefficient a^.93) (4. we obtain heVr-WAE). RADIATION DAMPING AND EXCITATION 439 Figure 4.il + -)ds = .5 illustrates damped synchrotron motion.^ — . (4./P 7 (l + ~^)ds. The damping partition To evaluate the damping rate. with i/o = eVosin(wrfrs).
and we have used cdt/ds = (1+rr/p). p is the radius of curvature.D1 d^ cf \ Eo BoEodx Eo p j E Thus the damping coefficient becomes a £ = 2 ^ ^ ^ = ^ 2 + 2?) - (4'100) Here T> is the damping partition number.440 CHAPTER 4. Since we are interested in the dependence of total radiation energy on the off-energy coordinate and (xp) = 0. . 14The transverse displacement x is the sum of betatron displacement and off-momentum closed orbit. 14 the derivative of radiation energy with respect to particle energy w=e±mifi&+°z\ dE c J [dE p E JE Using F 7 ~ E2B2 of Eq. The damping partition number V is a property of lattice configuration. (4. we obtain dE and rft/rad = Eo „.84). we replace x by D(AE/E0). . /dipole (4. ds. cC/o/1 7 VP Bdx)]Eo = [/f (?+ »<•>)*] [/?]"'' V = ~<fD(s)(-2+2K(s)) Z7!" J ("01) where A'(s) = Bi/Bp is the quadrupole gradient function with Bi = dB/dx. PHYSICS OF ELECTRON STORAGE RINGS where D is the dispersion function. For an isomagnetic ring.97) Eo Bo dE Eo Bo dE dx Eo Bo Eo dx' K > If f ^ 2^rjDd5 P.102) \P The integral is to be evaluated only in dipoles.4.
RADIATION DAMPING AND EXCITATION Example 1: Damping partition for separate function accelerators 441 For an isomagnetic ring with separate function magnets. The damping coefficient for separate function machines becomes The damping time constant.II. Figure 4.105) and OE « 2(Py)/E. Example 2: Damping partition for combined function accelerators For an isomagnetic combined function accelerator. to be discussed in the next section. The momentum change resulting from recoil of synchrotron .103) ' y where QC is the momentum compaction factor.6: Schematic drawing of the damping of vertical betatron motion due to synchrotron radiation. we find (see Exercise 4. The synchrotron motion is highly damped at the expense of horizontal betatron excitation. where K(s) = 0 in dipoles.2. II. is nearly equal to the time it takes for the electron to radiate away its total energy.2 Damping of Betatron Motion A. which is the inverse of OE. Since normally ac -C 1 in synchrotrons. This process damps the vertical betatron oscillation to a very small value.1) £> = 2 . Transverse (vertical) betatron motion A relativistic electron emits synchrotron radiation primarily along its direction of motion within an angle I/7. V -C 1 for separate function machines. The energy loss through synchrotron radiation along the particle trajectory with an opening angle of I/7 is replenished in the rf cavity along the longitudinal direction.^ (4. V=^l^ds = ^ 2K pJ p p (4.
442 CHAPTER 4. Now the energy gain from rf accelerating force is on the average parallel to the designed orbit (see Fig. where vertical betatron coordinate z is plotted as a function of longitudinal coordinate s. dipole magnets. PHYSICS OF ELECTRON STORAGE RINGS radiation is exactly opposite to the direction of particle motion. p E The corresponding change of amplitude A in one revolution becomes ASA = (fz'Az1) = -<(/?z') 2 )^. Since the betatron motion is sinusoidal. the betatron amplitude is unchanged except for a small increment in effective focusing force.109) = -z'^. z' = ?±. Eq.e. and the energy of each photon is small in comparison with particle energy. such that 5P is parallel and opposite to P with \c5P\ = u. and (3 is betatron function.106) where A is betatron amplitude.6). <j> is betatron phase.108) is valid because the momentum direction of photon emitted is along the trajectory of betatron motion.6 illustrates betatron motion with synchrotron radiation. we have ({pz<?) = A2/2. however. (4. . (4. where electrons emit synchrotron radiation.. are distributed in a storage ring but rf cavities are usually located in a small section of a storage ring. Let p±_ be the component of momentum p that is perpendicular to the designed orbit. (4. When an electron loses an amount of energy u by radiation. The betatron phase-space coordinates are z = Acos(f>.) averages over betatron oscillations in one revolution. and The time variation of the amplitude function is then I^ Adt 15Although = !M = _J^ To A 2ET0' ( 4H2) K ' . it does not change z either. i. z' = . Figure 4. (4. A2 = z2 + {pz'f. the momentum vector P changes by 5P. the new slope is decreased by the increment of longitudinal momentum at cavity locations where the change of z' is15 ^^-7(1-7'-y(1-7»Az' = -z'^ (4"108) (4.107) P When an accelerating field is applied to the electron.. 4.s i n 0 . Since the radiation loss changes neither slope nor position of the trajectory.110) where (.. and UQ is synchrotron radiation energy per revolution.
Since phase-space coordinates are not changed by any finite impulse.116). The radiation damping arises from the combination of energy loss in the direction of betatron orbit and energy gain in the longitudinal direction from rf systems. The horizontal displacement from the reference orbit is A ri An x = xp + xe. xe is the off-energy closed orbit. (4.108).114) The resulting change of betatron amplitude can be obtained from the betatron phase average along an accelerator. xe = D{s)—.118) 16Here we use SI = (1 + x/p)ds with x = xp. + %) %-ds. where xp is the betatron displacement. . Horizontal betatron motion The horizontal motion of an electron is complicated by the off-momentum closed orbit. as shown in Eq.116) into Eq. x' = x'g + x'e. x'e = D'{s)—. and D(s) is the dispersion function. = Aco84>. x'0 = -~sm<j>. Substituting the energy loss u in an element length S£ with (4. The off-momentum closed orbit does not contribute to the change in betatron amplitude. When the energy of an electron is changed by an amount u due to photon emission. (4.II. (4. We consider betatron motion with Xf. 6x'0 = -5x'e = -D'(s)^. A2 = x} + (px'p)2.115) the change in betatron amplitude becomes ASA = xpSxf. y B dx p J eh (4. + px'pSx'p = -(Dip + P2D'x'e)^.7. 4. because we are interested in the effect on betatron motion. B. the off-energy closed orbit xe changes by an amount 5xe = D(s) (u/E) shown schematically in Fig.16 we obtain the change in betatron amplitude as ASA = xeD (l + l^-xf. (4. the resulting betatron amplitude is Sip = -Sxe = -D(a)l. RADIATION DAMPING AND EXCITATION and the damping coefficient is 443 The radiation loss alone does not result in betatron phase-space damping.
119) is positive. there is an increase in horizontal betatron amplitude due to synchrotron radiation.101). . az = Jza0. This resembles the random walk problem.121) as = ( l . (4. and the electron energy is changed by u.122) 17This is easy to understand. i. The fractional betatron amplitude increment in one turn becomes where V is the damping partition number given in Eq. we observe that the right side of Eq. and the resulting betatron amplitude will increase with time. At a location marked by a vertical dashed line. we obtain the net horizontal amplitude change per revolution as The damping (rate) coefficient becomes (4. which perturbs the betatron motion. Emission of a photon excites betatron motion of the electron. and thus the off energy closed orbit is shifted by Sxe.7: Schematic illustration.e. aE = JEOC0. where (xp) = 0 and (zjj) = \A^.^ . In particular. (4. the electron emits a photon.444 CHAPTER 4.101). A small and not so important effect is a stronger focusing field for betatron motion.112).. (4. Here we have neglected all terms linear in x'p. We are now looking for the time average over the betatron phase. radiation damping coefficients for the three degrees of freedom in a bunch are ax .2 > ) . Sands [27]. of quantum excitation of horizontal betatron motion arising from photon emission at a location with nonzero dispersion functions. (4.17 Including the phasespace damping due to rf acceleration given by Eq. where the damping partition V is given by Eq.JxaQ. In summary. PHYSICS OF ELECTRON STORAGE RINGS Figure 4. Hot. after M. (4. because their average over the betatron phase is zero.
Wiggler magnets.II. XE = T0/TE.124) provided that all fields acting on the particle are predetermined and are not influenced by the motion of electrons. . Note that the damping time. Rev. for a fixed B-field.{P. Some typical damping times for electron storage rings are listed in Table 1. depend on radiation energy Uo per turn. insertion devices.) = ~ jjT0 °' Tz _ 2E _ AirRp _ IE ~ J.123) (4.3 Damping Rate Adjustment The damping partition and damping times are determined by the lattice design. The corresponding damping decrements are defined as K=T0/TX. Phys. Increase U to increase damping rate (damping wiggler) Phase-space damping rates.JXE3 MP-. which consist of strings of dipole magnets 18 K. longitudinal and transverse dampers powered by amplifiers sensing beam displacement.7. (4. = 1-2?. The corresponding damping time constants are _ Tx = 2E _ 4-irRp _ 2E CC. and the damping partition numbers . such as undulators and wigglers.JzE* ~~JjT00' 2E AnRp _ IE ~ JE(P7) ~ CCJJEE* ~ JETTO °' TE where To is the revolution period. is inversely proportional to the cubic power of energy and. apart from damping partition numbers.) ~ cC. I l l . for constant p. We discuss below some techniques for damping rate adjustment. Robinson. \Z=T0/TZ. induced current in rf cavity. wakefields. 373 (1958).125) The damping rate of an individual particle or a portion of a bunch can be modified if additional forces are introduced that depend on the details of particle motion. II. A. and electron and stochastic cooling devices. Some examples are image current on vacuum chamber wall. However. can be used to adjust beam characteristic parameters.4. is inversely proportional to the square of energy. satisfy the Robinson theorem18 52Ji = Jx + Jz + JE = 4 or JX + JE = 3 Jz = h JE = 2 + V 445 (4. RADIATION DAMPING AND EXCITATION where a0 = (P7}/2E.
Stability of the electron beam can be achieved only by having a positive damping partition number. PHYSICS OF ELECTRON STORAGE RINGS with alternate polarities excited so that the net deflection is zero. The growth time at 3.126) and the damping rate is enhanced by a w = —~ = a0 + awiggier(4. used combined function isomagnetic magnets.130) Since xco < 0.z% (4. K > 0 for a focusing quadrupole. Thus the energy oscillations are strongly damped (JE ~ 4) and the horizontal oscillations become anti-damped (Jx ss — 1). At the CERN PS. If the rf frequency is increased without changing the dipole field. The resulting energy loss per revolution becomes Uy. which is much shorter than the cycle time of 1. the 33 GeV AGS at BNL. (4.5 GeV as part of the LEP injection chain.129) The actual closed orbit can be expressed as x = xc0 + x$.128) where K = (\/Bp)(dBz/dx) is the focusing function. The potential for betatron motion in a quadrupole is V0 = \K(S) (X2 . p = 70 m).446 CHAPTER 4. etc. (4. and xp is the betatron coordinate. (l/Bz)(dBz/dx) < 0.1). (4.2 s. = Uo + C/wjggier. which can be facilitated by decreasing the orbit radius R.e.2. The potential for betatron motion becomes V0 = l-K{s) (xj -z2 + 2x0xco + x\o)..127) The damping time is shortened by a factor of (1 + f/wiggier/^o)"1B. the 28 GeV PS at CERN. This is similar to the effect of a . i. where xco < 0 is a new closed orbit relative to the center of a quadrupole. The reason for the change in damping partition due to orbit radius variation is as follows. the effective dipole field xC0K(s) in a quadrupole and the quadrupole field have opposite signs. and K < 0 for a defocussing quadrupole. and the change of radius ARis ±L = _ ^ = -aA.6 to 3. can be used to increase the radiation energy and thus enhance damping rate.5 GeV is about 76 ms {Jx « —1. the mean radius will move inward. horizontal emittance is an important issue. where V « 2 (see Exercise 4. Change V to repartition the partition number Many early synchrotrons. in facilitating the acceleration of e+/e~ from 0. such as the 8 GeV synchrotron (DESY) in Hamburg.
32) The CERN PS lattice is composed of Ncen = 50 nearly identical combined function FODO cells with a mean radius of R = 100 m.II. RADIATION DAMPING AND EXCITATION 447 Robinson wiggler. Hubner.117) we get the change in damping partition due to closed orbit variation (see Exercise 4. (4. where Bp is the momentum rigidity.101) or Eq. From K. with loss of useful aperture. Robinson wiggler Without a Robinson wiggler. (4. 4. 4. The resulting change of damping partition is (see also Exercise 4.8 shows Jx. and the fractional off-momentum shift <5S = —Af/acf. JE vs AR for the CERN PS.8).118) as A ( T ) =^?/^2JD2^S' (-3) 411 where we have used xco = D5S.8: The variation of the damping partition number of the CERN PS with the strength of the Robinson wiggler.2.117) gives the additional change of betatron amplitude in Eq. 7T / \Bp) TT2R (4.133) Figure 4.9) f={2JK^ds)[f^S]~l. C. it is preferable to change the damping partition number by using the Robinson wiggler. AV = ^<fD(^P\2dsARK^fAR. (4. p. (4. and this limits the dynamical aperture of circulating beams. a fairly large change in AR is needed to attain Jx = 1. If the gradient and dipole field of each magnet satisfy Kp < 0. The effective dipole field arising from the closed orbit in a quadrupole is given by BpK {xp + xco). changing the damping partition requires a large shift of the mean orbiting radius (Fig. as shown in Fig. Thus. CERN 85-19. Without the Robinson wiggler. which consists of gradient dipoles.9. discussed below. Using Eq. Substituting the contribution of quantum excitation from the quadrupole into Eq.2. (4. the damping . 226 (1985). Figure 4. The combined effect is that the damping partition V will get a negative contribution from these quadrupoles.9).
<0 partition of Eq. and Lw are respectively the bending radius. Bw. The change of damping partition is AV = m^^l(l + ^lY\ 2irplJ (4.101) can be made negative. The resulting line density of beam bunches is likewise reduced to prevent collective instabilities. A string of four identical magnet blocks having zero net dipole and quadrupole fields will not produce global orbit and tune distortion in the machine. and the length of each wiggler.448 CHAPTER 4. which enhances damping of horizontal emittance and reduces damping in energy oscillation. The emission time is short and thus the synchrotron radiation can be considered as instantaneous. the wiggler field strength. When a photon is emitted. its derivative. PHYSICS OF ELECTRON STORAGE RINGS Figure 4. where gradient dipoles with B^ are used to change the damping partition number. the wiggler contributes a negative term to the damping partition of Eq. dB^/dx. p is the radius of curvature.4 Radiation Excitation and Equilibrium Energy Spread Electromagnetic radiation is emitted in quanta of discrete energy. Since this time is very short compared with the revolution period and the periods of synchrotron and betatron oscillations. and p is the bending radius of ring magnets and (D) the average dispersion function in wiggler locations. (4. In a semi-classical picture.9: Schematic drawing of a Robinson wiggler.101). II. The Robinson wiggler has been successfully employed in the CERN PS to produce Jx « 3. This can be verified as follows. (4. Since these magnets have Kwpw < 0. quantum emission can be considered instantaneous.34) ' Bw dx 2npl \ where p w . the time during which a quantum is emitted is about P® c P C7 6 B[Tesla] 12 where 7 is the relativistic Lorentz factor. and B is the magnetic flux density. . the electron energy makes a small discontinuous jump.
t0). . the probable change in amplitude will be 5A2 = (A2 . where p = (n) is the average rate per second. <-5"> = -W Z = Vtt' (4139) 19The probability of an electron emitting n photons per second is given by a Poisson distribution f(n) = p"e~p/ni.I I RADIATION DAMPING AND EXCITATION 449 Another important feature of synchrotron radiation is that emission times of individual quanta are statistically independent. . is AE = Aoejul!!{t-to\ (4. The amplitude of oscillation will grow until the rates of quantum excitation and radiation damping are on the average balanced.. (t > h). Now if the energy is suddenly decreased by an amount u at instant t\ via quantum emission. Since the time t\ is unpredictable. Since the energy of each photon [keV] is a very small fraction of electron energy.dA2. The cumulative effect of many such small disturbances introduces diffusion similar to random noise. Effects of quantum excitation When a quantum of energy tiu is emitted.138) . expressed in complex representation. the emission of successive quanta is a purely random process. P{n) = (l/V3ip>-("-") 2 /2p. (4. In the limit of large p.136) where (. The impulse disturbance sets up a small energy oscillation. A.137) The quantum emission has changed the amplitude of synchrotron oscillation. i.e. In the absence of any disturbance and damping. d(A2) . (4.135) where ^o is the amplitude of synchrotron motion. which satisfies Poisson distribution. The variance of Poisson distribution a2 is equal to p.2A0ucosuj%{tl .)t stands for time average. the energy of the electron is suddenly decreased by an amount hui. the energy deviation AE from the synchronous energy. The growth is limited by damping. The cumulative effect of many such random disturbances causes energy oscillation to grow (as in a random walk). the amplitude growth rate becomes . the energy oscillation of the particle becomes AE = Aoeju"{t-to) where A2 = A2 + u2.ue^1'^ = A^^-^. . The damping process depends only on the average rate of energy loss.A2)t = u2. Poisson distribution approaches Gaussian distribution.19 Discontinuous quantized photon emission disturbs electron orbits. Qualitatively. where JV" is the rate of photon emission. (4. whereas the quantum excitation fluctuates about its average rate. and LJS is the synchrotron frequency.
the damping time of A2 is TE/2. the radiated power is P" deseed orbit = ^ ^ = ( V ^ V - ( 4 M 5 ) 20For an order of magnitude estimation. PHYSICS OF ELECTRON STORAGE RINGS B.142) This shows that the amplitude growth rate depends on mean energy loss (u2) of electrons.450 CHAPTER 4. and is proportional to 7 2 . and TE « E/Py to obtain an rms energy oscillation amplitude of UE O \/Efujc ~ 7 2 . (4./tu^c. The equation for the synchrotron amplitude thus becomes ^>=-2<^+A^.141) To attain a better calculation on the equilibrium beam momentum spread. We define the mean square energy fluctuation rate GE as GE = Win2}}. = ^ fN{u2)ds. it is reasonable to average the excitation rate by averaging M{u2) over one revolution around the accelerator. Let n(u)du be the photon density at energy between u and u + du.144) On the design orbit. Equilibrium rms energy spread Since damping time of the amplitude A is TE = I/as. The mean square equilibrium energy width becomes O\ = \GETE.140) where the stationary state solution is (A2) = | JVU2TE . at TE (4. (4. we use u RJ hu)c. which depends on electron energy E and local radius of curvature p. A qualitative estimation of the rms beam energy spread for sinusoidal energy oscillation is20 a B2 = ^ = j ^ « V (4.143) where the subscript s indicates an average over the ring. M a P-. (4. The amplitude growth rate due to quantum fluctuation becomes ^1LZ=/ dt Jo u2n{u)du = N(u2). The energy fluctuation is roughly the C geometric mean of electron energy and critical photon energy. the quantum fluctuation should be obtained from the sum of the entire frequency spectrum because the photon spectrum of synchrotron radiation is continuous. and damping time TE and synchrotron period l/ws are much longer than revolution period To. as shown in Eq. .94). (4. JV = Jo n{u)du. Since the radius of curvature may vary widely along the ring.
J \pw\2 + ^)(l +:|i)~\ (4.147) where Cu = 55/24^3. such as undulators and wigglers. RADIATION DAMPING AND EXCITATION Equation (4. . can change the rms energy spread of Eq. the bunch length is shorter with higher rf voltage. GE = and 3-Cuhcj3-^-}(l/p3) The fractional energy spread is then -i-Sw= (4148) (4I49) ' <f>° = ^ ( 1 / A J5 n_ = x io_13 m where c » 9 4mc 32\/3wc For an isomagnetic ring.Using Eq. |p w | < p.152) are radiation integrals for ring dipoles and wigglers respectively. the bunch length is also affected by wakefields [3]. ^ F \±/ h> / (4.144). Adjustment of rms momentum spread Insertion devices. C. the rms energy spread will normally be increased by insertion devices.83) then gives 451 N{u>) designed orbit = tchclt+jjL. we obtain (f)2 = i ^ ! i r c ^ h. yJJEp[m\ ^4-151) Note that the energy spread is independent of the rf voltage. and the resulting phase-space area is smaller.143) and TE = 2E/JE(P1). J |pw|3 I2w = / -. i.146) we obtain (4.—r^ds. Two competing effects determine the equilibrium energy spread. Because the magnetic field of insertion devices is usually larger than that of ring dipoles. (4.II. the resulting equilibrium energy spread becomes 4 = 4o(l where ^3 = / r-^ds. which will increase quantum fluctuation GESince the damping time is also shortened. Insertion devices increase radiation power. J \p\3 I2 = / r-rrds. In many electron storage rings. (4. For a bunch with a given momentum spread. J |p|2 I3w = / -—prds. 4&VSJEE or JEP f-(°-62xl0"6)7^rit.e. with lower rf voltage phase-space area is larger.
1 (4. 2ir/u>s. Beam distribution function in momentum The energy deviation AE at any instant t is a result of contributions from the emission of quanta at an earlier time £. (4. and \J2-KOE V27T(TE The bunch length in time is Or = -^-VE.155) the corresponding longitudinal time component relative to a synchronous particle [see Eq.. which are positive and negative with equal probability. Normally the damping time is much longer than the synchrotron period.6 = Eu>&r/ac). For a particle executing synchrotron motion with AE(t) = Acos(ust . and the distribution function becomes g{A) = N^e'A2l2^ °E = N24e-All°i. Since the normalized phase-space ellipse is a circle.U)]. the sum at any time t consists of a large number of individual terms. The central limit theorem (see Appendix A) implies that the distribution function of energy amplitude is Gaussian: 9{AE) = ^ = ^ e .158) which depends on the rf voltage. (4.153) where Ui is the energy of a quantum emitted at time U.87)] is T=^sm(ujst-x).159) . We define the invariant amplitude A2 = AE2 + 92.X). The normalized phase-space coordinates are (AE. (4.{t . and £*'s are randomly distributed. °A (4. (4. the Gaussian distribution of a beam bunch is tf (A£. (4. We can write AE{t) = £ Uie-aE{t-u) cos [u. 6 ) = NB^(AE)^(0). \J2-KOE (4. and x is an arbitrary phase factor.154) where OE is the rms standard deviation. Since the typical value of AE(t) is much larger than the energy of each photon. PHYSICS OF ELECTRON STORAGE RINGS D./VB is the number of particles in a bunch.156) where ac is the momentum compaction factor.452 CHAPTER 4.A £ 2 / 2 ^ .157) where .
i. The rate of change of betatron amplitude (emittance) is obtained by replacing u2 with M(u2) and averaging over the accelerator. i. Using the variable W = A2 with dW = 2AdA. RADIATION DAMPING AND EXCITATION 453 where a\ = {A2} = 2a2E. it is not invariant in regions with dipoles. (4." 7 W . U = j ^ [D2 + (PXD' .f z W . we obtain OX Tx The equilibrium rms width becomes (a2) = -TxGx 21The and o*xfil = ^ & (a2).+ A ^ + {PxD' .e.fD)'] (J)». we get the probability distribution function as h(W) = tf J L e . (4. the resulting amplitude growth becomes 8(a2) = %{^-f. (4.112). Sx'g = -D' {u/Eo).161) The resulting change in the Courant-Snyder invariant is 6* = I [DH + {pxD> . Adding the damping term of Eq. Averaging betatron coordinates xp. the %-function is invariant.x'p. 5 Radial Bunch Width and Distribution Function Emission of discrete quanta in synchrotron radiation also excites random betatron motion.165) emittance growth in a transport line is de/dt = -^ $* N(u2)Hds.162) where the ^-function depends on the lattice design. with (W) = 2<r|. In an accelerator straight section.II. .\p'xDf] . (4.21 where (•••)„ stands for an average over a complete revolution. where there is no dipole.160) II. The emission of a quantum of energy u results in a change of betatron coordinates.e. Sxp = -D {u/E0). (4. where /3X and f}'x are the horizontal betatron amplitude function and its derivative with respect to longitudinal coordinate s.f x)] | .
unn r i 3(P.e. (4. The emittance of Eq. PHYSICS OF ELECTRON STORAGE RINGS Using Eq. Since the betatron and synchrotron frequencies differ substantially. Comparing with the energy width for the isomagnetic ring. Gaussian quadrature can be applied to obtain o-x = 4 » . where 6 is the dipole angle of a half cell. the natural emittance of an electron storage ring is proportional to j263. i.g is the average "H-function in dipoles. the result can be simplified to ex—— -Uq Px — -Jxy . where Cq = 3.7 i r — e x p j .168) Since the H-function is proportional to LO2 ~ pO3. + * « (4-172) .166) is also called the natural emittance. (4. the normalized natural emittance of an electron storage ring increases with energy.' « ^ ' ' ' } . we find & ~ Jx \ E ) • ( ' The horizontal distribution function The distribution function for particles experiencing uncorrelated random forces with zero average in a simple harmonic potential well is Gaussian: *(*/0 = . For isomagnetic storage rings.Lb7) where (H)ma.)(n/\p\3) E2{1/p2) 3Cqcro75(-H/\p3\) 3(p2)(1/p2) . The normalized emittance is proportional to 7303.)- ' V2naxffx np {-'» + ' ^ .454 CHAPTER 4. (4.83 x 1CT13 m is given by Eq. (4.150). we obtain _ 3 r f ox--. (4.83) for M{u2). Unless the orbital angle of each dipole is inversely proportional to 7.m> Now the total radial spread has contributions from both betatron and energy oscillations. (H)mag = ^~f Z7T/9 Jdipole nds. the distribution in phase-space coordinates follows the Courant-Snyder invariant ^•^. { 2axfjx ) <.^ } - (4-17°) Since the betatron oscillation period is much shorter than the damping time.
When the electron emits a photon at a nonzero angle with respect to its direction of motion. Recalling that obtain = GE.179) . z axes respectively. Let ex and ez be the horizontal and vertical emittances with e* + e z =enat. r7 a*= % II. Emittance in the presence of linear coupling Sometimes it is desirable to introduce intentional horizontal and vertical betatron coupling. we obtain o\ = TZGZ/3Z ^ rEGE ~ Jrf&or ezHCq(fi)m/P. Including both damping and quantum fluctuation. Thus the vertical oscillation is energy independent and is less than the radial oscillation by a factor of I/7 2 . Emission of a single photon with energy u gives rise to an average change of invariant betatron emittance 8{a2z) = (u/E0)292zfiz. The transverse angular kicks on phase-space coordinates become 5x = 0.— + ~17\ • (4'173) Vertical Beam W i d t h Synchrotron radiation is emitted in the forward direction within a cone of angular width I/7. we o\ Using Jz = 1. we neglect it. The vertical beam size is damped almost to zero. We consider only the effect of random kick on vertical betatron motion. Consider the emission of a photon with momentum u/c at angle 91 from the electron direction of motion. •&0 Sz = 0. -fro (4.6 2 Px(s){n)™s . The transverse kick is then equal to 97u/c. we obtain 455 . (4. Sz' = ^9Z.II. RADIATION DAMPING AND EXCITATION For an isomagnetic ring. 6x' = ±9X. D2(s)] —J. 9Z are projections of 9y onto x.161). where we expect 97 < 1/7. JE{Pl) ^U'] (4-178) °l*CM/p which is very small. it experiences a small transverse impulse. the equilibrium beam width is 0% = -ATZGZ$Z. When the coupling is introduced.174) where 9X. (4.175) (N(v?9ppz)s _ (N(u2){9l)pz)s G* = (Af{u2))(pz) * 7 2£2 & ^ ^ > (JV(M 2 )) (4-176) where we have used the fact that (Of) ~ I/7 2 . the quantum excitation is shared up to an equal division. Since Sx' is small compared with that of Eq. (4.
PHYSICS OF ELECTRON STORAGE RINGS where the natural emittance enat is Eq.166). the Gaussian distribution. Here (5) is the spin polarization. Since the aperture of an accelerator is limited by accelerator components such as vacuum chambers. injection or extraction kickers. etc. K £z — Z ! 1+ K ^natj (4. which has an infinitely long tail. .180) where the coupling coefficient K is (see Exercise 4.8). beam position monitors.7.74). A. can produce a radial displacement as large as the aperture. 11 = J D/pds ac = II/2TTR Uo = 1. 11. (4. Table 4.7 Radiation Integrals To summarize the properties of electron beams. V = hll2 6nRax = recy3{I2-h). Quantum lifetime Even when the aperture is large.8 Beam Lifetime We have used a Gaussian distribution function for the electron beam distribution function. QirRaE = recj3{2I2 + h) ex = Crfh/(I2-h) 11. The horizontal and vertical emittances can be redistributed with appropriate linear betatron coupling £x = Z . is only an ideal representation when the aperture is much larger than the rms width of the beam so that particle loss is small. electrons. we list radiation integrals in the left column of Table II. 1 1+K Enat. JE = 2 + Ii/I2. and the corresponding physical quantities in the right column.404 E4 [GeV] 72 [GeV] 12 = J i/p^ds h = I l/\p\3ds ha = I 1/P3ds I4 = f(D/p)(l/p2 + 2K)ds K=(l/Bp)(dBz/dx) h = fH/\p\3dS (aE/Ef = Cg72I3/(2I2 + 74) (S) = PsTha/h Jx = l-h/I2.3: Radiation integrals and their effects on properties of electrons.456 CHAPTER 4. and PST = —8/5-\/3 is the Sokolov-Ternov radiative polarization limit. which suffer sufficient energy fluctuation through quantum emission.2.. 6nRaz = recj3{I2 .
it is most likely to return to the main body of the distribution because of faster damping at large amplitude.m. The loss rate becomes N dt rq K ' where rq is the quantum lifetime. Rev. We discuss quantum lifetime for radial and longitudinal motion below.II. To estimate beam lifetime. i. we set up a diffusion equation for h(W). f=M. an equal flux of electron passes inward and outward through Wo. Bai et al.e. See M. Phys.187) 22 Note that the formula is valid only in a weakly damping system. is small. 3493 (1997). RADIATION DAMPING AND EXCITATION 457 If the chance of an electron being lost at the aperture limit. • * = — • ( 4 1 8 4 ) The flux inward through Wo due to damping is = 2NWoh(Wo) W at w0 TX In a stationary state. Thus the quantum lifetime is 22 r rq = f^.e. TX(W) (4. with Wo > (W). so that the probability for the electron to have W > Wo is small.186) where Wo has been replaced by W. We assume an equilibrium distribution without aperture limit and consider an electron at amplitude Wo. within its damping time. then the loss probability per unit time is the same for all electrons.. W (4. 1 ^ =-I. .183) h(W) = ~e-w^w\ where W = a2.181) Radial oscillation We consider radial betatron oscillation x = acoswpt. w at = ™wm TX = Nw_e-*. dW 2W . Once the electron gets into the tail region (W > Wo) of the distribution. (4. (4.182) Quantum excitation and radiation damping produce an equilibrium distribution given by {W) = 2al. E 5 5 . (4. i.
0S) and (0. the rms beam velocity spreads in the beam moving frame satisfy the characteristic property (W/2 » <(4)2)1/2 * <(ApbM.^ [ c o s <j> .)2>1/2. (j> = her. (0. The Hamiltonian of synchrotron motion is H ( 5 .0.190) (4.t = Ha/(H)).^T-JE— ooirna uc \~ cos & + (£ . (4-194) where xp and z@ are betatron coordinates. <j>) = -huac62 + ^ .193) Thus the momentum deviation in the rest frame of the beam is reduced by the relativistic factor 7. (4.c o s 0 s + (^-0s)sin^]. the aperture is limited by rf voltage and bucket area. From Eq.188) where 5 = Ap/p = AE/E. Because of synchrotron radiation damping and quantum fluctuation in the horizontal plane. the deviation of the momentum Apb of a particle from that of the synchronous particle.187). (4. If the nonlinear term in the momentum compaction factor is negligible and the synchrotron tune differs substantially from zero. the Hamiltonian is invariant. and h is the harmonic number. (4.7r-^) = ^ ^ [ .cj>s) sin & ] .192) B.458 CHAPTER 4. L 2 J (4. T The Hamiltonian has two fixed points.cos </>B + (<j>.189) The stable rf phase angle (f>s is determined by the energy loss due to synchrotron radiation with eVosin^s = Uo = C7E4/p. is related to the momentum deviation in the laboratory frame Ap by Aph = Ap/-y. PHYSICS OF ELECTRON STORAGE RINGS Synchrotron oscillations For synchrotron motion. and £ . (4. z'p = dzp/ds are the slopes of the horizontal and vertical betatron oscillations.191) where the average value of the Hamiltonian is (H) = hojoac{aE/E)2. The value of the Hamiltonian at the separatrix is Hsx = J ff(O.) sin J . which has zero momentum. T — <j>8). the quantum lifetime is T = * 1P (. Touschek lifetime In the beam moving frame. and p0 is the momentum of a . (4. x'p — dxp/ds.
10. 407 (1963).195) v = 2px/m.10.init = (-px. ^_Ji_M dn~ (v/cyUnH 3_i sin20j' . 4. In the spherical coordinate system.23 The Touschek effect has been found to be important in many low emittance synchrotron radiation facilities. The velocity difference between two particles in the CMS is (4. . Rev. Particle loss resulting from large angle Coulomb scattering gives rise to the Touschek lifetime. Since the transverse radial momentum component of the orbiting particle is much larger than the transverse vertical and longitudinal components. as shown in Fig.. and z base vectors. This process was first pointed out by Touschek et al. which becomes a limiting factor for high brightness electron storage rings. where the momenta are expressed in the x. s.0).10. With the geometry shown in Fig. We consider the Coulomb scattering of two particles in their center of mass system (CMS) with momentum pi.197) Bernardini et at.scatt = (px sin x cos (p. we assume that the initial particle momenta of scattering particles are only in the horizontal direction. and z as orthonormal curvilinear coordinate system. px cos x. which transfers horizontal momentum into longitudinal momentum in the center of mass frame of scattering particles. Let x De the angle between the momentum Pi. and let (p be the angle between the i-axis and the projection of the momentum of the scattered particle onto the x-z plane. Since the transverse horizontal momentum spread of the beam is much larger than the momentum spread of the beam in the longitudinal plane. RADIATION DAMPING AND EXCITATION 459 synchronous particle.10: The schematic geometry of Touschek scattering. the momentum of a scattered particle is Pi. s. 0. (4. 23C. 4. Lett.II. px sin x sin ip). 0.scatt of a scattered particle and the s-axis. 4196) ( ' where r^ is the classical electron radius. Phys. large angle Coulomb scattering can transfer the radial momentum to the longitudinal plane and cause beam loss. in the Frascati e+e" storage ring (AdA). the differential cross-section is given by the Moller formula. We use x.init = (px. Figure 4.0) and p2.
201) (4. and the Touschek loss rate becomes24 dN N2 1 —r. we get the integrals of the vertical and longitudinal planes as (2V^7TCTZ)~1 and (2y/7rcrs)~1 respectively. N is the total number of particles in the bunch. i.198) and the momentum transfer to the longitudinal plane in the CMS is APcms=px\cosx\(4. (4. Thus the total cross-section leading to particle loss in the CMS is crT = ~ / . x'2)5(x1 . (4.= 2 — dt 7 vK(jzas J r / va p(xj. the Touschek loss rate becomes where the factor I/7 2 takes into account the Lorentz transformation of aTv from the CMS to the laboratory frame. the vertical and longitudinal planes can be integrated easily.The scattering angle 9 is related to x a n d <fi by cos 6 = sin x cos ip. and v = dx/dt. |cosx|>— (4.scatt.l + m^l. (4. In the laboratory frame.460 CHAPTER 4. where dV is the volume element.e. and the factor 2 indicates that two particles are lost in each Touschek scattering.202) where n is the density of the beam bunch. da y27r Sm X X J\cosx\>£p/lPx Arl rcos-1 (Ap/jpx) I" V 4 3 1 (v/c)i Jo Jo [(l-sin 2 xcos 2 (/j) 2 ~ 1 . . The number of particles lost by Touschek scattering in the CMS becomes dN = 2aTNndx. PHYSICS OF ELECTRON STORAGE RINGS where the momentum of the other scattered particle is — pi.199) Now we assume that the scattered particles will be lost if the scattered longitudinal momentum is larger than the momentum aperture.x2)dxidx'1dx2dx'2. Thus the loss rate in the CMS is dN/dt = 2 / aTvn2dV.200) where Ap = {2vs/hac)Y(<ps) is the rf bucket height.s i n 2 x c o s 2 ^ J = T ^ f ^ . ndx is the target thickness. Since Touschek scattering takes place only in the horizontal plane.204) 24 Using the Gaussian distribution.x'1)p(x2.
and + £>(£) = >/£/0°° ( ( ^ j 5 [u + \tlnt \t ln^w + $} e " ? ) e""du- (4207 ) The Touschek loss rate is inversely proportional to the 3D volume axazas. RADIATION DAMPING AND EXCITATION 461 where az and as are respectively the rms bunch height and bunch length. p is the bending radius. (4. Figure 4. and the function 6(xi .7 r C. and 6 is the orbital bending angle in one half period. [see Eq. Using the Gaussian density function P{X>X>) = 2Sf 6XP ["2^ (^ + {PxX' " f " )2 )] ' ldN_ Ndt~ Nrlc HrncV W*axv.204) to obtain ' where £ = (Ap/ja^)2 = (pxAp/j2mcax)2. (4. the parameter £ is ^W^WJE (4208) where J7L and . ax = With typical parameters Ap w ap.<x. ap/p = JCqj/^/JEp s/(5xex. (4. the betatron amplitude function can change appreciably.x2) indicates that the scattering process takes place in a short range between two particles.11.211) Sec. as shown in Fig.II. D(£) is a function varying slowly with the parameter £ in accelerator applications. and ex = .7 2 0 3 /^ [see Eq. In a low emittance storage ring. The actual Touschek scattering rate should be averaged over the entire . Ill]. 4.11: The Touschek integral D{0 ofEq. In this parameter region. { Ap ) m h [ (4205) we easily integrate the integral of Eq.7k are the damping partition numbers. aPx = jmccrx//3x.207). (4. T is the lattice dependent factor.149)]. Thus the typical £ parameter for Touschek scattering is about 10~3 to 1.
0 is the bending angle of a half FODO cell. p. i. See. (a) In thin-lens approximation. It can be affected by linear coupling. the rf voltage increases with energy with Vrf oc 7 2 . Exercise 4. and show that the damping partition number for the separate function FODO cell lattice is l-fsin 2 (c&/2) R62 sin 2 ($/2) p ' where R is the average radius of the ring. LeDufF. peak intensity. (c) Use the midpoint rule to evaluate the integral of the damping partition T>. Show that the damping partition number is V = 2 — (acR/p) for an isomagnetic combined function lattice. p is the bending radius of the dipole.e. The damping partition number of DBA lattices is independent of the betatron tunes. 25Actual calculation of Touschek lifetime should include the effect of the dispersion function. p is the bending radius of the dipoles. we can approximate (-D(f)) = 1/6 to obtain 48 7 W^/Ag\ 3 Nrlc \ p ) x ' The Touschek lifetime is a complicated function of machine parameters. i.2 1. etc.25 The beam current in many high brightness synchrotron radiation light sources is limited by the Touschek lifetime. and at a fixed energy the Touschek lifetime is proportional to Vrf because as oc VrJ1'2.g. show that the damping partition number for an isomagnetic combined function accelerator made of N FODO cells is given by g -o R( 2- V p \2Nsm{$/2)J ' where R is the mean radius of the accelerator. Touschek lifetime calculation is also available in MAD [19]. (b) Show that the damping partition for a separated function double bend achromat with sector dipoles (discussed in Exercise 2. CERN 89-01. PHYSICS OF ELECTRON STORAGE RINGS ring. 114 (1989).462 CHAPTER 4. .4. and 6 is the bending angle of a half DBA cell.. and $ is the phase advance per cell. and V = (acR/p) for an isomagnetic separate function lattice with sector magnets. If we choose Ap « Wap. J. rf parameters.16) is / sin(^/iV)\ ^ 62 V (*/N) ) ~ J' where N is the number of DBA cells for the entire lattice.e. and $ is the phase advance per cell. e. we obtain rT oc 7 6 . -T=\N^)s 1 / 1 dN\ = ^fN-dTds- 1 / 1 dNJ (4 ' 209) Since D(£) a a slowly varying function.
where the radiation integrals are ha. (a) For a separate function isomagnetic machine with sector dipoles. 6.2lf GerV ' For a SPEAR-like ring. (b) Show that the contribution from the edge angles of a non-sector type magnet to the integral 7 4b is26 tan<$i tanc52 where 5\ and 62 are entrance and exit angles of the beam. NS-20. and M.063 MeV and F(ip' : 3685) = 0. D is the dispersion function.2 463 2. on Nucl. 26 R. find the energy spread at the J/tp and tp' energies. 5.149). we learn that the beam energy spread can reduce the effective reaction rate. and K = is the quadrupole gradient function. Sands. 900 . Verify Eq.. The rms beam energy spread is given by Eq. = f -gds. What is the constraint of the IR design such that the total center of mass energies for all electron-positron pairs are identical? Discuss possible difficulties. Discuss your result. From the previous problem.215 MeV. J p h= -jrfs.)lh. the production rate is reduced by a factor of T/OE4. IEEE Trans. Show that the vertical emittance resulting from residual vertical dispersion is given c z _ C .2(?WIP| 3 ) ~ ql J*WP2) ' where Hz = ±-[Dl + (pzD'z + azDz)2]. Lee. The damping partition number V for energy spread and natural emittance is given by V = (74a + 1hx. T(J/ip : 3100) = 0. D\ and £>2 are values of the dispersion function at the entrance and exit of the dipole with £>2 = (1 . P.EXERCISE 4. Sci. show that /4a = 2nacR/p2 and /4b = 0. Morton. For example. 3. (4.cos 9)p + Di cos d + [pD[ + Dx tan 5{j sinfl. Helm. where a c is the momentum compaction factor and R is the average radius of the synchrotron. The beam energy spread of a collider should be of the order of the width of the resonance in the energy region of interest. Note that. when the energy spread is large. J p2(l/Bp)dBz/dx Here p is the bending radius. J ps I4h = i K—ds.[MeV] = 1. Show that . (4.J.H. with p = 12 m and JE ~ 2. Now imagine that you want to design an interaction region (IR) such that the higher energy electrons will collide with lower energy positrons or vice versa.L.. Pz (1973).162) for the change of betatron amplitude in photon emission. M.
(a) The synchrotron radiation power is P = ^2^E2B2. ^ . ~C{e2 .118) show that the average rate of betatron amplitude diffusion per revolution is <£ = <¥4(E0 + sef ID \^ A vncti J y + B'X^+2B'B0 + p 2B.J J *. as shown in Eq. 7. where ax. (4.e 0 ).ax(ex . the horizontal action of each particle can interchange with its vertical action.^ + (ax + az + 2C)-^. and the magnetic field can be expanded as B = Bo+B'xco+B'xp. (4.ex) azez.+ [axaz + C{ax + az)]ex = ax{az + C)e0. show that the emittance can be expressed by Eq. Use the following model to find emittances of electron storage rings. the average radius and the beam energy are changed by AR/R = -Af/fo and Eo + 8e. Using Eq. Use the following steps to derive the expression for AV/AR. . eo is the natural emittance. The equation of motion for emittance of an electron storage ring near a linear coupling resonance is —j^ = -£• = -C(ex . while the total action of the particle is conserved.363). and C is the linear coupling constant. Z7T If the rf frequency is altered.464 CHAPTER 4. Make a realistic estimate of the magnitude of the vertical emittance arising from the residual vertical dispersion.e2) . Find the equilibrium emittances. Near a betatron coupling resonance. The damping partition T> can be decreased by moving the particle orbit inward. az are damping rates. PHYSICS OF ELECTRON STORAGE RINGS fiz and az are vertical betatron amplitude functions.+ {az + az + 2 C ) ^ + [axaz + C(ax + az))ez = axCe0. (a) Show that the equations of motion for horizontal and vertical emittances are . (2.180) where the K parameter is given by C 8. (b) For ax = az = a. and Dz and D'z are the residual vertical dispersion function and its derivative with respective to s.
Show also that the quadrature horizontal beam size of the electron beam is cr2 = 3pC?72/[n(3 .8 for the CERN PS. show that ASS ~ sin 2 ($/2) " TT^B Aii- and A P (d) Compare your estimation with that in Fig.2 (b) Show that the change in damping partition with respect to xc0 is 465 £-('/o"*)(/>r A P „ 8JVc2ell Axco ~ TT2E ' For an isomagnetic FODO cell combined function machine.2n)/(l .An)}. where p is the bending radius. In fact. .n.n) 3 / 2 .n). Show that (H) = p/(l . ^ = n/(l . and e^ = Cq^2/n^/l . 9.n).4.5) with focusing index 0 < n < 1. 4.n). J £ = (3 4n)/(l . where 1 A / _ 1 Afl ac /o a c il is the fractional momentum deviation from the momentum at frequency foShow that the variation of the damping partition with respect to Ss is For a FODO cell combined function lattice. V = (1 . (c) The above analysis assumes that xco = AR. Consider a weak focusing synchrotron (Exercise 2. xco = D5S.EXERCISE 4. show that where iVcen is the number of FODO cells.
72^3. . Because synchrotron light sources from electron storage rings are tunable.1% of bandwidth). and the %-function is given by Eq. See e. electronic processing. Jx « 1 is the damping partition number.. Wiedemann. H. (4. cell biology. the {'H) and the resulting natural emittance obey the scaling laws: {•H)/Jx = fuuicep03 and e. the synchrotron light fans out to an angle equal to the bending angle of the dipole magnet. etc. where 7 is the Lorentz factor. they have been widely applied in basic research areas such as atomic. it would be useful to understand the limit of achievable emittance in order to determine the optimal solution for a given lattice.258). The synchrotron light spectrum is continuous up to a critical frequency of 3c73 Beyond the critical photon frequency. Computer codes such as MAD [19] or SYNCH [20] can be used to optimize {%). Horizontally. molecular. chemistry. (2. Thus a small electron beam emittance is desirable for a high brightness synchrotron radiation storage ring. Low emittance Ring Design.466 CHAPTER 4.g.27 The amplitudes of the betatron and synchrotron oscillations are determined by the equilibrium between the quantum excitation due to the emission of photons and the damping due to the rf acceleration field used to compensate the energy loss of the synchrotron radiation. where the product of the solid angle and the spot size dSldS is proportional to the product of electron beam emittances exez. Since % ~ L62 = p93. The brilliance of a photon beam is defined as dtdfldS(d\/X) y ' in units of photons/(s-mm2-mrad2 0. the power of the synchrotron light decreases exponentially e1. microbiology. 390 in Ref. For an isomagnetic ring.— LJ/UJC). and solid state physics. the horizontal emittance reduces to ex = Cqj2{H)dipole/JxP. condensed matter. The horizontal (natural) emittance is where Cq = 3.atticeC. However. (4.167) The objective of low emittance optics is to minimize {H) in dipoles. [14] (1988).211) 27Many review articles have been published on this subject. PHYSICS OF ELECTRON STORAGE RINGS III Emittance in Electron Storage Rings The synchrotron light emitted from a dipole spans vertically an rms angle of 1/7 around the beam trajectory at the point of emission.83 x 10 13 m. p. = ^. p is the bending radius.
III. three-bend achromat. Morton. In this section. and each application has its special design characteristics. Sommer. Figure 4. Internal report DCI/NI/20/81 (1981). The low emittance point of a FODO cell lattice at 8 GeV corresponds to that of a PEP low emittance lattice [G. Lee and P.212) depends essentially only on the lattice design factor ^lattice for electron storage rings at constant 7$. the lattice of a high energy collider is usually composed of arcs with many FODO cells and low 0 insertions for high energy particle detectors. four-bend (QBA). Popular arrangements include the double-bend achromat. D.J. etc.12: Normalized emittances of some electron storage rings plotted vs the designed beam energies. and 6 is the total dipole bending angle in a bend-section. 461 (1987)].28 Sci. For example. Figure 4. IEEE PAC. three-bend (TBA). Electron storage rings have many different applications. lattices for synchrotron radiation sources are usually arranged such that many insertion devices can be installed to enhance coherent radiation while attaining minimum emittance for the beam. M. we review the basic beam characteristics of these lattices.^) 3 (4.. . Note that the emittances tend to be larger for machines with FODO cell lattices than for those with DBA or TBA lattices.K. in Proc. On the other hand. etc.l Emittance of Synchrotron Radiation Lattices Storage ring lattices are designed to attain desirable electron beam properties. p. M. Possible lattice design includes FODO cells.L. The resulting normalized emittance 6n = jex = ^atticeC. Nucl. Internal 28G. IEEE Trans. NS-20. The function of arcs is to transport beams in a complete revolution. BNL-50522 (1976). III. the double-bend achromat (DBA) or Chasman-Green lattice. and n-bend achromats (nBA). Brown et al. Green.12 compiles normalized emittances of some electron storage rings. Potaux. H. 900 (1973). R. EMITTANCE IN ELECTRON STORAGE RINGS 467 where the scaling factor lattice depends on the design of the storage ring lattices. Helm.
Nucl. PEP-303 (1979). ' Z. 2. Y.29 A FODO cell is usually configured as { | Q F B Q D B | Q F } . Note that the dispersion invariant does not change appreciably within the FODO cell. Some high energy colliders have been converted into synchrotron light sources in parasitic operation mode. p. 33 (1980).3.1). $. the optical function is /3 ' = S 2L . Wiedemann. we can approximate {H) in the dipole by averaging %F and Ha (see also Exercise 4. Ropert. SLAC Tech Note. 1 ~ S „ m 2 ) $. Wiedemann. Here we discuss the characteristics of FODO cell lattices.[28]. D° = L9 . 30 R. Argonne Report (1985). Helm and H. ^(1 + Sm . the change of the dispersion functions of a FODO cell is shown in Fig. where Q F and QD are focusing and defocussing quadrupoles and B is a dipole magnet (see Chap. 2.. Kamiya and M. The %-function is therefore % is invariant outside the dipole region. as shown in the left plot of Fig. / is the focal length.30 ^ 1 . PHYSICS OF ELECTRON STORAGE RINGS A. 158 in Ref. 9 is the bending angle in a half cell. Kihara. Instr. A. In thin lens approximation. L. and $ is the phase advance per cell. 4. Methods 172. H. . $ 2f=Sm2' < J > and D' = L6 . 2 9 H. Since the dispersion invariant does not vary much from QF to QD.468 CHAPTER 4. Wiedemann. Teng. II). where two invariant circles of radii JH^ and J'HT at the defocussing and focusing quadrupole locations are joined at dipole locations to form a small loop.13. $. D/\/]3). ^1-2**2)> 1 where L is the half cell length of a FODO cell. Report ESRP-IRM-71/84 (1984). LS-17. Sec. FODO cell lattice FODO cells have been widely used as building blocks for high energy colliders and storage rings. 3 cos($/2) r(l + isin($/2)) 2 ~ 2 P sin 3 ($/2) [ (l + sin($/2)) (l-|sin($/2))2l (1 . 2)' o ^ =^ 2L . ri?f(1+28in2)' 1 . KEK 83-16 (1983).34. In normalized coordinates ((aD + PD')/y/P. The ratio 'HF/'HD is typically less than 1.sin($/2)) J " ' W + [ The coefficient T of the FODO cell becomes FODO _ l-fsin2($/2) " sin 3 ($/2)cos($/2) Jx • [ b) report DCI/NI/30/81 (1981).
III.14). The coefficient decreases rapidly with phase advance of the FODO cell. or a pair of doublets.13: Left: the ratio HT/HD. Wrulich.31 The resulting emittance of the FODO cell dominated lattice is (4.3 at <j> « 140°. Nonlinear magnetic fields can become critical in determining the dynamical aperture. undulators. chromatic sextupoles are 31A. The {O QF 0 } section may consist of a single focusing quadrupole. 22. Part. where we assume Jx = 1. and rf cavities. At this phase advance. Since the dispersion function is nonzero only in this section. The right plot of Fig.217) W o = ^PODOC^3B.13 shows the coefficient T as a function of phase advance per cell. 4. We note that the factor T has a minimum of about 1. or triplets with reflection symmetry for dispersion matching. right: T with Jx = 1 for a FODO cell lattice. The betatron function matching [00] section can be made of doublets or triplets for attaining optical properties suitable for insertion devices such as wigglers. . Double-bend achromat (Chasman-Green lattice) The simplest Chasman-Green lattice is made of two dipole magnets with a focusing quadrupole between them to form an achromatic cell (see Exercise 2. the chromaticity and the sextupole strength needed for chromaticity correction are large.5. Accel. 257 (1987). EMITTANCE IN ELECTRON STORAGE RINGS 469 Figure 4. A possible configuration is [00] B {O Q F 0 } B [00].
/30.2a o psin 0(1 . PHYSICS OF ELECTRON STORAGE RINGS also located in this section. (4. (4.| B + | c } . (4.40 sin 6 + 5 sin 20)/65.| F ) di + | A . B(6) = (6 .221) where L and 6 = L/p are the length and bending angle of dipole(s) in a half DBA cell. E-+1. E{9) = 2 ( 1 .14) H((t>) = Ho + 2(a0D0 + /3oD'o) sin c/> . and a 0 .^pe3B(9) + f/e'ae). D'=(l °-)sm<P + D'0cos<j) .3sin20)/(403). With the normalized scaling parameters do = §' d'0 = ^' P° = T' ^ = ^oL' "o = a o.470 CHAPTER 4. In general.220) where Ho = 7O-DQ + 2aoDoD'o + PQD'O2. B->1.cos (j>) + D o cos <t> + pD'o sin (f>.cos9)/92. we need Do = 0 and D'Q — 0 to attain the achromatic condition. The evolution of the "H-function in a dipole is (see Exercise 2.cos <j>). p is the bending radius. (4.8 cos 0 + 2 cos 20)/0\ C{0) = (306 . we get (H) = (aoDo + PoDo)e2E(6)-±(joDo +^e2A(e) + aoD'o)P62F(e) .2(j0D0 + a0D'0)p{l . F{6)=6{6-sme)/63. we find A->1. (4. and A{9) = (66 . and Do and D'o are respectively the values of the dispersion function and its derivative at s = 0. C-»l.223) .219) where <f> = s/p is the bend angle at a distance s from the entrance of the dipole.222) the averaged %-function becomes (H) = pe3\^od2 + 2aodod'o + hd'o2+(&aE-1^F^do + {PoE .218) (4. In the small angle limit.cos (j>)2 . Averaging the %-function in the dipole. For the Chasman-Green lattice. and 7Q are the Courant-Snyder parameters at s = 0.4. the dispersion function inside the dipole is D = p(l .cos 0) +Po sin2 4> + 7op2(l . F->1.
3. and the corresponding betatron amplitude functions are 6C . In zero gradient approximation.227) In thin lens approximation.224) With the identity /3o7o = (1 + &l). (4. decreases slightly with increasing 9 because of the horizontal focusing of the bending radius. a longer dipole magnet will give a smaller emittance. i. shown in Fig. (4. the minimum of (H) becomes (see Exercise 4. (H) = H(6)/4.15B2. and we obtain 1 (^)MEDBA = J y f f ^ Wlth 3 ^MEDBA = 3 SMEDBA = ^ ^ Q ^ ' g^" The corresponding minimum emittance is ^MEDBA = FMEDBACql2e3. since %(</>) ~ 4>3. The dispersion action %{&) outside the dipole is an important parameter in determining the aperture requirement. and the ^-function at the end of the dipole is (4.e. y/TEB .228) where FUEDBA = 1/(4^15 Jx). the horizontal betatron phase advance across a dipole for the MEDBA lattice is 156. In small angle approximation. i.e. 2. we get the average ^-function as <W)=pfl»[|A-|B + | c ] .7°.37. EMITTANCE IN ELECTRON STORAGE RINGS Bl. we find H — 0 at s = 0. For a minimum emittance (ME) DBA lattice. 8V5A Po = 7TEd' °° = — • 7o = W (4226) The factor G = y/16AC — 15B2.4) MMBDBA = •jjfiPP' (4225) where G = y/16AC . Minimum emittance DBA lattice 471 Applying the achromatic condition with d0 — d'0 = 0. the average of % is 1/4 of its maximum value. the dispersion "H-function for a MEDBA lattice at the end of a dipole is W) = -LPe>. and the phase advance in the dispersion .III.
The resulting emittance is smaller than the corresponding FODO cell lattice by a factor of 20 to 30.472 CHAPTER 4. PHYSICS OF ELECTRON STORAGE RINGS matching section is 122° (see Exercise 4. Since the phase advance is large. B2. Thus each MEDBA module will contribute about 1. The ELETTRA lattice has 12 superperiods. Examples of low emittance DBA lattices Many high brilliance synchrotron radiation light sources employ low emittance DBA lattice for the storage ring. The total phase advance of each ELETTRA DBAperiod is about 429°. which does not include the phase advance of the zero dispersion betatron function matching section for the insertion devices. and the low emittance DBA lattice of APS at Argonne for 7 GeV electron storage ring (right).9439 to increase damping partition number Jx (see Sec.4). III.38 £ MEDBA and — « 3.14 shows the lattice functions of a nearly minimum emittance DBA lattice ELETTRA at Trieste in Italy for 2 GeV electron storage ring (left). while the corresponding phase advance of APS DBA-period is about 319°. The ELETTRA lattice employs defocussing combined-function dipole with q = y |J5i|/Bp£dipoie = 0.l.14: The low emittance lattice functions for a superperiod of ELETTRA (left) and APS (right).64.2 unit to the horizontal betatron tune. £ MEDBA Figure 4. and the APS lattice has 40 superperiods. Figure 4.D).4°. the chromatic properties of lattices should be carefully corrected. The resulting horizontal emittances of these lattices are respectively « 1.3. . Thus the minimum phase advance for the MEDBA module is 435.
EMITTANCE IN ELECTRON STORAGE RINGS B3. The optical functions that minimize (71).229 ) where /?* is the value of the betatron amplitude function at the symmetry point of the dispersion free straight section.min = ^ .230) (H) = ^P0 3 (faA . Minimum ('H)-function lattice Without the achromat constraint. each module of an accelerator lattice has only one dipole. First. this minimum emittance condition can not be reached. . Triplet DBA lattice 473 A variant of the DBA lattice is the triplet DBA.37.e.232 ) where G = ylQAC . 2 (4. Because there is no quadrupole in the [00] section of the DBA. are symmetric with respect to the center of the dipole. C. Note also that G is nearly equal to G. C = -C . the minimization procedure for (H) can be achieved through the following steps.30). 32See Exercise 4. 2.6.221). (4. The minimum emittance is32 WPI« = ^jCrf9*' ( 4 .231) With the relation /?o7o = 1 + QQ> *he minimum emittance is (^)ME = J^P03' ( 4 . 6 and d'aMa = -\E.3E2. where we find that the stability condition is incompatible with the achromat condition. i.3. the lattice is very simple (see the lower plot of Fig. From Eq.a0B + ^ c ) with A = 4A. and I is the length of the dipole. 4 4 (4. B = W2EF. Therefore. (H) can be minimized by finding the optimal dispersion functions with ddQ ' dd'o ' where we obtain rfo.-F2.III. 2. where a quadrupole triplet is used in the dispersion matching section for the achromat condition.15B2 is also shown in Fig. the dispersion and betatron amplitude functions.
The required minimum betatron amplitude function is B* = -B* It is interesting that the minimum B value for a ME lattice is actually larger than that of a MEDBA lattice.230) and (4. we obtain H(0) = H(9) = ~^=p93 [WE2 . ao = —• V15B .235) In small bending angle approximation. The horizontal beam width is given by the quadrature of the betatron beam width and the momentum beam width. we find that the minimum {%) without achromatic constraint is smaller by a factor of 3 than that with the achromat condition.236) where S2 = {aE/E)2 = Cqj2/pJE is the equilibrium energy spread in the beam.e.3. 7o = ^ - 2VTEA (4233) The waist of the optimal betatron amplitude function for minimum ("H) is located at the center of the dipole. s*ME = Lji. It is appropriate to define the dispersion emittance as ed = lx{D5)2 .232). (4. and the dispersion matching section is 133.234) where J-ME = l/(12\/l5Ji). The brilliance of the photon beam from an undulator depends essentially on the electron beam width.B'X(D5)(D'5) + BX(D'6)2 = U(0)62. PHYSICS OF ELECTRON STORAGE RINGS From Eq.4° (see Exercise 4.233) for the ME condition. Using Eq.79. the corresponding minimum betatron amplitude function at the waist is 8^B = L/\/60. In small angle approximation with ^ C l . The values of the dispersion H-function on both sides of the dipole are important in determining the beam size in the straight sections. i. Each minimum emittance module with a single dipole would contribute a horizontal betatron tune of 0.474 CHAPTER 4. Thus the horizontal betatron tune of this minimum emittance single dipole module is 284.^-BEF + ^-AF2} G"1.5). 3vl5 I 2 2 J (4. To attain the minimum emittance. e^ is invariant in the . (4.4°. The minimum condition corresponds to = PO = 8C 7EG> . we have 7i(9) = j^pO3 = 4("H)ME. where insertion devices such as undulators are located. the betatron phase advance across the dipole is 151°. which is equal to |H(0)| MEDBA . Because the "H-function is invariant in the straight section. (4. where A -» 1. The attainable emittance is eME = ?u*Cql2e\ (4. and C -> 1. B ->• 1.
the divergence of the ME lattice is smaller than that of the MEDBA lattice. To simplify the design of a DBA in a synchrotron storage ring.33 D. A defocussing combined function dipole has the advantage of having minimum /3X inside the dipole.°^B(q) + ^ C ( 9 ) ] . the dispersion function is D(s) = .240) .7 ^ ( c o s h JlK^s p\Kx\ and {%) is (H) = p63 ^A(q) . J i « 1 or J"£ « 2 ^ . a0 = a 0 .40 sinh q + 5 sinh 2q -5 • 33 The brilliance of a photon beam is inversely proportional to the phase space areas of the electron beam in the straight section.III. we obtain 475 For a separated function lattice. /30 = /30/L. The dispersion function in a combined function dipole satisfies D" + KXD = . P where Kx = (1/p2) + B\/Bp < 0 is the effective defocussing strength function and p is the bending radius of the dipole. combined function dipoles have often been used.(4.1).239) where q = ^J\KX\L.236). (4. (4. 7o = loL.a S a m m photon brilliance by minimizing the betatron beam-emittance.5. Thus designing the lattice may be slightly easier. and thus the resulting photon brilliance is proportional t 0 l/V£MEeiot. (4.i> i-e. Although the total electron rms beam size in the straight section for a MEDBA lattice is the same as that of an equivalent ME lattice. EMITTANCE IN ELECTRON STORAGE RINGS straight section. e. The total effective emittance for a bi-Gaussian distribution becomes 1 Crffi tA?W\ The decrease in betatron beam size in minimum emittance lattice is accompanied by an equal amount of increment in the dispersion beam size. CW = _ 6 . . in the Elettra at Trieste and in the UVU and X-ray rings in NSLS (see Exercise 2.235) into Eq. JE « 2. . Substituting 7/(0) of Eq. Minimizing emittance in a combined function DBA We have discussed the minimum {H) only for sector dipoles.22).8 cosh q + 2 cosh 2q 30q . and 3(sinh 2q-2q) ..g. For a DBA.
PHYSICS OF ELECTRON STORAGE RINGS Figure 4. The TBA is a combination of DBA lattices with a single dipole cell at the center. the emittance can be reduced accordingly. R is the average radius. The emittance factor V16AC .476 CHAPTER 4. we use small angle approximation. a combined function DBA gives rise to a larger (Ti). etc. Three-bend achromat Now we are ready to discuss the minimum emittance for three-bend achromat (TBA) lattices. To simplify our discussion.15S2 for a combined function DBA lattice is shown as a function of quadrupole strength q = y/Kt. the Pohang Light Source (PLS). (4. However.15: The factor V16AC . we find y/16AC — 15B2 > 1. there is another factor that can change the emittance of the machine. the Taiwan Light Source (TLS).15 shows %/16/lC — 155 2 vs quadrupole strength. and p is the bending radius.e. Note that the combined function DBA can achieve lower emittance due to damping partition. Depending on the focusing strength. which is good provided that the bending angle for each dipole is less than 30°. The damping partition number for radial betatron motion is given by ~g-^. which have been used in synchrotron radiation sources such as the Advanced Light Source (ALS) at LBNL. i. S i n h g ^ = l+ 2 E.15B2/JX is also shown. The normalized dispersion coordinates for the minimum emittance DBA and minimum emittance single dipole lattices are given respectively by VP O Pi . Thus the minimum of (%) is _ V16AC-15B* {n)mtn 3 ~ WE p • Figure 4. As expected.241) 3 P where ac is the momentum compaction factor.
Thus we have proved a theorem stating that an isomagnetic TBA with equal length dipoles can not be matched to attain the advertised minimum emittance.235). 1940 (1996). where the normalized dispersion functions are transformed by coordinate rotation.76°. For an isomagnetic storage ring. The necessary condition for finite angle can be obtained by equating Eq. Optical matching between the MEDBA module and the ME single dipole module is accomplished with quadrupoles. l^. see S. and the matching condition of Eq. the center dipole for the TBA should be longer by a factor of 3 1//3 than the outer dipoles in order to achieve dispersion matching. (4. . (4. where p\ and Lx are the bending radius and length of the DBA dipoles.247) requires Li = 2>1I3L\ for isomagnetic storage rings. (4. or pi = \/3p2 for storage rings with equal length dipoles.e. we can prove the following trivial theorem: The emittance of the matched minimum TBA (QBA. {X**\-{ 1p / ^ rME ' V cos # sin $ W XMEDBA \ V-sin$ cos<3?MP /' b111 * LOb ^ / V -"MEDBA / . In this case. provided the middle dipole is longer by a factor of 3 1 / 3 than the outer dipoles. ' V*-™) at the dispersive ends of the dipoles in the MEDBA lattice. i. Phys. The formula for the attainable minimum emittance is identical to that for the MEDBA. Lee.Y.I l l EMITTANCE IN ELECTRON STORAGE RINGS 477 aD + PD' ^MEDBA^ " 7 8(15)V4 LT pi . E 54.227) and Eq. or nBA) lattice is = ^ A (4 248) 4V15JX' [ ' where 9\ is the bending angle of the outer dipoles.zwj where $ is the betatron phase advance. and . Rev. e METBA 34This necessary condition is valid in small angle approximation. The necessary condition for achieving dispersion phase space matching is34 §=4- (-4) 4 27 The phase advance is $ = 127. and pi and L2 are those of the ME dipoles. = D V2(15)V^f 3 T 4V2(15)V4 (4244) oD + 0D'= V^ Lf p2 ' [*-Mb) at the entrance and exit locations of the dipole in the ME lattice.
0E=<'Eo[1 ( PW. will not affect the dispersion function outside the wiggler.20).4.2 Insertion Devices A. I40. For insertion devices in zero dispersion regions. Sec. Damping wigglers have been successfully employed in LEP to enhance the momentum spread for Landau damping of coherent instability and.-20) : I ( Pyr 6) I S 3LW 4LW 0 L_ : • 2LW Figure 4.(2LW . the wiggler. /4W. 9 = 0 W = £ w / p w is the bending angle of each dipole. where /?w = p/eBy. Since the rectangular magnet wiggler is an achromat (see Exercise 2. I30.e.4.478 CHAPTER 4. B) I (-p w .r ) . /3 W . Lw < s < 2LW ' . PHYSICS OF ELECTRON STORAGE RINGS III. is the bending radius. located in a zero dispersion straight section.s) 2 ]/2p w ' V [S)~ I -[2L W . Effects of insertion devices on the emittances The rm beam emittance ex and the fractional energy spread (JE/E in electron storage rings can be expressed in terms of the radiation integrals (listed in Table II.s ] / P w . Depending on the radiation integrals. and L w is the length of each wiggler dipole.16: A schematic drawing of a section of a vertical field wiggler. II. a n d ^50 a r e radiation integrals of bending dipoles. However. this wiggler can generate it's own dispersion (see Exercise 2.251) \ 730 / V JI20 + ho / where I20. and 75w are radiation integrals of wigglers. to reduce the horizontal emittance. at the same time. i.7): Since insertion devices also contribute to the radiation integrals. (4. the emittance can be reduced while the momentum spread can be enhanced. Example 1: Ideal vertical field wiggler in zero dispersion sections We consider a simple ideal vertical field wiggler (Fig.20). the emittance and the energy spread can increase or decrease.7. 4. V J50 / V •'20 ~~ -"40 / (4-25°) + -j—l[l+OT . and 72w.16). U{S) ~ \ -[2L2W . the natural emittance and the energy spread of the beam can be expressed as *-= ^ ( 1 + 7=) (1 + 7=^7=)"'.
/PW The contribution of each wiggler period to I2 is Now. EMITTANCE IN ELECTRON STORAGE RINGS 479 Now we assume that the wiggler magnet is located in a region with ax = — \@'x ~ 0 with high jjx. (4. the ideal dipole field discussed in the last section does not exist. wigglers or undulators.z cos £ws. (4. in synchrotron radiation storage rings can greatly enhance the brilliance and wavelength of the radiation.e.e.254) where we have used J5o = 2TT('H)O/P2 and 720 = 2TT/P for the isomagnetic storage ring with /40 « 0 and 74w « 0. ~ 4X' z " 47 y 7 ~ 4.III.257) . < 4252) (4. Since we normally have fix S> p w . cosh ky. (4. i.w = fxo (1 + o 2P/o/\ ^ w & e t ) (1 + —iVwOw . we assume that there are Nw wiggler periods in an isomagnetic storage ring.255) This condition is usually satisfied.rp2 ' (4256) where LWitotai = 4ArwZ/w is the total length of the undulator. Bz = By. thus there is no net focusing in the horizontal plane. P2 Pv. Since all magnetic fields must satisfy Maxwell's equation. Example 2: Effects of undulators and wigglers with sinusoidal fields Insertion devices. Thus the condition for e xw < eI>0 is —p^P^l < I- (4.250) becomes e*. The focal length of the vertical betatron motion and the tune shift resulting from the rectangular wiggler dipole are respectively f ~ 4 ^ e .253) where each dipole contributes an equal amount to this radiation integral with 6 W = LY. and (/3Z) is the average betatron amplitude function in the wiggler region. and the radiation integral 75w is approximately *-5*f-^ /2w = 4 % = — 6 W . We consider a simple model of a nonlinear undulator with a planer vertical modulation field. the H-function can be approximated by 7i « f3xD'2. i. It is worth pointing out that the edge defocussing in the rectangular vertical field magnets cancels the dipole focusing gradient of 1/p2. adding wiggler magnets in regions where the dispersion function is zero will generally reduce the beam emittance. The emittance of Eq.
.z sin KWS.480 CHAPTER 4. or ^|| = w X /^^i=(^l-^-^sin 2 fcw S j / i K2 \l/2 !_lJ^l4^£ 27 2 = 1_i±M_^sin2. The velocity vector of an electron in the planar undulator is /? = /3j_x + P\\s. x'co = (3j_ = ——sinfc w s = —^sinfe w s. .l/j2. and the corresponding horizontal and longitudinal magnetic fields are Bx = 0 and Bs = —Bw sinh kwz sin k^s. (4.258) Thus the Hamiltonian of particle motion is H=-(px-r cosh Kzsin A:ws)2 + .e.rms = Kw/V^ is called the rms undulator parameter. • x. For Kw < 1. The quantity ii'w. the device is called an undulator. The corresponding vector potential is Ax =--~-Bw cosh k^z sin ky.w = Kw/fiy « Kw/y with the wiggler parameter defined as Kv = ^ ^ = 0.cosfc w s).w is the wiggler wave number.s.261) „ Pw "'w ^ w w ^ where we use l/pwA.p 2 . As = 0. (4. The transverse electron angular divergence inside the undulator or wiggler is equal to Kw/j. Az = 0.z cos kws.263) Note that the magnitude of the longitudinal velocity oscillates at two times the undulator wave number. it is called a wiggler. Pw 2fc w Pw T h e nonlinear magnetic field can b e neglected if t h e vertical b e t a t r o n motion is small with kwz <C 1. T h e horizontal closed orbit becomes 1 TC 1 xco = — — ( 1 . z H 5 — = — sinh ky.4 lists wiggler parameters of the some insertion devices for third generation light sources. (4-260) sin^/cwssmh2fcwz px . PHYSICS OF ELECTRON STORAGE RINGS where A. the wiggler period is Aw = 2ir/kw.259) where p w is the bending radius of the wiggler field. The equation of motion is x" = — cosh ky. .934 B^ [T] Aw [cm].wS.262) Table 4. (4. 27 2 472 (4. where 02=01 + tf\=l. (4. for ivTw ^> 1. i. P \ . i?wpw = vle with particle momentum p.
The nonlinear field in the wiggler can also affect the dynamical aperture.5 5 14 1. Thus the nonlinear wiggler is achromatic if kwLw is an integer multiple of 2n.4: parameters of some undulators and wigglers Machine 1 E [GeV] I B [T] I Aw [cm] 1 L [m] I K~ ALS 1.65 I 2.III.2 |5 | 1.5 1.267) . it also produces vertical ^-function modulation.2 Photon Factory 2.63 5. Since the vertical field undulator introduces a vertical quadrupole field error. The emittance and the energy spread become 4 = 4 o (1 + ^ ( ^ ) 3 ) (4.18 14 .5 5.2 481 APS I7 I 0.5 ESRF 6 1.25 TO 2 12~~ . where Lw is the wiggler length. For an off-momentum particle.63 2. EMITTANCE IN ELECTRON STORAGE RINGS Table 4.8 9.2 5.96 65 1.5 6 3. The betatron tunes should avoid all low order nonlinear resonances. Pvf "• D'= i-sin/c w s.45 6 3.3~ The vertical closed orbit is not affected by the vertical field undulator. the vertical field generates average vertical focusing strength and vertical betatron tune shift given by sin2fcws 1 _ 1 r j3z{s)ds _ (/?2)Lw.7 Elettra 2 5 30 3 140 1.5 10 3. However.5 6.totai where Lv is the total length of the undulator.15 9 4. Pw "* (4.264) where we have assumed Do — D'o = 0. the vertical field undulator also gives rise to a dispersion function in the insertion region: D= l— (l-cosifcws). The radiation integrals of the sinusoidal wiggler are 2 = lt' 3 = ^' /w /w '-"d^2(l + T ^ ( ^ ) 2 ) ~l • (25 46) where we have approximated ~H ss fixDa.
4. .n ~ 7?r mm-mrad at 6 GeV. .482 CHAPTER 4. The transverse equation of motion for electrons traveling at nearly the speed of light in the longitudinal direction inside the wiggler is dp n ymc— = Pcs x B.s) + p\\s. (4.= (z cos A. (4. (4. we need to include higher order nonlinear terms in the magnetic field. i.e. The n can be written as (see Fig. (4. to a normalized natural emittance of enat. .272) 35 In order for the ideal helical magnetic field to obey the Maxwell's equation. dt or -* By. the helical undulator does not produce a large tune shift in linear approximation. —. PHYSICS OF ELECTRON STORAGE RINGS Since the dispersion generated by an undulator is usually small. z) are unit vectors of the curvilinear coordinate system for the transverse radial.268) Aw Aw where (£. longitudinal.s + zsmky.17). T^l h = </>x + ipz+(l- ]-02)s (4.269): = ^-(xsmujy. we neglect all higher order terms in the following discussions.ZCOSLOJ) + put's. „ .t' . Note that the magnitude of the transverse velocity vector is /3j_ = -R"W/T with P* = ^ + ^ = 1-1. . (4.ws — x sin rews). J. = By.269) where the wiggler parameter Ky.271) c ww7 where t' is the reference frame of the moving electrons. «!_!+*£. as -ymc P = —-(xcosky. fl. {x cos dp eBy. at the expense of rms momentum spread. the emittance can be reduced by wigglers located in zero dispersion regions. .262). and transverse vertical directions. Example 3: Ideal helical undulators or wigglers We next consider a helical wiggler with magnetic field35 — • 2TT S 2TT S hisin——). Installation of damping wigglers in PEP had once been proposed to reduce the emittance by a factor of 10. is defined in Eq. The displacement vector of the electron in the wiggler is obtained by integrating Eq. Let the observer be located at one end of the wiggler.270) Unlike the planer undulator. For linear betatron motion. fC (4.
irw Thus wL corresponds to the characteristic frequency of the device in the observer's frame. The integrand of the radiation integral in Eq. with (j>2 4.17: Coherent addition of radiation from electrons in wigglers or undulators. (4. i.273) can be transformed to I + Kl + W ^ t . EMITTANCE IN ELECTRON STORAGE RINGS 483 Figure 4. (4.e.273) Let £ = wwt'. i. t t =t h-f(t') i + Kl + —^ = ^ c 2Y 12e\. (4. ^ w smw w i H cos uwt. ww7 ww7 (4. where these angles are of the order of -. The actual frequency should be obtained by solving Eq. (4. Eq. Longitudinal coherence gives rise to resonance condition of single frequency of diffraction like structure. When 4> and ip are not zero. The radiation integral of Eq.277) 6 = "' ( s ^ ) V 2 fl ([^ . (4. we expect to have higher harmonic in the spectrum.e.III. (4.I + Kl + W^+I + Kl + W"**- (4274) It is apparent to see that the periodic motion of the electron in the wiggler are transformed to the observer at a frequency boosted by the factor shown in Eq.ip2 = 92.276) for t' as a function of t. *>>• = I + K ( 27^w + 1 ^ - ( 4 .13) of the classical radiation formula is given by — K K n x (n x ft) = x[(j) cos wwt'] + z[<t> sin w w i']. The observer's time t is related to the electron's time t' via the retarded condition.274).3.1 C 0 S ^ + [4>~ Tsin^)e"^- .274) as wLt = £ — puiL sin f + quih cos ^.275 > We can rewrite Eq. Let us use the notation wL for the laser frequency.47) becomes (4. 1 <j>K» . with 27y.
Aw and Kw.282) Due to the coherent interference nature.J j w 5 q i (as)'"*•*""•*>Lk*-Tcosfl* +[(f> -sinf]£J x e x p j .L((?) = no.278) where JVW is the number of the wiggler period. \ L = £L(I + KI) (4.. PHYSICS OF ELECTRON STORAGE RINGS Now considering the periodic structure of the wiggler. we obtain s . Since a wiggler magnet may have a .279) and the spectral coherent factor S(u)/u>h) is sharply peaked at integer harmonics of 5(W/Wj Wn .e.« »£. the spectra are similar to those of synchrotron radiation from dipoles. the frequency spectrum is discrete.p s i n £ +gcos£) 1 df. (4'280) = na.[iV w sin^J ~ == [ ^ W ( W . or AiW- ^ p ^ • (4-281) Thus the photon energy can be adjusted by tunning the electron energy. The spectral distribution of the diffraction pattern has a full width half maximum at the n-th harmonic: ^ « -4. B.484 CHAPTER 4. The frequency spectrum will also be broadened by the momentum spread of the electron beam. Synchrotron radiation has a continuous spectrum up to the critical frequency wC]W = 373c/2pw.1(1+ ^)A w [cm] ei-M0)-(1 + ia)Aw[cm]. (4. Summary on characteristics of radiation from undulators and wigglers If the wiggler parameter is large.^ ) K j ' * . Kw > 1. the apparent angular frequency wL(0) at the forward direction is CJL(0)=LUL(9 = 0) = Y^CUW. i. The maximum power is proportional to N%. L (0) ( l + ^ ^ J The corresponding photon energy at the fundamental frequency is _0 1 95^[GeVL .j — ( £ . or the wiggler parameters. The photon flux is proportional to the number of electron due to incoherent nature. 13. (4.
.III. Figure 4.3 ^ 2 . during the time that the electron travels one undulator period. [A]. The emittance of the photon beam is equal to A/4TT. The angular aperture and the source radius of the radiation are (6 2 ) 1 / 2 = ^JX/NWXW and y/XN^X^/A-K.18: Schematic drawing of the sinusoidal orbit of an electron in a planar undulator and the electromagnetic wave (vertical bars).. Figure 4. the synchrotron radiation spectrum generated in a wiggler is shifted upward in frequency. The pulse length of a photon from a short electron bunch is A i = iVwAw_A^cos0%A^Ai /3|. The fractional bandwidth is then Au/uji = l/(2iVw). J = w = ' ^ (n = 1.18 shows schematically the sinusoidal electron orbit and electromagnetic radiation (vertical bars).B [ T ] ^ [m\ 18. .6 B [ T ) £2 [GeV] r .2. If Kw < 1. Such a wiggler is also called a wavelength shifter. where the electron (circle) lags behind the electromagnetic wave by one wave length in traversing one undulator period for n = l.e. (4-283) where 0 is the observation angle with respect to the undulator plane. The resonance condition for constructive interference is achieved when the path length difference between the photon and electron. EMITTANCE IN ELECTRON STORAGE RINGS 485 stronger magnetic field..c c c } Thus the frequency bandwidth is *»-s=]Sr=5b (4-285) where Ai is the wavelength of the fundamental radiation. is an integer multiple of the electromagnetic wavelength.1 Aw [cm] nE2 [GeV] ( 2 w 7 _2 2 . Optical resonance cavities have been used to enhance the radiation 3 6 The critical wavelength from a regular dipole is _ i-Kmc _ 0. _ Ac. the radiation from each undulator period can coherently add up to give rise to a series of spectral lines given by36 " l+i^+72e2 2^f 13.dipole . i. The resonance condition is achieved when the electron travels one undulator period. Aw//?|| .).A w c o s 0 = n\n. it lags behind the electromagnetic wave by one full wave length for the n = 1 mode.007135 f .
1708 in Ref. minimizing the natural emittance in an accelerator lattice and minimizing the vertical emittance by correcting the linear coupling will provide higher beam brightness. See. beam lifetime. III. Torre. efforts are being made in many laboratories to demonstrate the self-amplified spontaneous emission (SASE) principle. and to achieve single pass X-ray FELs such as the Linac Coherent Light Source (LCLS) at SLAC and DESY. emittance preservation in linacs. This is a subject of active research in thefieldof accelerator physics and technology.486 CHAPTER 4. If we neglect the effects of the residual vertical dispersion function. p.Thus.H. the vertical emittance is determined mainly by the residual vertical dispersion and the linear betatron coupling. G. and S. The beam brightness is proportional to NB/CXCZ.E. etc. longitudinal bunch compression. beam brightness limitation. CERN 89-03 (1989). where NB is number of electrons per bunch. The natural emittance of an electron storage ring obeys the scaling law £nat = TCql26\ where 9 is the total bending angle of dipoles in a half-cell.l. CERN 90-03 p. Giannessi. R. to produce an infrared FEL. l 2&?] I l/(4Vl5Jx) | 2/3'/{3LJx) [ (5 + 3 cos $)/[2(l . 254 (1990). Deacon et al. Pantell. Dopanfilis. the vertical emittance is arrived from the linear betatron coupling with ex + ez = enat.. 38. this field has been very active. and C l/(12\/l5X) T = (4.A. Madey's group [D. TBA or nBA . with many regular workshops and conferences. Since then. e. [12]. III. Low emittance lattices and the dynamical aperture In Sec. which can be attained by high quality linacs with high brightness rf-gun electron sources or by high brightness storage rings. G. Rev. and precise undulators. L. PHYSICS OF ELECTRON STORAGE RINGS called the free electron laser (FEL). beam intensity limitation. A.cos $) sin $ Jx] for ME triplet DBA for FODO cell lattice.g. Some of these issues are the emittance. dynamical aperture. At the same time. Dattoli. Torre.286) for ME lattice for MEDBA. we discuss only the physics issues relevant to high brightness electron storage rings.. A. ' ' 3 7 The free electron laser was realized in 1977 by J. Lett. Dattoli and A. 892 (1977)]. . Here. Phys.37 With the progress in small emittance beam sources from photocathode rf guns.3 Beam Physics of High Brightness Storage Rings High brilliance photon beams are generally produced by the synchrotron radiation of high brightness electron beams. we have studied methods of attaining a small natural emittance.
ground motion. the high brightness lights emitted from undulators in many synchrotron light sources can reach the diffraction limit. where k = 2TT/A is the wave number in the longitudinal direction. Thus DBA. L is the length of the dipole. To maximize beam brightness for synchrotron radiation with insertion devices. Figure 4. Thus we find axax> = crx{akx/k) > l/{2k) = A/(4TT). where ax and <Jkx are the rms beam width and the rms value of the conjugate wave number. the electron beam emittance that reaches the diffraction limit is ediff > ~(4.. The equality is satisfied for a Gaussian wave packet.^ .288) where the subscript r stands for radiation.19 shows the required bending angle per half period as a function of beam energy and the corresponding critical wavelength.. and other error sources. With emittance given by Eq. the required emittance is about tag « 10~ n m. lattices with zero dispersion-function straight sections are favorable. (4. Since a strong focusing machine is much more sensitive to the dipole and quadrupole errors. Note that the dipole angles of all existing synchrotron light sources are above the diffraction limit (solid line). High energy linacs may be the only way to reach such a small emittance. the diffraction limit condition is TC 7203 .289) 4TT For hard X-ray at energies 10 keV. and $ is the phase advance of a FODO cell. The correction of large chromaticities in these lattices requires strong chromaticity sextupoles. . This means that the synchrotron radiation at the critical frequency emitted from these light sources can not reach the diffraction limit However.287). or nBA lattices are often used in the design of synchrotron radiation sources (see Sec. B. The circle symbols are bending angles per dipole for existing synchrotron light sources.— (4 290) ql ~373 ~ 3 B 7 2 ' [ ' where the critical wavelength of synchrotron radiation is used.III. EMITTANCE IN ELECTRON STORAGE RINGS 487 Here ft* is the betatron amplitude function at the symmetry point of the dispersion free straight section. Diffraction limit Since the phase space area of a photon beam with wavelength A is38 Ax r A4 = AzrAz'r = ara'T > A/4TT = ephoton. the lifetime and brightness of the beam can be considerably reduced by power supply ripple. TBA. Low emittance lattices require strong focusing optics. Dynamical aperture can be limited by strong nonlinear resonances and systematic chromatic stopbands. which is difficult to attain in electron storage rings. Multiple-families of sextupoles are needed to correct geometric and chromatic aberrations. III. 3 8 The conjugate phase space coordinates of a wave packet obey the uncertainty relation axokx > i .l). (4.
many high brightness storage rings employ positrons with full energy injection. and it is usually alleviated by increasing the beam energy. The beam gas scattering processes include elastic and inelastic scattering with electrons and nuclei of the gases. The quantum lifetime can be controlled by the rf cavity voltage. the corresponding bunch length will be decreased and the peak beam current may be limited by collective beam instabilities. which results in emittance dilution. The beam emittances in low energy storage rings are usually determined by the intrabeam scattering.8). Beam lifetime Since high energy photons can desorb gases in a vacuum chamber. The Touschek scattering discussed in Sec. p. E. C. and B = 1 T.19: The solid line shows the required bending angle vs energy for a synchrotron light source. II. n = 3. This is particularly important for high-charge density lowenergy beams (< 1 GeV). Two high energy machines with small bending angles are PEP and PETRA.22 x 1022P [torr] m~3 is the density of the gas. Circles show the bending angle of each dipole for existing synchrotron light sources. ion trapping. The Touschek lifetime depends on a high power of 7.39 bremsstrahlung. etc. and /3c is the speed of the particle. ionization.488 CHAPTER 4. An effect associated with beam gas scattering is the multiple small angle Coulomb scattering. vacuum pressure is particularly important to beam lifetime in synchrotron radiation sources (see Exercise 4. 39See e. with parameters T = l/A\/TE.1. The beam-gas scattering lifetime is T = ~ ^ ? =a ? n g WC' ('9) 42 1 where <7tot is the total cross-section.. Because of these problems. Another solution is to increase the rf voltage. If the longitudinal momentum of the scattered particle is outside the rf bucket. where the emittance of the electron beam is equal to the emittance of the photon beam at the critical wavelength. Weihreter. CERN 90-03.8 arises from the Coulomb scattering that transfers transverse horizontal momentum into longitudinal momentum. However. The dashed line shows the corresponding critical wavelength. Jx = 1.g. PHYSICS OF ELECTRON STORAGE RINGS Figure 4. 427 (1990) for analysis on the vacuum requirement for compact synchrotron radiation sources. the particle will be lost. The small angle multiple Coulomb scattering between beam particles within a bunch is called the intrabeam scattering. .
(b) Show that the dispersion invariant at the center of the dipole is U= sin 3 (*/2)L(*/2) (1 " I Sln2 f + h Sln4 f >" . Those issues have been discussed in Chapters 2 and 3. de-Qing HOMs of rf cavities. (a) Using thin lens approximation. VII. Dividing the dipole into two pieces. we can express the dispersion function transfer matrix of the half dipole by (I MkB=[0 VO \L 1 0 L9/S\ 9/2 .EXERCISE 4. In storage ring. The turbulent bunch lengthening or microwave instability leads to increase in bunch length and momentum spread (see Sec. enlarging the tune spread with Landau cavities. These operational issues should be addressed in the operation of a storage ring facility.3 489 D. 3). Collective beam instabilities Collective instabilities are important to high intensity electron beams. 1 / where L and 9 are the length and the bending angle of the dipole in the half cell. lifetime degradation. ground motion. Chap. The broadband impedance can be reduced by minimizing the discontinuities in the vacuum chamber. there are high-Q components such as the rf cavities. show that the dispersion function at the center of the dipole is £0(1 . etc.3 1.1 sin2 f ) ' sin 2 ($/2) 9__ sin($/2)' where $ is the phase advance per cell and L is the half cell length. fluctuation. The results are emittances dilution. stability of the beam orbit is also an important issue. etc. The transverse microwave instability has usually a larger threshold provided that the chromaticities are properly corrected. un-shielded beam position monitors. Exercise 4. The single beam instabilities are usually driven by broadband impedance. Power supply ripple. Methods to combat these collective instabilities are minimizing the impedance by careful design of vacuum chamber. and active feedback systems to damp the collective motion [3]. Besides collective beam instabilities. mechanical vibration. and/or human activities can perturb the beam. These accelerator components can lead to coupled bunch oscillations. intensity limitation.4.
(4. Plot T vs the phase advance of the FODO cell.3 n ~™%6) fa .4. the dispersion transfer matrix is cos <p / M = I — (l/p)sin(f \ 0 p sin (p p (1 — cos tp) \ cosy s'm(p I 0 1 / where p is the bending radius. 2/3 ~ ) sin2(9. PHYSICS OF ELECTRON STORAGE RINGS (c) Applying Simpson's rule. show that the average of the %-function in the dipole is (H) = Ho + 2(a0DQ + poD'o)(1 p. 2. In a zero gradient dipole.g. e. (a) Using the relation .2( 7 0 A. show that the average of H-function is ' [ sin 3 ($/2) cos($/2) j ' X P The number in brackets is the T factor of Eq. . and <p = s/p is the beam bending angle along the dipole. + a o ^ ) p ( l sin2i9. where £ is the length of the dipole.211). Express the {H) in Eq.11. cos26^ 2sini9 where 9 is the bending angle of dipoles in a half cell and p is the bending radius. 6 < 60°. For a double-bend achromat (DBA).221). show that average H in a dipole is <«>-*•(!-?•£). Using Exercise 2. (4. using the small bending angle approximation.490 CHAPTER 4.0070 = 1 + ajji show that the minimum of {H) is WMEDBA = ^7J^ 3 with /— 6 8VT5 (b) Show that the minimum (H) occurs at s* = | l with B* 3 P 4%/60 (c) Show that the horizontal betatron phase advance across the dipole for a MEDBA lattice is (tan" 1 VT5 + tan" 1 5\/l5/3). 3. where the numerator depends slightly on the dipole configuration.
show that the dispersion and the betatron amplitude functions inside the dipole are where s = 0 corresponds to the entrance edge of the dipole. i is the length of the dipole magnet. Verify the following properties of a minimum emittance (ME) lattice. 5. and /?* = £/V60. in small angle approximation. Extend your result to find a formula for the condition necessary for a matched MEnBA without using small angle approximation. This configuration appears in the SOR Ring in Tokyo and the ACO Ring in Orsay. (c) Evaluate (aD + /3D')/y/]3^ and D/i/fi^ at the exit point of the dipole magnet for the ME condition and show that Use the result to show that the phase advance of the matching section is 2tan" 1 (9/\/l5). 6. A variant of the double bend achromat is to replace the focusing quadrupole by a triplet. (a) When (%) is minimized. A minimum emittance n-bend achromat (MEnBA) module is composed of n — 2 ME modules inside a MEDBA module. The configuration of the basic cell is40 40Because there is no quadrupole in the straight section. Show that the necessary condition for matching ME modules to the MEDBA module in small angle approximation is ^ ME = 3 P - MEDBA Thus an isomagnetic nBA can achieve optical matching for the minimum emittance only if the middle dipole is longer than the outer dipole by a factor of 3 1 / 3 . such a configuration has the advantage of a very compact storage ring for synchrotron light with dispersion free insertions.3 491 (d) Evaluate (aD + fiD')/y/fi^ and D/yffix at the exit points of the dipole magnet for the MEDBA condition and show that Use the result to show that the phase advance of the dispersion function matching section of the MEDBA is 2tan" 1 (7/\/l5)4.EXERCISE 4. where combined function dipoles are used. (b) Show that the horizontal betatron phase advance in the dipole is 2tan~x vT5. Find the minimum emittance. .
(b) Show that the betatron phase advance of the dispersion matching section for a minimum emittance triplet DBA is i/> = 2 arctan / At 2 + 9 f . jo. Plot the betatron phase advance of the matching section and 3* 11 as a function of £. The method is applicable to a sector dipole or a rectangular dipole.492 • CHAPTER 4. and I. ('H)min = pO ~~op~i where 2Li is the length of the zero dispersion straight section.240) should be used./3o. and £ is the length of the dipole. (c) What happens to (H) and the natural emittance if the dipole is replaced by a combined function magnet? (d) Study the linear stability of the triplet DBA lattice. the emittance will be altered by insertion devices that alter the betatron amplitude function. and D'o into Eq.221). B • Here 2L\ is the length of the zero dispersion straight section. 13 \ Ue + u+iJ . the betatron amplitude function inside the dipole is P-P + p where s = 0 corresponds to the entrance of the dipole. is the length of the dipole. 41The formula can be obtained by substituting ao. PHYSICS OF ELECTRON STORAGE RINGS • \ \ Triplet DBA • • n B QF u QD n QF • . (a) In small angle approximation. Eq.Do. (4. show that the average of the 7i function in the dipole is 41 <«>^'[!+Mti+T^)]. Show that the minimum emittance of the triplet DBA is 20* where I VP U 20' Since the emittance is proportional to the betatron amplitude function at the insertion region. (4. Since the mid-point of the straight section is the symmetry point for the lattice function. For a combined function dipole. where £ = L\jl. .
q = \fKL is the defocussing strength of the dipole. where 9 = L/p is the bending angle of the dipole. where A = 4A . and Dg and D'g are respectively the values of the dispersion function and its derivative at s = 0. with (H) = ±p930oA-aoB + ^C).^ 5 _ sinh^(cosh^. A) = Po/L. First.3 7.Do co s n 0.EXERCISE 4. . d'Oimin = --E{q).I) 2 . Aw .. and _ 2(coshg-l) _ 6(sinhg-g) _ 3sinh2g-6g ^3 .min = -F{q). and ao.— ^ 3 .40 sinh q + 5 sinh 2q B(q) = _ .1) + . 70 = 7o£.2EF. C(q) = -5 .8 cosh g + 2 cosh 2<j 3Qq . ^w -2 ' Fw . pvK where K = -Bi/Bp— 1/p2 is the defocussing strength with B\ = dBz/dx. L is the length of the dipole. B = 3B . 6 .1). and 70 are the Courant-Snyder parameters at s = 0. d'Q = D'Q/0. the normalized betatron amplitude functions are So = «o. (b) The minimization procedure can be achieved through the following steps. pK vK 493 7=)sinh</i + . <f> = \fKs is the betatron phase. . C=\C\F2.3E2./3o. (H) can be minimized byfindingthe optimal dispersion functions with d(H) dd0 Ul d{U) _ dd'o U' Show that the solution is do. s = 0 corresponds to the entrance of the dipole. The dispersion function in the combined function dipole is 0 D = ^— (cosh < .~(jodo + aod'o)F(q) 4A(9)-^)+^)]. where HQ = 7oi?o + 2otoDoD'0 + PQD'Q.Do cosh <j> + ~^D'O sinh<j>. The evolution of the 'H-function in a dipole is D' = {DQVK-\ 2 2 %{<t>) = •Ho + —7={aoDa+/3oD'0)sinh4>-—(y0D0 + a0D'0){cosh<l>-l) pVK pK+ ^ s i n h 2 ^ + A ( c 0 S h ^ . (a) Averaging the 'H-function in the dipole. show that (H) = Ho + p93 [(5orfo + M)E(q) . do = DQ/L9.
= -G-' \/l5S ^ = —G— . (d) Show that the value of the dispersion "H-function at both ends of the dipole for the ME condition is W(0) = U{q) = ^=^p03{6CE2 .1 . (a) Using the parameters of PEP with Jx = 1. If the phase advance is tuned to 98° per FODO cell.0159 m. What happens if similar undulators fill 30 straight sections? . (f) Discuss the effect of damping partition number for the combined function ME lattice. To decrease the emittance further.6 x 10"6iVw + 2.9 2 J . The PEP is a high energy e+e~ collider at SLAC with circumference C = 2200 m and bending radius p = 165 m. Using the parameter listed in Table 4.4 for the APS.1 and the undulator parameters listed in Table 4. wigglers installed at zero dispersion locations. (b) Using a typical set of the wiggler parameters: ~B^ (T) I Aw (cm) I K I 6 W (mr) I p w (m) L26 I 12 I 14.15B2 with s A=VTf6' 8(5 Q° . 2 ^ 1 Plot G vs q. show that the minimum (H) is where G = Vl6AC . (e) Show that the damping partition number Jx for horizontal motion is Jx = l . where (/3X) « 16 m.ac+ -2 (coshq . can be used to decrease the damping time with a minimum increase in quantum diffusion integrals.12 I 1.20 | 25 show that the emittance is ex ' w ~ £a:0 l 1 + 1.^BEF + ^AF2}. PHYSICS OF ELECTRON STORAGE RINGS (c) Using the relation /3o7o = 1 + <*o. the natural emittance of the electron beam is e nat = 5.1 nm at 6 GeV.494 CHAPTER 4. where (H)o is the average of the ^-function for the storage ring without wigglers. show that ('H)o = 0.. How many wiggler periods are needed to reduce the emittance by a factor of 10? What is the total length of the wigglers? What will be the momentum spread of the beam? 9. 8.5xl0-3iVw' where JVW is the number of wiggler periods. estimate the effect of an undulator in the zero dispersion straight section (/3X « 10 m) on the emittance and momentum spread of the beam.
639333739. 2TTS „ / 27rs\l D =— a.#S/E TWISS STOP (a) In thin lens approximation.S3.80 Q3: QUAD.L6. ANGLE=PI/40. E2=PI/80.78365 L8: DRIFT. 7 = 800.35 L9: DRIFT.22365 L6: DRIFT.0 cm. Study the attached lattice d a t a file for the APS and answer the questions below.S4.5. L=0.06. L=.Q3. Aw = 8. 2TT7 L Aw V Aw J\ Find the ratio of the transverse beam sizes arising from the dispersion function and betatron motion. TITLE.L8.L1.L7.S1 . L=. L=0. s i n \-z [1 .-HSECTOR) USE.Q2. L=.1400.1. "APS STORAGE RING LATTICE '96 VERSION" L0: DRIFT. L=. SUPER=40 PRINT.Q5. L=. .22365 L6: DRIFT.83365 L5: DRIFT. El=PI/80.L3.— ..66 L2: DRIFT.1194. K2= 15.L9) SECTOR: LINE=(HSECTOR.50 Q2: QUAD. Show that the dispersion function generated by a helical wiggler in a dispersion-free straight section is „ #wAw L . L=. L=.60 SI: SEXTUPOLE. L=3.3 495 10.17365 L3: DRIFT. Kl=-. L=0. as = 0. and eN = 2ir mm-mrad. L=.1 %. L=. L=0. Ql: QUAD.2527 S4: SEXTUPOLE. HARM0N=1296 HSECTOR: LINE=(LO. SECTOR. L=0.& S2.17365 M: SBEND.Q4.80954550.780136057. where we assume Kv = 5.M.2527 S3: SEXTUPOLE. L=O.36 LI: DRIFT. K2=-16. L=0.. Px — Pz = 10 m.22365 L7: DRIFT. what are the quadrupole strengths of Q4 and Q5 for the achromat condition? Do the data in the MAD input file agree with your thin-lens approximation calculation? (b) What is the purpose of sextupoles pairs (SI and S2) and (S3 and S4)? (c) What is the absolute minimum emittance of this lattice at 7 GeV? Compare your result with the emittance listed in Table 4.2527 S2: SEXTUPOLE. L=.c o s . Kl= .EXERCISE 4.5150.50 Q5: QUAD. L=0. L=3. Kl=-.5O Q4: QUAD.L2. 11.L5. V0LT=9. Kl= .4700.17365 L4: DRIFT.2527 RF: RFCAVITY. L=0.Q1. Kl=-.L4. K2= 5. K2=-11.45435995.41158941.
.
Lett. (4. and collective beam instabilities. 497 . In Chapter 4.M. where a collective instability induces microbunching in electron beam for coherent laser action in a long undulator. laser-particle interaction. The stimulated radiation can generate high power coherent radiation from infrared to Xray. Phys. we discussed incoherent spontaneous synchrotron radiation of each individual electron in dipole or wiggler fields. Rev.W. 36 (1976) 717.1 The idea has been extended to vacuum ultra-violet (VUV) and X-ray production by a process called Self-Amplified Spontaneous Emission (SASE). The radiation is incoherent. Robinson and P. 13. the radiated electromagnetic wave plays no role on the motion of electrons. 42 (1971) 1906. there is no correlation between electromagneticwaves radiated by any two electrons. Elias et al.e. 2J. beam cooling. 914 in Ref. [10]. R. Sprangle. The spectral coherence of synchrotron radiation in undulators (see Eq. the effects of space-charge force.J.280)) is attained through the electromagnetic-wave interference radiated by a single electron. I would like to provide introduction to the following two topics: free electron laser and beam beam interaction. The power or intensity of the radiation is proportional to the number of electrons in a bunch. Beside the quantum fluctuation and energy dissipation. p. The first section in this chapter addresses physics of beam-laser interaction and the free electron laser. advanced nonlinear beam dynamics. radiation damping and quantum fluctuation in electron storage rings. The efficiency of these radiation is only a few percent. a Review of FELs. Appl. see also C. 12. Phys. There are many textbooks and workshop proceedings on these advanced topics [10. and synchrotron radiation. However. 11. For high power operation.L. Madey J. i. impedance and collective beam instabilities. nonlinear beam dynamics. Nevertheless.. 14]. beam-beam interaction. linac.Chapter 5 Special Topics in Beam Physics In preceding chapters. it is necessary to induce laser oscillation in a laser cavity consisting of undulator and mirrors. we have focused on particle dynamics of betatron and synchrotron motions. this introductory textbook does not address advanced topics including free-electron laser.
The radiation is generated by coherent transition from population-inverted states to a low-lying state of a lasing medium made of atomic or molecular systems. For a complete updated list.1.ucsb. The force is highly non-linear. in SLAC-R-521 Chapter 4.08.2 Figure 5. Its wavelengths are tunable from millimeter to visible and potentially ultraviolet to x-ray. Herefco= 2TT/A. and is a slowly varying function of * and s. coherent. the beam-beam interaction becomes an important topic in accelerator physics because it plays a major role in limiting the luminosities of all high energy colliders. high power radiation. UQ = 2TTC/X.html.edu/www/vLfel. Since 1960's. <j>o is an arbitrary initial phase of the EM wave. When two beams collide. see the World Wide Web Virtual Library of the Free Electron Laser at http://sbfel3.268)3 is E = Eo\xsm(koS — tx>ot + <f>a) + zeos(fcos — u>ot + 4>o)}.1 summarizes the existing laboratories with free electron laser research facilities. I Free Electron Laser (FEL) Lasers are coherent and high power light (radiation) sources. the limit of beam-beam interaction in colliders is found to be about 0. For simplicity.1. The circularly polarized plane electromagnetic (EM) wave. In the presence of the electromagnetic fields. we limit our discussion to ID FEL-theory. Since the advance of the collider concept. 3For 2See . (4. The space charge force between two countertraveling bunches produces large impulse on each other. Its optical properties possess characteristic of conventional lasers: high spatial coherence and near the diffraction limit. see Exercise 5. FEL Physics. accelerator scientists devote great efforts in developing colliders. and t is the time coordinate. SPECIAL TOPICS IN BEAM PHYSICS The center of mass energy available in fixed target experiments is limited by the kinematic transformation. and induces noises in the detector area. degrades beam lifetime and beam stability.1) propagating along the wiggler axis s. When the beam-beam potential is coupled with the betatron and synchrotron motion in particle accelerators. A free electron laser employs relativistic electron-beams in undulators to generate tunable.02 to 0. where the amplitude Eo is independent of the transverse coordinates. the equation of motion for e. s is the longitudinal distance.498 CHAPTER 5. produced by the relativistic electron-beam in a helical wiggler magnetic field Bw of Eq.g. it perturbs the beam distribution. (2001) and reference there in. physicists and engineers have discovered many techniques to minimize the effects of beam-beam interaction. where two counter-traveling beams are made to collide at the interaction points. Methods of finding a larger tolerable beam-beam interaction is needed to enhance luminosities in high energy colliders. radiation from planar undulator. Depending on the beam-damping time. B = -s x E (5.
I FREE ELECTRON LASER (FEL) 499 Figure 5.2 2 * oi"6 ^Gev»2 **w«' is satisfied. + Nation- (5. Since the space charge force (see Exercise 2. 5-sm^.3 (K + ko)s .269). the importance effect of the EM fields is that it can cause the electron beam to microbunch itself for producing possible coherent radiation.2) is proportional to I/7 2 . where P 7 is the instantaneous radiation power in the wiggler and r0 is the electron classical-radius.c. Besides these operational facilities listed in the graph. or i =— = as where 4>= . dj eEa(3i_ . electron is ^=eE + ec0x{B + Bw) + FS. The effect of the electromagnetic waves E and B on the electron orbit is small.2) where fie is the speed of the electron. The wavelengths of these projects are of the order of 0.1: A compilation of the existing FEL laboratories with associated FEL wavelength. we neglect the radiation force. we obtain the energy-exchange between the electron and electromagnetic wave: mc 2 7 = — eE • j3c. The effect of radiation reaction force is also small.u>ot + (/>o- (5. it is negligible at the energy of our consideration. High gain Xray FEL projects. provided that the condition: ^ r = J t = s ^ = 4 .3. Using Eqs. there are about 10 FEL development centers in universities and National Laboratories. the electron orbital motion is essentially determined by the wiggler magnetic field.1) and (4. and Fradiation are respectively the space charge force and the radiation reaction force.C.e. jmc1 5. However. The energy exchange is maximum when the stationary . (5. i. are not listed on this graph. — sin0 = mcz eEoKv.1 nm. Hereafter.4) The wiggler field provides electron trajectory while the EM-fields interact with electrons for energy exchange. such as the LCLS and XFEL to be completed around 2007. Fs.
500 CHAPTER 5. and thus the resonance condition should be replaced by the rms undulator parameter KWiTms = K^j\pi. <j>) are conjugate phase-space coordinates and the longitudinal coordinate s is the independent variable. uj0At = wo( j^~^f) = 2TT.3) and (5.e. (4. The corresponding Hamiltonian is . the longitudinal velocity vector is given by Eq.1.263). or for resonance photon wavelength at a given beam energy 7. See also Exercise 5.4 The resonance condition can also be expressed as .I Small Signal Regime In a small radiation loss regime.270) is used. the electron energy is near the resonance energy. = _eEoK^ f = 2U (5.11) 4For a planar undulator.18. (5.7) can be derived from the Hamiltonian tf = A:w(l + ^ ) 7 . graphically represented in Fig. 4.^ ^ c o s ^ (5-7) (5-8) where (7. (4. i. I. The equation of motion for the phase angle cj> becomes 4>' = M i . The energy exchange between the electron and the external electromagneticfieldscan be obtained by solving Hamiltonian's equation.4>) are conjugate phase-space coordinates and longitudinal distance s serves as the independent "time" coordinate.10) m& 7^ where (r\. When this resonance condition is satisfied.1. _ Aw(l + ^ ) _ l + Kl '^6d» + 4-s)]"4-*^H 7r2A ' °r K~K^f~- (55) (5-6) for resonance electron beam energy at a given photon wavelength A. electrons lag behind the EM wave by one wavelen
|
__label__pos
| 0.984294 |
Database Backend Redesign - Phase 3
Status
Date: 2020 Nov, 26th
Staus: Mostly Implemented
Tickets: https://issues.redhat.com/browse/IDMDS-302
Motivation
See backend redesign (initial phases)
High level summary
This document is the continuation of ludwig’s work about Berkeley database removal. backend redesign (initial phases)
It focus on:
Current state
Specific issues (solved in this phase)
VERY HIGH LEVEL API
dbimpl API is part of libback-ldbm and dbimpl API users needs to include dbimpl.h and link with libback-ldbm
When initializing the dblayer API (or when requesting a private access to a file), the value of nsslapd-backend-implement configuration parameter is used to call value_init function (within libback-ldbm) that fills a set of callbacks in li->priv.
API
Include file: dbimpl.h
struct typedef
Name Role Opaque Old bdb name
dbi_env_t The global environment PseudoOpaque(1) DB_ENV
dbi_db_t A database instance PseudoOpaque(1) DB
dbi_txn_t A transaction Yes(3) DB_TXN
dbi_cursor_t A cursor (i.e: iterator on DB data) PseudoOpaque(1) DBC
dbi_data_t A key or a value No DBT
dbi_cb_t Contains all DB implementation callbacks No N/A
(1) DB_ENV is used as opaque struct except dbenv->get_open_flags that is used in db_uses_feature that should be moved in bdb plugin anyway
(2) already used as an opaque struct
PseudoOpaque type are: Typedef struct { DBI_CB *cb;The callbacks void *<name>;The implementation opaque struct (name is env,db or cursor) void *plg_ctx;A context that implementation plugin is free to use. (may be not needed) } PseudoOpaque
They are used because the code sometime use function that only have access to underlying element And not the upper layer context (i.e cursor without backend or li_instance)
typedef struct {
DBI\_CB *cb;
DBI\_MEM\_OPTION flags;
void *data;
size\_t size;
void *ctx; /* Context handled by db implementation plugin */
} DBI_DATA;
typedef struct {
struct DBI\_CB *cb;
void *cursor;
} DBI_CURSOR;
Enum values
DBI_OP /* Represents a cursor operation */
‘Name’ ‘Role’ ‘Old bdb function’ ‘Old bdb value’
DBI_OP_MOVE_TO_KEY Move cursor to first record having the key and get its value c_get DB_SET
DBI_OP_MOVE_NEAR_KEY Move cursor to record having smallest key greater or equal than the specified one. Then it gets the record c_get DB_SET_RANGE
DBI_OP_MOVE_TO_DATA Move cursor to key+value record c_get DB_GET_BOTH
DBI_OP_MOVE_NEAR_DATA Move cursor to record having specified key and smallest data greater or equal than the specified data and get the value c_get DB_GET_BOTH_RANGE
DBI_OP_MOVE_TO_RECNO Move record to specified record number then get it. c_get DB_SET_RECNO
DBI_OP_MOVE_TO_FIRST Move cursor to first record then get it. c_get DB_FIRST
DBI_OP_MOVE_TO_LAST Move cursor to last record then get it. c_get DB_LAST
DBI_OP_GET Get record from key. get DB_GET
DBI_OP_GET_RECNO Get current record number. c_get DB_GET_RECNO
DBI_OP_NEXT Move cursor to next record then get it. c_get DB_NEXT
DBI_OP_NEXT_DATA Move cursor to next record having the same key then get the value. c_get DB_NEXT_DUP
DBI_OP_NEXT_KEY Move cursor to next record having different key then get the record. c_get DB_NEXT_NODUP
DBI_OP_PREV Move cursor to previous record then get it. c_get DB_PREV
DBI_OP_PUT Insert new key-data put DB_PUT
DBI_OP_REPLACE Overwrite current position value c_put DB_CURRENT
DBI_OP_ADD Insert new key-data if it does not already exists put DB_NODUPDATA
DBI_OP_ADD Insert new key-data if it does not already exists c_put DB_NODUPDATA
DBI_OP_DEL Delete key-data record del 0
DBI_OP_DEL Delete record at cursor position c_del 0
DBI_OP_CLOSE Close cursor c_close N/A
dbi_val_t flags
Name Role Berkeley db flags
0 data should be alloc or realloc DB_DBT_MALLOC (if data is NULL) or DB_DBT_REALLOC
DBI_VF_PROTECTED data should not be freed
DBI_VF_DONTGROW data should not be realloced N/A
DBI_VF_DONTGROW+DBI_VF_PROTECTED data should not be realloced DB_DBT_USERMEM
DBI_VF_READONLY data should not be modified DB_DBT_READONLY
dbi_val_t flags to DBT flags mapping
‘dbi_val_t’ DBT
0 DB_DBT_MALLOC ( or DB_DBT_REALLOC
DBI_VF_PROTECTED data should not be freed
dbi_bulk_t flags
Name Role
DBI_VF_BULK_DATA Bulk operation on data only
DBI_VF_BULK_RECORD Bulk operation on key+data
error codes
Name Role Old bdb value
DBI_RC_SUCCESS No error 0
DBI_RC_NOMEM Memory allocation error
(usually it does not happen because slapi_ch_malloc cannot returns NULL)
DB_BUFFER_SMALL
DBI_RC_KEYEXIST Key exists and duplicate keys are not allowed. DB_KEYEXIST
DBI_RC_RETRY Transient error: operation should be retried. DB_LOCK_DEADLOCK
DBI_RC_NOTFOUND Record not found: Key does not exists. DB_NOTFOUND
DBI_RC_RUNRECOVERY Recovery must be performed. DB_RUNRECOVERY
DBI_RC_OTHER Other database errors N/A
Note: the implementation plugin should log an error with error code and error text when getting an error that cannot be mapped ( To ease diagnostic in case of unexpected error )
Callbacks
(TODO: get the callback name and prototype from dblayer.h and put them in this document to have the full API
Name Role Old bdb value
dblayer_start_fn_t *dblayer_start_fn
dblayer_close_fn_t *dblayer_close_fn
dblayer_instance_start_fn_t *dblayer_instance_start_fn
dblayer_backup_fn_t *dblayer_backup_fn
dblayer_verify_fn_t *dblayer_verify_fn
dblayer_db_size_fn_t *dblayer_db_size_fn
dblayer_ldif2db_fn_t *dblayer_ldif2db_fn
dblayer_db2ldif_fn_t *dblayer_db2ldif_fn
dblayer_db2index_fn_t *dblayer_db2index_fn
dblayer_cleanup_fn_t *dblayer_cleanup_fn
dblayer_upgradedn_fn_t *dblayer_upgradedn_fn
dblayer_upgradedb_fn_t *dblayer_upgradedb_fn
dblayer_restore_fn_t *dblayer_restore_fn
dblayer_txn_begin_fn_t *dblayer_txn_begin_fn
dblayer_txn_commit_fn_t *dblayer_txn_commit_fn
dblayer_txn_abort_fn_t *dblayer_txn_abort_fn
dblayer_get_info_fn_t *dblayer_get_info_fn
dblayer_set_info_fn_t *dblayer_set_info_fn
dblayer_back_ctrl_fn_t *dblayer_back_ctrl_fn
dblayer_get_db_fn_t *dblayer_get_db_fn
dblayer_delete_db_fn_t *dblayer_delete_db_fn
dblayer_rm_db_file_fn_t *dblayer_rm_db_file_fn
dblayer_import_fn_t *dblayer_import_fn
dblayer_load_dse_fn_t *dblayer_load_dse_fn
dblayer_config_get_fn_t *dblayer_config_get_fn
dblayer_config_set_fn_t *dblayer_config_set_fn
instance_config_set_fn_t *instance_config_set_fn
instance_config_entry_callback_fn_t *instance_add_config_fn
instance_config_entry_callback_fn_t *instance_postadd_config_fn
instance_config_entry_callback_fn_t *instance_del_config_fn
instance_config_entry_callback_fn_t *instance_postdel_config_fn
instance_cleanup_fn_t *instance_cleanup_fn
instance_create_fn_t *instance_create_fn
instance_create_fn_t *instance_register_monitor_fn
instance_search_callback_fn_t *instance_search_callback_fn
dblayer_auto_tune_fn_t *dblayer_auto_tune_fn
dblayer_cursor_op(DBI_CUR *cur, DBI_OP op, DBI_DATA *key, DBI_DATA *data) Move cursor and get record cursor->c_get
dblayer_cursor_op(DBI_CUR *cur, DBI_OP op, DBI_DATA *key, DBI_DATA *data) Add/replace a record cursor->c_put
dblayer_cursor_op(DBI_CUR *cur, DBI_OP op, DBI_DATA *key, DBI_DATA *data) Remove a record cursor->c_del
dblayer_cursor_op(DBI_CUR *cur, DBI_OP op, DBI_DATA *key, DBI_DATA *data) Close a record cursor->c_close
dblayer_new_cursor(be,db,txn, cursor) Should store the backend in cldb_Handle to retrieve it. db->cursor(db, db_txn, &cursor, 0);
dblayer_db_op(DBI_DB *db, DBI_OP op, DBI_DATA *key, DBI_DATA *data) Move cursor and get record db->get
dblayer_db_op(be, DBI_DB *db, DBI_OP op, DBI_DATA *key, DBI_DATA *data) Add/replace a record db->put
dblayer_db_op(be, DBI_DB *db, DBI_OP op, DBI_DATA *key, DBI_DATA *data) Delete a record db->del
dblayer_get_db_id db->fname
dblayer_init_bulk_op(DBI_DATA *bulk) Initialize iterator for bulk operation DB_MULTIPLE_INIT
dblayer_next_bulk_op(DBI_DATA *bulk, DBI_DATA *key, DBI_DATA *data) Get next operation from bulk operation DB_MULTIPLE_NEXT
db-bdb plugin
That is the plugin that implements the dbimpl API callbacks and calls libdb functions. The important points are:
Note: In both case isresponse is set to PR_FALSE before the operation and PR_TRUE after it. if a key or data get alloced/realloced, the original key/data get freed (if the value flags allows it)
Alternatives
Proposed solution
* Solution 1
* Remap the errors to generic values
* Add a function in bdb that remap the value (should be a simple switch) If the value cannot be mapped we could:
* add a string in thread local storage and return DBI\_RC\_OTHER The string should contains the original return code and its associated message (i.e: bdb error code: %d : %s", native\_rc, db\_strerror(native\_rc))
* Modify dblayer\_strerror to print a message for generic errors and if DBI\_RC\_OTHER to generate a message from the thread local data string.
* This solution has the advantage that:
* it does not impact the back-ldm/changelog code (except for dblayer\_strerror)
* It is quite efficient in the usual case as it handles a switch with few values
* Keep the ability to diagnose errors in the unexpected case
* The drawbacks:
* Message can be wrong if creative error handling is performed (i.e
rc1 = dblayer\_xxx(li, ...)
rc2 = dblayer\_xxx(li, ...)
log(dblayer\_strerror(rc1)) prints rc2 message if both values are are DBI\_RC\_OTHER)
Should double check that when hitting unexpected errors we just logs an error message and aborts the operation (as it is possible that we abort the txn before logging the errr)
* Error handling should be done in the same thread than the operation (This is IMHO the case)
* Solution 2 I thought about keeping the db code as it, but then it implies a lot of changes as we need to access the db plugin to determine what action to do or to log the error. (but the dblayer instance context is not always easily available when the message is logged)
* Solution 3 Same as solution 1 but without storing data in thread local storage: problem is that we got clueless in case of unexpected database error. (unless an error message is logged by the plugin (Note: that is finally the implemented solution))
Open Questions
These questions will need to be solved in phase 4.
Phasing
*The phase 3 is about being able to remove the bdb dependencies (i.e being able to build ns-slapd libbck-ldbm and replication without the bdb include and lib) Due to the size of these changes (FYI: Phase 3a already impacts 53 files), it seems better to split the phase in sub phases:
Last modified on 7 April 2021
|
__label__pos
| 0.941711 |
Disclosure: This article may contain affiliate links. When you purchase, we may earn a small commission.
Review - Is Full Stack Web Development with Angular Course on Coursera worth it?
Hello guys, if you are looking for the best Coursera course to learn Angular or want to know whether the Full Stack Web Development with Angular Specialization on Coursera is worth your time and money or not, then you have come to the right place. Earlier, I have shared the best web development courses from Coursera, and in this article, I will review the most popular Angular course - Full Stack Web Development with Angular Specialization. This is also one of the best Coursera specializations for Angular, and it contains 3 best courses to learn Bootstrap, Angular, and Node.js to become a complete full-stack developer using JavaScript.
Top 6 Courses to Learn TypeScript for Web Development in 2022 - Best of Lot
Hello guys, if you are thinking of learning TypeScript this year and looking for some excellent resources like books, courses, and tutorials, then you have come to the right place. In my last few articles, I have shared some of the best Angular framework tutorials and courses, and today, I will share some of the best TypeScript online courses you can join to learn it by yourself. Many programmers and web developers are learning TypeScript because of its powerful syntax and advanced OOP features and, more importantly, to develop Angular-based applications. Since the Angular team has chosen TypeScript as the official language for Angular development, it's crucial to know TypeScript if you want to make full use of Angular, but that's not the only reason you should learn TypeScript.
[Solved] How to Find maximum Product of a sub-array in Java? Example
In this article, we shall be finding the maximum product of a sub-array in java. This problem has a lot to do with arrays. But first, we'll solve the problem then we talk about Array and how it operates. The problem we are to solve here is to find the maximum product of a subarray in Java. we won't just jump to the writing of codes like code monkeys but, it is essential to understand the problem we are solving first, so we can give the best approach in solutions to it. when we say finding the maximum product of a sub-array it means getting the total of a product in an array!
Top 10 Educative.io Courses to Learn Essential Programming Skills in 2022 - Best of Lot
Hello guys, today, I am going to talk about a new online learning platform called Educative, a text-based, interactive learning platform. If you are an online learner like me, you might have heard about Educative or come across some of its excellent and most popular courses like Grokking the System Design Interviews course, which I have mentioned earlier in my article about System design Interviews questions. So, what is so special about Educative? How different is it from other popular online platforms like Udemy, Coursera, Pluralsight, and Codecademy? Well, Educative is different becuase it is mainly a text-based learning platform that allows you to code and program right in the browser.
Review - Is Grokking the System Design interview Course on Educative Worth it?
Hello guys, we are here again today for another exciting topic to discuss. But today, we will not discuss something related to Java or any other language or spring boot. Today, we will discuss something that is immensely practical and has the potential to land you very high-paying jobs. Today we are going to review a course that focuses on System Design! System Design is crucial for coding interviews! And it's also one of the most challenging topics to master. I have shared the best System design courses for coding interviews in the past. Today, I will review one of the top system design courses for technical discussions, Grokking the System Design Interview by Design Gurus Educative.io.
How to Rotate an Array to Left or Right in Java? Example - LeetCode Solution
Hello guys, rotating an array in Java is a common coding problems which are often used to teach beginners coding as well used during interviews to check candidate's programming and data structure skills. This problem may look easy but its not that easy, especially if you are not coding regular. In order to rotate an array of n elements to the right by kth index, you need to rearrange the item in such a way that the array will start from k + 1the element. For example, with n = 7 and k = 3, the array [1, 2, 3, 4 ,5, 6, 7] is rotated to [5, 6, 7, 1, 2, 3, 4]. See, it looks like you pick the the 4th element and rotated the array in right direction. The problem becomes even more interesting when interviewer ask you to rotate the array by left or right and in place. Could you do it in-place with O(1) extra space?
Is Grokking the Machine Learning Interview on Educative Worth it? Review
Hello friends, we are here again today for another exciting topic to discuss. But, today we are not gonna discuss something which is related to Java or any other language or spring boot. Today we are gonna discuss something which is immensely practical and has the potential to land you very high-paying data science jobs. Today we are gonna review a course that focuses on Machine Learning! Machine Learning is very important when we are considering data science interviews! So what's the wait? Let's start! On Educative.io, there is a great course called Grokking the Machine Learning Interview. It couldn't have come at a better moment, with machine learning expected to be a $3.6 billion business by 2024.
Top 15 Java Multithreading, Concurrency Interview Questions Answers asked in Investment banks
Multi-threading and concurrency questions are an essential part of any Java interview. If you are going for any Java interview on any Investment bank like Barclays, Citibank, Morgan Stanley, etc for the Cash Equities Front Office Java Developer position, you can expect a lot of multi-threading interview questions on your way. Multi-threading and concurrency are favorite topics on Investment banking interviews, especially on electronic trading development jobs and they grill candidate on many tricky java thread interview questions. They just want to ensure that the guy has a solid knowledge of multi-threading and concurrent programming in Java because most of them are in the business of performance which provides them a competitive advantage and it's hard to write correct and robust concurrent code.
Is Educative.io worth to Learn Tech Skills? Should You join Eductaive? Review
Hello guys, if you are thinking bout joining Educative to learn new tech skills in a guided, an interactive manner but not sure then you have come to the right place. In the past, I have shared best Educative courses for programmers and software developers as well their best free text based courses to learn programming, and also reviewed their best online courses like Grokking the System Design course, and OOP Design course and in this article, I will review the Educative.io for learning Tech skills and preparing for Coding Interviews using online courses in 2022.
5 Best Books To Learn Cyber Security in 2022
Hello guys, if you want to learn Cyber Security in 2022 and looking for best resources like best books and online courses then you have come to the right place. Earlier, I have shared best Cyber Security Courses, Tools, and Skills and today, I am going to share best Cyber Security books for both beginners and experienced IT professionals. You can read these books to learn important Cyber Security concepts and tools. Nowadays, cyber security is fun and increases awareness since the bad guys are attacking users' computers and other devices and other companies for stealing sensitive information and money. If you want to protect yourself from these attacks, I highly suggest taking one of these books t help you understand cyber security.
Top 15 Java NIO, Socket, and Networking Interview Questions Answers for Experienced Developers
Hello guys, if you are preparing for Java developer interview then you may know that Networking and Socket Programming is one of the important areas of Java programming language, especially for those programmers, who are working in client server-based applications. Knowledge of important protocols like TCP and UDP in detail is very important, especially if you are in the business of writing high-frequency trading applications, which communicate via FIX Protocol or native exchange protocol. In this article, we will some of the frequently asked questions on networking and socket programming, mostly based around TCP IP protocol.
5 Best Programming Languages To Start Your Career in Software Development and Best Courses To Learn Them
Hello guys, If you want to become a Programmer or Software developer in 2022, you should be an expert in not one, but multiple programming languages. It is an absolute necessity to be skilled and fluent in more than one programming language. But which programming languages should you master, you might be asking. Well, don't worry. We have got your back. Gone are the time when you can just learn one programming language like Python, Java, or JavaScript and done, nowadays every job demands more and there is always a couple of programming language you can find in job description.
Top 5 Cloud Computing Platforms Java Programmers Should Know
Cloud computing is Hot, it's the biggest IT trend of the last few years and will continue to grow strong in the coming future. Cloud computing provides several not-so-easy-to-ignore advantages, especially to public and small enterprises, which cannot afford to own and maintain expensive data centers. Since most online businesses nowadays need high availability, scalability, and resiliency, with-in a quick time, it's not possible to achieve all these on your own, and cloud computing becomes the best alternative here. Cloud service providers like Amazon Web Services (AWS) has helped several firms to remain focus on their business, without worrying for IT and infrastructure too much, this has yield big result for them.
How to Set Classpath for Java on Windows and Linux? Steps and Example
What is CLASSPATH in Java? Classpath in Java is the path to the directory or list of the directory which is used by ClassLoaders to find and load classes in the Java program. Classpath can be specified using CLASSPATH environment variable which is case insensitive, -cp or -classpath command-line option or Class-Path attribute in manifest.mf file inside the JAR file in Java. In this Java tutorial, we will learn What is Classpath in Java, how Java resolves classpath and how Classpath works in Java alongside How to set the classpath for Java in Windows and UNIX environment.
How to Transpose a Matrix in Java? Example Tutorial
Hello guys, if you are wondering how to transpose a matrix in Java then you have come to the right place. Matrix related coding problems are great way to learn multi-dimensional array and nested loop and they are good programming exercise for beginners. In the past, I have taught you how to multiply matrices in Java and how to add/subtract matrices in Java, and in this article, I will show you how to create transpose of a given matrix in Java, but before that let's first understand what is transpose of a matrix means and how do you transpose a matrix in maths? Well, a transpose of a matrix is nothing but a matrix whose rows and columns are reversed.
Top 20 Amazon and Google Programming Interview Questions for Software Developers
Hello, In this article I am going to sharing some frequently asked programming job interviews from technical giants and startups. If you are going for a programming job interview with Microsoft, Google, or Amazon, you better be prepared for all kinds of questions. These companies are known to ask tough questions, tricky puzzles, and lots of data structure and algorithm questions. Since it's hard to prepare all these in a short time, it makes sense to at least have a good idea of frequently asked programming questions in Microsoft, Google, or Amazon.
Top 25 DevOps Interview Questions and Answers for Experienced Developers
Hello guys, if you re preparing for DevOps Engineer interviews and looking for frequently asked DevOps Interview questions then you have come to the right place. Earlier, I have shared the DevOps RoadMapbest DevOps Courses, and DevOps books and in this article, I will share the frequently asked DevOps Interview Questions and their Answers. But, before we get to the most frequently asked DevOps interview questions, let me tell you what DevOps actually is. I know that most of you may already be familiar with it, but just bear with me for a minute, okay?
[Solved] How to find Largest Prime Factor of a Number in Java? Example
Hello guys, one of the common programming kata to learn coding is to write a program to find the largest prime factor of a number. Earlier, we have solved how to check if number is prime or not and in this article, we will calculate prime factors of a given number in Java. Like any other programming problem, you need to build the logic to solve this problem. Before solving the problem, let's revise the concept of number theory. Prime factors of a positive integer are the prime numbers that divide the number exactly i.e. without any remainder, and prime factorization is the process of finding all prime numbers when multiplied together to make the original number.
How to Swap Two Numbers Without Temp or Third Variable in Java - Interview Question Example
How to swap two numbers without using temp or third variable is a common interview question not just on Java interviews but also on C and C++ interviews. It is also a good programming question for freshers. This question was asked to me long back and didn't have any idea about how to approach this question without using temp or third variable, maybe lack of knowledge on bitwise operators in Java or maybe it didn't click at that time. Given some time and trial error, I eventually come out with a solution with just an arithmetic operator but the interviewer kept asking about other approaches of swapping two variables without using temp or third variable.
How to Print a left triangle star pattern in Java? Example Tutorial
Pattern based exercises are very common on Interviews as they are tricky for beginners and also offers coding practice. In the past, I have shared article on how to print pyramid pattern of stars in Java and Pyramid pattern of albhabets, and in this article, I will show you how to print left triangle star pattern in Java. There are different ways of printing different patterns, but most of them involves using loops and print methods like print() and println() to print characters like star, alphabets or numbers. If you know how to use loops and when to break from loop then you can easily solve pattern based coding problems. In this section, we shall be writing a program to print a left triangle star pattern. We would first implement that before I explain other things that you need to know in getting this task done.
Difference between Direct, Non Direct and Mapped ByteBuffer in Java?
ByteBuffer is one of the important classes of Java NIO API. It was introduced in java.nio package on JDK 1.4, it not only allows you to operate on heap byte arrays but also with direct memory, which resides outside the JVM. There are mainly three types of ByteBuffer in Java - Direct Byte Buffer, Non-Direct ByteBuffer, and mapped byte buffers. You can create both direct and non-direct buffers using java.nio.ByteBuffer class, while MappedByteBuffer is a subclass of ByteBuffer, which is created by FileChannel.map() method, to operate on memory-mapped file
How to Find Largest and Smallest of N numbers without using Array in Java? Example
One of the common programming questions is, how do you find the largest and smallest number in N numbers without using arrays in Java? Can you write a program to solve this problem? Well, it's very similar to the problem we have seen before, find the largest and smallest of 3 integers. You can use the same approach and generalize it for N numbers. All you need to do is start with largest as Integer.MIN_VALUE and smallest number as Integer.MAX_VALUE and loop through N numbers. At each iteration, compare the number with the largest and smallest number, if the current number is larger than the largest then it's a new largest, and if the current number is smaller than the smallest then it's a new smallest number.
How to Remove Duplicate Characters from String in Java? Example
This week's coding exercise is to remove duplicate characters from String in Java. For example, if the given String is "aaaaaa" then the output should be "a", because the rest of the "a" are duplicates. Similarly, if the input is "abcd" then the output should also be "abcd" because there is no duplicate character in this String. By the way, you can not use any third-party library or Java API method to solve this problem, you need to develop your own logic or algorithm and then write code to implement that algorithm. This is one of the interesting problems from Java coding interviews and you can use this program to weed out Java programmers who cannot write code.
Difference between ByteBuffer vs byte array in Java
There are several differences between a byte array and ByteBuffer class in Java, but the most important of them is that bytes from byte array always reside in Java heap space, but bytes in a ByteBuffer may potentially reside outside of the Java heap in case of direct byte buffer and memory mapped files. Buffer is a byte array like abstraction which was introduced in Java NIO release to read and write data from FileChannel. It is extensively used in Java NIO for transferring data from one place to another and its also an essential Java concepts to know for any backend developer, particularly those who wants to create non-blocking server application using NIO in Java
The 2022 Laravel Developer RoadMap
Hello folks, if you want to learn Laravel for Web Development but no idea from where to start it then you have come to the right place. Laravel is one of the top PHP Framework for web development and also quite popular one. In the past, I have shared best Laravel Courses and best PHP courses and in this article, I am going to share the full 2022 Laravel RoadMap. I love these roadmap and in the past have shared many of them which you can find at the end of these article. They are often the most comprehensive guide to learn a new technology.
How to Reverse a String in place in Java - Example
It's possible to reverse a String in place by using a StringBuilder. Since String is Immutable in Java, it's not possible to reverse the same String, but you can minimize the number of intermediate String objects by using StringBuilder or StringBuffer, which are mutable. The algorithm to reverse the String in place is similar to the algorithm we have used earlier to reverse an array in place. You need to traverse the String from one end, swapping characters at another end until you reach the middle of the String. At the point characters in your String are reversed. This algorithm only requires one extra character of memory to facilitate the swapping of characters. The time complexity of this algorithm is O(n/2)I mean O(n) where n is the length of String.
How to create an Array of Prime numbers in Java [ Sieve of Eratosthenes Algorithm Example]
Hello guys, I have said many times that a good knowledge of Data Structure and Algorithms is the first step towards becoming a better programmer and that's why I share a lot of Data structure and Algorithm stuff in this blog. To continue the tradition, I am going to share an interesting algorithm today, The Sieve of Eratosthenes algorithm, which can be used to generate prime numbers up to a given number. There are many occasions when you need to generate all prime numbers up to a specified integer and one algorithm which is most often used to generate prime numbers is the Sieve of Eratosthenes Algorithm. Surprisingly, not many developers know about this algorithm, particularly Java programmers, which is mainly because of not doing enough competitive programming.
Top 20 Kubernetes Interview Questions with Answers
Hello guys, if you are preparing for DevOps Engineer interview or a Developer interview, knowledge of Kubernetes is very important given the rise of Cloud computing and cloud native development. If you are looking for frequently asked Kubernetes interview questions to quickly revise key Kubernetes concepts then you have come to the right place. Earlier, I have shared 20 Docker Interview Questions and in this article, I am going to share frequently asked Kubernetes Interview questions with Answers. But, before we get to the 20 most important Kubernetes interview questions, let me tell you more about Kubernetes. In the most simple terms, Kubernetes is actually a bundle of software solutions that allow developers and engineers to scale and service server setups.
The 2022 Data Analyst Roadmap
Hello guys, if you are want to become a Data Analyst but not sure which skills you need and how to acquire those skills then you have come to the right place. Earlier, I have shared Java Developer RoadMap, Python Developer RoadMap, Web Developer RoadMapiOS Developer RoadMap, and DevOps Engineer RoadMap, and in this article, I will share Data Analyst RoadMap which will help you to become a Data Analyst in 2022. All companies have data about their customers to improve their service and get valuable insight and a much better understanding of the customer's behavior. This can be done by hiring data analysts in your company to leverage the benefits of this hug customers' data.
[Solved] Fibonacci Series in Java using Recursion and Iteration - Example Tutorial
Printing Fibonacci Series In Java or writing a program to generate Fibonacci number is one of the interesting coding problems, used to teach college kids recursion, an important concept where function calls itself. It is also used a lot as coding problems while interviewing graduate programmers, as it presents lots of interesting follow-up questions as well. In the Fibonacci series, the next number is equal to the sum of the previous two numbers. First two numbers of series are always 1 and 1, third number becomes 1 + 1 = 2, subsequently fourth number becomes 2 + 1 = 3. So a Fibonacci series looks like 1, 1, 2, 3, 5, 8, 11, 19, and so on, as shown in the image as well.
Top 20 Docker Container Interview Questions Answers for Programmers and DevOps
Hello guys, if you are preparing for Software developer job interviews like Java developer then preparing Docker is a good idea. Docker has become an essential tool and you can expect a couple of questions about Docker during Interview to check your knowledge. Having absolutely no idea of Docker before going into interview can be detrimental to your prospect considering the importance of container on deploying apps and services on Cloud. That's why I always suggest my students to prepare Docker interview questions and revise key Docker concepts before interview. If you are wondering where you can find Docker interview questions then don't worry, in this article, I have shared common Docker related questions you can prepare for interviews. They are also great to revise key Docker concepts and they cover essential areas.
Top 12 SQL Query Questions from Interviews for Practice with Solutions
SQL, a short form of Structured Query Language is one of the essential skills in today's programming world. No matter whether you are a Java developer, C++ developer or Python developer, you must know how to write SQL queries. Every programming job interview has at least one or two questions that require you to write SQL queries for a given requirement and many developers struggle there. It's easy to answer theoretical questions like what is the difference between clustered and non-clustered index (see) or what is the difference between correlated and non-correlated subqueries (see), but when it comes time to actually write SQL queries to solve problems, it's not that easy, especially if you haven't done your homework and practice.
Quicksort Sorting Algorithm in Java - Example and Explanation
Quicksort algorithm is one of the most used sorting algorithms, especially to sort the large lists, and most of the programming languages, libraries have implemented it in one or another way. In Java, Arrays.sort() method sorts primitive data types using a double-pivot Quicksort algorithm, authored by Joshua Bloch and others. This implementation provides better performance for a lot of data sets, where traditional quicksort algorithms reduced into quadratic performance. This method also uses MergeSort, another good sorting algorithm, to sort objects. Quicksort implementations are also available in the C++ STL library.
10 Essential Skills For Cyber Security Professionals to Learn in 2022
Hello guys, if you want to become a Cyber Security Professional but not sure which skills you should learn to start your Cyber Security career then you have come to the right place. Earlier, I have shared essentials skills for Java Developers, Python Developers, app developers, and Data Analyst and in this article, I will share important skills for Cyber Security Professionals. Cyber Security is one of the most lucrative career in today's age where every company and service is going online. Most companies infrastructure are connected to the internet, such as the employee's computers and the servers where the company has their valuable and confidential data, which means it can be hacked by people outside their network and cause significant damage to their system and even reputation so they need to hire cyber security professionals to help them secure their network.
[Solved] How to Implement Binary Search in Java without Recursion? Iterative Algorithm Example Tutorial
Hey Java programmers, if you want to implement a binary search in Java, and looking for both iterative and recursive binary search algorithms then you have come to the right place. Earlier, I have shared the free courses to learn Data Structure and algorithms in Java, and today, I am going to teach you an important algorithm. In computer science, a binary search or half-interval search is a divide and conquer algorithm which locates the position of an item in a sorted array. Binary search works by comparing an input value to the middle element of the array. The comparison determines whether the element equals the input, less than the input or greater.
The 2022 Python Developer Roadmap
Hello guys, if you want to become a Python developer and looking for a complete 2022 Python Developer RoadMap then you have come to the right place. In the past, I have shared Java Developer RoadMapWeb Developer RoadMapiOS Developer RoadMapData Analyst RoadMap, and even a DevOps Engineer RoadMap and in this article, I am going to share with you the Python Developer RoadMap. Before writing this article, I looked for various roadmaps available online which list a lot of things you need to learn to become a Python Developer, which is really not needed. You may need them if you want to become a Python expert which can take years but just to start your career with Python, you don't need them at all.
10 Essential Skills For Data Analyst in 2022
Hello guys, if you want to become a Data Analyst in 2022 but not sure which skills you need to succeed in this field or become a successful Data Analyst then you have come to the right place. In the past, I have shared essentials skills for Java developers and Python developers in 2022 and today I will share with you which skills you need to become a Data Analyst in 2022. Data analysis is a job in demand by most companies in the world who want to leverage the benefits of their data and make better decisions but analyzing data is not just knowing how to use a simple analysis software such as the Excel spreadsheet or visualize the data. It has many other skills you need to call yourself a data analyst.
[Solved] How to reverse an ArrayList in place in Java? Example
You can reverse an ArrayList in place in Java by using the same algorithm we have used to reverse an array in place in Java. If you have already solved that problem then It's a no-brainer because ArrayList is nothing but a dynamic array, which can resize itself. All elements of an array are stored in the internal array itself. By the way, if you need to reverse an ArrayList then you should be using the Collections.reverse() method provided by the Java Collection framework. It's a generic method, so you can not only reverse an ArrayList but also Vector, LinkedList, CopyOnWriteArrayList, or any other List implementation.
2 Ways to Check if a String is Rotation of Other in Java? Example
Write a program to check if one String is a rotation of another String is a common coding problem you will find on programming job interviews. A String is said to be a rotation of another String, if it has the same length, contains the same characters, and they were rotated around one of the characters. For example, String"bcda" is a rotation of "abcd" but "bdca" is not a rotation of String "abcd". One of the simplest solutions to this interesting problem is first to check if two String has the same length, if not then one String cannot be the rotation of another. If they are of the same length then just create another String by concatenating first String with itself, now check if second String is a substring of this concatenated String or not, if yes, the second String is a rotation of first.
How to Find Multiple Missing Integers in Given Array of Numbers with Duplicates in Java?
Hello guys, It's been a long time since I have discussed any coding or algorithm interview questions, so I thought to revisit one of the most popular array-based coding problems of finding missing numbers in a given array of integers. You might have heard or seen this problem before on your programming job interviews and you might already know how to solve this problem. But, there are a lot of different versions of this problem with increasing difficulty levels which interviewers normally use to confuse candidates and further test their ability to adapt to frequent changes, which is key to surviving in the ever-changing software development world.
50 Free Spring Professional Certification Practice Questions with Answers [VMWARE EDU-1202 Exam]
Hello guys, preparing for IT certification like Oracle's Java certification or Vmware's Spring Certification required a lot of hard-work. I have seen many experienced Java developers failing these certifications and losing money and time due to over-confidence and lack of preparation. A structured preparation involves reading books, joining course and doing practice questions. When it comes to Spring certification, practice questions are quite hard to find and that's why I created my Udemy course with 250+ Spring Certification questions. This course has helped more than 9000 students in their Spring certification preparation journey.
The 2022 iOS App Developer RoadMap
Hello guys, if you want to become an iOS App developer and looking for a solid roadmap then you are not alone. I was also looking for iOS app developer roadmap when I stumbled upon this awesome looking iOS developer RoadMap on Reddit. This is one of the comprehensive roadmap to take your from zero to master in iOS App Development but its also too much comprehensive and hard to follow. To be honest, I cannot learn all the skills mentioned in this RoadMap unless I spend all of my time on learning them for another 5 to 10 years. So, I created a simplified version of my own iOS developer RoadMap where you only need to learn essential skills to start doing iOS Development and start your career as iOS App developer.
Top 30 Linked List Algorithm Questions from Programming/Coding Interviews
The linked list is one of the most common and essential data structure and that's why you would frequently find linked list based coding questions on interviews. The range of questions can be from simple questions like finding the length of a linked list to very difficult like merging two sorted linked lists. Nevertheless, the point is that you should be familiar with linked list data structure and must know how to perform basics task in the linked list e.g. adding or removing nodes from a linked list, traversing order linked list and implementing linked list in your choice of programming language like Java, C++, C, or Python.
How to Print Fibonacci Series in Java without Recursion - Coding Problem for Beginners
Fibonacci series is a great example of Dynamic Programming, Recursion, and how the use of Recursion can result in a clear and concise solution. That's why whenever asked about writing a Java program to get Fibonacci numbers or print the Fibonacci series of certain numbers, it's quite natural for programmers to resort to recursion. The interviewer often challenged this practice by asking candidates to implement the Fibonacci series without using recursion. Yes, you read it right, you can't use recursion and this is what you will learn in this article. If you have attended your programming classes regularly then you may know that many recursive algorithms also have their iterative counterpart which uses loops instead of recursion or calling itself. We will take advantage of that concept to devise a solution to this problem.
How to set an "Accept:" header on Spring RestTemplate request? Example Tutorial
RestTemplate is one of the most commonly used tools for REST service invocations. So one of the major problems you might have in this RestTemplate is that how to set an "Accept" header on Spring RestTemplate request. In the last article, I have shown you how to POST and Consume JSON using RestTemplate in a Spring Based Java application and In this tutorial, we will go through some important points on how to add headers to RestTemplate and fix the errors related to them.
Difference between Statement vs PreparedStatement vs CallableStatement in Java JDBC
Hello Java programmers, if you are looking to find out the difference between Statement, PreparedStatement, and CallableStatement in Java then you have come to the right place. Earlier, I have shared common JDBC Interview Questions and in this article, I am going to explain what is the real difference between these Statement types in Java and when to use Statement, PreparedStatement, and CallableStatement in Java programs. JDBC API provides several classes and interfaces for various things, but three of the most important types of Statement classes are Statement, PreparedStatment, and CallableStatement. They are designed to execute different types of SQL queries
What is Bean scope in Spring MVC Framework with Example
Java classes or POJO which are managed by Spring Framework are called Bean or Spring Bean and Bean scope in Spring framework or Spring MVC is scope for a bean managed by Spring IOC container. You may know that Spring is a framework that is based on Dependency Injection and Inversion of Control and provides bean management facilities to Java application. In Spring-managed environment bean (Java Classes) are created and wired by the Spring framework. Spring allows you to define how those beans will be created and the scope of the bean is one of those details. Scope are similar to access modifiers in Java which specifies visibility of a particular class.
Top 10 Udemy Instructors to Learn Software Development in 2022 - Best of Lot
Hello guys, if you are thinking to learn Software development on Udemy but not sure which Udemy instructor has best Software development courses or which is the best software development instructor then you have come to the right place. Earlier, I have shared best Software development courses from Coursera and best coding courses from Educative and in this article I will share the best Udemy instructor to learn Software development But, before we get to the 10 best Udemy instructors that will teach you everything you need to know about software development, let me tell you more about Udemy.
String vs StringBuffer vs StringBuilder in Java? Example
Difference between String, StringBuffer, and StringBuilder
The String is one of the most important classes in Java and anyone who starts with Java programming uses String to print something on the console by using famous System.out.println() statements. Many Java beginners are not aware that String is immutable and final in Java and every modification in String creates a new String object. For example, when you get the substring, you get a new String, when you convert uppercase String to lowercase, a new String is created. Even when you remove space by calling the trim() method, a new String is returned.
[Solved] How to find first recurring character in given String? [Google Interview Question]
Hello guys, while surfing the Internet for a couple of weeks back, I come to know that this problem was asked on Google interviews, find the first recurring character in a given String. I don't know if that's true but this looks like a very simple coding problem from Google's Interview standard. If it was indeed asked, then that guy must have been very lucky. Anyway, I liked this coding problem and thought to write about it, because it's a good coding problem to check candidates' data structure and algorithms skills because it's tricky. It's tricky because it's very easy to make a mistake assuming just one recurring character in String, which you should avoid.
5 Ways to find length of String in Java - Example Tutorial
On another day, someone asked me, is there a way to find the length of String without using the length() method from java.lang.String class? I didn't ask why, because I know it might have been asked to him on Interviews. Before I explore ways to find the length of String, let's recap what does the length of String means in Java? Well, it's no different than C here, a number of characters in a String including whitespace, newlines are known as length of String. By knowing this, you can think of many approaches to calculating length e.g. getting a char array from String and counting a number of characters or many are by applying some clever tricks.
5 Projects You can do to learn Flutter in 2022
Learning Flutter to build mobile apps for android and iOS does not make you a professional developer that people can rely on you to build their app. In fact, you need to train as much as possible to create mobile apps so you can consider yourself a mobile apps developer. If you are now in the stage of learning Flutter for creating mobile apps and you want to enhance your skills by building as much as possible mobile apps for both platforms android and iOS you’ve come to the right place.
10 Examples of Joining String in Java - String.join vs StringJoiner
It's quite common in day to day programming to join Strings e.g. if you have an array or List of String let's say {Sony, Apple, Google} and you want to join them by a comma to produce another String "Sony, Apple, Google", there is not an easy way to do it in Java. You need to iterate through an array or list and then use a StringBuilder to append a comma after each element and finally to remove the last comma because you don't want a comma after the last element. A JavaScript-like Array.join() method or join() method of Android's TextUtils class is what you need in this situation. Still, you won't find any such method on String, StringBuffer, StringBuilder, Arrays, or Collections class until Java 8.
Difference between Period and Duration class in Java 8? [Example]
What is the difference between Period and Duration class in Java is one of the popular Java 8 interview questions and has been asked too many of my readers recently. If you were also wondering the difference between Period vs Duration and when to use Period over Duration and vice-versa then you have come to the right place. Java 8 has two classes to represent differences in time like Duration and Period. The main difference between Period and Duration is that they represent the difference in different units, A Duration is used to calculate time difference using time-based values (seconds, millisecond, or hours) but Period is used to measure the amount of time in date-based values like days, months and year.
3 Ways to Remove Duplicates from a table in SQL - Query Example
There are a couple of ways to remove duplicate rows from a table in SQL e.g. you can use temp tables or a window function like row_number() to generate artificial ranking and remove the duplicates. By using a temp table, you can first copy all unique records into a temp table and then delete all data from the original table and then copy unique records again to the original table. This way, all duplicate rows will be removed, but with large tables, this solution will require additional space of the same magnitude as the original table. The second approach doesn't require extra space as it removes duplicate rows directly from the table. It uses a ranking function like row_number() to assign a row number to each row.
How to use EXISTS and NOT Exists in SQL? Example Query and Tutorial
Hello Guys, you might have heard about how useful the EXISTS clause is helpful in writing sophisticated queries. Still, at the same time, I have also seen that many programmers struggle to understand and use EXISTS and NOT EXISTS clauses while writing SQL queries. If you are one of them, then you have come to the right place. Today you will learn how to use the EXISTS clause in SQL by picking up a real-world example and an excellent SQL exercise from the LeetCode. Suppose that a website contains two tables, the Customers table, and the Orders table. Can you write an SQL query to find all customers who have never ordered anything?
10 Best Courses Of Brad Traversy on Udemy to Learn Web Development
Hello guys, if you are looking for best web development courses then learning from Brad Traversy is a great idea. He is one of the most engaging instructor on Udemy and having attended his web development courses on Udemy and watching his crash courses on Youtube, I really liked his crystal clear teaching style. A lot of you asked me about the best web development courses so I decided to compile all of his best courses into one article and here we are. But, before we get to the 10 best courses of Brad Traversy, let me tell you who he really is and why he is one of the most popular instructors on Udemy.
5 Examples of GROUP BY Clause in SQL with Aggregate Functions
There is no doubt that SQL is an essential skill and every programmer, developer, DevOps, and Business analyst should know SQL. If you want to learn SQL from scratch then you have come to the right place. Earlier, I have shared many SQL interview questions and the best SQL courses for beginners, and today, I am going to share some GROPU By examples in SQL to write aggregation queries. THE GROUP BY clause in SQL is another important command to master for any programmer. We often use the GROUP BY command along with a select clause for reporting purposes, since the GROUP BY clause is mainly used to group related data together it's one of the most important SQL commands for reporting purposes.
What is difference between SQL, T-SQL and PL/SQL? [Answered]
Today, we are going to see another common and interesting SQL interview question, what is the difference between SQL, T-SQL, and PL/SQL? It is also one of the most common doubts among SQL beginners. It's common for programmers to think that why there are many types of SQL languages, why not just single SQL across DB? etc. Well, let's first understand the difference between SQL, T-SQL, and PL/SQL, and then we will understand the need for these dialects. SQL is standard for querying, inserting, and modifying data in a relational database. It is categorized into DDL and DML and is powerful enough to create database objects e.g. table, view, stored procedure, and can perform CRUD operation (SELECT, INSERT, UPDATE, and DELETE) query.
3 ways to learn MERN stack in depth in 2022
Hello guys, if you want to learn MERN Stack in 2022 but not sure where to start then you have come to the right place. Earlier, I have shared best courses to learn MERN Stack and in this article, I will share 3 ways to learn MERN stack from scratch. If you don't know MERN stack is one of the most popular and widely used web development stacks in the world. MERN stack uses React on the client-side while Node.js with Express.js on the server-side and MongoDB is used as the database. All the four technologies used in the MERN stack are widely used and because of this, their combination is also very popular.
How to check for Null in SQL Query? IS NULL Example Tutorial
One of the most common SQL Interview questions on Programming interviews is to select some rows from a table that also contains null values. Since many SQL developers are used to using = and != operator on WHERE clause, they often tend to forget the fact that column allows NULL or not. Using = or != is perfectly fine if your column has NOT NULL constraint and you know for sure that there are no NULL values in that column, but it does contain NULLs then your SQL query will return the incorrect result at times. This is one of the most common mistakes but at the same time hard to find SQL bugs if it managed to get into the real environment. In this article, you will learn the right way to check NULL values in SQL queries using IS NULL and IS NOT NULL predicates.
How to Find Duplicate values in a Table? SQL GROUP BY and Having Example| Leetcode Solution
Hello guys, if you are wondering how to find duplicate values in a table then don't worry, there are many ways to find duplicate rows or values from a given table. For example, you can use the GROUP BY and HAVING clause in SQL with count function to find all the rows which has same values for a particular column and then filter out rows where count is just one, I mean unique values. This way you can find all the duplicate from a given table. Using group by you can create groups and if your group has more than 1 element it means it's kind of duplicate. For example, you need to write a SQL query to find all duplicate emails in a table named Person. This is a popular SQL Query interview question as well as a Leetcode problem. You can see that email [email protected] is a duplicate email as it appears twice in the table.
Java 8 forEach() Loop Example
Java 8 has introduced a new way to loop over a List or Collection, by using the forEach() method of the new Stream class. You can iterate over any Collection like List, Set, or Map by converting them into a java.util.sttream.Stream instance and then calling the forEach() method. This method performs given operation on every element of Stream, which can be either simply printing it or doing something else. Since stream can be sequential or parallel, the behavior of if this method is not deterministic if used with a parallel stream
Top 10 Google Interview Questions for Software Engineer - Books, Resources
Hello guys, if you are preparing for Google's Software Development Engineer roles and looking or Google Software Interview questions then you have come to the right place. Earlier, I have shred Amazon and Microsoft Interview questions and in this article, I am going to share popular questions from Google Interviews. These Google interview questions are some of my favorites collected from different sources. Every Programmer knows that Google is one of the best technology companies and its dream for many software developers to work for Google, but at the same time interview process at Google is very tough and only a few genuine intelligent programmers get through their interview process
Difference between Transient, Persistent, and Detached Objects in Hibernate
In the Hibernate framework, an entity can be in three states, transient, persistent, and detached. When an object is in a transient state, it is commonly referred to as a transient object, similarly, if it is in persistence and detached state, it is known as a persistent and detached object. When an entity is first created using the new operator like new User() and not associated with Hibernate session like you haven't called session.save(user) method then it is known as a transient object. At this stage, Hibernate doesn't know anything about this object and the object doesn't have any representation in the database like a corresponding row in the User table.
Top 5 programming languages for Artificial Intelligence or AI Development
Hello guys, if you want to do AI Development or want to create Artificial Intelligence based apps and looking for best programming language then you have come to the right place. Earlier, I have shared best programming language for web developmentapp development, and data science development and today, I am going to share best programming language for AI Development. All programming languages are not created equal. Only a handful of programming languages remain and serve the community out of countless. The programming languages we'll be discussing presently have stood the test of time. For decades, they've been used for a variety of undertakings.
10 Reasons to Learn SQL for Programmers and Software Developers in 2022
Hello guys, if you are on the fence whether to learn SQL or not, or want to learn SQL but not sure whether learning SQL is worth your time and effort then you have come to the right place. Earlier, I have shared best SQL books and courses to learn SQL for Beginners and in this article, I am going to share 10 Reasons to learn SQL. From my 18 years of experience as Software developer and 12 years as a blogger I can safely say that you should learn SQL. In all of these times, I have constantly worked with SQL in my projects and job. While database changes form Oracle to MySQL, to SQL Server, and now PostgreSQL but the knowledge of SQL still pays off.
How Long does It take To Learn Linux?
Hello guys, if you want to learn Linux but not sure how to start then you have come to the right place. Earlier, I have shared best places to learn Linux and best Linux books for beginners and Linux interview questions with answers and in this article, I Am going to share the best way to learn Linux and answer frequently asked question, how long does it take to Learn Linux. In general, you can learn Linux in one weekend but it can take weeks before you become a Linux master as there are a lot of Linux commands and concepts to master. In this article, I will answer this question objectively depending upon your goal, for example, for a developer it can take a week to Learn Linux but for System Admin it could be months because they need more in-depth knowledge.
Top 20 PostgreSQL Interview Questions With Answers
Hello guys, if you are preparing for Postgres Interview or a Java development role where PostgreSQL skills are needed but not sure how to prepare, what to prepare etc and looking for PostgreSQL Interview questions with answers then you have come to the right place. Earlier, I have shared 50 SQL Phone interview questions and 6 SQL Query questions and in this article, I am going to share frequently asked PostgreSQL questions with answers. You can use these questions and answers to prepare well for your Job interview and you can also learn essential PostgreSQL concepts by going through these questions.
How to return JSON, XML or Thymeleaf Views from Spring MVC Controller?
Hello guys, if you are working in Spring based web application and you wan to return JSON, XML, or Thymeleaf View from your application but don't know how to do that then you have come to the right place. Earlier, I have shared how to create REST API in Spring and In this tutorial we are going to discuss, how to return to JSON, XML, or Thymeleaf view from the Spring MVC controller. To ensure that your payload from the MVC endpoint, ensure your project is using the Spring Boot starter web. You can use the following dependency to include spring boot starter web in your project.
How to validate incoming payload on Spring MVC controller? Example Tutorial
Hello guys, if you are wondering how to validate incoming request payload in Spring MVC based Java web application then you have come to the right place. Earlier, I have sharebest Spring MVC courses for Java developers and In this tutorial, we are going to discuss how to validate incoming payloads on the Spring MVC controller which is also can be defined as validating the request body in the RESTful web services. So first let's have a look at validating the request body in the RESTful web services. Think you have a JSON post request and you are going to consume it. There should be a validation to this post request as the requested input will be zero or in a not accepted format.
10 Best Udemy Courses of Stephane Maarek to Learn AWS and Kafka in 2022
Hello guys, if you are learning AWS and Apache Kafaka and looking or best online courses or you have heard about Stephane Maarek and his popular Udemy courses on AWS certification, Apache Kafka, and Google gRPC but not sure whether to join or not then you have come to the right place. Earlier, I have shared best AWS courses and best Kafka courses where I have featured Stephane's Udemy courses but in this article, I am going to share all of the best Udemy courses by Stephane Maarek on Udemy which you can join in 2022. But, before we get to the 10 best Udemy courses of Stephane Maarek, let me tell you who Stephane really is and why his courses are really popular on the platform.
[2022 Udemy Course Review] - The Web Developer Bootcamp by Colt Steele
Hello guys, if you want to learn Web Development and looking for a beginner friendly course or you have heard about Colt Steele's Web Development 2022 Bootcamp course on Udemy and wondering whether its wroth to join this course in 2022 or not then you have come to the right place. In the past, I have shared best web development online courses and in this article, I will share my 2 cents on Colt Steel's popular Web Developer bootcamp course on Udemy. Learning web development nowadays is such a huge work to do because you are going to learn not only to design the front-end or the web interface but you are also going to learn the back-end as well as design and build the database system for that website or online service and that’s what’s known as Full-stack web developer
Top 5 Online Courses to Learn C# in 2022 - Best of Lot
If there is one programming language that deserves more credit, than it currently receives from developers, then it would be Microsoft's C# or C-Sharp. When we talk about popular programming languages, we mostly talk about how Java is ruling the programming world for the last three decades, how JavaScript changed the web world, or how Python has taken over all programming languages in the last couple of years, but we seldom mention C#, which is silently providing jobs and making a career with .NET, Unity, and became a preferred choice for creating desktop GUI applications. If you follow the StackOverflow survey, then you know that C# is always one of the top 5 Programming languages rated by programmers, and this year also close to 31.0% has said that they use C#, which is significant.
Top 5 Online Courses to Learn Maven in 2022 - Best of Lot
The Apache Maven or commonly known as just "Maven," is an essential tool for Java Programmers. It allows you to build your project, manage dependencies, generate documentation, and a lot more. I can vouch for Maven's usefulness because I have come from the pre-Maven world of Software development, where you need to manage all the JAR files required by your project. It may seem easy to you that just download the JAR file but it's not so easy in practice. For example, you added a new library in your project say Spring framework which also needs log4j but you thought log4j is already there so you didn't do anything, only to realize that your application is not starting anymore and throwing long and convoluted errors. This can happen because a version mismatch like Spring needed a higher version of log4j than available in your project.
10 Best Udemy Courses of Neal Davis to Learn AWS and Cloud Computing in 2022
Before getting to the 10 best Udemy courses of Neal Davis, let me tell you who Neal Davis really is. Neal Davis is one of the most popular instructors on the Udemy platform. He has taught more than 350,000 students on Udemy and more than 77,000 of those students have given him a 5-star rating. Neal Davis is a highly experienced AWS Cloud Solutions Architect, a successful IT instructor, and the founder of Digital Cloud Training. He has been working in IT for more than 20 years in a number of different roles like support and architecture.
Top 10 Coursera Certifications and Courses to Learn Python in 2022 - Best of Lot
While there are many online platforms out there to learn Python Programming from scratch, Coursera is one of the most popular and reputed websites to learn Python for beginners. The best thing about Coursera is that it provides access to courses taught at the World's top universities like the University of Michigan and Rice University, one of the top 20 universities in the USA. It has also got the best Python certifications offered by the world's most reputed companies like IBM and Google and the world's top universities like the University of Michigan and Johns Hopkins University. That's why many people flock to Coursera to learn Python and other Computer Science and Software Engineering skills.
Top 5 Project-Based Courses to learn Coding with Java, Python, and JavaScript in 2022 - Best of Lot
Hello guys, if you are aiming to learn programming and code in 2022 with Java, Python, or JavaScript, the top 3 programming languages of the world then I suggest you join a project-based course. These are the courses where you will learn things by doing and I think that's the best way to learn programming and coding. Reading a book is Ok, watching videos are also Ok but they will not make you a Programmer or Coder, you must code to become a coder and these project-based courses give you that opportunity.
|
__label__pos
| 0.545557 |
Radon in Water – The Radon Specialist
Radon in Water
Radon in Water, testing for radon, glass of water, The Radon Specialist
Radon gas can also enter homes through the water supply. Radon dissolves and builds up in water from underground sources, such as wells. The radon in your water can enter the air in your home when you use water for household activities such as showering, washing clothes and cooking. For every 10,000 picocuries per liter (pCi/L) of radon in your water, it is estimated that 1 pCi/L is added to your radon in the air. If your water comes from a lake, river, or reservoir (surface water), radon is not a concern. The radon is released into the air before it reaches your home. Some states like Connecticut, New Hampshire and Vermont recommend fixing radon in water if the levels are above 5000 pCi/L.
The North Carolina Radon Program recommends a radon-in-water advisory be set at two levels. At the moderate level, concentrations between 4,000 and 10,000 pCi/L in water, treatment is considered optional. At the elevated level, concentrations at or above 10,000 pCi/L in water, treatment should be considered in conjunction with the treatment of indoor air radon released from soil gas. In most cases, mitigation of soil gas radon will have the greatest impact on reducing overall radon exposure and will usually take precedence over treatment of radon in water.
Some radon stays in the water. Radon in the water you drink can also contribute to a very small increase in your risk of stomach cancer. However this risk is almost insignificant compared to your risk of lung cancer from radon.
It is suggested by the EPA that if you have elevated air radon levels and are on a private well, you should have your water radon tested.
Removal of Radon from Water
There are only two practical techniques for removing radon from water in a residential setting. One technique uses activated carbon. The carbon adsorbs the radon from the water. The radon then finishes decaying in the carbon. Activated carbon should only be used if the radon water levels are below 5000 pCi/L. This low level is recommended by the EPA because of the concern over the buildup of radioactivity.
Aeration systems are is used on very high levels of radon. The radon is released from the water by bubbling air through the water. The radon is then vented to the outdoors. There is no buildup of radioactive materials when this technique is used. The removal of well over 99% of the radon from the water can be achieved with these units. These units do require the repressurization of the water after it is treated and care must be taken to properly vent the gas. This venting should be done above the roof line just like an air radon system and there should always be an auxiliary fan outside of the living space to provide for the save removal of the gas. Water aeration is considered by the U.S. EPA to be the best available technology for removing radon from well water. Unlike other methods, such as granular activated carbon tanks, aeration does not pose the threat of waste buildup.
|
__label__pos
| 0.928827 |
Back
JAMP Vol.9 No.7 , July 2021
A New Insight into the Observations and Analysis of Type Ia Supernovae
Abstract: In this paper, we have given some analysis from observations of type Ia supernovae (SNIa). We find that the average total observational error of SNIa is obviously greater than 0.55m. On the other hand, a popular view of circumstantial evidence for the accelerating universe comes from the comparison of theoretical models simulating the accelerating expansion of the universe with observations from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite deviating from the observed isotropic temperature of the Cosmic Microwave Background (CMB). Due to the fact that the velocity space is not isotropic, then the theoretical simulations are incredibly consistent with observations from the WMAP and Planck satellites. We conclude that the anisotropy of the velocity space will inevitably lead to an anisotropic distribution of the CMB temperature, and the above indirect evidence of the cosmic acceleration is inadequate and inappropriate.
1. The Origin of the Cosmic Dark Energy Problem
Accelerating expansion of the universe may be caused by dark energy, which is one of the most important ideas of researches in astrophysics and cosmology today. Accelerated by dark energy, this motion is different from the outward expansion of the universe [1]. The so-called Advanced Philips Relation (hereafter APR) was derived on the absolute magnitude statistics at maximum luminance of Type Ia supernovae (SNIa) related with both the width of light-curve (Δm15, the decline in magnitudes 15 days after the peak luminosity) and the variation of the color index (B-V) of SNIa (e.g., [2] [3] [4] [5] [6] ). The Direct evidence of cosmic accelerated expansion comes from observations of SNIa using the Advanced Philips Relation ( [6] [7] ). The distance modulus μ is
μ = 5 log ( D ) 5 = m M A + k + (1)
where D is the distance in the unit of pc, m and M are the apparent magnitude and absolute magnitude of SNIa, respectively. A, K, and “... ” are the intergalactic extinction, the K-correction, and the errors caused by gravitational lensing and the peculiar motion of the host galaxy, respectively.
The APR is by far the most accurate method. However, in the processes of the explosive nucleosynthesis, we hold the opinion that Δm15 is closely related to the quantity of radioactive nuclide produced. On the other hand, during the processes of the explosion, the color index varies with the expansion and cooling down rates of outer aerosphere. Based on the APR, SALT2 (Spectral Adaptive Light-curve Template) [5] is an SNIa light curve fitting software package. According to the data from 685 SNIa, which is from the SALT2, UNION2 [6], the system error of the absolute magnitudes of SNIa was found by minimizing χ2, which is the normalized quadratic sum of distance modulus residual [6]. As a result, they came to a conclusion that the expansion of the universe that began with the Big Bang is speeding up. Then, Saul Perlmutter, Brian Schmidt and Adam Reiss share the 2011 Nobel Prize in Physics for their SNIa observations indicating that the expansion of our universe is accelerating.
As well known, the most direct evidence has been provided for the presence of dark energy from SNIa cosmology. Recently, the evidence for downsizing of early-type host galaxies of the SNIa has been shown by Kang et al. (2016) [8]. Their results shown that the stellar population age is mainly responsible for the relation between host mass and Hubble residual. In the systematic uncertainties of SNIa cosmology, their results shown that the luminosity evolution is very important and plays a key role. The evidences for luminosity evolution in SNIa cosmology have also been discussed by Kang et al. (2020) [9]. Between the stellar population age at a 99.5% confidence level and SNIa luminosity after the standardization, they found a significant correlation. For the population age effect, which would inevitably cause a serious systematic bias with look-back time, the light-curve fitters used by the SNe Ia community may be not capable of correcting. They suggested that we must consider the systematic bias in SN cosmology for studying the dark energy [9]. In this paper, we have discussed the same error analysis of SNIa. One sees that the average of total observational error of SNIa is greater than 0.55m. These results show that the universe may be not accelerating expansion.
2. The Standard Candles of SNIa Becoming Invalidated
Advances on the SNIa remnants have shown that the idea of a single accreting white dwarf model (known as the “standard model”) for the SNIa explosion, which has been negated due to the researches on the Tycho’s SNR from 2008 to 2010 [10] [11]. Because of the different origins of SNIa, their peak luminosities are no longer taken as standardized candles. Besides, it has been discovered that some remnants of SNIa are obviously asymmetric in spatial direction [12]. At the same time, some explosion simulations of SNIa showed that there may be significant asymmetry in the explosion of the SNIa [13] (to see Figure 1 in this paper). For these objects, Maeda et al. (2010) discussed the observations of SNIa and implicated a lopsided explosion mechanism. Their simulation shows that a white dwarf is initially ignited slightly away from the center (see Figure 1(a)), and a thermonuclear flame begins to consume the star (see Figure 1(b)). The burned material is hot and buoyant, and so the flame and ash quickly float upward (see Figure 1(c)), resulting in one side of the star being more completely incinerated and more rapidly expelled than the other (see Figure 1(d)).
Wang et al. (2013) [14] showed the evidence for two distinct populations of SNIa. More importantly, many physical problems, such as the mechanism and process of SNIa explosion, the explosive nuclear burning and the production of elements (especially radionuclides) in the thermonuclear explosion, as well as the expansion and cooling of the outer atmosphere at the time of the explosion remain undetermined.
According to the Advanced Philips Relation in Refs. [2] [3] [4] [5] [6], the research on SNIa is still in the exploratory stage, then these absolute magnitudes based on fitting the SALT2 SNIa light-curve and spectrum are the peak luminosity
Figure 1. Lopsided supernova explosion [12] [13].
of ’modeling SNIa’ rather than ones of real SNIa. In this paper, we will analyze the data, which is the latest and most complete SNIa compilation from UNION2.
3. Some Serious Faults in Error Analysis of Type Ia Supernova Research Papers
3.1. Error in the Absolute Magnitude
At the maximum light of SNIa, the errors of the absolute bolometric magnitude are given as follows:
1) At the maximum luminance, the absolute magnitude intrinsic error (ΔMint), is just the half width at the statistic distribution curve of the number of SNIa with the maximum luminance, rather than the systematic error established using the χ2 check way in some papers (e.g., [1] [2] [3] [4] [5] )
2) In addition to ΔMint, part of M comes from the transfer error caused by statistical errors of the parameters a and b in original Phillips relation (or of the parameters α x , β in the APR), we call it as the transfer error, ΔMint(a, b).
3) Part of M is caused by ΔMobs, the error of some observational quantities of both the light-curve and color index in the Advanced Phillips’s way.
The total error of absolute bolometric magnitude at the maximum light (ΔMtotal) is given by
( Δ M total ) 2 = ( Δ M int ) 2 + ( Δ M max phillips ) 2 (2)
( Δ M max phillips ) 2 = ( Δ M ( a , b ) ) 2 + ( Δ M obs ) 2 (3)
where SALT2 [5] and UNION2 [6] did not give the aforementioned errors separately. They merged them into the system error caused by χ 2 -minimization. The minimum of Δ M max phillips is larger than observational apparent magnitude error, | Δ M max phillips | > | δ m | (the observational error of apparent magnitude). Because the high red-shift SNIa is faint, so its | δ m | is much larger than that of nearby SNIa.
3.2. Incorrect Systematic Error Established by Using the χ2 Check Test
The error of distance modulus for the set of SNIa obeys the Gaussian distribution. It is the premise of the χ2 check test in this paper. However, the set of SNIa modeling doesn’t really satisfy Gaussian distribution in Ref. [6]. Although the UNION2 contains 685 SNIa, the average error is 0.16m, which over 10% of total SNIa are outline of 10σ. If we take a subsample including 217 SNIa with very small observational average error to do the same statistics, One finds that over 10% of total SNIa are outline of 5σ. So UNION2 shows a strong non-Gaussian distribution. Really, the critical permitted outline value of 2.6σ in the standardized normal distribution is 0.805%. Following the SATL2, performing the χ2 check test in the UNION2 work, the average of the total observational error of SNIa’s distance modulus is 0.31m. The result comes out that the 3.796% of the data is derived from 2.6σ element with an average error of 0.31m. Obviously, the distance modulus error deviates from the Gaussian distribution, and it is incorrect to obtain the systematic error σsys of SNIa by the χ2 check test method.
We think that the real intrinsic error of an SNIa compilation should be based on statistical diagram of the number of SNIa (to see Figure 2). As we don’t know the exact luminosities (the absolute bolometric magnitude) of SNIa with high redshift, it is the only way to use SALT2 to get the absolute bolometric magnitudes of “modeling SNIa”. At the maximum luminosity, the intrinsic error of the absolute magnitude is the half width at half maximum of the statistic distribution curve of the number of SNIa with the maximum luminosity (to see Figure 2). The intrinsic error ΔMint = 0.38m, which is larger than the systematic error given by the χ2 check test.
4. Query on Accelerating Expansion of the Universe (I)
Figure 3 shows the average total observation error of distance modulus from modeling SNIa samples as a function of red-shift, z. The average total observation error of distance modulus is ( Δ μ ) 2 = ( Δ M total ) 2 + ( δ m ) 2 . Based on the observational apparent magnitude error from the UNION2 and SNIa data, we divided intervals per Δz = 0.1. By using the same χ2 check test method, we give the statistics to calculate this sample’s average total observation error of distance modulus. One can find that the observation error of the distance modulus increases greatly with the increase of red-shift of SNIa in the very high red-shift region. As can be seen from Figure 4, the residual error of SNIa’s distance modulus is a function of red-shift of SNIa. The curves of three from top to bottom represent the models of cosmic accelerating, constant speed, and slow down expansion, respectively. It is also found that the average total observational error of SNIa is obviously greater than 0.55m, which is much larger than 0.40m (see in Figure 3 and Figure 4). So we don’t know for sure if the universe is accelerating. Recently, Ref. [15] discussed the marginal evidence in detail for cosmic acceleration
Figure 2. The Statistic distribution of the absolute magnitude at maximum luminosity (Mmax) for SNIa. The abscissa is Mmax f SNIa, the ordinate is the number of SNIa with Mmax. The half width at the half height for the peak of the distribution curve (HMHW) is just the intrinsic error (or the proper error) of the absolute magnitude at the maximum luminosity for the samples of SNIa.
Figure 3. Varies of (average) the observational error of the distance modulus with redshift of SNIa. The abscissa is the red-shift of SNIa, the ordinate is the “modeling SNIa” sample’s average total observational errors of distance modulus. It shows that the observational error of the distance modulus increases with the increasing redshift of SNIa in region of the remote high red-shift.
Figure 4. The residual error for the distance modulus of SNIa. The abscissa is the red-shift of SNIa, the ordinate the residual error for the distance modulus of SNIa. The three curves from left to right, from top to bottom, represent calculating curves of the universe expansion, which is accelerating, uniform or decelerating, respectively. They show that the residual error bars of the distance modulus of SNIa are too large (>0.55m) to judge the universe expansion being accelerating, uniform or decelerating.
from type Ia supernovae. From the larger database of supernovae, they performed rigorous statistical tests to check whether these ’standard candles’ really do indicate an accelerating expansion of the universe. Taking into account of the empirical procedure, by which corrections are made to their absolute magnitudes to allow for the varying shape of the light curve and extinction of dust, they found that the data are still quite consistent with a constant expansion rate. On the other hand, direct observational evidence of the idea of dark energy is also lost in the observational error analysis of SNIa.
5. Anisotropy of the Observed Cosmic Microwave Background Temperature
The prevailing idea of indirect observational evidence for the accelerated cosmic expansion is to compare theoretical simulations of the accelerated cosmic expansion with the observational data of the WMAP satellite deviating from isotropy of the observed CMB temperature. Of course, a wealth of observational data of temperature deviations from the CMB isotropy have been obtained by the WMAP (2003-2008) and Planck satellites (2012 up to date).
The maximum observed temperature increment deviating isotropic from the CMB temperature is ( Δ T ) max = 3 .346 ± 0.0017 mK in the direction l = 2636.85 ± 0.1 , b = 48.25 ± 0.04 [16] (the direction of the Virgo cluster: l = 284 and b = 74 ). This departure, mainly caused by the Earth’s motion with the velocity of β = 37 0 km / s / c = 0.0013 (i.e., the dipole anisotropy) is given as
Δ T / T = T T / T = β 2 / 6 β P 1 ( cos ( θ ) ) + 2 β 2 P 2 ( cos ( θ ) ) / 3 + (4)
where P n ( x ) is the Legendre polynomials, θ is the direction angle of the field point alone with the direction of the Earth’s motion.
The book of Ref. [16], Weinberg described in detail the contributions to the anisotropy of the observed CMB. According to Ref. [16], we list the main contributions to the anisotropy of CMB as follows:
1) Departure from isotropy of the observed CMB, arising from the Earth’s motion.
2) Anisotropy due to the scattering of photons by intergalactic electrons in clusters of galaxies. (The Sunyaev-Zel’dovich effect via solution of the Kompaneets equation)
3) The primary anisotropy left over from the early universe. Afterwards, Weinberg analyzed and discussed four factors causing the primary anisotropy of the CMB. Taking out the influence of the Earth’s motion, the residual anisotropy of the CMB temperature is about several 10−5 K.
The primary anisotropy in the CMB temperature arises from several sources. In the eletron-nucleon-photon plasma at the time of last scattering, the corresponding red-shift, z 1.090 , the first source is the intrinsic temperature fluctuations. The second source is the Doppler effect due to velocity fluctuations in the plasma at the last scattering. The third source is the gravitational red-shift or blue-shift due to fluctuations in the gravitational potential at the last scattering. This is known as the Sachs-Wolfe effect. The last source may be the integrated Sachs-Wolfe effect due to time dependent fluctuations in the gravitational potential between the time of the last scattering and the present time.
The WMAP and Planck satellites had provided very rich observational data. These observational data were fitted theoretically by including all the given physical factories in some accelerated cosmic expansion models and using more than two thousands spherical harmonic functions (l > 2000). It seems to be very beautiful for supporting the accelerated cosmic expansion. However, it is still not complete, because an important physical factor that is anisotropic velocity space has not been taken into account to date. The anisotropy of velocity space has been shown in the velocity dispersion of galaxies for cluster of galaxies.
6. Query on Accelerating Expansion of the Universe (II)
6.1. The Standard Cosmology with an Expansion of the Universe
It is well known that the Robertson Walker metric in the standard cosmology was derived from the Einstein field equation of the general relativity based on the Mach principle with an assumption of homogeneity and isotropy everywhere. For the details, see the book of ’Gravitation and Cosmology’, which was written by Ref. [17]. The Robertson Walker metric measures the scale of the expanding universe, and is given by
d s 2 = d t 2 + α 2 ( t ) ( d r 2 / ( 1 k r 2 ) + r 2 d θ 2 + r 2 sin 2 θ d φ 2 ) (5)
where the scaling factor α ( t ) . According to the Friedmann equation, the CMB temperature, T(t), decreases inversely with the expansion rate of the expanding universe in the standard cosmology. Thus, we have
α ( t ) T ( t ) = c o n s t (6)
When the velocity space is not isotropic, we may take a small anisotropy (small difference) in the velocity velocity space as a perturbation of the velocity space. A perturbation of the scaling factor will be caused by the velocity space perturbation through the energy momentum tensor in the Einstein field equation. A perturbation of the CMB temperature will be also caused by the perturbation of the scaling factor through the relation given by Equation (6).
6.2. Anisotropy of the Velocity Space of the Universe
| V | 300 - 500 km / s , It is well known that the velocity dispersions of stars in the solar neighborhood in our Galaxy are given as σ r 30 - 50 km / s , σ φ 2 / 3 σ r , σ z σ r / 2 . They are anisotropic and the scope of the anisotropy is about (30 - 50)%. All the galaxies including our Galaxy have angular momentums, which are anisotropic.
Similarly, the velocity dispersion of galaxies is also anisotropic, due to the clusters of galaxies being rotating and having angular momentum. The velocity dispersion for the galaxies in clusters of galaxies is about | V | / c ( 1 - 2 ) × 10 3 . How much is the anisotropy of the clusters of galaxies? To date, the anisotropy extent of the velocity dispersion for the galaxies in clusters of galaxies has not been well determined because it is very difficult to measure the proper motion of very remote galaxies. It is reasonable to estimate the anisotropy of the galaxies in clusters of galaxies, which is estimated as (1 - 5)%. Thus, | V | / c ( 1 - 6 ) × 10 5 .
The logical relationship of our idea is given as following: The anisotropy of the velocity dispersion for the galaxies in clusters of galaxies is estimated as ( 1 - 6 ) × 10 5 c as given a small perturbation via the Einstein field equation and a small anisotropic perturbation of metric for the expanding universe (about ( 1 - 6 ) × 10 5 ). Then, utilizing the Friedmann equation, we get a small anisotropic perturbation of the cosmic scale, α ( t ) ( 1 - 6 ) × 10 5 , and obtain a small anisotropic perturbation of the CMB temperature (i.e., about ( 1 - 6 ) × 10 5 ) by Equation (6). Finally, we can get the observational data of WMAP and Planck satellites by fitting the above information.
Thus, we may come to a conclusion that the indirect observational evidence of ’Accelerated expansion of the universe’ from fitting the WMAP and Planck satellites’s observational data is not reliable. It has to be reinvestigated at least.
7. Observational Evidence for the Anisotropy of the Velocity Space
For the standard CMB anisotropy, we give the two fundamental assumptions as follows. The first assumption is the initial fluctuations, which are statistically isotropic. The second assumption is the Gaussian, which are rigorously tested by using maps of the CMB anisotropy from the Planck satellite (Planck et al. 2014).
By using a fiducially Λ-CDM model and incorporating essential aspects of the Planck measurement process, four independent estimates of the CMB, which are compared with simulations have been obtained. The above two assumptions are derived from results of it. From isotropy to be robust against component separation algorithm, mask choice, and frequency dependence, Planck et al. (2014) [18] found the deviations. Although these analyses represent a step forward in building an understanding of the anomalies, a satisfactory explanation based on physically motivated models is still lacking. By using observations from the Planck satellite, Planck et al. (2014) test the statistical isotropy and Gaussianity of the CMB anisotropies.
Based on the full Planck mission for temperature, which includes some polarization measurements, they obtained some results. For the temperature anisotropies, they found excellent agreement between results based on these sky maps over both a very large fraction of the sky and a broad range of angular scales. However, the theoretic fitting the WMAP (and Planck) satellite observational data is not reliable due to the following reason that an important physical factor has not been taken account up to date, in which the velocity space is not isotropic.
Based on the full Planck temperature mission, which included some polarization measurements, they obtained some results. For the temperature anisotropy, between results based on these sky maps over a very large fraction of the sky and a broad range of angular scales, an excellent agreement has been found by them. However, the theoretically fitting the WMAP (and Planck) satellite observational data is not reliable, because up to date they have not taken into account an important physical factor, which is that the velocity space is not isotropic.
Except a large pool spot near the north pole of the Galaxy, the observations from WMAP (2008) and Planck (2013) show another important observational evidence for the anisotropy of the velocity space. This is a question on the axis of evil. We cite the results of Planck et al., (2014) in Table 1 [18]. The directions (i.e., galactic longitude (l) and galactic latitude (b)) of orientation vectors for quadrupole and octopole are given in columns 2 and 3 in Table 1. The angular distances of orientation vectors for quadrupole and the octopole are given in column 4. We can extracted the low multipole orientations from different separated CMB maps, obtained from maximizing the angular momentum dispersion. Between the orientation vectors of the quadrupole and octopole, the absolute values of scalar-product are given in the second last column. One can see that the latter is uniformly distributed on the interval [0, 1] in an isotropic universe. The probability of such an alignment (or stronger than that) to occur will be given in the last column when the universe is really isotropic.
From Table 1, one can see that our universe is not isotropic. However, Planck et al., (2014, 2016) [18] [19] had not understood its physical reasons in their papers. Our analysis above on the anisotropic of the velocity dispersion of galaxies from the velocity space of galaxy clusters shows that the velocity space is also anisotropic. These ideas may be one of causes for this phenomenon.
8. Summary and Discussions
In summary, we conclude that the anisotropy from the velocity space will inevitably lead to the anisotropy of CMB temperature distribution. So far, people have not yet studied the effect of this factor in detail. However, some scholars arbitrarily conclude that this is just the indirect evidence of the cosmic acceleration due to the fact that it is well fitted to the accelerating expansion model of the universe. We think that this is not serious and proper.
Besides, it is well known that the mass-density distribution structure of remote galaxies is a network-like shape. This shows that it is not completely isotropic in the space. The anisotropy of the mass-density distribution structure of remote galaxies is more than 10−5. Similar to the analysis above for the perturbation in the velocity space, we may take the small anisotropy (a small difference) of the mass density distribution in the space. A perturbation of the scaling factor
Table 1. Planck 2013 results. XXIII. Isotropy and statistics of the CMB (e.g., [18] [19] ).
will be caused by the perturbation of the mass density distribution in the space through the energy momentum tensor in the Einstein field equation, while a perturbation of the CMB temperature will be also caused by the perturbation of the scaling factor through the relation of α ( t ) T ( t ) = const.
On baryon acoustic oscillation (BAO) theory, in the popular idea, another indirect evidence for the accelerating expansion of the universe comes from some baryon acoustic oscillation (BAO) theories. However, the baryon acoustic oscillation (BAO) theories are actually the cosmic density wave theories and they are really the linear perturbation theories of cosmic dynamics, including the Einstein field equation. A relation of the cosmic peak density and matter with red-shift may be obtained by the dispersion relation in the linear perturbation theory.
On the other hand, the effect of the non-linear perturbation theory cannot be neglected in the very early universe, because the Einstein’s gravity is much stronger than the Newtonian gravity. So the linear perturbation theory of cosmic dynamics cannot get the conclusion of the accelerated expansion of the our universe. This is just of our idea.
Acknowledgements
This work was supported in part by the NSFC under grants 11965010, 11565020, and the Natural Science Foundation of Hainan Province under grants 2019RC239, 118MS071, 114012 and the Counterpart Foundation of Sanya under grant 2016 PT43, 2019PT76, the Special Foundation of Science and Technology Cooperation for Advanced Academy and Regional of Sanya under grant 2016YD28, the Scientific Research Starting Foundation for 515 Talented Project of Hainan Tropical Ocean University under grant RHDRC201701.
Cite this paper: Peng, Q. and Liu, J. (2021) A New Insight into the Observations and Analysis of Type Ia Supernovae. Journal of Applied Mathematics and Physics, 9, 1808-1820. doi: 10.4236/jamp.2021.97115.
References
[1] Luca, A. and Shinji, T. (2010) Dark Energy: Theory and Observation. Cambridge University Press, London.
https://ui.adsabs.harvard.edu/abs/2010deto.book.....A/abstract
[2] Riess, A.D., Filippenko, A.V., Challis, P., et al. (1998) Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. The Astronomical Journal, 116, 1009-1038.
https://iopscience.iop.org/article/10.1086/300499
https://doi.org/10.1086/300499
[3] Schmidt, B.P., Suntzeff, N.B., Phillips, M.M., et al. (1998) The High-Z Supernova Search: Measuring Cosmic Deceleration and Global Curvature of the Universe Using Type Ia Supernovae. The Astrophysical Journal, 507, 46-63.
https://iopscience.iop.org/article/10.1086/306308
https://doi.org/10.1086/306308
[4] Perlmutter, S., Aldering, G., Goldhaber, G., et al. (1999) Measurements of Ω and Λ from 42 High-Redshift Supernovae. The Astrophysical Journal, 517, 565-586.
https://iopscience.iop.org/article/10.1086/307221
https://doi.org/10.1086/307221
[5] Guy, J., Astier, P., Baumont, S., et al. (2007) SALT2: Using Distant Supernovae to Improve the Use of Type Ia Supernovae as Distance Indicators. A and A, 466, 11-21.
https://www.aanda.org/10.1051/0004-6361:20066930
https://doi.org/10.1051/0004-6361:20066930
[6] Amanullah, R., Lidman, C., Rubin, D., et al. (2010) Spectra and Hubble Space Telescope Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation. The Astrophysical Journal, 716, 712.
https://iopscience.iop.org/article/10.1088/0004-637X/716/1/712/pdf
https://doi.org/10.1088/0004-637X/716/1/712
[7] Phillips, M.M. (1993) The Absolute Magnitudes of Type IA Supernovae. Astrophysical Journal Letters, 413, L105.
https://ui.adsabs.harvard.edu/abs/1993ApJ...413L.105P/abstract
https://doi.org/10.1086/186970
[8] Kang, Y.J., Kim, Y.L., Lim, D., et al. (2016) Early-Type Host Galaxies of Type Ia Supernovae. I. Evidence for Downsizing. The Astrophysical Journal Supplement Series, 223, 7.
https://iopscience.iop.org/article/10.3847/0067-0049/223/1/7
https://doi.org/10.3847/0067-0049/223/1/7
[9] Kang, Y.J., Lee, Y.W., Kim, Y.L., et al. (2020) Early-Type Host Galaxies of Type Ia Supernovae. II. Evidence for Luminosity Evolution in Supernova Cosmology. The Astrophysical Journal, 889, 8.
https://iopscience.iop.org/article/10.3847/1538-4357/ab5afc
https://doi.org/10.3847/1538-4357/ab5afc
[10] Isern, J. (2010) Type Ia Supernova: Observations and Theory. Proceedings of the 11th Symposium on Nuclei in the Cosmos, Heidelberg, 19-23 July 2010, 66.
http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=100
[11] Ropke, F.K., Hillebrandt, W., Kasen, D., et al. (2010) Modeling the Diversity of Type Ia Supernova Explosions. Numerical Modeling of Space Plasma Flows: ASTRONUM-2009 ASP Conference Series, Vol. 429, 142-147.
http://articles.adsabs.harvard.edu/pdf/2010ASPC..429..142R
[12] Kasen, D. (2010) The Supernova Has Two Faces. Nature, 466, 37-38.
https://ui.adsabs.harvard.edu/link_gateway/2010Natur.466...37K/doi:10.1038/466037a
https://doi.org/10.1038/466037a
[13] Maeda, K., Benetti, S., Stritzinger, M., et al. (2010) An Asymmetric Explosion as the Origin of Spectral Evolution Diversity in Type Ia Supernovae. Nature, 466, 82-85.
https://doi.org/10.1038/nature09122
[14] Wang, X.F., Wang, L.F., Alexei, V.F., et al. (2013) Evidence for Two Distinct Populations of Type Ia Supernovae. Science, 340, 170-173.
https://science.sciencemag.org/content/340/6129/170
https://doi.org/10.1126/science.1231502
[15] Nielsen, J.T., Guffanti, A. and Sarkar, S. (2016) Marginal Evidence for Cosmic Acceleration from Type Ia Supernovae. Scientific Reports, 6, Article No. 35596.
https://ui.adsabs.harvard.edu/link_gateway/2016NatSR...635596N/doi:10.1038/srep35596
https://doi.org/10.1038/srep35596
[16] Weinberg, S. (2008) Cosmology. Oxford University Press, Oxford.
https://ui.adsabs.harvard.edu/abs/2008cosm.book.....W/abstract
[17] Weinberg, S. (1972) Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley-VCH, Hoboken, 688.
https://ui.adsabs.harvard.edu/abs/1972gcpa.book.....W/abstract
[18] Alves, J., Bertout, C., Combes, F., et al. (2014) Planck 2013 Results. Astronomy and Astrophysics, 571, E1.
https://www.aanda.org/articles/aa/pdf/2014/11/aa25195-14.pdf
[19] Alves, J., Combes, F., Ferrara, A., et al. (2016) Planck 2015 Results. Astronomy and Astrophysics, 594, E1.
https://www.aanda.org/articles/aa/pdf/2016/10/aa29543-16.pdf
Top
|
__label__pos
| 0.753135 |
Telomeres and Skin care
Telomerase Activation and Skin Rejuvenation
The human epidermis, or skin as it is commonly called, is the largest organ within the human body and it self-renews throughout a person’s lifetime. Laboratory researchers have discovered that the activation of telomerase has a primary role in maintaining the skin’s proper function as well as in augmenting its renewal. (Telomerase is an enzyme that repairs the tips of chromosomes which otherwise get shorter as humans age. The chromosome tips, called telomeres, make the skin look older as the telomeres approach the end of their life cycle. In fact, it only takes approximately 50 replications of the DNA within the body’s skin cells before the skin begins to show visible signs of aging. Without intervention, eventually the cell degrades to the point that the DNA inside it can no longer replicate. This is a primary cause of aged and wrinkled skin.
At the National Institutes of Health (NIH), researchers have reported in the Journal of Clinical Investigation the identification of a new means by which to “set a clock” for the programmed aging in healthy skin, as well as in other cells. Their research focuses upon the interaction between progerin and telomeres. Progerin is a toxic protein., a mutated type of the normal cell protein known as lamin A, which is found within the coding of the healthy LMNA gene. Lamin A maintains the health of a cell’s nucleus, which is where the DNA is kept. Progerin is one of the primary components of normal aging. The researchers discovered that short and/or dysfunctional telomeres can activate progerin production, which accelerates cellular damage related to age. As the chromosome tips naturally shorten, they make more and more progerin. According to Kan Cao, Ph.D., an assistant professor of cellular biology and as well as molecular genetics at the University of Maryland, this then disrupts the manner in which other alternative genes splice. It is currently thought that this combination of progerin production with telomere shortening and fraying are together responsible for the visible signs of cellular aging. Therefore this study is an insightful glimpse into the ways in which progerin might participate in the normal human aging process.
Words such as telomeres telomerase might sound a bit futuristic, but they are very much a part of the current scientific investigative platform, particularly where their affect on cellular aging is concerned. Telomerase is a ribonucleoprotein type enzyme with the power to extend the telomeres for the purpose of allowing the cells to continue to replicate. Cells that are provided a constant intake of telomerase produce very little progerin RNA and therefore age very little. Each time the telomeres are ready to split from the cell as it divides in two the telomerase fills the gap and re-lengthens the telomeres, which in turn sustains the cell’s life. At this time it appears the only way to lengthen telomeres is via telomerase arousal; try CA-98. In practical terms so far as appearance is concerned, this means that supplementation with CA-98 will support to tighten your skin, make your crows feet go away, and eliminate wrinkles, age spots and will also restore lost moisture and plumpness to the skin.
Please note: product statements have not been evaluated by the Food and Drug Administration or their equivalent organisation in any country. No product is intended to diagnose, treat, cure or prevent any disease.
One Response to Telomerase Activation and Skin Rejuvenation
1. Ami potts August 29, 2016 at 07:11 #
What is your view on Skincerity’s new product Nucerity Renew with Telomere protection?
Leave a Reply
|
__label__pos
| 0.595918 |
| Home | E-Submission | Sitemap | Contact Us |
top_img
Soonchunhyang Med Sci > Volume 27(2); 2021 > Article
Cho: Torsion of a Wandering Spleen Treated by Laparoscopic Surgery: A Case Report
ABSTRACT
The spleen is an organ located in the upper left portion of the abdomen. Wandering spleen is defined as the location of the spleen is the shift to other parts of the abdomen rather than the left upper quadrant. Wandering spleen is a rare clinical condition and can lead to hilar torsion and subsequent infarction requiring emergency surgery. The author presents a case of torsion of a wandering spleen in a 34-year-old female presenting with abdominal pain. The patients underwent emergent laparoscopic splenectomy. She had an uncomplicated postoperative course and recovered well.
INTRODUCTION
A wandering spleen is a rare variation, defined as the location of the spleen shifted to other parts of the abdomen rather than the left upper quadrant [1]. A normal spleen is attached to several ligaments that normally fix the spleen to the region below the left dome of the diaphragm. As a result of an absence or loosening of these splenic ligaments, the spleen could move to other parts of the abdomen and rotate by itself. This condition is very rare, with an incidence of less than 0.2% [2], and makes susceptible the spleen to acute torsion and infarction with splenic vein obstruction, leading to the formation of gastric varices [3]. Although many conservative treatment options have been reported for the treatment of wandering spleen, the most effective and safest option is accepted to be surgery [4].
Herein, we present a 34-year-old female with a wandering spleen with splenic torsion that was successfully treated by laparoscopic splenectomy.
CASE REPORT
A 34-year-old female was presented to the emergency department with a history of abdominal pain with nausea for 2 weeks. She reported 10 days of mild left upper quadrant abdominal pain, with a sudden increase in the intensity of pain for the last few days. The pain was intermittent and then turned to continuous and severe before the patient was admitted to the hospital. There was no history of fever or trauma. She underwent laparoscopic appendectomy for acute appendicitis 4 years ago. She gave birth to a child 2 months ago.
On arrival at the emergency department, the patient was afebrile (36.4°C), pulse rate of 98 beats/min, blood pressure of 120/85 mm Hg, respiratory rate of 20 breaths/min, and pulse oximetry of 100% on room air. She appeared in moderate distress from pain; however, no pallor, jaundice, finger clubbing, or lymphadenopathy was noticed. On abdominal physical examination, abdominal distension was noted. There was diffuse abdominal tenderness more prominent in the epigastric area, but no definite palpable mass was detected.
Laboratory parameters showed white blood cell counts of 6.83× 103/μL, hemoglobin level of 13.5 g/dL, platelet count of 193×103/μL, C-reactive protein level of 0.39 mg/L (reference, 0.0–0.5 mg/L), erythrocyte sedimentation rate of 6 mm/hr (reference, 0–27 mm/hr), serum amylase level of 102 U/L (reference, 28–100 U/L), and serum lipase level of 31 U/L (reference, 7–60 U/L). Liver function tests and electrolytes were normal values.
Urgent computed tomography (CT) scan of abdomen and pelvis with contrast was performed, which demonstrated findings consistent with splenomegaly and developed splenic infarction, with swirling of the splenic vascular pedicle (Fig. 1). She was taken emergently to the operating room for laparoscopic exploration with splenectomy. A total of three trocars were used in the operation. Intraoperatively, her spleen was noted as congested and twisted on the left abdomen (Fig. 2). Laparoscopic splenectomy was performed successfully, and the pathologic result of specimen was no diagnostic abnormalities. Her postoperative course was uneventful, and she was discharged on the 5th postoperative day. After 6 months of operation, she visited the outpatient clinic for routine examination. She was healthy and performed the usual activities of daily living. The incision scars 6 months after surgery had no specific features (Fig. 3).
The patient provided oral informed consent for the publication of clinical details and images.
DISCUSSION
The wandering spleen is a rare entity that was first described in 1854 by the Polish physician Jozef Doetl [5]. The spleen is normally located in the left upper quadrant of abdomen fixed by several ligaments. These ligaments are derived from the dorsal mesogastrium. Among the ligaments, the splenorenal ligament anchors the spleen to the left kidney. The gastrosplenic ligament and splenocolic ligament hold the spleen to the posterior aspect of the stomach and left colic flexure, respectively. The phrenicosplenic ligament anchors the spleen to the left diaphragm [6]. If these ligaments have not been developed or failed to their function, the spleen wanders into the abdominal cavity.
The etiology of wandering spleen includes congenital causes of the inadequate fusion between the abdominal wall and dorsal mesogastrium during embryogenesis and acquired causes such as trauma, ligament laxity, and pregnancy [7]. Wandering spleen by congenital causes is common in children between 3 months and 10 years of age. The acquired wandering spleen usually occurs in young women aged 20–40 years and is 10 times more frequent in multiparous women due to laxity of the abdominal wall and hormonal changes as a result of pregnancy [8].
When diagnosing patients suspected of wandering spleen with torsion, a contrast-enhanced CT scan is considered as the modality of choice [6,9]. CT findings could give clinicians various information about the size and position of the spleen, the appearance of the splenic pedicle, and the viability of the spleen. This information is essential for making a decision about performing the emergency operation.
In young and asymptomatic patients, preservation of the spleen is recommended; therefore, the splenopexy is considered a reasonable surgical option for these patients [10]. On the contrary, emergency splenectomy should be performed when there is obvious evidence of splenic infarction. Currently, minimally invasive surgeries such as laparoscopic approach for the splenopexy and splenectomy were widely performed owing to the advances in laparoscopic instruments, devices, and techniques. Therefore, in the current case, splenectomy was performed because the splenic infarction was revealed on the CT scan, and laparoscopic approach was decided to take advantage of minimally invasive surgery.
The torsion of wandering spleen is rare in patients presenting with acute abdominal pain and extremely difficult to detect early. Contrast enhanced CT scan is crucial in making an accurate and timely diagnosis. When torsion and infarction of wandering spleen are diagnosed, splenectomy is the treatment of choice. Laparoscopic splenectomy is feasible and less invasive than open splenectomy. We report a rare case of wandering spleen with splenic torsion requiring the emergency operation, and that was successfully treated by laparoscopic splenectomy.
CONFLICT OF INTEREST
CONFLICT OF INTEREST
No potential conflict of interest relevant to this article was reported.
Fig. 1
Computed tomography scan showed swirling of the splenic vascular pedicle (A, white arrow) and splenomegaly and infarction of spleen (B, white arrow). Coronal image (C, D)
sms-27-2-114f1.jpg
Fig. 2
Intraoperative image showing the torsion of splenic vascular pedicle and consequent several engorged veins (A) and enlarged spleen (B).
sms-27-2-114f2.jpg
Fig. 3
Incision scars after 6 months of operation. a)12-mm trocar site for camera, b)5-mm trocar site, c)12-mm trocar site, and d)previous incision scar for laparoscopic appendectomy (4 years ago).
sms-27-2-114f3.jpg
REFERENCES
1. Goksu M, Baykan AH. Torsion of wandering spleen: a case report. J Emerg Med 2020;58: e189-92.
crossref pmid
2. Viana C, Cristino H, Veiga C, Leao P. Splenic torsion, a challenging diagnosis: case report and review of literature. Int J Surg Case Rep 2018;44: 212-6.
crossref pmid pmc
3. Chue KM, Tan JKH, Pang NQ, Kow AWC. Laparoscopic splenectomy for a wandering spleen with resultant splenomegaly and gastric varices. ANZ J Surg 2020;90: 2124-5.
crossref pmid
4. Termos S, Redha A, Zbibo R, Alduwaisan A, AlKabbani M, Elyousif N, et al. Torsion of huge wandering accessory spleen: case report and review of literature. Int J Surg Case Rep 2017;38: 131-5.
crossref pmid pmc
5. Magowska A. Wandering spleen: a medical enigma, its natural history and rationalization. World J Surg 2013;37: 545-50.
crossref pmid
6. Reisner DC, Burgan CM. Wandering spleen: an overview. Curr Probl Diagn Radiol 2018;47: 68-70.
crossref pmid
7. Karapolat B, Korkmaz HAA, Kocak G. Torsion of the wandering spleen. Am J Med Sci 2019;357: e17-8.
crossref pmid
8. Ben Ely A, Seguier E, Lotan G, Strauss S, Gayer G. Familial wandering spleen: a first instance. J Pediatr Surg 2008;43: E23-5.
crossref
9. Parada Blazquez MJ, Rodriguez Vargas D, Garcia Ferrer M, Tinoco Gonzalez J, Vargas Serrano B. Torsion of wandering spleen: radiological findings. Emerg Radiol 2020;27: 555-60.
crossref pmid
10. Awan M, Gallego JL, Al Hamadi A, Vinod VC. Torsion of wandering spleen treated by laparoscopic splenopexy: a case report. Int J Surg Case Rep 2019;62: 58-61.
crossref pmid pmc
TOOLS
PDF Links PDF Links
PubReader PubReader
ePub Link ePub Link
XML Download XML Download
Full text via DOI Full text via DOI
Download Citation Download Citation
Supplement Supplement
Print
Share:
METRICS
0
Crossref
961
View
21
Download
Editorial Office
Soonchunhyang Medical Research Institute.
31 Soonchunhyang6-gil, Dongnam-gu, Cheonan, Choongnam, 31151, Korea
Tel : +82-41-570-2475 E-mail: [email protected]
About | Browse Articles | Current Issue | For Authors and Reviewers
Copyright © 2022 by Soonchunhyang Medical Research Institute. Developed in M2PI
|
__label__pos
| 0.803777 |
top of page
• Writer's pictureOren Zarif
How Frontal Lobe Damage Affects Emotion, Memory, and Behavior - Oren Zarif - Frontal Lobe Damage
Damage to the frontal lobe affects the functions of the brain that are responsible for emotion, memory, and behavior. Damage to this region impairs insight, and patients may experience anosognosia, a condition where the individual lacks awareness of any change in their abilities. Individuals with frontal lobe damage may exhibit changes in motivation, attention, and behavior that may make them feel disorganized, childlike, or lack social inhibition.
Oren Zarif pre stroke symptoms
Oren Zarif tbi medical
The resulting clinical picture of the frontal syndrome is complex and requires specialized knowledge of the causes of the symptoms. Because the frontal syndrome can be a symptom of a variety of diseases, it is important to distinguish it from other brain lesions in order to determine the most appropriate treatment. Moreover, the specific clinical features of a particular condition help to narrow down the cause of the syndrome. These symptoms often begin abruptly after a stroke, injury, or degenerative process, and gradually increase with the presence of tumors or other malformations.
Oren Zarif brain and spinal cord
Oren Zarif brain contusion
A face-to-face interview conducted by professionals can mask or exaggerate any frontal lobe impairment. This is particularly common when frontal lobe damage is the cause of delusional behavior. A standardized test may exaggerate or mask the severity of an impairment, and it does not reflect the reality of the person's actual functioning. For instance, a woman once convinced medical professionals that she could live alone after sustaining a brain injury.
Oren Zarif closed head injury
Oren Zarif massive stroke
Unfortunately, she was unable to prepare a meal or remember life-saving medications.
However, this finding is not conclusive because other brain regions may also be affected. Although the frontal lobe is not the only region affected by brain lesions, the voxel-based lesion-behavior mapping of the right anterior insula has been shown to be crucial to FAB performance. Furthermore, lesions in the right anterior insula are highly relevant for conceptualization, inhibitory control, and mental flexibility scores.
Oren Zarif posterior circulation stroke
Oren Zarif mini stroke symptoms in the elderly
As a result, people with frontal lobe damage may be more likely to display impulsive, rude, and aggressive behavior. They may also have trouble planning projects, performing steps correctly, and regulating emotions. In some cases, they may even exhibit symptoms of emotional incontinence. Furthermore, patients with frontal lobe damage may exhibit unusual sexual behavior or reduced sexual interest. A frontal lobe disorder may also cause motor plan disorders.
Oren Zarif post traumatic amnesia
Oren Zarif tia medical
Neuropsychological tests used to diagnose frontal lobe damage may involve performing tests to assess motor and language skills. Other tests, such as the Wisconsin Card Sorting Test, involve tracking the eye movements of individuals who have experienced frontal lobe damage. Many of these tests are simple and do not require advanced technology. Often, the severity of the condition is determined by the severity of the damage. This assessment is important for determining whether or not a person has frontal lobe damage.
Oren Zarif anoxic encephalopathy
Oren Zarif post tia symptoms
A study on the effect of frontal lobe damage on multi-attribute decision-making has also shown that people with frontal lobe damage are more impulsive. These behaviors are associated with reward-based decision-making and response disinhibition. Impulsive individuals tend to make rash decisions without self-control. People with frontal lobe damage are more likely to jump at an opportunity that rewards them.
Oren Zarif ischemic stroke treatment
Oren Zarif tbis
The frontal lobe is one of the last parts of the brain to develop. Although it is important for movement, it may not be fully developed until the mid-thirties. Researchers have mapped the areas of the frontal lobe that control movement. One such case is that of Phineas Gage, who suffered frontal lobe damage from an explosion while working on a railroad. The damage to the frontal lobe changed his personality dramatically.
Oren Zarif ischemic attack
Oren Zarif mechanical thrombectomy
Memory performance is an important aspect of mental flexibility, and damage to the frontal lobe may impact this function. According to Henry and Crawford, FAB mental flexibility is sensitive to left cortical and frontal lesions. Ramier and Hecaen suggested that there was a left hemisphere factor that mediated the performance of lexical verbal fluency. The effects of frontal lobe damage on memory were seen in two separate studies.
0 views0 comments
Comments
bottom of page
|
__label__pos
| 0.899056 |
Skip to content
Understanding the Life Cycle of Threads in Java: A Comprehensive Guide with Code Examples
As a Java developer, it‘s crucial to have a solid grasp of how threads work and the various states they go through during their life cycle. Threads allow you to write efficient, responsive applications by enabling concurrent execution of tasks. By understanding the life cycle of threads, you can effectively manage their creation, execution, and termination.
In this comprehensive guide, we‘ll dive deep into the life cycle of threads in Java. We‘ll explore each state in detail, provide code examples to illustrate how threads transition between states, and discuss best practices for managing threads in your Java applications. Whether you‘re a beginner or an experienced Java developer, this guide will give you the knowledge you need to master thread management.
What are Threads in Java?
Before we dive into the life cycle, let‘s first define what threads are in the context of Java. A thread is a lightweight unit of execution that represents an independent path of control within a program. Each thread has its own call stack and local variables, allowing it to execute concurrently with other threads.
The main advantage of using threads is that they enable parallelism and efficient utilization of system resources. By dividing a program into multiple threads, you can perform multiple tasks simultaneously, such as handling user input, updating the UI, and performing background processing. This results in more responsive and performant applications.
Java provides built-in support for creating and managing threads through the Thread class and the Runnable interface. You can create a new thread by either extending the Thread class or by implementing the Runnable interface.
The Life Cycle of a Java Thread
Now that we understand what threads are, let‘s explore the different states that a thread goes through during its life cycle. The life cycle of a Java thread consists of the following states:
1. New
2. Runnable
3. Running
4. Blocked/Waiting
5. Terminated
Let‘s take a closer look at each state and see how threads transition between them.
1. New State
When a thread is created using the new keyword, it enters the New state. At this point, the thread has not yet started executing and is not eligible for CPU time. It remains in the New state until the start() method is called on it.
Here‘s an example of creating a new thread:
public class MyThread extends Thread {
@Override
public void run() {
System.out.println("Thread is running");
}
}
MyThread thread = new MyThread();
In this example, we create a new thread by extending the Thread class and overriding the run() method. The thread is in the New state until we call the start() method.
2. Runnable State
Once the start() method is called on a thread, it enters the Runnable state. In this state, the thread is eligible to run and is waiting for CPU time to be allocated to it by the thread scheduler. The thread scheduler determines which thread gets to run based on factors such as thread priority and available system resources.
Here‘s an example of starting a thread:
MyThread thread = new MyThread();
thread.start();
By calling the start() method, we transition the thread from the New state to the Runnable state. The thread is now ready to be executed by the CPU.
3. Running State
When the thread scheduler allocates CPU time to a thread in the Runnable state, it enters the Running state. In this state, the thread is actively executing its task by running the code inside its run() method.
A thread can transition from the Running state back to the Runnable state in the following scenarios:
• The thread voluntarily yields control of the CPU by calling the yield() method.
• The thread is preempted by the thread scheduler to allow other threads to run.
• The thread is blocked or enters the waiting state.
Here‘s an example of a thread in the Running state:
public class MyThread extends Thread {
@Override
public void run() {
System.out.println("Thread is running");
// Perform some task
}
}
MyThread thread = new MyThread();
thread.start();
Once the start() method is called, the thread enters the Running state and executes the code inside the run() method.
4. Blocked/Waiting State
A thread can enter the Blocked or Waiting state in several situations:
• When a thread is waiting for a lock to be acquired, it enters the Blocked state. This happens when the thread tries to enter a synchronized block or method, but the lock is currently held by another thread.
• When a thread calls the wait() method on an object, it enters the Waiting state. The thread remains in this state until another thread calls the notify() or notifyAll() method on the same object.
• When a thread calls the sleep() or join() method, it enters the Timed Waiting state. The thread remains in this state for a specified period of time or until the joined thread completes its execution.
Here‘s an example of a thread entering the Blocked state:
public class SharedResource {
public synchronized void doSomething() {
// Critical section
}
}
public class MyThread extends Thread {
private SharedResource resource;
public MyThread(SharedResource resource) {
this.resource = resource;
}
@Override
public void run() {
resource.doSomething();
}
}
SharedResource resource = new SharedResource();
MyThread thread1 = new MyThread(resource);
MyThread thread2 = new MyThread(resource);
thread1.start();
thread2.start();
In this example, if thread1 acquires the lock on the SharedResource object and enters the doSomething() method, thread2 will be blocked until thread1 releases the lock.
5. Terminated State
A thread enters the Terminated state when it completes its execution or is explicitly terminated using the stop() method (which is deprecated and should be avoided). Once a thread is terminated, it cannot be restarted.
Here‘s an example of a thread entering the Terminated state:
public class MyThread extends Thread {
@Override
public void run() {
System.out.println("Thread is running");
// Perform some task
System.out.println("Thread is terminated");
}
}
MyThread thread = new MyThread();
thread.start();
When the run() method completes execution, the thread automatically enters the Terminated state.
Special Case States
In addition to the main states, there are a few special case states that a thread can enter:
• Timed Waiting: A thread enters this state when it calls the sleep() or wait() method with a specified timeout. The thread remains in this state until the specified time elapses or it is interrupted.
• Parked: A thread can be parked using the LockSupport.park() method. It remains parked until it is unparked using the LockSupport.unpark() method or interrupted.
• Interrupted: A thread can be interrupted by calling the interrupt() method on it. This sets the interrupted status of the thread, which can be checked using the isInterrupted() method.
Here‘s an example of a thread entering the Timed Waiting state:
public class MyThread extends Thread {
@Override
public void run() {
try {
Thread.sleep(5000); // Sleep for 5 seconds
System.out.println("Thread resumed");
} catch (InterruptedException e) {
System.out.println("Thread interrupted");
}
}
}
MyThread thread = new MyThread();
thread.start();
In this example, the thread enters the Timed Waiting state for 5 seconds when it calls the sleep() method. After the specified time elapses, the thread resumes execution.
Best Practices for Managing Threads
When working with threads in Java, there are some best practices to keep in mind:
1. Avoid using the stop() method to terminate threads, as it can lead to resource leaks and inconsistent state. Instead, use a flag or condition variable to signal the thread to stop gracefully.
2. Be cautious when using the suspend(), resume(), and destroy() methods, as they are deprecated and can cause deadlocks and other synchronization issues.
3. Use synchronization mechanisms like synchronized blocks and methods to ensure thread safety when accessing shared resources.
4. Be mindful of the potential for deadlocks when multiple threads are waiting for each other to release locks.
5. Use higher-level concurrency utilities like ExecutorService, CountDownLatch, and CyclicBarrier to manage threads and coordinate their execution.
6. Properly handle interruptions by checking the interrupted status and responding appropriately.
Debugging Thread Issues
When working with threads, you may encounter various issues such as deadlocks, race conditions, and thread starvation. Here are some tips for debugging thread-related issues:
1. Use logging statements to track the execution flow and identify potential issues.
2. Utilize thread dumps to gather information about the state of threads and identify deadlocks.
3. Use the jconsole or jvisualvm tools to monitor thread activity and detect resource contention.
4. Employ synchronization mechanisms correctly and avoid nested locks to prevent deadlocks.
5. Test your code thoroughly with different thread configurations and scenarios to identify race conditions and synchronization issues.
Conclusion
Understanding the life cycle of threads in Java is essential for writing efficient and robust concurrent applications. By knowing the different states a thread can be in and how it transitions between them, you can effectively manage thread creation, execution, and termination.
Remember to follow best practices when working with threads, such as avoiding deprecated methods, using synchronization appropriately, and handling interruptions gracefully. When debugging thread-related issues, utilize logging, thread dumps, and monitoring tools to identify and resolve problems.
With a solid grasp of the Java thread life cycle and best practices, you‘ll be well-equipped to write high-performance, concurrent applications that make the most of system resources.
Happy threading!
|
__label__pos
| 0.9995 |
There are numerous organizations within the academic, federal, and commercial sectors conducting large scale advanced research in the field of sustainable energy. This research spans several areas of focus across the sustainable energy spectrum. Most of the research is targeted at improving efficiency and increasing overall energy yields.[94] Multiple federally supported research organizations have focused on sustainable energy in recent years. Two of the most prominent of these labs are Sandia National Laboratories and the National Renewable Energy Laboratory (NREL), both of which are funded by the United States Department of Energy and supported by various corporate partners.[95] Sandia has a total budget of $2.4 billion [96] while NREL has a budget of $375 million.[97]
A report by the United States Geological Survey estimated the projected materials requirement in order to fulfill the US commitment to supplying 20% of its electricity from wind power by 2030. They did not address requirements for small turbines or offshore turbines since those were not widely deployed in 2008, when the study was created. They found that there are increases in common materials such as cast iron, steel and concrete that represent 2–3% of the material consumption in 2008. Between 110,000 and 115,000 metric tons of fiber glass would be required annually, equivalent to 14% of consumption in 2008. They did not see a high increase in demand for rare metals compared to available supply, however rare metals that are also being used for other technologies such as batteries which are increasing its global demand need to be taken into account. Land, whbich might not be considered a material, is an important resource in deploying wind technologies. Reaching the 2030 goal would require 50,000 square kilometers of onshore land area and 11,000 square kilometers of offshore. This is not considered a problem in the US due to its vast area and the ability to use land for farming and grazing. A greater limitation for the technology would be the variability and transmission infrastructure to areas of higher demand.[54]
As competition in the wind market increases, companies are seeking ways to draw greater efficiency from their designs. One of the predominant ways wind turbines have gained performance is by increasing rotor diameters, and thus blade length. Retrofitting current turbines with larger blades mitigates the need and risks associated with a system-level redesign. As the size of the blade increases, its tendency to deflect also increases. Thus, from a materials perspective, the stiffness-to-weight is of major importance. As the blades need to function over a 100 million load cycles over a period of 20–25 years, the fatigue life of the blade materials is also of utmost importance. By incorporating carbon fiber into parts of existing blade systems, manufacturers may increase the length of the blades without increasing their overall weight. For instance, the spar cap, a structural element of a turbine blade, commonly experiences high tensile loading, making it an ideal candidate to utilize the enhanced tensile properties of carbon fiber in comparison to glass fiber.[47] Higher stiffness and lower density translates to thinner, lighter blades offering equivalent performance. In a 10 (MW) turbine—which will become more common in offshore systems by 2021—blades may reach over 100 m in length and weigh up to 50 metric tons when fabricated out of glass fiber. A switch to carbon fiber in the structural spar of the blade yields weight savings of 20 to 30 percent, or approximately 15 metric tons.[48]
Wind-to-rotor efficiency (including rotor blade friction and drag) are among the factors impacting the final price of wind power.[16] Further inefficiencies, such as gearbox losses, generator and converter losses, reduce the power delivered by a wind turbine. To protect components from undue wear, extracted power is held constant above the rated operating speed as theoretical power increases at the cube of wind speed, further reducing theoretical efficiency. In 2001, commercial utility-connected turbines deliver 75% to 80% of the Betz limit of power extractable from the wind, at rated operating speed.[17][18][needs update]
2010 was a record year for green energy investments. According to a report from Bloomberg New Energy Finance, nearly US $243 billion was invested in wind farms, solar power, electric cars, and other alternative technologies worldwide, representing a 30 percent increase from 2009 and nearly five times the money invested in 2004. China had $51.1 billion investment in clean energy projects in 2010, by far the largest figure for any country.[155]
Several groups in various sectors are conducting research on Jatropha curcas, a poisonous shrub-like tree that produces seeds considered by many to be a viable source of biofuels feedstock oil.[117] Much of this research focuses on improving the overall per acre oil yield of Jatropha through advancements in genetics, soil science, and horticultural practices. SG Biofuels, a San Diego-based Jatropha developer, has used molecular breeding and biotechnology to produce elite hybrid seeds of Jatropha that show significant yield improvements over first generation varieties.[118] The Center for Sustainable Energy Farming (CfSEF) is a Los Angeles-based non-profit research organization dedicated to Jatropha research in the areas of plant science, agronomy, and horticulture. Successful exploration of these disciplines is projected to increase Jatropha farm production yields by 200-300% in the next ten years.[119]
The array of a photovoltaic power system, or PV system, produces direct current (DC) power which fluctuates with the sunlight's intensity. For practical use this usually requires conversion to certain desired voltages or alternating current (AC), through the use of inverters.[4] Multiple solar cells are connected inside modules. Modules are wired together to form arrays, then tied to an inverter, which produces power at the desired voltage, and for AC, the desired frequency/phase.[4]
×
|
__label__pos
| 0.92726 |
Take the 2-minute tour ×
Stack Overflow is a question and answer site for professional and enthusiast programmers. It's 100% free, no registration required.
I'm working on a Twitternetwork based on follower-relations in R. In this Network I want to determine the size of the largest cliques within everybody can read each others tweets in his or her timeline. Therefore I would need largest.cliques. But this function is ignoring directionality. I know its not integrated in the igraph package but is there a way to find cliques in directed networks, where every node is actively and passivly connected to each other?
share|improve this question
1 Answer 1
up vote 5 down vote accepted
For this problem, you can convert the directed instance of the problem to an undirected instance. Consider any two nodes, if there is only one directed edge between them, you know they cannot be part of a clique by your definition. Hence, we can dismiss any edge (u,v) if there is no corresponding (v,u). Otherwise, if we have both (v,u) and (u,v) it is equivalent to an undirected edge.
In other words, we create an undirected graph G' with edges between u and v if and only if there is are directed edges u -> v and v -> u. Finding a clique in G' should find you the equivalent clique in G.
share|improve this answer
Your Answer
discard
By posting your answer, you agree to the privacy policy and terms of service.
Not the answer you're looking for? Browse other questions tagged or ask your own question.
|
__label__pos
| 0.897571 |
DEV Community
Roberto Junior Amarante Calderón
Roberto Junior Amarante Calderón
Posted on • Updated on
React Native e2e tests and Automatic Deploys (Detox + Fastlane + CircleCI)
A little bit of context (skippable)
These past weeks I've been struggling trying to set up a pipeline where for every PR pointing to our staging branch, e2e tests run automatically, and for every PR that gets merged, test flight builds, and google internal beta builds are created. My experience has been... difficult, but it doesn't mean yours should too.
tl;dr; PAIN.
What do I need for this?
1. Circle CI's performance plan.
Since we are going to use macs for building our apps. If you only need android builds, you can easily achieve this with github actions, seethis project for an example and this amazing post.
2. Apple connect account & Google play console account.
This will be needed for automatic deployments(2nd part).
3. Patience
Trust me, you'll need it. CIs can smell fear.
Let's get this started
1. Add detox into your react native project.
Please, follow this guide using JEST step by step in order to have it correctly configured in your project. Here is anexample of a .detoxrc.json.
Once you can run e2e tests locally, you're ready to go for the next step.
2. Set up CircleCI.
If you don't have CircleCI, you can learn how to add it here.
Don't worry too much about the content on the config.yml, since we are going to completely modify it. :)
At this point, you should have a folder named .circleci/ with a config.yml file.
Let's make magic using orbs!
Add this to your /app/build.gradle since we are going to use the react-native-circleci-orb.
task downloadDependencies() {
description 'Download all dependencies to the Gradle cache'
doLast {
configurations.findAll().each { config ->
if (config.name.contains("minReactNative") && config.canBeResolved) {
print config.name
print '\n'
config.files
}
}
}
}
Enter fullscreen mode Exit fullscreen mode
Feeling lucky?
React native community example of how to use this orb is the following:
version: 2.1
orbs:
rn: react-native-community/[email protected]
# Custom jobs which are not part of the Orb
jobs:
checkout_code:
executor: rn/linux_js
steps:
- checkout
- persist_to_workspace:
root: .
paths: .
analyse_js:
executor: rn/linux_js
steps:
- attach_workspace:
at: .
- rn/yarn_install
- run:
name: Run ESLint
command: yarn eslint
- run:
name: Flow
command: yarn flow
- run:
name: Jest
command: yarn jest
workflows:
test:
jobs:
# Checkout the code and persist to the Workspace
# Note: This is a job that is defined above and not part of the Orb
- checkout_code
# Analyze the Javascript using ESLint, Flow, and Jest
# Note: This is a job that is defined above and not part of the Orb
- analyse_js:
requires:
- checkout_code
# Build the Android app in debug mode
- rn/android_build:
name: build_android_debug
project_path: "android"
build_type: debug
requires:
- analyse_js
# Build and test the Android app in release mode
# Note: We split these into separate jobs because we can build the Android app on a Linux machine and preserve the expensive MacOS executor minutes for when it's required
- rn/android_build:
name: build_android_release
project_path: "android"
build_type: release
requires:
- analyse_js
- rn/android_test:
detox_configuration: "android.emu.release"
requires:
- build_android_release
# Build the iOS app in release mode and do not run tests
- rn/ios_build:
name: build_ios_release
project_path: ios/Example.xcodeproj
device: "iPhone X"
build_configuration: Release
scheme: Example
requires:
- analyse_js
# Build and test the iOS app in release mode
- rn/ios_build_and_test:
project_path: "ios/Example.xcodeproj"
device: "iPhone X"
build_configuration: "Release"
scheme: "Example"
detox_configuration: "ios.sim.release"
requires:
- analyse_js
Enter fullscreen mode Exit fullscreen mode
But there is a catch, in my experience, it did not work. Here are the docs of every helper function on this orb.
What's next?
Welp let's go step by step and create something that works ;)
Orb
version: 2.1
orbs:
rn: react-native-community/[email protected]
Enter fullscreen mode Exit fullscreen mode
Note that we call it rn, this name can be whatever you want, and it's just used to specify when a job is coming from the orb. Ex. rn/yarn_install
Jobs
checkout_code
Check out the code and persist to the Workspace, needed in order to do stuff in the project root.
checkout_code:
executor:
name: rn/linux_js
node_version: "12"
steps:
- checkout
- persist_to_workspace:
paths: .
root: .
Enter fullscreen mode Exit fullscreen mode
analyse_js
Running jest test on Linux. Note how we use an executor from our orb and define the node_version version for our project.
analyse_js:
executor:
name: rn/linux_js
node_version: "12"
steps:
- attach_workspace:
at: .
- rn/yarn_install
- run:
command: yarn test
name: Run Tests
Enter fullscreen mode Exit fullscreen mode
Android e2e
In a perfect world, the example on the docs is all you need. But this is programming, specifically, React native that we're talking about, the example is the following:
- rn/android_build:
build_type: debug
name: build_android_debug
project_path: android
requires:
- analyse_js
- rn/android_build:
build_type: release
name: build_android_release
project_path: android
requires:
- analyse_js
Enter fullscreen mode Exit fullscreen mode
The main issue with this approach is that rn/android_build builds the app as a normal build and not as a detox build which can lead to weird issues and false-negative e2e tests.
So... yeah, we have to re-do this step manually, but feel free to try! If it works for you, shame me on Twitter!.
Please read the comments to understand what is going on here.
android_e2e_test:
# Using a mac (:
executor:
name: rn/macos
steps:
- attach_workspace:
at: .
- rn/setup_macos_executor:
homebrew_cache: true
node_version: "12"
- rn/yarn_install:
# basically because of this https://github.com/react-native-community/react-native-circleci-orb/issues/66
cache: false
- run:
# For my app and react native in general java8 is needed. The default version on this executor was default to java10 for some reason, so this kinda solve that issue.
# just installing java, android sdk, and needed tools.
command: >
java -version
brew tap adoptopenjdk/openjdk
brew install --cask adoptopenjdk/openjdk/adoptopenjdk8
java -version
export JAVA_HOME=$(/usr/libexec/java_home -v 1.8)
mkdir -p ~/.android && touch ~/.android/repositories.cfg
java -version
yes | sdkmanager "platform-tools" "tools" >/dev/null
yes | sdkmanager "platforms;android-29"
"system-images;android-29;default;x86_64" >/dev/null
yes | sdkmanager "emulator" --channel=3 >/dev/null
yes | sdkmanager "build-tools;29.0.2" >/dev/null
yes | sdkmanager --licenses >/dev/null
yes | sdkmanager --list
name: Install Android Emulator
shell: /bin/bash -e
- run:
command: |
adb start-server
adb devices
adb kill-server
ls -la ~/.android
name: ADB Start Stop
- run:
# Note we are using a pixel_xl as the test device, feel free to change it for one better fits your app
command: |
export JAVA_HOME=$(/usr/libexec/java_home -v 1.8)
avdmanager create avd --force --name Pixel_2_API_29 --package "system-images;android-29;default;x86_64" --tag default --device pixel_xl
name: Create Android Emulator
- run:
background: true
command: |
export JAVA_HOME=$(/usr/libexec/java_home -v 1.8)
$ANDROID_HOME/emulator/emulator @Pixel_2_API_29 -version
$ANDROID_HOME/emulator/emulator @Pixel_2_API_29 -cores 2 -gpu auto
-accel on -memory 2048 -no-audio -no-snapshot -no-boot-anim
-no-window -logcat *:W | grep -i
'ReactNative\|com.reactnativecommunity'
name: Start Android Emulator (background)
- run:
command: >
# export JAVA_HOME=$(/usr/libexec/java_home -v 1.8)
export BOOT=""
echo "Waiting for AVD to finish booting"
export PATH=$(dirname $(dirname $(command -v
android)))/platform-tools:$PATH
until [[ "$BOOT" =~ "1" ]]; do
sleep 5
export BOOT=$(adb -e shell getprop sys.boot_completed 2>&1)
done
sleep 15
adb shell settings put global window_animation_scale 0
adb shell settings put global transition_animation_scale 0
adb shell settings put global animator_duration_scale 0
echo "Android Virtual Device is now ready."
name: Wait for AVD to be ready
no_output_timeout: 5m
# Creates the detox build using the orb job
- rn/detox_build:
configuration: "android.emu.release"
# Tests the app, you can use rn/detox_test, but I wanted to take screenshots when test fails so I can have a better idea of why did they fail.
- run:
command: >-
detox test -c android.emu.release -l warn --headless
--take-screenshots failing --artifacts-location /tmp/detox_artifacts
name: Detox Test
# Save the screenshots as artifacts, you can see then in the artifact tab for the job in CircleCI
- store_artifacts:
path: /tmp/detox_artifacts
Enter fullscreen mode Exit fullscreen mode
Note that all of this can be achieved using the rn/linux_android executor.
iOS e2e
In a perfect world, the example on the docs is all you need. And it was for me... until it wasn't. Try the following, if that works for you, shame me on Twitter!.
# Build and test the iOS app in release mode
- rn/ios_build_and_test:
project_path: "ios/Example.xcodeproj"
device: "iPhone X"
build_configuration: "Release"
scheme: "Example"
detox_configuration: "ios.sim.release"
requires:
- analyse_js
Enter fullscreen mode Exit fullscreen mode
Fortunately, ios is better than android. Yeah, I said it... At least development wise. In order to recreate the ios_build_and_test all we need is:
# Build and test the iOS app in release mode
ios_e2e_test:
executor: rn/macos
steps:
- checkout
- attach_workspace:
at: .
- rn/setup_macos_executor:
homebrew_cache: true
node_version: "12"
- rn/ios_simulator_start:
device: "iPhone 11"
- rn/yarn_install:
# basically because of this https://github.com/react-native-community/react-native-circleci-orb/issues/66
cache: false
- rn/pod_install:
pod_install_directory: ios
# Yep, it doesn't really matter if you don't run detox build for ios, it works like a charm. But if you prefer, you can replace this step with a custom one.
- rn/ios_build:
build_configuration: "Release"
cache: false
derived_data_path: "ios/build"
device: "iPhone 11"
project_path: "ios/example.xcworkspace"
project_type: workspace
scheme: "example"
- run:
command: >-
detox test -c ios.sim.release -l warn --headless --take-screenshots
failing --artifacts-location /tmp/detox_artifacts
name: Detox Test
- store_artifacts:
path: /tmp/detox_artifacts
Enter fullscreen mode Exit fullscreen mode
Congratulations! You have e2e tests running in your app! Give yourself a pat in the back and go get a drink, because Fastlane is coming.
The hardest thing is doing the configurations for your project. Feel free to ask in the comments, but fastlane documentation should be enough to get you ready for the next steps.
Checkout these if you need a place to start:
Alt Text
Fastlane android
This is easier than what you already did. :) All we need is to install Fastlane on Linux and run our Fastlane lane.
fastlane_android_internal:
executor: rn/linux_android
steps:
- attach_workspace:
at: .
- rn/yarn_install
- run:
command: gem install bundler
name: Install bundler
- run:
command: gem install fastlane
name: Install Fastlane
# Note that my lane is name upload_to_googleplay replaced for yours
- run:
# can be fancier and use working_directory
command: cd android && fastlane upload_to_googleplay
name: Upload to google play via Fastlane
Enter fullscreen mode Exit fullscreen mode
Fastlane ios
I'm pretty sure adding Fastlane to ios was not an easy task. So... Congratulations Shinji! These are basically the same steps but for ios.
# submit app to apple connect testflight
fastlane_ios_testflight:
executor:
name: rn/macos
steps:
- attach_workspace:
at: .
- rn/yarn_install:
cache: false
- run:
working_directory: ios
command: pod install
- run:
command: gem install bundler
name: Install bundler
- run:
command: gem install fastlane
name: Install Fastlane
- run:
working_directory: ios
command: fastlane beta
name: Upload to Testflight via Fastlane
Enter fullscreen mode Exit fullscreen mode
So... tips for Fastlane.
• Fastlane Docs.
• 2fa for apple connect.
• CircleCI Docs.
• Use date for build numbers. (There are other ways to get incremental build numbers, if you want to try them, Can't recommend any since I haven't used any for the ci).
• android: in the build.gradle (int)(date.getTime() / 10000)
• ios: in fastlane/Fastfile build_number: DateTime.now.strftime("%Y%m%d%H%M")
One more thing
In order to make everything work, we need to create a workflow where we define the order of the steps.
So... here's a proposal:
workflows:
# name of the workflow
main:
jobs:
- checkout_code
# Do jest tests
- analyse_js:
requires:
- checkout_code
# Build and test the android app in release mode
- android_e2e_test:
requires:
- analyse_js
# Build and test the iOS app in release mode
- ios_e2e_test:
requires:
- analyse_js
# Release apps to stores for testing
- fastlane_android_internal:
# We only want to deploy to google play when things get merged into the main branch
filters:
branches:
only:
- main
# Note that e2e need to pass in order to release
requires:
- android_e2e_test
- fastlane_ios_testflight:
# We only want to deploy to google play when things get merged into the main branch
filters:
branches:
only:
- main
# Note that e2e need to pass in order to release
requires:
- ios_e2e_test
Enter fullscreen mode Exit fullscreen mode
If react native, detox, CircleCI and Fastlane decided you can rest today, you should see something like this in your pipeline.
Alt Text
Discussion (9)
Collapse
kierano547 profile image
Kieran Osgood • Edited on
When you chose the macos executor instead of the linux_android for the android e2e tests: "Note that all of this can be achieved using the rn/linux_android executor." was there any reason for that choice? The macos minutes are more expensive AFAIK, and you chose to mention both would work, so just curious if it was more difficult to do or something?
p.s. I found that the rn/ios_build_and_test command worked just fine when used like this:
- rn/ios_build_and_test:
yarn_cache: false
xcodebuild_cache: false
homebrew_cache: false
project_type: "workspace"
project_path: "ios/punchline.xcworkspace"
device: "iPhone 11"
build_configuration: "Release"
scheme: "punchline"
detox_configuration: "ios.sim.release"
requires:
- checkout_code
- analyse_js
- update_homebrew
Enter fullscreen mode Exit fullscreen mode
Currently trying to decide how I can most efficiently configure the e2e tests on release, and ideally use the same build artifacts from that to release through fastlane or something
Collapse
kyonru profile image
Roberto Junior Amarante Calderón Author
In the beginning, I tried with the linux_executor. I don't remember exactly why I changed, I think it was related to all the detox dependencies and setting up the environment. (But later other issues came up, so I had to do all of that... At this point, it should be that hard to change the executor, but idk since I need to try it again).
Thanks for the suggestion! I'll make an update with your suggestion with iOS.
Collapse
kyonru profile image
Roberto Junior Amarante Calderón Author
That definitely would save some time. I'm not sure of the implications of publishing the detox build for android. But It would definitely help for ios.
Collapse
kyonru profile image
Roberto Junior Amarante Calderón Author
Yeah.... Mayor update, you can get the same result with:
version: 2.1
orbs:
rn: react-native-community/[email protected]
jobs:
checkout_code:
executor:
name: rn/linux_js
node_version: '12'
steps:
- checkout
- persist_to_workspace:
paths: .
root: .
analyse_js:
executor:
name: rn/linux_js
node_version: '12'
steps:
- attach_workspace:
at: .
- rn/yarn_install
- run:
command: yarn lint
name: Run Linter
- run:
command: yarn jest
name: Run Tests
# submit app to playstore for internal test
fastlane_android_internal:
executor: rn/linux_android
steps:
- attach_workspace:
at: .
- rn/yarn_install
- run:
command: bash create_staging_env_files.sh
name: Create env files
- run:
command: cat .env
name: Print env files
- run:
command: gem install bundler
name: Install bundler
- run:
command: gem install fastlane
name: Install Fastlane
- run:
command: cd android && fastlane googleplay
name: Upload to google play via Fastlane
# submit app to apple connect testflight
fastlane_ios_testflight:
executor:
name: rn/macos
steps:
- attach_workspace:
at: .
- rn/yarn_install:
cache: false
- run:
command: bash create_staging_env_files.sh
name: Create env files
- run:
command: cat .env
name: Print env files
- run:
working_directory: ios
command: pod install
- run:
command: gem install bundler
name: Install bundler
- run:
command: gem install fastlane
name: Install Fastlane
- run:
command:
git config --global --add url."[email protected]:".insteadOf
"https://github.com/"
name: Use SSH
- run:
working_directory: ios
command: fastlane beta
env:
MATCH_GIT_BASIC_AUTHORIZATION: $MATCH_GIT_BASIC_AUTHORIZATION
name: Upload to Testflight via Fastlane
# submit app to playstore for beta, ready to release to prod
fastlane_android_beta:
executor: rn/linux_android
steps:
- attach_workspace:
at: .
- rn/yarn_install
- run:
command: bash create_prod_env_files.sh
name: Create env files
- run:
command: cat .env
name: Print env files
- run:
command: gem install bundler
name: Install bundler
- run:
command: gem install fastlane
name: Install Fastlane
- run:
command: cd android && fastlane googleplaymanualprod
name: Upload to google play via Fastlane
# submit app to apple connect ready for review
fastlane_ios_app_store:
executor:
name: rn/macos
steps:
- attach_workspace:
at: .
- rn/yarn_install:
cache: false
- run:
command: bash create_prod_env_files.sh
name: Create env files
- run:
command: cat .env
name: Print env files
- run:
working_directory: ios
command: pod install
- run:
command: gem install bundler
name: Install bundler
- run:
command: gem install fastlane
name: Install Fastlane
- run:
command:
git config --global --add url."[email protected]:".insteadOf
"https://github.com/"
name: Use SSH
- run:
working_directory: ios
command: fastlane prod
env:
MATCH_GIT_BASIC_AUTHORIZATION: $MATCH_GIT_BASIC_AUTHORIZATION
SENTRY_AUTH_TOKEN: $SENTRY_AUTH_TOKEN
ASCAPI_KEY_ID: $ASCAPI_KEY_ID
ASCAPI_ISSUER_ID: $ASCAPI_ISSUER_ID
ASCAPI_KEY_CONTENT: $ASCAPI_KEY_CONTENT
name: Upload to Testflight via Fastlane
workflows:
test:
jobs:
- checkout_code
- analyse_js:
requires:
- checkout_code
- rn/android_build:
name: build_android_release
project_path: 'android'
build_type: release
on_after_initialize: |
bash create_env_files.sh
requires:
- analyse_js
- rn/android_test:
name: android_e2e_test
detox_configuration:
'android.emu.release --take-screenshots failing --artifacts-location
/tmp/detox_artifacts --cleanup --record-logs failing'
device_name: Pixel_2_API_29
platform_version: android-29
build_tools_version: '29.0.3'
yarn_cache: false
requires:
- build_android_release
detox_loglevel: 'verbose'
store_artifact_path: '/tmp/detox_artifacts'
should_on_after_initialize: true
on_after_initialize: |
HOMEBREW_NO_AUTO_UPDATE=1 brew tap adoptopenjdk/openjdk
HOMEBREW_NO_AUTO_UPDATE=1 brew install --cask adoptopenjdk/openjdk/adoptopenjdk8
echo 'export JAVA_HOME=$(/usr/libexec/java_home -v 1.8)' >> $BASH_ENV
# Build and test the iOS app in release mode
- rn/ios_build_and_test:
name: ios_e2e_test
checkout: true
project_path: 'ios/mobileApp.xcworkspace'
project_type: workspace
device: 'iPhone 11'
pod_install_directory: ios
on_after_initialize: |
bash create_env_files.sh
build_configuration: 'Release'
scheme: 'appScheme'
detox_configuration:
'ios.sim.release --take-screenshots failing --artifacts-location
/tmp/detox_artifacts --cleanup --record-logs failing'
detox_loglevel: 'verbose'
store_artifact_path: '/tmp/detox_artifacts'
yarn_cache: false
xcodebuild_cache: false
requires:
- analyse_js
# Release apps to stores for testing
- fastlane_android_internal:
filters:
branches:
only:
- staging
requires:
- android_e2e_test
- fastlane_ios_testflight:
filters:
branches:
only:
- staging
requires:
- ios_e2e_test
# Release apps to stores for release [manual]
- fastlane_android_beta:
filters:
branches:
only:
- main
requires:
- android_e2e_test
- fastlane_ios_app_store:
filters:
branches:
only:
- main
requires:
- ios_e2e_test
Enter fullscreen mode Exit fullscreen mode
Collapse
kyonru profile image
Roberto Junior Amarante Calderón Author
I'll make sure to update this post when I get some time ToT
Collapse
acro5piano profile image
Kay Gosho
Thanks for the great article! Do you have any experience in GitHub actions? I tried it before and not works as well as CircleCI.
Collapse
kyonru profile image
Roberto Junior Amarante Calderón Author
Sadly I have just use github actions to test detox, but I'm planning on doing this workflow sooner than later for this app in github actions. github.com/Kyonru/just-a-review-app
Collapse
acro5piano profile image
Kay Gosho • Edited on
Thanks! I think maybe there is a problem running iOS build on GitHub actions, whereas CircleCI works much better thanks to the ORB. Looking forward to the GitHub Actions version!
Collapse
blashadow_62 profile image
Luis
sounds good to automate some react-native dev-ops things, also reading the documentation from react-native-circleci-orb really makes sure you know how hard is what you're about to do.
|
__label__pos
| 0.994585 |
A General Introduction to Medication-Induced Movement Disorders
A General Introduction to Medication-Induced Movement Disorders
For every time we turn on the television, we often land on a commercial involving joyous people while promoting a certain medication and its side effects. In addition, we’re always notified about the side effects such as heart failure, seizures, or death that might potentially happen. As bothersome and even morbid as it may be to hear or think about, side effects like this can happen when you’re on prescribed medications. This is known as medication-induced movement disorders.
According to the DSM-5, the definition of medication-induced movement disorders is included because “the management by medication of mental disorders or other medical conditions and the differential diagnosis of mental disorders (e.g., anxiety disorder versus neuroleptic-induced akathisia; malignant catatonia versus neuroleptic malignant syndrome)” (American Psychiatric Association, 2013 p. 709) According to a study conducted by scholars Stephen R Duma, John Morris, and Victor SC Fung, one of the most common culprits that causes movement disorders is antipsychotics and antiemetics (Duma, Fung, & Morris, 2019). Therapeutic and illicit drugs can potentially cause neurological adverse effects and movement disorders. However, if there is early intervention, there is a probability that these effects can be reversed or prevented.
The DSM-5 has divided the definition of medication-induced movement disorders into multiple sections as it has a myriad of effects on an individual. Furthermore, it is important to emphasize that the following disorders are not mental disorders, but instead are disorders that impact the individual physically. The following disorders include medication-induced acute dystonia, medication-induced acute akathisia, tardive disorders including dyskinesia, dystonia, and akathisia. While there are a few notable differences in each movement disorder, generally symptoms include irritability, restlessness, excessive and sporadic movements, and the inability to sit or stand still (American Psychiatric Association, 2013 p. 711).
Acute drug-induced movement disorders are one of the common medication-induced movement disorders. It is described to “occur within minutes to days of drug ingestion. They include akathisia, tremor, neuroleptic malignant syndrome, serotonin syndrome, parkinsonism-hyperpyrexia disorder and acute dystonic reactions” (Duma, Fung, & Morris, 2019). According to the DSM-5, medication-induced acute dystonia causes “Abnormal and prolonged contraction of the muscles of the eyes (oculogyric crisis), head, neck (torticollis or retrocollis), limbs, or trunk developing within a few days of starting or raising the dosage of a medication (such as a neuroleptic) or after reducing the dosage of a medication used to treat extrapyramidal symptoms” (American Psychiatric Association, 2013).
Akathisia is actually a common yet an identifiably difficult medication-induced movement disorder that is the result of experiencing side effects from prescribed antipsychotic or antidepressant medication.When it comes to acute akathisia, an individual would display what the DSM-5 describes as “complaints of restlessness, often accompanied by observed excessive movements (e.g., fidgety movements of the legs, rocking from foot to foot, pacing, inability to sit or stand still), developing within a few weeks of starting or raising the dosage of a medication (such as a neuroleptic) or after reducing the dosage of a medication used to treat extrapyramidal symptoms” (American Psychiatric Association, 2013).
Tardive dyskinesia disorder blocks the brain chemical known as dopamine and can cause visible side effects in your limbs. This includes involuntary thrusting, kicking, waving your arms, and tapping your foot. Studies have also shown that a person who is on antipsychotic medication is more likely to experience these symptoms if they are middle aged. The DSM-5 explains that tardive dystonia and akathisia disorders “are distinguished by their late emergence in the course of treatment and their potential persistence for months to years, even in the face of neuroleptic discontinuation or dosage reduction” (American Psychiatric Association, 2013).
Having perpetual tremors would seem exhausting and would get in the way of everyday tasks naturally. As far as treating any of the following disorders would go, it would involve withdrawal from the drugs and adjusting the dosage or being weaned off of it completely. However, there isn’t a specific treatment that exists for movement disorders that were a result from illicit drug use.
References
American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). https://doi.org/10.1176/appi.books.9780890425596
Duma, S., & Fung, V. (2019, April). Drug-induced movement disorders. Retrieved March 09, 2021, from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6478951/
Leave a Reply
Your email address will not be published. Required fields are marked *
[ Back To Top ]
|
__label__pos
| 0.509009 |
Unsafe Application State Restoration (iOS)
Unsafe Application State Restoration (iOS)
What Does Unsafe Application State Restoration Actually Mean?
Despite the fancy title, it essentially means that a mobile application saves the state of a view location that is only presented to an authenticated user, or that contains sensitive data. Within the event of the application being unexpectedly terminated, the state is restored and loaded back into the UI without first validating or re-authenticating the current user.
Conceptually this happens all the time within mobile applications. A developer focused on making things easy and enjoyable for the user, will implement this type of functionality, so if by chance the application closes, the user will be brought back into the same state they left off at.
This functionality makes sense, and is a nice addition to many of the applications we use day in and day out, but what if this existed in your mobile banking application, or on a shared device in a hospital for an application that stored and operated on PHI? If an attacker has direct access to an unlocked device with these applications, he can potentially re-open them after they have been closed, and be presented with very critical data.
So hopefully we can start understanding what this vulnerability actually means and its potential impact.
Preservation and Restoration
For this specific scenario we will explore the technical details surrounding the vulnerability paired with Apple’s UIKit Framework. The UIKit Framework has a state restoration system that allows for the preservation and restoration for the application’s view controller objects. UIKit allows the developer to choose which view controllers and views he wants to ultimately preserve and restore. To do this, a restoration identifier marks a restorable object, which is a string that identifies the view or the view controller to UIKit and the application.
During preservation the application will:
• Tell UIKit it supports state preservation
• Tell UIKit which view controllers to preserve
• Encode all data for the targeted objects
Preservation
During restoration the application will:
• Tell UIKit it supports state restoration
• Provide the restorable objects
• Decode the state for all relevant objects and return
Restoration
Class Dump Inspection
Methods
To figure out whether or not the application supports preservation and restoration, we can take a look at the output from class-dump-z.
We can see within the Application’s Delegate the method ‘application:willEncodeRestorableStateWithCoder:‘ – this is used to encode the state information for the targeted object. You can also see the corresponding method for decoding – ‘application didDecodeRestorableStateWithCoder:‘ – which is called when the application finishes its restoration of the decoded objects.
Unsafe Application State Restoration, So What Is The Risk?
The problem is rooted purely in context, meaning it is all based off what the application’s overall business impact will be (i.e. Healthcare). The biggest recommendation I have so far is there really isn’t a good reason to mark view objects for preservation that exist in a post-authenticated world. Even if it is solely meant to provide a better user experience, it still is inherently dangerous.
If by chance a developer still chooses to implement this risky functionality, the user still needs to be forced to identify themselves and authenticate back into the application. It would make the most sense that this process begins before initializing and decoding object state.
|
__label__pos
| 0.713086 |
Vaatate praegu abisisu järgmise versiooni jaoks::
Overview of Storage in AEM 6
One of the most important changes in AEM 6 are the innovations at the repository level.
Currently, there are two node storage implementations available in AEM6: Tar storage, and MongoDB storage.
Tar Storage
Running a freshly installed AEM instance with Tar Storage
Hoiatus.
The PID for the Segment node store has changed from org.apache.jackrabbit.oak.plugins.segment.SegmentNodeStoreService in previous versions of AEM 6 to org.apache.jackrabbit.oak.segment.SegmentNodeStoreService in AEM 6.3. Make sure you make the necessary configuration adjustments to reflect this change.
By default, AEM 6 uses the Tar storage to store nodes and binaries, using the default configuration options. To manually configured its storage settings, follow the below procedure:
1. Download the AEM 6 quickstart jar and place it in a new folder.
2. Unpack AEM by running:
java –jar cq-quickstart-6.jar -unpack
3. Create a folder named crx-quickstart\install in the installation directory.
4. Create a file called org.apache.jackrabbit.oak.segment.SegmentNodeStoreService.cfg in the newly created folder.
5. Edit the file and set the configuration options. The following options are available for Segment Node Store, which is the basis of AEM's Tar storage implementation:
• repository.home: Path to repository home under which various repository related data is stored. By default segment files would be stored under the crx-quickstart/segmentstore directory.
• tarmk.size: Maximum size of a segment in MB. The default is 256MB.
6. Start AEM.
Mongo Storage
Running a freshly installed AEM instance with Mongo Storage
AEM 6 can be configured to run with MongoDB storage by following the below procedure:
1. Download the AEM 6 quickstart jar and place it into a new folder.
2. Unpack AEM by running the following command:
java –jar cq-quickstart-6.jar -unpack
3. Make sure that MongoDB is installed and an instance of mongod is running. For more info, see Installing MongoDB.
4. Create a folder named crx-quickstart\install in the installation directory.
5. Configure the node store by creating a configuration file with the name of the configuration you want to use in the crx-quickstart\install directory.
The Document Node Store (which is the basis for AEM's MongoDB storage implementation) uses a file called org.apache.jackrabbit.oak.plugins.document.DocumentNodeStoreService.cfg
6. Edit the file and set your configuration options. The following options are available:
• mongouri: The MongoURI required to connect to Mongo Database. The default is mongodb://localhost:27017
• db: Name of the Mongo database. By default new AEM 6 installations use aem-author as the database name.
• cache: The cache size in MB. This is distributed among various caches used in DocumentNodeStore. The default is 256
• changesSize: Size in MB of capped collection used in Mongo for caching the diff output. The default is 256
• customBlobStore: Boolean value indicating that a custom data store will be used. The default is false.
7. Create a configuration file with the PID of the data store you wish to use and edit the file in order to set the configuration options. For more info, please see Configuring Node Stores and Data Stores.
8. Start the AEM 6 jar with a MongoDB storage backend by running:
java -jar cq-quickstart-6.jar -r crx3,crx3mongo
Where -r is the backend runmode. In this example, it will start with MongoDB support.
Maintaining the Repository
Each update to the repository creates a new content revision. As a result, with each update the size of the repository grows. To avoid uncontrolled repository growth, old revisions need to be be cleaned up to free disk resources. This maintenance functionality is called Revision Cleanup. The Revision Cleanup mechanism will reclaim disk space by removing obsolete data from the repository. For further details about Revision Cleanup, read the Revision Cleanup page.
|
__label__pos
| 0.735471 |
Risk Factor Hypertension Aha
|
However, quitting cold turkey can be dangerous as well, depending on the symptoms. “if you do consume alcohol in any form, it is critical to drink only in moderation — one to two drinks a day,” said dr. Symptoms of aortic infection may vary depending on the type of infection and its location. refined salt contains large amounts of sodium. Well it is already legal everywhere in the us except for indiana which banned one of the alkaloids extracted from the plant but did not mention the plant itself. Foods high in vitamin e include wheat germ, almonds, sunflower seeds and dark leafy greens. However, your healthcare provider will need to determine an appropriate therapy based on your current condition with your past history of tia. Men who routinely skipped breakfast had a 27 percent higher risk of heart attack or death by heart disease, compared to those ate breakfast. Heart palpitations often cease as soon as women begin taking progesterone cream or estrogen, stop caffeine, and also normalize their blood sugar and insulin levels through a change of diet. Do you mean what do you do to be able to take riding level 3.
Pain medications are off-limits because of associated bleeding risks and. Get active: regular exercise helps condition muscles to use oxygen more efficiently. Phosphorous balances and metabolizes other vitamins and minerals including vitamin d which is so important to ckd patients. Using the scan to make this decision is not correct. “continue with the sexual practice with which you are most comfortable. Research for the ex vivo kidney perfusion project was supported by the canadian national transplant research program (cntrp), a national research network designed to increase organ and tissue donation in canada and enhance the survival and quality of life of canadians who receive transplants. Blood is watery and cholesterol is fatty.
While the elite field spent the night before the race at luxury hotels, he slept in a camper van parked on his cousinâs drive to save money. Eating pineapples regularly can help prevent utis in the future as well. Back pain, which is a common reason that people visit their health care practitioner, can be debilitating. • bend elbows and bring hands close to the shoulder with palms placed on the floor. It is usually worn for one to three days and sometimes up to a week. this med should be taken within 15 minutes of the scheduled time. I was diagnosed with hypertension at 22 years of age.
Signs of chronic liver disease may include:. Defect of the immune system. The board of veterans appeal is the board of law judges that reside in washington dc. In the study i just talked about, those exposed consistently to loud noises at work and during leisure time reported higher rates of tinnitus. Nigel has also included recipes in this book. A reason why age should be a factor in the dosage.
These are all signs of high blood pressure. Normally, when an individual stands up, the blood vessels constrict to maintain normal blood pressure in the new position. However, if you think that you still need help, check this recipe. Preventive services task force found adequate evidence that low-dose aspirin as preventive medication does not increase the risk for placental abruption, postpartum hemorrhage, or fetal intracranial bleeding. " she also swears by her purple uv lights and keeps them on and sits by them during the day. but the trade-off is that you will not be conveniently located near any big malls or hospitals. Risk for impaired skin integrity r/t vitamin deficiency. New research suggests that sprue-like enteropathy side effects of benicar, which can cause users to suffer severe abdominal pain and chronic diarrhea, do not appear to be a risk with other blood pressure drugs that are part of the same class of medications, known as angiotensin receptor blockers (arbs).
Long-term prophylactic nitrate therapy is the development of tolerance (both to. Young living essential oils for high blood pressure. One of the main factors affecting the risk of hypertension is people’s lifestyle, for which appropriate changes in lifestyle-related factors creating cardiovascular risks need to be developed through new and effective approaches in long-term. Diameter of a slim pencil, and the blood flow through such large. Gravitypulls gasmolecules in the atmosphere towards the earth'ssurface causing airpressure. Blood pressure increases transiently while smoking a cigarette or when exposed to passive smoking and returns to the initial levels 20 minutes after. "to date, no clinical studies have been conducted that demonstrate a patient-oriented benefit from these immunomodulation properties". Pressure and heart rate, then ventricular.
The greatest risk for people with polycystic kidney disease is. High blood pressure (hypertension) occurs when that force is too high and begins harming the heart and blood vessels. A 94-year-old ill-appearing patient presenting with epigastric pain, vomiting, and probable dehydration should be considered a high-risk esi level-2 patient. This structure is located just beneath the iris. A research finding suggests that hibiscus tea slows down the growth of cancer cells through a mechanism called apoptosis. You can can take lemon or orange juice twice a day or also can take a vitamin c capsule. These monitors even can check for episodes while the patient sleeps, when many will experience severe hypoglycemia but not know it. B correspond to stage 3 in the above table.
When new growth begins, the first hairs maybe soft and barely visible. Massaging your scalp gently with your fingers every day to stimulate blood circulation and the delivery of oxygen and nutrients to your hair follicles. As more research is done, there will likely be new hangover treatments developed. Increased when melatonin is added to nifedipine, a calcium channel blocker:. Can develop” said william erwin, md ofcatawba valley pulmonology. The various forms of sulphur compounds found inside each clove are responsible for the unique smell of the garlic.
Can i try not taking medication. Don’t make your partner abstain for more than seven days in a row. Enhancement of public awareness about the risk factors hypertension mnemonic pertaining to hypertension is also an excellent strategy towards alleviating the high prevalence rates of hypertension among african americans. Pain in the abdominal region can also be caused due to presence of worms in the digestive tract, constipation, indigestion, wind and distention, gastritis, food poisoning or food allergies ,acidity and diarrhea. And with the announcement, lanza says, he felt the weight of the es-cell field fall on his shoulders. Those most at risk of the disease are blacks and people of. As noted, it is extremely important to.
Prepare yourself a soup specially targeted for people having low blood pressure. 4-6 compared with 24-hour ambulatory blood pressure monitoring, home monitoring is less expensive, much more widely available and provides information about the day-today variability of blood pressure. White coat hypertension and the new blood pressure guidelines. Meantime, you should keep hydrated, drink lots of fluids and stay off solids until you get to a doctor. Checking your blood sugar, also called blood glucose, is an important part of diabetes care. But combine them with one or more other health problems — such as high blood pressure or high blood sugar — and these health risks can create a perfect storm known as metabolic syndrome. Elective surgeries are incredibly successful: if doctors monitor an aneurysm and its growth and repair the aorta when necessary, death from the operation or its complications is less than one per cent. It’s so common now, in fact, that it’s difficult to believe that, at one stage, metallic aluminium was so hard to make that having aluminium plates was a symbol of wealth. However, this may not be the case in lesser lung resections, with a restrictive therapy threatening to cause acute kidney injury. 01) were also independently associated with preeclampsia.
The study authors refused claiming proprietary ownership and that this was only the first in a series of papers. Often times, even when we are doing everything we can to be healthy, we still fall short on our daily intake of vitamins, supplements and minerals. Adjust your fluid intake next time, if necessary. However a number of definite risk factors have been identified. If you’re not busy dealing with acne, you can still benefit from beetroot in order to achieve that youthful glow. To efficiently control hypertension, it is important to exercise and eat healthier along with taking the prescribed medications. For example, did anyone find their blood pressure got worse and they needed more antihypertensive tablets. Functional relations of the proximal components of the portal system: a preliminary report. 8 if the problem is a tension pneumothorax, with air leaking into the pleural space through a tear in the lung, you may also hear ipsilateral crackles or wheezes.
Note: everyone is different and maybe not all will able to completely cure their blood pressure without medications (this is kind of a legal disclaimer). Time: a kap survey takes between six and twelve weeks. Anyhow, i took it 8 hours after we had sex and i had stomach pains and cramps until july 17. Hypertension is sadly becoming increasing prevalent in younger people and dr lobo is seeing more and more teenagers in his practice as time goes by. Make a note of his answer, as it may be useful to have this information. Pulmonary arterial hypertension (pah) is an elevation in blood pressure in the arteries leading from the heart to the lungs.
Public health interventions should aim to reduce sodium intake and simultaneously increase potassium intake through foods. all they did was give me pain pills to ease them. Subdural hematomas often occur in association with damage to the veins overlying the brain which rupture and leak into the space between the two outermost membranes (meninges) surrounding the brain. Taken together, rask-madsen says, the findings of the two studies suggest that “when we look at new ways to prevent atherosclerosis, we should focus on improving insulin signaling in vascular cells rather than blocking the action of insulin in these cells. ► previous cardiac arrest or sustained ventricular tachycardia,. To flow through the vessels, which reduces blood pressure. The expiry date refers to the last day of the month. Objectives to study the association between lifestyle risk factors and chronic hypertension by history of hypertensive disorders of pregnancy (hdp: gestational hypertension and pre-eclampsia) and investigate the extent to which these risk factors modify the association between hdp and chronic hypertension.
Careful planning of lessons is essential for experienced as well as beginner teachers. Dental cavities are so common that people may not take them seriously. Regardless of how the issue is approached, it’s important to remember that the change in risk with increasing glucose intolerance is gradual, not abrupt. It performs many functions that help control blood pressure, such as regulating blood vessel constriction, inflammation, anti-oxidant activity, and the ability of plaque to form within the arteries. If you can learn to do this the panic will literally fizzle in minutes. It is a known fact that many fruits have large water content. D) be sure their are screens in all windows. "many researchers think that pregnancy acts as a [heart disease] stress test and that it helps to identify women who are predisposed to developing high blood pressure and other cardiovascular risk factors," explained study author jennifer stuart.
Since finding out i have nmh i take a salt pill daily along with an increased intake of water. i always learn at least a dozen new things every time i talk to you. Earlier studies showed that when treatment lowers nt-probnp by at least 40%, survival is excellent [26]. Thanks & god bless , bob replydelete. It can be very beneficial for your heart health and is known as an effective remedy for tachycardia. A pain assessment should be performed before and after pain medication administration to assess the need for and. The committee agreed that it was important that healthcare professionals help people with long-term symptoms related to lyme disease to access support if needed.
Risk Factor Hypertension Aha
However, quitting cold turkey can be dangerous as well, depending on the symptoms. “if you do consume
Risk Factors Hypertension Pubmed
This medication could be very useful to treat the high blood vessels because this medication...
|
__label__pos
| 0.752634 |
Logo: Relish
1. Sign in
Project: Message-driver 0.5.0
Middleware Basics
• @bunny
• @in_memory
Middlewares can be used to transform messages that are about to be published
or that are about to be consumed. This allows for handling of things like
serializing and deserializing the message body in a way that is transparent to
your application code.
Middlewares are applied in a stack to destinations, much like Rack middleware.
As a message that is about to be consumed, it starts by coming in the top of
the middleware stack and works it's way down before it is returned by
pop_message or passed to a consumer.
For messages that are being published, they start at the bottom of the stack
and work their way up until they are finally passed to the underlying driver
and sent to the message broker.
Background
Given
I am connected to the broker
And
I have a destination :middleware_queue with no messages on it
And
I have a middleware class
class ExampleMiddleware < MessageDriver::Middleware::Base
def on_publish(body, headers, properties)
[body+':about_to_publish', headers, properties]
end
def on_consume(body, headers, properties)
['about_to_be_consumed:'+body, headers, properties]
end
end
Scenarios
The middleware stack of a destination is initially empty
When
I execute the following code
destination = MessageDriver::Client.find_destination(:middleware_queue)
expect(destination.middleware).to be_empty
Then
I expect to have no errors
Adding a piece of middleware to a destination
When
I execute the following code
destination = MessageDriver::Client.find_destination(:middleware_queue)
destination.middleware.append ExampleMiddleware
Then
I expect the following check to pass
destination = MessageDriver::Client.find_destination(:middleware_queue)
expect(destination.middleware).to include(an_instance_of(ExampleMiddleware))
Middleware is applied to messages as they are published
When
I append middleware "ExampleMiddleware" to :middleware_queue
And
I send the following messages to :middleware_queue
body
Test Message 1
Test Message 2
Then
I expect to find the following 2 messages on :middleware_queue
raw_body
Test Message 1:about_to_publish
Test Message 2:about_to_publish
Middleware is applied to messages as they are consumed
Given
I have a destination :dest_queue with no messages on it
When
I send the following messages to :middleware_queue
body
Test Message 1
Test Message 2
And
I append middleware "ExampleMiddleware" to :middleware_queue
And
I create a subscription
MessageDriver::Client.subscribe_with(:middleware_queue) do |message|
MessageDriver::Client.publish(:dest_queue, message.body)
end
And
I let the subscription process
Then
I expect to find no messages on :middleware_queue
And
I expect to find the following 2 messages on :dest_queue
raw_body
about_to_be_consumed:Test Message 1
about_to_be_consumed:Test Message 2
Last published about 7 years ago by soupmatt.
|
__label__pos
| 0.589439 |
Category:
What are the Best Ways to Prevent Melanoma?
Article Details
• Written By: M. DePietro
• Edited By: Bronwyn Harris
• Last Modified Date: 13 July 2017
• Copyright Protected:
2003-2017
Conjecture Corporation
• Print this Article
Free Widgets for your Site/Blog
Between 1953 and 1979, hurricanes and tropical storms in the North Atlantic were named exclusively after women. more...
August 17 , 1998 : US President Bill Clinton admitted to having an affair with Monica Lewinsky. more...
Basal cells, squamous cells and melanocytes are the different types of cells which make up the epidermis, which is the outer layer of the skin. Skin cancer can develop from anyone of the three types of skin cells. Basal cell and squamous cell skin cancers usually are not serious, because they usually don’t spread to other organs. The third type of skin cancer is melanoma and it tends to be the most serious because it can metastasize, or spread to other organs fast.
There are several risk factors associated with skin cancer, including a family history and advanced age. One of the biggest risk factors associated with developing melanoma is excess sun exposure. Sun exposure, especially during childhood, appears to increase the chances of developing melanoma as an adult.
Ultraviolet (UV) rays can penetrate the skin and cause changes in the skin cells. UV rays are emitted from the sun and tanning beds. Exposure to UV rays has a cumulative effect, which means the more sun exposure a person gets, the more damage he or she may have to the skin.
Ad
Although certain risk factors, such as family history can’t be controlled, there are several ways to reduce the chances of developing melanoma. One of the best ways to prevent melanoma is by staying out of the sun, from about 10AM to 3PM, when the ultraviolet rays are the strongest. People who work outdoors and may have to be in the sun during peak times should consider wearing long-sleeved shirts which are made from a lightweight material.
Using sunscreen is also essential to preventing skin cancers. Sunscreen helps block the ultraviolet rays from penetrating the skin. Sunscreen is classified with the level of sun protection factor (SPF) it has, which simply means how much protection it provides. Generally a higher SPF provides longer sun protection. Most dermatologists recommend using a sunscreen with an SPF of 15 or higher.
Sunscreen should be applied about fifteen minutes prior to going outside to allow the skin to absorb it. Also reapply the sunscreen every two hours or after swimming. Keep in mind; ultraviolet rays can still penetrate the earth’s atmosphere on a cloudy day, therefore sunscreen should be used. Other ways to prevent melanoma from developing include, wearing a hat which blocks the sunlight from the face. Sunglasses also provide some protect against UV rays and should be worn.
As with many types of cancer, the prognosis is better if melanoma is detected early. See a dermatologist annually to check for changes in the skin. Watch for changes in moles, such as increase in size, change in color or shape. See your doctor as soon as possible if you notice changes, or develop new moles which have irregular borders or are larger than the eraser of a pencil.
Ad
You might also Like
Recommended
Discuss this Article
Post your comments
Post Anonymously
Login
username
password
forgot password?
Register
username
password
confirm
email
|
__label__pos
| 0.785057 |
Skip to main content
eScholarship
Open Access Publications from the University of California
Reconstruction algorithms for x-ray nanocrystallography via solution of the twinning problem
• Author(s): Donatelli, Jeffrey J.
• Advisor(s): Sethian, James A
• et al.
Abstract
X-ray nanocrystallography is an emerging technique for imaging nanoscale objects that alleviates the large crystallization requirement of conventional crystallography by collecting diffraction patterns from a large ensemble of smaller and easier to build nanocrystals, which are typically delivered to the x-ray beam via a liquid jet. In order to determine the structure of an imaged object, several parameters must first be determined, including the crystal sizes, incident photon flux densities, and crystal orientations. Autoindexing techniques, which have been used extensively to orient conventional crystals, only determine the orientation of the nanocrystals up to symmetry of the crystal lattice, which is often greater than the symmetry of the diffraction information, resulting in what is known as the twinning problem. In addition, the image data is corrupted by large degrees of shot noise due to low collected signal, background signal due to the liquid jet and detector electronics, as well as other sources of noise. Furthermore, diffraction only measures the magnitudes of the Fourier transform of the object and, thus, one must recover phase information in order to invert the data and recover a three-dimensional reconstruction of the constituent molecular structure. Previous approaches for handling the twinning problem have mainly relied on having a known similar structure available, which may not be present for fundamentally new structures. We present a series of techniques to determine the crystal sizes, incident photon flux densities, and crystal orientations in the presence of large amounts of noise common in experiments. Additionally, by using a new sampling strategy, we demonstrate that phase information can be computed from nanocrystallographic diffraction images using only Fourier magnitude information, via a compressive phase retrieval algorithm. We demonstrate the feasibility of this new approach by testing it on simulated data with parameters and noise levels common in current experiments.
Main Content
Current View
|
__label__pos
| 0.996205 |
Open in App
Log In Start studying!
Select your language
Suggested languages for you:
Vaia - The all-in-one study app.
4.8 • +11k Ratings
More than 3 Million Downloads
Free
|
|
Wohl Degradation
Delve into the fascinating world of Organic Chemistry with a thorough exploration of the Wohl Degradation. This comprehensive resource unravels complicated chemical processes, from understanding the Wohl Degradation mechanism to its practical applications and significance in Biochemistry. You'll gain an in-depth knowledge of this reaction, its history, and its role in glucose metabolism. Benefit from case studies like the degradation of glucose and the involvement of dehydration in the mechanism. As well as definitions and the meaning of technical terms within this scientific field.
Content verified by subject matter experts
Free Vaia App with over 20 million students
Mockup Schule
Explore our app and discover over 50 million learning materials for free.
Wohl Degradation
Illustration
Lerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persönlichen Lernstatistiken
Jetzt kostenlos anmelden
Nie wieder prokastinieren mit unseren Lernerinnerungen.
Jetzt kostenlos anmelden
Illustration
Delve into the fascinating world of Organic Chemistry with a thorough exploration of the Wohl Degradation. This comprehensive resource unravels complicated chemical processes, from understanding the Wohl Degradation mechanism to its practical applications and significance in Biochemistry. You'll gain an in-depth knowledge of this reaction, its history, and its role in glucose metabolism. Benefit from case studies like the degradation of glucose and the involvement of dehydration in the mechanism. As well as definitions and the meaning of technical terms within this scientific field.
Understanding the Wohl Degradation in Organic Chemistry
The Wohl Degradation is a notable reaction employed in organic chemistry, specifically used for the transformation of sugars into smaller fragments. This reaction was pioneered by Alfred Wohl, hence its nomenclature. Be aware that the comprehension of this reaction is valuable to your proficiency in the sphere of organic chemistry.
The Wohl Degradation technique is essentially used when a sugar molecule needs to be broken down into smaller pieces, through the conversion of a sugar into an aldehyde and a ketone.
Exploring the Wohl Degradation mechanism process
Now let's delve deeper into the Wohl Degradation process, to understand how it works. A detailed study of the process will help you gain a better understanding of not only this specific degradation technique but also organic chemistry reactions in general.
Consider Fructose, a hexose sugar. When it undergoes the Wohl Degradation process, the outcome will be a four-carbon product (tetrose) like Erythrose, in addition to a two-carbon fragment (dihydroxyacetone).
Events leading up to the Wohl Degradation reaction
To begin with, the sugar molecule is turned into a glycosylamine through the reaction with hydroxylamine. This is then followed by the formation of an osazone via a series of steps.
• Conversion of sugar into glycosylamine, which is performed by reacting the sugar with hydroxylamine (\( NH2OH \)).
• Followed by the transformation of glycosylamine into an osazone.
• Subsequently, the osazone is heated with an acid to induce degradation.
• Finally, the process results in the formation of an aldehyde or ketone, alongside a new, smaller sugar.
Enumerating the steps involved in the mechanism process
The key component of the Wohl Degradation process is the series of steps leading to the transformation from glycosylamine to osazone.
Step 1: The sugar is converted into a glycosylamine by reacting the sugar with hydroxylamine (NH2OH).
Step 2: The glycosylamine is transformed into an osazone.
Step 3: The osazone, upon heating with acid, breaks down - this is the key Wohl Degradation event.
Step 4: This process results in the formation of an aldehyde or ketone, alongside a new, smaller sugar.
Fascinatingly, the Wohl Degradation process doesn't just randomly split the sugar molecule. It neatly splits the sugar into an aldehyde or ketone and a smaller sugar, which is exactly half the size of the original sugar. This is because of the symmetrical nature of many sugar molecules. This careful, calculated degradation is what makes this reaction so useful in organic chemistry.
Wohl Degradation Mechanism Dehydration: A Closer Look
In the realm of organic chemistry, and more specifically within the Wohl Degradation reaction, dehydration plays a huge part in the execution of the process. It is the dehydration step that propels the forward motion of the reaction, allowing for the degradation to take place.
Identifying the role of dehydration in the Wohl Degradation mechanism
This pivotal role of dehydration, in terms of its function within the Wohl Degradation mechanism, is chiefly accentuated during the transformation of osazone. The vital part to understand here is that the process hinges on expedient and accurate dehydration reactions.
Think of it like this: without the dehydration step, the Wohl Degradation reaction would fail to reach completion. The water molecules, still held within the osazone, act as a barrier to degradation. But with them removed by dehydration, the reaction is able to progress.
To understand this further, let's explore what happens before and after dehydration occurs. Prior to dehydration, the sugar molecule is converted into a hydrazone. This is achieved by nucleophilic addition of the amine to the carbonyl, followed by protonation of nitrogen and loss of water. The hydrazone then cyclizes to a furanose-like structure which is subsequently transformed into an osazone.
Dehydration in this context refers to the removal of water from the structure, transforming it into an osazone.
Following the removal of water, the osazone structure is then ready to be split apart in the actual degradation step of the Wohl Degradation reaction. Here, the dehydration role is implying that water (a usual by-product of many chemical reactions) isn’t produced, but is instead actively removed from the reacting molecule to allow the reaction to progress.
How does dehydration facilitate the Wohl Degradation reaction?
In essence, the dehydration within the Wohl Degradation reaction acts as a preparatory step for the actual degradation, or breakdown, of the molecule. By removing the constituent water molecules through dehydration, the chemical rigidity of the osazone is lowered, permitting the further series of reactions that follow.
• Step 1: The dehydration process begins with an osazone molecule. In the case of a sugar, osazone is the result of a reaction with phenylhydrazine.
• Step 2: The dehydration of osazone can be induced by heating with acetic acid, facilitating the removal of water molecules from the osazone.
• Step 3: Two phenylhydrazine molecules are liberated in the process, leaving behind a dehydrated portion of the original sugar molecule.
• Step 4: This dehydrated product is more reactive, allowing for the subsequent degradation mechanism to occur more readily.
This illustrates just how vital hydration levels are to organic chemistry reactions, such as the Wohl Degradation. By following the specific dehydration step, you are enabling the osazone to become primed for the degradation process, making it less stable and thus more reactive. Without this crucial dehydration step, the Wohl Degradation reaction wouldn't be able to proceed as effectively or at all.
Importantly, the specific details of these steps can vary slightly depending on the specific sugar molecule which is being degraded. However, the general principles regarding dehydration remain the same.
Practical Examples of Wohl Degradation
In the context of learning chemistry, practical examples can go a long way in cementing the understanding of a given concept. This holds true for the Wohl Degradation as well, an organic chemistry reaction that is not only theoretical but also has extensive practical applications. To understand this better, let's explore some practical examples in the world of organic chemistry.
Wohl Degradation examples in Organic Chemistry
The Wohl Degradation reaction is frequently used in organic chemistry to break down larger sugar molecules into smaller ones. This happens through a series of steps that result in an aldehyde or a ketone, as well as a smaller sugar molecule.
For instance, if a six-carbon sugar (hexose) such as glucose or fructose undergoes Wohl Degradation, it will yield a four-carbon product (tetrose) and a two-carbon fragment (dihydroxyacetone). This is a fine practical instance of how the Wohl Degradation technique is applied in the chemical degradation of sugars.
Two vital steps involved in this process include the concerted cyclization of the sugar molecule while it is in its phenylhydrazone form, and the subsequent elimination of the phenylhydrazine molecules. Both of these steps involve the dehydration of the sugar molecule, which is a prerequisite for the degradation process to occur.
Cyclization, based on its name, involves the formation of a cyclic (ring) structure within the sugar molecule, which sets up the scene for the elimination of the phenylhydrazine molecules. Elimination, as the term suggests, is the process where unneeded molecules (phenylhydrazine in this case) are eliminated from the structure.
Observing Wohl Degradation in an aldohexose situation
Using an aldohexose as a practical example, such as glucose or mannose, can demonstrate the Wohl Degradation reaction very efficiently.
To start off, the hexose sugar gets transformed into a glycosylamine via the reaction with hydroxylamine to create the osazone. This osazone then undergoes a series of reactions which include dehydration and a ring closure mechanism that transforms it into a furanose-like structure. This furanose-like structure, when heated with acid, then undergoes degradation via a concerted mechanism that ends up forming two smaller sugar fragments.
The final degradation process can be simplified as such:
Hexose \( \rightarrow \) Glycosylamine \( \rightarrow \) Furanose-like structure \( \rightarrow \) Tetrose + Dihydroxyacetone
Case study: Wohl Degradation of glucose
Delving even deeper, we can delve into the case study of Wohl Degradation of glucose. As a hexose sugar, glucose proves to be the perfect candidate for this reaction process.
Initially, glucose pairs with phenylhydrazine in order to form the phenylglycosazone. This then undergoes cyclical dehydration to form a cyclic structure, which prepares it for the subsequent degradation.
Following the cyclical dehydration, the structure undergoes a phenylhydrazone elimination, leading to the degradation of the glucose into a tetrose and dihydroxyacetone.
In essence, the Wohl Degradation of glucose can be summarized as:
Glucose \( \rightarrow \) Glucosazone \( \rightarrow \) Cyclic Dehydration \( \rightarrow \) Phenylhydrazone elimination \( \rightarrow \) Tetrose + Dihydroxyacetone
The Wohl Degradation reaction provides an elegant and precise way to degrade larger sugar molecules, like glucose, into smaller fragments, allowing organic chemists to study and harness the properties of these smaller sugar structures. As you can see, this reaction is key to molecule degradation in organic chemistry, and understanding it opens doors to understanding more complex organic reactions.
Interpreting the Wohl Degradation Meaning
As you delve into the natural sciences, particularly organic chemistry, you will come across a multitude of complex terminologies. 'Wohl Degradation' is one such term. Like all scientific terms, 'Wohl Degradation' has a precise and specific meaning. However, understanding this term is more than just a taxonomy exercise. At its core, the meaning of 'Wohl Degradation' revolves around the process which it refers to, a distinct reaction mechanism used extensively in the field.
Breaking down the technical terms: Wohl Degradation definition
In order to understand the full significance and interpretation of the Wohl Degradation, it's instrumental to first comprehend its technical definition. In simplest terms, the Wohl Degradation is an organic chemistry process that leads to the degradation of a specific type of molecules known as sugars, or more accurately pentoses and hexoses - five and six carbon sugars respectively.
The term 'degradation' here denotes a reduction or breakdown of these sugar molecules into smaller fragments. Importantly, the Wohl Degradation is characterised by a unique series of reaction steps which include cyclisation, dehydration steps and a concerted degradation step.
Naturally, these terms may be confusing without further elaboration, so let's break these down:
• Cyclisation – a reaction step that involves the formation of a ring or cyclic compound from a linear molecule. This is often an enzymatic process, which brings two distant atoms within reach to create a new bond.
• Dehydration – a chemical reaction that involves the removal of water (H2O) from a molecule. The outcome of this process is a more condensed molecule that is primed for further chemical interaction.
• Concerted degradation – a multi-step process leading to the cleavage of the molecule leading to the production of smaller fragments via a sequence of actions that take place together, or 'in concert'.
Together, these complex steps comprise the Wohl Degradation, named after the chemist who discovered this sequence of reactions, and collectively they function to facilitate the controlled degradation of sugar molecules.
History and origin of the Wohl Degradation term
The genesis of the Wohl Degradation term is inevitably tied with the legacy of Wilhelm Rudolph Wohl. Born in the late 19th century, Wohl was a German chemist who is most recognised for his contributions to carbohydrate chemistry, particularly his discovery of the degradation process that now bears his name.
The degradation of sugar molecules explored by Wohl was a relatively new field of study in the early 1900s. His work marked a significant milestone in the understanding of sugar chemistry leading to advancements in the structural elucidation of carbohydrates.
First publicised around 1912, the degradation technique revealed an elegant method of converting an aldohexose into an aldotriose, and ketohexose into a diketotriose. It was subsequently named the Wohl Degradation in honour of Wohl's groundbreaking discovery.
One of Wohl's most famous experimentations involved breaking down glucose, a six-carbon sugar, into glyceraldehyde, a three-carbon sugar using phenylhydrazine. It is here where he first observed chemical dehydration playing a key role in the reaction sequence. This study became a primary model for what we now know as the Wohl Degradation.
A historical understanding of the Wohl Degradation term helps to contextualise this reaction within the broader field of organic chemistry. Wohl's discovery sparked new research avenues and has since been a cornerstone in the study of carbohydrates and the biochemistry of sugar metabolism.
In summary, understanding the in-depth meaning of terms such as 'Wohl Degradation' goes beyond the mere definition. It can embolden a more profound comprehension of the reactions involved, give a nod of respect to the pioneers of the field, and appreciate the transformation that has taken place within the scientific landscape over the past century.
Application of the Wohl Degradation in Biochemistry
The landscape of biochemistry is studded with numerous crucial natural processes, and the application of the Wohl Degradation is a facet that cannot be overlooked. In essence, the Wohl Degradation has paved the way for the in-depth investigation of saccharides, particularly aldohexoses, and has answered several questions related to the structural elucidation of carbohydrates.
Understanding the Significance of Wohl Degradation of Aldohexose
Among the myriad chemical reactions in biochemistry, the Wohl Degradation holds a notable place due to its significant function in the breakdown of aldohexose. When applied to an aldohexose, a six-carbon sugar with an aldehyde functional group, Wohl Degradation facilitates a reduction process converting this sugar into an aldotetrose, a four-carbon sugar.
To grasp the importance of this conversion, it's pivotal to first understand the role of aldohexoses. These sugars provide an essential energy source for living organisms. Being soluble, they can be easily transported through the body. A perfect example illustrating this application is glucose, a primary aldohexose, which is the main energy source for cells.
The process of converting an aldohexose into a smaller sugar molecule, an aldotetrose, via the Wohl Degradation consists of several critical steps:
• The aldohexose reacts with phenylhydrazine to form a phenylhydrazone compound.
• Subsequent treatment with phenylhydrazine leads to the formation of glycosazone via a series of reactions.
• The glycosazone facilitates cyclization resulting in a three-membered ring structure.
• Further treatment leads to a phenylhydrazone elimination which degrades the original aldohexose into a smaller sugar molecule.
A common biochemical application of this reaction lies in the structural determination of unknown sugars. By performing Wohl Degradation on an unknown sample, you can identify smaller derivatives, which are typically easier to analyse. This can provide valuable clues to the identity of the original larger sugar molecule.
Role and Importance of Wohl Degradation in Glucose Metabolism
The biochemistry of glucose metabolism is the cornerstone of energy production in cells, and strikes as a representative example to illustrate the application of Wohl Degradation. During metabolism, glucose - an aldohexose - is broken down, primarily through a process called glycolysis. However, the complexity of the glycolytic pathway can be simplified if we introduce Wohl Degradation.
Indeed, Wohl Degradation reaction can be employed to mimic glycolysis. In general terms, glucose metabolism involves similar steps to Wohl Degradation, such as the formation of an intermediate compound that is later broken down into smaller derivative products. Even more, these smaller products are often substrates for comprehending metabolic pathways.
Let's break down this process:
• First, glucose reacts with phenylhydrazine to produce a phenylhydrazone compound, phenylglucosazone.
• Then, the phenylglucosazone undergoes cyclization and dehydration, forming a three-membered ring structure.
• Upon further treatment, phenylhydrazone is eliminated.
• This results in the Wohl Degradation of glucose, yielding erythrose and dihydroxyacetone.
In essence, the reactions depicted in the Wohl Degradation could be considered as a greatly simplified version of glucose metabolism. Here, glucose degradation yields two three-carbon compounds that are applicable in further metabolic pathways. This process, resembling a step in glycolysis, underscores the importance of the Wohl Degradation and its application in biochemistry.
The breaking down of glucose aids in the understanding of more complex biochemical pathways. It offers insights into the inner workings of carbohydrate metabolism and bioenergetic processes, making it fundamental to the comprehension of overall glucose metabolism.
In a broader perspective, this reaction technique uncovers the intricacies of the sugar molecule degradation process, and facilitates human understanding of how cells derive energy from glucose. This also prompts the further exploration of complicated processes such as glycolysis, thereby enriching the span of biochemistry, and illuminating how it's crucial to life and human understanding of it.
Wohl Degradation - Key takeaways
• The Wohl Degradation process carefully splits a sugar molecule into an aldehyde or ketone and a smaller sugar, due to the symmetrical nature of many sugar molecules.
• In the Wohl Degradation reaction, dehydration is a key step, particularly during the transformation of osazone, and it propels the forward motion of the reaction.
• Dehydration removes water molecules from the osazone, a key step for the Wohl Degradation reaction to progress and reach completion.
• The Wohl Degradation reaction has been practically applied in organic chemistry to break down larger sugar molecules into smaller ones, for instance, a six-carbon sugar (hexose) like glucose or fructose can be degraded into a smaller four-carbon product (tetrose) and a two-carbon fragment (dihydroxyacetone).
• The Wohl Degradation is named after Wilhelm Rudolph Wohl, who discovered this sequence of reactions. It's primarily applied in the controlled degradation of sugar molecules, particularly the carbohydrates, pentoses and hexoses (five and six carbon sugars respectively).
Frequently Asked Questions about Wohl Degradation
The Wohl degradation mechanism is a chemical process used to shorten the carbon chain of sugars. It involves the oxidation of an aldose to an aldonic acid, followed by a reduction and then an elimination reaction, producing an aldose with one less carbon atom.
An example of Wohl Degradation is the breakdown of maltose into two glucose molecules. This reaction involves steps of acetylation, reduction, and hydrolysis to degrade the disaccharide into monosaccharides.
Wohl degradation is a popular method in carbohydrate chemistry used for structural transformations of sugars. It involves the conversion of an aldose into an aldonic acid, followed by decarboxylation and reduction to produce an aldose with one less carbon atom.
Wohl's method of degradation is a chemical process used to breakdown carbohydrates into simpler forms. It involves halogenation followed by reduction, effectively shortening the carbohydrate chain. It's named after German chemist and researcher, Alfred Walter Wohl.
In the Wohl Degradation process, an aldose is first converted into an acyclic diketone through oxidative cleavage. This diketone then undergoes a series of chemical reactions resulting in the formation of a ketose, a type of carbohydrate, that has one less carbon atom than the original aldose.
Final Wohl Degradation Quiz
Wohl Degradation Quiz - Teste dein Wissen
Question
What is the Wohl Degradation in organic chemistry?
Show answer
Answer
The Wohl Degradation is a reaction employed in organic chemistry for the conversion of sugars into smaller fragments, specifically through turning a sugar into an aldehyde and a ketone.
Show question
Question
How does the Wohl Degradation process work?
Show answer
Answer
The Wohl Degradation process starts by transforming a sugar molecule into a glycosylamine through reacting with hydroxylamine. Then, it is turned into an osazone, which, when heated with acid, breaks down to form an aldehyde or ketone along with a new, smaller sugar.
Show question
Question
What is the initial step in the Wohl Degradation process?
Show answer
Answer
The initial step in the Wohl Degradation process is the conversion of a sugar molecule into a glycosylamine by reacting with hydroxylamine.
Show question
Question
What is the role of dehydration in the Wohl Degradation mechanism?
Show answer
Answer
Dehydration in the Wohl Degradation mechanism removes water molecules from the osazone structure, making it less stable and thus more reactive. This allows the degradation process to occur more readily.
Show question
Question
What happens during the dehydration process in the Wohl Degradation mechanism?
Show answer
Answer
In the case of a sugar molecule, the dehydration process begins with an osazone molecule, produced by reaction with phenylhydrazine. Dehydration is induced by heating with acetic acid, facilitating the removal of water molecules from the osazone. This results in a more reactive, dehydrated product.
Show question
Question
How does hydration level impact the Wohl Degradation reaction?
Show answer
Answer
The hydration level significantly impacts the Wohl Degradation reaction. Without dehydration, the osazone structure remains stable, acting as a barrier to degradation. Therefore, dehydration is essential to make the osazone structure less stable and more reactive, allowing for the degradation process.
Show question
Question
What is the Wohl Degradation reaction used for in organic chemistry?
Show answer
Answer
The Wohl Degradation reaction is used in organic chemistry to break down larger sugar molecules into smaller ones, yielding an aldehyde or ketone and a smaller sugar molecule.
Show question
Question
What are the two vital steps involved in the Wohl Degradation process?
Show answer
Answer
The two vital steps in the Wohl Degradation process are the concerted cyclization of the sugar molecule and the subsequent elimination of the phenylhydrazine molecules. Both steps involve dehydration of the sugar molecule.
Show question
Question
How can the degradation of an aldohexose like glucose be summarised using the Wohl Degradation process?
Show answer
Answer
The Wohl Degradation of glucose can be summarised as: Glucose to Glucosazone, cyclical dehydration, Phenylhydrazone elimination, and finally yielding a tetrose and dihydroxyacetone.
Show question
Question
What does the term "Wohl Degradation" refer to in organic chemistry?
Show answer
Answer
Wohl Degradation is an organic chemistry process that leads to the degradation of a specific type of molecules known as sugars, comprising a unique series of reaction steps including cyclisation, dehydration and a concerted degradation step.
Show question
Question
What does the term 'cyclisation' mean in the context of Wohl Degradation?
Show answer
Answer
'Cyclisation' is a reaction step in Wohl Degradation that involves the formation of a ring or cyclic compound from a linear molecule.
Show question
Question
Who is the Wohl Degradation named after and what is his contribution in the field of organic chemistry?
Show answer
Answer
The Wohl Degradation is named after Wilhelm Rudolph Wohl, a German chemist recognised for his contributions to carbohydrate chemistry, particularly his discovery of the sugar degradation process that bears his name.
Show question
Question
What is the Wohl Degradation in the context of biochemistry?
Show answer
Answer
The Wohl Degradation in biochemistry is a process that facilitates the breakdown of aldohexose, a six-carbon sugar with an aldehyde functional group, into an aldotetrose, a four-carbon sugar. This reaction enables in-depth investigation and structural elucidation of carbohydrates.
Show question
Question
What is the importance of the Wohl Degradation in the investigation of saccharides?
Show answer
Answer
The Wohl Degradation enables the conversion of larger sugar molecules into smaller ones, which are easier to analyse. This allows for the structural determination of unknown sugars, providing valuable clues to the identity of the original larger sugar molecule.
Show question
Question
How is the Wohl Degradation process involved in glucose metabolism?
Show answer
Answer
The Wohl Degradation can be employed to mimic glycolysis, a pathway in glucose metabolism. The degradation of glucose yields two three-carbon molecules, which are applicable in further metabolic pathways. It simplifies the understanding of complex biochemical pathways.
Show question
Test your knowledge with multiple choice flashcards
What is the Wohl Degradation in organic chemistry?
How does the Wohl Degradation process work?
What is the initial step in the Wohl Degradation process?
Next
Flashcards in Wohl Degradation15
Start learning
What is the Wohl Degradation in organic chemistry?
The Wohl Degradation is a reaction employed in organic chemistry for the conversion of sugars into smaller fragments, specifically through turning a sugar into an aldehyde and a ketone.
How does the Wohl Degradation process work?
The Wohl Degradation process starts by transforming a sugar molecule into a glycosylamine through reacting with hydroxylamine. Then, it is turned into an osazone, which, when heated with acid, breaks down to form an aldehyde or ketone along with a new, smaller sugar.
What is the initial step in the Wohl Degradation process?
The initial step in the Wohl Degradation process is the conversion of a sugar molecule into a glycosylamine by reacting with hydroxylamine.
What is the role of dehydration in the Wohl Degradation mechanism?
Dehydration in the Wohl Degradation mechanism removes water molecules from the osazone structure, making it less stable and thus more reactive. This allows the degradation process to occur more readily.
What happens during the dehydration process in the Wohl Degradation mechanism?
In the case of a sugar molecule, the dehydration process begins with an osazone molecule, produced by reaction with phenylhydrazine. Dehydration is induced by heating with acetic acid, facilitating the removal of water molecules from the osazone. This results in a more reactive, dehydrated product.
How does hydration level impact the Wohl Degradation reaction?
The hydration level significantly impacts the Wohl Degradation reaction. Without dehydration, the osazone structure remains stable, acting as a barrier to degradation. Therefore, dehydration is essential to make the osazone structure less stable and more reactive, allowing for the degradation process.
Join over 22 million students in learning with our Vaia App
The first learning app that truly has everything you need to ace your exams in one place
• Flashcards & Quizzes
• AI Study Assistant
• Study Planner
• Mock-Exams
• Smart Note-Taking
Join over 22 million students in learning with our Vaia App Join over 22 million students in learning with our Vaia App
Discover the right content for your subjects
Sign up to highlight and take notes. It’s 100% free.
Start learning with Vaia, the only learning app you need.
Sign up now for free
Illustration
|
__label__pos
| 0.999812 |
o7planning
Java Buffer Tutorial with Examples
View more Tutorials:
Websites to learn foreign languages for free:
Follow us on our fanpages to receive notifications every time there are new articles. Facebook Twitter
1- Buffer
Java NIO Buffer represents a container with a fixed capacity to store primitive data. It is often used in conjunction with the Java NIO Channel(s). Specifically, data will be read from the Channel into the Buffer or write data from the Buffer into the Channel.
public abstract class Buffer extends Object
Hierarchy of classes and interfaces related to Java NIO Buffer:
The relationship between Channel and Buffer is similar to the relationship between a bowl and a spoon. The spoon can be used as a small container to take the sugar from the bowl and it can also be used as a small container to put the sugar from the outside into the bowl. Thus, the spoon acts as a Buffer and the bowl acts as a Channel.
Capacity, limit, position and mark are the 4 most important terms of Java NIO Buffer, they will be explained in detail below. In both read and write modes, the cursor always moves to the right.
2- Buffer Methods
public final int capacity()
public final int position()
public Buffer position(int newPosition)
public final int limit()
public Buffer limit(int newLimit)
public Buffer mark()
public Buffer reset()
public Buffer clear()
public Buffer flip()
public Buffer rewind()
public final int remaining()
public final boolean hasRemaining()
public abstract boolean isReadOnly();
public abstract boolean hasArray();
public abstract Object array();
public abstract int arrayOffset();
public abstract boolean isDirect();
public abstract Buffer slice();
public abstract Buffer duplicate();
3- capacity()
public final int capacity()
The capacity() method returns the capacity of this Buffer.
Although you can only read or write to elements from index 0 to limit-1, if you set limit = capacity, you can access (read, write) to all the elements of the Buffer.
4- position()
public final int position()
Return the current position of the cursor. Both read and write operations move the cursor to the end of the Buffer. The returned value is always less than or equal to limit.
• 0 <= mark <= position <= limit <= capacity
5- position(int newPosition)
public Buffer position(int newPosition)
Set the new position for the pointer.
• newPostion must be greater than or equal to 0 and less than or equal to limit.
• If newPosition < mark then the mark will be discarded.
6- limit()
public final int limit()
Returns the limit of this Buffer.
Buffer only supports reading and writing to elements at index 0 to limit-1, elements at index limit to capacity-1 are disabled. However, you can set limit = capacity to be able to access (read or write) to all the elements of the Buffer.
• 0 <= mark <= position <= limit <= capacity
In the example below: A CharBuffer with capacity = 10, and limit = 7, you can only read from and write to elements at index from 0 to 6. Violation of an exception will be thrown.
Buffer_limit_ex1.java
// Allocate a character type buffer.
CharBuffer buffer = CharBuffer.allocate(10); // capacity = 10
buffer.limit(7); // limit = 7
String text = "abcdefghij";
System.out.println("Input text: " + text);
System.out.println("Text length: " + text.length()); // 10
for (int i = 0; i < text.length(); i++) {
char chr = text.charAt(i);
// put character in buffer.
buffer.put(chr);
System.out.println(i + ". put: " + chr);
}
Output:
Input text: abcdefghij
Text length: 10
0. put: a
1. put: b
2. put: c
3. put: d
4. put: e
5. put: f
6. put: g
Exception in thread "main" java.nio.BufferOverflowException
at java.base/java.nio.Buffer.nextPutIndex(Buffer.java:665)
at java.base/java.nio.HeapCharBuffer.put(HeapCharBuffer.java:199)
at org.o7planning.buffer.ex.Buffer_limit_ex1.main(Buffer_limit_ex1.java:21)
7- limit(int newLimit)
public Buffer limit(int newLimit)
Set the new limit value for this Buffer. newLimit must be less than capacity, otherwise IllegalArgumentException will be thrown.
• If newLimit < position, the postion will be set to newLimit.
• If newLimit < mark then the mark will be discarded.
Example:
Buffer_limit_newLimit_ex1.java
// Allocate a character type buffer.
CharBuffer buffer = CharBuffer.allocate(10); // capacity = 10
System.out.printf("Buffer capacity: %d%n%n", buffer.capacity()); // 10
buffer.limit(9); // limit = 9
System.out.printf("Buffer limit: %d, position: %d%n%n", buffer.limit(), buffer.position());
System.out.println("Set newPostion: 8");
buffer.position(8);
System.out.printf("Buffer limit: %d, position: %d%n%n", buffer.limit(), buffer.position());
System.out.println("Set newLimit: 7");
// Set limit = 7.
buffer.limit(7);
System.out.printf("Buffer limit: %d, position: %d%n", buffer.limit(), buffer.position());
Output:
Buffer capacity: 10
Buffer limit: 9, position: 0
Set newPostion: 8
Buffer limit: 9, position: 8
Set newLimit: 7
Buffer limit: 7, position: 7
8- mark()
public Buffer mark()
The mark() method is used to mark the current position of the cursor. In the process of manipulating Buffer, the position of the cursor may change, calling the reset() method will help the cursor return to the previously marked position.
• 0 <= mark <= position <= limit <= capacity
The mark will be discarded in the following cases:
• Call the setPosition(newPosition) method with newPosition < mark.
• Call the setLimit(newLimit) method with newLimit < mark.
• Call the clear(), rewind() or flip() method.
9- reset()
public Buffer reset()
The reset() method is used to return the cursor to the previously marked position. (See the mark() method).
This method can throw an InvalidMarkException if the mark is not defined or has been discarded.
The mark will be discarded in the following cases:
• Call the setPosition(newPosition) method with newPosition < mark.
• Call the setLimit(newLimit) method with newLimit < mark.
• Call the clear(), rewind() or flip() method.
Example:
Buffer_reset_ex1.java
CharBuffer buffer = CharBuffer.allocate(10); // capacity = 10
System.out.println("Set newPostion: 5");
buffer.position(5);
System.out.println("Mark current position!");
buffer.mark(); // marked position = 5
System.out.println("Call buffer.get() twice!");
char ch1 = buffer.get();
char ch2 = buffer.get();
System.out.printf("Position: %d%n%n", buffer.position()); // position = 7
System.out.println("Reset!");
buffer.reset();
System.out.printf("Position: %d%n%n", buffer.position()); // position = 5
Output:
Set newPostion: 5
Mark current position!
Call buffer.get() twice!
Position: 7
Reset!
Position: 5
10- clear()
public Buffer clear()
The clear() method sets position = 0; limit = capacity, discard the mark and return this Buffer. Calling this method does not affect the data on the Buffer.
Example:
Buffer_clear_ex1.java
CharBuffer buffer = CharBuffer.allocate(7); // capacity = 7
// Write data to buffer:
buffer.put('A');
buffer.put('B');
buffer.position(3); // Set position to 3.
buffer.limit(5); // Set limit to 5.
System.out.printf("buffer, capcity: %d, limit: %d, position: %d%n%n", //
buffer.capacity(), buffer.limit(), buffer.position());
System.out.println("Clear...");
buffer.clear();
System.out.printf("buffer, capcity: %d, limit: %d, position: %d%n%n", //
buffer.capacity(), buffer.limit(), buffer.position());
// Read data in buffer:
while (buffer.hasRemaining()) {
char chr = buffer.get();
System.out.println(chr + " --> " + (int) chr); // char and code.
}
Output:
buffer, capcity: 7, limit: 5, position: 3
Clear...
buffer, capcity: 7, limit: 7, position: 0
A --> 65
B --> 66
--> 0
--> 0
--> 0
--> 0
--> 0
11- flip()
public Buffer flip()
The flip() method will set limit = current position, position = 0 and return this Buffer, and discard the mark. (See illustration below).
The example below corresponds to the illustration above:
Buffer_flip_ex1.java
CharBuffer buffer = CharBuffer.allocate(10); // capacity = 10
System.out.printf("Position: %d, Limit: %d, Capacity: %d%n%n",
buffer.position(), buffer.limit(), buffer.capacity());
System.out.println("Write 3 characters to buffer\n");
for(char ch : new char[] {'A','B','C'}) {
buffer.put(ch);
}
System.out.printf("Position: %d, Limit: %d, Capacity: %d%n%n",
buffer.position(), buffer.limit(), buffer.capacity());
System.out.println("Set limit = 7, position = 5\n");
buffer.limit(7);
buffer.position(5);
System.out.printf("Position: %d, Limit: %d, Capacity: %d%n%n",
buffer.position(), buffer.limit(), buffer.capacity());
System.out.println(" --- flip() --- \n");
buffer.flip();
System.out.printf("Position: %d, Limit: %d, Capacity: %d",
buffer.position(), buffer.limit(), buffer.capacity());
Output:
Position: 0, Limit: 10, Capacity: 10
Write 3 characters to buffer
Position: 3, Limit: 10, Capacity: 10
Set limit = 7, position = 5
Position: 5, Limit: 7, Capacity: 10
--- flip() ---
Position: 0, Limit: 5, Capacity: 10
The flip() method is usually used after finishing writing data to the Buffer, which helps move the cursor to index 0. Ready to read out useful data on Buffer. (See illustrations and examples below).
Buffer_flip_ex2.java
CharBuffer buffer = CharBuffer.allocate(5); // capacity = 5
// WRITE MODE:
System.out.println("Write 3 characters to buffer\n");
for(char ch : new char[] {'A','B','C'}) {
buffer.put(ch);
}
// (Now position = 3, limit = 5, capacity = 5).
System.out.println(" --- flip() --- \n");
buffer.flip();
// READ MODE:
// (Now position = 0, limit = 3, capacity = 5).
while(buffer.position() < buffer.limit()) {
char ch = buffer.get();
System.out.println(ch);
}
Output:
Write 3 characters to buffer
--- flip() ---
A
B
C
12- rewind()
public Buffer rewind()
The rewind() method is used to rewind this Buffer, in other words, it sets position = 0, and discard the mark.
13- remaining()
public final int remaining()
Returns the number of elements between position and limit-1.
14- hasRemaining()
public final boolean hasRemaining()
Returns true if there are any elements between position and limit-1. Otherwise, return false.
15- slice()
public abstract Buffer slice();
Returns a new Buffer that is a partial snapshot of this Buffer. The new Buffer includes the elements between the position and limit-1 of this Buffer. The marked position of the new Buffer is not defined, the position of the new Buffer is 0. (See illustration below).
These two Buffer(s) are related to each other, data changes on one will be seen on the other and vice versa. mark, position, limit, capacity values of these two Buffer(s) are independent of each other.
Example:
Buffer_slice_ex1.java
CharBuffer buffer1 = CharBuffer.allocate(10); // capacity = 10
// Write data to buffer1:
buffer1.put('A');
buffer1.put('B');
buffer1.put('C');
buffer1.position(1); // Set position to 1.
buffer1.limit(7); // Set limit to 7.
CharBuffer buffer2 = buffer1.slice();
System.out.printf("buffer2, capcity: %d, limit: %d, position: %d%n%n",
buffer2.capacity(), buffer2.limit(), buffer2.position());
// Change data in buffer2:
buffer2.put('D');
buffer2.put('E');
buffer2.put('F');
//
buffer1.position(0);
buffer1.limit(4);
// Read data in buffer1:
while(buffer1.hasRemaining()) {
System.out.println(buffer1.get());
}
Output:
buffer2, capcity: 6, limit: 6, position: 0
A
D
E
F
16- duplicate()
public abstract Buffer duplicate();
Returns a new Buffer that is a snapshot of this Buffer.
The data of the new Buffer will be that of this Buffer. Changes to this Buffer's data will be visible in the new Buffer, and vice versa; the two Buffer(s)' position, limit, and mark values will be independent. When newly created, two Buffer(s) has the same values position, limit, mark.
Example:
Buffer_duplicate_ex1.java
CharBuffer buffer1 = CharBuffer.allocate(10); // capacity = 10
// Write data to buffer1:
buffer1.put('A');
buffer1.put('B');
buffer1.put('C');
buffer1.position(1); // Set position to 1.
buffer1.limit(7); // Set limit to 7.
CharBuffer buffer2 = buffer1.duplicate();
System.out.printf("buffer2, capcity: %d, limit: %d, position: %d%n%n",
buffer2.capacity(), buffer2.limit(), buffer2.position());
// Change data in buffer2:
buffer2.put('D');
buffer2.put('E');
buffer2.put('F');
//
buffer1.position(0);
buffer1.limit(4);
// Read data in buffer1:
while(buffer1.hasRemaining()) {
System.out.println(buffer1.get());
}
Output:
buffer2, capcity: 10, limit: 7, position: 1
A
D
E
F
17- array()
public abstract Object array(); // Optional Operation.
Returns an array contain the elements of this Buffer if indeed this Buffer uses arrays as a technique to store the elements. This is an optional operation, which may not be supported in the subclass of Buffer. If this method is not supported, it will throw an UnsupportedOperationException. Check if this Buffer supports arrays using the hasArray() method..
Most of the Buffer subclasses available in the JDK use an internal array to store the elements.
Class Has Array?
ByteBuffer true
MappedByteBuffer true
ShortBuffer true
IntBuffer true
FloatBuffer true
LongBuffer true
DoubleBuffer true
CharBuffer true
Example:
Buffer_array_ex1.java
CharBuffer charBuffer = CharBuffer.allocate(5); // capacity = 5
// Write data to charBuffer:
charBuffer.put('A');
charBuffer.put('B');
charBuffer.put('C');
boolean hasArray = charBuffer.hasArray(); // true
if(hasArray) {
char[] charArray = charBuffer.array();
System.out.println("charArray.length: " + charArray.length); // 5
for(char ch: charArray) {
System.out.println(ch + " --> " + (int)ch); // char and code
}
}
Output:
charArray.length: 5
A --> 65
B --> 66
C --> 67
--> 0
--> 0
18- hasArray()
public abstract boolean hasArray();
Returns true if this Buffer uses arrays as a technique to store elements, otherwise return false. This is an optional operation, which may not be supported in the subclass of Buffer.
Most of the Buffer subclasses available in the JDK use an internal array to store the elements.
Class Has Array?
ByteBuffer true
MappedByteBuffer true
ShortBuffer true
IntBuffer true
FloatBuffer true
LongBuffer true
DoubleBuffer true
CharBuffer true
19- arrayOffset()
public abstract int arrayOffset();
20- isReadOnly()
public abstract boolean isReadOnly();
Checks whether this Buffer is read-only or not. This is an optional operation, which may not be supported in the subclass of Buffer and an UnsupportedOperationException will be thrown.
Most of the Buffer subclasses available in the JDK support both read and write modes (by default):
Class Read-Only
by default?
Support
Read-Only?
ByteBuffer false true
MappedByteBuffer false true
ShortBuffer false true
IntBuffer false true
FloatBuffer false true
LongBuffer false true
DoubleBuffer false true
CharBuffer false true
Example:
Buffer_isReadOnly_ex1.java
Buffer b1 = ByteBuffer.allocate(10);
Buffer b2 = MappedByteBuffer.allocate(10);
Buffer b3 = ShortBuffer.allocate(10);
Buffer b4 = IntBuffer.allocate(10);
Buffer b5 = FloatBuffer.allocate(10);
Buffer b6 = LongBuffer.allocate(10);
Buffer b7 = DoubleBuffer.allocate(10);
Buffer b8 = CharBuffer.allocate(10);
Buffer[] buffers = new Buffer[] { b1, b2, b3, b4, b5, b6, b7, b8 };
for (Buffer buffer : buffers) {
System.out.println(buffer.getClass().getSimpleName() + " --> " + buffer.isReadOnly());
}
Output:
HeapByteBuffer --> false
HeapByteBuffer --> false
HeapShortBuffer --> false
HeapIntBuffer --> false
HeapFloatBuffer --> false
HeapLongBuffer --> false
HeapDoubleBuffer --> false
HeapCharBuffer --> false
Example: Create a read-only CharBuffer:
Buffer_isReadOnly_ex2.java
CharBuffer charBuffer = CharBuffer.allocate(10); // capacity = 10
// Write data to charBuffer.
charBuffer.put('A');
charBuffer.put('B');
charBuffer.put('C');
// Create a read-only CharBuffer.
CharBuffer readOnlyBuffer = charBuffer.asReadOnlyBuffer();
System.out.println("Write data to read-only buffer:");
readOnlyBuffer.put('D'); // ==> java.nio.ReadOnlyBufferException
Output:
Write data to read-only buffer:
Exception in thread "main" java.nio.ReadOnlyBufferException
at java.base/java.nio.HeapCharBufferR.put(HeapCharBufferR.java:202)
at org.o7planning.buffer.ex.Buffer_isReadOnly_ex2.main(Buffer_isReadOnly_ex2.java:18)
Example: Create other read-only Buffer(s): ByteBuffer, MappedByteBuffer, ShortBuffer, ...
Buffer_isReadOnly_ex3.java
package org.o7planning.buffer.ex;
import java.io.IOException;
import java.nio.Buffer;
import java.nio.ByteBuffer;
import java.nio.CharBuffer;
import java.nio.DoubleBuffer;
import java.nio.FloatBuffer;
import java.nio.IntBuffer;
import java.nio.LongBuffer;
import java.nio.MappedByteBuffer;
import java.nio.ShortBuffer;
import java.nio.channels.FileChannel;
import java.nio.file.Files;
import java.nio.file.Path;
import java.nio.file.Paths;
import java.nio.file.StandardOpenOption;
public class Buffer_isReadOnly_ex3 {
public static void main(String[] args) throws IOException {
ByteBuffer b1 = ByteBuffer.allocate(10);
//
Path pathToWrite = Paths.get("/Volumes/Data/test/out-file.txt");
FileChannel fileChannel = (FileChannel) Files.newByteChannel(pathToWrite, //
StandardOpenOption.READ,
StandardOpenOption.WRITE,
StandardOpenOption.TRUNCATE_EXISTING);
CharBuffer charBuffer = CharBuffer.wrap("This will be written to the file");
MappedByteBuffer b2 = fileChannel.map(FileChannel.MapMode.READ_WRITE, 0, charBuffer.length());
//
ShortBuffer b3 = ShortBuffer.allocate(10);
IntBuffer b4 = IntBuffer.allocate(10);
FloatBuffer b5 = FloatBuffer.allocate(10);
LongBuffer b6 = LongBuffer.allocate(10);
DoubleBuffer b7 = DoubleBuffer.allocate(10);
CharBuffer b8 = CharBuffer.allocate(10);
Buffer[] buffers = new Buffer[] { b1, b2, b3, b4, b5, b6, b7, b8 };
for (Buffer buffer : buffers) {
System.out.println(buffer.getClass().getSimpleName() + " --> " + buffer.isReadOnly());
}
System.out.println(" --------- ");
ByteBuffer b1r = b1.asReadOnlyBuffer();
MappedByteBuffer b2r = (MappedByteBuffer) b2.asReadOnlyBuffer();
ShortBuffer b3r = b3.asReadOnlyBuffer();
IntBuffer b4r = b4.asReadOnlyBuffer();
FloatBuffer b5r = b5.asReadOnlyBuffer();
LongBuffer b6r = b6.asReadOnlyBuffer();
DoubleBuffer b7r = b7.asReadOnlyBuffer();
CharBuffer b8r = b8.asReadOnlyBuffer();
Buffer[] readOnlyBuffers = new Buffer[] { b1r, b2r, b3r, b4r, b5r, b6r, b7r, b8r };
for (Buffer buffer : readOnlyBuffers) {
System.out.println(buffer.getClass().getSimpleName() + " --> " + buffer.isReadOnly());
}
}
}
Output:
HeapByteBuffer --> false
DirectByteBuffer --> false
HeapShortBuffer --> false
HeapIntBuffer --> false
HeapFloatBuffer --> false
HeapLongBuffer --> false
HeapDoubleBuffer --> false
HeapCharBuffer --> false
---------
HeapByteBufferR --> true
DirectByteBufferR --> true
HeapShortBufferR --> true
HeapIntBufferR --> true
HeapFloatBufferR --> true
HeapLongBufferR --> true
HeapDoubleBufferR --> true
HeapCharBufferR --> true
21- isDirect()
public abstract boolean isDirect();
View more Tutorials:
|
__label__pos
| 0.965597 |
IgE-binding factors from mouse T lymphocytes. I. Formation of IgE-binding factors by stimulation with homologous IgE and interferon
T. Uede, K. Sandberg, B. R. Bloom, K. Ishizaka
Research output: Contribution to journalArticlepeer-review
Abstract
Incubation of normal mouse spleen cells with homologous IgE resulted in the formation of soluble factors that inhibited rosette formation of mouse FcεR+ cells with IgE-coated ox erythrocytes. The soluble factors could be adsorbed with mouse or rat IgE coupled to Sepharose and recovered from the beads by acid elution. However, the factors had no affinity for either human IgE or mouse IgG. The IgE-binding factors were derived from T cells. Production of the factors required Lyt1+ T cells and FcγR+ cells, which suggests that the factors are derived from FcγR+ Lyt 1+ T cells. The molecular size of Ige-binding factors was approximately 15,000 daltons. When IgE-binding factors were formed by BALB/c spleen cells, nearly one-half of the factors had affinity for lentil lectin, and the remaining half of the factors failed to bind to the lectin. The proportion of the two species of IgE-binding factors differed depending on mouse strains. The majority of the factors formed by B6D2F1 spleen cells had affinity for lentil lectin, but those formed by SJL spleen cells failed to bind to the lectin. The IgE-binding factors were also induced by incubation of normal spleen cells with polyinosinic-polycytidylic acid (pI:pC). The nucleotide stimulated splenic adherent cells to form 'inducers' of IgE-binding factors, which in turn induced normal lymphocytes to form IgE-binding factors. The inducers of IgE-binding factors were inactivated (or neutralized) by antibodies specific for mouse Type I interferon. It was also found that purified mouse β interferon could induce the formation of IgE-binding factors. IgE-binding factors induced by pI:pC consisted of two different molecules: one had a m.w. of 15,000 daltons, and another had a m.w. of between 40,000 and 60,000 daltons.
Original languageEnglish (US)
Pages (from-to)649-654
Number of pages6
JournalJournal of Immunology
Volume130
Issue number2
StatePublished - 1983
ASJC Scopus subject areas
• Immunology and Allergy
• Immunology
Fingerprint Dive into the research topics of 'IgE-binding factors from mouse T lymphocytes. I. Formation of IgE-binding factors by stimulation with homologous IgE and interferon'. Together they form a unique fingerprint.
Cite this
|
__label__pos
| 0.875118 |
设计模式-观察者模式
1、简单了解
在对象之间定义了一对多的依赖，这样一来，当一个对象改变状态，依赖它的对象会收到通知并自动更新，成为观察者模式。
观察者模式又称为发布/订阅(Publish/Subscribe)模式。
2、该模式包含四个角色
• 抽象被观察者角色：也就是一个抽象主题，它把所有对观察者对象的引用保存在一个集合中，每个主题都可以有任意数量的观察者。抽象主题提供一个接口，可以增加和删除观察者角色。一般用一个抽象类和接口来实现。
• 抽象观察者角色：为所有的具体观察者定义一个接口，在得到主题通知时更新自己。
• 具体被观察者角色：也就是一个具体的主题，在集体主题的内部状态改变时，所有登记过的观察者发出通知。
• 具体观察者角色：实现抽象观察者角色所需要的更新接口，一边使本身的状态与制图的状态相协调
3、我们来看一个例子
公众号推送消息的案例(来源：https://www.cnblogs.com/luohanguo/p/7825656.html)
1）定义一个抽象被观察者接口
/**
抽象被观察者接口
*/
public interface Observerable {
void registerObserver(Observer o);
void removeObserver(Observer o);
void notifyObserver();
}
2)定义一个抽象观察者接口
public interface Observer {
void update(String message);
}
3)定义被观察者，实现了Observerable接口，对Observerable接口的三个方法进行了具体实现，同时有一个List集合，用以保存注册的观察者，等需要通知观察者时，遍历该集合即可
public class WechatServer implements Observerable {
// 注意到这个List集合的泛型参数为Observer接口，设计原则：面向接口编程而不是面向实现编程
private List<Observer> list;
private String message;
public WechatServer() {
list = new ArrayList<Observer>();
}
@Override
public void registerObserver(Observer o) {
list.add(o);
}
@Override
public void removeObserver(Observer o) {
if (!list.isEmpty())
list.remove(o);
}
@Override
public void notifyObserver() {
for (int i = 0; i < list.size(); i++) {
Observer oserver = list.get(i);
oserver.update(message);
}
}
public void setInfomation(String s) {
this.message = s;
System.out.println("微信服务更新消息： " + s);
// 消息更新，通知所有观察者
notifyObserver();
}
}
4)定义具体观察者，微信公众号的具体观察者为用户User
public class User implements Observer {
private String name;
private String message;
public User(String name) {
this.name = name;
}
@Override
public void update(String message) {
this.message = message;
read();
}
public void read() {
System.out.println(name + " 收到推送消息： " + message);
}
}
5)测试
首先注册了三个用户，ZhangSan、LiSi、WangWu。公众号发布了一条消息"PHP是世界上最好用的语言！"，三个用户都收到了消息。
用户ZhangSan看到消息后颇为震惊，果断取消订阅，这时公众号又推送了一条消息，此时用户ZhangSan已经收不到消息，其他用户
还是正常能收到推送消息。
public static void main(String[] args) {
WechatServer server = new WechatServer();
Observer userZhang = new User("ZhangSan");
Observer userLi = new User("LiSi");
Observer userWang = new User("WangWu");
server.registerObserver(userZhang);
server.registerObserver(userLi);
server.registerObserver(userWang);
server.setInfomation("PHP是世界上最好用的语言！");
System.out.println("----------------------------------------------");
server.removeObserver(userZhang);
server.setInfomation("JAVA是世界上最好用的语言！");
}
20200115125233
4、总结
• 优点
1）观察者和被观察者之间抽象耦合。观察者模式容易扩展，被观察者只持有观察者集合，并不需要知道具体观察者内部的实现。
2）对象之间的保持高度的协作。当被观察者发生变化时，所有被观察者都会通知到，然后做出相应的动作。
• 缺点
1）如果观察者太多，被观察者通知观察者消耗的时间很多，影响系统的性能。
2）当观察者集合中的某一观察者错误时就会导致系统卡壳，因此一般会采用异步方式。
Copyright: 采用 知识共享署名4.0 国际许可协议进行许可
Links: https://www.fengpt.cn/archives/设计模式-观察者模式
|
__label__pos
| 0.982715 |
ggarman
1 Copper
Inspiron 11 - 3147 Power off but still on!!!????
Just installed Windows 10 Home with the anniversary release and upgraded BIOS to A10. Now, the really weird part is if I power it off completely it is still running somehow because the case is warm back around the CPU vent slots. It isn't plugged in charging, Windows goes through its shutdown normally, screen goes completely black, all lights are off, but it stays warm and eventually drains the battery. I've also had the difficulties resuming from sleep like others have had.
Has anyone else had the "staying on after power off" issue?
Is reverting to A07 BIOS the only solution? Is A11 coming out soon with the fix?
Thanks!
0 Kudos
|
__label__pos
| 0.899741 |
sound waves
Sound is converted into electricity by a telephone and then transmitted as an analog signal.
These waves have 3 fundamental characteristics:
1. Amplitude, meaning the height (intensity) of the wave
2. Frequency, which is the number of waves that pass in a single second and is measured in Hertz (cycles/second) (wavelength, the length of the wave from crest to crest, is related to frequency.).
3. Phase is a third characteristic that describes the point in the wave’s cycle at which a wave begins and is measured in degrees. (For example, changing a wave’s cycle from crest to trough corresponds to a 180 degree phase shift).
wave
2 thoughts on “sound waves
1. Hello alicia I am sorry about replying late , the next blog on the subject of modulation is still under process . I shall email notify you as soon as it publishes 🙂
Leave a Reply
Fill in your details below or click an icon to log in:
WordPress.com Logo
You are commenting using your WordPress.com account. Log Out / Change )
Google photo
You are commenting using your Google account. Log Out / Change )
Twitter picture
You are commenting using your Twitter account. Log Out / Change )
Facebook photo
You are commenting using your Facebook account. Log Out / Change )
Connecting to %s
This site uses Akismet to reduce spam. Learn how your comment data is processed.
|
__label__pos
| 0.659108 |
Peter M. May
Learn More
Formation constants for the calcium(II), magnesium(II) and zinc(II) complexes of the orally effective iron chelator, pyridoxal isonicotinoyl hydrazone (PIH) and three analogues, pyridoxal benzoyl hydrazone (PBH), pyridoxalp-methoxybenzoyl hydrazone (PpMBH) and pyridoxalm-fluorobenzoyl hydrazone (PmFBH) have been determined by potentiometry at 25\dg C(More)
Formation constants for the calcium(II), copper(II), iron(II), magnesium(II), manganese(II) and zinc(II) complexes ofdl-NN'-dicarboxamidomethyl-NN'-dicarboxymethyl-1,2-diaminopropane (ICRF 198) and the 1,2-diamino-butane homologue (ICRF 226) have been measured potentiometrically at 37°C andI=150 mmol dm−3 [NaCl]. The constants are used in computer(More)
Estimates of the concentrations and identity of the predominant complexes of iron with the low-molecular-mass ligands in vivo are important to improve current understanding of the metabolism of this trace element. These estimates require a knowledge of the stability of the iron-citrate complexes. Previous studies on the equilibrium properties of the(More)
The ionic product of water, pK(w)=-log[H(+)][OH(-)], has been determined in aqueous solutions of sodium perchlorate over the concentration range of 1.0-8.0 M at 25 degrees C from high-precision potentiometric titrations carried out in cells with liquid junction using both glass and hydrogen electrodes. The glass electrode results are systematically lower(More)
Although the absolute concentrations of metal complexes in blood plasma are controlled by protein binding, the percentage distribution of transition metal ions amongst low molecular weight ligands is not. Thus, computer simulations which omit protein equilibria can nevertheless afford reliable information about such metals in the biofluid.
Formation constants for copper(II) and zinc(II) complexes of isonicotinoylhydrazine (isoniazid) and guanosine-5′-monophosphate have been measured potentiometrically at 37°C,I=150 mmol dm−3 [NaCl]. These constants have been used in computer models to assess the extent of complex formation by the drugin vivo. The simulations indicate that the predominant(More)
The metal complexing properties of two antihypertensive drugs, hydralazine (1-hydrazinophthalazine) and prizidilol (a hydrazinopyridazine), and some related ligands, have been studied using potentiometry, elemental analysis, spectrophotometry and computer simulation. The coordination chemistry of 1-hydrazinophthalazine and the hydrazinopyridazines is(More)
The thermodynamic database of the JESS (Joint Expert Speciation System) software package is described. It overcomes many existing problems associated with solution-chemistry databases. The system is fully interactive. Reactions can be expressed in any form. Any number of equilibrium constants, enthalpy, entropy and Gibbs-free energy values can be associated(More)
|
__label__pos
| 0.647236 |
• Masahiro Yamada's avatar
flash: complete CONFIG_SYS_NO_FLASH move with renaming · e856bdcf
Masahiro Yamada authored
We repeated partial moves for CONFIG_SYS_NO_FLASH, but this is
not completed. Finish this work by the tool.
During this move, let's rename it to CONFIG_MTD_NOR_FLASH.
Actually, we have more instances of "#ifndef CONFIG_SYS_NO_FLASH"
than those of "#ifdef CONFIG_SYS_NO_FLASH". Flipping the logic will
make the code more readable. Besides, negative meaning symbols do
not fit in obj-$(CONFIG_...) style Makefiles.
This commit was created as follows:
[1] Edit "default n" to "default y" in the config entry in
common/Kconfig.
[2] Run "tools/moveconfig.py -y -r HEAD SYS_NO_FLASH"
[3] Rename the instances in defconfigs by the following:
find . -path './configs/*_defconfig' | xargs sed -i \
-e '/CONFIG_SYS_NO_FLASH=y/d' \
-e 's/# CONFIG_SYS_NO_FLASH is not set/CONFIG_MTD_NOR_FLASH=y/'
[4] Change the conditionals by the following:
find . -name '*.[ch]' | xargs sed -i \
-e 's/ifndef CONFIG_SYS_NO_FLASH/ifdef CONFIG_MTD_NOR_FLASH/' \
-e 's/ifdef CONFIG_SYS_NO_FLASH/ifndef CONFIG_MTD_NOR_FLASH/' \
-e 's/!defined(CONFIG_SYS_NO_FLASH)/defined(CONFIG_MTD_NOR_FLASH)/' \
-e 's/defined(CONFIG_SYS_NO_FLASH)/!defined(CONFIG_MTD_NOR_FLASH)/'
[5] Modify the following manually
- Rename the rest of instances
- Remove the description from README
- Create the new Kconfig entry in drivers/mtd/Kconfig
- Remove the old Kconfig entry from common/Kconfig
- Remove the garbage comments from include/configs/*.h
Signed-off-by: default avatarMasahiro Yamada <[email protected]>
e856bdcf
M5253DEMO_defconfig 279 Bytes
|
__label__pos
| 0.777663 |
Click Here to Start Increasing Your Metabolism and Losing Weight
Check
Waters Powerful Role in Healthy Brain Function
Are you worried about losing your memory? Learn why drinking fresh and pure water is a natural way to maintain healthy brain function throughout your life.
Waters Role in Functional Brain Function
Water plays a very important role in the diet and function of your body. Many parts of your brain draw a lot of their energy from water.
Water must be brought into your body in a natural, natural way, maximizing your weight in ounces every day.
Water is essential for energy production in cells and in your overall metabolism, and neurotransmission. Nerve transmission is highly dependent on water. A small stream of water, or a micro-stream runs along the length of your nerves. This stream applies neurotransmitters along the microtubules to the nerve endings.
When your body is dehydrated, nerve transmission is compromised and brain function decreases. Chronic nerve pain can only be the end result of chronic dehydration.
Many chronic and painful conditions, including arthritis and fibromyalgia, are often significantly reduced after adequate rehydration.
Another important consideration is that water actually holds your body cells together. Water keeps the cell membranes together by forming hydronium ions that make water sticky and help bind your cells together. This gives your cells a higher viscosity that helps increase the efficiency of proteins and enzymes.
In dehydrated cells, their metabolism is greatly reduced. Dehydration has a dramatic effect especially on sugar metabolism, immune system and detoxification. Dehydration greatly affects the movement of the lymph through the body and causes the lymph system to clog up and break down.
From the cellular point of view, the delivery of nutrients through the cell wall is done by water. Many deficiencies are often specific dehydration problems.
Dehydration is an important producer of free radicals in your body and hydration effectively removes free radicals faster than most other therapies. Fully hydrated body can reduce your need for antioxidant supplements.
Lung dehydration is considered an important factor in respiratory disease. Sometimes the most dramatic results can be found in asthma and chronic bronchitis with simple rehydration.
Dehydration is a major source of stress in the body and changes the amino acid balance. This can cause DNA damage during cell division which can lead to many diseases such as cancer and other cell mutation problems.
Water is an important energy conductor such as your meridian and chakra energy systems. When your body is dry, it's very difficult for energy-based therapies like acupunture, Reiki, Bowenwork® and BodyTalk (TM) to work.
Due to imbalances in the cellular environment many cells of the human body and brain tissue are dehydrated, despite drinking enough water. The BodyTalk system has specific procedures that address any underlying factors that may limit the absorption of water throughout your body.
------------------
No comments
|
__label__pos
| 0.886465 |
Why the Buzz About H.264?
H.264 Technology: It’s the bitrate!
H.264 is getting so much attention because it can encode video with approximately 3 times fewer bits than comparable MPEG-2 encoders.
Because H.264 is up to twice as efficient as MPEG-4 Part 2 (natural video) encoding, it has recently been welcomed into the MPEG-4 standard as Part 10 – Advanced Video Coding. Many established encoder and decoder vendors are moving directly to h.264 and skipping the intermediate step of MPEG-4 Part 2.
H.264 TechnologyGoals & Approach of H.264
The International Telecommunications Union (ITU) initiated the h.26L (for long term) effort in 1998 as a continuation of work following the MPEG-2 and h.263 standards. The overriding goal was to achieve a factor-of-2 reduction in bit rate compared to any competing standard.
Recall that MPEG-2 was optimized with specific focus on Standard and High Definition digital television services, which are delivered via circuit-switched head-end networks to dedicated satellite uplinks, cable infrastructure or terrestrial facilities. MPEG2’s ability to cope is being strained as the range of delivery media expands to include heterogeneous mobile networks, packet-switched IP networks, and multiple storage formats, and as the variety of services grows to include multimedia messaging, security, increased use of HDTV, and others. Thus, a second goal for h.264 was to accommodate a wider variety of bandwidth requirements, picture formats, and unfriendly network environments that throw high jitter, packet loss, and bandwidth instability into the mix.
The h.264 approach is a strictly evolutionary extension of the block-based encoding approach so well established in the MPEG and ITU standards. Key steps include:
• Use of Motion Estimation to support Inter-picture prediction for eliminating temporal redundancies
• Use of spatial correlation of data to provide Intra-picture prediction.
• Construction of residuals as the difference between predicted images and source images.
• Use of a discrete spatial transform and filtering to eliminate spatial redundancies in the residuals.
• Entropy coding of the transformed residual coefficients and of the supporting data such as motion vectors.
Major Features of H.264
Improved Inter-Prediction and Motion Estimation
First recall the limitations of motion estimation in MPEG-2, which searches reference pictures for a 16×16 set of pixels that closely matches the current macro block. The matching set of pixels must be completely within the reference picture. In contrast, H.264 provides:
• Fine-grained motion estimation. Temporal search seeks matching sub-macro blocks of variable size as small as 4×4, and finds the motion vector to _ pel resolution. Searches may also identify motion vectors associated with matching sub-macro blocks of 4×8, 8×4, 8×8, 8×16, 16×8, or the full 16×16. [In future, even finer 1/8 pel resolution will be supported.]
• Multiple reference frames. H.264 provides additional flexibility for frames to point to more than multiple frames – which may be any combination of past and future frames. This capability provides opportunities for more precise inter-prediction, but also improved robustness to lost picture data.
• Unrestricted motion search . Motion search allows for reference frames that may be partly outside the picture; missing data can be spatially predicted from boundary data. Users may choose to disable this feature by specifying a Restricted Motion search.
• Motion vector prediction. Where sufficient temporal correlation exists, motion vectors may be accurately predicted and only their residuals transmitted explicitly in the bitstream.
Such techniques not only provide for more accurate inter-prediction, but also help to partition and scale the bitstream with priority given to data that is more globally applicable. Thus, they not only improve compression but also resilience to errors and network instabilities.
Motion Compensation Accuracy
Improved Intra Spatial Prediction and Transform
Because “intra prediction” is concerned with only one picture at a time, it relies upon spatial rather than temporal correlations. As the algorithm works through a picture’s macro blocks in raster scan order, earlier results may be used to “predict” the downstream calculations. Then we need only transmit residuals as refinements to the predicted results.
H.264 performs intra prediction in the spatial domain (prior to the transform, and it is a key part of the approach. Even for an intra-picture, every block of data is predicted from its neighbors before being transformed and coefficients generated for inclusion in the bitstream.
• Coarse versus fine intra prediction. Intra prediction may be performed either on 4×4 blocks, or 16×16 macro blocks. The latter is more efficient for uniform areas of a picture.
• Direction Dependent Intra Modes. By doing intra prediction in the spatial domain (rather than in the transform domain), h.264 can employ prediction that is direction dependent, and thus can focus on the most highly correlated neighbors. For Intra 16×16 coding and Intra 4 x 4 coding, there are 9 and 4 directional modes, respectively.
• 4×4 transform of Residual Data. For initially supported profiles, residual data transforms are always performed for 4×4 blocks of data, and coefficients transmitted on this fine-grained basis.
• Variable block sizes for spatial transform*. Future profiles will allow transform of variable size blocks (4×8, 8×8, etc.) with the same level of flexibility as motion estimation blocks. This will provide more flexibility and further reduction of bitrate.
• Integer transforms. Efficiency in both computation and bitrate is gained by implementing the traditional Discrete Cosine Transform (DCT) as an integer transform that requires no multiplications, except for a single normalization. It can also be inverted exactly without mismatch.
• Deblocking filter. To eliminate fine structure blockiness that might be aggravated by the smaller transform blocks, a context-sensitive deblocking filter smoothes out the internal edges. Its filter strength depends upon the prediction modes and relationship between the neighboring blocks. In addition to increasing signal-to-noise ratio (S/N), this technique significantly improves the subjective quality of the image for a given S/N.
Improved Algorithms for Encoding
Two alternative methods improve efficiency of the entropy coding process by selecting variable length codes depending upon context of the data being encoded.
• Context-Adaptive Variable Length Coding (CAVLC) employs multiple variable length codeword tables to encode transform coefficients, which consume the bulk of bandwidth. Based upon a priori statistics of already processed data, the best table is selected adaptively. For non-coefficient data, a simpler scheme is used that relies upon only a single table.
• Context-Adaptive Binary Arithmetic Coding (CABAC*) provides an extremely efficient encoding scheme when it is known that certain symbols are much more likely than others. Such dominant symbols may be encoded with extremely small bit/symbol ratios. The CABAC method continually updates frequency statistics of the incoming data and adaptively adjusts the algorithm in real-time. This method is an advanced option available in profiles beyond the baseline profile.
Techniques for Mitigation of Errors, Packet Losses, and Network Variability
Error containment and scalability
H.264 includes several other features that are useful in containing the impact of errors, and in enabling the use of scalable or multiple bit streams:
• Slice coding. Each picture is subdivided into one or more slices. The slice is given increased importance in H.264 as the basic spatial segment that is independent from its neighbors. Thus, errors or missing data from one slice cannot propagate to any other slice within the picture. This also increases flexibility to extend picture types (I, P, B) down to the level of “slice types.” Redundant slices are permitted.
• Data partitioning is supported to allow higher priority data (e.g., sequence headers) to be separated from lower priority data (e.g., B-picture transform coefficients).
• Flexible macro block ordering (FMO) can be used to scatter the bits associated with adjoining macro blocks more randomly throughout the bit stream. This reduces the chance that a packet loss will affect a large region and enables error concealment by ensuring that neighboring macro blocks will be available for prediction of a missing macro block.
• The Multiple Reference Frames that are used for improved motion estimation also allow for partial motion compensation for a P picture when one of its referenced frames is missing or corrupted.
SI and SP Pictures (or slices)*
MPEG-2 practice is to insert intra pictures (I) at regular intervals to contain errors that otherwise could propagate through the picture sequence indefinitely. In addition, intra-pictures provide a means for random access or fast-forward actions, because intra frames do not require any knowledge of other referenced frames. Similarly, regular I pictures would be necessary to switch promptly from between higher and lower bitrate streams – an important feature for accommodating the bandwidth variability in mobile networks. However, I pictures typically require far more bits than P pictures and thus are an inefficient means for addressing these two requirements.
H.264 introduces two new slice types, “Switching I Pictures” (SI) and “Switching P Pictures” (SP), which help address these needs with significantly reduced bit rate. Identical SP frames can be obtained even though different reference frames are used – thus, they can be substituted for I frames as temporal resynchronization points, but with significantly reduced bitrate. SP pictures rely upon the transformation and quantization of predicted inter blocks. Because SP pictures do not take full advantage of intra-prediction, at the cost of some bits they can be extended to SI pictures which do so.
Note that because slices are coded independently, switching slices (SI or SP) can be defined at that level.
Low Latency Feature
Arbitrary Slice Ordering (ASO) relaxes the constraint that all macro blocks must be sequenced in decoding order, and thus enhances flexibility for low-delay performance important in teleconferencing, surveillance and interactive Internet applications.
Simplified Profiles
H.264 is completely focused on efficient coding of natural video and does not directly address the object-oriented functionality, synthetic video, and other systems functionality in MPEG-4, which carries a very complex structure of over 50 profiles.
In contrast, H.264 is initially defined with only three profiles:
• Baseline Profile. A basic goal of H.264 was to provide a royalty-free baseline profile to encourage early application of the standard. The baseline profile consists most of the major features described above, with the exception of: B slices and weighted prediction; CABAC encoding; field coding; and SP & SI slices. Thus, the baseline profile is appropriate for many progressive scan applications such as video conferencing and video-over-IP, but not for interlaced television or multiple stream applications.
• Main Profile. Main profile contains all of the features in Baseline, except flexible macro block ordering (FMO), arbitrary slice order (ASO) and redundant slices. However, it adds field coding, B slices and weighted prediction, and CABAC entropy coding. This profile is appropriate for efficient coding of interlaced television applications where bit or packet error is not excessive, and where low latency is not a requirement.
• Extended Profile. This profile contains all features from the baseline profile and main profiles, except that CABAC is not supported. In addition, the Extended profile adds SP and SI for stream switching, and up to 8 slice groups. This profile is appropriate for server-based streaming applications where bit-rate scalability and error rate is very important. Security Applications and Mobile video services would be an example.
Where will H.264 have the biggest impact?
Any video application can benefit from a reduction in bandwidth requirements, but highest impact will involve applications where such reduction relieves a hard technical constraint, or which makes more cost-effective use of bandwidth as a limiting resource.
In addition, other h.264 features such error containment, error concealment, and efficient bitstream switching is especially useful for IP and wireless environments.
Squeeze More Services into a Broadcast Channel
Reduction in bandwidth requirements by factors of 2-3 provide cost savings for bandwidth-constrained services such as satellite and DVB-Terrestrial, or alternatively allow such providers to expand services at reduced incremental cost.
Facilitate High Quality Video Streaming over IP Networks
H.264 can produce very good quality, TV Quality streaming at less than 1Mbps (standard definition). This slips under 1 Mbps thresholds for xDSL and thus opens possibilities for new access methods for high quality, larger format video.
High Definition Transmission and Storage
Recall that MPEG-2 consumes 15-20 Mbps for High Definition video at suitable quality for broadcast or DVD. Use of h.264 will bring this down to about 8 Mbps, making it possible for bandwidth-strapped satellite service providers to fit 4 HD channels per QPSK channel.
Even more significant is that this reduction enables burning one HD movie onto a conventional DVD, thus avoiding the need for the industry to adapt a higher density (“blue laser”) DVD format.
Mobile Video Applications
3G Mobile networks present an unusual array of technical challenges that have driven many features in h.264. Applications include video conferencing, streaming video on demand, multimedia-messaging services, and low resolution broadcast. Some key issues, and h.264 tools for dealing with them, include:
• Low bandwidth (50 – 300 kbps) is the key issue. The expected trend is for 3G deployment to start with h.263 and move up to h.264 as it matures. An industry analyst points out “… 3G networks are only likely to offer 57.6kbit/s initially. As those bit rates increase, mobiles and networks will move to the new H.264 codec, which offers twice the performance of H.263. This should result in the same picture quality being achieved at half the bit rate.”
• Small devices with many formats; variability of available bandwidth. For streaming applications, these two separate issues can be addressed by providing multiple streams with different formats and bandwidths, and selecting the appropriate stream at run-time. H.264’s SP and SI pictures facilitate dynamic switching among multiple streams to accommodate bandwidth variability.
• High bit error rates, packet losses, and latency. For video applications, retransmissions are impractical for dropped or delayed packets, so h.264 provides several means (e.g., FMO, data partitioning, etc.) to contain error impacts and facilitate error concealment.
What is the relationship to MPEG-4 and MPEG-2?
Compared to MPEG-2
H.264 employs the same general approach as MPEG 1 & 2 as well as the h.261 and h.263 standards, but adds many incremental improvements to obtain coding efficiency improvement of about a factor-of-3.
MPEG-2 was optimized with specific focus on Standard and High Definition digital television services, which are delivered via circuit-switched head-end networks to dedicated satellite uplinks, cable infrastructure or terrestrial facilities. MPEG2’s ability to cope is being strained as the range of delivery media expands to include heterogeneous mobile networks, packet-switched IP networks, and multiple storage formats, and as the variety of services grows to include multimedia messaging, increased use of HDTV, and others. Thus, a second goal for h.264 was to accommodate a wider variety of bandwidth requirements, picture formats, and unfriendly network environments that throw high jitter, packet loss, and bandwidth instability into the mix.
Compared to MPEG-4
During 2002, the h.264 Video Coding Experts Group combined forces with MPEG4 experts to form the Joint Video Team (JVT), so H.264 is being published as MPEG-4 Part 10 (Advanced Video Coding).
MPEG-4 is really a family of standards whose overall theme is object-oriented multimedia applications. It thus has much broader scope than H.264, which is strictly focused on more efficient and robust video coding. The comparable part of MPEG-4 is Part 2 Visual (sometimes called “Natural Video”). Other parts of MPEG address scene composition, object description and java representation of behavior, animation of human body and facial movements, audio and systems.
MPEG-4
|
__label__pos
| 0.610337 |
periph: periph.io/x/periph/conn/gpio Index | Examples | Files | Directories
package gpio
import "periph.io/x/periph/conn/gpio"
Package gpio defines digital pins.
All GPIO implementations are expected to implement PinIO but the device driver may accept a more specific one like PinIn or PinOut.
Code:
// Make sure periph is initialized.
if _, err := host.Init(); err != nil {
log.Fatal(err)
}
// Use gpioreg GPIO pin registry to find a GPIO pin by name.
p := gpioreg.ByName("GPIO6")
if p == nil {
log.Fatal("Failed to find GPIO6")
}
// A pin can be read, independent of its state; it doesn't matter if it is
// set as input or output.
fmt.Printf("%s is %s\n", p, p.Read())
Index
Examples
Package Files
func.go gpio.go
Constants
const (
// Inputs
IN pin.Func = "IN" // Input
IN_HIGH pin.Func = "In/High" // Read high
IN_LOW pin.Func = "In/Low" // Read low
// Outputs
OUT pin.Func = "OUT" // Output, drive
OUT_OC pin.Func = "OUT_OPEN" // Output, open collector/drain
OUT_HIGH pin.Func = "Out/High" // Drive high
OUT_LOW pin.Func = "Out/Low" // Drive low; open collector low
FLOAT pin.Func = "FLOAT" // Input float or Output open collector high
CLK pin.Func = "CLK" // Clock is a subset of a PWM, with a 50% duty cycle
PWM pin.Func = "PWM" // Pulse Width Modulation, which is a clock with variable duty cycle
)
type Duty Uses
type Duty int32
Duty is the duty cycle for a PWM.
Valid values are between 0 and DutyMax.
const (
// DutyMax is a duty cycle of 100%.
DutyMax Duty = 1 << 24
// DutyHalf is a 50% duty PWM, which boils down to a normal clock.
DutyHalf Duty = DutyMax / 2
)
func ParseDuty Uses
func ParseDuty(s string) (Duty, error)
ParseDuty parses a string and converts it to a Duty value.
Code:
d, err := gpio.ParseDuty("33%")
if err != nil {
log.Fatal(err)
}
fmt.Println(d)
Output:
33%
func (Duty) String Uses
func (d Duty) String() string
func (Duty) Valid Uses
func (d Duty) Valid() bool
Valid returns true if the Duty cycle value is valid.
type Edge Uses
type Edge int
Edge specifies if an input pin should have edge detection enabled.
Only enable it when needed, since this causes system interrupts.
const (
NoEdge Edge = 0
RisingEdge Edge = 1
FallingEdge Edge = 2
BothEdges Edge = 3
)
Acceptable edge detection values.
func (Edge) String Uses
func (i Edge) String() string
type Level Uses
type Level bool
Level is the level of the pin: Low or High.
const (
// Low represents 0v.
Low Level = false
// High represents Vin, generally 3.3v or 5v.
High Level = true
)
func (Level) String Uses
func (l Level) String() string
type PinIO Uses
type PinIO interface {
pin.Pin
// PinIn
In(pull Pull, edge Edge) error
Read() Level
WaitForEdge(timeout time.Duration) bool
Pull() Pull
DefaultPull() Pull
// PinOut
Out(l Level) error
PWM(duty Duty, f physic.Frequency) error
}
PinIO is a GPIO pin that supports both input and output. It matches both interfaces PinIn and PinOut.
A GPIO pin implementing PinIO may fail at either input or output or both.
var INVALID PinIO
INVALID implements PinIO and fails on all access.
type PinIn Uses
type PinIn interface {
pin.Pin
// In setups a pin as an input.
//
// If WaitForEdge() is planned to be called, make sure to use one of the Edge
// value. Otherwise, use NoEdge to not generated unneeded hardware interrupts.
//
// Calling In() will try to empty the accumulated edges but it cannot be 100%
// reliable due to the OS (linux) and its driver. It is possible that on a
// gpio that is as input, doing a quick Out(), In() may return an edge that
// occurred before the Out() call.
In(pull Pull, edge Edge) error
// Read return the current pin level.
//
// Behavior is undefined if In() wasn't used before.
//
// In some rare case, it is possible that Read() fails silently. This happens
// if another process on the host messes up with the pin after In() was
// called. In this case, call In() again.
Read() Level
// WaitForEdge() waits for the next edge or immediately return if an edge
// occurred since the last call.
//
// Only waits for the kind of edge as specified in a previous In() call.
// Behavior is undefined if In() with a value other than NoEdge wasn't called
// before.
//
// Returns true if an edge was detected during or before this call. Return
// false if the timeout occurred or In() was called while waiting, causing the
// function to exit.
//
// Multiple edges may or may not accumulate between two calls to
// WaitForEdge(). The behavior in this case is undefined and is OS driver
// specific.
//
// It is not required to call Read() to reset the edge detection.
//
// Specify -1 to effectively disable timeout.
WaitForEdge(timeout time.Duration) bool
// Pull returns the internal pull resistor if the pin is set as input pin.
//
// Returns PullNoChange if the value cannot be read.
Pull() Pull
// DefaultPull returns the pull that is initialized on CPU/device reset. This
// is useful to determine if the pin is acceptable for operation with
// certain devices.
DefaultPull() Pull
}
PinIn is an input GPIO pin.
It may optionally support internal pull resistor and edge based triggering.
A button is semantically a PinIn. So if you are looking to read from a button, PinIn is the interface you are looking for.
Code:
// Make sure periph is initialized.
if _, err := host.Init(); err != nil {
log.Fatal(err)
}
// Use gpioreg GPIO pin registry to find a GPIO pin by name.
p := gpioreg.ByName("GPIO6")
if p == nil {
log.Fatal("Failed to find GPIO6")
}
// Set it as input, with a pull down (defaults to Low when unconnected) and
// enable rising edge triggering.
if err := p.In(gpio.PullDown, gpio.RisingEdge); err != nil {
log.Fatal(err)
}
fmt.Printf("%s is %s\n", p, p.Read())
// Wait for rising edges (Low -> High) and print when one occur.
for p.WaitForEdge(-1) {
fmt.Printf("%s went %s\n", p, gpio.High)
}
type PinOut Uses
type PinOut interface {
pin.Pin
// Out sets a pin as output if it wasn't already and sets the initial value.
//
// After the initial call to ensure that the pin has been set as output, it
// is generally safe to ignore the error returned.
//
// Out() tries to empty the accumulated edges detected if the gpio was
// previously set as input but this is not 100% guaranteed due to the OS.
Out(l Level) error
// PWM sets the PWM output on supported pins, if the pin has hardware PWM
// support.
//
// To use as a general purpose clock, set duty to DutyHalf. Some pins may
// only support DutyHalf and no other value.
//
// Using 0 as frequency will use the optimal value as supported/preferred by
// the pin.
//
// To use as a servo, see https://en.wikipedia.org/wiki/Servo_control as an
// explanation how to calculate duty.
PWM(duty Duty, f physic.Frequency) error
}
PinOut is an output GPIO pin.
A LED, a buzzer, a servo, are semantically a PinOut. So if you are looking to control these, PinOut is the interface you are looking for.
Code:
// Make sure periph is initialized.
if _, err := host.Init(); err != nil {
log.Fatal(err)
}
// Use gpioreg GPIO pin registry to find a GPIO pin by name.
p := gpioreg.ByName("GPIO6")
if p == nil {
log.Fatal("Failed to find GPIO6")
}
// Set the pin as output High.
if err := p.Out(gpio.High); err != nil {
log.Fatal(err)
}
Code:
// Make sure periph is initialized.
if _, err := host.Init(); err != nil {
log.Fatal(err)
}
// Use gpioreg GPIO pin registry to find a GPIO pin by name.
p := gpioreg.ByName("GPIO6")
if p == nil {
log.Fatal("Failed to find GPIO6")
}
// Generate a 33% duty cycle 10KHz signal.
if err := p.PWM(gpio.DutyMax/3, 10*physic.KiloHertz); err != nil {
log.Fatal(err)
}
type Pull Uses
type Pull uint8
Pull specifies the internal pull-up or pull-down for a pin set as input.
const (
PullNoChange Pull = 0 // Do not change the previous pull resistor setting or an unknown value
Float Pull = 1 // Let the input float
PullDown Pull = 2 // Apply pull-down
PullUp Pull = 3 // Apply pull-up
)
Acceptable pull values.
func (Pull) String Uses
func (i Pull) String() string
type RealPin Uses
type RealPin interface {
Real() PinIO // Real returns the real pin behind an Alias
}
RealPin is implemented by aliased pin and allows the retrieval of the real pin underlying an alias.
Aliases are created by RegisterAlias. Aliases permits presenting a user friendly GPIO pin name while representing the underlying real pin.
The purpose of the RealPin is to be able to cleanly test whether an arbitrary gpio.PinIO returned by ByName is an alias for another pin, and resolve it.
Code:
// Make sure periph is initialized.
if _, err := host.Init(); err != nil {
log.Fatal(err)
}
// Use gpioreg GPIO pin registry to find a GPIO pin by name.
p := gpioreg.ByName("P1_3")
if p == nil {
log.Fatal("Failed to find P1_3")
}
fmt.Printf("P1_3: %s", p)
// Resolve the real underlying pin.
if r, ok := p.(gpio.RealPin); ok {
// On Raspberry Pis, pin #3 on header P1 is an alias for GPIO2.
fmt.Printf("%s is in fact %s", p, r.Real())
} else {
log.Printf("%s is not an alias", p)
}
Directories
PathSynopsis
gpioregPackage gpioreg defines a registry for the known digital pins.
gpiostreamPackage gpiostream defines digital streams.
gpiostream/gpiostreamtestPackage gpiostreamtest enables testing device driver using gpiostream.PinIn or PinOut.
gpiotestPackage gpiotest is meant to be used to test drivers using fake Pins.
Package gpio imports 6 packages (graph) and is imported by 108 packages. Updated 2018-11-21. Refresh now. Tools for package owners.
|
__label__pos
| 0.511325 |
[SciPy-dev] Input value from data file to 2D array
tournesol tournesol33@gmail....
Thu Apr 17 22:23:57 CDT 2008
Hi All.
I'm a newbie of python and scipy, numpy and
try to rewriting the Fortran77 code to Python.
First, here is my Fortran code.
DIMENSION A(10,10), B(10,10)
OPEN(21,FILE='aaa.dat')
DO 10 K=1,2
READ(21,1602) ((A(I,J),J=1,3),I=1,2)
READ(21,1602) ((B(I,J),J=1,3),I=1,2)
10 CONTINUE
WRITE(6,1602) ((A(I,J),J=1,3),I=1,2)
WRITE(6,1602) ((B(I,J),J=1,3),I=1,2)
1602 FORMAT(3I4)
END
and aaa.dat file is
0 1 1
1 1 1
2 1 1
; ; ;
; ; ;
18 1 1
19 1 1
The code is going to read each value of the data file(aaa.dat)
and input the value to the array A, B. According the "DO 10 K=1,2"
which means a loop of Fortran it is going to try to read 1st 2x3 array
and set them to A, also read 2nd 2x3 array to B.
Two "WRITE(6,1602) "s mean that the final value of array A and B are
3rd 2x3 array adn 4th 2x3 array
4 1 1
5 1 1
6 1 1
7 1 1
Question 1: How to input value from data file to 2D array ?
Can I write code like following ?
a=zeros([2,3], Float)
for i in range(1,2):
for j in range(1,3):
a[i][j]=i,j
(If the size of data file is very big , using
read_array() or fromfile() will be very hard. )
Question 2: Such like "DO 10 K=1,1500", I just read a part of
data file(<=very big file). How cat write this with Python ?
Any advice please!
More information about the Scipy-dev mailing list
|
__label__pos
| 0.824116 |
1
How to create customize primary key in MySQL?, example i have table and the table name is X, I have a table field as ID,Code,Name.
I am afraid if I have 1000 users and when they input together will result in destruction
and i want to :
INSERT INTO `X` (`ID`,`Code`,`Name`) VALUES
('P3K','Alex'), // this primary key is "P3K-1"
('SOS','Force'), // this primary key is "SOS-1"
('P3K','Bash'), // this primary key is "P3K-2"
Right now, i using TRIGGER (BEFORE INSERT) for this, like this one:
SET NEW.`ID` = CONCAT(NEW.`Code`,'-',IFNULL(SUBSTRING_INDEX((
SELECT `x`.`Code` FROM `X` WHERE
X.`Code` = NEW.`Code` and
ORDER BY X.`Code` DESC
LIMIT 1 ),'-',-1),0) + 1))
I did not try this code, but my point is:
1. User insert
2. Before insert I checking LAST Primary
3. IF Null then i set 0, else i cut the symbol (-) and take the last part
4. I increments (using [+ 1])
5. Final, i concat CODE and New Number.
am i misguided? LOL, and if true, how to create like this one? (I THINK) We can do it and maybe no one knows about this, how does AI in MySQL work so perfectly?
2
Do not make auto_increment any column you want to manipulate explicitly. That can confuse an engine and cause serious problems. If no column you have used for primary key are auto_increment you can do anything you want with them via triggers. Sure generated values will be rejected if they violate the mandatory uniqness of the primary key.
Your Answer
By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy
Not the answer you're looking for? Browse other questions tagged or ask your own question.
|
__label__pos
| 0.995618 |
Pages Menu
TwitterRssFacebook
Categories Menu
Posted by on Jun 7, 2015 in Tell Me Why Numerous Questions and Answers |
How Does a Light Bulb Work?
How Does a Light Bulb Work?
Inside a light bulb, a glass rod supports a thin, coiled wire called a filament. It is made of tungsten, a special metal that can stand extreme heat. When electricity passes through the tungsten filament, the filament becomes so hot that it glows with a bright light.
Before the bulb and its contents are sealed up tight all the air is pumped out, and a special non-burning gas is put in. This is done because the hot filament would quickly burn up if exposed to air. The inside of the bulb is given a white coat to make the bulb’s light softer.
Another common type of light is the fluorescent lamp. A fluorescent lamp is a glass tube filled with argon gas and a trough of mercury. When electrical current is passed through the gas the atoms of the gas pick up energy and radiate it in the form of ultra-violet light and some heat. The UV light then strikes the inside of the tube, which is coated with a phosphor. The phosphor glows, giving off the light we see.
Fluorescent lamps don’t require high temperatures to produce light, like incandescent bulbs do. Energy must be used in heating the incandescent bulb, and a large part of that energy is lost as heat, not light. In the fluorescent lamp, a larger portion of the energy is radiated as light.
Content for this question contributed by Wendy Palagyi, resident of Madison, Ohio, USA
|
__label__pos
| 0.998071 |
The Well-Grounded Rubyist, Second Edition
David A. Black
• June 2014
• ISBN 9781617291692
• 536 pages
• printed in black & white
Once again, the definitive book on Ruby from David Black. A must-have!
William Wheeler, TekSystems
The Well-Grounded Rubyist, Second Edition addresses both newcomers to Ruby as well as Ruby programmers who want to deepen their understanding of the language. This beautifully written and totally revised second edition includes coverage of features that are new in Ruby 2.1, as well as expanded and updated coverage of aspects of the language that have changed.
Listen to this book in liveAudio! liveAudio integrates a professional voice recording with the book’s text, graphics, code, and exercises in Manning’s exclusive liveBook online reader. Use the text to search and navigate the audio, or download the audio-only recording for portable offline listening. You can purchase or upgrade to liveAudio here or in liveBook.
Table of Contents detailed table of contents
preface
preface to the first edition
acknowledgments
about this book
about the cover illustration
Part 1 Ruby foundations
1. Bootstrapping your Ruby literacy
1.1. Basic Ruby language literacy
1.1.1. A Ruby syntax survival kit
1.1.2. The variety of Ruby identifiers
1.1.3. Method calls, messages, and Ruby objects
1.1.4. Writing and saving a simple program
1.1.5. Feeding the program to Ruby
1.1.6. Keyboard and file I/O
1.2. Anatomy of the Ruby installation
1.2.1. The Ruby standard library subdirectory (RbConfig::CONFIG[rubylibdir])
1.2.2. The C extensions directory (RbConfig::CONFIG[archdir])
1.2.3. The site_ruby (RbConfig::CONFIG[sitedir]) and vendor_ruby (RbConfig::CONFIG[vendordir]) directories
1.2.4. The gems directory
1.3. Ruby extensions and programming libraries
1.3.1. Loading external files and extensions
1.3.2. "Load"-ing a file in the default load path
1.3.3. "Require"-ing a feature
1.3.4. require_relative
1.4. Out-of-the-box Ruby tools and applications
1.4.1. Interpreter command-line switches
1.4.2. A closer look at interactive Ruby interpretation with irb
1.4.3. ri and RDoc
1.4.4. The rake task-management utility
1.4.5. Installing packages with the gem command
1.5. Summary
2. Objects, methods, and local variables
2.1. Talking to objects
2.1.1. Ruby and object orientation
2.1.2. Creating a generic object
2.1.3. Methods that take arguments
2.1.4. The return value of a method
2.2. Crafting an object: The behavior of a ticket
2.2.1. The ticket object, behavior first
2.2.2. Querying the ticket object
2.2.3. Shortening the ticket code via string interpolation
2.2.4. Ticket availability: Expressing Boolean state in a method
2.3. The innate behaviors of an object
2.3.1. Identifying objects uniquely with the object_id method
2.3.2. Querying an object’s abilities with the respond_to? method
2.3.3. Sending messages to objects with the send method
2.4. A close look at method arguments
2.4.1. Required and optional arguments
2.4.2. Default values for arguments
2.4.3. Order of parameters and arguments
2.4.4. What you can’t do in argument lists
2.5. Local variables and variable assignment
2.5.1. Variables, objects, and references
2.5.2. References in variable assignment and reassignment
2.5.3. References and method arguments
2.5.4. Local variables and the things that look like them
2.6. Summary
3. Organizing objects with classes
3.1. Classes and instances
3.1.1. Instance methods
3.1.2. Overriding methods
3.1.3. Reopening classes
3.2. Instance variables and object state
3.2.1. Initializing an object with state
3.3. Setter methods
3.3.1. The equal sign (=) in method names
3.3.2. Syntactic sugar for assignment-like methods
3.3.3. Setter methods unleashed
3.4. Attributes and the attr_* method family
3.4.1. Automating the creation of attributes
3.4.2. Summary of attr_* methods
3.5. Inheritance and the Ruby class hierarchy
3.5.1. Single inheritance: One to a customer
3.5.3. El Viejo’s older brother: BasicObject
3.6. Classes as objects and message receivers
3.6.1. Creating class objects
3.6.2. How class objects call methods
3.6.3. A singleton method by any other name…
3.6.4. When, and why, to write a class method
3.6.5. Class methods vs. instance methods
3.7. Constants up close
3.7.1. Basic use of constants
3.7.2. Reassigning vs. modifying constants
3.8. Nature vs. nurture in Ruby objects
3.9. Summary
4. Modules and program organization
4.1. Basics of module creation and use
4.1.1. A module encapsulating "stacklikeness"
4.1.2. Mixing a module into a class
4.1.3. Using the module further
4.2. Modules, classes, and method lookup
4.2.1. Illustrating the basics of method lookup
4.2.2. Defining the same method more than once
4.2.3. How prepend works
4.2.4. The rules of method lookup summarized
4.2.5. Going up the method search path with super
4.3. The method_missing method
4.3.1. Combining method_missing and super
4.4. Class/module design and naming
4.4.1. Mix-ins and/or inheritance
4.4.2. Nesting modules and classes
4.5. Summary
5. The default object (self), scope, and visibility
5.1. Understanding self, the current/default object
5.1.1. Who gets to be self, and where
5.1.2. The top-level self object
5.1.3. Self inside class, module, and method definitions
5.1.4. Self as the default receiver of messages
5.1.5. Resolving instance variables through self
5.2. Determining scope
5.2.1. Global scope and global variables
5.2.2. Local scope
5.2.3. The interaction between local scope and self
5.2.4. Scope and resolution of constants
5.2.5. Class variable syntax, scope, and visibility
5.3. Deploying method-access rules
5.3.1. Private methods
5.3.2. Protected methods
5.4. Writing and using top-level methods
5.4.1. Defining a top-level method
5.4.2. Predefined (built-in) top-level methods
5.5. Summary
6. Control-flow techniques
6.1. Conditional code execution
6.1.1. The if keyword and friends
6.1.2. Assignment syntax in condition bodies and tests
6.1.3. case statements
6.2. Repeating actions with loops
6.2.1. Unconditional looping with the loop method
6.2.2. Conditional looping with the while and until keywords
6.2.3. Looping based on a list of values
6.3. Iterators and code blocks6.3.1. The ingredients of iteration
6.3.1. Iteration, home-style
6.3.2. The anatomy of a method call
6.3.3. Curly braces vs. do/end in code block syntax
6.3.4. Implementing times
6.3.5. The importance of being each
6.3.6. From each to map
6.3.7. Block parameters and variable scope
6.4. Error handling and exceptions
6.4.1. Raising and rescuing exceptions
6.4.2. The rescue keyword to the rescue!
6.4.3. Raising exceptions explicitly
6.4.4. Capturing an exception in a rescue clause
6.4.5. The ensure clause
6.4.6. Creating your own exception classes
6.5. Summary
Part 2 Built-in classes and modules
7. Built-in essentials
7.1. Ruby’s literal constructors
7.2. Recurrent syntactic sugar
7.2.1. Defining operators by defining methods
7.2.2. Customizing unary operators
7.3. Bang (!) methods and "danger"
7.3.1. Destructive (receiver-changing) effects as danger
7.3.2. Destructiveness and "danger" vary independently
7.4. Built-in and custom to_* (conversion) methods
7.4.1. String conversion: to_s
7.4.2. Array conversion with to_a and the * operator
7.4.3. Numerical conversion with to_i and to_f
7.4.4. Role-playing to_* methods
7.5. Boolean states, Boolean objects, and nil
7.5.1. True and false as states
7.5.2. true and false as objects
7.5.3. The special object nil
7.6. Comparing two objects
7.6.1. Equality tests
7.6.2. Comparisons and the Comparable module
7.7. Inspecting object capabilities
7.7.1. Listing an object’s methods
7.7.2. Querying class and module objects
7.7.3. Filtered and selected method lists
7.8. Summary
8. Strings, symbols, and other scalar objects
8.1. Working with strings
8.1.1. String notation
8.1.2. Basic string manipulation
8.1.3. Querying strings
8.1.4. String comparison and ordering
8.1.5. String transformation
8.1.6. String conversions
8.1.7. String encoding: A brief introduction
8.2. Symbols and their uses
8.2.1. Chief characteristics of symbols
8.2.2. Symbols and identifiers
8.2.3. Symbols in practice
8.2.4. Strings and symbols in comparison
8.3. Numerical objects
8.3.1. Numerical classes
8.3.2. Performing arithmetic operations
8.4. Times and dates
8.4.1. Instantiating date/time objects
8.4.2. Date/time query methods
8.4.3. Date/time formatting methods
8.4.4. Date/time conversion methods
8.5. Summary
9. Collection and container objects
9.1. Arrays and hashes in comparison
9.2. Collection handling with arrays
9.2.1. Creating a new array
9.2.2. Inserting, retrieving, and removing array elements
9.2.3. Combining arrays with other arrays
9.2.4. Array transformations
9.2.5. Array querying
9.3. Hashes
9.3.1. Creating a new hash
9.3.2. Inserting, retrieving, and removing hash pairs
9.3.3. Specifying default hash values and behavior
9.3.4. Combining hashes with other hashes
9.3.5. Hash transformations
9.3.6. Hash querying
9.3.7. Hashes as final method arguments
9.3.8. A detour back to argument syntax: Named (keyword) arguments
9.4. Ranges
9.4.1. Creating a range
9.4.2. Range-inclusion logic
9.5. Sets
9.5.1. Set creation
9.5.2. Manipulating set elements
9.5.3. Subsets and supersets
9.6. Summary
10. Collections central: Enumerable and Enumerator
10.1. Gaining enumerability through each
10.2. Enumerable Boolean queries
10.3. Enumerable searching and selecting
10.3.1. Getting the first match with find
10.3.2. Getting all matches with find_all (a.k.a. select) and reject
10.3.3. Selecting on threequal matches with grep
10.3.4. Organizing selection results with group_by and partition
10.4. Element-wise enumerable operations
10.4.1. The first method
10.4.2. The take and drop methods
10.4.3. The min and max methods
10.5. Relatives of each
10.5.1. reverse_each
10.5.2. The each_with_index method (and each.with_index)
10.5.3. The each_slice and each_cons methods
10.5.4. The cycle method
10.5.5. Enumerable reduction with inject
10.6. The map method
10.6.1. The return value of map
10.6.2. In-place mapping with map!
10.7. Strings as quasi-enumerables
10.8. Sorting enumerables
10.8.1. Where the Comparable module fits into enumerable sorting (or doesn’t)
10.8.2. Defining sort-order logic with a block
10.8.3. Concise sorting with sort_by
10.9. Enumerators and the next dimension of enumerability
10.9.1. Creating enumerators with a code block
10.9.2. Attaching enumerators to other objects
10.9.3. Implicit creation of enumerators by blockless iterator calls
10.10. Enumerator semantics and uses
10.10.1. How to use an enumerator’s each method
10.10.2. Protecting objects with enumerators
10.10.3. Fine-grained iteration with enumerators
10.10.4. Adding enumerability with an enumerator
10.11. Enumerator method chaining
10.11.1. Economizing on intermediate objects
10.11.2. Indexing enumerables with with_index
10.11.3. Exclusive-or operations on strings with enumerators
10.12. Lazy enumerators
10.12.1. FizzBuzz with a lazy enumerator
10.13. Summary
11. Regular expressions and regexp-based string operations
11.1. What are regular expressions?
11.2. Writing regular expressions
11.2.1. Seeing patterns
11.2.2. Simple matching with literal regular expressions
11.3. Building a pattern in a regular expression
11.3.1. Literal characters in patterns
11.3.2. The dot wildcard character (.)
11.3.3. Character classes
11.4. Matching, substring captures, and MatchData
11.4.1. Capturing submatches with parentheses
11.4.2. Match success and failure
11.4.3. Two ways of getting the captures
11.4.4. Other MatchData information
11.5. Fine-tuning regular expressions with quantifiers, anchors, and modifiers
11.5.1. Constraining matches with quantifiers
11.5.2. Greedy (and non-greedy) quantifiers
11.5.3. Regular expression anchors and assertions
11.5.4. Modifiers
11.6. Converting strings and regular expressions to each other
11.6.1. String-to-regexp idioms
11.6.2. Going from a regular expression to a string
11.7. Common methods that use regular expressions
11.7.1. String#scan
11.7.2. String#split
11.7.3. sub/sub! and gsub/gsub!
11.7.4. Case equality and grep
11.8. Summary
12. File and I/O operations
12.1. How Ruby’s I/O system is put together
12.1.1. The IO class
12.1.2. IO objects as enumerables
12.1.3. STDIN, STDOUT, STDERR
12.1.4. A little more about keyboard input
12.2. Basic file operations
12.2.1. The basics of reading from files
12.2.2. Line-based file reading
12.2.3. Byte- and character-based file reading
12.2.4. Seeking and querying file position
12.2.5. Reading files with File class methods
12.2.6. Writing to files
12.2.7. Using blocks to scope file operations
12.2.8. File enumerability
12.2.9. File I/O exceptions and errors
12.3. Querying IO and File objects
12.3.1. Getting information from the File class and the FileTest module
12.3.2. Deriving file information with File::Stat
12.4. Directory manipulation with the Dir class
12.4.1. Reading a directory’s entries
12.4.2. Directory manipulation and querying
12.5. File tools from the standard library
12.5.1. The FileUtils module
12.5.2. The Pathname class
12.5.3. The StringIO class
12.5.4. The open-uri library
12.6. Summary
Part 3 Ruby dynamics
13. Object individuation
13.1. Where the singleton methods are: The singleton class
13.1.1. Dual determination through singleton classes
13.1.2. Examining and modifying a singleton class directly
13.1.3. Singleton classes on the method-lookup path
13.1.4. The singleton_class method
13.1.5. Class methods in (even more) depth
13.2. Modifying Ruby’s core classes and modules
13.2.1. The risks of changing core functionality
13.2.2. Additive changes
13.2.3. Pass-through overrides
13.2.4. Per-object changes with extend
13.2.5. Using refinements to affect core behavior
13.3. BasicObject as ancestor and class
13.3.1. Using BasicObject
13.3.2. Implementing a subclass of BasicObject
13.4. Summary
14. Callable and runnable objects
14.1. Basic anonymous functions: The Proc class
14.1.1. Proc objects
14.1.2. Procs and blocks and how they differ
14.1.3. Block-proc conversions
14.1.4. Using Symbol#to_proc for conciseness
14.1.5. Procs as closures
14.1.6. Proc parameters and arguments
14.2. Creating functions with lambda and →
14.3. Methods as objects
14.3.1. Capturing Method objects
14.3.2. The rationale for methods as objects
14.4. The eval family of methods
14.4.1. Executing arbitrary strings as code with eval
14.4.2. The dangers of eval
14.4.3. The instance_eval method
14.4.4. Using class_eval (a.k.a. module_eval)
14.5. Parallel execution with threads
14.5.1. Killing, stopping, and starting threads
14.5.2. A threaded date server
14.5.3. Writing a chat server using sockets and threads
14.5.4. Threads and variables
14.5.5. Manipulating thread keys
14.6. Issuing system commands from inside Ruby programs
14.6.1. The system method and backticks
14.6.2. Communicating with programs via open and popen3
14.7. Summary
15. Callbacks, hooks, and runtime introspection
15.1. Callbacks and hooks
15.1.1. Intercepting unrecognized messages with method_missing
15.1.2. Trapping include and prepend operations
15.1.3. Intercepting extend
15.1.4. Intercepting inheritance with Class#inherited
15.1.5. The Module#const_missing method
15.1.6. The method_added and singleton_method_added methods
15.2. Interpreting object capability queries
15.2.1. Listing an object’s non-private methods
15.2.2. Listing private and protected methods
15.2.3. Getting class and module instance methods
15.2.4. Listing objects' singleton methods
15.3. Introspection of variables and constants
15.3.1. Listing local and global variables
15.3.2. Listing instance variables
15.4. Tracing execution
15.4.1. Examining the stack trace with caller
15.4.2. Writing a tool for parsing stack traces
15.5. Callbacks and method inspection in practice
15.5.1. MicroTest background: MiniTest
15.5.2. Specifying and implementing MicroTest
15.6. Summary
index
About the Technology
This is a good time for Ruby! It's powerful like Java or C++, and has dynamic features that let your code react gracefully to changes at runtime. And it's elegant, so creating applications, development tools, and administrative scripts is easier and more straightforward. With the long-awaited Ruby 2, an active development community, and countless libraries and productivity tools, Ruby has come into its own.
About the book
The Well-Grounded Rubyist, Second Edition is a beautifully written tutorial that begins with your first Ruby program and goes on to explore sophisticated topics like callable objects, reflection, and threading. The book concentrates on the language, preparing you to use Ruby in any way you choose. This second edition includes coverage of new Ruby features such as keyword arguments, lazy enumerators, and Module#prepend, along with updated information on new and changed core classes and methods.
What's inside
• Clear explanations of Ruby concepts
• Numerous simple examples
• Updated for Ruby 2.1
• Prepares you to use Ruby anywhere for any purpose
About the author
David A. Black is an internationally known Ruby developer, author, trainer, speaker, event organizer, and founder of Ruby Central, as well as a Lead Consultant at Cyrus Innovation.
buy
combo $44.99 pBook + eBook + liveBook
includes previous edition
eBook $35.99 pdf + ePub + kindle + liveBook
includes previous edition
Add liveAudio for only $19.99
placing your order...
Don't refresh or navigate away from the page.
FREE domestic shipping on three or more pBooks
All wheat, no chaff—takes you from Ruby programmer to full-fledged Rubyist.
Doug Sparling, Andrews McMeel Universal
Provides powerful insights and digs into Ruby’s quirks. Revelatory.
Ted Roche, Ted Roche & Associates, LLC
The best way to learn Ruby fundamentals.
Derek Sivers, sivers.org
|
__label__pos
| 0.999996 |
blob: 5ab8f052b3874c7f19e50b9aa12c0ca655fe3834 [file] [log] [blame]
//
// Copyright (C) 2015 The Android Open Source Project
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
#include "update_engine/image_properties.h"
#include <string>
#include <vector>
#include <base/files/file_util.h>
#include <base/logging.h>
#include <brillo/key_value_store.h>
#include "update_engine/common/constants.h"
#include "update_engine/common/hardware_interface.h"
#include "update_engine/common/platform_constants.h"
#include "update_engine/common/utils.h"
#include "update_engine/system_state.h"
namespace {
const char kLsbRelease[] = "/etc/lsb-release";
const char kLsbReleaseAppIdKey[] = "CHROMEOS_RELEASE_APPID";
const char kLsbReleaseAutoUpdateServerKey[] = "CHROMEOS_AUSERVER";
const char kLsbReleaseBoardAppIdKey[] = "CHROMEOS_BOARD_APPID";
const char kLsbReleaseBoardKey[] = "CHROMEOS_RELEASE_BOARD";
const char kLsbReleaseCanaryAppIdKey[] = "CHROMEOS_CANARY_APPID";
const char kLsbReleaseIsPowerwashAllowedKey[] = "CHROMEOS_IS_POWERWASH_ALLOWED";
const char kLsbReleaseUpdateChannelKey[] = "CHROMEOS_RELEASE_TRACK";
const char kLsbReleaseVersionKey[] = "CHROMEOS_RELEASE_VERSION";
const char kDefaultAppId[] = "{87efface-864d-49a5-9bb3-4b050a7c227a}";
// A prefix added to the path, used for testing.
const char* root_prefix = nullptr;
std::string GetStringWithDefault(const brillo::KeyValueStore& store,
const std::string& key,
const std::string& default_value) {
std::string result;
if (store.GetString(key, &result))
return result;
LOG(INFO) << "Cannot load ImageProperty " << key << ", using default value "
<< default_value;
return default_value;
}
enum class LsbReleaseSource {
kSystem,
kStateful,
};
// Loads the lsb-release properties into the key-value |store| reading the file
// from either the system image or the stateful partition as specified by
// |source|. The loaded values are added to the store, possibly overriding
// existing values.
void LoadLsbRelease(LsbReleaseSource source, brillo::KeyValueStore* store) {
std::string path;
if (root_prefix)
path = root_prefix;
if (source == LsbReleaseSource::kStateful)
path += chromeos_update_engine::kStatefulPartition;
store->Load(base::FilePath(path + kLsbRelease));
}
} // namespace
namespace chromeos_update_engine {
namespace test {
void SetImagePropertiesRootPrefix(const char* test_root_prefix) {
root_prefix = test_root_prefix;
}
} // namespace test
ImageProperties LoadImageProperties(SystemState* system_state) {
ImageProperties result;
brillo::KeyValueStore lsb_release;
LoadLsbRelease(LsbReleaseSource::kSystem, &lsb_release);
result.current_channel = GetStringWithDefault(
lsb_release, kLsbReleaseUpdateChannelKey, "stable-channel");
// In dev-mode and unofficial build we can override the image properties set
// in the system image with the ones from the stateful partition, except the
// channel of the current image.
HardwareInterface* const hardware = system_state->hardware();
if (!hardware->IsOfficialBuild() || !hardware->IsNormalBootMode())
LoadLsbRelease(LsbReleaseSource::kStateful, &lsb_release);
// The release_app_id is used as the default appid, but can be override by
// the board appid in the general case or the canary appid for the canary
// channel only.
std::string release_app_id =
GetStringWithDefault(lsb_release, kLsbReleaseAppIdKey, kDefaultAppId);
result.product_id = GetStringWithDefault(
lsb_release, kLsbReleaseBoardAppIdKey, release_app_id);
result.canary_product_id = GetStringWithDefault(
lsb_release, kLsbReleaseCanaryAppIdKey, release_app_id);
result.board = GetStringWithDefault(lsb_release, kLsbReleaseBoardKey, "");
result.version = GetStringWithDefault(lsb_release, kLsbReleaseVersionKey, "");
result.omaha_url =
GetStringWithDefault(lsb_release,
kLsbReleaseAutoUpdateServerKey,
constants::kOmahaDefaultProductionURL);
// Build fingerprint not used in Chrome OS.
result.build_fingerprint = "";
result.allow_arbitrary_channels = false;
return result;
}
MutableImageProperties LoadMutableImageProperties(SystemState* system_state) {
MutableImageProperties result;
brillo::KeyValueStore lsb_release;
LoadLsbRelease(LsbReleaseSource::kSystem, &lsb_release);
LoadLsbRelease(LsbReleaseSource::kStateful, &lsb_release);
result.target_channel = GetStringWithDefault(
lsb_release, kLsbReleaseUpdateChannelKey, "stable-channel");
if (!lsb_release.GetBoolean(kLsbReleaseIsPowerwashAllowedKey,
&result.is_powerwash_allowed))
result.is_powerwash_allowed = false;
return result;
}
bool StoreMutableImageProperties(SystemState* system_state,
const MutableImageProperties& properties) {
brillo::KeyValueStore lsb_release;
LoadLsbRelease(LsbReleaseSource::kStateful, &lsb_release);
lsb_release.SetString(kLsbReleaseUpdateChannelKey, properties.target_channel);
lsb_release.SetBoolean(kLsbReleaseIsPowerwashAllowedKey,
properties.is_powerwash_allowed);
std::string root_prefix_str = root_prefix ? root_prefix : "";
base::FilePath path(root_prefix_str + kStatefulPartition + kLsbRelease);
if (!base::DirectoryExists(path.DirName()))
base::CreateDirectory(path.DirName());
return lsb_release.Save(path);
}
void LogImageProperties() {
std::string lsb_release;
if (utils::ReadFile(kLsbRelease, &lsb_release)) {
LOG(INFO) << "lsb-release inside the old rootfs:\n" << lsb_release;
}
std::string stateful_lsb_release;
if (utils::ReadFile(std::string(kStatefulPartition) + kLsbRelease,
&stateful_lsb_release)) {
LOG(INFO) << "stateful lsb-release:\n" << stateful_lsb_release;
}
}
} // namespace chromeos_update_engine
|
__label__pos
| 0.940709 |
Skip to content
tucnak/climax
master
Switch branches/tags
Code
Latest commit
Files
Permalink
Failed to load latest commit information.
Type
Name
Latest commit message
Commit time
Climax
Climax is an alternative CLI that looks like Go command
GoDoc Travis
Climax is a handy alternative CLI (command-line interface) for Go apps. It looks pretty much exactly like the output of the default go command and incorporates some fancy features from it. For instance, Climax does support so-called topics (some sort of Wiki entries for CLI). You can define some annotated use cases of some command that would get displayed in the help section of corresponding command also.
Why creating another CLI?
I didn't like existing solutions (e.g. codegangsta/cli | spf13/cobra) either for bloated codebase (I dislike the huge complex libraries) or poor output style / API. This project is just an another view on the subject, it has slightly different API than, let's say, Cobra; I find it much more convenient.
A sample application output, Climax produces:
Camus is a modern content writing suite.
Usage:
camus command [arguments]
The commands are:
init starts a new project
new creates flavored book parts
Use "camus help [command]" for more information about a command.
Additional help topics:
writing markdown language cheatsheet
metadata intro to yaml-based metadata
realtime effective real-time writing
Use "camus help [topic]" for more information about a topic.
Here is an example of a trivial CLI application that does nothing, but provides a single string split-like functionality:
demo := climax.New("demo")
demo.Brief = "Demo is a funky demonstation of Climax capabilities."
demo.Version = "stable"
joinCmd := climax.Command{
Name: "join",
Brief: "merges the strings given",
Usage: `[-s=] "a few" distinct strings`,
Help: `Lorem ipsum dolor sit amet amet sit todor...`,
Flags: []climax.Flag{
{
Name: "separator",
Short: "s",
Usage: `--separator="."`,
Help: `Put some separating string between all the strings given.`,
Variable: true,
},
},
Examples: []climax.Example{
{
Usecase: `-s . "google" "com"`,
Description: `Results in "google.com"`,
},
},
Handle: func(ctx climax.Context) int {
var separator string
if sep, ok := ctx.Get("separator"); ok {
separator = sep
}
fmt.Println(strings.Join(ctx.Args, separator))
return 0
},
}
demo.AddCommand(joinCmd)
demo.Run()
Have fun!
About
Climax is an alternative CLI with the human face
Resources
License
Stars
Watchers
Forks
Releases
No releases published
Packages
No packages published
Languages
|
__label__pos
| 0.83837 |
sw24.exe Process Information
Process Name: sw24
Author: Unknown
Download PC Repair Tool & fix sw24.exe Windows errors automatically
System Process:
No
Uses network:
No
Hardware related:
No
Background Process:
Yes
Spyware:
No
Trojan:
No
Virus:
No
Security risk 0-5:
0
What is sw24 exe?
sw24.exe is a process
This executable file is an MSI D.O.T component.(Dynamic Over clocking Technology).
The “.exe” file extension stands for Windows executable file. Any program that is executable has the .exe file extension. Find out if sw24.exe is a virus and sould be removed, how to fix sw24.exe error, if sw24 exe is CPU intensive and slowing down your Windows PC. Any process has four stages of the lifecycle including start, ready, running, waiting, terminated or exit.
Should You Remove sw24 exe?
If you are asking yourself if it is safe to remove sw24.exe from your Windows system then it is understandable that it is causing trouble. sw24.exe is not a critical component and a non-system process. Any process that is not managed by the system is known as non-system processes. It is safe to terminate the non-system process as they do not affect the general functionality of the operating system. However, the program using the non-system processes will be either terminated or halted.
Download PC Repair Tool & fix sw24.exe Windows errors automatically
Fix sw24.exe Error?
There are many reasons why you are seeing sw24.exe error in your Windows system including:
Malicious software
Malicious software infects the system with malware, keyloggers, spyware, and other malicious actors. They slow down the whole system and also cause .exe errors. This occurs because they modify the registry which is very important in the proper functioning of processes.
Incomplete installation
Another common reason behind sw24.exe error is an incomplete installation. It can happen because of errors during installation, lack of hard disk space, and crash during install. This also leads to a corrupted registry causing the error.
Application conflicts and Missing or corrupt windows drivers can also lead to sw24.exe error.
The solution to fixing sw24.exe error include any one of the following
• Make sure your PC is protected with proper anti-virus software program.
• Run a registry cleaner to repair and remove the Windows registry that is causing sw24.exe error.
• Make sure the system’s device drivers are updated properly.
It is also recommended that you run a performance scan to automatically optimize memory and CPU settings.
Download PC Repair Tool & fix sw24.exe Windows errors automatically
Is a sw24.exe CPU intensive?
Windows process requires three resource types to function properly including CPU, Memory, and Network. CPU cycles to do computational tasks, memory to store information and network to communicate with the required services. If any of the resources are not available, it will either get interrupted or stopped.
Any given process has a process identification number(PID) associated with it. A user can easily identify and track a process using its PID. Task Manager is a great way to learn how much resources sw24.exe process is allocating to itself. It showcases process resource usage in CPU/Memory/Disk and Network. If you have a GPU, it will also showcase the percentage of GPU it is using to run the process.
|
__label__pos
| 0.94381 |
Should the next standby power target be 0-watt?
Should the next standby power target be 0-watt?
TitleShould the next standby power target be 0-watt?
Publication TypeReport
Year of Publication2017
AuthorsAlan K Meier, Hans-Paul Siderius
Date Published06/2017
Abstract
The standby power use of appliances continues to consume large amounts of electricity. Considerable success has been made in reducing each device's use, but these savings have been offset by a huge increase in the number of products using standby power and new power requirements for maintaining network connections. Current strategies to reduce standby have limitations and may not be most appropriate for emerging energy consumption trends. A new strategy for further reductions in standby, the "Standzero" option, encourages electrical products to be designed to operate for short periods without relying on mains-supplied electricity. Energy savings are achieved through enhanced efficiency and by harvesting ambient energy. A sensitivity analysis suggests many appliances could be designed to operate for at least an hour without relying on mains power and, in some cases, may be able to operate indefinitely at zero watts until activated.
LBNL Report Number
LBNL-2001019
|
__label__pos
| 0.876522 |
Sorocarp
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
A sorocarp (from the Greek word soros "a heap" + karpos "fruit") is the fruiting body characteristic of certain cellular slime moulds (e.g., Dictyosteliida). Each sorocarp consists of both a sorophore (stalk) and a sorus.[1][2] Sorocarps release spores.
References[edit]
1. ^ http://www.wordnik.com/words/sorocarp
2. ^ Lawrence, E. 2005. Henderson's Dictionary of Biology, 13th Ed. Prentice Hall, London
|
__label__pos
| 0.681725 |
≡ Menu
Trends in Chronic Fatigue Syndrome Research
This paper examines the quantity and focus of CFS research over time and draws some conclusions regarding their implications for CFS patients.
Background
After CFS burst upon the scene in the mid eighties it didn’t take it long to become a major research topic. The first study PubMed cites on CFS (in the 1980’s) was published in 1987* and by 1988/9 the field was up and running. Since 1991 papers with CFS or its equivalent in the title have never numbered less than 100 a year.
Similarly the number of citations PubMed cites for ‘Chronic fatigue syndrome’ are astounding; a search on 2/22/05 brought up 2949 citations with some connection to CFS. These numbers appear at first blush to demonstrate an impressive commitment by the medical establishment to the resolution of CFS.
Progress in our understanding of CFS, however, has been slow. The cause of the disease is still obscure and treatments are still largely ineffective. Instead of addressing the core dysfunctions found in CFS, physicians are often relegated to treat it symptomatically.
There is still no accepted biomarker for this disease and, of course, we still have its unfortunate name. While few in the medical field, at least, appear to believe it has a psychological origin, the role psychology plays in the course of the disease has raised quite controversial. Few findings in this disease, in fact, are without controversy.
The survey was prompted by the discordance between all this activity and the lack of progress in the disease. How could we – 18 years after the ‘advent’ of CFS and some 3000 PubMed citations later – still be saddled with this unfortunate name? Why is there still no test for CFS or an acceptable definition of it?
It is true that CFS is a very complex disease that is difficult to analyze given its changing definitions and the different subsets of patients found within it. But is it THAT mysterious? THAT impervious to investigation? THAT much of an enigma? Or have other factors contributed to the slow pace of knowledge? This question prompted a survey of how the quantity, focus and ‘potential’ of CFS research has changed over time.
The survey
The papers included in this survey were those cited when ‘chronic fatigue syndrome’ was entered into the search bar at PubMed. PubMed is a search engine sponsored by the National Library of Medicine that accesses over 15 million citations of biomedical papers dating back to the 1950’s (but not the Journal of Chronic Fatigue Syndrome (JCFS)).
A list of titles and abstracts for the JCFS dating back to 1998 on the Haworth Press website were used) Only those articles (with a very few exceptions) with chronic fatigue syndrome or myalgic encephalitis in the title were included. (Prior to 1992 when the term CFS was essentially codified citations with pseudonyms for CFS such as postviral fatigue syndrome, EBV syndrome, etc. were included.)
Based either on the title or the abstract provided by PubMed or the Haworth web site the papers were grouped into the following broad categories based on my assessment of their primary orientation; clinical, immune, psychological, brain/CNS. endocrine, metabolic, cardiac, oxidative, cognitive – neuropsychological, sleep, muscles, tilt table, others. A few papers had more than one focus.
The survey examined PubMed citations from 1988/9, 1991, 1994, 1997, 2000, 2003 and 2004 and JCFS papers from 2000, 2003 and 2004.
Quantity
The most surprising finding was that except for very recently over the past 13 years the quantity of PubMed citations has remained more or less stable. One would have thought that as the field matured and became better known the number of citations would increase. Except perhaps for the last year or so this has not occurred. (The number of articles in the table below appears to pick up a bit after 1997.
This was due to the publication of the Journal of Chronic Fatigue Syndrome. This publication may have (a) sparked interest in the field and/or (b) provided a venue for theories, studies, etc. not readily accepted in other publications. The trend in PubMed cited articles was flat.) An average of approximately 130 articles that have CFS or myalgic encephalitis in their title have been published every year for the last 10 years (based on 1994, 97, 00, 03, 04).
Trends in CFS research
Total % Clinical % Immune % Psychology % Brain/CNS % Endocrinology % Epidemiology % Cognitive
1988-9
77
36
39
0
0
0
0
0
1991
117
34
31
19
3
1
2
1
1994
132
24
24
14
8
2
4
4
1997
122
21
17
22
7
6
3
7
*2000
130
25
13
12
4
8
2
4
*2003
140
16
24
17
12
8
5
0
*2004
148
28
14
11
15
8
5
3
%Meta-bolism %Oxida-tion %Cardiac %Sleep %OrthostaticIntolerance %Muscles %Others
1988-9
0
2
2
1
0
1
5
1991
4
0
0
0
0
3
3
1994
2
0
2
4
0
2
7
1997
6
0
1
2
3
0
5
*2000
7
3
1
0
4
1
13
*2003
1
5
2
2
4
4
3
*2004
2
3
0
2
3
1
10
*contains citations from the Journal of Chronic Fatigue Syndrome
Trends in research focus
One would expect to see different trends of interest emerge over time in any research area and this has proved true in CFS. The percentage of papers focused on the immune system – the dominant early interest in CFS – declined from a high of 45% of citations in 1988-89 to about 17% of citations in 2000/03 and 04.
Within the immune category research trends have changed as well; research into viruses, while still a significant topic, has declined markedly since 1991 (1991 – 20 citations; 2003/4 – 5 citations) as interest in bacteria (mycoplasma, chlamydiae, staphylococcus) has picked up (1991/1993 – 0 studies; 2003/2004 – 10 studies).
Another area of diminishing interest have been the clinical aspects of CFS. The clinical category primarily contains doctor to doctor talk; it centers on the diagnosis, treatment, management and prognosis of CFS as well as reviews of CFS and discussions regarding CFS’s validity (controversy). Still one of the most cited subjects (@20-25%) it makes up substantially smaller portion of the total citations than it used to (30—35%).
Interest in the psychological aspects of CFS has also changed dramatically over time. While no interest was seen early on (0 citations 1988/9 – 0) psychology in CFS rapidly assumed a major focus (1991 – 22). Psychology studies reached a peak in 2001 but have fluctuated dramatically and may have even declined since then.
The two years with the lowest number of psychologically oriented studies were 2000 (16) and 2004 (11). Within the field the focus of interest has changed dramatically. In the early 1990’s depression was a major topic but has been replaced since about 1997 by cognitive behavior therapy (CBT) was a major research interest.
CBT et. al. accounted for from 25% to 60% of psychology citations in 1997, 2000, 2003, 2004. Aside from these two topics, there appears to be little coherence in this field; research topic range from psychiatric morbidity to the effects of birth order to the radicalization of the self, to parenting, etc.
While interest in the immunological and clinical aspects of CFS appears to have declined, interest in three fields; the brain/CNS, endocrinology and oxidation/metabolism has increased sharply in the last 4 to 7 years. Interest in the brain/CNS has, not surprisingly given the cognitive difficulties associated with CFS, always garnered some interest but in the last two years that interest has jumped markedly with 12 and 14% of all citations devoted to it. Two subtopics, in particular – serotonin and cholinergic function – have gained in popularity lately.
The endocrine system attracted little interest early on. No citations concerning the endocrine system occurred in 1988/91 and only 2 in 1991 and 1994. Since 2000, however, over ten papers have been published on endocrinological topics every year with a dominant focus on cortisol.
Since its discovery in CFS in 1995 by Rowe, orthostatic intolerance has remained a relatively small but nevertheless consistent source of citations. Similarly, while not being a major source of citations, free radicals and the oxidation/antioxidant balance (@4) arrived as a research interest in CFS in the last four years.
It is difficult to discern any trends in muscle activity, metabolic processes or sleep. Interest in each has been present since the early days of CFS research but none has become a major research topic and interest in each has fluctuated greatly. Driven primarily by one research group, interest in cardiology has been consistent but low.
Interestingly alternative health therapies, long a treatment mainstay for CFS patients, were a major source of citations for the first time in 2004 with 8 citations devoted to them. In the past five years genetics has arrived on the scene with several citations devoted to it in 2000, 2003 and 2004.
The implications for CFS patients
What do these numbers mean for CFS patients? Can they be confident that the medical research community has marshalled it’s considerable resources on their behalf? Even if the numerical trends are flat or only mildly positive one would think 130 or so ‘papers’ a year would be sufficient to guarantee real progress.
It sounds, after all, like a lot of work is being done – enough one would think to give CFS patients hope that before too many more years pass, significant breakthroughs in the understanding of and treatment of their disease will occur. A closer look at the ‘research’ cited in PubMed indicates this is anything but true. Few of the citations for CFS signify papers that have the potential to make a difference in the understanding of CFS.
A mixed bag
The papers cited by PubMed vary widely in focus and quality. PubMed citations include everything from letters to reviews, from small one page studies to complex, multi-dimensional studies, from one person treatment ‘trials’ to double- blinded, placebo controlled, multi-group treatment trials.
In PubMed papers on CFS in animals and birth order sit next to large, multi-year studies on prevalence in humans, e.g. a citation in PubMed is not necessarily indicative of a significant contribution to CFS.
What a person suffering from CFS really desires is a breakthrough in our understanding or treatment of CFS. In lieu of that they want to know that significant work is being undertaken to understand CFS. They want to feel that the depth of the research effort into CFS is somehow congruent with the pain caused by CFS; that something that can so overwhelmingly alter their lives is being dealt with seriously by the medical research community.
They want to have an idea that significant progress will occur in CFS before the productive period of their lives is over. The next part of this paper, which examines whether this appears likely to occur, determines how many of the 3000 or so papers PubMed cites have the potential to significantly advance our understanding of CFS.
In order to do that distinctions are made between three categories of papers; insignificant, important but not difference making and potentially difference making papers.
Unimportant vs important papers
A certain number of papers cited by PubMed every year have little change of making an important contribution. Chief among these are papers published in a foreign language. These papers are often not abstracted and are probably little read. These papers can be surprisingly abundant; in 2004 they made up about 6% of all PubMed citations on CFS.
Important vs potentially difference-making papers
Some papers are important to the overall understanding and treatment of CFS but have no potential to advance our understanding of the biological processes occurring in CFS. They mostly involve medical professionals talking to medical professionals about peripheral issues common to any disease; i.e. how to characterize, diagnose or treat it, how common it is, what issues its patients face. They mainly occur in the following categories.
Clinical (@20-25%) – A substantial number of papers every year focus on the clinical aspects of CFS (diagnosis, management, prognosis, controversy).
Psychological (@17%) – It is clear, at least to CFS patients, that psychological studies will have little effect on the ultimate resolution of this disease. At their best they may help CFS patients cope with rigors of CFS. At their worst they divert attention and funding from more fundamental aspects of CFS and alienate CFS patients.
Epidemiological (@5%) – Epidemiological papers are vitally important for assessing the prevalence and economic costs of CFS and providing a rationale for more funding. Given the abysmal levels of current funding these papers may, in fact, be the most important papers published. Nevertheless they do not contribute to our understanding of the biological processes operating in CFS.
Neuropsychological/cognitive – (@ 4%) These papers elucidate the problems in cognitive functioning found in CFS patients. As such they provide evidence of brain dysfunction in CFS that is important for disability claims and for promoting more interest in the CFS. They do not, however, advance our knowledge of CFS pathophysiology.
According to this survey about half of the papers PubMed cites every year deal do not have the potential to further our understanding of the biological processes occurring in CFS.
This leaves us with about 70 articles published a year that might make a more less immediate difference in understanding the cause, mapping out its dysfunctions or uncovering a treatment for CFS. Even that sounds like a good number – 70 papers a year should surely offer real hope for CFS patients. Even this number is misleadingly high, however.
Potentially Difference Making Papers – Two general categories of potentially difference making papers can be formed; theoretical papers and studies. While purely theoretical papers have the ability to make a difference in CFS by elucidating creative new approaches to CFS, their impact is always impossible to ascertain at the time of publication. Their impact is further obscured by the fact that many, probably most theoretical papers receive either no or inadequate follow up. Ultimately, the only papers able to have animmediate and significant impact on CFS patients are ones examining the biological processes (the pathophysiology) present in CFS. In a very real way they are the papers that really matter.
Surprisingly, though, given their fundamental importance, studies addressing CFS pathophysiology are not common. Many more papers are published every year on essentially peripheral subjects such as clinical reviews, psychological studies, etc. In 2004 PubMed listed only 35 studies (not including treatment trials) that actually examined examined an aspect of CFS pathophysiology. Thus of all the citations that PubMed pulls for CFS only about 15% of them are engaged in uncovering the cause of CFS.
Even within this category there are subcategories and gradations of value. About 30% of all studies of CFS pathophysiology in 2004 simply undertook to confirm or deny prior findings (apoptosis, Th1/Th2 cytokine imbalance, ACTH/cortisol, salivary cortisol, serum erythropoietin). These studies are an important part of the march of science but they are not difference making because they do not forward the science, i.e. they do not bring our understanding of CFS to a deeper level.
A significant number of studies every year are exploratory studies that seek to determine if X occurs in CFS or not (gene expression, brain imaging, EBV, borna virus antibodies, urinary electrophoretic profiles). Is there brain damage in CFS? Is gene expression different? Is X virus present in CFS? Are abnormal levels of sympathetic nervous system activity present in CFS? These studies advance our understanding of CFS but their significance is unclear as well. They open up new avenues for research that may or may not pay off in the future.
The really difference making studies, the ones that might send a jolt of excitement up a patients or researchers spine, are those that have identified an abnormality and are working their way down a chain of causation to its source nd thus to CFS. Only a few papers in 2004, however, actually extended our knowledge of the causal factors of CFS. The corticosteroid gene polymorphism study, for instance, posits a cause for the low cortisol levels present in some CFS patients. The skin vasodilation study examined potential causes of skin vasodilation and by extension orthostatic intolerance.
One reason these papers are so few and much of the emphasis in CFS research is still on exploratory studies is that only a few abnormalities have been consistently found in CFS. Several factors contribute to this including poor funding, different diagnostic criteria over time, the lack of standardization, the occurrence of subsets in CFS, and the waxing and waning nature of the disease.
The lack of standardization is puzzling given the sophistication of the medical research establishment but is a very real problem. Two recent overviews of immune and neuroendocrine research in CFS cited the lack of standardization and poor study methodology as reasons for the conflicting results sometimes seen in CFS research studies. Nancy Klimas was able to explain away several inconsistencies concerning cytokine studies simply by noting the different laboratory techniques used. This problem has been frequently noted by the NIH yet it has taken no steps to address it.
Funding woes
The greatest problem facing CFS research, however, is inadequate funding. This is a disease, after all, that can affect the immune, cardiovascular, endocrine and nervous systems.. In how many diseases are brain scans and spinal taps as well as hormonal, immune, orthostatic, metabolic, sleep and exercise tests part of the research protocol? In how many diseases do psychological studies take up a significant amount of research funds?
Despite its needs CFS remains one of the most poorly funded diseases in the United States. Despite productivity losses to the US economy from disabled CFS patients totaling some $9,000,000,000 a year, the National Institutes of Health (NIH) saw fit last year to fund CFS research to the tune of only $6,000,000. Of the 175 research areas funded by the NIH in 2004 CFS was 170th in funds awarded.
The NIH gave temporal mandibular joint (TMJ) researchers 3’xs as much money as CFS; Lyme’s disease was given 5 x’s the money CFS was; Crohn’s disease 9 x’s, anthrax research 17 x’s. asthma 50 x’s and AIDS 500 x’s as much money. Just theincrease in asthma funding over the past two years – the increase! – was five times the total funding given CFS last year. This does not take into account the fact that a significant proportion of the funds the NIH says were devoted to ‘CFS research’ did not investigate CFS pathophysiology.
It is clear there is simply too little money and too many areas of interest for research in any one area to move ahead rapidly in CFS. Research into serotonin activity in CFS provides a case study of how slowly even a ‘major research effort’ proceeds in CFS.
Serotonin: A Case Study: Bakheit et. al. first uncovered evidence of increased serotonergic HPA axis activity in response to busiprone in CFS patients in 1992. In the same year Demitrack et. al. found evidence of increased serotonin activity in the spinal fluid. Since 1992 seven studies (about one every other year) have assessed serotonergic levels or activity in the spinal fluid, hypothalamus and brain in CFS using different serotonin agonists and different techniques (PET scan, CSF levels, provocation). Some heterogeneous findings have been found but for the most part studies have indicated increased serotonin activity in CFS.
Thirteen years after serotonin levels were first seen to be abnormal in CFS researchers now appear to beapproaching a consensus that serotonergic activity is increased in CFS. That is a long time in the life of a CFS patient. It is about third of ones productive years. It is a very long time to wait for researchers to reach an agreement about the importance of one substance – and researchers are still not there yet. That consensus may still be several years and several studies away.
What is most unsettling about this situation is that serotonin is not an obscure compound. One of the major neurotransmitters in the body, serotonin is involved in gastric secretion, and smooth muscle (vascular) and central nervous system activity.
A whole class of drugs, selective serotonin reuptake inhibitors (SSRI’s) has been developed to battle depression and other mood disorders. Because serotonin has the potential to effect so many different systems, one would think serotonin activity in CFS would have been assessed extensively once studies indicating a possible upregulation was present.
Instead the ‘serotonin question’ has been attacked in a piecemeal fashion by researchers using different protocols. Remember we have hardly even begun to assess the cause of a possible serotonergic up regulation in CFS; it has taken over a decade just to arrive at a consensus that it probably exists.
The same story plays out regarding cortisol, the most important adrenal hormone. Thirteen years after low cortisol levels were first noted cortisol levels are still being assessed in CFS. While heterogeneous cortisol findings do complicate matters to some degree, this slow progress cannot simply be laid at the feet of a wildly heterogeneous patient population.
Instead it is largely a function of a poorly funded and poorly organized research community. When researchers take a decade or more to assess the levels of one major substance in the body, can CFS patients any confidence that the resolution of their disease is anywhere in sight?
CFS is a complex disease. Understanding it will undoubtedly require venturing out into new ground and piecing together findings in novel ways. A new disease process will most likely need to be explicated. Cortisol and serotonin, however, hardly constitute ‘new ground’.
If it takes so long to simply assess the levels of these substances, how long will it take to investigate the lesser known or still unknown substances or processes that most likely lie at the heart of CFS? If the research community is this poor at assessing the ‘easy’ stuff how in the world will it be able to muster the ability to tackle the more problematic stuff?
Innovation quenched
Benjamin Natelson’s recent travails concerning finding funding for a spinal fluid gene/protein expression study are illustrative of the funding travails that confront CFS researchers. Dr. Natelson has been the most prolific CFS researcher in the world over the past five years and gene and protein expression studies are arguably the two most potentially helpful research field concerning CFS.
They have the potential to fundamentally alter our understanding of CFS. Despite Dr. Natelson’s reputation and the NIH’s recognition of the urgent need to break new ground in this disease it has refused to even partially fund his gene/protein expression CSF study.
This was notwithstanding the fact that Dr. Natelson recently co-authored a study finding abnormal cytokine levels in the spinal fluid of CFS patients, or the fact that he already has the spinal fluid. Perhaps not surprisingly a year after Dr. Natelson was denied funding a proteomics study by another researcher found a potential protein biomarker in the CSF of CFS patients.
One is tempted to ask if this eminent researcher cannot get funding for such a worthwhile project then what chance do lesser known researchers CFS have? The history of CFS research is littered with promising studies that had positive outcomes but received little or no follow up (hypercoagulation, PKR, adenosine levels, G-actin, etc.).
Innovative theories regarding CFS pathophysiology are regularly advanced but are rarely adequately tested. Despite demonstrating tie-ins with several other theories of CFS and being the topic of much discussion, Pall’s nitric oxide/peroxynitrite theory has been the object of only one small study in six years.
This petty pace
The 3000 papers so often cited with regards to CFS research is misleading as only a small portion of those papers actually involve research efforts. Even the small amount of research done on CFS might be sufficient if we had a clear focus on CFS pathophysiology – if we knew what part of the body to zero in on, but we don’t. Research into CFS is spread all over the body. This means, given the small amount of research funding CFS receives, our progress in understanding this disease is doomed to be achingly slow.
The funding is simply not available for research teams to target an area and quickly and exhaustively investigate it. An examination of the CFS research ‘groups’ of the past five years indicates that most are very small groups that are able to produce a study once every year and a half or so.
These groups, always subject to a tenuous funding environment, manage to slowly chip away at their subject of interest over time but given their resources the amount of progress they can make is limited. Stewart, for instance, lists 16 different possible causes of the microcirculatory difficulties found in a subset (low-flow POTS) of a subset of CFS patients.
Similarly Spence and Khan list 9+ items that could be affecting acetylcholinesterase activity in CFS. Given the current pace of CFS research it can take many years for a consensus to form around any positive findings. A research effort that could take a year or two in a well funded disease can easily take ten years or more in CFS.
By under funding CFS research the powers that be have essentially decreed it will move forward at a petty pace. They have decided there are more important things for them to focus on. While researchers scramble for funding CFS patients watch the decades and their lives and dreams dribble away.
Shakespeare’s description of the human condition in Macbeth never resonated more strongly than it does with both CFS researchers and patients who seem, at times, relegated to irrelevance while the great public research institutions entrusted with the nation’s health look away.
“To-morrow, and to-morrow, and to-morrow,
Creeps in this petty pace from day to day,
To the last syllable of recorded time…
Life’s but a walking shadow; a poor player…”
——————————————————————
*The first two papers on CFS in the eighties were
Buchwald D, Sullivan JL, Komaroff AL..Frequency of ‘chronic active Epstein-Barr virus infection’ in a general medical practice. JAMA. 1987 May 1;257(17):2303-
Caligiuri M, Murray C, Buchwald D, Levine H, Cheney P, Peterson D, Komaroff AL, Ritz J. Phenotypic and functional deficiency of natural killer cells in patients with chronic fatigue syndrome. J Immunol. 1987 Nov 15;139 (10):3306-13.
It’s amazing how quickly what would become an important cadre of researchers and physicians congealed around CFS. Of the authors of the first two papers on CFS Buchwald has co-authored 69 papers on CFS, Komaroff 63, Levine 32 and Peterson 30. Dr. Cheney became one of the most creative CFS clinicians. CFS was not only a defining moment for their patients; it changed the lives of many of the earliest physicians on the scene as well. Several have dedicated their careers to understanding and treating CFS.
Donate to Phoenix Rising – help keep the lights on!
|
__label__pos
| 0.795852 |
Programación en C
Lenguajes de Programación. Organización lógica datos. Algoritmos. Subalgoritmos. Estructuras dinámicas lineales de datos
• Enviado por: Glistig
• Idioma: castellano
• País: España España
• 25 páginas
publicidad
ORGANIZACIÓN LÓGICA DE DATOS. ESTRUCTURAS ESTATICAS
A. INTRODUCCION
Las estructuras estáticas son conjuntos de datos homogéneos que se trata como una sola unidad. Hay dos tipos de estructuras: internas y externas (en soportes físicos).
Internas: se almacenan en la memoria principal del ordenador, que es la memoria RAM.
Array o tabla o matriz: se utilizan en cualquier lenguaje de programación para almacenar datos que son del mismo tipo o demás.
B. Conceptos y definiciones
1. Tabla o array: consiste en un (conjunto) numero fijo y ordenado de elementos, todos del mismo tipo y bajo un mismo nombre.
2. Componentes: son los elementos que forman el array.
3. Índices: la posición de cada componente dentro del array viene determinado por el índice o índices (uno o varios).
4. Dimensiones: de una tabla o array es el número de índices que se utiliza.
5. Longitud: es el tamaño de la tabla o array, el número de elementos que contiene el array.
6. Tipo de array: el tipo de sus componentes.
Todos los componentes de un array los vamos a utilizar como variables y se va a poder realizar operaciones con los arrays.
Representación grafica de un array:
Alumnos
Array
Jose
Rosa
Luis
Lola
Andres
Maria
Nombre del array: Alumnos.
Componentes: Alumnos(1), Alumnos(2), ......... , Alumnos(7).
Índices: 1
Dimensión:1
Longitud: 7
Tipo de array: Alfanumérico.
C. TIPOS DE ARRAYS
• Unidimensionales
• Bidimensionales
• Multidimensionales
• 1. Unidimensionales: van a tener una sola dirección y por lo tanto un solo índice. Se les llama a este tipo de arrays Vectores.
Si queremos intercambiar el contenido entre dos vectores, vamos a declarar primero una variable auxiliar.
AUX=Alumnos(1)
Alumnos(1)=Alumnos(2)
Alumnos(2)=AUX
SWITCH
Es un campo de memoria que puede tomar dos valores exclusivos (uno u otro) y se utiliza para lo siguiente:
- Recordar en un determinado punto de un programa la ocurrencia o no de un suceso anterior.
- Salir de un bucle.
- Para decidir en una instrucción alternativa que acción realizar.
- Para hacer que dos acciones diferentes se ejecuten alternativamente dentro de un bucle.
a) OPERACIONES CON VECTORES: asignación, lectura/escritura, recorrido y actualización.
• Asignación: es dar un valor a algún elemento del vector. Los vectores son sucesiones ordenadas de elementos. Cuando veamos x[1], x[2], .... , x[n] sabremos que es un vector. En los vectores no es obligatorio empezar desde 1, pueden empezar desde 0, un número negativo o un número positivo distinto de 1.
Tipo
Array[dimensión]tipo de datos: nombre del array
Var
Nombre del array: N (variable que se va a utilizar para cada elemento del array).
• Lectura y escritura:
Leer (A): leer el array entero.
Escribir(A): escribir el array entero.
Leer V(1): leer el elemento 1 del array.
• Recorrido o acceso secuencial al vector: es la operación con la que vamos a realizar una acción general sobre todos los elementos del vector. Dependiendo de la dimensión del array se hace de una manera o de otra. En los bidimensionales se realiza de forma más compleja. Se puede leer del principio a fin o del final al principio.
• Actualización: esta compuesta de tres operaciones: añadir, insertar y borrar.
• Añadir: significa agregar un elemento al final del array. Se trata de una asignación. Esto lo podemos hacer cuando tenemos uno o más elementos al final del array vacíos. Tenemos que fijarnos en la dimensión.
• Insertar: introducir un elemento entre los ya existentes. Tiene que haber elementos vacíos y tenemos que cambiar los que van después del que insertamos.
2. Bidimensionales: Son arrays de dos dimensiones y se les conoce con el nombre de matrices. Tienen 2 índices por lo que cada componente de la matriz se direcciona con el nombre de la matriz seguido de dos índices separados por comas.
Tratamiento secuencial o recorrido de una matriz
El recorrido de una matriz se realiza mediante el anidamiento de dos bucles desde. El bucle externo recorre cada una de las filas y el interno todos los componentes de una fila. Este tratamiento también se puede realizar por columnas en casos en los que nos interese y además en ambos casos en orden creciente y decreciente para las filas y columnas.
3. Arrays MULTIDIMENSIONALES: Son los arrays desde 3 hasta n dimensiones. También se les llama poliedros. Es necesario que los n subíndices estén declarados o identificados, para poder localizar un elemento individual del poliedro. Un array de n dimensiones se puede identificar de la siguiente manera.
A [P1:U1, P2:U2, ...... , PN:UN]
A [I1, I2, ...... , In] (estos I son los índices que nos van a ayudar a localizar un elemento).
Componentes:
P[1,1,1], P[1,1,2]....P[1,1,n]
P[1,2,1], P[1,2,2]....P[1,2,n]
P[1,n,n],.....P[n,n,n].
Índices:
[1......n]
[1......n]
[1......n]
Longitud: N.
Tratamiento secuencial o recorrido de un poliedro
Requiere tantos bucles desde anidados como dimensiones tenga el poliedro. Cada índice de un bucle recorre una dimensión y puede hacerse en cualquier orden de anidamiento.
SUBALGORITMOS O SUBPROGRAMAS: PROCEDIMIENTOS Y FUNCIONES
El método para solucionar un programa complejo es dividirlo en subprogramas que sean sencillos de resolver. Cuando se trabaja de esta manera existirá un algoritmo principal o conductor que transfiera el control a los distintos subalgoritmos, los cuales, cuando terminen su tarea, devolverán el control al algoritmo que los llamo. Existen dos tipos de subprogramas: funciones y procedimientos.
1. FUNCIONES
Una función a partir de uno o más valores llamados argumentos o parámetros devuelve un resultado en el nombre de la función.
Declaración de funciones: una función constaría de:
a) Cabecera: también se le llama definición de la función. En la definición de la función deben figurar una serie de parámetros, llamados parámetros formales para que cuando se llame a la función se pueda establecer una correspondencia 1 a 1 y de izquierda a derecha entre los parámetros actuales y formales.
b) En el cuerpo de la función estarán el bloque de declaraciones y el bloque de instrucciones. Debe incluir una instrucción mediante la cual la función tomaría un valor para devolverlo al programa principal o llamador.
Función < nombre de la función > (lista de parámetros formales): tipo de dato devuelto.
Declaración de las variables locales.
Instrucciones (Inicio).
Los tipos de datos validos como resultado de una función son: ordinales, reales, cadenas, punteros y lógicos.
En una lista de parámetros formales es posible separar estos parámetros con ; y hay que indicar cada tipo.
2. PROCEDIMIENTOS
Un procedimiento es un subprograma o subalgoritmo que realiza una tarea especifica y que puede ser definido mediante 0, 1 o n parámetros.
Tanto la entrada de información al procedimiento como la devolución de resultados desde el procedimiento al programa principal o llamador o conductor se realiza a través de los parámetros. El nombre de un procedimiento no esta asociado a ninguno de los resultados que obtiene. La llamada a un procedimiento se realiza con la instrucción “Llamar_a” o directamente con el nombre del procedimiento, es decir:
<nombre del procedimiento> (lista de parámetros que se llaman actuales o reales).
Declaración de procedimientos: es similar a la de una función excepto que el nombre del procedimiento no se encuentra asociado a ningún resultado.
Procedimiento <nombre del procedimiento>(lista de parámetros formales)
(declaración de variables locales)
Inicio
.
.
.
Fin_procedimiento
La lista de parámetros formales se debe separar por ; y debemos indicar el tipo de cada uno de ellos.
3. VARIABLES LOCALES Y GLOBALES
Las variables utilizadas en los programas principales y en los subprogramas se clasifican en dos tipos: variables locales y variables globales.
• Variables locales: una variable es local si esta declarada y definida dentro de un subprograma y es distinta de las variables que tengan el mismo nombre que hayan sido declaradas en el programa principal.
Cuando otro subprograma utiliza el mismo nombre al declarar una variable ambas serán distintas y tendrán diferentes posiciones de memoria, por lo tanto solo tendrán vigencia en el subprograma donde han sido declaradas. El uso de variables locales tiene la ventaja de hacer a los subprogramas independientes y la comunicación con el programa principal se realizara exclusivamente a través de los parámetros.
• Variables globales: una variable es global cuando el ámbito (SCOPE) en el que dicha variable se conoce es el programa completo y debe haber sido declarada en el programa principal. Tienen la ventaja de compartir información de diferentes subprogramas. Sin una correspondiente entrada en la lista de parámetros.
4. COMUNICACIÓN CON SUBPROGRAMAS: PASO DE
PARÁMETROS
Cuando un programa llama a un subprograma, la información se comunica a través de una lista de parámetros y se establece una correspondencia automática entre los parámetros formales y actuales. Los parámetros actuales son sustituidos o utilizados en lugar de los parámetros formales. La declaración del subprograma se hace:
Procedimiento <nombre>(tipo de dato: dato; tipo de dato: dato; ...) Parámetros formales.
Y la llamada al subprograma se hace con:
Llamar_a <nombre del procedimiento> (valores que va a tomar el procedimiento: )
Existen dos métodos para establecer la correspondencia de parámetros:
• Correspondencia posicional: es la que se utiliza en C. La correspondencia se establece emparejando los parámetros reales y formales, según su posición en las listas. Fi se corresponde con Ai (F: formal, A: actual).
• Correspondencia por el nombre explicito o método de paso de parámetros por el nombre. En este método en las llamadas se indica explícitamente la correspondencia entre los parámetros reales y formales.
• 5. TRANSMISIÓN DE PARÁMETROS
Los métodos de transmisión de parámetros más utilizados son:
• Por valor: el paso de un parámetro por valor significa que el valor del argumento (parámetro actual o real) se asigna al parámetro formal, es decir, antes de que el subprograma comience a ejecutarse el argumento toma un valor especifico. Este valor se copia en el correspondiente parámetro formal dentro del subprograma. Una vez que el procedimiento empieza a ejecutarse, cualquier cambio de valor de uno de los parámetros formales no se refleja en un cambio en el correspondiente argumento (parámetros reales), es decir, que cuando el subprograma termine de ejecutarse el argumento actual (parámetros actuales) tendrá el mismo valor que cuando el subprograma comenzó, independientemente de lo que les haya sucedido a los parámetros formales. A estos parámetros se les llama parámetros valor. Y cuando hagamos la declaración tendremos que hacerlo a través de E (entrada).
• Por referencia: el paso de parámetros por referencia, que se les llama también parámetros variables, significa que la posición o dirección de (no del valor) del argumento o parámetro actual se envía al subprograma, es decir, que si a un parámetro formal se la da el atributo de parámetro por referencia y si el parámetro actual es una variable, entonces un cambio en el parámetro formal se refleja en un cambio en el correspondiente parámetro actual, porque ambos tienen la misma posición de memoria. Para indicar que deseamos transmitir un parámetro por dirección cuando hagamos la declaración de los parámetros, lo haremos a través de E/S o S.
• 6. EFECTOS LATERALES
Las modificaciones que se produzcan mediante una función o procedimiento en los elementos situados fuera del subprograma se llaman efectos laterales. En algunos casos son beneficiosos para la programación pero no es recomendable no utilizarlos.
• Efectos laterales en procedimientos: la comunicación del procedimiento con el resto del programa se tiene que hacer a través de los parámetros. Cualquier otra comunicación entre el procedimiento y el resto del programa son efectos laterales. Estos efectos son perjudiciales en la mayoría de los casos. Si un procedimiento modifica una variable global (distinta de un parámetro actual) esto es un efecto lateral, por ello excepto en contadas ocasiones, no debe aparecer en la declaración del procedimiento. Si se necesita una variable temporal en un procedimiento es mejor utilizar una variable local, que habría que declarar en el procedimiento.
• Si queremos que el programa modifique el valor de una variable global es mejor utilizar un parámetro formal, variable en la declaración del procedimiento, y después usar la variable global como el parámetro actual en una llamada al procedimiento.
En general, se debe seguir la regla de no utilizar ninguna variable global en procedimiento, aunque esto no significa que los procedimientos no puedan manipular variables globales.
En el cuerpo de un procedimiento es mejor utilizar un parámetro formal o una variable local. En los lenguajes donde es posible declarar constantes, se puede utilizar constantes globales ya que no pueden ser modificadas por el procedimiento.
• Efectos laterales en funciones: Una función toma los valores de los argumentos y devuelve un único valor. Sin embargo, al igual que en los procedimientos, una función puede hacer cosas similares a ellos.
• Una función puede tener parámetros variables, además de parámetros valor (no devuelven nada) en una lista de parámetros formales. Una función puede cambiar el contenido de una variable global y ejecutar instrucciones de E/S. Estas operaciones se conocen como parámetros laterales y se deben evitar. Toda la información que se transmite entre procedimientos y funciones debe realizarse (al igual que en los procedimientos) a través de la lista de parámetros y no a través de las variables globales. Esto convertirá al procedimiento o función en módulos independientes que pueden ser comprobados y depurados por si solos, lo que evitara preocuparnos por el resto de las partes del programa.
7. RECURSIVIDAD
Un subprograma puede llamar a cualquier otro subprograma y este a otro y así sucesivamente, que es lo que se llama anidación. Pero también se pueden llamar a si mismos.
• llamar_a A
• --------------------
• Llamar_a B
• Llamar_a A
• Otra función o procedimiento que se puede llamar así mismo se llama recursivo. Es una herramienta muy potente en algunas aplicaciones, sobre todo en calculo, y puede ser utilizada como una alternativa a la repeticion o estructura repetitiva. La escritura de un procedimiento o función recursiva es similar a los procedimientos o funciones normales, sin embargo, para evitar que la recursion continúe indefinidamente es preciso incluir una condición de terminación.
La razón de que existan lenguajes que admitan la recursividad se debe a la existencia de estructuras especificas tipo pilas y memorias dinámicas. Las direcciones de retorno y el estado de cada subprograma se guardan en estructuras tipo pilas.
TEMA 7: ESTRUCTURAS DINAMICAS LINEALES DE DATOS
Hay otro tipo de estructuras que pueden ampliar o limitar su tamaño mientras se ejecuta el programa: estructuras dinámicas
ESTRUCTURAS DINAMICAS
Estas estructuras son generadas mediante un tipo de dato conocido con el nombre de puntero. Una variable de tipo puntero almacena la dirección o posición de otra variable. La principal ventaja que tiene usar este tipo de datos es que se pueden adquirir posiciones de memoria cuando se necesitan y liberarlas cuando ya no se necesitan. De esta manera se pueden crear estructuras dinámicas que se expandan o contraigan según agreguemos o eliminemos elementos. Un puntero es una variable que almacena la posición de una variable dinámica de un tipo determinado y llega a la variable numérica apuntada. El tipo de dato puede ser simple o estructurado y podemos realizar las siguientes operaciones:
• Inicialización:
• Programación en C
• Comparación: p=q, p<>q
• Asignación: p!q
• Creación de variables dinámicas: consiste en reservar un espacio en memoria para la variable dinámica. Reservar (p).
Eliminación de variables dinámicas: consiste en desocupar el espacio en memoria que está siendo utilizado por las variables dinámicas. Liberar (p)
Una variable dinámica es una variable simple o estructurada de datos sin nombre y creada en tiempo de ejecución, por lo tanto, para poder acceder a una variable numérica apuntada como no tiene nombre usaremos "!". Las variables dinámicas pueden intervenir en cualquier operación o expresión para una variable estática de su mismo tipo. Pueden ser de dos tipos: lineales y no lineales.
1. LINEALES
a) LISTAS
Son secuencias de 0 o más elementos de un tipo de datos almacenado en memoria. Son estructuras lineales donde cada elemento de una lista excepto el primero tiene un único predecesor y cada elemento de la lista excepto el ultimo tiene un sucesor. Al número de elementos de una lista se le llama longitud, y decimos que una lista está vacía si tiene 0 elementos. Se pueden añadir nuevos elementos o suprimirlos de cualquier posición.
Tipos de listas lineales:
• Listas contiguas: los elementos son adyacentes en la memoria del ordenador y tienen unos limites (izquierdo y derecho o inferior y superior) que no pueden ser rebasados cuando se añade un nuevo elemento. Se implementan a través de arrays y la inserción o eliminación de un elemento necesitará una traslación por parte de los elementos de la lista, excepto para la cabecera y el final de la lista.
• Listas enlazadas: los elementos se almacenan en posiciones de memoria que no son adyacentes o contiguas, por lo que cada elemento necesita almacenar la posición del siguiente elemento de la lista. Son bastante más flexibles y potentes que las listas contiguas y la inserción o el borrado de un elemento no requiere el desplazamiento de los demás elementos de la lista. Se implementan, normalmente, de forma dinámica, pero si el lenguaje de programación no lo permite se utilizaran arrays, con lo cual tendremos limitaciones en cuanto al número de elementos que pueda contener la lista y además establece una ocupación de memoria constante.
Gráficamente se representa de la siguiente forma:
• Listas circulares: son una modificación de las listas enlazadas en las que el puntero del ultimo elemento apunta al primero de la listas.
Gráficamente se representa de la siguiente forma:
Programación en C
Debemos diseñar un nodo especial llamado nodo cabecera que está permanentemente asociado a la existencia de la lista y cuyo campo para almacenar información no se utiliza. Así, al efectuar un recorrido de la lista, el nodo cabecera nos permitirá detectar cuándo han sido visitados todos los demás nodos.
• Listas doblemente enlazadas: Se pueden recorrer tanto del final al principio como de principio a fin. Cada nodo de las listas de este tipo consta de un campo con información y de otros dos campos que son de tipo puntero y que podríamos denominar anterior y siguiente, uno desde su nodo anterior y otro de su nodo sucesor.
• Listas doblemente encadenadas circulares: en este tipo de listas el campo anterior del primer nodo apunta al ultimo nodo y el campo siguiente del ultimo nodo apunta al primero.
b) PILAS
Son unas estructuras que son más utilizadas siempre que se quieran recuperar una serie de elementos en orden inverso a como se introdujeron.
Tanto la extracción como la inserción de un elemento en la pila se realiza por la parte superior, por lo tanto, el único elemento al que podemos acceder es el ultimo, y como el ultimo elemento que se pone en la pila es el primero que se puede sacar, a estas estructuras dinámicas llamadas pilas se les conoce como LIFO (Last In First Off). Las pilas se deben implementar de forma dinámica utilizando punteros, pero si el lenguaje de programación que estamos utilizando no admite punteros, entonces tendremos que utilizar arrays, y además una variable que normalmente se le da el nombre de `cima' y es la que apunta al último elemento de la pila.
Programación en C
Aplicaciones de las pilas: el uso más común que suele darse a las pilas es cuando hacemos una llamada desde un programa a otro subprograma. Se utiliza las pilas para guardar el lugar desde donde se hizo la llamada y para almacenar el estado de las variables en el momento en que se hace la llamada. También se utilizan en todos los algoritmos recursivos para almacenar el valor de las variables y los parámetros.
c) COLAS
Una cola es también una estructura de datos lineal en donde las eliminaciones se realizan por uno de sus extremos que normalmente se llama frente, y las inserciones se realizan por el otro extremo que normalmente se llama final. A estas estructuras se les llama FIFO (First In First Out).
Se tiene que implementar de forma dinámica usando punteros a menos que el lenguaje que utilicemos lo permita, y entonces tendremos que utilizar arrays.
Representación grafica de colas hechas con arrays.
Programación en C
Programación en C
SOLUCIONES en el caso de que la variable `final' coincida con el máximo del array aunque haya posiciones libres.
• Retroceso: consiste en mantener fijo a 1 el valor de la variable `frente' realizando un desplazamiento de una posición para todos los elementos ocupados cada vez que se produce una eliminación.
• Programación en C
• Reestructuración: la variable `final' llega al máximo de los elementos, los elementos ocupados se deben desplazar hacia atrás, las posiciones que hagan falta para que el principio de la lista coincida con el principio del array, es decir:
• Programación en C
• Mediante un array circular: se considera que el elemento primero sigue al elemento ultimo. Para esta implementación debemos dejar una posición libre que separe el principio y el final de la cola.
• Programación en C
MALLOC
#include <stdio.h>
#include <stdlib.h>
void main ()
{
int i,j,fl,nel=0;
int **ptabla;
printf("\n\t Escribe el numero de nombres \n");
scanf("%i",&fl);
printf("\n\t Escribe el numero de columnas \n");
scanf("%i",&cl);
ptabla=(int**)malloc(fl*sizeof(int));
for (i=0;i<cl;i++)
{
ptabla[i]=(int*)malloc(cl*sizeof(int));
}
for (i=0;i<fl;i++)
{
for(j=0;j<cl;j++)
{
printf("Escribe el elemento \n");
scanf("%i",&ptabla[i][j]);
}
}
for (i=0;i<fl;i++)
{
for(j=0;j<cl;j++)
{
printf("%4i",*(*ptabla)++);
}
printf("\n");
*ptabla-=cl;
ptabla++;
}
ptabla-=fl;
for (i=0;i<fl;i++)
{
free(ptabla[i]);
}
free(ptabla);
}
MALLOC (2ª PARTE)
#include <stdio.h>
#include <stdlib.h>
crear(int **ptabla,int *cuan)
{
*ptabla=(int *)malloc(sizeof(int)**cuan);
}
rellenar(int *ptabla,int cuan)
{
int i;
for (i=0;i<cuan;i++)
{
printf("\n\t escribe el elemento: ");
scanf("%i",ptabla++);
}
}
listar(int *ptabla,int cuan)
{
int i;
for(i=0;i<cuan;i++)
{
printf("\n\t el elemento es: %i",*ptabla++);
}
fflush(stdin);
getchar();
}
ordenar(int *ptabla,int cuan)
{
fflush(stdin);
getchar();
for (i=0;i<cuan;i++)
{
for(j=0;j<cuan-1;j++)
{
if(*ptabla<*(ptabla+1))
{
aux=*ptabla+1;
*(ptabla+1)=*ptabla;
*(ptabla)=aux;
}
ptabla++;
}
ptabla-=cuan;
}
}
}
void main()
{
int opci;
int* ptabla;
int cuantos;
printf("\n\t escribe cuantos elementos \n");
scanf("%i",&cuantos);
do
{
system("clear");
printf("\n\t 1 para crear tabla");
printf("\n\t 2 para rellenar tabla");
printf("\n\t 3 listar tabla");
printf("\n\t 4 para ordenar");
printf("\n\t 5 para salir \n");
scanf("%i",&opci);
switch (opci)
{
case 1:
crear(&ptabla,&cuantos);
break;
case 2:
rellenar(&ptabla,cuantos);
break;
case 3:
listar(&ptabla,cuantos);
break;
case 4:
ordenar(&ptabla,cuantos);
break;
case 5:
free(*ptabla);
exit(0);
}
}while(opci!=5 );
}
ESTRUCTURAS
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
union t_variable
{
char autor[15];
int edicion;
};
struct t_biblio
{
int codigo;
char nombre[30];
char tipo;
union t_variable unvariable;
};
void listar(struct t_biblio alma[],int *cant);
void alta(struct t_biblio alma[],int *cant);
void main()
{
struct t_biblio fichas[10];
int cantidad=0,opcion;
do
{
system("clear");
printf("\n\t Escribe lo que quieres hacer 1 listar 2 para dar de alta\n\t ");
printf("\n\t Escribe la opcion \t");
scanf("%i",&opcion);
if (opcion==1)
{
listar(fichas,&cantidad);
}
else
{
alta(fichas,&cantidad);
}
}
while(opcion!=199);
}
void listar(struct t_biblio alma[],int *cant)
{
int i;
for(i=0;i<*cant;i++)
{
system("clear");
printf("\n\tnombre: %s ",alma[i].nombre);
printf("\n\tcodigo: %i ",alma[i].codigo);
printf("\n\ttipo: %c ",alma[i].tipo);
if(alma[i].tipo=='l')
{
printf("\n\tautor: %s ",alma[i].unvariable.autor);
}
else
{
printf("\n\tedicion: %i ",alma[i].unvariable.edicion);
}
fflush(stdin);
printf("\n\t pulsa una tecla para continuar");
getchar();
}
}
void alta(struct t_biblio alma[],int *cant)
{
char opci;
system("clear");
printf("\n\tescribe el tipo p(periodicos) l(libros): ");
fflush(stdin);
scanf("%c",&opci);
switch (opci)
{
case 'p':
printf("\n\tescdribe el nombre: ");
fflush(stdin);
gets(alma[*cant].nombre);
printf("\n\t escribe el codigo : ");
fflush(stdin);
scanf("%i",&alma[*cant].codigo);
printf("\n\t escribe la edicion: ");
fflush(stdin);
scanf("%i",&alma[*cant].unvariable.edicion);
alma[*cant].tipo='p';
(*cant)++;
break;
case 'l':
printf("\n\t escribe el nombre: ");
fflush(stdin);
gets(alma[*cant].nombre);
printf("\n\t escribe el codigo: ");
fflush(stdin);
scanf("%i",&alma[*cant].codigo);
printf("\n\t escribe el autor: ");
fflush(stdin);
gets(alma[*cant].unvariable.autor);
alma[*cant].tipo='l';
(*cant)++;
break;
}
}
STRING DINAMICAS
#include <string.h>
#include <stdio.h>
#include <stdlib.h>
void main ()
{
int i,j,fl,nel=0;
char nombre[50];
char **ptabla;
printf("\n\t Escribe el numero de nombres \n");
scanf("%i",&fl);
ptabla=(char**)malloc(fl*sizeof(char));
for (i=0;i<fl;i++)
{
printf("Escibe el nombre");
gets(nombre);
ptabla[i]=(char*)malloc((strlen(nombre)+1)*sizeof(char));
strcpy(ptabla[i],nombre);
}
for (i=0;i<fl;i++)
printf("%4s\n",*ptabla++);
ptabla-=fl;
for (i=0;i<fl;i++)
{
free(ptabla[i]);
}
free(ptabla);
}
RECURSIVIDAD
#include <stdio.h>
#include <stdlib.h>
void main()
int factorial(int n)
{
res=num*factorial-1;
return(res);
}
{
int num,res;
printf("Escribe el numero");
scanf("%i",&num);
if (num > 1)
{
res=num*factorial(num-1);
}
return res;
printf("resultado es %i",res);
}
MENU
#include <stdlib.h>
#include <stdio.h>
void maximo(int datos[],int cantidad)
{
int i,mayor=0;
system("clear");
for (i=0;i<cantidad;i++)
{
if (datos[i]>=mayor)
mayor=datos[i];
}
printf("el mayor es %i \n",mayor);
fflush(stdin);
getchar();
system("clear");
}
void leer(int numeros [],int *cantidad)
{
int i;
char op='n';
system("clear");
while(op!='s')
{
printf("escribe un numero -s- para salir \n");
scanf("%i",&numeros[*cantidad]);
(*cantidad)++;
printf("escribe s para salir \n");
scanf("%s",&op);
}
system("clear");
}
void menor(int numeros [],int cantidad)
{
int i;
long menor=100000;
system("clear");
for (i=0;i<cantidad;i++)
{
if(numeros[i]<=menor)
menor=numeros[i];
}
printf(" el menor es %i \n",menor);
fflush(stdin);
getchar();
system("clear");
}
void ordenar(int numeros [],int cantidad)
{
int i,c,aux;
system("clear");
for(c=0;c<cantidad;c++)
{
for (i=0;i<cantidad-1;i++)
{
if (numeros[i]>numeros[i+1])
{
aux=numeros[i+1];
numeros[i+1]=numeros[i];
numeros[i]=aux;
}
}
}
system("clear");
}
void visualizar(int numeros[],int cantidad)
{
int i;
system("clear");
for(i=0;i<cantidad;i++)
{
printf("\n el elemento %i es %i ",i,numeros[i]);
}
fflush(stdin);
getchar();
system("clear");
}
void anadir(int numeros[],int *cantidad)
{
if(*cantidad<=10)
{
system("clear");
printf(" dime el numero \n");
scanf("%i",&numeros[*cantidad]);
(*cantidad)++;
}
else
{
printf("\n\t no se pueden anadir mas numeros ");
}
}
void eliminar(int numeros[], int *cantidad)
{
int pos,i;
if (*cantidad!=0)
{
printf("dime la posicion que quieres borrar hay %i posiciones",*cantidad);
scanf("%i",&pos);
for(i=pos-1;i<*cantidad-1;i++)
{
numeros[i]=numeros[i+1];
}
(*cantidad)--;
}
else
{
printf("\n\tno hay valores que eliminar");
}
}
void main()
{
int datos[10],cant;
char opci;
system("clear");
do
{
printf(" \n\t pulsa 1 para introducir datos \n");
printf(" \n\tpulsa 2 para ordenar los datos \n");
printf(" \n\tpulsa 3 para ver el mayor \n");
printf(" \n\tpulsa 4 para ver el menor \n");
printf(" \n\tpulsa 5 para ver los datos \n");
printf(" \n\tpulsa 6 para anadir \n");
printf(" \n\tpulsa 7 para eliminar \n");
printf(" \n\tpulsa 8 para salir \n");
printf(" \n\telige una opcion :");
scanf("%s",&opci);
switch (opci)
{
case '1':
leer(datos,&cant);
break;
case '2':
ordenar(datos,cant);
break;
case '3':
maximo(datos,cant);
break;
case '4':
menor(datos,cant);
break;
case '5':
visualizar(datos,cant);
break;
case '6':
anadir(datos,&cant);
break;
case '7':
eliminar(datos,&cant);
break;
case '8':
exit(0);
default:
continue;
}
}
while(opci>=1||opci<=7);
}
FICHEROS
#include <stdlib.h>
#include <stdio.h>
void maximo(int datos[],int cantidad)
{
int i,mayor=0;
system("clear");
for (i=0;i<cantidad;i++)
{
if (datos[i]>=mayor)
mayor=datos[i];
}
printf("el mayor es %i \n",mayor);
fflush(stdin);
getchar();
system("clear");
}
void leer(int numeros [],int *cantidad)
{
int i;
char op='n';
system("clear");
while(op!='s')
{
printf("escribe un numero -s- para salir \n");
scanf("%i",&numeros[*cantidad]);
(*cantidad)++;
printf("escribe s para salir \n");
scanf("%s",&op);
}
system("clear");
}
void menor(int numeros [],int cantidad)
{
int i;
long menor=100000;
system("clear");
for (i=0;i<cantidad;i++)
{
if(numeros[i]<=menor)
menor=numeros[i];
}
printf(" el menor es %i \n",menor);
fflush(stdin);
getchar();
system("clear");
}
void ordenar(int numeros [],int cantidad)
{
int i,c,aux;
system("clear");
for(c=0;c<cantidad;c++)
{
for (i=0;i<cantidad-1;i++)
{
if (numeros[i]>numeros[i+1])
{
aux=numeros[i+1];
numeros[i+1]=numeros[i];
numeros[i]=aux;
}
}
}
system("clear");
}
void visualizar(int numeros[],int cantidad)
{
int i;
system("clear");
for(i=0;i<cantidad;i++)
{
printf("\n el elemento %i es %i ",i,numeros[i]);
}
fflush(stdin);
getchar();
system("clear");
}
void anadir(int numeros[],int *cantidad)
{
if(*cantidad<=10)
{
system("clear");
printf(" dime el numero \n");
scanf("%i",&numeros[*cantidad]);
(*cantidad)++;
}
else
{
printf("\n\t no se pueden anadir mas numeros ");
}
}
void eliminar(int numeros[], int *cantidad)
{
int pos,i;
if (*cantidad!=0)
{
printf("dime la posicion que quieres borrar hay %i posiciones",*cantidad);
scanf("%i",&pos);
for(i=pos-1;i<*cantidad-1;i++)
{
numeros[i]=numeros[i+1];
}
(*cantidad)--;
}
else
{
printf("\n\tno hay valores que eliminar");
}
}
void main()
{
int datos[10],cant;
char opci;
system("clear");
do
{
printf(" \n\t pulsa 1 para introducir datos \n");
printf(" \n\tpulsa 2 para ordenar los datos \n");
printf(" \n\tpulsa 3 para ver el mayor \n");
printf(" \n\tpulsa 4 para ver el menor \n");
printf(" \n\tpulsa 5 para ver los datos \n");
printf(" \n\tpulsa 6 para anadir \n");
printf(" \n\tpulsa 7 para eliminar \n");
printf(" \n\tpulsa 8 para salir \n");
printf(" \n\telige una opcion :");
scanf("%s",&opci);
switch (opci)
{
case '1':
leer(datos,&cant);
break;
case '2':
ordenar(datos,cant);
break;
case '3':
maximo(datos,cant);
break;
case '4':
menor(datos,cant);
break;
case '5':
visualizar(datos,cant);
break;
case '6':
anadir(datos,&cant);
break;
case '7':
eliminar(datos,&cant);
break;
case '8':
exit(0);
default:
continue;
}
}
while(opci>=1||opci<=7);
}
FICHEROS (2ª PARTE)
#include <stdio.h>
struct tdatos{
int nume;
float real;
};
void main(){
struct tdatos dato[10];
FILE *pfich;
pfich=fopen("ficher","w");
dato.nume[0]=1;
dato.real[0]=23.4;
fwrite(&dato,sizeof(dato),1,pfich)
fclose("ficher");
pfich=fopen("ficher","r");
PASAR ARGUMENTOS DE L DE COMANDO
#include <stdio.h>
int main(int c,char* args[])
{
int i;
/* mostrar los argumentos pasados atraves de la linea de comandos */
while (i<c)
{
printf("los argumentos pasados son :%s\n",args[i]);
i++;
}
}
25
|
__label__pos
| 0.772645 |
Autotechiq
issues
Navigation
Hey, Why Is My Radiator Leaking?
If you are short on time and want to fast-track the process to professional help, click Yes
Four common causes for a vehicle Radiator Leaking and their related parts.
The radiator is a component of the engine's cooling system. It is located in the front of the vehicle and uses airflow across the radiator core to transfer the heat developed during engine combustion to the outside air. The system is under pressure to allow the system to operate at higher temperatures to help with complete combustion and minimize vehicle emissions.
Have You Noticed a Leak In Your Vehicle's Radiator?
A radiator leak is commonly caused by a loose/broken radiator cap, damage in the radiator hose, internal chemical electrolysis, or a crack in the tank due to impact or wear. Also, note that a coolant reservoir leak can be commonly mistaken for a radiator leak.
This can result in overheating, engine damage, and unreliable performance. So, it's crucial not to overlook the bad signs and take prompt action. For example, if you notice coolant puddles or a decrease in your vehicle's coolant level, it indicates that the radiator fluid is seeping out. Ignoring these warnings can lead to costly repairs and inconvenience down the road.
Remember, promptly addressing a leaking radiator is an investment in your vehicle's longevity and peace of mind.
Let's Get To The Bottom Of It!
• Q: Do you see a red, yellow, or green crust around the radiator hose ends?
The radiator hoses are like flexible tubes made of rubber. They connect to the radiator and the engine block through firm hose adapters. They carry the coolant from the engine to the radiator and back again. Over time, the rubber hoses can become stiff and fragile because they're made of rubber. Additionally, when the coolant becomes acidic, it gradually weakens the hoses from the inside. If you notice a coolant leak, it may be because the hoses start leaking at the connections between the fittings and the hose itself. You might see a dried, crusty material of a specific color, meaning that the coolant has been leaking.
• Q: Is the engine oil texture resembling a milkshake?
The head gasket is like a seal that connects the engine's head to its block. Its main job is to keep the coolant passages separate from the oil passages and the combustion chamber. However, the coolant can become acidic if the engine gets too hot or the cooling system wears out. This acidity and electrolysis can damage the head gasket and create leaks. As a result, the coolant can enter the cylinder and pass through the piston rings, eventually ending up in the crankcase where the engine oil is stored; this results in a mix of coolant and oil. When this happens, the engine oil looks milky, resembling a dark milkshake.
• Q: Are there pinhole leaks in the radiator?
The coolant must have a certain alkalinity level to stay healthy. However, as time goes by and the coolant gets used, it becomes more acidic. This acidity allows the coolant to conduct electricity. This creates a process called electrolysis, which can damage plastic and aluminum parts in the engine. As a result, these components start to wear out, and small holes, called pinhole leaks, can form.
• Q: Do you notice coolant puddles under your vehicle?
The radiator comprises two tanks on each end of the core. Its purpose is to allow coolant to flow from one tank through the core, into the other tank, and back to the engine. The radiator's core is typically made of aluminum or copper, while the tanks are made of plastic. A rubber seal between the core and the tanks is in place to keep them connected. However, as time passes and the radiator is used, this seal can become weak and brittle, eventually cracking. When this happens, it can lead to a leak underneath the vehicle.
Find Professional Help
Please select your vehicle's brand and location so we can locate the best professional help for you
If you are a shop owner and sick of business directories that are based on the cost of repair, AutoTechIQ is for you. If your customers receive Digital Inspection results then AutoTechIQ is definitely for you. Check out the certification page or how to rank in your area.
Vehicle Health Inspection Proof
Explore the following typical inspection results that show a potential cause for the symptom and select the one you believe is similar to your vehicle's issue.
The coolant reservoir is leaking and causing the low coolant warning light to appear on the dashboard, resulting in engine overheating
The proof image shows the coolant reservoir leaking at the seam, which explains the low coolant level. Therefore, the coolant reservoir must be replaced with a new one to fix the issue.
When the customer brought in their vehicle, they were concerned about the low coolant light popping on the dashboard every morning. The light would turn off after driving for a while, but now it's consistent. The customer also mentioned they hadn't noticed any coolant puddle on the ground.
During a test drive, the technician confirmed that the low coolant light was on. As part of a vehicle health inspection, the technician discovered that the coolant level was low, and there was evidence of coolant underneath the coolant reservoir.
To further investigate, the technician used a coolant pressure system tester. After filling the coolant correctly, they pressurized the system to 12 psi. Unfortunately, the coolant reservoir was leaking at the seams during this test. This leakage was the cause of the low coolant level, and the reservoir will need to be replaced.
Does the issue look like this? if not accessible your shop will document it
The coolant is overflowing the reservoir because the radiator cap is not holding the specified psi to keep coolant healthy
The proof image shows the radiator cap being tested and failing to hold pressure. This explains why the coolant is boiling over and causing the overflow tank to overflow. The technician will replace the faulty radiator cap with a new one to resolve the issue.
When the customer brought in their vehicle, they were worried because the overflow tank in the cooling system was boiling over, even though the engine didn't seem to overheat. They mentioned that they had been adding coolant every morning to keep up with it.
During a test drive, the technician confirmed the coolant overflowing in the overflow reservoir. However, during the initial vehicle health inspection, the technician found no issues related to the customer's concern.
To investigate further, the technician checked the acidity level of the coolant, and it was within the acceptable range. They then used a cooling system pressure checker to look for leaks but found none.
Next, the technician examined the radiator cap and discovered it held less pressure. The radiator cap is supposed to hold up to 12 pounds per square inch (psi), but it was failing and only holding less than 4 psi. Therefore, the radiator cap needs to be replaced.
Does the issue look like this? if not accessible your shop will document it
The radiator is leaking coolant, causing fluid loss, resulting in engine overheating.
The proof image shows the radiator leaking, explaining why a coolant puddle is under the vehicle. This confirms the need for a radiator replacement to resolve the issue.
When the customer dropped off their vehicle, they mentioned noticing a red liquid puddle where they usually park.
During a test drive, the technician encountered no issues related to the customer's concern. However, during a vehicle health inspection, the technician noticed the coolant level was low.
To investigate further, the technician used a cooling system pressure tester. They connected the tester to the same place where the radiator cap goes and increased the pressure to 12 pounds per square inch (PSI), which is the rating of the radiator cap.
The technician discovered the radiator was leaking between the tank and the core through the test. As a result, the radiator will need to be replaced.
Does the issue look like this? if not accessible your shop will document it
Testing the coolant on a tool. The result showsh that the coolant is acidic and needs to be exchanged
The proof image shows the voltage test, demonstrating the need for coolant replacement. In addition, it helps confirm the presence of electrolysis in the coolant. Finally, it supports the technician's recommendation to replace the corroded radiator and perform a cooling system flush to prevent further issues.
When the customer brought in their vehicle, they mentioned noticing coolant on the ground underneath it. They even saw a tiny leak in the radiator that looked like a small hole, as if someone had poked it with a needle.
During a test drive, the technician detected the smell of coolant after driving for a bit. Upon pulling the vehicle into the service bay, they saw coolant coming out of the radiator through a pinhole.
During a vehicle health inspection, the technician discovered the radiator leaking from a pinhole. They also noticed that the coolant level was low. To investigate further, the technician checked the pH level of the coolant. They found that it was highly imbalanced, going beyond the normal range.
In this case, chemical electrolysis might be causing damage from the inside of the radiator and creating the pinhole. So, the technician conducted a test using a digital voltmeter. They placed the positive probe of the voltmeter in the coolant and connected the other end to the negative battery cable.
The results showed a current of 400 millivolts in the coolant, confirming that electrolysis was the cause of the pinhole leak. Therefore, the radiator needs to be replaced. The mechanic used handy tools in this whole process; this is the type of service you should expect regardless if you're servicing a Japanese or American vehicle.
In addition to replacing the radiator, the technician recommends a cooling system flush. This is necessary due to the imbalanced pH level of the existing coolant. Flushing the system and using fresh coolant will significantly reduce the risk of electrolysis and causing future leaks.
Does the issue look like this? if not accessible your shop will document it
The dipstick shows a very brownish milkshake-like oil. This indicates the head gasket is leaking, allowing coolant to mix with engine oil
The proof image provided shows the milkshake-like appearance of the engine oil, indicating the faulty radiator gasket. This is a significant issue that requires further investigation and action to resolve.
When the customer brought in their vehicle, they mentioned it was difficult to start it. Additionally, they had been checking the engine oil and noticed that it looked like a milkshake in color.
During a test drive, the technician observed a puff of white smoke from the exhaust when starting the vehicle. They also noticed that the engine took longer to crank before starting.
The technician performed a vehicle health inspection and found the coolant level low. But unfortunately, they also discovered that the engine oil had coolant mixed into it, resulting in a chocolate milkshake-like appearance.
The technician used a block tester and special testing fluid to investigate the issue further. They replaced the radiator cap with the block tester and started the vehicle. Almost immediately, the testing fluid changed color from blue to yellow. This confirmed that the head gaskets had failed.
Based on these findings, the technician recommends a more extensive engine tear-down to verify the damage's extent. This will help determine whether the head gaskets and the engine can be repaired or if a complete replacement is necessary.
Does the issue look like this? if not accessible your shop will document it
A coolant leak can build up crustic material around the leaking area, like coolant hoses
The proof image provided shows the crusty build-up of dried coolant, confirming the need to replace the radiator hoses. The crusty material is a clear indication of coolant leakage. By replacing these hoses, the technician will address the issue and prevent further leaks in the cooling system.
When the customer brought in their vehicle, they noticed some pink crusty stuff around one of the hoses while checking the engine oil. They described it as similar to the crusty material that forms around battery cable ends, even though the hose is nowhere near the battery.
During a test drive, the technician didn't notice anything about the customer's concern. However, during a vehicle health inspection, the technician observed that the coolant level was low, and the radiator hose had a crusty build-up around the adapter where the feed hose connects from the de-gas bottle.
To investigate further, the technician used a cooling system pressure tester. They connected it to the de-gas bottle and increased the pressure to the maximum limit recommended by the manufacturer, 12 pounds per square inch (PSI).
Through this test, which is also common for DOT inspections, the technician confirmed that the coolant hose was leaking. As a result, they recommend replacing both the upper and lower radiator hoses, as well as both heater hoses.
Does the issue look like this? if not accessible your shop will document it
Typical Fixes to Address the Cause(s)
The following chapters bases themselves on experiences from our auto repair shop; we'll describe related problems' causes and fixes.
"Coolant Reservoir Replacement" fixes "Leaking coolant reservoir"
The AutoTechIQ ranking for Safety, Cost Avoidance, and Environmental Impact is
Safetyi
env level
env level
Cost Avoidancei
env level
env level
Environmental Impacti
env level
env level
Hey, Why Is My Radiator Leaking?
Sometimes a problem is more challenging to describe than it initially looked like. If you are not sure your problem is described by this article, please find below similar vehicle symptoms, which might describe better the issue you are experiencing.
Other things your auto repair shop might talk about:
Coolant leaking. Internal combustion engine. Losing coolant. leaky radiator valve. water pump.
|
__label__pos
| 0.850624 |
Gas-Phase Oxidation of Reactive Organometallic Ions Anuj Joshi Sofia Donnecke Ori Granot Dongju Shin Scott Collins Irina Paci J Scott McIndoe 10.26434/chemrxiv.11909397.v1 https://chemrxiv.org/articles/Gas-Phase_Oxidation_of_Reactive_Organometallic_Ions/11909397 Analysis of highly reactive compounds at very low concentration in solution using electrospray ionization mass spectrometry requires the use of exhaustively purified solvents. It has generally been assumed that desolvation gas purity needs to be similarly high, and so most chemists working in this space have relied upon high purity gas. However, the increasingly competitiveness of nitrogen generators, which provide gas purity levels that vary inversely with flow rate, prompted an investigation of the effect of gas-phase oxygen on the speciation of ions. For moderately oxygen sensitive species such as phosphines, no gas-phase oxidation was observed. Even the most reactive species studied, the reduced titanium complex [Cp<sub>2</sub>Ti(NCMe)<sub>2</sub>]<sup>+</sup>[ZnCl<sub>3</sub>]<sup>–</sup> and the olefin polymerization precatalyst [Cp<sub>2</sub>Zr(µ-Me)<sub>2</sub>AlMe<sub>2</sub>]<sup>+</sup> [B(C<sub>6</sub>F<sub>5</sub>)<sub>4</sub>]<sup>–</sup>, only exhibited detectable oxidation when they were rendered coordinatively unsaturated through in-source fragmentation. Computational chemistry allowed us to find the most plausible pathways for the observed chemistry in the absence of observed intermediates. The results provide insight into the gas-phase oxidation of reactive species and should assure experimentalists that evidence of significant oxidation is likely a solution rather than a gas-phase process, even when relatively low-purity nitrogen is used for desolvation. 2020-02-28 13:13:52 Oxidation Mass spectrometry electrospray ionization decomposition oxygen olefin polymerization
|
__label__pos
| 0.925183 |
How Does SNAP-8 Work, And Does It Deserve Its Status?
How Does SNAP-8 Work, And Does It Deserve Its Status?
The peptide recognised as SNAP-8 is regarded by its scientific title, acetyl glutamyl heptapeptide-1. Its probable software in anti-wrinkle lotions is now becoming investigated. According to scientific tests, the qualities of SNAP 8 make it feasible for it to lessen the visual appearance of wrinkles manufactured by the purely natural getting old system of muscle contractions that occur throughout the day. Animal studies have proven significant consequences on the eyes and brow location. This merchandise is assumed to be a Botulinum Toxin substitute that is fewer harsh, far more charge-successful, and safer than the latter. SNAP 8 performs a perform equivalent to that of botulinum toxin in that it targets the creation of wrinkles, but it does so in a distinctive method.
Effects of the Assessments Conducted on the SNAP 8 Peptide
Researchers carried out a sequence of VIVO assays to verify how little peptides can ensure the SNARE complex’s steadiness. For the reason that of this, the scientists could observe the temperature balance of the reconstituted SNARE protein sophisticated and its generation. This observation assesses the efficacy of peptides intended like SNAP-25 N and their capacity to assemble with synaptobrein and syntaxin as section of the generated SNARE advanced. The final final result was that the short peptides originating from the N-terminal finish of SNP-25 could efficiently contend with the all-natural protein and protect against it from forming the SNARE advanced by modifying its steadiness. Scientists attained this outcome by altering the stability of the primary protein.
The exam members participated in still a different experiment. The cream that experts utilized experienced 10% SNAP 8 in its composition. Silicon impressions were being taken from the spot surrounding the eyes of 17 individuals in the review. Gurus received these impressions on silicon right before the commencing of the exam. The analyze contributors utilised the cream twice day-to-day, and then 28 days later on, researchers collected one more sample. The imprints have been examined applying command laser scanning microscopy to observe the alter in the skin surface area in between the sample attained in advance of remedy and the sample taken immediately after treatment method. Skin topography pictures were being generated to get hold of a three-dimensional standpoint of the samples. Immediately after managing wrinkles for 28 days, researchers found that the depth of the wrinkles experienced considerably diminished, as revealed in these photographs. A most lessen of 63.18 percent was noticed when applying the SNAP 8 solution containing 10 percent.
Operating of the SNAP 8 Peptides
The N-terminal conclude of SNAP-25 has been copied and pasted into SNAP 8. This intricate competes with SNAP-25 for a area inside the SNARE intricate, which then influences the development of the SNARE advanced. It is difficult for the vesicle to release neurotransmitters in a way that is both successful and successful when the SNARE sophisticated is just minimally destabilized. This destabilization lowers muscular contractions, which in change aids to avoid the development of lines and wrinkles. By blocking the production of SNARE complexes and the launch of catecholamine, it will also assistance reduce the physical appearance of great traces and wrinkles that are previously present. It was also demonstrated to inhibit the formation of wrinkles and lines in test participants when employed regularly.
Clinical research have demonstrated that working with SNAP 8 may well help decrease the physical appearance of wrinkles by as considerably as 63.13 percent all-around the eyes. In accordance to the final results of in vitro and in vivo testing, the SNAP-8 activity amount is about 30 p.c better than that of the dad or mum peptide Argireline.
If you want to uncover a trustworthy business that sells reliable products, pay a visit to this website. This company sells a single of the most qualitative and inexpensive peptides presently.
Leave a Reply
|
__label__pos
| 0.898887 |
Discrete Differential Geometry Assignment 0
DDG Week2 Writing Assignment
2.1
Show that VE+F=1V - E + F = 1 for any polygonal disk.
For a simple n-sided polygon with n vertices, n edges, and 1 face, the equation above holds. When conncting another n-sided polygon to form a disk, the polygon can connect to the existing disk by merging mm edges. This will generate nmn-m edges, n(m+1)n-(m+1) vertices, and 1 new face.
V=V+nm+1E=E+nmF=F+1VE+F=VE+F+(n(m+1))(nm)+1=VE+F=1V' = V + n - m + 1 \\ E' = E + n - m \\ F' = F + 1 \\ V' - E' + F' = V - E + F + (n-(m+1)) - (n-m) + 1 = V - E + F = 1
The last equality stems from our inductive assumption.
2.2
In a platonic solid, there are FF m, n-gons meeting at VV vertices.
(F/m)(nF/2)+F=2(F/m) - (nF/2) + F = 2
2.8
Cl(S)
St(S)
Lk(S)
2.9
2.10
2.11
A0 = [
[1,1,0,0,0],
[1,0,1,0,0],
[1,0,0,1,0],
[1,0,0,0,1],
[0,1,0,0,1],
[0,1,1,0,0],
[0,0,1,1,0],
[0,0,0,1,1]
]
A1 = [
[1,0,0,1,1,0,0,0],
[1,1,0,0,0,1,0,0],
[0,1,1,0,0,0,1,0],
[0,0,1,1,0,0,0,1]
]
Coding
Code is somewhere, I haven't decided where to put it. The screenshots below should verify that the c++ code is working to solve the exercises.
All tests green: 11 tests passed
Star star
Link Link
Closure closure
|
__label__pos
| 0.998949 |
298
I have been reading some articles on memory leaks in Android and watched this interesting video from Google I/O on the subject.
Still, I don't fully understand the concept, and especially when it is safe or dangerous to user inner classes inside an Activity.
This is what I understood:
A memory leak will occur if an instance of an inner class survives longer than its outer class (an Activity). -> In which situations can this happen?
In this example, I suppose there is no risk of leak, because there is no way the anonymous class extending OnClickListener will live longer than the activity, right?
final Dialog dialog = new Dialog(this);
dialog.setContentView(R.layout.dialog_generic);
Button okButton = (Button) dialog.findViewById(R.id.dialog_button_ok);
TextView titleTv = (TextView) dialog.findViewById(R.id.dialog_generic_title);
// *** Handle button click
okButton.setOnClickListener(new OnClickListener() {
public void onClick(View v) {
dialog.dismiss();
}
});
titleTv.setText("dialog title");
dialog.show();
Now, is this example dangerous, and why?
// We are still inside an Activity
_handlerToDelayDroidMove = new Handler();
_handlerToDelayDroidMove.postDelayed(_droidPlayRunnable, 10000);
private Runnable _droidPlayRunnable = new Runnable() {
public void run() {
_someFieldOfTheActivity.performLongCalculation();
}
};
I have a doubt regarding the fact that understanding this topic has to do with understanding in detail what is kept when an activity is destroyed and re-created.
Is it?
Let say I just changed the orientation of the device (which is the most common cause of leaks). When super.onCreate(savedInstanceState) will be called in my onCreate(), will this restore the values of the fields (as they were before orientation change)? Will this also restore the states of inner classes?
I realize my question is not very precise, but I'd really appreciate any explanation that could make things clearer.
612
What you are asking is a pretty tough question. While you may think it is just one question, you are actually asking several questions at once. I'll do my best with the knowledge that I have to cover it and, hopefully, some others will join in to cover what I may miss.
Nested Classes: Introduction
As I'm not sure how comfortable you are with OOP in Java, this will hit a couple of basics. A nested class is when a class definition is contained within another class. There are basically two types: Static Nested Classes and Inner Classes. The real difference between these are:
• Static Nested Classes:
• Are considered "top-level".
• Do not require an instance of the containing class to be constructed.
• May not reference the containing class members without an explicit reference.
• Have their own lifetime.
• Inner Nested Classes:
• Always require an instance of the containing class to be constructed.
• Automatically have an implicit reference to the containing instance.
• May access the container's class members without the reference.
• Lifetime is supposed to be no longer than that of the container.
Garbage Collection and Inner Classes
Garbage Collection is automatic but tries to remove objects based on whether it thinks they are being used. The Garbage Collector is pretty smart, but not flawless. It can only determine if something is being used by whether or not there is an active reference to the object.
The real issue here is when a inner class has been kept alive longer than its container. This is because of the implicit reference to the containing class. The only way this can occur is if an object outside of the containing class keeps a reference to the inner object, without regard to the containing object.
This can lead to a situation where the inner object is alive (via reference) but the references to the containing object has already been removed from all other objects. The inner object is, therefore, keeping the containing object alive because it will always have a reference to it. The problem with this is that unless it is programmed, there is no way to get back to the containing object to check if it is even alive.
The most important aspect to this realization is that it makes no difference whether it is in an Activity or is a drawable. You will always have to be methodical when using inner classes and make sure that they never outlive objects of the container. Luckily, if it isn't a core object of your code, the leaks may be small in comparison. Unfortunately, these are some of the hardest leaks to find, because they are likely to go unnoticed until many of them have leaked.
Solutions: Inner Classes
• Gain temporary references from the containing object.
• Allow the containing object to be the only one to keep long-lived references to the inner objects.
• Use established patterns such as the Factory.
• If the inner class does not require access to the containing class members, consider turning it into a static class.
• Use with caution, regardless of whether it is in an Activity or not.
Activities and Views: Introduction
Activities contain a lot of information to be able to run and display. Activities are defined by the characteristic that they must have a View. They also have certain automatic handlers. Whether you specify it or not, the Activity has an implicit reference to the View it contains.
In order for a View to be created, it must know where to create it and whether it has any children so that it can display. This means that every View has an reference to the Activity (via getContext()). Moreover, every View keeps references to its children (i.e. getChildAt()). Finally, each View keeps a reference to the rendered Bitmap that represents its display.
Whenever you have a reference to an Activity (or Activity Context), this means that you can follow the ENTIRE chain down the layout hierarchy. This is why memory leaks regarding Activities or Views are such a huge deal. It can be a ton of memory being leaked all at once.
Activities, Views and Inner Classes
Given the information above about Inner Classes, these are the most common memory leaks, but also the most commonly avoided. While it is desirable to have an inner class have direct access to an Activities class members, many are willing to just make them static to avoid potential issues. The problem with Activities and Views goes much deeper than that.
Leaked Activities, Views and Activity Contexts
It all comes down to the Context and the LifeCycle. There are certain events (such as orientation) that will kill an Activity Context. Since so many classes and methods require a Context, developers will sometimes try to save some code by grabbing a reference to a Context and holding onto it. It just so happens that many of the objects we have to create to run our Activity have to exist outside of the Activity LifeCycle in order to allow the Activity to do what it needs to do. If any of your objects happen to have a reference to an Activity, its Context, or any of its Views when it is destroyed, you have just leaked that Activity and its entire View tree.
Solutions: Activities and Views
• Avoid, at all costs, making a Static reference to a View or Activity.
• All references to Activity Contexts should be short lived (the duration of the function)
• If you need a long-lived Context, use the Application Context (getBaseContext() or getApplicationContext()). These do not keep references implicitly.
• Alternatively, you may limit the destruction of an Activity by overriding Configuration Changes. However, this does not stop other potential events from destroying the Activity. While you can do this, you may still want to refer to the above practices.
Runnables: Introduction
Runnables are actually not that bad. I mean, they could be, but really we've already hit most of the danger zones. A Runnable is an asynchronous operation that performs a task independant from the thread it was created on. Most runnables are instantiated from the UI thread. In essence, using a Runnable is creating another thread, just slightly more managed. If you class a Runnable like a standard class and follow the guidelines above, you should run into few problem. The reality is that many developers do not do this.
Out of ease, readability and logical program flow, many developers utilize Anonymous Inner Classes to define their Runnables, such as the example you create above. This results in an example like the one you typed above. An Anonymous Inner Class is basically a discrete Inner Class. You just don't have to create a whole new definition and simply override the appropriate methods. In all other respects it is a Inner Class, which means that it keeps an implicit reference to its container.
Runnables and Activities/Views
Yay! This section can be short! Due to the fact that Runnables run outside of the current thread, the danger with these comes to long running asynchronous operations. If the runnable is defined in an Activity or View as an Anonymous Inner Class OR nested Inner Class, there are some very serious dangers. This is because, as previously stated, it has to know who its container is. Enter the orientation change (or system kill). Now just refer back to the previous sections to understand what just happened. Yes, your example is quite dangerous.
Solutions: Runnables
• Try and extend Runnable, if it doesn't break the logic of your code.
• Do your best to make extended Runnables static, if they must be nested classes.
• If you must use Anonymous Runnables, avoid creating them in any object that has a long-lived reference to an Activity or View that is in use.
• Many Runnables could just as easily have been AsyncTasks. Consider using AsyncTask as those are VM Managed by default.
Answering the Final Question Now to answer the questions that were not directly addressed by the other sections of this post. You asked "When can an object of an inner class survive longer than its outer class?" Before we get to this, let me reemphasize: though you are right to worry about this in Activities, it can cause a leak anywhere. I shall provide a simple example (without using an Activity) just to demonstrate.
Below is a common example of a basic factory (missing the code).
public class LeakFactory
{//Just so that we have some data to leak
int myID = 0;
// Necessary because our Leak class is an Inner class
public Leak createLeak()
{
return new Leak();
}
// Mass Manufactured Leak class
public class Leak
{//Again for a little data.
int size = 1;
}
}
This is a not as common example, but simple enough to demonstrate. The key here is the constructor...
public class SwissCheese
{//Can't have swiss cheese without some holes
public Leak[] myHoles;
public SwissCheese()
{//Gotta have a Factory to make my holes
LeakFactory _holeDriller = new LeakFactory()
// Now, let's get the holes and store them.
myHoles = new Leak[1000];
for (int i = 0; i++; i<1000)
{//Store them in the class member
myHoles[i] = _holeDriller.createLeak();
}
// Yay! We're done!
// Buh-bye LeakFactory. I don't need you anymore...
}
}
Now, we have Leaks, but no Factory. Even though we released the Factory, it will remain in memory because every single Leak has a reference to it. It doesn't even matter that the outer class has no data. This happens far more often than one might think. We don't need the creator, just its creations. So we create one temporarily, but use the creations indefinitely.
Imagine what happens when we change the constructor just slightly.
public class SwissCheese
{//Can't have swiss cheese without some holes
public Leak[] myHoles;
public SwissCheese()
{//Now, let's get the holes and store them.
myHoles = new Leak[1000];
for (int i = 0; i++; i<1000)
{//WOW! I don't even have to create a Factory...
// This is SOOOO much prettier....
myHoles[i] = new LeakFactory().createLeak();
}
}
}
Now, every single one of those new LeakFactories has just been leaked. What do you think of that? Those are two very common examples of how a inner class can outlive an outer class of any type. If that outer class had been an Activity, imagine how much worse it would have been.
Conclusion
These list the primarily known dangers of using these objects inappropriately. In general, this post should have covered most of your questions, but I understand it was a loooong post, so if you need clarification, just let me know. As long as you follow the above practices, you will have very little worry of leakage.
• 3
Thanks a lot for this clear and detailed answer. I just don't get what you mean by "many developers utilize closures to define their Runnables" – Sébastien Jun 10 '12 at 19:37
• 1
Closures in Java are Anonymous Inner Classes, like the Runnable you describe. Its a way to utilize a class (almost extend it) without writing a defined Class that extends Runnable. It's called a closure because it is "a closed class definition" in that it has its own closed memory space within the actual containing object. – Fuzzical Logic Jun 10 '12 at 20:00
• 22
Enlightening write-up! One remark regarding terminology: There is no such thing as a static inner class in Java. (Docs). A nested class is either static or inner, but cannot be both at the same time. – jenzz Jun 16 '13 at 19:53
• 2
While that is technically correct, Java allows you to define static classes inside static classes. The terminology is not for my benefit, but for the benefit of others who do not understand the technical semantics. This is why it is first mentioned that they are "top-level". The Android developer docs also use this terminology, and this is for people looking at Android development, so I thought it better to keep consistency. – Fuzzical Logic Jun 20 '13 at 7:39
• 12
Great post, one of the best at StackOverflow, esp for Android. – StackOverflowed Jul 21 '13 at 23:49
Your Answer
By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy
Not the answer you're looking for? Browse other questions tagged or ask your own question.
|
__label__pos
| 0.928506 |
Common Pipistrelle
Common PipistrelleCommon Pipistrelle
Latin name: Pipistrellus pipistrellus
The Common Pipistrelle is the most commonly encountered bat in Aldernery and is recognisable from it’s broad wings and jerky flight pattern. Often hunts in fixed paths over grasslands, woodland and urban areas. Most active for two hours before and after dawn and dusk respectively. During this period a single individual is capable of consuming over 3000 insects which they eat on the wing.
Echolocation Frequency: Strongest at 45 kHz.
|
__label__pos
| 0.798387 |
Excitability of Dopamine Neurons: Modulation and Physiological Consequences | BenthamScience
Excitability of Dopamine Neurons: Modulation and Physiological Consequences
Author(s): F. J. White, X- T. Hu, M. Marinelli, C. N. Rudick.
Journal Name: CNS & Neurological Disorders - Drug Targets
Volume 5 , Issue 1 , 2006
Abstract:
This aim of this chapter is to review literature on the excitability and function of dopamine neurons that originate in the midbrain and project to cortico-limbic and motor structures (A9 and A10 dopamine pathways). Electrophysiological studies on rodent or non-human primates have shown that these dopamine neurons are silent or spontaneously active. The spontaneously active neurons show slow regular firing, slow irregular firing or fast bursting activity. In the first section, we will review how neuronal firing is modulated by intrinsic factors, such as impulseregulating somatodendritic dopamine autoreceptors, a balance between inward voltage-gated sodium and calcium currents and outward potassium currents. We will then review the major excitatory and inhibitory pathways that play important roles in modulating dopamine cell excitability. In the second section, we will discuss how, in addition to being modulated by intrinsic and synaptic factors, excitability of dopamine neurons can also be modulated by life experiences. Dopamine neurons change their firing rate throughout the developmental period, their activity can be modified by stressful life events, and the firing mode can change as a consequence of acute or repeated exposure to psychoactive drugs. Finally, these cells change their firing pattern in response to behaviorally relevant stimuli and learning experiences. We will conclude by discussing how changes in the physiology of the dopamine neurons could participate in the development or exacerbation of psychiatric conditions such as drug addiction.
Keywords: stress, addiction, electrophysiology, Dopamine, ventral tegmental area, synaptic
Rights & PermissionsPrintExport
Article Details
VOLUME: 5
ISSUE: 1
Year: 2006
Page: [79 - 97]
Pages: 19
DOI: 10.2174/187152706784111542
Article Metrics
PDF: 40
HTML: 0
EPUB: 0
PRC: 0
|
__label__pos
| 0.671323 |
Archive for December, 2011
Windows Domain Controller and their Roles
December 10, 2011
I really favour Linux/Unix working environmental but sadly commercialism has engulfed our societies as the likes of Windows platforms while the former one doesn’t matter how much is rated high still lives in the shadows. And now I have to grasp the Windows lingo all along to fit in an organization. So lets learn something about Windows Domain Controller and their roles.
Before going into any details first its important to understand the differences between the following terms.
• Active Directory: is a directory service that serves as a central location for network administration and security which is responsible for authenticating and authorizing all users and computers within a network of windows domain.
• Forest: is the top-level container of Active Directory (AD) infrastructure. Can contain one or more domains. These domains are interconnected trough a transitive trust. A forest shares a single schema database.
• Domain: is one level below AD forest. Can consist of one or more Organizational Units (OU). A domain shares a single administrator group and same set of objects.
• Domain Controller: A domain can consists one or more domain controllers (DC). A DC holds a directory DB of its perspective domain. The directory DB consists of user, objects, computer objects or more.
• Organizational Unit: is a container within a domain and is used to organize set of users and computers. It is helpful in implementing set of policies to a group, user or computer within a domain.
• Windows DC: A server running the version of Windows Server OS and has AD installed on it and is responsible for allowing host access to Windows Domain resources.
Now coming to the roles; there are specialized DC roles that perform specific roles in Active Directory Domain Services (AD DS) environment. The specialized roles are:
• Global Catalog Servers: A DC designated as a global catalog server stores the objects from all domains in a forest. This is usually the first DC in a forest. Later on other DC can be specified as global catalog servers.
• Operations Master: This is a DC that is designated to perform specific tasks to ensure consistency and to eliminate the potential for conflicting entries in the AD DB.
AD DS defines five operation master roles called:
1. Schema Master: Responsible for propagating changes to all DCs within a forest. Changes regarding schemas required throughout forest should be made on DC serving as schema master. There can be only one schema master in a forest at any time.
2. Domain Naming Master: It is required to keep track of all the domains within an AD forest. The DC with domain naming master is accessed whenever domains are address/removed from a tree or forest. There can be only one domain naming master per forest. It ensures that no two domains have the same name existing in the same tree.
3. Relative Identifier (RID): Allocates blocks of RIDs to each DC in a domain. When a DC creates a new security principal (user, group etc.) it assigns the object a unique security identifier SID. The SID contains a domain SID which us same for all the security principals created in the domain and a RID which uniquely identifies each security principal created in the domain.
4. Primary Domain Controller (PDC) Emulator: PDC receives prefential replication of password changes that are performed by other DCs in the domain and is the source for latest password information. It’s also the default time source.
5. Infrastructure Master: is responsible for updating object references in the domain that point to object in another domain. It updates object references locally and uses replication to being all other replicas of domain up to date. Object reference contains GUID global unique identifier, distinguished name and possible a SID. The distinguished name and SID on object reference are periodically updated to reflect changes made to actual object.
– Schema Master and Domain Naming Master performs operations that must occur on only one DC in the forest.
– PDC, RID, Infrastructure Master perform operations that must occur on only one DC in a domain.
Advertisements
%d bloggers like this:
|
__label__pos
| 0.827333 |
Anthropocene Epoch, unofficial interval of geologic time, making up the third worldwide division of the Quaternary Period (2.6 million years ago to the present), spanning the period from the second half of the 18th century to the present. It is characterized as the time in which the collective activities of human beings (Homo sapiens) began to substantially alter Earth’s surface, atmosphere, oceans, and systems of nutrient cycling. A growing group of scientists argue that the Anthropocene Epoch should follow the Holocene Epoch (a formal interval of geologic time that spans the most recent 11,700 years). The name Anthropocene is derived from Greek and means the “recent age of man.”
Although American biologist Eugene Stoermer coined the term in the late 1980s, Dutch chemist and Nobelist Paul Crutzen is largely credited with bringing public attention to it at a conference in 2000, as well as in a newsletter printed the same year. In 2008 British geologist Jan Zalasiewicz and his colleagues put forth the first proposal to adopt the Anthropocene Epoch as a formal geological interval.
The scale of human activity
Changes in rock strata and the makeup of the fossils they contain are used to mark the boundaries between formal intervals of geologic time. Throughout Earth’s history, periods of upheaval characterized by mass extinctions, changes in sea level and ocean chemistry, and relatively rapid changes in prevailing climate patterns are captured in the layers of rock. Often these periods mark the end of one interval and the beginning of another. The formalization of the Anthropocene hinges on whether the effects of humans on Earth are substantial enough to eventually appear in rock strata. Most scientists agree that the collective influence of humans was small before the dawn of the Industrial Revolution during the middle of the 18th century; however, advancements in technology occurring since then have made it possible for humans to undertake widespread, systematic changes that affect several facets of the Earth system.
At present, human beings have a profound influence over Earth’s surface, atmosphere, oceans, and biogeochemical nutrient cycling. By 2005, humans had converted nearly two-fifths of Earth’s land area for agriculture. (Cultivated land accounted for one-tenth of the land surface, whereas roughly three-tenths were used for pasture.) An additional one-tenth of Earth’s land area was given over to urban areas by this time. According to some estimates, humans have harvested or controlled roughly one-quarter to one-third of the biomass produced by the world’s terrestrial plants (net primary production) on a yearly basis since the 1990s. Such sweeping control over Earth’s plant production has been attributed in large part to the development of a method of industrial nitrogen fixation called the Haber-Bosch process, which was created in the early 1900s by German chemist Fritz Haber and later refined by German chemist Carl Bosch. The Haber-Bosch process synthesizes ammonia from atmospheric nitrogen and hydrogen under high temperatures and pressures for use in artificial fertilizers and munitions. The industrialization of this process increased the amount of usable nitrogen in the world by 150 percent, which has greatly enhanced crop yields and, along with other technological developments, facilitated the exponential rise in the world’s human population from about 1.6–1.7 billion in 1900 to 6.9 billion by 2010.
As the human population grew, energy use increased, and energy derivation from wood and easily obtained fossil fuels (i.e. petroleum, natural gas, and coal) expanded. Carbon dioxide (CO2) released by cooking fires and other sources during preindustrial times was dwarfed by the amount released by industrial furnaces, boilers, coal-fired power plants, gasoline-powered vehicles, and concrete production during the 20th and early 21st centuries. In the 1950s climate scientists began to track the annual increase in average global carbon dioxide concentrations in the atmosphere, which rose from approximately 316 parts per million by volume (ppmv) in 1959 to 390 ppmv a half century later. Many climatologists contend that the buildup of CO2 in the atmosphere has contributed to a global rise in average surface temperatures of 0.74 °C (1.3 °F) between 1906 and 2005, loss of sea ice in the Arctic Ocean and the breakup of ice shelves along the Antarctic Peninsula, reduction in the size of mountain glaciers, changes in prevailing weather patterns, and more-frequent occurrence of extreme weather events in different parts of the world.
Furthermore, the oceans absorb much of the CO2 released into the atmosphere by human activities, and this absorption has driven the process of ocean acidification. Seawater pH has fallen by 0.1 between about 1750 and 2010, a 30 percent increase in acidity. Marine scientists fear that continued increases in ocean acidity will slow, and possibly cease, the construction of reefs by corals in many parts of the world, dissolve the shells and skeletons of mollusks and corals, and interfere with the metabolic processes of larger marine animals. Since coral reefs are hubs of biodiversity in the oceans, the loss of coral will likely contribute to the demise of multitudes of other marine species either directly, through habitat loss, or indirectly, through changes in marine food chains. Other human-induced changes to the hydrosphere include the damming and diversion of rivers and streams, the rapid extraction of groundwater from freshwater aquifers, and the creation of large oxygen-depleted areas near the mouths of rivers.
What made you want to look up Anthropocene Epoch?
(Please limit to 900 characters)
Please select the sections you want to print
Select All
MLA style:
"Anthropocene Epoch". Encyclopædia Britannica. Encyclopædia Britannica Online.
Encyclopædia Britannica Inc., 2015. Web. 26 Jan. 2015
<http://www.britannica.com/EBchecked/topic/1492578/Anthropocene-Epoch>.
APA style:
Anthropocene Epoch. (2015). In Encyclopædia Britannica. Retrieved from http://www.britannica.com/EBchecked/topic/1492578/Anthropocene-Epoch
Harvard style:
Anthropocene Epoch. 2015. Encyclopædia Britannica Online. Retrieved 26 January, 2015, from http://www.britannica.com/EBchecked/topic/1492578/Anthropocene-Epoch
Chicago Manual of Style:
Encyclopædia Britannica Online, s. v. "Anthropocene Epoch", accessed January 26, 2015, http://www.britannica.com/EBchecked/topic/1492578/Anthropocene-Epoch.
While every effort has been made to follow citation style rules, there may be some discrepancies.
Please refer to the appropriate style manual or other sources if you have any questions.
Click anywhere inside the article to add text or insert superscripts, subscripts, and special characters.
You can also highlight a section and use the tools in this bar to modify existing content:
We welcome suggested improvements to any of our articles.
You can make it easier for us to review and, hopefully, publish your contribution by keeping a few points in mind:
1. Encyclopaedia Britannica articles are written in a neutral, objective tone for a general audience.
2. You may find it helpful to search within the site to see how similar or related subjects are covered.
3. Any text you add should be original, not copied from other sources.
4. At the bottom of the article, feel free to list any sources that support your changes, so that we can fully understand their context. (Internet URLs are best.)
Your contribution may be further edited by our staff, and its publication is subject to our final approval. Unfortunately, our editorial approach may not be able to accommodate all contributions.
MEDIA FOR:
Anthropocene Epoch
Citation
• MLA
• APA
• Harvard
• Chicago
Email
You have successfully emailed this.
Error when sending the email. Try again later.
Or click Continue to submit anonymously:
Continue
|
__label__pos
| 0.882429 |
Category:
What is the UV Index?
Article Details
• Written By: Darlene Goodman
• Edited By: Michelle Arevalo
• Last Modified Date: 05 July 2017
• Copyright Protected:
2003-2017
Conjecture Corporation
• Print this Article
Free Widgets for your Site/Blog
Astronauts have captured images inside the International Space Station that can be seen on Google Street View. more...
July 26 , 2006 : Andrea Yates was found not guilty of killing her five children by reason of insanity. more...
Many scientists suggest that the sun’s ultraviolet (UV) light waves are harmful to human skin and eye tissue. As a result, the World Health Organization (WHO) created the UV index, a standard system for measuring the amount of UV light that penetrates Earth’s atmosphere. The linear scale is one way for governments and scientists to measure and track ultraviolet light intensity, as well as to warn the public about potential dangers associated with high UV levels.
UV radiation is a specific set of wavelengths on the light spectrum. The waves are shorter than visible light. Often classified as UVA and UVB, these light waves are typically considered more dangerous to the skin and eyes than visible light. The UV index measures the amount of these potentially harmful waves that reaches the lower atmosphere.
There are several factors affecting the ultraviolet light in a given area. First, the position of the sun in the sky is often important. Seasons can affect UV by changing the sun’s distance and angle of light in relation to Earth. Also, UV is often strongest at latitudes closer to the equator.
For the most part, the UV index measures the intensity of light waves at solar noon, or the time of day when the sun is highest in the sky. Sunlight is typically strongest at this time. Solar noon may not be the same as noon on a clock.
Second, atmospheric conditions may affect ultraviolet levels, as well. A thicker atmosphere results in lower radiation, so the UV index level is often different from mountain to valley. Cloud cover may also have an effect, but it does not make a large change, because UV radiation can typically penetrate clouds better than other light wavelengths. In addition, ozone in the high atmosphere may filter harmful UV rays.
Finally, ground reflection may also play a role in the UV index. Snow, water, and sand can reflect UV light. This reflection can intensify the level of ultraviolet rays striking an individual outdoors in these conditions because, not only do they receive UV directly from the sun, but it is reflected back up at them from the ground.
There are several ways to limit an individual’s exposure to UV light. Sunglasses with UVA and UVB filters can protect a person’s eyes from damaging rays. Sunscreens of at least Sun Protection Factor (SPF) 15 are often recommended to protect skin.
Individuals may also wish to seek shade, remain indoors, or at least avoid direct sunlight during peak sunlight hours. Depending on the time zone, this period usually falls between 10:00 a.m. and 4:00 p.m. People may also wish to cover their skin by wearing long sleeves, trousers, and a wide-brimmed hat.
Ad
You might also Like
Recommended
Discuss this Article
Princelety
Post 1
Besides providing a UV index forecast, a local weather service -- in conjunction with the EPA -- can also issue warnings and advisories if the atmospheric conditions make going outside for extended periods of time potentially harmful.
A UV Alert will be issued if the next day's UV forecast is unusually high for a given area in a given time of year. Essentially it's an opportunity to remind people about sun safety (using sunscreen, covering skin exposed to the sun's rays, wearing sunglasses, etc.) when the risk of sunburn and other damage is especially high.
Post your comments
Post Anonymously
Login
username
password
forgot password?
Register
username
password
confirm
email
|
__label__pos
| 0.636029 |
“Nine out of ten people with lupus are women.”
Lupus
Lupus, also known as systemic lupus erythematosus (SLE), is an autoimmune disease that causes various tissues in the body to become chronically inflamed. It can affect many parts of the body, typically the skin, joints, kidneys, various types of blood cells, the brain, and the lining of the heart and lungs. A butterfly-shaped rash across the face is a characteristic sign of the disease. Lupus can be mild or life-threatening, depending on which parts of the body are affected.
Lupus affects one in 700 Australians. Nine out of every ten people with lupus are women, with the onset of disease usually occurring between 20 and 50 years of age. People from all ethnic backgrounds can develop the disease although it tends to be more severe in African Americans and Asians than Caucasians.
The causes of lupus
The immune system normally protects the body against foreign invaders, like bacteria and viruses. However, in autoimmune diseases like lupus, for reasons which are not fully understood, immune cells are reprogrammed to attack the body’s own cells and tissues. In addition to lupus other examples of autoimmune diseases are rheumatoid arthritis , type 1 diabetes, Sogrens syndrome and multiple sclerosis. Together autoimmune diseases of various kinds affect approximately 5% of the population.
The exact cause of lupus is unknown, although it is likely that environmental factors trigger the autoimmune attack in genetically susceptible people. As a result, autoantibodies are made to DNA and various blood cells with which they combine to form ‘immune complexes’. These complexes are then deposited in the blood vessels supplying various organs in the body leading to tissue damage and the typical clinical features of the disease like skin rash.
The symptoms of lupus
Symptoms vary greatly between individuals and can fluctuate between active periods (flares) and times of minimal or no symptoms (remission). They include:
• Sunlight sensitive rashes on the face and body
• Painful inflammation of one or more joints, which may cause the disease to be mistaken for rheumatoid arthritis
• Impaired kidney function due to severe inflammation and immune cell blockage of the blood vessels
• Mouth ulcers
• Chest pain due to pleurisy (inflammation of the lining surrounding the lungs)
• Blood clotting problems
• Hair loss
• Unexplained headaches, fits or mood swings
• Extreme fatigue
• Recurrent miscarriages
Options for lupus treatment
In view of the great variation in clinical presentations, it is most important to confirm the diagnosis of lupus. This is done by performing a blood test for anti-DNA antibodies which are a hallmark of the diseases, taking biopsies of skin and other tissues to ascertain the extent of the disease and checking for abnormalities in blood cells.
In the absense of a definite cause, treatment is designed to minimise sun exposure when relevant, to suppress immune complex-induced inflammation and to restore organ function in the case of more severe disease. A range of drugs are available for this purpose including non Steroidal anti-inflammatory agents, antimalarials, and cortisone combined if necessary with cytotoxic drugs( eg cyclophosphamide) when organ function is severely impaired.
Garvan's research into lupus
The immunology division at the Garvan has a major interest in working out why a small proportion of people (<10%) make the autoantibodies that cause autoimmune diseases like lupus; and others do not. A range of experimental models is being used for this purpose with the current focus being on a particular structure in lymph glands and spleen called the ‘germinal centre’.
The white blood cells destined to make antibodies( B lymphocytes) collect there after stimulation and normally mature into cells which produce antibodies to foreign microorganisms. According to our recent work it is becoming apparent that the maturation process in germinal centres is defective in autoimmune diseases, resulting in escape of autoantibody producing B lymphocytes and a breakdown in immune tolerance.
Particularly exciting in the fact that we can now visualise the selective procedure in germinal centres directly under a special 2 photon microscope. Based on such information the next step will be to devise therapeutic strategies for reprogramming the germinal centre to shut down autoimmunity.
Help us continue our research into lupus and other autoimmune diseases
Donate Now
Further Information
Lupus Foundation of America
The Lupus Association of NSW
Quick Facts
• “Lupus affects one in 700 Australians.”
• “African Americans and Asians tend to get lupus far more frequently and more severely than Caucasians.”
Related News
© Garvan Institute 2017
|
__label__pos
| 0.531651 |
1 Replies - 1650 Views - Last Post: 13 September 2011 - 03:25 PM Rate Topic: -----
#1 h4nnib4l Icon User is offline
• The Noid
• member icon
Reputation: 1193
• View blog
• Posts: 1,710
• Joined: 24-August 11
Fluent NHibernate use object as attribute?
Posted 13 September 2011 - 01:53 PM
I'm new to Fluent NHibernate (or to ORMs in general for that matter), and I'm in a philosophical standstill (okay, maybe that's a BIT dramatic)...
I'm writing a module that will allow a manager to delegate reports to his or her direct reports. Managers and Delegates are both instances of Employee:
public class Employee : IPersistable
{
public virtual string EmployeeId { get; set; }
public virtual DateTime AsOfDate { get; set; }
public virtual string FirstName { get; set; }
public virtual string Middle { get; set; }
public virtual string LastName { get; set; }
public virtual string CompanyNumber { get; set; }
public virtual string JobNumber { get; set; }
public virtual string JobTitle { get; set; }
public virtual string Division { get; set; }
public virtual DateTime EmploymentDate { get; set; }
public virtual SupportingData Rate { get; set; }
public virtual SupportingData Status { get; set; }
public virtual int SalaryGrade { get; set; }
public virtual string Email { get; set; }
public virtual string SupervisorId { get; set; }
public virtual string UserName { get; set; }
public virtual IList<Employee> Employees { get; set; }
}
The ReportDelegation table has a ManagerId, DelegateId, ReportId, and DateCreated.
My conundrum is whether, in my fluent ReportDelegation class, to go with:
public class ReportDelegation : IPersistable
{
public virtual Employee Manager { get; set; }
public virtual Employee Recipient { get; set; }
public virtual ReportInfo ReportInfo { get; set; }
public virtual DateTime CreateDate { get; set; }
}
OR...
public class ReportDelegation : IPersistable
{
public virtual string ManagerId { get; set; }
public virtual string RecipientId { get; set; }
public virtual int ReportId { get; set; }
public virtual DateTime CreateDate { get; set; }
}
I would rather do it the first way, so that I can pass the entire object around and pull attributes as needed. However, I don't know how to set up the mapping between the defined attributes and the DB columns. The lure of the second method is that all I need is:
public class ReportDelegationMap : ClassMap<ReportDelegation>
{
public ReportDelegationMap()
{
CompositeId()
.KeyProperty(x => x.ManagerId, "Manager_EmpId")
.KeyProperty(x => x.RecipientId, "Delegate_EmpId")
.KeyProperty(x => x.ReportId, "ReportID");
Map(x => x.CreateDate)
.Column("DateCreated");
}
}
Again, I feel like the first way, using object instances, is the better way to do it. If so, how do I map to my DB table?
Is This A Good Question/Topic? 0
• +
Replies To: Fluent NHibernate use object as attribute?
#2 h4nnib4l Icon User is offline
• The Noid
• member icon
Reputation: 1193
• View blog
• Posts: 1,710
• Joined: 24-August 11
Re: Fluent NHibernate use object as attribute?
Posted 13 September 2011 - 03:25 PM
Well, I'm an idiot.
public ReportDelegationMap()
{
CompositeId()
.KeyProperty(x => x.Manager.EmployeeId, "Manager_EmpId")
.KeyProperty(x => x.Recipient.EmployeeId, "Delegate_EmpId")
.KeyProperty(x => x.ReportInfo.Id, "ReportID");
Map(x => x.CreateDate)
.Column("DateCreated");
}
It helps if you use the object's attribute name, in case any of you were wondering... If intellisense likes it, then so do I!
Now I just have to teach the web service what an Employee is... :/
Was This Post Helpful? 0
• +
• -
Page 1 of 1
|
__label__pos
| 0.992942 |
Dashboard > OverDrive > Home > Gist
Gist
Added by Ted Husted, last edited by Ted Husted on Nov 04, 2005 (view change)
Labels:
(None)
The OverDrive project is constructing a set of realistic "best practice" applications for the Nexus framework.
Nexus Framework
At a Glance
Presentation Layer ASP.Net Spring.Web Nexus ViewControl Nexus ViewHelper (View)
Application Layer Spring.Net Nexus Catalog Nexus Commands Nexus Contexts (Controller)
Persistence Layer iBATIS.Net DataMaps Database Web Services (Model)
The Nexus framework exposes the application layer to the presentation layer through one or more Helper objects. The Helpers are a facade. A ViewControl base class works with the Helpers to read values from the controls, invoke the application logic, and determine the result. The result may include error messages, a set of values, or a list of values – all ready to display.
By "ready to display", we mean that all the type conversions, text formatting, and localizations have already been done. The UI controls can wrap the text in markup without additional post-processing. Providing ready-to-display text is an essential feature, since Nexus is designed to be used with multiple presentation layers. And, yes, we do consider unit tests to be a presentation layer!
Nexus does not replace presentation frameworks like ASP.NET or Struts. Nexus provides the missing link between presentation frameworks and the business logic that drives your application.
The Nexus back-end is an extended version of the Commons Chain of Responsibility (CoRe). Our Agility product is a port of the original Jakarta Commons CoRe codebase. The Nexus product is our extension to Agility. Nexus adds the features we need to use a Chain of Responsiblity as a business facade.
"Chain of Responsibility pattern"
"Avoid coupling the sender of a request to its receivere by giving more than one object a chance to handle the request. Chain the receiving objects and pass the request along the chain until an object handles it."
Design Patterns by Gamma, Helm, Johnson, and Vlissides (ISBN 0201633612).
The Nexus extensions to Agility feature an advanced Context with attributes common to most applications. There are attributes for storing an Exception, lists of Errors, and lists of generic Messages (Fault, Alerts, and Hints). A convenient "IsNominal" property tells us if there are Alerts or a Fault to display.
Nexus Catalog
The Nexus Catalog makes it easy to retrieve a Context and Command in one call. The caller can pass a Command ID and get back a Context with the Command embedded as an attribute. After filling the Context with values, we can "execute" the Context. The Catalog retrieves the Command, and then passes the Context to its Command. For populating a page, we can also ask for a Command ID, and get back the Context after the Command has executed, in a single call.
Nexus Context
The Context provides a "Criteria" attribute, which is used like a sandbox to store input and output values. The Helpers utilize the Criteria rather than the Context. Other framework Commands automatically convert or format the values between the Criteria and Context.
Request Processing
The Nexus Catalog is extended so that we can execute any given Command as part of a larger Chain of Commands. At runtime, the Catalog creates a Chain and wraps "pre-opt" and "post-op" chains around the instant Command (which could also be a Chain). The pre-op and post-opt chains are configured along with other Commands in the Catalog. In effect, the Catalog creates a "Back Controller" to ensure certain things always happen on each request (Command invocation). The pre-opt Chain, instant Command (or Chain), and post-op Chain work as a request processor.
The standard pre-op Chain converts input, and the standard post-op Chain formats output. But we can also do things like link a logger into the post-op Chain. It's very much like the way Subversion uses pre-commit and post-commit triggers, except that the "commit" is a Command.
Nexus Processors
Pluggable Processors handle the conversion and/or formatting for a kind of field. The "kind" might be a data type, like "integer", or a formatting type, like "telephone number", a combination of both, or even a calculated attribute.
The Processors are linked to a Field Table. Each field that needs special handling can be listed in the Field Table and associated with a Processor. The Field Table and Processors also contain the message templates that are used to create validation errors. For lists returned from a database, a special Processor can iterate over each row of the list, and call the Processor for each column, to create a formatted version in the Critiera.
Input and Output
When listing a Command in the Catalog, we can also list the input and output values the command expects. Input can be specified as "required" or as "related". A Chain automatically aggregates the input field list from its Commands, to insure that all required input is provided. We can also specify a command's output values, and the Chain will consider the output from one command valid input to a subsequent command.
The Helpers use the Command's list of input fields to to automatically read or bind values to the controls. The standard pre-op Chain also uses the field list and Field Table to generate validation errors.
Form Binding and Reading
Most often, you can read or bind an entire form with a single line of code. A complete block, including error checking, may take four or five lines.
Binding
Here is a typical idiom for populating a form:
IViewHelper helper = ExecuteBind(FIND_COMMAND);
bool okay = helper.IsNominal;
if (!okay) Page_Alert = helper;
Reading
Here is a typical idiom for reading input from a form:
IViewHelper helper = ReadExecute(SAVE_COMMAND);
bool okay = helper.IsNominal;
if (!okay) Page_Alert = helper;
For more about Nexus, see the WhitePaper page and PhoneBook application.
OVR-2@OVR-JIRA
Site running on a free Atlassian Confluence Open Source Project License granted to OSS. Evaluate Confluence today.
Powered by Atlassian Confluence, the Enterprise Wiki. (Version: 2.5.5 Build:#811 Jul 25, 2007) - Bug/feature request - Contact Administrators
|
__label__pos
| 0.569345 |
Cython: Speed up your Python Code
Introduction:
Cython, is a variation of Python which actually was made to act like a superset of Python. Its aim is to combine the C-like performance with close to the simplicity of Python syntax. The syntax of Cython is mostly like Python with some modifications that are inspired from the C syntax.
Cython is a compiled language, unlike Python. It is compiled to generate CPython Extension Modules. Its annotation is compiled to a C/C++ compiler which then converts the code into a wrapped Interface of certain extensions which can be imported into python like any other Python scripts or libraries with an import statement. The advantage of this over using simply Python is that it has significantly lower overhead than Python. Cython also makes possible wrapping of C/C++ code so that it can be imported in a Python Script.
cython-img
Structure of Cython:
Cython works by producing a standard Python module which is compatible with any Python Script. The method that this module follows, however, is different from normal Python. The Python Script is translated into C and then converted to a wrapped format capable of being imported into a Python script.
The Cython code imported into Python is definitely faster than Python. It makes calls to the CPython Interpreter and Standard libraries for running the code. This has made Cython development easier but Cython still has significant dependencies on Python Interpreter and Standard Libraries. The Cython, in short, uses the Interpreters of both Python and C together.
Cython uses CPython Virtual Machine for interpreting the code. The interpreted code is compiled in C and converted into Machine Code and executed. Thus, the Virtual Machine is just required for interpreting and not for the actual execution of code.
Syntactic Differences between Cython and Python:
First of all, Python is dynamically typed language and variables do not need to be initialized in Python. Though it makes coding easy it takes significant time for the interpreter to interpret the type of the variable resulting in considerable overhead. Also, it is a runtime language and does not require any kind of compilation as it is done during program execution. This results in latency during execution.
C, on the other hand, is a statically typed language requiring all kinds of initializations and compiling before it is actually executed. Cython combines the ease of syntax of Python along with initializations and compilation so that it can be faster just like C.
Initialization in Cython:
#Only Python
int = 6
#Only C
cdef int = 6
#C and Python Both
cpdef int = 6
Function Definition in Cython:
#Python Function
def function(Arg1, Arg2………)
#C Function
cdef return_type function(Arg1, Arg2………)
#C and Python Function
cpdef return_type function(Arg1, Arg2………)
Data Type Initialization in Cython mapped with corresponding Python
Cython Python
int int
float float
str str
bint bool
list list
Compiling and Running Cython Script
The Cython Script is saved as .pyx. The sample script may look like below:
Name of file: Cython_Test.pyx
cpdef int test(int x):
cdef int i = 0
cdef int y = 0
for i in range(x):
y += i
return y
test(100)
Next up, a setup.py script is created in the same directory as the Cython Script.
Name of file: setup.py
from setuptools import setup
from Cython.Build import cythonize
setup(
ext_modules = cythonize(“Cython_Test.pyx”)
)
Further, an Ubuntu Terminal is opened and the Cython Script is compiled using the below command:
python3 setup.py build_ext –inplace
After this command is executed, a build folder, a .so file and a C file are generated.The command below also generates a similar output. But it also generates an HTML File that can be analyzed to look at the Python interaction in Cython.
cython -a Cython_Test.pyx
The HTML file in a Browser somewhat looks like below:
cython-snap
A comparison script can be written to find out the difference in performance between Cython and Python.
import python_test
import cython_test
import time
import argparse
import matplotlib.pyplot as plt
parser = argparse.ArgumentParser()
parser.add_argument(“-n”,”–number”, type=int, help=”maximum iterations”,default=100)
args = parser.parse_args()
n = args.number
py = [ ]
cy = [ ]
for i in range(n):
a=time.time()
python_test.test(i)
b=time.time()
c=time.time()
cython_test.test(i)
d=time.time()
py.append(b-a)
cy.append(d-c)
try:
print(“Cython is {} times faster than Python”.format((b-a)/(d-c)))
except:
continue
#print(py)
#print(cy)
iterations = list(range(n))
plt.plot(iterations, py)
plt.plot(iterations, cy)
plt.title(‘Python vs Cython Performance Comparison’)
plt.ylabel(‘execution time’)
plt.xlabel(‘iterations’)
plt.legend([‘python’, ‘cython’], loc=’upper left’)
plt.show()
plt.savefig(‘comparison.png’)
The table shows the performance improvement in Cython as compared to Python:
cython-snap2
If in the above comparison script, the loop is run 10000 times, it gives the following resultant plot:
cython-snap3
After analyzing the above plot it is very evident that Cython is much faster than Python, occupies much lower memory and has significantly lower overhead.
Thank you for reaching out to Wobot.ai. Someone from our team will contact you soon.
|
__label__pos
| 0.954696 |
questions narrowly about terminal.app alone should use this tag. Please consider using **command-line** for any question not specifically about the native terminal app
learn more… | top users | synonyms
5
votes
1answer
1k views
How to have terminal close tab when shell exits?
I just recently upgraded from 10.6 to 10.8. On 10.6 I could set the terminal to close the tab/window when the shell exits. Mountain Lion's terminal just says the process is completed and the tab/...
38
votes
5answers
8k views
Is there a way to access a Mac's geolocation from terminal?
Some GUI apps use OS X location services, but I want to retrieve a Mac's physical location from the command line. This could be useful for running scripts, switching settings etc. The mechanism should ...
2
votes
1answer
9k views
For a startup volume encrypted with Core Storage, System Preferences show that FileVault is disabled
My iMac has a SSD and a HDD. The OS is installed on the SSD. I performed a clean installation of Mountain Lion to the SSD, and cloned my SSD using a backup from my Time Capsule in OS X Recovery. ...
0
votes
3answers
564 views
Producing/archiving an overview of a directory structure
I try to find a way to make an archive of my ~/ directory so that I can go back in case I've lost something. I've found several recommendations for this. The first being OS X Hints saying a simple ls -...
0
votes
2answers
932 views
How can I connect Linux server with Applescript using iTerm or Terminal?
I want to connect and run bash script on Linux server automatically by using Applescript and iTerm or Terminal on OS X. How can I connect Linux server with Applescript use iTerm or Terminal?
4
votes
4answers
11k views
Get disk temperature in terminal
Is there a command I can use just to get the hard disk temperature in the terminal? Is this possible without a third party app?
2
votes
1answer
678 views
Set terminal window title in a script
I would like to change the entire title of the terminal window for a particular bash script. I googled out but I couldn't find much more than this suggestion: printf "\e]0;My Custom Title\a" After ...
0
votes
2answers
730 views
How to change the color and format of the static host/path/user string in the Terminal or iTerm?
Example: cookie:~ j$ date Sun Aug 5 02:14:29 CEST 2012 cookie:~ j$ Just as it's pasted here, all three lines are of the same color. I would like to have "cookie:~ j$" or at least part of the ...
0
votes
0answers
2k views
Installation of Wine via MacPorts not working with 10.8 and XCode 4.4
I had installed wine on my computer with then 10.7.4. It worked perfectly. Then I updated to 10.8 and wine did not work, so I uninstalled wine and macports. It gave me an error that winetricks (I ...
1
vote
2answers
567 views
What is the format I should write the command to SSH into Linux VPS?
I am trying to use SSH and log in from the terminal into a Linux VPS. I have tried a few variations around the following: ssh [user]@[hostname].[my.ip.address.xx]:22 and keep getting: ssh: Could ...
11
votes
5answers
13k views
Open an app in fullscreen via Terminal
I wonder if it's possible to open a program in Lion fullscreen mode via the Terminal. I want to write a short script which starts a bunch of programs in fullscreen mode, so that I only have to click ...
0
votes
0answers
534 views
How can I play a sound from the command line running as sudo?
While typing afplay danger.mp3 in the Terminal will play the .mp3, doing sudo afplay danger.mp3 or sudo su and then afplay danger.mp3 does not. Any idea why is this? How can I use the afplay command ...
3
votes
3answers
6k views
PHP 5.4 Installation on Mountain Lion
I just installed Mountain Lion, and of course I've had to set up Xcode Command Line Tools, reinstall Git, and do other things to get up and running again for programming. Naturally, PHP was pushed ...
9
votes
3answers
13k views
How to fix Terminal error DYLD_ environment variables being ignored because main executable (/usr/bin/login) is setuid or setgid?
Any time I open a new terminal window (independent of terminal app), the console stderr displays dyld: DYLD_ environment variables being ignored because main executable (/usr/bin/login) is setuid or ...
1
vote
1answer
1k views
Is it possible to first enter a command and then choose “run in Terminal” in Quicksilver?
Is it possible to first enter a command and then choose "run in Terminal" in Quicksilver? Is there another way of doing it other than Quicksilver (though I would prefer Quicksilver)?
9
votes
2answers
2k views
What has changed in Terminal.app in OS X 10.8?
Just upgraded OS X to Mountain Lion and noticed that Terminal.app version has changed from 2.2.3 to 2.3. Unfortunately, can`t find any information about what has changed. Do you know if there is any ...
0
votes
1answer
2k views
$PATH error on a terminal
Before you raise your pitchforks, this is NOT another "How do I change my $PATH variable value?" question. I had installed Oh my zsh on my machine(Macbook Pro), and didn't like it. So I uninstalled it....
9
votes
3answers
5k views
error: There was a problem with the editor 'vi' when using it with git
I have this strange problem with using vi as the editor for git commit -a. Normal flow is: I type git commit -a, vi appears, I enter my commit message, and then :wq to save & exit from vi. This ...
2
votes
2answers
35k views
How can I re-run the initial Setup Assistant on Mountain Lion?
As described in my write-up on custom keyboard layouts, in some situations it can be useful to re-run the Setup Assistant (the app that you get when you start a new Mac for the first time, or do a ...
10
votes
1answer
2k views
How to share history between terminal tabs?
I generally find myself using two or three tabs in my Terminal on OS X. A minor inconvenience is often that the tabs don't share a command history. So things like history | grep thingIamlooking for ...
0
votes
1answer
1k views
How can I access a remote machine via SSH from behind a proxy?
I’m trying to connect to a Linux machine via SSH. The problem is that my Mac is in a different network, behind a proxy that routes HTTP and HTTPS through port 80. How can I access the Linux machine ...
172
votes
8answers
90k views
How can I trigger a Notification Center notification from an AppleScript or shell script?
I'd love to be able to take advantage of 10.8's Notification Center features in AppleScripts and shell scripts I write. Is there a built-in command or a third-party library I can use from either an ...
0
votes
0answers
1k views
ifconfig - get IPs of connected USB devices
In Ubuntu, ifconfig lists all the USB devices with the header "usb0, usb1, ..etc" I need to know the IP addresses of all the connected USB devices. It would be really helpful if on Mac it displayed ...
9
votes
3answers
16k views
How do I check the download progress of Mountain Lion through the terminal?
I am downloading Mountain Lion, I know I can monitor download progress through the Mac App Store purchases screen but I want to know if I can monitor progress through Terminal.app using a shell ...
1
vote
1answer
145 views
difference between disk size in console vs disk utility
Console results df -h disk utility results What explains the large difference here in capacity as well as used memory? And which is more reliable.
0
votes
1answer
481 views
Can't create alias for 'nano ~/.bash_profile'
I tried to make an alias to edit my bash profile, but when I save and relaunch a new window, I get the following: Last login: Sun Jul 22 12:00:25 on ttys001 -bash: alias: nano ~/.bash_profile: not ...
2
votes
2answers
2k views
Mac: how to securely delete an SD card?
Nothing I have tried gives me read/WRITE access to my SD card from my Canon camera. How can I secure-delete before selling the card on eBay? (the lock switch is on: unlocked - tried the other position ...
0
votes
1answer
197 views
Applescript to monitor terminal changes
I want to be able to check if a word appears in a terminal window running a java application and then display a notification. Any ideas?
2
votes
2answers
218 views
How to get + metacharacter for sed in Terminal?
It looks like sed that comes with Mac OS 1.7.4 is the original one, without the + metacharacter. Can I get the + metacharacter functionality?
4
votes
2answers
2k views
How to get a “modern” emacs that runs in a terminal on os x lion?
I just installed Prompt on my iPad so I could possiby do some real work on my iMac via ssh. so far Mutt and Vim and emacs seemto work responsively enough for me. I've made a few tries at emacs ...
5
votes
4answers
1k views
pbpaste, pbcopy using wrong pasteboard?
I'm converting a shell script which xclip and similar tools on Linux, to use pbpaste and pbcopy on Mac. The problem is the default pasteboard ('general' according to the man-page) for these tools is ...
3
votes
2answers
2k views
Unable to save hosts file after adding websites to block.
I'm unable to save hosts file after adding websites to block,as well as unable to flush cache. I am not a techie, just researching on the web, and trying to follow directions for terminal and Text ...
3
votes
3answers
520 views
Any way to force command line terminal to control a Mac?
I'm experimenting a little with Automator at the moment and often get stuck with some pre-recorded automation running very slowly while the whole Mac (an 2010 iMac in my case) doesn't respond to any ...
17
votes
3answers
5k views
How do I find the windowid to pass to screencapture -l?
The command line utility screencapture claims to be able to capture a single window without requiring interaction, but I can't figure out what to pass it. -l<windowid> capture this windowsid ...
3
votes
4answers
7k views
How to list all files in directory excluding any that start with a dot?
I'm currently using the command find /Volumes/DriveName > driveName.txt to create a file listing of all files that are on the drive. How could I modify my command (or what would be a better ...
2
votes
3answers
8k views
Change label on USB drive in OSX Terminal
I am trying to write a program in Python that will rename a USB drive (from the standard "USB DISK" to my custom "MYDISK"). However, I can't find any way to do this neither in Python nor in OSX ...
4
votes
1answer
7k views
How can I move Dashboard widgets to the desktop in Lion?
In the OS X Terminal, there is a command that allows me to drag Dashboard widgets onto my desktop. In OS X Lion, the Dashboard became a Space. I am no longer able to use this command. What is a ...
2
votes
1answer
232 views
Why does my terminal show a string like this?
When I open my terminal it shows this: wpa-2-602:~ david$ I just curious what the wpa-2-602 means? "david" is my user name, and sometimes it was something else. What makes it change?
10
votes
4answers
3k views
iTunes track notifications for Mountain Lion
In OS X Lion there was the preference (via a Terminal command) to enable iTunes track notifications that were displayed as a popup in the dock. So far it seems as though Mountain Lion does not allow ...
6
votes
2answers
2k views
Change my shell to a different bash version at /usr/local/bin/bash?
How can I set my /usr/local/bin/bash (which is the 4.2 version that allows auto-completion of 'cd to directory with directory name') to be my default bash for a new window instead of my regular (v3.2....
1
vote
3answers
3k views
Change owner for all files owned by x
I copyied files from my MacBook, mainly files from /usr. The one and only user on my computer is called 'Julian' (like on my MacBook). A lot of the copied files are now owned by '501' (id of "Julian" ...
1
vote
1answer
482 views
Search all hidden .htaccess files inside a folder and run a terminal command?
Searching for the issue, I found this Q&A: How can I show only an .htaccess file in the Finder? [...] you could create a symlink to the file in its directory, omitting the dot in the name: ...
138
votes
6answers
69k views
git auto-complete for *branches* at the command line?
On my linux machine I have autocomplete for branches with git. [Note we are talking about git branch completion, not bash completion (e.g. commands, files, etc). Thus NOT lane's answer at all] For ...
1
vote
2answers
734 views
How do I disable DVD player auto start when a DVD is inserted by using Terminal
If anyone can help me with this it would be the best! I have just installed 150 Mac minis in a hotel and I'm using remote desktop management to control them. Now I need to disable DVD player auto ...
0
votes
2answers
2k views
Executing program through Terminal
I have Sage (math program) and I want to execute it through terminal. I know I can go to the directory and execute it with - open Sage.app But would I really want to do is simply type sage in ...
2
votes
1answer
887 views
Why doesn't the screen command source my .profile?
When I start a new screen, the aliases that I have set in my ~/.profile do not seem to be sourced. Does anyone know where I can change this or which file is actually read when starting a new screen?
3
votes
1answer
3k views
Is there a way to get gnome-terminal on Lion?
Is there a port of gnome-terminal, or a way to compile it, or some other program that is typographically comparable, under Lion? There is a typographic difference, and I can't duplicate it in ...
6
votes
1answer
393 views
Is it possible that some hacker is logged in to my computer?
When I type w at the terminal I see myself logged in two times. What are console and s000? Is it possible that one of these neos is actually somebody else?
14
votes
2answers
3k views
cd to a directory by typing its name?
For example if a directory 'blob' exists and I just type 'blob[return]' then the system cds into the blob directory for me. In Linux (Ubuntu) I can add shopt -s autocd to my .bashrc file, but on OS X ...
1
vote
3answers
9k views
Where can I find gcc in Xcode 3.2.6?
I have a Mac with OS X 10.6.8 Snow Leopard. I'm trying very hard to learn the basics of programming in C, but I can't get my first simple program to run. I read online to go to Xcode Preferences -> ...
|
__label__pos
| 0.855954 |
@article{10272/8286, year = {2008}, url = {http://hdl.handle.net/10272/8286}, abstract = {Planktonic foraminifer assemblages from core PRGL1-4 have been studied to reconstruct sea surface temperatures (SST) in the Gulf of Lions during Marine Isotope Stages 6 and 7 based on the modern analog technique. This method consists of a comparison between core and modern sample assemblages assuming that similar planktonic foraminifer assemblages develop under the same ecological conditions and that foraminifer ecological preferences have not changed in time. During stage 6 (glacial) a strong millennial variability is observed in SST, whereas in stage 7 (interglacial) the astronomical forcing controls SST. These features have been already reported in temperature records from other areas out of the Mediterranean Sea, which means that SST in the Gulf of Lions during stages 6 and 7 was influenced by global climate changes. Moreover, some differences exist between paleotemperature records from different areas in the Mediterranean region. In the Gulf of Lions temperature records are more extreme since this area is directly influenced by Mistral and Tramontane winds, which cause important water cooling during cold periods. Furthermore, this study suggests that seasonality in the Gulf of Lions is not influenced by Northern Hemisphere summer insolation}, keywords = {Modern analog technique}, keywords = {Sea surface temperatures}, keywords = {Gulf of Lions}, keywords = {Marine Isotope Stages 6 and 7}, title = {Reconstrucción de paleotemperaturas en el golfo de León durante los estadios isotópicos 6 y 7 utilizando la técnica de los análogos modernos}, title = {Paleotemperature estimates in the Gulf of Lions during Marine Isotope Stages 6 and 7 based on the modern analog technique}, author = {González Mora, Beatriz and Sierro, Francisco Javier and Berné, S.}, }
|
__label__pos
| 0.999281 |
Invasive Species Compendium
Detailed coverage of invasive species threatening livelihoods and the environment worldwide
Abstract
Infection with a trematode parasite differentially alters competitive interactions and antipredator behaviour in native and invasive crayfish.
Abstract
Parasites can have profound effects on host behaviour and species interactions, but the consequences of these impacts are inadequately understood. Three common crayfish in northern Wisconsin and Michigan (native Orconectes virilis, non-native O. propinquus and non-native and invasive O. rusticus) are intermediate hosts for trematode parasites, Microphallus spp. Some species in the genus Microphallus alter host behaviour, increasing their predation risk, but the effects of microphallids on crayfish are unknown. Orconectes propinquus replaces O. virilis in most lakes where they are introduced, and O. rusticus replaces both. These species replacements have major effects on macrophytes, macroinvertebrates and fish. Therefore, differential parasite impacts on crayfish could have community-level effects if competitive outcomes are altered. We examined the shelter affinity of infected and uninfected individuals of all three species in laboratory experiments in the presence and absence of a conspecific. We also observed behaviour during agonistic interactions, and measured boldness by quantifying how quickly crayfish emerged from shelter with a predatory fish present. Infection with Microphallus substantially altered crayfish shelter affinity, shelter competition and boldness, though infection affected each species differently. Infection reduced shelter affinity in O. propinquus and the ability of O. virilis to compete for shelter against uninfected conspecifics. Infected crayfish were bolder in the presence of a predatory fish. Our results suggest that infection with Microphallus alters crayfish behaviour so that all three species are more vulnerable to predation. Orconectes propinquus is likely to suffer the greatest increase in predation when infected, due to a reduced affinity for shelter coupled with increased boldness. In lakes where crayfish species coexist, O. rusticus will probably be less affected by the parasite than either congener. Therefore, crayfish parasites could alter crayfish abundance and species composition in north temperate lakes via behavioural modifications.
|
__label__pos
| 0.964143 |
Skip to contentSkip to navigation
Philips Sleep Apnea Device Recall - Click for details
Your Questions — 4 minutes
What types of water should be used in your continuous positive airway pressure (CPAP) device?
Biron
Distilled, demineralized, bottled, ozonated, boiled or tap water? Which ones are recommended, and which ones should be avoided?
CPAP tanks are usually made of materials that tend to degrade when in contact with heated minerals. Therefore, using mineral-free water prevents premature wear and build-up of a whitish residue. That's why only two types of purified water are recommended for CPAP tanks: demineralized water and distilled water.
Distilled water
This water is free of minerals and microorganisms. It is the purest commercially sold water as it contains the fewest organic contaminants.
Demineralized (or deionized) water
This water has been stripped of all its salts and minerals using a process of demineralization (or deionization).
You can find both types of water in grocery stores, pharmacies, and supermarkets. To avoid potential contamination, keep the bottles in a cool, dark place.
Also, there are domestic water demineralization devices, such as reverse osmosis systems. When properly maintained, they make it possible to use tap water in CPAP equipment.
The following types of water are not recommended for everyday use but can be used occasionally for troubleshooting. As they contain minerals (calcium, magnesium, iron, etc.), it is necessary to thoroughly clean the tank after using the device (see the box for cleaning instructions).
Ozonated water
Ozonation is a water sterilization process designed to destroy pathogens. Indeed, ozone is an oxidizing agent and a powerful disinfectant capable of eliminating viruses and bacteria that may have survived the filtration stage.
Boiled water
Contrary to popular belief, using tap water is not harmful to you, as long as it is safe to drink. Still, it can affect the lifespan of your accessories, especially your reservoir.
Tap water
Contrary to popular belief, using tap water is not harmful to you, as long as it is safe to drink. Still, it can affect the lifespan of your accessories, especially your reservoir.
Bottled spring water shares the same properties as tap water.
Note that a water softener does not make tap water usable since it usually removes only calcium and magnesium. Purifiers equipped with a carbon filter (e.g., Brita) reduce the chlorine content without removing minerals and leave impurities that can damage your equipment.
Important reminders
• Never add essential or scented oils to the water as they can damage the device.
• Remember to empty and rinse the tank after each use.
• Every week, wash the tank with warm, soapy water and rinse with plenty of clean water. You can place certain models in the top rack of the dishwasher (check the manufacturer's instructions). Allow it to dry away from direct sunlight or any heat source before reassembling.
• In case of mineral deposits, soak the tank for 10 minutes in a solution of one part white vinegar (5% acetic acid) to two parts water. Empty the solution and rinse thoroughly before letting it dry.
Biron
|
__label__pos
| 0.814618 |
Skip to main content
Mitigative effect of caffeine against diclofenac-induced hepato-renal damage and chromosomal aberrations in male albino rats
Abstract
Background
Among the most commonly consumed non-steroidal anti-inflammatory drugs (NSAID) is Diclofenac (Dic), especially in low-income countries due to its high efficiency and affordable price. However, the continuous administration of Diclofenac may induce toxic effects on various body organs including the liver and kidney. Caffeine (Caf) (1,3,7-trimethylxanthine) is a pharmacologically active alkaloid type with antioxidant and anti-inflammatory actions.
Aim
The current study aims to evaluate the ameliorative effect of Caffeine against Dic-induced hepato-renal toxicity and damage.
Methods
Twenty-four male albino rats type were assigned randomly into four groups (n = 6): (Group 1): Control group, (Group 2): Six male rats were exposed to Dic 10 mg/kg intraperitoneally (I.P) for 28 days, (Group 3): Six male rats were exposed to Caf (15 mg/kg orally) for 28 days; (Groups 4): Six male rats were exposed to Dic (10 mg/kg, i.p) + Caf (15 mg/kg, orally) for 28 days. Histopathological study and various biological parameters were estimated among the four groups including hemoglobin (Hb%) red blood cells (RBCs), Hematocrit (HT%), total leucocyte count (WBCs), lipid peroxidation (LPO), glutathione peroxidase (GPx), alanine aminotransferase (ALT), aspartate aminotransferase (AST), urea, creatinine, tumor necrosis factor-α (TNF-α), and nitric oxide (NO).
Results
The administration of Diclofenac resulted in significant deteriorations in the histopathological findings and estimated biological parameters. Whereas, daily Caffeine administration ameliorated Diclofenac-induced toxicity in the kidney and liver by three mechanisms including antioxidant, anti-inflammatory, and DNA damage inhibition.
Conclusion
The current study demonstrated the promising ameliorative and protective effects of Caffeine against Diclofenac-induced hepatic and renal injury.
Peer Review reports
Introduction
NSAIDs are the type of the most commonly used drug as an analgesic, anti-inflammatory, and for the treatment of rheumatoid and osteoarthritis [1]. It was previously reported that NSAIDs directly inhibit cyclooxygenase-1 (COX-1) and cyclooxygenase-2 (COX-2) enzymes activity and thereby suppress the release of thromboxane and prostaglandin [2, 3]. Prolonged and misused chronic intake of NSAIDs may lead to undesirable drawbacks including neurotoxicity, nephrotoxicity, hepatotoxicity, cardiovascular diseases, and gastrointestinal injury [4,5,6]. Diclofenac (2-[(2,6-diclorophenyl)amino]phenyl acetate) is the most abundant and widely used NSAID phenylacetic acid derivative for its wide actions including antipyretic, anti-inflammatory, and pain relief [7]. The reason why Dic administration may results in renal damage is mainly due to reduced renal blood flow resulting in ischemia and necrosis along with elevated oxidative stress and inflammatory cytokines release [8]. Meanwhile, Dic-induced liver damage may also be related to inflammation, oxidative stress, and cytochrome P450 activation [9, 10].
Both the liver and kidney play vital roles in the elimination process of wastes produced in all living organisms. Thereby, any damage in both organs results in metabolic dysfunctions and the accumulation of toxins in the body leading to systematic toxicity, and atrophy [10, 11]. In addition to filtering unnecessary products from the blood, kidneys mainly maintain electrolytes/water balance, control the secretion of erythropoietin to regulate hematopoiesis, and modulate controlled blood pressure [12, 13]. Additionally, kidneys also regulate vascular tone and sodium level, by maintaining prostaglandins secretion in order to keep a balanced renin-angiotensin system [12, 13]. By reinforcing renin secretion, prostaglandins increase potassium secretion and prevent tubular reabsorption of sodium. Since the main function of prostaglandins secretion is to maintain normal kidneys’ glomerular filtration rate (GFR), their inhibition can be a drawback of excessive daily use of diclofenac leading to abnormal renal functions and chronic kidney diseases (CKD) on the long-term [14]. Diclofenac may induce renal injury by targeting the kidney’s mitochondria leading to the reactive oxygen species (ROS) over production, apoptosis and DNA lesions [15]. Meanwhile, regarding the mechanism of diclofenac-induced chronic liver diseases (CLDs) is idiosyncratic where excessive diclofenac is metabolized by multiple cytochrome P-450 enzymes in hepatocyte resulting in glutathione (GSH) conjugation, irreversible mitochondrial dysfunction and organ severe damage [16]. Chronic kidney and liver damages can also be related to severe cellular damage induced by exaggerated release of ROS and oxidative stress including hydroxyl radicle resulting in severe activated inflammatory responses [17]. These activated inflammatory responses mediate the release of nuclear factor-kappa B (NF- B), tumor necrosis factor-alpha (TNF-α), NO, and interleukin 6 (IL-6) [18].
The absence of potential compounds that can alleviate and protect vital organs from any damage is a major problem, especially in conventional medicine. Thereby it is extremely crucial to find out natural compounds that may protect our vital organs from induced damage and cytotoxicity due to daily misused consumed drugs [19]. Caffeine is a natural methylxanthines compound commonly found in beverages and coffee. Thus, caffeine has been recently studied for its various biochemical and physiological effects, including anti-inflammatory effects and antioxidant actions [20]. It was reported previously that Caffeine administration may exert hepatoprotective and nephroprotective effects by maintaining normal AST, ALT, creatinine, and urea [21, 22]. Some studies attributed these protective effects of Caffeine due to its anti-inflammatory and antioxidant actions by scavenging reactive oxygen species (ROS) such as hydroxyl radical (OH) along with decreasing lipid peroxidation and NO [23]. Several studies have reported the protective effect of daily caffeine consumption on liver and kidney against induced oxidative stress and activated inflammatory responses [24, 25]. Ruhl and Everhart [24, 26] reported that higher caffeine consumption hinders elevated alanine aminotransferase (ALT) and aspartate aminotransferase (AST) as a marker of liver injury resulting in decreased CLDs. On the other hand, several studies have reported a renal protective effect of caffeine consumption against CKDs by increasing the GFR and maintaining the renin-angiotensin system [25, 27].
The main aim of the current study was to assess whether Dic administration as a type of analgesic OTC drug may exert severe hepato-renal toxicity represented by biological changes, and histopathological damage. The study was also designed to evaluate the protective efficiency of daily Caffeine administration on hepatic and renal tissues against the induced damage by diclofenac. Our findings reported that caffeine may be considered as a protective agent against hepatic and renal toxicity by attenuating inflammatory responses and oxidative stress.
Materials and methods
Chemicals
Diclofenac sodium (Dic) was obtained from Novartis Pharmaceutical Company, Cairo, Egypt. Meanwhile, Caffeine was purchased from sigma Aldrich company (St. Louis, MO) (CAS Number: 58-08-2). Thiobarbituric acid (TBA) was purchased from Fluka Chemical company, and trichloroacetic acid (TCA) was purchased from Merck, USA. While Dinitrophenylhydrazine (DNPH) and 5-5-dithiobis-2-nitrobenzoic acid (DTNB) were obtained from Sigma chemicals, USA.
Animals
All the conducted experimental procedures of the current study were initially approved by the Animal Research and Ethical committee of National organization of Drug Control and Research (NODCAR) approval number (NODCAR/II/53/2022) guided by the 3Rs principles (refine, reduce and replace). Twenty-four male Wistar Albino rats weighing from 200 to 250 gm (5–7 weeks old) were obtained from the animal facility house of (NODCAR, Cairo, Egypt). Rats were housed in the maintained conditions including 12 h. light/dark cycle, controlled temperature 22 ± 1℃ and with complete free access to food and water ad libitum. More importantly, the order of treatments assigned for each rat in the experimental design was equally balanced and onset period effects was considered along with rats body weight to avoid confounding effects and experimental error in the statistical study.
Study design
The twenty-four male Wistar Albino rats were assigned randomly and equally divided into four Groups (n = 6 per group). (Group 1): Ctrl group received normal saline intraperitoneally and a daily 1 mL distilled water by oral gavage to provide the same conditions as the other three groups, (Group 2) (Dic exposed group): Six male albino rats were exposed to Dic 10 mg/kg intraperitoneally (I.P) for 28 days [28] with certain modifications, (Group 3) (Caf exposed group): Six male albino rats were exposed to Caf only (15 mg/kg orally) for 28 days [29] with certain modifications; (Groups 4) (Dic + Caf exposed group): Six male albino rats were exposed to Dic (10 mg/kg, i.p) + Caf (15 mg/kg, orally) for 28 days [28, 29].
Samples handling procedures
At the end of the experimental design, rats’ body weight was first measured on day 0 and then on day 29 using automatic balance. A blood sample was taken from each rat retro-orbital vein followed by centrifugation for 5–10 min at 4℃ /3500 rpm. Serum was stored at -20℃ till being used. Subjected rats were killed by cervical dislocation followed by rapid isolation of the liver and kidney. Each isolated liver and kidney was initially weighted and then prepared for histopathology and biological studies. From each rat, part of the liver and kidney was directly fixed in formalin 10% and then being transferred to ethanol. After sectioning, the separated liver and kidney parts were stained with Hematoxylin &Eosin (H&E) for histopathology studies. While the other parts of the liver and kidney were homogenized in phosphate buffer saline (PBS) according to manufacturer instructions. Isolated supernatant of liver and kidney tissue homogenate was stored till being used. On the other hand, Femurs from each rat were aseptically Isolated and placed in DMEM (Dulbecco’s Modified Eagle Medium). Isolated cells were centrifuged and then fixed using Carnoy’s fixative (3 methanol: 1 acetic acid). Slides were prepared using flame-drying followed by being stained using buffered Giemsa (pH = 6.8). Several metaphase spreads per animal were analyzed for chromosomal aberrations [30, 31].
Assessment of serum hematology and biological parameters
The assessment of biological parameters in serum was conducted including Hemoglobin [32], Red blood cells (RBCs) [33], and Hematocrit (HCT %) [33]. Additionally, serum AST, ALT, creatinine, and urea levels were determined using available commercial kits purchased from Biodiagnostic, Cairo, Egypt.
Assessment of tissue biological parameters
Lipid peroxidation content (LPO) was measured using thiobarbituric acid procedure. The resulted chromogen was extracted by using n-butyl alcohol and detected at 532 nm. [34, 35]. Glutathione peroxidases (GPx) was estimated based on the ability of the enzyme to convert glutathione to oxidized glutathione compound. Then the remained glutathione reduces 2-nitrobenzoic acid to form a yellow colored complex measured at 412 nm. GPx activity is indirectly proportional to the degree of color intensity [36, 37]. Meanwhile, nitric Oxide (NO) was estimated using griess reaction where the colored formed product was detected at 540 nm [38], and TNF-α was detected using Elisa kit purchased from (MyBioSource, USA). All these parameters were all detected in the prepared supernatant from liver and kidney homogenate according to the mentioned references and kit instructions.
Histopathology
The isolated liver and kidney parts were mainly fixed in 10% formalin followed by being transferred to ethanol. After cryosectioning, the separated liver and kidney parts were stained with Hematoxylin and Eosin (H&E) then directly being examined under the light microscope [39].
Statistical analysis
The obtained data were expressed in the form of Mean ± SD using SPSS 18 and GraphPad Prism 5.0 software. The variance between groups was analyzed using One-Way ANOVA followed by multiple-group comparisons using the Dunnett’s test. Results were considered significant at p < 0.05. Graphs were illustrated using GraphPad Prism 5.0 software.
Results
Effects of diclofenac administration on organs and body weight
Illustrated Table 1 showed that the daily administration of Caf (group3) resulted in a non-significant difference in the measured whole body weight in addition to kidney and liver body organs weight when compared with the control group (group1) (p > 0.05). On the other hand, Table 1 revealed that the administration of Dic (group2) resulted in a significant reduction in the weight of isolated liver and kidney from each rat associated with a relevant significant increase in the whole body weight when compared with the control group (group1). The obtained data also demonstrated that the daily administration of Dic associated with the daily Caf administration for 28 days attenuated the damaging effects of Dic on organs and body weight. Whereas, an observed decrease in whole body weight in addition to significant improvement in organs weight was observed in (group4) (Dic + Caf exposed group) when compared with other subjected groups 1,2&3 as shown in Table 1 (p < 0.05).
Table 1 Mitigation effect of caffeine against diclofenac-induced damage on body and organs weight (liver & kidney)
Caffeine ameliorative effects on Diclofenac-induced hematologic disorders
It was observed that administration of Dic (group2) resulted in a significant decrease in the hematologic parameters including Hb%, RBCs, and HCT% associated with a relevant increase in WBCs count when compared with the control group (group1) (p < 0.05) as shown in Table 2. Meanwhile, the administration of Caffeine alone (group 3) resulted in no change and non-significant difference in the hematologic parameters when compared with the control group (group 1) (p > 0.05) as shown in Table 2. On the other hand, the group of rats received Dic (10 mg/kg, i.p) + Caf (15 mg/kg, orally) represented as (group 4) displayed a well-marked improvement in Hb%, RBCs, HCT%, and WBCs count when compared with other subjected groups 1, 2 & 3 as shown in Table 2 (p < 0.05).
Table 2 Mitigation effect of caffeine against diclofenac-induced hematologic disorders
Ameliorative effect of caffeine on liver and kidney functions in Diclofenac-induced liver and kidney damage
Illustrated Fig. 1a, b, c and d demonstrated that the effect of Caf sole administration (group3) for 28 days elicited no change and non-significant difference in AST, Alt, urea, and creatinine serum levels when compared with the control group (group I) (p > 0.05). Data of the current study also represented in Fig. 1a, b, c and d demonstrated that the daily administration of Dic (group2) resulted in elevated AST, Alt, urea, and creatinine serum levels when compared with the control group (group1) (p < 0.05). On the other hand, the administration of Dic (10 mg/kg, i.p) + Caf (15 mg/kg, orally) represented as (group 4) proved that caffeine administration attenuated the undue effect of Dic on liver and kidney function tests represented as AST, Alt, urea, and creatinine serum levels when compared with other subjected groups 1,2&3 as shown in Fig. 1a, b, c and d (p < 0.05).
Fig. 1
figure 1
Mitigation effect of Caffeine against Diclofenac-induced damage on liver and kidney functions. a, b Liver function tests (AST, ALT). c, d Kidney functions tests (Urea, Creatinine). Values are represented in the form of mean ± SD of (n = 6 per group) (p < 0.05). Same represented small letters indicate non-significant different (p > 0.05)
Antioxidant efficiency and Lipid peroxidation suppressed level by Caffeine administration in Diclofenac-induced liver and kidney damage
Observed results revealed that the administration of Dic (group 2) resulted in a significant increase in LPO level in addition to decreased GPx level in both liver and kidney tissue as illustrated in Fig. 2a, b, c and d when compared with the control group (group1) (p < 0.05). Whereas, a major significant decrease in LPO level associated with increased GPx liver and kidney tissue level was observed following the administration of Dic (10 mg/kg, i.p) + Caf (15 mg/kg, orally) (group 4) indicating the ameliorative effect of Caf against Dic-induced liver and kidney damage when compared with other subjected groups 1, 2 & 3 as shown in Fig. 2a, b, c and d (p < 0.05). on the other hand, Fig. 2a, b, c and d also demonstrated that the administration of Caf alone represented as (group3) revealed a non-significant change in LPO and GPx liver and kidney tissue levels when compared with the control group (group1) (p > 0.05).
Fig. 2
figure 2
Mitigation effect of Caffeine against Diclofenac-induced damage on oxidative stress in rats’ liver and kidney tissues. a, b LPO and GPx levels in liver tissue. c, d LPO and GPx levels in kidney tissue. Values are represented in the form of mean ± SD of (n = 6 per group) (p < 0.05). Same represented small letters indicate non-significant different (p > 0.05)
Triggered inflammatory markers in Diclofenac-induced liver and kidney damage
As an indicator of the degree of inflammatory damage in liver and kidney tissues, TNF-α and Nitric Oxide (NO) were significantly increased in Dic (group 2) exposed group when compared with the control group (group1) (p < 0.05) as shown in Fig. 3a, b, c and d. Meanwhile, these triggered inflammatory levels (TNF-α and NO) were restored after the administration of Dic (10 mg/kg, i.p) + Caf (15 mg/kg, orally) (group 4) indicating the ameliorative effect of Caf against Dic-induced liver and kidney damage when compared with other subjected groups 1,2&3 as shown in Fig. 3a, b, c and d (p < 0.05). On the other hand, the administration of Caf alone (group3) revealed a non-significant change in TNF-α and NO liver and kidney tissue levels when compared with the control group (group 1) (p > 0.05) as shown in Fig. 3a, b, c and d.
Fig. 3
figure 3
Mitigation effect of Caffeine against Diclofenac-induced damage on inflammatory markers in liver and kidney tissues. a, b TNF-α and NO levels in Liver tissue. cTNF-α and NO levels in Kidney tissue. Values are represented in the form of mean ± SD of (n = 6 per group) (< 0.05). Same represented small letters indicate non-significant different (p > 0.05)
Caffeine ameliorates chromosomal aberrations in Diclofenac-induced damage on bone marrow:
Illustrated Table 3 and Fig. 4 summarized the degree of bone marrow (BM) chromosomal aberrations following the administration of Dic and/or caffeine where results were represented as follow: chromatid deletions (D), dicentric (D.C), fragment (F), centric separation (CS), ring (R) and polyploidy. These mentioned structural and illustrated types of changes were indicated and identified according to the control Group1. An observed relevant decrease in the degree of chromosomal aberrations was observed following the administration of Dic (10 mg/kg, i.p) + Caf (15 mg/kg, orally) (group 4) when compared with other subjected groups 1, 2 & 3 as illustrated in Table 3 and Fig. 4 (p < 0.05). Meanwhile, the degree of total chromosomal aberrations was significantly increased following the administration of Diclofenac (group 2) indicating the degree of bone marrow damage following the daily exposure to Diclofenac (p < 0.05). Meanwhile, the sole caffeine administration (group 3) revealed normal chromosomal aberrations level when compared with the control group1 (p > 0.05) as illustrated in Table 3 and Fig. 4.
Fig. 4
figure 4
Mitigation effect of Caffeine against Diclofenac-induced damage on bone marrow chromosomal aberrations. a, b, c, d Represent the degree of bone marrow chromosomal aberrations in groups (1, 2, 3, 4) respectively. Colored arrows represent chromosomal aberrations structures: (black arrow) dicenteric, (orange arrow) deletion, (red arrow) acenteric fragment, and (blue arrow) translocation in Dic exposed group (group 2)
Table 3 Mitigation effect of caffeine against diclofenac-induced bone marrow chromosomal aberrations in male albino rats
Histopathological liver and kidney tissue examination
No histopathological alterations with intact characterized normal liver and kidney structures were detected in the control (group 1) as shown in Fig. 5a and e respectively. Meanwhile, severe atrophy, degeneration, inflamed liver and kidney tissues were observed in Dic exposed group (group2) as shown in Fig. 5b and f respectively. Whereas, normal and intact histopathological liver and kidney findings were detected in Caf exposed group (group 3) as shown in Fig. 5c and g respectively. On the other hand, very mild atrophy was detected in liver and kidney tissues following the administration of Dic (10 mg/kg, i.p) + Caf (15 mg/kg, orally) (group 4) as shown in Fig. 5d and h.
Fig. 5
figure 5
Histopathological illustrations of liver and kidney sections stained in Hematoxylin &Eosin (100x). ae Photomicrograph of the control group (group1) intact liver and kidney structures respectively. b, Photomicrograph of Dic exposed liver and kidney damages respectively (group2) indicating constricted portal area with proliferated bile duct (arrow), periportal inflammation (IF) and proliferated van Kupfer cells along with showing glomerular tuft (GT) with dilated congested blood capillaries, and dilated bowman’s space (Arrow). cg Photomicrograph of Caf exposed liver and kidney tissues respectively (group3) showing normal intact liver and kidney structure when compared with the control group (group1). d, h photomicrograph of Dic (10 mg/kg, i.p) + Caf (15 mg/kg, orally) exposed liver and kidney sections respectively (group4) showing constricted portal area (arrow) with very mild vacuolated hepatocytes (head of arrow) and slight aggregation of inflammatory cells in lobulated glomerular tuft (GT) and convoluted tubules in addition to slight cytoplasmic atrophy (Arrow)
Discussion
The overdose administration of Diclofenac can be considered toxic to all subjects including humans or animals. In the current study, the exposure to daily Dic administration for 28 days resulted in increased body weight, exaggerated inflammatory responses, altered normal hematological parameters, abnormal liver and kidney functions, triggered oxidative stress release, and suppressed antioxidant levels [8, 40, 41]. These observed toxicities can be related to the accumulation of reactive metabolites known as 4’ and 5’-hydroxydiclofenac associated with the very highly reactive benzoquinone imines compound [8, 42]. The accumulation of these compounds mainly results in increased inflammatory and oxidative stress responses in addition to decrease glutathione peroxidase capacity level. Thereby, these altered body mechanism results in suppressed body defense actions and abnormal body functions [8, 19, 42,43,44].
In agreement with our results, Diclofenac daily administration has been observed to cause a direct liver and kidney injuries in subjected rats [45]. Since AST, ALT, urea, and creatinine contents are considered the main serum biological parameters indicators of hepatic and renal damages; therefore any observed raise in the level of these parameters can be implied as hepatic and renal impairments [45]. The current study demonstrated that the daily exposure to Diclofenac resulted in elevated serum levels of AST, ALT, urea, and creatinine associated with increased LPO, NO, and TNF-α levels of both liver and kidney tissues. All these alterations are associated with modified normal hematological and suppressed antioxidants level. Whereas, these findings are in accordance with [8, 40, 41, 46, 47] who reported the severity of hepatic damages and renal toxicity as a drawback of Diclofenac misuse. Meanwhile, the increased creatinine and urea levels were found to be mainly controlled by the GFR (glomerular filtration rate). Thereby, any detected alteration in GFR can be directly correlated with elevated creatinine and urea serum levels accompanied with water retention symptoms [46, 48]. Additionally, these detected alterations are considered major signs of kidney atrophy and necrosis in addition to being considered predisposing factors for renal failure especially in the long term. On the other hand, it is suggested that elevated AST and ALT serum levels may indicate hepatotoxic tissue membrane damage due to the leakage of these enzymes to the systemic circulation [41]. Meanwhile, the increased LPO, and NO liver-kidney tissue levels can be related to decreased antioxidant capacity and free radical scavenging activity [49]. These elevated oxidative stress factors are suggested to activate various transcription factors leading to triggered inflammatory cytokines release such as TNF-α. The elevated TNF-α level in hepatic and renal tissues is suggested to be the main cascading factor for the observed hepatic and renal tissue atrophy in the histopathological studies. Additionally, chromosomal aberrations cytogenetic marker which is the most validated indicator for detecting the degree of DNA damage was significantly induced following Dic administration. These altered chromosomal aberrations may be due to damaged DNA, DNA synthesis inhibition, and topoisomerase II suppression [49].
Caffeine is a compound rich in photochemical derivatives including triterpenes, trigonelline, melanoidins, and flavonoids [50]. The antioxidant and anti-inflammatory capacity can be related to Caffeine related compounds [51], thus the administration of Caffeine significantly reduced the elevated hepatic and renal parameters in Dic exposed rats. Interestingly, the detected ameliorative and protective effect following the administration of Caffeine in Dic exposed group (group4) and in the sole Caffeine exposed rats (group3) on the liver and kidney tissues indicate that Caf has the ability to eliminate ROS and scavenger free radicals due to its efficient antioxidant and anti-inflammatory actions [52, 53]. In accordance with our results, [54] reported that Caffeine consumption activate antioxidant response elements (AREs) which induce the cellular antioxidant system expression [54, 55]. ARE proteins are vital part of the antioxidant-anti-inflammatory system that are responsible for protecting the body by neutralizing the release of free radicals and oxidizing dexterous agents. Whereas, these elevated AREs are suggested to be responsible for regulating chromosomal aberration and DNA damage [54, 55]. Thereby, Caffeine consumption decrease chromosome aberrations following the administration of Diclofenac in rats. Additionally, the anti-inflammatory properties of Caffeine can be related to its suppression ability against COX, NO, and LPO resulting in the hindered release of IL-6, nuclear factor-κB (NF-κB) and TNF-α [53, 54]. On the other hand, the beneficial activity of Caffeine against Dic toxicity on the liver and kidney could be also attributed to its ability in enhancing GPx release level. Meanwhile, the histopathological findings from both the liver and kidney tissues in the current study revealed severe lesions and atrophy following Dic administration. On the other hand, the Caffeine exposed groups demonstrated highly intact hepatic and renal architecture. Thus, indicating the hepato-renal protective efficiency of Caffeine by maintaining normal functions and structural integrity of the liver and kidney against NSAIDs toxicity. Whereas, this observed efficacy can be related to the following caffeine-mediated mechanisms: antioxidant, anti-inflammatory, DNA damage inhibitor, and diuretic potentials [56].
Several previously conducted epidemiological studies have reported the direct link between Dic misuse and hepatic/renal damages in addition to highlighting the ability of caffeine to alleviate or hinder these Dic-induced damages. Owumi, Dim [28] and Elshopakey, Elazab [45] reported in line with our findings that prolonged chronic intake of Dic enhance cellular oxidative damage and inflammatory cytokines release including ROS, NO, TNF-α, and NF-kB resulting in severe deteriorations on the liver and kidney. Herein, we provide a clear evidence in agreement with previously reported results that the treatment with caffeine significantly alleviated the severe degree of liver and kidney damages induced by Dic administration [20, 21, 53, 57, 58]. This indicates the efficiency of daily caffeine administration on protecting the liver and kidney form Dic deleterious effect on prolong use due to its antioxidant, anti-inflammatory, diuretic potentials, and protective effect against DNA damage [20, 21, 28, 45, 53, 57, 58].
Study limitations
This study was only conducted on male rats where this can be considered a kind of limitations as female hormones might augments the alleviating actions of caffeine against Dic-induced liver and kidney damages [59]. Previous studies have reported that gender differences may affect caffeine metabolism and physiological responses to daily caffeine administration [59]. Thus, further studies are required to study the effects of female sex hormones against daily caffeine administration.
Conclusion
The findings of the current study displayed that the daily exposure to Diclofenac elicited severe hepatic and renal damage in rats which can be related to triggered oxidative stress, DNA damages and inflammatory cytokines release. Caffeine is highly rich in several photochemical derivatives including flavonoids, triterpenes, and polyphones where its beneficial actions can be attributed to its several constituents. Thus, our observed results indicated that daily Caffeine administration relieved Diclofenac-induced hepatic and renal damages by enhancing the overall antioxidant capacity status, and suppressing pro-inflammatory cytokines release, inhibiting chromosomal aberrations, and adjusting hematological abnormalities. Thereby it can be concluded that the daily administration of Caffeine can help to alleviate drugs and chemicals-induced hepatic and renal damage via various mechanisms indicating the importance of developing novel pharmaceutically designed drugs containing caffeine compounds for it various therapeutic potentials. Thus, it is recommended to subsequently consider Caffeine to be further assessed in major clinical trials for reducing hepatic and renal induced damages as a drawback of the daily administration of OTC drugs such as Diclofenac to be more ascertain of its efficacy and efficiency clinically.
Availability of data and materials
The obtained data analyzed during the current study are available from the corresponding author on reasonable request.
Abbreviations
Dic:
Diclofenac
NSAID:
Non-steroidal anti-inflammatory drug
ROS:
Reactive Oxygen Species
DMEM:
Dulbecco’s Modified Eagle Medium
LPO:
Lipid peroxidation
TNF-α:
Tumor Necrosis Factor-α
AST:
Aspartate Aminotransferase
ALT:
Alanine Aminotransferase
NO:
Nitric Oxide
References
1. Blanca-Lopez N, Canto MG, Blanca M. Chapter 18 - other NSAIDs reactions. In: Khan DA, Banerji A, editors. Drug Allergy Testing: Elsevier; 2018. pp. 177–96.
Google Scholar
2. Bevaart L, Vervoordeldonk MJ, Tak PP. Evaluation of therapeutic targets in animal models of arthritis: how does it relate to rheumatoid arthritis? Arthr Rhuem. 2010;62(8):2192–205.
Article CAS Google Scholar
3. Gan TJ. Diclofenac: an update on its mechanism of action and safety profile. Curr Med Res Opin. 2010;26(7):1715–31.
Article CAS Google Scholar
4. Bindu S, Mazumder S, Dey S, Pal C, Goyal M, Alam A, et al. Nonsteroidal anti-inflammatory drug induces proinflammatory damage in gastric mucosa through NF-κB activation and neutrophil infiltration: anti-inflammatory role of heme oxygenase-1 against nonsteroidal anti-inflammatory drug. Free Radic Biol Med. 2013;65:456–67.
Article CAS Google Scholar
5. Olayaki LA, Adeyemi WJ, Yinusa JS, Adedayo GA. Omega-3 fatty acids moderate oxidative and proinflammatory events in experimental hepatotoxicity in Wistar rats: comparison with livolin. Synergy. 2018;7:17–24.
Article Google Scholar
6. Ahmed AY, Gad AM, El-Raouf OMA. Curcumin ameliorates diclofenac sodium-induced nephrotoxicity in male albino rats. J Biochem Mol Toxicol. 2017;31(10):e21951.
Article Google Scholar
7. Altman R, Bosch B, Brune K, Patrignani P, Young C. Advances in NSAID development: evolution of diclofenac products using pharmaceutical technology. Drugs. 2015;75(8):859–77.
Article CAS Google Scholar
8. Aycan İ, Elpek Ö, Akkaya B, Kıraç E, Tuzcu H, Kaya S, et al. Diclofenac induced gastrointestinal and renal toxicity is alleviated by thymoquinone treatment. Food Chem Toxicol. 2018;118:795–804.
Article CAS Google Scholar
9. Näslund J, Fick J, Asker N, Ekman E, Larsson DGJ, Norrgren L. Diclofenac affects kidney histology in the three-spined stickleback (Gasterosteus aculeatus) at low µg/L concentrations. Aquat Toxicol. 2017;189:87–96.
Article Google Scholar
10. Kh Z, El-Ashmawy IM, Arabia S, editors. Hepato-Renal and Hematological Effects of Diclofenac Sodium in Rats 2013.
11. Baravalia Y, Vaghasiya Y, Chanda S. Hepatoprotective effect of Woodfordia fruticosa Kurz flowers on diclofenac sodium induced liver toxicity in rats. Asian Pac J Trop Med. 2011;4(5):342–6.
Article Google Scholar
12. Francois H, Facemire C, Kumar A, Audoly L, Koller B, Coffman T. Role of microsomal prostaglandin E synthase 1 in the kidney. J Am Soc Nephrol. 2007;18(5):1466–75.
Article CAS Google Scholar
13. Breyer MD, Hao C, Qi Z. Cyclooxygenase-2 selective inhibitors and the kidney. Curr Opin Crit Care. 2001;7(6):393–400.
Article CAS Google Scholar
14. Ungprasert P, Cheungpasitporn W, Crowson CS, Matteson EL. Individual non-steroidal anti-inflammatory drugs and risk of acute kidney injury: a systematic review and meta-analysis of observational studies. Eur J Intern Med. 2015;26(4):285–91.
Article CAS Google Scholar
15. Ng LE, Vincent AS, Halliwell B, Wong KP. Action of diclofenac on kidney mitochondria and cells. Biochem Biophys Res Commun. 2006;348(2):494–500.
Article CAS Google Scholar
16. Huang T, Zhang G, Chong S, Liu Y, Zhang N, Fang S, et al. Effects and mechanism of diclofenac degradation in aqueous solution by US/Zn0. Ultrason Sonochem. 2017;37:676–85.
Article CAS Google Scholar
17. Jena NR. DNA damage by reactive species: mechanisms, mutation and repair. J Biosci. 2012;37(3):503–17.
Article CAS Google Scholar
18. Lu YC, Yeh WC, Ohashi PS. LPS/TLR4 signal transduction pathway. Cytokine. 2008;42(2):145–51.
Article CAS Google Scholar
19. Anwar MM, Laila IMI. Protective and restorative potency of diosmin natural flavonoid compound against tramadol-induced testicular damage and infertility in male rats. Nat Prod Res. 2022:1–5. https://0-doi-org.brum.beds.ac.uk/10.1080/14786419.2022.2090937.
20. Olcina GJ, Muñoz D, Timón R, Caballero MJ, Maynar JI, Córdova A, et al. Effect of caffeine on oxidative stress during maximum incremental exercise. J sports Sci Med. 2006;5(4):621–8.
Google Scholar
21. Lv X, Chen Z, Li J, Zhang L, Liu H, Huang C, et al. Caffeine protects against alcoholic liver injury by attenuating inflammatory response and oxidative stress. Inflamm Res. 2010;59(8):635–45.
Article CAS Google Scholar
22. Tommerdahl KL, Hu EA, Selvin E, Steffen LM, Coresh J, Grams ME, et al. Coffee Consumption May mitigate the risk for acute kidney Injury: results from the atherosclerosis risk in Communities Study. Kidney Int Rep. 2022;7(7):1665–72.
Article Google Scholar
23. Rezaie A, Pashmforosh M, Haghi M, Fazlara A, Haghighat N, Shahriari A. Hepatoprotective effect of caffeine on diethylnitrosamine-induced liver injury in rats. Bulgarian J Veterinary Med. 2014;17:183-–90.
Google Scholar
24. Ruhl CE, Everhart JE. Coffee and tea consumption are associated with a lower incidence of chronic liver disease in the United States. Gastroenterology. 2005;129(6):1928–36.
Article Google Scholar
25. Kennedy OJ, Pirastu N, Poole R, Fallowfield JA, Hayes PC, Grzeszkowiak EJ, et al. Coffee consumption and kidney function: a mendelian randomization study. Am J Kidney Dis. 2020;75(5):753–61.
Article CAS Google Scholar
26. Ruhl CE, Everhart JE. Coffee and caffeine consumption reduce the risk of elevated serum alanine aminotransferase activity in the United States. Gastroenterology. 2005;128(1):24–32.
Article CAS Google Scholar
27. Srithongkul T, Ungprasert P. Coffee Consumption is Associated with a decreased risk of incident chronic kidney disease: a systematic review and Meta-analysis of Cohort Studies. Eur J Intern Med. 2020;77:111–6.
Article Google Scholar
28. Owumi SE, Dim UJ. Biochemical alterations in diclofenac-treated rats: Effect of selenium on oxidative stress, inflammation, and hematological changes. Toxicol Res Application. 2019;3:2397847319874359.
CAS Google Scholar
29. Sheth S, Sheehan K, Dhukhwa A, Al Aameri RFH, Mamillapalli C, Mukherjea D, et al. Oral administration of Caffeine exacerbates Cisplatin-Induced hearing loss. Sci Rep. 2019;9(1):9571.
Article Google Scholar
30. Tice RR, Hayashi M, MacGregor JT, Anderson D, Blakey DH, Holden HE, et al. Report from the working group on the in vivo mammalian bone marrow chromosomal aberration test. Mutat Res. 1994;312(3):305–12.
Article CAS Google Scholar
31. Moore FR, Urda GA, Krishna G, Theiss JC. An in vivo/in vitro method for assessing micronucleus and chromosome aberration induction in rat bone marrow and spleen 1. Studies with cyclophosphamide. Mutat Res/Environ Mutagen Relat Subj. 1995;335(2):191–9.
CAS Google Scholar
32. Drabkin DL, Austin JH. Spectrophotometric studies: I. Spectrophotometric constants for common hemoglobin. Derivatives in human, dog, and rabbit blood. J Biol Chem. 1932;98(2):719–33.
Article CAS Google Scholar
33. Onyinyechukwu AA. Haematology and Clinical Biochemistry Findings Associated with equine Diseases - a review. Notulae Scientia Biologicae. 2017;9(1):1–21. https://0-doi-org.brum.beds.ac.uk/10.15835/nsb919939.
34. Mihara M, Uchiyama M. Determination of malonaldehyde precursor in tissues by thiobarbituric acid test. Anal Biochem. 1978;86(1):271–8.
Article CAS Google Scholar
35. Moreno I, Pichardo S, Jos A, Gómez-Amores L, Mate A, Vazquez CM, et al. Antioxidant enzyme activity and lipid peroxidation in liver and kidney of rats exposed to microcystin-LR administered intraperitoneally. Toxicon. 2005;45(4):395–402.
Article CAS Google Scholar
36. Brigelius-Flohé R. Tissue-specific functions of individual glutathione peroxidases. Free Radic Biol Med. 1999;27(9–10):951–65.
Article Google Scholar
37. Chiu DTY, Stults FH, Tappel AL. Purification and properties of rat lung soluble glutathione peroxidase. Biochim et Biophys Acta (BBA) - Enzymol. 1976;445(3):558–66.
Article CAS Google Scholar
38. Green LC, Wagner DA, Glogowski J, Skipper PL, Wishnok JS, Tannenbaum SR. Analysis of nitrate, nitrite, and [15 N]nitrate in biological fluids. Anal Biochem. 1982;126(1):131–8.
Article CAS Google Scholar
39. Bancroft JD, Gamble M, Jones ML, Totty BA. Theory and practice of histological techniques. Connective tissues and stains, 15thedn Churchill Livingstone Publications. 2004:139–200.
40. Galati G, Tafazoli S, Sabzevari O, Chan TS, O’Brien PJ. Idiosyncratic NSAID drug induced oxidative stress. Chemico-Biol Interact. 2002;142(1–2):25–41.
Article CAS Google Scholar
41. Alabi QK, Akomolafe RO, Olukiran OS, Adeyemi WJ, Nafiu AO, Adefisayo MA, et al. The Garcinia kola biflavonoid kolaviron attenuates experimental hepatotoxicity induced by diclofenac. Pathophysiol. 2017;24(4):281–90.
Article CAS Google Scholar
42. Lazarska KE, Dekker SJ, Vermeulen NPE, Commandeur JNM. Effect of UGT2B7*2 and CYP2C8*4 polymorphisms on diclofenac metabolism. Toxicol Lett. 2018;284:70–8.
Article CAS Google Scholar
43. Dragovic S, Boerma JS, Vermeulen NP, Commandeur JN. Effect of human glutathione S-transferases on glutathione-dependent inactivation of cytochrome P450-dependent reactive intermediates of diclofenac. Chem Res Toxicol. 2013;26(11):1632–41.
Article CAS Google Scholar
44. Masubuchi Y, Nakayama S, Horie T. Role of mitochondrial permeability transition in diclofenac-induced hepatocyte injury in rats. Hepatology (Baltimore MD). 2002;35(3):544–51.
Article CAS Google Scholar
45. Elshopakey GE, Elazab ST. Cinnamon aqueous extract attenuates diclofenac sodium and oxytetracycline mediated hepato-renal toxicity and modulates oxidative stress, cell apoptosis, and inflammation in male albino rats. Vet Sci. 2021;8(1). https://0-doi-org.brum.beds.ac.uk/10.3390/vetsci8010009.
46. Sahu N, Mishra G, Chandra HK, Nirala SK, Bhadauria M. Naringenin mitigates antituberculosis drugs induced hepatic and renal injury in rats. J Traditional Complement Med. 2020;10(1):26–35.
Article Google Scholar
47. Peter SJ, Basha SK, Giridharan R, Lavinya BU, Sabina EP. Suppressive effect of Spirulina fusiformis on diclofenac-induced hepato-renal injury and gastrointestinal ulcer in Wistar albino rats: A biochemical and histological approach. Biomed Pharmacother. 2017;88:11 – 8.
48. Anderson AH, Yang W, Hsu CY, Joffe MM, Leonard MB, Xie D, et al. Estimating GFR among participants in the chronic renal insufficiency cohort (CRIC) study. Am J Kidney Dis. 2012;60(2):250–61.
Article Google Scholar
49. Motawi TK, Ahmed SA, El-Boghdady NA, Metwally NS, Nasr NN. Impact of betanin against paracetamol and diclofenac induced hepato-renal damage in rats. Biomarkers. 2020;25(1):86–93.
50. Jabir NR, Islam MT, Tabrez S, Shakil S, Zaidi SK, Khan FR, et al. An insight towards anticancer potential of major coffee constituents. BioFactors. 2018;44(4):315–26.
Article CAS Google Scholar
51. Lee KJ, Choi JH, Jeong HG. Hepatoprotective and antioxidant effects of the coffee diterpenes kahweol and cafestol on carbon tetrachloride-induced liver damage in mice. Food Chem Toxicol. 2007;45(11):2118–25.
Article CAS Google Scholar
52. Guth I, Matos-Pardal CF, Ferreira-Lima R, Loureiro-Rebouças R, Sobral AC, Moraes-Marques CA, et al. Caffeine attenuates liver damage and improves neurologic signs in a rat model of hepatic encephalopathy. Revista de Gastroenterologia de Mexico. 2022;87(2):159–69.
Article CAS Google Scholar
53. Devasagayam TP, Kamat JP, Mohan H, Kesavan PC. Caffeine as an antioxidant: inhibition of lipid peroxidation induced by reactive oxygen species. Biochim Biophys Acta. 1996;1282(1):63–70.
Article Google Scholar
54. Choi S, Jung S, Ko KS. Effects of Coffee extracts with different roasting degrees on antioxidant and anti-inflammatory Systems in mice. Nutrients. 2018;10(3):363.
Article Google Scholar
55. Volz N, Boettler U, Winkler S, Teller N, Schwarz C, Bakuradze T, et al. Effect of Coffee Combining Green Coffee Bean constituents with typical Roasting Products on the Nrf2/ARE pathway in Vitro and in vivo. J Agric Food Chem. 2012;60:9631–41.
Article CAS Google Scholar
56. Khazaei M, Bayat PD, Ghanbari A, Khazaei S, Feizian M, Khodaei A, et al. Protective effects of subchronic caffeine administration on cisplatin induced urogenital toxicity in male mice. Indian J Exp Biol. 2012;50(9):638–44.
CAS Google Scholar
57. Salomone F, Galvano F, Li Volti G. Molecular bases underlying the hepatoprotective effects of coffee. Nutrients. 2017;9(1). https://0-doi-org.brum.beds.ac.uk/10.3390/nu9010085.
58. Pashmforoosh M, Rezaie A, Haghi-Karamallah M, Fazlara A, Shahriari A, Najafzadeh H. Effects of Caffeine on Renal Toxicity. Induc Diethylnitrosamine. 2015;17(1):e1917.
Google Scholar
59. Temple JL, Ziegler AM. Gender differences in subjective and physiological responses to Caffeine and the role of Steroid Hormones. J Caffeine Res. 2011;1(1):41–8.
Article CAS Google Scholar
Download references
Acknowledgements
Not applicable.
Funding
Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB). The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.
Author information
Authors and Affiliations
Authors
Contributions
All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [MM.A], and [IMIL]. [MM.A] wrote the main manuscript and prepared the figures. All authors read and approved the final manuscript.
Corresponding author
Correspondence to Mai M. Anwar.
Ethics declarations
Ethics approval and consent to participate
Written permission of the animal facility house of NODCAR was taken to get the twenty-four male Wistar Albino rats weighing from 200 to 250 gm in order to perform the experimental design. All the conducted experimental procedures of the current study were approved by the Animal Research and Ethical committee of National organization of Drug Control and Research (NODCAR) approval number (NODCAR/II/53/2022). The experimental design was conducted under relevant regulations and guidelines of the Laboratory Animals use in Biomedical Research in compliance with the ARRIVE guidelines.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.
Reprints and permissions
About this article
Check for updates. Verify currency and authenticity via CrossMark
Cite this article
Anwar, M.M., Laila, I.M.I. Mitigative effect of caffeine against diclofenac-induced hepato-renal damage and chromosomal aberrations in male albino rats. BMC Complement Med Ther 22, 327 (2022). https://0-doi-org.brum.beds.ac.uk/10.1186/s12906-022-03802-y
Download citation
• Received:
• Accepted:
• Published:
• DOI: https://0-doi-org.brum.beds.ac.uk/10.1186/s12906-022-03802-y
Keywords
|
__label__pos
| 0.604361 |
{"markup":"\u003C?xml version=\u00221.0\u0022 encoding=\u0022UTF-8\u0022 ?\u003E\n \u003Chtml version=\u0022HTML+RDFa+MathML 1.1\u0022\n xmlns:content=\u0022http:\/\/purl.org\/rss\/1.0\/modules\/content\/\u0022\n xmlns:dc=\u0022http:\/\/purl.org\/dc\/terms\/\u0022\n xmlns:foaf=\u0022http:\/\/xmlns.com\/foaf\/0.1\/\u0022\n xmlns:og=\u0022http:\/\/ogp.me\/ns#\u0022\n xmlns:rdfs=\u0022http:\/\/www.w3.org\/2000\/01\/rdf-schema#\u0022\n xmlns:sioc=\u0022http:\/\/rdfs.org\/sioc\/ns#\u0022\n xmlns:sioct=\u0022http:\/\/rdfs.org\/sioc\/types#\u0022\n xmlns:skos=\u0022http:\/\/www.w3.org\/2004\/02\/skos\/core#\u0022\n xmlns:xsd=\u0022http:\/\/www.w3.org\/2001\/XMLSchema#\u0022\n xmlns:mml=\u0022http:\/\/www.w3.org\/1998\/Math\/MathML\u0022\u003E\n \u003Chead\u003E\u003Cscript type=\u0022text\/javascript\u0022 src=\u0022\/\/cdn.jsdelivr.net\/qtip2\/2.2.1\/jquery.qtip.min.js\u0022\u003E\u003C\/script\u003E\n\u003Cscript type=\u0022text\/javascript\u0022 src=\u0022https:\/\/www.g3journal.org\/sites\/default\/files\/js\/js_YjAJQgxDlFX6S-O02jj9jCrVbrwlY3CGgCg1FzPlvBs.js\u0022\u003E\u003C\/script\u003E\n\u003Cscript type=\u0022text\/javascript\u0022\u003E\n\u003C!--\/\/--\u003E\u003C![CDATA[\/\/\u003E\u003C!--\nif(typeof window.MathJax === \u0022undefined\u0022) window.MathJax = { menuSettings: { zoom: \u0022Click\u0022 } };\n\/\/--\u003E\u003C!]]\u003E\n\u003C\/script\u003E\n\u003Cscript type=\u0022text\/javascript\u0022 src=\u0022https:\/\/www.g3journal.org\/sites\/default\/files\/js\/js_gPqjYq7fqdMzw8-29XWQIVoDSWTmZCGy9OqaHppNxuQ.js\u0022\u003E\u003C\/script\u003E\n\u003Cscript type=\u0022text\/javascript\u0022\u003E\n\u003C!--\/\/--\u003E\u003C![CDATA[\/\/\u003E\u003C!--\n(function(i,s,o,g,r,a,m){i[\u0022GoogleAnalyticsObject\u0022]=r;i[r]=i[r]||function(){(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)})(window,document,\u0022script\u0022,\u0022\/\/www.google-analytics.com\/analytics.js\u0022,\u0022ga\u0022);ga(\u0022create\u0022, \u0022UA-35990348-1\u0022, {\u0022cookieDomain\u0022:\u0022auto\u0022});ga(\u0022set\u0022, \u0022anonymizeIp\u0022, true);ga(\u0022send\u0022, \u0022pageview\u0022);ga(\u0027create\u0027, \u0027UA-76034214-10\u0027, \u0027auto\u0027, {\u0027name\u0027: \u0027hwTracker\u0027});\r\nga(\u0027set\u0027, \u0027anonymizeIp\u0027, true);\nga(\u0027hwTracker.send\u0027, \u0027pageview\u0027);\n\/\/--\u003E\u003C!]]\u003E\n\u003C\/script\u003E\n\u003Cscript type=\u0022text\/javascript\u0022\u003E\n\u003C!--\/\/--\u003E\u003C![CDATA[\/\/\u003E\u003C!--\njQuery.extend(Drupal.settings, {\u0022basePath\u0022:\u0022\\\/\u0022,\u0022pathPrefix\u0022:\u0022\u0022,\u0022highwire\u0022:{\u0022ac\u0022:{\u0022\\\/ggg\\\/5\\\/9\\\/1815.atom\u0022:{\u0022access\u0022:{\u0022full\u0022:true},\u0022pisa_id\u0022:\u0022\u0022,\u0022apath\u0022:\u0022\\\/ggg\\\/5\\\/9\\\/1815.atom\u0022,\u0022jcode\u0022:\u0022ggg\u0022}},\u0022processed\u0022:[\u0022highwire_math\u0022],\u0022markup\u0022:[{\u0022requested\u0022:\u0022long\u0022,\u0022variant\u0022:\u0022full-text\u0022,\u0022view\u0022:\u0022full\u0022,\u0022pisa\u0022:\u0022ggg;5\\\/9\\\/1815\u0022}]},\u0022instances\u0022:\u0022{\\u0022highwire_abstract_tooltip\\u0022:{\\u0022content\\u0022:{\\u0022text\\u0022:\\u0022\\u0022},\\u0022style\\u0022:{\\u0022tip\\u0022:{\\u0022width\\u0022:20,\\u0022height\\u0022:20,\\u0022border\\u0022:1,\\u0022offset\\u0022:0,\\u0022corner\\u0022:true},\\u0022classes\\u0022:\\u0022qtip-custom hw-tooltip hw-abstract-tooltip qtip-shadow qtip-rounded\\u0022,\\u0022classes_custom\\u0022:\\u0022hw-tooltip hw-abstract-tooltip\\u0022},\\u0022position\\u0022:{\\u0022at\\u0022:\\u0022right center\\u0022,\\u0022my\\u0022:\\u0022left center\\u0022,\\u0022viewport\\u0022:true,\\u0022adjust\\u0022:{\\u0022method\\u0022:\\u0022shift\\u0022}},\\u0022show\\u0022:{\\u0022event\\u0022:\\u0022mouseenter click \\u0022,\\u0022solo\\u0022:true},\\u0022hide\\u0022:{\\u0022event\\u0022:\\u0022mouseleave \\u0022,\\u0022fixed\\u0022:1,\\u0022delay\\u0022:\\u0022100\\u0022}},\\u0022highwire_author_tooltip\\u0022:{\\u0022content\\u0022:{\\u0022text\\u0022:\\u0022\\u0022},\\u0022style\\u0022:{\\u0022tip\\u0022:{\\u0022width\\u0022:15,\\u0022height\\u0022:15,\\u0022border\\u0022:1,\\u0022offset\\u0022:0,\\u0022corner\\u0022:true},\\u0022classes\\u0022:\\u0022qtip-custom hw-tooltip hw-author-tooltip qtip-shadow qtip-rounded\\u0022,\\u0022classes_custom\\u0022:\\u0022hw-tooltip hw-author-tooltip\\u0022},\\u0022position\\u0022:{\\u0022at\\u0022:\\u0022top center\\u0022,\\u0022my\\u0022:\\u0022bottom center\\u0022,\\u0022viewport\\u0022:true,\\u0022adjust\\u0022:{\\u0022method\\u0022:\\u0022\\u0022}},\\u0022show\\u0022:{\\u0022event\\u0022:\\u0022mouseenter \\u0022,\\u0022solo\\u0022:true},\\u0022hide\\u0022:{\\u0022event\\u0022:\\u0022mouseleave \\u0022,\\u0022fixed\\u0022:1,\\u0022delay\\u0022:\\u0022100\\u0022}},\\u0022highwire_reflinks_tooltip\\u0022:{\\u0022content\\u0022:{\\u0022text\\u0022:\\u0022\\u0022},\\u0022style\\u0022:{\\u0022tip\\u0022:{\\u0022width\\u0022:15,\\u0022height\\u0022:15,\\u0022border\\u0022:1,\\u0022mimic\\u0022:\\u0022top center\\u0022,\\u0022offset\\u0022:0,\\u0022corner\\u0022:true},\\u0022classes\\u0022:\\u0022qtip-custom hw-tooltip hw-ref-link-tooltip qtip-shadow qtip-rounded\\u0022,\\u0022classes_custom\\u0022:\\u0022hw-tooltip hw-ref-link-tooltip\\u0022},\\u0022position\\u0022:{\\u0022at\\u0022:\\u0022bottom left\\u0022,\\u0022my\\u0022:\\u0022top left\\u0022,\\u0022viewport\\u0022:true,\\u0022adjust\\u0022:{\\u0022method\\u0022:\\u0022flip\\u0022}},\\u0022show\\u0022:{\\u0022event\\u0022:\\u0022mouseenter \\u0022,\\u0022solo\\u0022:true},\\u0022hide\\u0022:{\\u0022event\\u0022:\\u0022mouseleave \\u0022,\\u0022fixed\\u0022:1,\\u0022delay\\u0022:\\u0022100\\u0022}}}\u0022,\u0022qtipDebug\u0022:\u0022{\\u0022leaveElement\\u0022:0}\u0022,\u0022googleanalytics\u0022:{\u0022trackOutbound\u0022:1,\u0022trackMailto\u0022:1,\u0022trackDownload\u0022:1,\u0022trackDownloadExtensions\u0022:\u00227z|aac|arc|arj|asf|asx|avi|bin|csv|doc(x|m)?|dot(x|m)?|exe|flv|gif|gz|gzip|hqx|jar|jpe?g|js|mp(2|3|4|e?g)|mov(ie)?|msi|msp|pdf|phps|png|ppt(x|m)?|pot(x|m)?|pps(x|m)?|ppam|sld(x|m)?|thmx|qtm?|ra(m|r)?|sea|sit|tar|tgz|torrent|txt|wav|wma|wmv|wpd|xls(x|m|b)?|xlt(x|m)|xlam|xml|z|zip\u0022,\u0022trackColorbox\u0022:1},\u0022ajaxPageState\u0022:{\u0022js\u0022:{\u0022\\\/\\\/cdn.jsdelivr.net\\\/qtip2\\\/2.2.1\\\/jquery.qtip.min.js\u0022:1,\u0022sites\\\/all\\\/modules\\\/highwire\\\/highwire\\\/plugins\\\/highwire_markup_process\\\/js\\\/highwire_article_reference_popup.js\u0022:1,\u0022sites\\\/all\\\/modules\\\/highwire\\\/highwire\\\/plugins\\\/highwire_markup_process\\\/js\\\/highwire_at_symbol.js\u0022:1,\u00220\u0022:1,\u0022sites\\\/all\\\/modules\\\/contrib\\\/google_analytics\\\/googleanalytics.js\u0022:1,\u00221\u0022:1}}});\n\/\/--\u003E\u003C!]]\u003E\n\u003C\/script\u003E\n\u003Clink type=\u0022text\/css\u0022 rel=\u0022stylesheet\u0022 href=\u0022https:\/\/www.g3journal.org\/sites\/default\/files\/advagg_css\/css__uXgUByez87OKDsgffPHe7u5qNUzr7zOnqWrSJ87THKk__RR-QNYl6SsTObm37M1MaRCUwwzIP19wUZLcqO_pRc1Q__lDZC-66ftm82LH3sOPsR2Vb4UhP_It_P-8RUoCcL4wY.css\u0022 media=\u0022all\u0022 \/\u003E\n\u003Clink type=\u0022text\/css\u0022 rel=\u0022stylesheet\u0022 href=\u0022\/\/cdn.jsdelivr.net\/qtip2\/2.2.1\/jquery.qtip.min.css\u0022 media=\u0022all\u0022 \/\u003E\n\u003Clink type=\u0022text\/css\u0022 rel=\u0022stylesheet\u0022 href=\u0022https:\/\/www.g3journal.org\/sites\/default\/files\/advagg_css\/css__HGACIFBlu2o05y3afvqlt5wrE_5Dn6MXsexfuEpeIwg__q86Wxv3TZm7rY0DiT3-ukdsYcPpAsY783MkUOx0RQHY__lDZC-66ftm82LH3sOPsR2Vb4UhP_It_P-8RUoCcL4wY.css\u0022 media=\u0022all\u0022 \/\u003E\n\u003Clink rel=\u0027stylesheet\u0027 type=\u0027text\/css\u0027 href=\u0027\/sites\/all\/modules\/contrib\/panels\/plugins\/layouts\/onecol\/onecol.css\u0027 \/\u003E\u003C\/head\u003E\u003Cbody\u003E\u003Cdiv class=\u0022panels-ajax-tab-panel panels-ajax-tab-panel-jnl-genetics-tab-art\u0022\u003E\u003Cdiv class=\u0022panel-display panel-1col clearfix\u0022 \u003E\n \u003Cdiv class=\u0022panel-panel panel-col\u0022\u003E\n \u003Cdiv\u003E\u003Cdiv class=\u0022panel-pane pane-highwire-markup article-page-highwire\u0022 \u003E\n \n \n \n \u003Cdiv class=\u0022pane-content\u0022\u003E\n \u003Cdiv class=\u0022highwire-markup\u0022\u003E\u003Cdiv xmlns=\u0022http:\/\/www.w3.org\/1999\/xhtml\u0022 id=\u0022content-block-markup\u0022 data-highwire-cite-ref-tooltip-instance=\u0022highwire_reflinks_tooltip\u0022 xmlns:xhtml=\u0022http:\/\/www.w3.org\/1999\/xhtml\u0022\u003E\u003Cdiv class=\u0022article fulltext-view \u0022\u003E\u003Cspan class=\u0022highwire-journal-article-marker-start\u0022\u003E\u003C\/span\u003E\u003Cdiv class=\u0022section abstract\u0022 id=\u0022abstract-1\u0022\u003E\u003Ch2\u003EAbstract\u003C\/h2\u003E\u003Cp id=\u0022p-2\u0022\u003EKinship analyses are important pillars of ecological and conservation genetic studies with potentially far-reaching implications. There is a need for power analyses that address a range of possible relationships. Nevertheless, such analyses are rarely applied, and studies that use genetic-data-based-kinship inference often ignore the influence of intrinsic population characteristics. We investigated 11 questions regarding the correct classification rate of dyads to relatedness categories (relatedness category assignments; RCA) using an individual-based model with realistic life history parameters. We investigated the effects of the number of genetic markers; marker type (microsatellite, single nucleotide polymorphism SNP, or both); minor allele frequency; typing error; mating system; and the number of overlapping generations under different demographic conditions. We found that (i) an increasing number of genetic markers increased the correct classification rate of the RCA so that up to \u0026gt;80% first cousins can be correctly assigned; (ii) the minimum number of genetic markers required for assignments with 80 and 95% correct classifications differed between relatedness categories, mating systems, and the number of overlapping generations; (iii) the correct classification rate was improved by adding additional relatedness categories and age and mitochondrial DNA data; and (iv) a combination of microsatellite and single-nucleotide polymorphism data increased the correct classification rate if \u0026lt;800 SNP loci were available. This study shows how intrinsic population characteristics, such as mating system and the number of overlapping generations, life history traits, and genetic marker characteristics, can influence the correct classification rate of an RCA study. Therefore, species-specific power analyses are essential for empirical studies.\u003C\/p\u003E\u003C\/div\u003E\u003Cul class=\u0022kwd-group\u0022\u003E\u003Cli class=\u0022kwd\u0022\u003E\u003Ca href=\u0022\/keyword\/identity-descent-ibd\u0022 class=\u0022hw-term hw-article-keyword hw-article-keyword-identity-by-descent-ibd\u0022 rel=\u0022nofollow\u0022\u003Eidentity by descent (IBD)\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022kwd\u0022\u003E\u003Ca href=\u0022\/keyword\/relatedness\u0022 class=\u0022hw-term hw-article-keyword hw-article-keyword-relatedness\u0022 rel=\u0022nofollow\u0022\u003Erelatedness\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022kwd\u0022\u003E\u003Ca href=\u0022\/keyword\/pedigree-reconstruction\u0022 class=\u0022hw-term hw-article-keyword hw-article-keyword-pedigree-reconstruction\u0022 rel=\u0022nofollow\u0022\u003Epedigree reconstruction\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022kwd\u0022\u003E\u003Ca href=\u0022\/keyword\/relatedness-category-assignment\u0022 class=\u0022hw-term hw-article-keyword hw-article-keyword-relatedness-category-assignment\u0022 rel=\u0022nofollow\u0022\u003Erelatedness category assignment\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022kwd\u0022\u003E\u003Ca href=\u0022\/keyword\/intrinsic-population-characteristics\u0022 class=\u0022hw-term hw-article-keyword hw-article-keyword-intrinsic-population-characteristics\u0022 rel=\u0022nofollow\u0022\u003Eintrinsic population characteristics\u003C\/a\u003E\u003C\/li\u003E\u003C\/ul\u003E\u003Cp id=\u0022p-3\u0022\u003EKnowledge about kinship (pedigree and relatedness) is central to our understanding of ecological and evolutionary processes and an integral part of the management and conservation of endangered populations, such as trend and distribution of abundance as well as dispersal rates and individual fitness (\u003Ca id=\u0022xref-ref-3-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-3\u0022\u003EAvise 1992\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-11-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-11\u0022\u003EColtman \u003Cem\u003Eet al.\u003C\/em\u003E 2003\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-32-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-32\u0022\u003EPalsb\u00f8ll \u003Cem\u003Eet al.\u003C\/em\u003E 2010\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-50-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-50\u0022\u003EWang 2014\u003C\/a\u003E). In the past, inferring relatedness from molecular genetic data was regarded as an approximation to the true pedigree relatedness. However, as molecular techniques improve, the pedigree is being regarded as only an approximation to the true relatedness or identity by descent (IBD, rather than IBS, or identity by state) that can be found in each part of the genome (\u003Ca id=\u0022xref-ref-5-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-5\u0022\u003EBenjamin \u003Cem\u003Eet al.\u003C\/em\u003E 2012\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-40-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-40\u0022\u003ESpeed and Balding 2015\u003C\/a\u003E). Of course, cases remain in which insights into the pedigree is important, such as niche inheritance, cultural inheritance, as well as epigenetic inheritance (\u003Ca id=\u0022xref-ref-7-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-7\u0022\u003EBonduriansky 2012\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-14-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-14\u0022\u003EDanchin 2013\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-27-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-27\u0022\u003EKopps \u003Cem\u003Eet al.\u003C\/em\u003E 2014\u003C\/a\u003E). Therefore, it is possible to justify both reconstructed pedigrees and the approximation to true relatedness, and it is important to assess how well molecular and pedigree assessments of relatedness correspond to one another.\u003C\/p\u003E\u003Cp id=\u0022p-4\u0022\u003EPedigrees can be estimated on the basis of genetic similarity among individuals of a population (\u003Ca id=\u0022xref-ref-6-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-6\u0022\u003EBlouin 2003\u003C\/a\u003E). The equations used to assess genetic relatedness compare the observed genetic similarity between dyads to the population average (\u003Cem\u003Ee.g.\u003C\/em\u003E, \u003Ca id=\u0022xref-ref-35-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-35\u0022\u003EQueller and Goodnight 1989\u003C\/a\u003E) or provide likelihoods that a dyad belongs to several potential relationships based on Mendelian allele segregation (\u003Ca id=\u0022xref-ref-44-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-44\u0022\u003EThompson 1975\u003C\/a\u003E). The \u201ccorrect classification rate\u201d of these likelihood equations is defined as the frequency of dyads that are assigned to a category and that are true members of that category (\u003Ca id=\u0022xref-ref-42-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-42\u0022\u003EThomas and Hill 2000\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-46-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-46\u0022\u003EWang 2004\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-51-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-51\u0022\u003EWang and Santure 2009\u003C\/a\u003E). Most software used to assess genetic relationships based on genetic markers can deal with genotyping error (\u003Cem\u003Ee.g.\u003C\/em\u003E, \u003Ca id=\u0022xref-ref-29-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-29\u0022\u003EMarshall \u003Cem\u003Eet al.\u003C\/em\u003E 1998\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-22-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-22\u0022\u003EJones and Wang 2010\u003C\/a\u003E). However, except for parentage, there has been limited effort devoted to assessing the effects of intrinsic population characteristics and other aspects of the quality and quantity of data necessary to attain high correct classification rates in the estimation of relatedness among individuals (\u003Cem\u003Ee.g.\u003C\/em\u003E, \u003Ca id=\u0022xref-ref-2-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-2\u0022\u003EAnderson and Garza 2006\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-4-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-4\u0022\u003EAykanat \u003Cem\u003Eet al.\u003C\/em\u003E 2014\u003C\/a\u003E).\u003C\/p\u003E\u003Cp id=\u0022p-5\u0022\u003EIntrinsic population characteristics such as mating system and number of overlapping generations, which is determined by the relationship between generation time and life span, are expected to affect a population\u2019s \u201ckinship composition,\u201d that is, the distribution of the different relatedness categories in a population (\u003Ca id=\u0022xref-ref-46-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-46\u0022\u003EWang 2004\u003C\/a\u003E). For example, full sibs are unexpected in a population with a promiscuous mating system. Also, dyads related as parent and offspring cannot be observed at the same time in species with nonoverlapping generations. The equations used for relatedness analyses are solely based on Mendelian probabilities and therefore do not take such life history parameters into account. Therefore the correct classification rate of these equations may depend on intrinsic population characteristics due to different kinship compositions. In this paper, we assessed the correct classification rate in one commonly used estimation of pairwise categories of relatedness in three different mating systems (monogamy, polygyny, and promiscuity) and one or three overlapping generations (\u003Ca id=\u0022xref-table-wrap-1-1\u0022 class=\u0022xref-table\u0022 href=\u0022#T1\u0022\u003ETable 1\u003C\/a\u003E) as a function of the number (and kind) of loci.\u003C\/p\u003E\u003Cdiv id=\u0022T1\u0022 class=\u0022table pos-float\u0022\u003E\u003Cdiv class=\u0022table-inline table-callout-links\u0022\u003E\u003Cdiv class=\u0022callout\u0022\u003E\u003Cspan\u003EView this table:\u003C\/span\u003E\u003Cul class=\u0022callout-links\u0022\u003E\u003Cli class=\u0022view-inline first\u0022\u003E\u003Ca href=\u0022##\u0022 class=\u0022table-expand-inline\u0022 data-table-url=\u0022\/highwire\/markup\/466711\/expansion?postprocessors=highwire_tables%2Chighwire_reclass%2Chighwire_figures%2Chighwire_math%2Chighwire_inline_linked_media%2Chighwire_embed\u0026amp;table-expand-inline=1\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EView inline\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022view-popup last\u0022\u003E\u003Ca href=\u0022\/highwire\/markup\/466711\/expansion?width=1000\u0026amp;height=500\u0026amp;iframe=true\u0026amp;postprocessors=highwire_tables%2Chighwire_reclass%2Chighwire_figures%2Chighwire_math%2Chighwire_inline_linked_media%2Chighwire_embed\u0022 class=\u0022colorbox colorbox-load table-expand-popup\u0022 rel=\u0022gallery-fragment-tables\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EView popup\u003C\/a\u003E\u003C\/li\u003E\u003C\/ul\u003E\u003C\/div\u003E\u003C\/div\u003E\u003Cdiv class=\u0022table-caption\u0022\u003E\u003Cspan class=\u0022table-label\u0022\u003ETable 1\u003C\/span\u003E \u003Cspan class=\u0022caption-title\u0022\u003EQuestions, reasoning and results\u003C\/span\u003E\u003Cdiv class=\u0022sb-div caption-clear\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/div\u003E\u003Cp id=\u0022p-7\u0022\u003EThere are two main types of relatedness estimators (\u003Ca id=\u0022xref-ref-6-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-6\u0022\u003EBlouin 2003\u003C\/a\u003E). The first one, method of moments relatedness estimation (\u003Cem\u003Ee.g.\u003C\/em\u003E, \u003Ca id=\u0022xref-ref-35-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-35\u0022\u003EQueller and Goodnight 1989\u003C\/a\u003E), assigns a value to each dyad based on IBD allele sharing. Typically, these values range from \u22121 (no similarity) to +1 (perfect match). Relatedness estimates and pedigree relatedness (mean expectations, \u003Cem\u003Ei.e.\u003C\/em\u003E, 0.5 for parent-offspring, 0.25 for half sibs, etc.) are highly correlated; however, the variance of relatedness estimates is usually high and in many cases the estimated relatedness does not agree with the actual pedigree (\u003Ca id=\u0022xref-ref-38-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-38\u0022\u003ESanture \u003Cem\u003Eet al.\u003C\/em\u003E 2010\u003C\/a\u003E). This means that relatedness estimates are more suitable for assessing the relatedness for a group of individuals rather than dyadic relatedness. Even though the variance of the relatedness of a group of individuals declines with increasing number of loci (\u003Ca id=\u0022xref-ref-35-3\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-35\u0022\u003EQueller and Goodnight 1989\u003C\/a\u003E) the correlation between pedigree relatedness and pairwise relatedness estimates did not exceed 0.86 even when relatedness estimates were based on 771 single-nucleotide polymorphisms (SNPs; \u003Ca id=\u0022xref-ref-38-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-38\u0022\u003ESanture \u003Cem\u003Eet al.\u003C\/em\u003E 2010\u003C\/a\u003E).\u003C\/p\u003E\u003Cp id=\u0022p-8\u0022\u003EThe second type of relatedness estimator is the assignment of likelihood ratios to dyads belonging to certain relatedness categories {\u003Cem\u003Ei.e.\u003C\/em\u003E, parent-offspring [PO], full sibs [FS], relationships sharing on average a quarter of their genome IBD [R = 0.25: half sibs, grandparent\u2212grandchild, avuncular (any of the four combinations: aunt\/uncle-niece\/nephew)], relationships sharing on average one eighth of their genome IBD [R = 0.125: first cousins], and unrelated}. The assignment of dyads to relatedness categories is based on the likelihood that a pair of individuals shares zero (\u0394\u003Csub\u003E0\u003C\/sub\u003E), one (\u0394\u003Csub\u003E1\u003C\/sub\u003E) or two (\u0394\u003Csub\u003E2\u003C\/sub\u003E) alleles that are IBD (\u003Ca id=\u0022xref-ref-44-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-44\u0022\u003EThompson 1975\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-43-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-43\u0022\u003EThompson 1991\u003C\/a\u003E). This likelihood is calculated by multiplying probabilities across unlinked loci and it is different for each relatedness category. A dyad is assigned to the relatedness category for which it has the highest likelihood. We will focus on the relatedness category assignment (RCA) method in this paper because knowledge about relatedness categories provides essential information for niche inheritance, cultural inheritance, and epigenetic inheritance studies.\u003C\/p\u003E\u003Cp id=\u0022p-9\u0022\u003ETo date, studies assessing the power to assign dyads to relatedness categories are based on a null hypothesis category \u003Cem\u003Evs.\u003C\/em\u003E an alternative category (\u003Cem\u003Ee.g.\u003C\/em\u003E, full sib \u003Cem\u003Evs.\u003C\/em\u003E half sib) (\u003Cem\u003Ee.g.\u003C\/em\u003E, \u003Ca id=\u0022xref-ref-8-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-8\u0022\u003EBrookfield and Parkin 1993\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-47-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-47\u0022\u003EWang 2006\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-51-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-51\u0022\u003EWang and Santure 2009\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-38-3\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-38\u0022\u003ESanture \u003Cem\u003Eet al.\u003C\/em\u003E 2010\u003C\/a\u003E). This method is valid if previous knowledge is available, \u003Cem\u003Ee.g.\u003C\/em\u003E, are chicks in a nest full or half sibs? However, in a natural population and in the absence of any previous knowledge this kind of power analysis may be misleading in terms of underestimating the number of required loci for reliable RCAs. In addition to the relatedness category restrictions, the influence of intrinsic population characteristics on the correct classification rate of relationship assignments is often limited. For example, \u003Ca id=\u0022xref-ref-51-3\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-51\u0022\u003EWang and Santure (2009)\u003C\/a\u003E focused only on parentage and sibship inference in a polygamous population (here referred to as promiscuous) for studying the power of relationship assignments. We assessed the correct classification rate of RCA, including relatedness categories with relatively high IBD, and with a realistic degree of background relatedness in the study population.\u003C\/p\u003E\u003Cp id=\u0022p-10\u0022\u003EThe advances in new massive parallel sequencing methods facilitate the genotyping of an increased number of genetic loci per individual (\u003Ca id=\u0022xref-ref-16-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-16\u0022\u003EGardner \u003Cem\u003Eet al.\u003C\/em\u003E 2011\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-33-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-33\u0022\u003EPeterson \u003Cem\u003Eet al.\u003C\/em\u003E 2012\u003C\/a\u003E), which may increase the correct classification rate of RCAs. In studies estimating pairwise categories of relatedness, the class of loci most commonly used have been short tandem repeats (STRs), but the use of SNPs has been increasing (\u003Ca id=\u0022xref-ref-52-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-52\u0022\u003EWeir \u003Cem\u003Eet al.\u003C\/em\u003E 2006\u003C\/a\u003E). Each class of loci has its specific advantages and disadvantages. STRs are more informative per locus because they are usually more polymorphic than the often biallelic SNPs (\u003Ca id=\u0022xref-ref-30-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-30\u0022\u003EMorin \u003Cem\u003Eet al.\u003C\/em\u003E 2004\u003C\/a\u003E). On the other hand, SNPs are more abundant and more suitable for automated data analyses than STRs (\u003Ca id=\u0022xref-ref-45-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-45\u0022\u003EVignal \u003Cem\u003Eet al.\u003C\/em\u003E 2002\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-30-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-30\u0022\u003EMorin \u003Cem\u003Eet al.\u003C\/em\u003E 2004\u003C\/a\u003E).\u003C\/p\u003E\u003Cp id=\u0022p-11\u0022\u003EIn this study, we assessed the correct classification rate for assignment of dyads to relatedness categories, and how the correct classification rate is influenced by number and type of genetic markers, minor allele frequency (MAF), genotyping error, mating system, and including or excluding overlap of generations by looking at 11 questions outlined in \u003Ca id=\u0022xref-table-wrap-1-2\u0022 class=\u0022xref-table\u0022 href=\u0022#T1\u0022\u003ETable 1\u003C\/a\u003E.\u003C\/p\u003E\u003Cdiv class=\u0022section materials-methods\u0022 id=\u0022sec-1\u0022\u003E\u003Ch2 class=\u0022\u0022\u003EMaterials and Methods\u003C\/h2\u003E\u003Cp id=\u0022p-12\u0022\u003EEleven questions (\u003Ca id=\u0022xref-table-wrap-1-3\u0022 class=\u0022xref-table\u0022 href=\u0022#T1\u0022\u003ETable 1\u003C\/a\u003E) were investigated in this study using an individual-based model in which pedigree relatedness was tracked and compared with the most likely relatedness category, which was assigned based on genetic markers. Individual-based models provide a means to investigate characteristics influenced by stochastic processes such as Mendelian segregation of alleles. We developed a model capable of simulating different natural systems, modified from a similar model originally designed by \u003Ca id=\u0022xref-ref-25-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-25\u0022\u003EKopps and Sherwin (2012)\u003C\/a\u003E, which was aimed at the Shark Bay bottlenose dolphin population (\u003Cem\u003ETursiops\u003C\/em\u003E sp.). For this study, the modifications to the original model include the implementation of additional mating systems, variable number of overlapping generations, an increase in the maximum number of (unlinked) genetic markers, and the tracking of pedigree relatedness. For each individual in a simulation (except at the start of the simulation) the parents, grandparents and great-grandparents were known. Pedigree-based unrelated individuals were individuals that did not share any common ancestors in the three previous generations. All simulations were run in Matlab R2012a (MathWorks, Natick, MA).\u003C\/p\u003E\u003Cp id=\u0022p-13\u0022\u003EThe RCAs based on genetic markers were performed using the likelihood equations outlined in \u003Ca id=\u0022xref-ref-15-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-15\u0022\u003EEpstein \u003Cem\u003Eet al.\u003C\/em\u003E (2000)\u003C\/a\u003E. Each dyad was assigned to the relatedness category for which it had the highest likelihood. Unless otherwise stated, we assessed six relatedness categories: monozygotic twins, PO; FS; R = 0.25; R = 0.125; and unrelated.\u003C\/p\u003E\u003Cp id=\u0022p-14\u0022\u003EAll simulations were initiated with a population size of 600 individuals as in \u003Ca id=\u0022xref-ref-25-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-25\u0022\u003EKopps and Sherwin (2012)\u003C\/a\u003E and run for 100 time steps before assessing the correct classification rate of the relatedness estimation. One hundred time steps was considered a good compromise between being able to track three generations of ancestors and not losing much genetic variation due to genetic drift. Individuals in the simulation could lived for a maximum of 12 time steps (age class 12) and became sexually mature at age class 4. Unless otherwise stated, results shown were averaged over 10 independent simulations. Ten simulations proved sufficient because repeated sets of 10 simulations gave identical answers for the number of loci necessary to achieve a correct classification rate of 80 or 95% for assigning dyads to relatedness categories.\u003C\/p\u003E\u003Cdiv id=\u0022sec-2\u0022 class=\u0022subsection\u0022\u003E\u003Ch3\u003EMating system and generational overlap\u003C\/h3\u003E\u003Cp id=\u0022p-15\u0022\u003EMating systems influence the genetic make-up of a population including the kinship composition, and thus may influence the performance of RCAs. We therefore simulated three different, general mating systems: monogamy, polygyny, and promiscuity. Based on the life history values used in all three scenarios (\u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/019323SI.pdf\u0022\u003ESupporting Information\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppldoi:10.1534\/g3.115.019323\/-\/DC1\/TableS1.pdf\u0022\u003ETable S1\u003C\/a\u003E), the maximum number of overlapping generations during each time step was three, unless otherwise stated. In the case of the monogamy scenario, males and females were paired for life. In the event that a paired individual died, the surviving individual in the pair would be paired with an available, sexually mature individual of the opposite sex. In the polygynous scenario (\u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppldoi:10.1534\/g3.115.019323\/-\/DC1\/TableS1.pdf\u0022\u003ETable S1\u003C\/a\u003E), 60 territories were available and each was occupied by a single mature male. When a territory-holding male died he was replaced by a mature, nonterritory holding male, if possible from age classes 7 to 9. Females initially were assigned randomly to a male\u2019s territory, where they remained for life. In the promiscuous scenario, males and females were mated randomly.\u003C\/p\u003E\u003Cp id=\u0022p-16\u0022\u003EWith a small number of exceptions, monogamous, polygynous and promiscuous scenarios were modeled with identical life history parameter values (\u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppldoi:10.1534\/g3.115.019323\/-\/DC1\/TableS1.pdf\u0022\u003ETable S1\u003C\/a\u003E). The exceptions were required because of stochastic model constraints and included the alteration of the average number of offspring per female between simulations with different mating systems. We are aware that there is some artificiality in using the same life history data in scenarios with different mating systems. However, to investigate the effect of mating system on the correct classification rate of RCAs, it was essential to use the same life history data for each mating system scenario, in order to avoid confounding factors when drawing conclusions about the effect of the scenarios.\u003C\/p\u003E\u003Cp id=\u0022p-17\u0022\u003EOverlap of generations during the sampled time-period affects the kinship composition; for example, in populations with nonoverlapping generations there can be no detection of \u003Cem\u003Etrans\u003C\/em\u003E-generational kin such as parent-offspring, grandparent\u2013grand offspring, avuncular. To test whether the absence of certain pedigree relationships in the population influences the correct classification rate of an RCA we also adapted each mating scenario so that generations would not overlap during a sampled time-period. All simulation parameters were the same as in simulations with overlapping generations, except for age at maturity, life expectancy and average number of offspring per female (\u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppldoi:10.1534\/g3.115.019323\/-\/DC1\/TableS1.pdf\u0022\u003ETable S1\u003C\/a\u003E). The population size was kept constant by letting 550-650 offspring survive each generation to produce the next generation.\u003C\/p\u003E\u003C\/div\u003E\u003Cdiv id=\u0022sec-3\u0022 class=\u0022subsection\u0022\u003E\u003Ch3\u003ENumber of loci\u003C\/h3\u003E\u003Cp id=\u0022p-18\u0022\u003EWe estimated the correct classification rates of RCAs from data sets with 10, 20, 40, and 80 STRs, or 50, 100, 200, 400, 800, 1600, or 3200 SNPs. Additionally we performed single simulations with 50,000 SNPs. Because many laboratories are in transition from STR to SNP genotyping, we also considered whether the use of a combination of the two marker types may increase the correct classification rate of an RCA compared with the use of a single marker type. For that purpose, we combined the relatedness category probabilities of 20 STR loci with 50, 100, 200, 400, 800, 1600, or 3200 SNPs. To allow for direct comparisons, we used the same conditions for the combined marker types as for the SNPs only analyses. For the STRs-only analyses we used the same simulations as for the SNPs MAF 0.5 scenarios.\u003C\/p\u003E\u003Cp id=\u0022p-19\u0022\u003ENote that, at least for population structure studies based on STRs, the number of alleles has been found to be more informative than the number of loci (\u003Ca id=\u0022xref-ref-23-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-23\u0022\u003EKalinowski 2002\u003C\/a\u003E). All SNP loci were biallelic and the 80 STR loci implemented in the simulation consisted of eight identical (but independent) sets of 10 STRs (\u003Ca id=\u0022xref-ref-25-3\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-25\u0022\u003EKopps and Sherwin 2012\u003C\/a\u003E) so that the number of alleles doubled with every duplication of the number of markers used. At the start of the simulations, these sets of 10 STRs had an average of 5.6 alleles\/locus. This number is similar to that found in many empirical studies but in our simulations the loci had significantly higher expected heterozygosity (\u003Cem\u003Ee.g.\u003C\/em\u003E, \u003Ca id=\u0022xref-ref-25-4\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-25\u0022\u003EKopps and Sherwin 2012\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-26-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-26\u0022\u003EKopps \u003Cem\u003Eet al.\u003C\/em\u003E 2013\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-9-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-9\u0022\u003EBrown \u003Cem\u003Eet al.\u003C\/em\u003E 2014\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-13-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-13\u0022\u003ECrean \u003Cem\u003Eet al.\u003C\/em\u003E 2014\u003C\/a\u003E).\u003C\/p\u003E\u003C\/div\u003E\u003Cdiv id=\u0022sec-4\u0022 class=\u0022subsection\u0022\u003E\u003Ch3\u003EProportion of population sampled, MAF, and typing error\u003C\/h3\u003E\u003Cp id=\u0022p-20\u0022\u003EIn most field studies, it is not feasible to sample the entire population. Accordingly, we ran scenarios in which 50, 25, 12.5, and 6.25% of the population were sampled to assess how the sampled fraction impacted the correct classification rate of the RCA relative to sampling the entire population (\u003Cem\u003Ei.e.\u003C\/em\u003E, perfect allele frequency estimates). This assessment was conducted with data from 400 and 3200 SNP loci, as well as 400 and 3200 SNP loci combined with 20 STR loci, and 80 STR loci.\u003C\/p\u003E\u003Cp id=\u0022p-21\u0022\u003EWe also investigated the influence of genotyping errors and MAF upon the correct classification rate of RCAs. MAF was defined as the mean allele frequency of the rarer SNP allele at the start of the simulations, ranging from 0 to 0.5. We assessed the effect on correct classification rate of varying the mean MAF across loci at three different mean MAFs: 0.05; 0.25; 0.5. For some simulations, we implemented a typing error to assess any reduction in correct classification rate of RCAs. Each allele at each locus had the same probability of being mistyped (1%), leading to a 2% locus specific typing error rate, which is the error rate used in \u003Ca id=\u0022xref-ref-47-3\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-47\u0022\u003EWang (2006)\u003C\/a\u003E.\u003C\/p\u003E\u003C\/div\u003E\u003Cdiv id=\u0022sec-5\u0022 class=\u0022subsection\u0022\u003E\u003Ch3\u003EExclusion and inclusion of relatedness categories for assessment\u003C\/h3\u003E\u003Cp id=\u0022p-22\u0022\u003EThe correct classification rate of an RCA might be influenced by what categories of relatedness are chosen for assessment. We assessed whether the correct classification rate changed when the RCA did not attempt to identify certain categories of relatedness. For example, the proportion of false positives in the R = 0.125 category was high even when the estimation of relatedness was based upon data from 50,000 SNP loci. Therefore we tested whether not assessing the R = 0.125 category would increase the correct classification rate of the other relatedness categories.\u003C\/p\u003E\u003Cp id=\u0022p-23\u0022\u003EOn the other hand, it is also possible that assessment of an additional relatedness category would allow dyads that were previously wrongly classified to some other category to be more appropriately classified to the new category. This would improve the correct classification rate to assign dyads to other categories. To test this, some simulations included the assessment of the category R = 0.0625 (half first cousins [sharing one grandparent], first cousins once removed, double second cousins). The probability of identity states for sharing zero, one and two alleles\/locus used in the algorithm were: \u0394\u003Csub\u003E0\u003C\/sub\u003E = 0.875, \u0394\u003Csub\u003E1\u003C\/sub\u003E = 0.125, and \u0394\u003Csub\u003E2\u003C\/sub\u003E = 0.\u003C\/p\u003E\u003C\/div\u003E\u003Cdiv id=\u0022sec-6\u0022 class=\u0022subsection\u0022\u003E\u003Ch3\u003EIncorporating demographic and mitochondrial data (mtDNA)\u003C\/h3\u003E\u003Cp id=\u0022p-24\u0022\u003EIncorporating demographic and mtDNA data might improve the correct classification rate of an RCA by reducing the number of false positives (\u003Ca id=\u0022xref-ref-36-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-36\u0022\u003ERiester \u003Cem\u003Eet al.\u003C\/em\u003E 2009\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-12-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-12\u0022\u003ECope \u003Cem\u003Eet al.\u003C\/em\u003E 2014\u003C\/a\u003E). We ran three scenarios in which sex, age (in age classes) and\/or mitochondrial DNA haplotype mtDNA (five equifrequent haplotypes at the start of the simulation) were known. This led to the exclusion of particular relationships for certain dyads even if they had the highest likelihood, in which case that dyad was then assigned to the relatedness category with the second highest likelihood, according to the following criteria:\u003C\/p\u003E\u003Col class=\u0022list-ord \u0022 id=\u0022list-1\u0022\u003E\u003Cli id=\u0022list-item-1\u0022\u003E\u003Cp id=\u0022p-25\u0022\u003EmtDNA haplotype known. Individuals not sharing their mtDNA haplotypes could not be assigned to the category FS. Female-female dyads not sharing their mtDNA haplotypes could not be assigned to the category PO.\u003C\/p\u003E\u003C\/li\u003E\u003Cli id=\u0022list-item-2\u0022\u003E\u003Cp id=\u0022p-26\u0022\u003EAge known. Individuals whose age difference was less than the age at sexual maturity could not be assigned to PO.\u003C\/p\u003E\u003C\/li\u003E\u003Cli id=\u0022list-item-3\u0022\u003E\u003Cp id=\u0022p-27\u0022\u003EAge and mtDNA haplotype known. The same dyads were excluded as in (1) and (2). Additionally, dyads in which the older individual was female and which did not share their mtDNA haplotype could not be assigned to PO.\u003C\/p\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Cp id=\u0022p-28\u0022\u003EAlthough dyads could be excluded from being grandparent\u2212grand offspring using age data, there were no age or mtDNA haplotype restrictions for R = 0.25 because this category included other relationships without age restrictions.\u003C\/p\u003E\u003C\/div\u003E\u003Cdiv id=\u0022sec-7\u0022 class=\u0022subsection\u0022\u003E\u003Ch3\u003EData availability\u003C\/h3\u003E\u003Cp id=\u0022p-29\u0022\u003EThe simulation code is available on DRYAD (\u003Ca href=\u0022http:\/\/dx.doi.org\/10.5061\/dryad.sr61r\u0022\u003Ehttp:\/dx.doi.org\/10.5061\/dryad.sr61r\u003C\/a\u003E).\u003C\/p\u003E\u003C\/div\u003E\u003C\/div\u003E\u003Cdiv class=\u0022section results\u0022 id=\u0022sec-8\u0022\u003E\u003Ch2 class=\u0022\u0022\u003EResults\u003C\/h2\u003E\u003Cp id=\u0022p-30\u0022\u003EFor a clear arrangement of our results, they were summarized together with the questions and reasoning in \u003Ca id=\u0022xref-table-wrap-1-4\u0022 class=\u0022xref-table\u0022 href=\u0022#T1\u0022\u003ETable 1\u003C\/a\u003E. The correct classification rate of an RCA was affected by the number of loci, MAF, typing error rate, availability of additional data as well as intrinsic population characteristics (\u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/TableS2.pdf\u0022\u003ETable S2\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/TableS3.pdf\u0022\u003ETable S3\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/TableS4.pdf\u0022\u003ETable S4\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/TableS5.pdf\u0022\u003ETable S5\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/TableS6.pdf\u0022\u003ETable S6\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS1.pdf\u0022\u003EFigure S1\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS2.pdf\u0022\u003EFigure S2\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS3.pdf\u0022\u003EFigure S3\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS7.pdf\u0022\u003EFigure S7\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS8.pdf\u0022\u003EFigure S8\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS9.pdf\u0022\u003EFigure S9\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS10.pdf\u0022\u003EFigure S10\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS11.pdf\u0022\u003EFigure S11\u003C\/a\u003E, \u003Ca id=\u0022xref-fig-1-8\u0022 class=\u0022xref-fig\u0022 href=\u0022#F1\u0022\u003EFigure 1\u003C\/a\u003E, \u003Ca id=\u0022xref-fig-2-3\u0022 class=\u0022xref-fig\u0022 href=\u0022#F2\u0022\u003EFigure 2\u003C\/a\u003E, and \u003Ca id=\u0022xref-table-wrap-2-9\u0022 class=\u0022xref-table\u0022 href=\u0022#T2\u0022\u003ETable 2\u003C\/a\u003E). Note that the formula for the likelihood for monozygotic twins was used in the simulations but we do not show the correct classification rate of assigning dyads to this category in the results section. However, we observed that a few dyads were assigned to this category when the MAF was low and 50 or 100 SNPs were used.\u003C\/p\u003E\u003Cdiv id=\u0022F1\u0022 class=\u0022fig pos-float type-figure odd\u0022\u003E\u003Cdiv class=\u0022highwire-figure\u0022\u003E\u003Cdiv class=\u0022fig-inline-img-wrapper\u0022\u003E\u003Cdiv class=\u0022fig-inline-img\u0022\u003E\u003Ca href=\u0022https:\/\/www.g3journal.org\/content\/ggg\/5\/9\/1815\/F1.large.jpg?width=800\u0026amp;height=600\u0026amp;carousel=1\u0022 title=\u0022Promiscuity: correct classification rate of relatedness category assignment (RCA) in a promiscuous population (average over 10 simulations). Three different minor allele frequencies (MAF) for single-nucleotide polymorphisms (SNPs), seven different numbers of SNP loci (individual bars from left to right: 50, 100, 200, 400, 800, 1600, 3200), four different numbers of STR loci (from left to right: 10, 20, 40, 80), and a combination of SNP with 20 STR loci were simulated. On the left vertical axes, the proportion of the correct pedigree relatedness color in each category (PO: parent-offspring; FS: full sibs; unrel: unrelated) indicates the correct classification rate of the category-assignment based on the genetic loci. Other colors indicate source of erroneously assigned categories. The right vertical axes, and the lines in the subplots, indicate the number (No) of dyads that were assigned to each category (the true number of dyads can be inferred where almost 100% correct classification rates were achieved). The orders of magnitude at the top of the No dyads\/category scale of the first row apply to all No dyads\/category scales below it. Figure S1 and Figure S2 show the same plots for other mating systems. The variability between the 10 independent simulations is presented in Table S2.\u0022 class=\u0022highwire-fragment fragment-images colorbox-load\u0022 rel=\u0022gallery-fragment-images-993455445\u0022 data-figure-caption=\u0022\u0026lt;div class=\u0026quot;highwire-markup\u0026quot;\u0026gt;Promiscuity: correct classification rate of relatedness category assignment (RCA) in a promiscuous population (average over 10 simulations). Three different minor allele frequencies (MAF) for single-nucleotide polymorphisms (SNPs), seven different numbers of SNP loci (individual bars from left to right: 50, 100, 200, 400, 800, 1600, 3200), four different numbers of STR loci (from left to right: 10, 20, 40, 80), and a combination of SNP with 20 STR loci were simulated. On the left vertical axes, the proportion of the correct pedigree relatedness color in each category (PO: parent-offspring; FS: full sibs; unrel: unrelated) indicates the correct classification rate of the category-assignment based on the genetic loci. Other colors indicate source of erroneously assigned categories. The right vertical axes, and the lines in the subplots, indicate the number (No) of dyads that were assigned to each category (the true number of dyads can be inferred where almost 100% correct classification rates were achieved). The orders of magnitude at the top of the No dyads\/category scale of the first row apply to all No dyads\/category scales below it. Figure S1 and Figure S2 show the same plots for other mating systems. The variability between the 10 independent simulations is presented in Table S2.\u0026lt;\/div\u0026gt;\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003E\u003Cspan class=\u0022hw-responsive-img\u0022\u003E\u003Cimg class=\u0022highwire-fragment fragment-image lazyload\u0022 alt=\u0022Figure 1\u0022 src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 data-src=\u0022https:\/\/www.g3journal.org\/content\/ggg\/5\/9\/1815\/F1.medium.gif\u0022 width=\u0022291\u0022 height=\u0022440\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-fragment fragment-image\u0022 alt=\u0022Figure 1\u0022 src=\u0022https:\/\/www.g3journal.org\/content\/ggg\/5\/9\/1815\/F1.medium.gif\u0022 width=\u0022291\u0022 height=\u0022440\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003Cul class=\u0022highwire-figure-links inline\u0022\u003E\u003Cli class=\u0022download-fig first\u0022\u003E\u003Ca href=\u0022https:\/\/www.g3journal.org\/content\/ggg\/5\/9\/1815\/F1.large.jpg?download=true\u0022 class=\u0022highwire-figure-link highwire-figure-link-download\u0022 title=\u0022Download Figure 1\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EDownload figure\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022new-tab\u0022\u003E\u003Ca href=\u0022https:\/\/www.g3journal.org\/content\/ggg\/5\/9\/1815\/F1.large.jpg\u0022 class=\u0022highwire-figure-link highwire-figure-link-newtab\u0022 target=\u0022_blank\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EOpen in new tab\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022download-ppt last\u0022\u003E\u003Ca href=\u0022\/highwire\/powerpoint\/466659\u0022 class=\u0022highwire-figure-link highwire-figure-link-ppt\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EDownload powerpoint\u003C\/a\u003E\u003C\/li\u003E\u003C\/ul\u003E\u003C\/div\u003E\u003Cdiv class=\u0022fig-caption\u0022 xmlns:xhtml=\u0022http:\/\/www.w3.org\/1999\/xhtml\u0022\u003E\u003Cspan class=\u0022fig-label\u0022\u003EFigure 1\u003C\/span\u003E \u003Cp id=\u0022p-31\u0022 class=\u0022first-child\u0022\u003EPromiscuity: correct classification rate of relatedness category assignment (RCA) in a promiscuous population (average over 10 simulations). Three different minor allele frequencies (MAF) for single-nucleotide polymorphisms (SNPs), seven different numbers of SNP loci (individual bars from left to right: 50, 100, 200, 400, 800, 1600, 3200), four different numbers of STR loci (from left to right: 10, 20, 40, 80), and a combination of SNP with 20 STR loci were simulated. On the left vertical axes, the proportion of the correct pedigree relatedness color in each category (PO: parent-offspring; FS: full sibs; unrel: unrelated) indicates the correct classification rate of the category-assignment based on the genetic loci. Other colors indicate source of erroneously assigned categories. The right vertical axes, and the lines in the subplots, indicate the number (No) of dyads that were assigned to each category (the true number of dyads can be inferred where almost 100% correct classification rates were achieved). The orders of magnitude at the top of the No dyads\/category scale of the first row apply to all No dyads\/category scales below it. \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS1.pdf\u0022\u003EFigure S1\u003C\/a\u003E and \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS2.pdf\u0022\u003EFigure S2\u003C\/a\u003E show the same plots for other mating systems. The variability between the 10 independent simulations is presented in \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/TableS2.pdf\u0022\u003ETable S2\u003C\/a\u003E.\u003C\/p\u003E\u003Cdiv class=\u0022sb-div caption-clear\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/div\u003E\u003Cdiv id=\u0022F2\u0022 class=\u0022fig pos-float type-figure odd\u0022\u003E\u003Cdiv class=\u0022highwire-figure\u0022\u003E\u003Cdiv class=\u0022fig-inline-img-wrapper\u0022\u003E\u003Cdiv class=\u0022fig-inline-img\u0022\u003E\u003Ca href=\u0022https:\/\/www.g3journal.org\/content\/ggg\/5\/9\/1815\/F2.large.jpg?width=800\u0026amp;height=600\u0026amp;carousel=1\u0022 title=\u0022Effect of additional data on correct classification rate of relatedness category assignment in a monogamous population using 20 STRs. In addition to age and\/or mtDNA haplotype, the sex of the individuals was known. Plotted are mean and range of the correct classification rate based on 10 independent simulations.\u0022 class=\u0022highwire-fragment fragment-images colorbox-load\u0022 rel=\u0022gallery-fragment-images-993455445\u0022 data-figure-caption=\u0022\u0026lt;div class=\u0026quot;highwire-markup\u0026quot;\u0026gt;Effect of additional data on correct classification rate of relatedness category assignment in a monogamous population using 20 STRs. In addition to age and\/or mtDNA haplotype, the sex of the individuals was known. Plotted are mean and range of the correct classification rate based on 10 independent simulations.\u0026lt;\/div\u0026gt;\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003E\u003Cspan class=\u0022hw-responsive-img\u0022\u003E\u003Cimg class=\u0022highwire-fragment fragment-image lazyload\u0022 alt=\u0022Figure 2\u0022 src=\u0022data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\u0022 data-src=\u0022https:\/\/www.g3journal.org\/content\/ggg\/5\/9\/1815\/F2.medium.gif\u0022 width=\u0022440\u0022 height=\u0022205\u0022\/\u003E\u003Cnoscript\u003E\u003Cimg class=\u0022highwire-fragment fragment-image\u0022 alt=\u0022Figure 2\u0022 src=\u0022https:\/\/www.g3journal.org\/content\/ggg\/5\/9\/1815\/F2.medium.gif\u0022 width=\u0022440\u0022 height=\u0022205\u0022\/\u003E\u003C\/noscript\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003Cul class=\u0022highwire-figure-links inline\u0022\u003E\u003Cli class=\u0022download-fig first\u0022\u003E\u003Ca href=\u0022https:\/\/www.g3journal.org\/content\/ggg\/5\/9\/1815\/F2.large.jpg?download=true\u0022 class=\u0022highwire-figure-link highwire-figure-link-download\u0022 title=\u0022Download Figure 2\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EDownload figure\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022new-tab\u0022\u003E\u003Ca href=\u0022https:\/\/www.g3journal.org\/content\/ggg\/5\/9\/1815\/F2.large.jpg\u0022 class=\u0022highwire-figure-link highwire-figure-link-newtab\u0022 target=\u0022_blank\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EOpen in new tab\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022download-ppt last\u0022\u003E\u003Ca href=\u0022\/highwire\/powerpoint\/466654\u0022 class=\u0022highwire-figure-link highwire-figure-link-ppt\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EDownload powerpoint\u003C\/a\u003E\u003C\/li\u003E\u003C\/ul\u003E\u003C\/div\u003E\u003Cdiv class=\u0022fig-caption\u0022\u003E\u003Cspan class=\u0022fig-label\u0022\u003EFigure 2\u003C\/span\u003E \u003Cp id=\u0022p-32\u0022 class=\u0022first-child\u0022\u003EEffect of additional data on correct classification rate of relatedness category assignment in a monogamous population using 20 STRs. In addition to age and\/or mtDNA haplotype, the sex of the individuals was known. Plotted are mean and range of the correct classification rate based on 10 independent simulations.\u003C\/p\u003E\u003Cdiv class=\u0022sb-div caption-clear\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/div\u003E\u003Cdiv id=\u0022T2\u0022 class=\u0022table pos-float\u0022\u003E\u003Cdiv class=\u0022table-inline table-callout-links\u0022\u003E\u003Cdiv class=\u0022callout\u0022\u003E\u003Cspan\u003EView this table:\u003C\/span\u003E\u003Cul class=\u0022callout-links\u0022\u003E\u003Cli class=\u0022view-inline first\u0022\u003E\u003Ca href=\u0022##\u0022 class=\u0022table-expand-inline\u0022 data-table-url=\u0022\/highwire\/markup\/466661\/expansion?postprocessors=highwire_tables%2Chighwire_reclass%2Chighwire_figures%2Chighwire_math%2Chighwire_inline_linked_media%2Chighwire_embed\u0026amp;table-expand-inline=1\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EView inline\u003C\/a\u003E\u003C\/li\u003E\u003Cli class=\u0022view-popup last\u0022\u003E\u003Ca href=\u0022\/highwire\/markup\/466661\/expansion?width=1000\u0026amp;height=500\u0026amp;iframe=true\u0026amp;postprocessors=highwire_tables%2Chighwire_reclass%2Chighwire_figures%2Chighwire_math%2Chighwire_inline_linked_media%2Chighwire_embed\u0022 class=\u0022colorbox colorbox-load table-expand-popup\u0022 rel=\u0022gallery-fragment-tables\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EView popup\u003C\/a\u003E\u003C\/li\u003E\u003C\/ul\u003E\u003C\/div\u003E\u003C\/div\u003E\u003Cdiv class=\u0022table-caption\u0022\u003E\u003Cspan class=\u0022table-label\u0022\u003ETable 2\u003C\/span\u003E \u003Cspan class=\u0022caption-title\u0022\u003EMinimum number of SNP and\/or STR loci required per category for a relatedness category assignment with \u0026gt;95% (\u0026gt;80%) correct classification rates\u003C\/span\u003E\u003Cdiv class=\u0022sb-div caption-clear\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/div\u003E\u003Cp id=\u0022p-37\u0022\u003EPopulation size averaged 598.67 individuals, with range of 482\u2212703 individuals; note that these numbers of individuals are equal to 115,921 to 246,753 dyads. Within this large number of dyads, there were a few dyads that were assigned to more than one relatedness category based on pedigree (monogamy: mean = 0.63 dyads, range = 0\u22126; polygyny: 4.27, 0\u221213; promiscuity: 4.53, 0\u221213). This was possible because we assigned the dyads to the same categories based on pedigree as for the RCA. The most common categories that were shared were R = 0.25 and R = 0.125, \u003Cem\u003Ee.g.\u003C\/em\u003E, dyads shared one parent and two grandparents that were not the shared parent\u2019s parent. Because of genetic drift, during the 100 simulated time steps of MAF 0.05 scenarios, a number of the 3200 SNP loci lost variation (became fixed for one allele): 25.8 (0.8%) in monogamy, 60.6 (1.9%) in polygyny, and 37.0 (1.2%) in promiscuity. No loci became fixed in scenarios with MAF = 0.25 or 0.5.\u003C\/p\u003E\u003C\/div\u003E\u003Cdiv class=\u0022section discussion\u0022 id=\u0022sec-9\u0022\u003E\u003Ch2 class=\u0022\u0022\u003EDiscussion\u003C\/h2\u003E\u003Cp id=\u0022p-38\u0022\u003ESeveral relatedness categories can be assigned with 80 or 95% correct classification rates if certain pitfalls are avoided by considering life history parameters, number of loci used, mean MAF, and typing error rate. As expected, there is always a positive correlation between correct classification rate of the RCA and the number of loci loci. Note that when using a realistic number of 800 SNPs or 20 STRs, more categories could be assigned at a given correct classification rate level by SNPs than by STRs (\u003Ca id=\u0022xref-table-wrap-2-10\u0022 class=\u0022xref-table\u0022 href=\u0022#T2\u0022\u003ETable 2\u003C\/a\u003E). This favors SNPs (or a combination of SNPs and STRs) over STRs. The assignment of more distantly related dyads than R = 0.25 (rarely R = 0.125) appears to be impossible using RCAs, even when 10,000s of SNP loci are available (\u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS3.pdf\u0022\u003EFigure S3\u003C\/a\u003E), possibly because of stochasticity in allele segregation or deeper roots of coancestry.\u003C\/p\u003E\u003Cp id=\u0022p-39\u0022\u003EEven though few (around 100 SNPs or 10 STRs) loci are sufficient to correctly assign most real (pedigree-based) parent-offspring and full sib pairs to the correct relatedness categories, the high rate of false positives (SNPs MAF 0.05 and 0.25: PO: 0.81\u22120.85 and 0.11\u22120.19, FS 0.75\u22120.99 and 0.23\u22120.98; STRs: PO 0.85\u22120.89, FS 0.92\u22120.99 across all three mating systems) at these relatedness categories makes the use of this small number of loci problematic, as previously reported for parentage inference (\u003Ca id=\u0022xref-ref-2-3\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-2\u0022\u003EAnderson and Garza 2006\u003C\/a\u003E). A combined data set of SNP and STR loci may increase the correct classification rate of RCAs, especially for parent-offspring pairs when SNP data with low informativeness are available (\u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/TableS4.pdf\u0022\u003ETable S4\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/TableS5.pdf\u0022\u003ETable S5\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/TableS6.pdf\u0022\u003ETable S6\u003C\/a\u003E, and \u003Ca id=\u0022xref-table-wrap-2-11\u0022 class=\u0022xref-table\u0022 href=\u0022#T2\u0022\u003ETable 2\u003C\/a\u003E).\u003C\/p\u003E\u003Cp id=\u0022p-40\u0022\u003EFor our estimation we did not consider any prior knowledge of possible relationships. This approach seems realistic for many ecological studies in natural populations. Because of the absence of assumptions about the potential relationships, the numbers of loci suggested here (\u2265 40 STRs, 100\u22123200 SNPs) are much higher than the number of loci considered sufficient for the assignment of relatedness categories by \u003Ca id=\u0022xref-ref-8-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-8\u0022\u003EBrookfield and Parkin (1993\u003C\/a\u003E; 2\u22129+ STRs), \u003Ca id=\u0022xref-ref-47-4\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-47\u0022\u003EWang (2006\u003C\/a\u003E; 2\u221213 STRs, 11-92 SNPs 2006), or forensic studies (10\u221215 STRs, 51 SNPs, \u003Ca id=\u0022xref-ref-1-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-1\u0022\u003EAmorim and Pereira 2005\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-37-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-37\u0022\u003ESanchez \u003Cem\u003Eet al.\u003C\/em\u003E 2006\u003C\/a\u003E). This is because these studies\u2019 estimates were based on only two hypothetical relationships: null relatedness \u003Cem\u003Evs.\u003C\/em\u003E a single alternative relatedness category. Statistical significance for the support of the assignment of individual dyads to any relatedness category [by calculating LOD score (\u003Ca id=\u0022xref-ref-24-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-24\u0022\u003EKalinowski \u003Cem\u003Eet al.\u003C\/em\u003E 2007\u003C\/a\u003E) or FDR (\u003Ca id=\u0022xref-ref-39-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-39\u0022\u003ESkaug \u003Cem\u003Eet al.\u003C\/em\u003E 2010\u003C\/a\u003E)] was not inferred in our study, and, therefore, we might have underestimated the correct classification rate of the RCA. However, by assigning all dyads to the relatedness category with the greatest likelihood, all dyads were assigned to a relationship category.\u003C\/p\u003E\u003Cp id=\u0022p-41\u0022\u003ESome false-positive results may be identified through additional knowledge (\u003Ca id=\u0022xref-fig-2-4\u0022 class=\u0022xref-fig\u0022 href=\u0022#F2\u0022\u003EFigure 2\u003C\/a\u003E) such as mtDNA haplotype or age, which can be estimated from genetic samples (\u003Ca id=\u0022xref-ref-34-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-34\u0022\u003EPolanowski \u003Cem\u003Eet al.\u003C\/em\u003E 2014\u003C\/a\u003E). Besides increasing the correct classification rate of the category PO, age data also provide directionality to PO pairs, \u003Cem\u003Ei.e.\u003C\/em\u003E, identify who is the parent and who the offspring.\u003C\/p\u003E\u003Cp id=\u0022p-42\u0022\u003ESome false-positive results may be identified also by genetic data only: a polyadic approach, \u003Cem\u003Ei.e.\u003C\/em\u003E, comparing the compatibility of dyadic relationships by simultaneously assigning parentage and sibship, might filter out some incorrectly assigned dyads by identifying incompatible polyads. Borrowing the example from \u003Ca id=\u0022xref-ref-51-4\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-51\u0022\u003EWang and Santure (2009)\u003C\/a\u003E, if individuals A and B, and A and C, were assigned to the category full sibs the assignment of B and C to R = 0.25 is incompatible. A polyadic approach for sibship and parentage reconstruction was implemented in COLONY2 (\u003Ca id=\u0022xref-ref-51-5\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-51\u0022\u003EWang and Santure 2009\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-22-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-22\u0022\u003EJones and Wang 2010\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-49-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-49\u0022\u003EWang 2013\u003C\/a\u003E). Another approach which uses a third individual as reference when assigning a dyad to a relatedness category seems to perform better than a purely dyadic approach (\u003Ca id=\u0022xref-ref-48-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-48\u0022\u003EWang 2007\u003C\/a\u003E) and could change the number of required loci for an RCA presented here.\u003C\/p\u003E\u003Cp id=\u0022p-43\u0022\u003EThe exclusion from consideration of a single category (\u003Cem\u003Ee.g.\u003C\/em\u003E, R = 0.125, \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/TableS3.pdf\u0022\u003ETable S3\u003C\/a\u003E) in simulations decreased the correct classification rate of an adjacent category (\u003Cem\u003Ee.g.\u003C\/em\u003E, R = 0.25) and is therefore not recommended. However, the addition of an extra category (\u003Cem\u003Ei.e.\u003C\/em\u003E, R = 0.0625) may be beneficial (\u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/TableS4.pdf\u0022\u003ETable S4\u003C\/a\u003E and \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS7.pdf\u0022\u003EFigure S7\u003C\/a\u003E). To our knowledge, the category R = 0.0625 has not been used in previous studies (\u003Ca id=\u0022xref-ref-44-3\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-44\u0022\u003EThompson 1975\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-15-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-15\u0022\u003EEpstein \u003Cem\u003Eet al.\u003C\/em\u003E 2000\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-6-3\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-6\u0022\u003EBlouin 2003\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-47-5\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-47\u0022\u003EWang 2006\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-51-6\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-51\u0022\u003EWang and Santure 2009\u003C\/a\u003E) even though the expected proportion of shared genetic information is higher than for second cousins (R = 0.03125, described in \u003Ca id=\u0022xref-ref-47-6\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-47\u0022\u003EWang 2006\u003C\/a\u003E).\u003C\/p\u003E\u003Cp id=\u0022p-44\u0022\u003EThe categories R = 0.25 and R = 0.125 contain several relationships (half sibs\/grand-parent-grand-child\/avuncular and full cousins\/half-avuncular, quadruple second cousins, respectively). Methods to separate pedigree relationships sharing the same relationship coefficient have been proposed. They are based on the relationship between the number of chromosomal segments (approximately 2 Mb, as opposed to individual loci) shared IBD by two individuals and the number of meioses on the path relating these individuals (\u003Ca id=\u0022xref-ref-21-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-21\u0022\u003EHuff \u003Cem\u003Eet al.\u003C\/em\u003E 2011\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-10-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-10\u0022\u003EBrowning and Browning 2012\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-19-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-19\u0022\u003EHill and White 2013\u003C\/a\u003E; \u003Ca id=\u0022xref-ref-28-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-28\u0022\u003ELi \u003Cem\u003Eet al.\u003C\/em\u003E 2014\u003C\/a\u003E). With these methods, dyads may be assigned with reasonable confidence also to relatedness categories more distant than R = 0.25 (\u003Ca id=\u0022xref-ref-18-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-18\u0022\u003EHenn \u003Cem\u003Eet al.\u003C\/em\u003E 2012\u003C\/a\u003E). These methods sound promising and feasible for non-model species if long scaffolds of their genomes are available for each individual. However, even with next-generation genotyping, most studies on nonmodel organisms do not have adequate mapping information to assign the IBD blocks upon which \u003Ca id=\u0022xref-ref-10-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-10\u0022\u003EBrowning and Browning (2012)\u003C\/a\u003E rely.\u003C\/p\u003E\u003Cp id=\u0022p-45\u0022\u003EThe simulation data sets are unrealistically ideal in terms of completeness of sampling (or extent of random sampling), missing data (none), and typing error (none for most simulations). Genotyping error rates of current next-generation sequencing platforms are still substantial and the power of the conversion of the raw sequencing reads into genotypes depends on sequencing depth and SNP calling algorithms (\u003Ca id=\u0022xref-ref-31-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-31\u0022\u003ENielsen \u003Cem\u003Eet al.\u003C\/em\u003E 2011\u003C\/a\u003E). But even if three SNP calling algorithms agree on an individual genotype, the assigned genotype may be incorrect in 3.5% of individuals, as a recent study has shown (\u003Ca id=\u0022xref-ref-17-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-17\u0022\u003EGreminger \u003Cem\u003Eet al.\u003C\/em\u003E 2014\u003C\/a\u003E). Typing error should be taken into account because it can have profound effects on the power of kinship analyses. For most categories, with a 2% typing error rate, the number of loci required for any given correct classification rate of RCA is two to four times greater compared with error-free data (question 9 in \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/TableS5.pdf\u0022\u003ETable S5\u003C\/a\u003E, \u003Ca id=\u0022xref-table-wrap-1-5\u0022 class=\u0022xref-table\u0022 href=\u0022#T1\u0022\u003ETable 1\u003C\/a\u003E, and \u003Ca id=\u0022xref-table-wrap-2-12\u0022 class=\u0022xref-table\u0022 href=\u0022#T2\u0022\u003ETable 2\u003C\/a\u003E). PO and FS dyads are logically more susceptible to error than dyads of more distantly related categories; our data corroborate this (\u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/TableS5.pdf\u0022\u003ETable S5\u003C\/a\u003E and \u003Ca id=\u0022xref-table-wrap-2-13\u0022 class=\u0022xref-table\u0022 href=\u0022#T2\u0022\u003ETable 2\u003C\/a\u003E). Taking the ideal data sets generated by simulations into account, the number of loci we recommend to be used for RCAs are the minimum for best case data sets, meaning that researchers should estimate the error rate of their data and its impact on analyses. Also, it is important to bear in mind (and this is one aim of this study) that the necessary number of loci for an RCA to be able to have an adequate correct classification rate might differ for populations with other characteristics not present in the simulated populations.\u003C\/p\u003E\u003Cp id=\u0022p-46\u0022\u003EThe decline in correct classification rate with increasing proportion of individuals sampled in the population (question 6 in \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS4.pdf\u0022\u003EFigure S4\u003C\/a\u003E and \u003Ca id=\u0022xref-table-wrap-1-6\u0022 class=\u0022xref-table\u0022 href=\u0022#T1\u0022\u003ETable 1\u003C\/a\u003E) may be puzzling at first. Here it is important to note that the number of dyads increases as the square of the number of individuals sampled, with a faster increase of the number of unrelated dyads compared to related dyads (\u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS5.pdf\u0022\u003EFigure S5\u003C\/a\u003E, \u003Ca id=\u0022xref-ref-39-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-39\u0022\u003ESkaug \u003Cem\u003Eet al.\u003C\/em\u003E 2010\u003C\/a\u003E). It seems that the influence of misclassifying unrelated individuals outweighs any correct classification rate gain due to improved estimates of allele frequencies (\u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\/FigureS6.pdf\u0022\u003EFigure S6\u003C\/a\u003E) due to more complete sampling.\u003C\/p\u003E\u003Cp id=\u0022p-47\u0022\u003ECensus population size is a parameter space that we did not explore, even though it might influence the correct classification rate of an RCA. Some effects may be inferred from the subsampling simulations: the correct classification rate of the RCA decreased with increasing number of pedigree-based unrelated dyads. This finding suggests that in comparison with small populations, relationship assignments of samples originating from large populations potentially may require more loci for similar correct classification rate and\/or certain categories may not reach satisfactory correct classification rates.\u003C\/p\u003E\u003Cp id=\u0022p-48\u0022\u003EWe would like to emphasize that, especially with the facilitated development of genetic markers, (i) the effect of intrinsic population characteristics on correct classification rate should be taken into account for RCAs, and (ii) 95% correct classification rate can be achieved and should be favored over the 80% threshold that is widely used in paternity studies (\u003Ca id=\u0022xref-ref-29-2\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-29\u0022\u003EMarshall \u003Cem\u003Eet al.\u003C\/em\u003E 1998\u003C\/a\u003E). Also, the correct classification rate of a set of loci should be evaluated at the beginning of a project and considered in downstream analyses and interpretation. Unfortunately, sorely-needed software simulating populations that have realistic population parameters and track pedigrees through time are very rare, making RCA power analyses difficult. Instead, available simulation software uses simple demographic and life history models (\u003Ca id=\u0022xref-ref-20-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-20\u0022\u003EHoban 2014\u003C\/a\u003E) or researchers use custom-made simulations (this study, \u003Ca id=\u0022xref-ref-41-1\u0022 class=\u0022xref-bibr\u0022 href=\u0022#ref-41\u0022\u003ETaylor \u003Cem\u003Eet al.\u003C\/em\u003E 2015\u003C\/a\u003E). Until software that simulates populations with realistic parameters are available, the relationship between correct classification rate, population characteristics, and genetic marker characteristics suggested in this study could be used as a rough guideline for power estimates.\u003C\/p\u003E\u003C\/div\u003E\u003Cdiv class=\u0022section ack\u0022 id=\u0022ack-1\u0022\u003E\u003Ch2 class=\u0022\u0022\u003EAcknowledgments\u003C\/h2\u003E\u003Cp id=\u0022p-49\u0022\u003EWe are grateful to Bob Dr\u00f6ge from the Millipede team for his advice on running the simulations on a HPC cluster and to Jo\u00e3o B. L. Gusm\u00e3o Junior for improving the resolution of \u003Ca id=\u0022xref-fig-1-9\u0022 class=\u0022xref-fig\u0022 href=\u0022#F1\u0022\u003EFigure 1\u003C\/a\u003E. We would like to thank two anonymous reviewers for their helpful comments. A.M.K. was supported by a fellowship for prospective researchers from the Swiss National Science Foundation. \u003C\/p\u003E\u003C\/div\u003E\u003Cdiv class=\u0022section fn-group\u0022 id=\u0022fn-group-1\u0022\u003E\u003Ch2\u003EFootnotes\u003C\/h2\u003E\u003Cul\u003E\u003Cli class=\u0022fn-supplementary-material\u0022 id=\u0022fn-6\u0022\u003E\u003Cp id=\u0022p-50\u0022\u003ESupporting information is available online at \u003Ca href=\u0022http:\/\/www.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\u0022\u003Ewww.g3journal.org\/lookup\/suppl\/doi:10.1534\/g3.115.019323\/-\/DC1\u003C\/a\u003E\u003C\/p\u003E\u003C\/li\u003E\u003Cli class=\u0022fn\u0022 id=\u0022fn-7\u0022\u003E\u003Cp id=\u0022p-51\u0022\u003E\u003Cem\u003ECommunicating editor: S. I. Wright\u003C\/em\u003E\u003C\/p\u003E\u003C\/li\u003E\u003C\/ul\u003E\u003C\/div\u003E\u003Cul class=\u0022history-list\u0022\u003E\u003Cli xmlns:hwp=\u0022http:\/\/schema.highwire.org\/Journal\u0022 class=\u0022received\u0022 hwp:start=\u00222015-03-27\u0022\u003E\u003Cspan class=\u0022received-label\u0022\u003EReceived \u003C\/span\u003EMarch 27, 2015.\u003C\/li\u003E\u003Cli xmlns:hwp=\u0022http:\/\/schema.highwire.org\/Journal\u0022 class=\u0022accepted\u0022 hwp:start=\u00222015-06-23\u0022\u003E\u003Cspan class=\u0022accepted-label\u0022\u003EAccepted \u003C\/span\u003EJune 23, 2015.\u003C\/li\u003E\u003C\/ul\u003E\u003Cul class=\u0022copyright-statement\u0022\u003E\u003Cli class=\u0022fn\u0022 id=\u0022copyright-statement-1\u0022\u003ECopyright \u00a9 2015 Kopps \u003Cem\u003Eet al.\u003C\/em\u003E\u003C\/li\u003E\u003C\/ul\u003E\u003Cdiv class=\u0022license\u0022 id=\u0022license-1\u0022\u003E\u003Cp id=\u0022p-1\u0022\u003EThis is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License (\u003Ca href=\u0022http:\/\/creativecommons.org\/licenses\/by\/4.0\/\u0022 rel=\u0022license\u0022\u003Ehttp:\/\/creativecommons.org\/licenses\/by\/4.0\/\u003C\/a\u003E), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.\u003C\/p\u003E\u003C\/div\u003E\u003Cdiv class=\u0022section ref-list\u0022 id=\u0022ref-list-1\u0022\u003E\u003Ch2 class=\u0022\u0022\u003ELiterature Cited\u003C\/h2\u003E\u003Col class=\u0022cit-list ref-use-labels\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-1-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-1\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.1\u0022 data-doi=\u002210.1016\/j.forsciint.2004.06.018\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EAmorim\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EPereira\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EL.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2005\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EPros and cons in the use of SNPs in forensic kinship investigation: a comparative analysis with STRs.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EForensic Sci. Int.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E150\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E17\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E21\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DForensic%2BScience%2BInternational%26rft.stitle%253DForensic%2BScience%2BInternational%26rft.aulast%253DAmorim%26rft.auinit1%253DA.%26rft.volume%253D150%26rft.issue%253D1%26rft.spage%253D17%26rft.epage%253D21%26rft.atitle%253DPros%2Band%2Bcons%2Bin%2Bthe%2Buse%2Bof%2BSNPs%2Bin%2Bforensic%2Bkinship%2Binvestigation%253A%2Ba%2Bcomparative%2Banalysis%2Bwith%2BSTRs.%26rft_id%253Dinfo%253Adoi%252F10.1016%252Fj.forsciint.2004.06.018%26rft_id%253Dinfo%253Apmid%252F15837005%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1016\/j.forsciint.2004.06.018\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=15837005\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-2-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-2\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.2\u0022 data-doi=\u002210.1534\/genetics.105.048074\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EAnderson\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EE.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EGarza\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2006\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EThe power of single-nucleotide polymorphisms for large-scale parentage inference.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EGenetics\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E172\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E2567\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E2582\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DGenetics%26rft_id%253Dinfo%253Adoi%252F10.1534%252Fgenetics.105.048074%26rft_id%253Dinfo%253Apmid%252F16387880%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6ODoiZ2VuZXRpY3MiO3M6NToicmVzaWQiO3M6MTA6IjE3Mi80LzI1NjciO3M6NDoiYXRvbSI7czoxODoiL2dnZy81LzkvMTgxNS5hdG9tIjt9czo4OiJmcmFnbWVudCI7czowOiIiO30=\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003Cspan class=\u0022cit-sep cit-reflinks-variant-name-sep\u0022\u003E\/\u003C\/span\u003E\u003Cspan class=\u0022cit-reflinks-full-text\u0022\u003E\u003Cspan class=\u0022free-full-text\u0022\u003EFREE \u003C\/span\u003EFull Text\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-3-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-3\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.3\u0022 data-doi=\u002210.2307\/3545516\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EAvise\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ. C.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E1992\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EMolecular population structure and the biogeographic history of a regional fauna: a case history with lessons for conservation biology.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EOikos\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E63\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E62\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E76\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DOikos%26rft.volume%253D63%26rft.spage%253D62%26rft_id%253Dinfo%253Adoi%252F10.2307%252F3545516%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.2307\/3545516\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=A1992HK90600008\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-4-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-4\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.4\u0022 data-doi=\u002210.1186\/1471-2148-14-68\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EAykanat\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ET.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EJohnston\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ES.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ECotter\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ED.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ECross\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ET.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EPoole\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ER.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-etal\u0022\u003Eet al.\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2014\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EMolecular pedigree reconstruction and estimation of evolutionary parameters in a wild Atlantic salmon river system with incomplete sampling: a power analysis.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EBMC Evol. Biol.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E14\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E68\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DBMC%2BEvol.%2BBiol.%26rft.volume%253D14%26rft.spage%253D68%26rft_id%253Dinfo%253Adoi%252F10.1186%252F1471-2148-14-68%26rft_id%253Dinfo%253Apmid%252F24684698%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1186\/1471-2148-14-68\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=24684698\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-5-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-5\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.5\u0022 data-doi=\u002210.1073\/pnas.1120666109\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBenjamin\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ED. J.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ECesarini\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ED.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003Evan der Loos\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM. J. H. M.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EDawes\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EC. T.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EKoellinger\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EP. D.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-etal\u0022\u003Eet al.\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2012\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EThe genetic architecture of economic and political preferences.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EProc. Natl. Acad. Sci. USA\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E109\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E8026\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E8031\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DProc.%2BNatl.%2BAcad.%2BSci.%2BUSA%26rft_id%253Dinfo%253Adoi%252F10.1073%252Fpnas.1120666109%26rft_id%253Dinfo%253Apmid%252F22566634%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6NDoicG5hcyI7czo1OiJyZXNpZCI7czoxMToiMTA5LzIxLzgwMjYiO3M6NDoiYXRvbSI7czoxODoiL2dnZy81LzkvMTgxNS5hdG9tIjt9czo4OiJmcmFnbWVudCI7czowOiIiO30=\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003Cspan class=\u0022cit-sep cit-reflinks-variant-name-sep\u0022\u003E\/\u003C\/span\u003E\u003Cspan class=\u0022cit-reflinks-full-text\u0022\u003E\u003Cspan class=\u0022free-full-text\u0022\u003EFREE \u003C\/span\u003EFull Text\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-6-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-6\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.6\u0022 data-doi=\u002210.1016\/S0169-5347(03)00225-8\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBlouin\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM. S.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2003\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EDNA-based methods for pedigree reconstruction and kinship analysis in natural populations.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003ETrends Ecol. Evol.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E18\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E503\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E511\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DTrends%2BEcol.%2BEvol.%26rft.volume%253D18%26rft.spage%253D503%26rft_id%253Dinfo%253Adoi%252F10.1016%252FS0169-5347%252803%252900225-8%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1016\/S0169-5347(03)00225-8\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000185728100007\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-7-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-7\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.7\u0022 data-doi=\u002210.1016\/j.tree.2012.02.003\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBonduriansky\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ER.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2012\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003ERethinking heredity, again.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003ETrends Ecol. Evol.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E27\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E330\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E336\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DTrends%2Bin%2BEcology%2B%2526%2BEvolution%26rft.stitle%253DTrends%2Bin%2BEcology%2B%2526%2BEvolution%26rft.aulast%253DBonduriansky%26rft.auinit1%253DR.%26rft.volume%253D27%26rft.issue%253D6%26rft.spage%253D330%26rft.epage%253D336%26rft.atitle%253DRethinking%2Bheredity%252C%2Bagain.%26rft_id%253Dinfo%253Adoi%252F10.1016%252Fj.tree.2012.02.003%26rft_id%253Dinfo%253Apmid%252F22445060%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1016\/j.tree.2012.02.003\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=22445060\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000305105000008\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-8-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-8\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.8\u0022 data-doi=\u002210.1038\/hdy.1993.94\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBrookfield\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ. F. Y.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EParkin\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ED. T.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E1993\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EUse of single-locus DNA probes in the establishment of relatedness in wild populations.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EHeredity\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E70\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E660\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E663\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DHeredity%26rft.volume%253D70%26rft.spage%253D660%26rft_id%253Dinfo%253Adoi%252F10.1038%252Fhdy.1993.94%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1038\/hdy.1993.94\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-9-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-9\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.9\u0022 data-doi=\u002210.1371\/journal.pone.0101427\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBrown\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. M.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EKopps\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. M.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EAllen\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ES. J.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBejder\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EL.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ELittleford-Colquhoun\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EB.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-etal\u0022\u003Eet al.\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2014\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EPopulation differentiation and hybridisation of Australian Snubfin (\u003Cem\u003EOrcaella heinsohni\u003C\/em\u003E) and Indo-Pacific humpback (\u003Cem\u003ESousa chinensis\u003C\/em\u003E) dolphins in North-Western Australia.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EPLoS One\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E9\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003Ee101427\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DPLoS%2BOne%26rft.volume%253D9%26rft.spage%253De101427%26rft_id%253Dinfo%253Adoi%252F10.1371%252Fjournal.pone.0101427%26rft_id%253Dinfo%253Apmid%252F24988113%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1371\/journal.pone.0101427\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=24988113\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-10-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-10\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.10\u0022 data-doi=\u002210.1146\/annurev-genet-110711-155534\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBrowning\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ES.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBrowning\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EB.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2012\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EIdentity by descent between distant relatives: detection and applications.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EAnnu. Rev. Genet.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E46\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E617\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E633\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DAnnual%2Breview%2Bof%2Bgenetics%26rft.stitle%253DAnnu%2BRev%2BGenet%26rft.aulast%253DBrowning%26rft.auinit1%253DS.%2BR.%26rft.volume%253D46%26rft.spage%253D617%26rft.epage%253D633%26rft.atitle%253DIdentity%2Bby%2Bdescent%2Bbetween%2Bdistant%2Brelatives%253A%2Bdetection%2Band%2Bapplications.%26rft_id%253Dinfo%253Adoi%252F10.1146%252Fannurev-genet-110711-155534%26rft_id%253Dinfo%253Apmid%252F22994355%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1146\/annurev-genet-110711-155534\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=22994355\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000311568300028\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-11-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-11\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.11\u0022 data-doi=\u002210.1046\/j.1365-294X.2003.01762.x\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EColtman\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ED. W.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EPilkington\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ. G.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EPemberton\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ. M.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2003\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EFine-scale genetic structure in a free-living ungulate population.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EMol. Ecol.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E12\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E733\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E742\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DMolecular%2BEcology%2B%2528Print%2529%26rft.stitle%253DMolecular%2BEcology%2B%2528Print%2529%26rft.aulast%253DColtman%26rft.auinit1%253DD.%2BW.%26rft.volume%253D12%26rft.issue%253D3%26rft.spage%253D733%26rft.epage%253D742%26rft.atitle%253DFine-scale%2Bgenetic%2Bstructure%2Bin%2Ba%2Bfree-living%2Bungulate%2Bpopulation.%26rft_id%253Dinfo%253Adoi%252F10.1046%252Fj.1365-294X.2003.01762.x%26rft_id%253Dinfo%253Apmid%252F12675828%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1046\/j.1365-294X.2003.01762.x\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=12675828\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-12-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-12\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.12\u0022 data-doi=\u002210.1111\/1755-0998.12219\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ECope\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ER. C.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ELanyon\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ. M.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ESeddon\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ. M.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EPollett\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EP. K.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2014\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EDevelopment and testing of a genetic marker-based pedigree reconstruction system \u2018PR-genie\u2019 incorporating size-class data.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EMol. Ecol. Resour.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E14\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E857\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E870\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DMol.%2BEcol.%2BResour.%26rft.volume%253D14%26rft.spage%253D857%26rft_id%253Dinfo%253Adoi%252F10.1111%252F1755-0998.12219%26rft_id%253Dinfo%253Apmid%252F24373173%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1111\/1755-0998.12219\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=24373173\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-13-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-13\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.13\u0022 data-doi=\u002210.1111\/ele.12373\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ECrean\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. J.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EKopps\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. M.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBonduriansky\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ER.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2014\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003ERevisiting telegony: offspring inherit an acquired characteristic of their mother\u2019s previous mate.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EEcol. Lett.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E17\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E1545\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E1552\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DEcol.%2BLett.%26rft.volume%253D17%26rft.spage%253D1545%26rft_id%253Dinfo%253Adoi%252F10.1111%252Fele.12373%26rft_id%253Dinfo%253Apmid%252F25270393%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1111\/ele.12373\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=25270393\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-14-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-14\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.14\u0022 data-doi=\u002210.1016\/j.tree.2013.02.010\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EDanchin\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003E\u00c9.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2013\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EAvatars of information: towards an inclusive evolutionary synthesis.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003ETrends Ecol. Evol.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E28\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E351\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E358\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DTrends%2BEcol.%2BEvol.%26rft.volume%253D28%26rft.spage%253D351%26rft_id%253Dinfo%253Adoi%252F10.1016%252Fj.tree.2013.02.010%26rft_id%253Dinfo%253Apmid%252F23540765%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1016\/j.tree.2013.02.010\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=23540765\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000320742700011\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-15-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-15\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.15\u0022 data-doi=\u002210.1086\/321195\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EEpstein\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM. P.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EDuren\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EW. L.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBoehnke\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2000\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EImproved inference of relationship for pairs of individuals.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EAm. J. Hum. Genet.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E67\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E1219\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E1231\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DAmerican%2Bjournal%2Bof%2Bhuman%2Bgenetics%26rft.stitle%253DAm%2BJ%2BHum%2BGenet%26rft.aulast%253DEpstein%26rft.auinit1%253DM.%2BP.%26rft.volume%253D67%26rft.issue%253D5%26rft.spage%253D1219%26rft.epage%253D1231%26rft.atitle%253DImproved%2Binference%2Bof%2Brelationship%2Bfor%2Bpairs%2Bof%2Bindividuals.%26rft_id%253Dinfo%253Adoi%252F10.1086%252F321195%26rft_id%253Dinfo%253Apmid%252F11032786%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1086\/321195\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=11032786\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000165091600019\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-16-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-16\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.16\u0022 data-doi=\u002210.1111\/j.1755-0998.2011.03037.x\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EGardner\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM. G.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EFitch\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. J.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBertozzi\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ET.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ELowe\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. J.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2011\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003ERise of the machines\u2014recommendations for ecologists when using next generation sequencing for microsatellite development.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EMol. Ecol. Resour.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E11\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E1093\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E1101\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DMol.%2BEcol.%2BResour.%26rft.volume%253D11%26rft.spage%253D1093%26rft_id%253Dinfo%253Adoi%252F10.1111%252Fj.1755-0998.2011.03037.x%26rft_id%253Dinfo%253Apmid%252F21679314%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1111\/j.1755-0998.2011.03037.x\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=21679314\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-17-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-17\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.17\u0022 data-doi=\u002210.1186\/1471-2164-15-16\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EGreminger\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EStolting\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EK.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ENater\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EGoossens\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EB.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EArora\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EN.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-etal\u0022\u003Eet al.\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2014\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EGeneration of SNP datasets for orangutan population genomics using improved reduced-representation sequencing and direct comparisons of SNP calling algorithms.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EBMC Genomics\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E15\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E16\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DBMC%2BGenomics%26rft.volume%253D15%26rft.spage%253D16%26rft_id%253Dinfo%253Adoi%252F10.1186%252F1471-2164-15-16%26rft_id%253Dinfo%253Apmid%252F24405840%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1186\/1471-2164-15-16\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=24405840\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-18-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-18\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.18\u0022 data-doi=\u002210.1371\/journal.pone.0034267\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EHenn\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EB. M.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EHon\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EL.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EMacpherson\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ. M.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EEriksson\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EN.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ESaxonov\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ES.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-etal\u0022\u003Eet al.\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2012\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003ECryptic distant relatives are common in both isolated and cosmopolitan genetic samples.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EPLoS One\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E7\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003Ee34267\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.stitle%253DPLoS%2BONE%26rft.aulast%253DHenn%26rft.auinit1%253DB.%2BM.%26rft.volume%253D7%26rft.issue%253D4%26rft.spage%253De34267%26rft.epage%253De34267%26rft.atitle%253DCryptic%2Bdistant%2Brelatives%2Bare%2Bcommon%2Bin%2Bboth%2Bisolated%2Band%2Bcosmopolitan%2Bgenetic%2Bsamples.%26rft_id%253Dinfo%253Adoi%252F10.1371%252Fjournal.pone.0034267%26rft_id%253Dinfo%253Apmid%252F22509285%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1371\/journal.pone.0034267\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=22509285\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-19-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-19\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-other\u0022 id=\u0022cit-5.9.1815.19\u0022 data-doi=\u002210.1534\/g3.113.007500\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EHill\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EW. G.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EWhite\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EI. M. S.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2013\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EIdentification of pedigree relationship from genome sharing.\u003C\/span\u003E \u003Cspan class=\u0022cit-source\u0022\u003EG3 (Bethesda)\u003C\/span\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E3\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E1553\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E1571\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DG3%2B%2528Bethesda%2529%26rft_id%253Dinfo%253Adoi%252F10.1534%252Fg3.113.007500%26rft_id%253Dinfo%253Apmid%252F23893739%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6MzoiZ2dnIjtzOjU6InJlc2lkIjtzOjg6IjMvOS8xNTUzIjtzOjQ6ImF0b20iO3M6MTg6Ii9nZ2cvNS85LzE4MTUuYXRvbSI7fXM6ODoiZnJhZ21lbnQiO3M6MDoiIjt9\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003Cspan class=\u0022cit-sep cit-reflinks-variant-name-sep\u0022\u003E\/\u003C\/span\u003E\u003Cspan class=\u0022cit-reflinks-full-text\u0022\u003E\u003Cspan class=\u0022free-full-text\u0022\u003EFREE \u003C\/span\u003EFull Text\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-20-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-20\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.20\u0022 data-doi=\u002210.1111\/mec.12741\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EHoban\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ES.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2014\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EAn overview of the utility of population simulation software in molecular ecology.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EMol. Ecol.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E23\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E2383\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E2401\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DMol.%2BEcol.%26rft.volume%253D23%26rft.spage%253D2383%26rft_id%253Dinfo%253Adoi%252F10.1111%252Fmec.12741%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1111\/mec.12741\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-21-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-21\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.21\u0022 data-doi=\u002210.1101\/gr.115972.110\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EHuff\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EC. D.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EWitherspoon\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ED. J.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ESimonson\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ET. S.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EXing\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EWatkins\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EW. S.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-etal\u0022\u003Eet al.\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2011\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EMaximum-likelihood estimation of recent shared ancestry (ERSA).\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EGenome Res.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E21\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E768\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E774\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DGenome%2BRes.%26rft_id%253Dinfo%253Adoi%252F10.1101%252Fgr.115972.110%26rft_id%253Dinfo%253Apmid%252F21324875%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6NjoiZ2Vub21lIjtzOjU6InJlc2lkIjtzOjg6IjIxLzUvNzY4IjtzOjQ6ImF0b20iO3M6MTg6Ii9nZ2cvNS85LzE4MTUuYXRvbSI7fXM6ODoiZnJhZ21lbnQiO3M6MDoiIjt9\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003Cspan class=\u0022cit-sep cit-reflinks-variant-name-sep\u0022\u003E\/\u003C\/span\u003E\u003Cspan class=\u0022cit-reflinks-full-text\u0022\u003E\u003Cspan class=\u0022free-full-text\u0022\u003EFREE \u003C\/span\u003EFull Text\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-22-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-22\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.22\u0022 data-doi=\u002210.1111\/j.1755-0998.2009.02787.x\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EJones\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EO. R.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EWang\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2010\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003ECOLONY: a program for parentage and sibship inference from multilocus genotype data.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EMol. Ecol. Resour.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E10\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E551\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E555\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DMol.%2BEcol.%2BResour.%26rft.volume%253D10%26rft.spage%253D551%26rft_id%253Dinfo%253Adoi%252F10.1111%252Fj.1755-0998.2009.02787.x%26rft_id%253Dinfo%253Apmid%252F21565056%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1111\/j.1755-0998.2009.02787.x\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=21565056\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000276407300017\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-23-2\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-23\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.23\u0022 data-doi=\u002210.1038\/sj.hdy.6800009\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EKalinowski\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ES. T.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2002\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EHow many alleles per locus should be used to estimate genetic distances?\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EHeredity\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E88\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E62\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E65\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DHeredity%26rft.stitle%253DHeredity%26rft.aulast%253DKalinowski%26rft.auinit1%253DS.%2BT.%26rft.volume%253D88%26rft.issue%253D1%26rft.spage%253D62%26rft.epage%253D65%26rft.atitle%253DHow%2Bmany%2Balleles%2Bper%2Blocus%2Bshould%2Bbe%2Bused%2Bto%2Bestimate%2Bgenetic%2Bdistances%253F%26rft_id%253Dinfo%253Adoi%252F10.1038%252Fsj.hdy.6800009%26rft_id%253Dinfo%253Apmid%252F11813108%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1038\/sj.hdy.6800009\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=11813108\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000176214400011\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-24-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-24\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.24\u0022 data-doi=\u002210.1111\/j.1365-294X.2007.03089.x\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EKalinowski\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ES. T.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ETaper\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM. L.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EMarshall\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ET. C.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2007\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003ERevising how the computer program CERVUS accommodates genotyping error increases success in paternity assignment.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EMol. Ecol.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E16\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E1099\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E1106\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DMolecular%2BEcology%2B%2528Print%2529%26rft.stitle%253DMolecular%2BEcology%2B%2528Print%2529%26rft.aulast%253DKalinowski%26rft.auinit1%253DS.%2BT.%26rft.volume%253D16%26rft.issue%253D5%26rft.spage%253D1099%26rft.epage%253D1106%26rft.atitle%253DRevising%2Bhow%2Bthe%2Bcomputer%2Bprogram%2BCERVUS%2Baccommodates%2Bgenotyping%2Berror%2Bincreases%2Bsuccess%2Bin%2Bpaternity%2Bassignment.%26rft_id%253Dinfo%253Adoi%252F10.1111%252Fj.1365-294X.2007.03089.x%26rft_id%253Dinfo%253Apmid%252F17305863%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1111\/j.1365-294X.2007.03089.x\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=17305863\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000244245300014\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-25-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-25\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.25\u0022 data-doi=\u002210.1016\/j.anbehav.2012.08.029\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EKopps\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. M.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ESherwin\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EW. B.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2012\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EModelling the emergence and stability of a vertically transmitted cultural trait in bottlenose dolphins.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EAnim. Behav.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E84\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E1347\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E1362\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DAnim.%2BBehav.%26rft.volume%253D84%26rft.spage%253D1347%26rft_id%253Dinfo%253Adoi%252F10.1016%252Fj.anbehav.2012.08.029%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1016\/j.anbehav.2012.08.029\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000311953200009\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-26-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-26\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.26\u0022 data-doi=\u002210.1007\/s12686-012-9727-1\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EKopps\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EMcDonald\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EP.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ERollins\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EL.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2013\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EIsolation and characterisation of polymorphic microsatellite loci for Noisy Miners \u003Cem\u003EManorina melanocephala\u003C\/em\u003E, with successful cross-amplification in Bell Miners \u003Cem\u003EM. melanophrys\u003C\/em\u003E.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EConserv. Genet. Resour.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E5\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E39\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E41\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DConserv.%2BGenet.%2BResour.%26rft.volume%253D5%26rft.spage%253D39%26rft_id%253Dinfo%253Adoi%252F10.1007%252Fs12686-012-9727-1%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1007\/s12686-012-9727-1\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-27-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-27\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.27\u0022 data-doi=\u002210.1098\/rspb.2013.3245\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EKopps\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. M.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EAckermann\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EC. Y.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ESherwin\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EW. B.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EAllen\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ES. J.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBejder\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EL.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-etal\u0022\u003Eet al.\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2014\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003ECultural transmission of tool use combined with habitat specialisations leads to fine-scale genetic structure in bottlenose dolphins\u003C\/span\u003E. \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EProc. Biol. Sci.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E281\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E20133245\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DProc.%2BBiol.%2BSci.%26rft_id%253Dinfo%253Adoi%252F10.1098%252Frspb.2013.3245%26rft_id%253Dinfo%253Apmid%252F24648223%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6Nzoicm95cHJzYiI7czo1OiJyZXNpZCI7czoxNzoiMjgxLzE3ODIvMjAxMzMyNDUiO3M6NDoiYXRvbSI7czoxODoiL2dnZy81LzkvMTgxNS5hdG9tIjt9czo4OiJmcmFnbWVudCI7czowOiIiO30=\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003Cspan class=\u0022cit-sep cit-reflinks-variant-name-sep\u0022\u003E\/\u003C\/span\u003E\u003Cspan class=\u0022cit-reflinks-full-text\u0022\u003E\u003Cspan class=\u0022free-full-text\u0022\u003EFREE \u003C\/span\u003EFull Text\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-28-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-28\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.28\u0022 data-doi=\u002210.1371\/journal.pgen.1004144\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ELi\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EH.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EGlusman\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EG.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EHu\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EH.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EShankaracharya\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ECaballero\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-etal\u0022\u003Eet al.\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2014\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003ERelationship estimation from whole-genome sequence data.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EPLoS Genet.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E10\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003Ee1004144\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DPLoS%2BGenet.%26rft.volume%253D10%26rft.spage%253De1004144%26rft_id%253Dinfo%253Adoi%252F10.1371%252Fjournal.pgen.1004144%26rft_id%253Dinfo%253Apmid%252F24497848%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1371\/journal.pgen.1004144\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=24497848\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-29-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-29\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.29\u0022 data-doi=\u002210.1046\/j.1365-294x.1998.00374.x\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EMarshall\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ET. C.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ESlate\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EKruuk\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EL. E. B.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EPemberton\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ. M.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E1998\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EStatistical confidence for likelihood-based paternity inference in natural populations.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EMol. Ecol.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E7\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E639\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E655\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DMolecular%2BEcology%2B%2528Print%2529%26rft.stitle%253DMolecular%2BEcology%2B%2528Print%2529%26rft.aulast%253DMarshall%26rft.auinit1%253DT.%2BC.%26rft.volume%253D7%26rft.issue%253D5%26rft.spage%253D639%26rft.epage%253D655%26rft.atitle%253DStatistical%2Bconfidence%2Bfor%2Blikelihood-based%2Bpaternity%2Binference%2Bin%2Bnatural%2Bpopulations.%26rft_id%253Dinfo%253Adoi%252F10.1046%252Fj.1365-294x.1998.00374.x%26rft_id%253Dinfo%253Apmid%252F9633105%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1046\/j.1365-294x.1998.00374.x\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=9633105\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000073810200009\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-30-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-30\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.30\u0022 data-doi=\u002210.1016\/j.tree.2004.01.009\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EMorin\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EP. A.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ELuikart\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EG.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EWayne\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ER. K.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E and the SNP workshop group, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2004\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003ESNPs in ecology, evolution and conservation.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003ETrends Ecol. Evol.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E19\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E208\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E216\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DTrends%2BEcol.%2BEvol.%26rft.volume%253D19%26rft.spage%253D208%26rft_id%253Dinfo%253Adoi%252F10.1016%252Fj.tree.2004.01.009%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1016\/j.tree.2004.01.009\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000220842400008\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-31-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-31\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.31\u0022 data-doi=\u002210.1038\/nrg2986\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ENielsen\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ER.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EPaul\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ. S.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EAlbrechtsen\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ESong\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EY. S.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2011\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EGenotype and SNP calling from next-generation sequencing data.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003ENat. Rev. Genet.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E12\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E443\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E451\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DNature%2Breviews.%2BGenetics%26rft.stitle%253DNat%2BRev%2BGenet%26rft.aulast%253DNielsen%26rft.auinit1%253DR.%26rft.volume%253D12%26rft.issue%253D6%26rft.spage%253D443%26rft.epage%253D451%26rft.atitle%253DGenotype%2Band%2BSNP%2Bcalling%2Bfrom%2Bnext-generation%2Bsequencing%2Bdata.%26rft_id%253Dinfo%253Adoi%252F10.1038%252Fnrg2986%26rft_id%253Dinfo%253Apmid%252F21587300%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1038\/nrg2986\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=21587300\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-32-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-32\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.32\u0022 data-doi=\u002210.1111\/j.1755-0998.2010.02887.x\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EPalsb\u00f8ll\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EP. J.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EPeery\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM. Z.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EB\u00e9rub\u00e9\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2010\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EDetecting populations in the \u2018ambiguous\u2019 zone: kinship-based estimation of population structure at low genetic divergence.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EMol. Ecol. Resour.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E10\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E797\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E805\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DMol.%2BEcol.%2BResour.%26rft.volume%253D10%26rft.spage%253D797%26rft_id%253Dinfo%253Adoi%252F10.1111%252Fj.1755-0998.2010.02887.x%26rft_id%253Dinfo%253Apmid%252F21565091%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1111\/j.1755-0998.2010.02887.x\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=21565091\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-33-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-33\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.33\u0022 data-doi=\u002210.1371\/journal.pone.0037135\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EPeterson\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EB.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EWeber\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EKay\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EE.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EFisher\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EH.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EHoekstra\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EH.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2012\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EDouble digest RADseq: an inexpensive method for de novo SNP discovery and genotyping in model and non-model species.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EPLoS One\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E7\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003Ee37135\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.stitle%253DPLoS%2BONE%26rft.aulast%253DPeterson%26rft.auinit1%253DB.%2BK.%26rft.volume%253D7%26rft.issue%253D5%26rft.spage%253De37135%26rft.epage%253De37135%26rft.atitle%253DDouble%2Bdigest%2BRADseq%253A%2Ban%2Binexpensive%2Bmethod%2Bfor%2Bde%2Bnovo%2BSNP%2Bdiscovery%2Band%2Bgenotyping%2Bin%2Bmodel%2Band%2Bnon-model%2Bspecies.%26rft_id%253Dinfo%253Adoi%252F10.1371%252Fjournal.pone.0037135%26rft_id%253Dinfo%253Apmid%252F22675423%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1371\/journal.pone.0037135\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=22675423\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-34-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-34\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.34\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EPolanowski\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. M.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ERobbins\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EChandler\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ED.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EJarman\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ES. N.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2014\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EEpigenetic estimation of age in humpback whales.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EMol. Ecol. Resour.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E14\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E976\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E987\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DMol.%2BEcol.%2BResour.%26rft.volume%253D14%26rft.spage%253D976%26rft_id%253Dinfo%253Apmid%252F24606053%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=24606053\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-35-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-35\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.35\u0022 data-doi=\u002210.2307\/2409206\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EQueller\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ED. C.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EGoodnight\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EK. F.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E1989\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EEstimating relatedness using genetic-markers.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EEvolution\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E43\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E258\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E275\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DEvolution%26rft.volume%253D43%26rft.spage%253D258%26rft_id%253Dinfo%253Adoi%252F10.2307%252F2409206%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.2307\/2409206\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=A1989T799700002\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-36-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-36\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.36\u0022 data-doi=\u002210.1093\/bioinformatics\/btp064\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ERiester\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EStadler\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EP. F.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EKlemm\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EK.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2009\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EFRANz: reconstruction of wild multi-generation pedigrees.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EBioinformatics\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E25\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E2134\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E2139\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DBioinformatics%26rft_id%253Dinfo%253Adoi%252F10.1093%252Fbioinformatics%252Fbtp064%26rft_id%253Dinfo%253Apmid%252F19202194%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6NzoiYmlvaW5mbyI7czo1OiJyZXNpZCI7czoxMDoiMjUvMTYvMjEzNCI7czo0OiJhdG9tIjtzOjE4OiIvZ2dnLzUvOS8xODE1LmF0b20iO31zOjg6ImZyYWdtZW50IjtzOjA6IiI7fQ==\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003Cspan class=\u0022cit-sep cit-reflinks-variant-name-sep\u0022\u003E\/\u003C\/span\u003E\u003Cspan class=\u0022cit-reflinks-full-text\u0022\u003E\u003Cspan class=\u0022free-full-text\u0022\u003EFREE \u003C\/span\u003EFull Text\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-37-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-37\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.37\u0022 data-doi=\u002210.1002\/elps.200500671\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ESanchez\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ. J.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EPhillips\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EC.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EB\u00f8rsting\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EC.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBalogh\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EK.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBogus\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-etal\u0022\u003Eet al.\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2006\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EA multiplex assay with 52 single nucleotide polymorphisms for human identification.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EElectrophoresis\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E27\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E1713\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E1724\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DElectrophoresis%26rft.stitle%253DElectrophoresis%26rft.aulast%253DSanchez%26rft.auinit1%253DJ.%2BJ.%26rft.volume%253D27%26rft.issue%253D9%26rft.spage%253D1713%26rft.epage%253D1724%26rft.atitle%253DA%2Bmultiplex%2Bassay%2Bwith%2B52%2Bsingle%2Bnucleotide%2Bpolymorphisms%2Bfor%2Bhuman%2Bidentification.%26rft_id%253Dinfo%253Adoi%252F10.1002%252Felps.200500671%26rft_id%253Dinfo%253Apmid%252F16586411%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1002\/elps.200500671\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=16586411\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000237685600004\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-38-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-38\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.38\u0022 data-doi=\u002210.1111\/j.1365-294X.2010.04554.x\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ESanture\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. W.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EStapley\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBall\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. D.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBirkhead\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ET. R.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBurke\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ET.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-etal\u0022\u003Eet al.\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2010\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EOn the use of large marker panels to estimate inbreeding and relatedness: empirical and simulation studies of a pedigreed zebra finch population typed at 771 SNPs.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EMol. Ecol.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E19\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E1439\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E1451\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DMolecular%2BEcology%2B%2528Print%2529%26rft.stitle%253DMolecular%2BEcology%2B%2528Print%2529%26rft.aulast%253DSanture%26rft.auinit1%253DA.%2BW.%26rft.volume%253D19%26rft.issue%253D7%26rft.spage%253D1439%26rft.epage%253D1451%26rft.atitle%253DOn%2Bthe%2Buse%2Bof%2Blarge%2Bmarker%2Bpanels%2Bto%2Bestimate%2Binbreeding%2Band%2Brelatedness%253A%2Bempirical%2Band%2Bsimulation%2Bstudies%2Bof%2Ba%2Bpedigreed%2Bzebra%2Bfinch%2Bpopulation%2Btyped%2Bat%2B771%2BSNPs.%26rft_id%253Dinfo%253Adoi%252F10.1111%252Fj.1365-294X.2010.04554.x%26rft_id%253Dinfo%253Apmid%252F20149098%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1111\/j.1365-294X.2010.04554.x\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=20149098\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000275761300016\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-39-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-39\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.39\u0022 data-doi=\u002210.1111\/j.1755-0998.2010.02833.x\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ESkaug\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EH. J.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBerube\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EPalsb\u00f8ll\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EP. J.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2010\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EDetecting dyads of related individuals in large collections of DNA-profiles by controlling the false discovery rate.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EMol. Ecol. Resour.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E10\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E693\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E700\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DMol.%2BEcol.%2BResour.%26rft.volume%253D10%26rft.spage%253D693%26rft_id%253Dinfo%253Adoi%252F10.1111%252Fj.1755-0998.2010.02833.x%26rft_id%253Dinfo%253Apmid%252F21565074%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1111\/j.1755-0998.2010.02833.x\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=21565074\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-40-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-40\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.40\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ESpeed\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ED.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EBalding\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ED. J.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2015\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003ERelatedness in the post-genomic era: is it still useful?\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003ENat. Rev. Genet.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E16\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E33\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E44\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DNat.%2BRev.%2BGenet.%26rft.volume%253D16%26rft.spage%253D33%26rft_id%253Dinfo%253Apmid%252F25404112%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=25404112\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-41-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-41\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.41\u0022 data-doi=\u002210.1007\/s10592-015-0709-1\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ETaylor\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EH.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EKardos\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ERamstad\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EK.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EAllendorf\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EF.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2015\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EValid estimates of individual inbreeding coefficients from marker-based pedigrees are not feasible in wild populations with low allelic diversity.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EConserv. Genet.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E16\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E901\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E913\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DConserv.%2BGenet.%26rft.volume%253D16%26rft.spage%253D901%26rft_id%253Dinfo%253Adoi%252F10.1007%252Fs10592-015-0709-1%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1007\/s10592-015-0709-1\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-42-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-42\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.42\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EThomas\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ES.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EHill\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EW.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2000\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EEstimating quantitative genetic parameters using sibships reconstructed from marker data.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EGenetics\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E155\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E1961\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E1972\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DGenetics%26rft.stitle%253DGenetics%26rft.aulast%253DThomas%26rft.auinit1%253DS.%2BC.%26rft.volume%253D155%26rft.issue%253D4%26rft.spage%253D1961%26rft.epage%253D1972%26rft.atitle%253DEstimating%2BQuantitative%2BGenetic%2BParameters%2BUsing%2BSibships%2BReconstructed%2BFrom%2BMarker%2BData%26rft_id%253Dinfo%253Apmid%252F10924488%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6ODoiZ2VuZXRpY3MiO3M6NToicmVzaWQiO3M6MTA6IjE1NS80LzE5NjEiO3M6NDoiYXRvbSI7czoxODoiL2dnZy81LzkvMTgxNS5hdG9tIjt9czo4OiJmcmFnbWVudCI7czowOiIiO30=\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003Cspan class=\u0022cit-sep cit-reflinks-variant-name-sep\u0022\u003E\/\u003C\/span\u003E\u003Cspan class=\u0022cit-reflinks-full-text\u0022\u003E\u003Cspan class=\u0022free-full-text\u0022\u003EFREE \u003C\/span\u003EFull Text\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-43-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-43\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-book\u0022 id=\u0022cit-5.9.1815.43\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EThompson\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EE.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E1991\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EEstimation of Relationships from Genetic Data\u003C\/span\u003E, pp. \u003Cspan class=\u0022cit-fpage\u0022\u003E255\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E269\u003C\/span\u003E in \u003Cspan class=\u0022cit-source\u0022\u003EHandbook of Statistics\u003C\/span\u003E, edited by \u003Cspan class=\u0022cit-ed\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ERao\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EC.\u003C\/span\u003E\u003C\/span\u003E, \u003Cspan class=\u0022cit-ed\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EChakrabort\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ER.\u003C\/span\u003E\u003C\/span\u003E. \u003Cspan class=\u0022cit-publ-name\u0022\u003EElsevier Science, Amsterdam\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-44-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-44\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.44\u0022 data-doi=\u002210.1111\/j.1469-1809.1975.tb00120.x\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EThompson\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EE. A.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E1975\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EThe estimation of pairwise relationships.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EAnn. Hum. Genet.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E39\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E173\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E188\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DAnnals%2Bof%2Bhuman%2Bgenetics%26rft.stitle%253DAnn%2BHum%2BGenet%26rft.aulast%253DThompson%26rft.auinit1%253DE.%2BA.%26rft.volume%253D39%26rft.issue%253D2%26rft.spage%253D173%26rft.epage%253D188%26rft.atitle%253DThe%2Bestimation%2Bof%2Bpairwise%2Brelationships.%26rft_id%253Dinfo%253Adoi%252F10.1111%252Fj.1469-1809.1975.tb00120.x%26rft_id%253Dinfo%253Apmid%252F1052764%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1111\/j.1469-1809.1975.tb00120.x\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=1052764\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=A1975AX72600006\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-45-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-45\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.45\u0022 data-doi=\u002210.1051\/gse:2002009\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EVignal\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EMilan\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003ED.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ESanCristobal\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EM.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EEggen\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2002\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EA review on SNP and other types of molecular markers and their use in animal genetics.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EGenet. Sel. Evol.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E34\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E275\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E305\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DGenetics%252C%2Bselection%252C%2Bevolution.%2B%253A%2B%2BGSE%26rft.stitle%253DGenet%2BSel%2BEvol%26rft.aulast%253DVignal%26rft.auinit1%253DA.%26rft.volume%253D34%26rft.issue%253D3%26rft.spage%253D275%26rft.epage%253D305%26rft.atitle%253DA%2Breview%2Bon%2BSNP%2Band%2Bother%2Btypes%2Bof%2Bmolecular%2Bmarkers%2Band%2Btheir%2Buse%2Bin%2Banimal%2Bgenetics.%26rft_id%253Dinfo%253Adoi%252F10.1051%252Fgse%253A2002009%26rft_id%253Dinfo%253Apmid%252F12081799%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1051\/gse:2002009\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=12081799\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000176561700001\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-46-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-46\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.46\u0022 data-doi=\u002210.1534\/genetics.166.4.1963\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EWang\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2004\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003ESibship reconstruction from genetic data with typing errors.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EGenetics\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E166\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E1963\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E1979\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DGenetics%26rft.stitle%253DGenetics%26rft.aulast%253DWang%26rft.auinit1%253DJ.%26rft.volume%253D166%26rft.issue%253D4%26rft.spage%253D1963%26rft.epage%253D1979%26rft.atitle%253DSibship%2BReconstruction%2BFrom%2BGenetic%2BData%2BWith%2BTyping%2BErrors%26rft_id%253Dinfo%253Adoi%252F10.1534%252Fgenetics.166.4.1963%26rft_id%253Dinfo%253Apmid%252F15126412%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6ODoiZ2VuZXRpY3MiO3M6NToicmVzaWQiO3M6MTA6IjE2Ni80LzE5NjMiO3M6NDoiYXRvbSI7czoxODoiL2dnZy81LzkvMTgxNS5hdG9tIjt9czo4OiJmcmFnbWVudCI7czowOiIiO30=\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003Cspan class=\u0022cit-sep cit-reflinks-variant-name-sep\u0022\u003E\/\u003C\/span\u003E\u003Cspan class=\u0022cit-reflinks-full-text\u0022\u003E\u003Cspan class=\u0022free-full-text\u0022\u003EFREE \u003C\/span\u003EFull Text\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-47-2\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-47\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.47\u0022 data-doi=\u002210.1016\/j.tpb.2005.11.003\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EWang\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2006\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EInformativeness of genetic markers for pairwise relationship and relatedness inference.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003ETheor. Popul. Biol.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E70\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E300\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E321\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DTheoretical%2Bpopulation%2Bbiology%26rft.stitle%253DTheor%2BPopul%2BBiol%26rft.aulast%253DSansone%26rft.auinit1%253DE.%26rft.volume%253D70%26rft.issue%253D3%26rft.spage%253D300%26rft.epage%253D321%26rft.atitle%253DInformativeness%2Bof%2Bgenetic%2Bmarkers%2Bfor%2Bpairwise%2Brelationship%2Band%2Brelatedness%2Binference.%26rft_id%253Dinfo%253Adoi%252F10.1016%252Fj.tpb.2005.11.003%26rft_id%253Dinfo%253Apmid%252F16388833%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1016\/j.tpb.2005.11.003\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=16388833\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-48-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-48\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.48\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EWang\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2007\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003ETriadic IBD coefficients and applications to estimating pairwise relatedness.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EGenet. Res.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E89\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E135\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E153\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DGenetical%2Bresearch%26rft.stitle%253DGenet%2BRes%26rft.aulast%253DWang%26rft.auinit1%253DJ.%26rft.volume%253D89%26rft.issue%253D3%26rft.spage%253D135%26rft.epage%253D153%26rft.atitle%253DTriadic%2BIBD%2Bcoefficients%2Band%2Bapplications%2Bto%2Bestimating%2Bpairwise%2Brelatedness.%26rft_id%253Dinfo%253Apmid%252F17894908%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=17894908\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000250908100002\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-49-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-49\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.49\u0022 data-doi=\u002210.1111\/1755-0998.12106\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EWang\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2013\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EA simulation module in the computer program colony for sibship and parentage analysis.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EMol. Ecol. Resour.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E13\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E734\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E739\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DMol.%2BEcol.%2BResour.%26rft.volume%253D13%26rft.spage%253D734%26rft_id%253Dinfo%253Adoi%252F10.1111%252F1755-0998.12106%26rft_id%253Dinfo%253Apmid%252F23615269%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1111\/1755-0998.12106\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=23615269\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-50-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-50\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.50\u0022 data-doi=\u002210.1111\/mec.12806\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EWang\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2014\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EEstimation of migration rates from marker-based parentage analysis.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EMol. Ecol.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E23\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E3191\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E3213\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DMol.%2BEcol.%26rft.volume%253D23%26rft.spage%253D3191%26rft_id%253Dinfo%253Adoi%252F10.1111%252Fmec.12806%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1111\/mec.12806\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-51-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-51\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.51\u0022 data-doi=\u002210.1534\/genetics.108.100214\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EWang\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EJ.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003ESanture\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. W.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2009\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EParentage and sibship inference from multilocus genotype data under polygamy.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003EGenetics\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E181\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E1579\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E1594\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DGenetics%26rft_id%253Dinfo%253Adoi%252F10.1534%252Fgenetics.108.100214%26rft_id%253Dinfo%253Apmid%252F19221199%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/ijlink\/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6ODoiZ2VuZXRpY3MiO3M6NToicmVzaWQiO3M6MTA6IjE4MS80LzE1NzkiO3M6NDoiYXRvbSI7czoxODoiL2dnZy81LzkvMTgxNS5hdG9tIjt9czo4OiJmcmFnbWVudCI7czowOiIiO30=\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-ijlink\u0022\u003E\u003Cspan\u003E\u003Cspan class=\u0022cit-reflinks-abstract\u0022\u003EAbstract\u003C\/span\u003E\u003Cspan class=\u0022cit-sep cit-reflinks-variant-name-sep\u0022\u003E\/\u003C\/span\u003E\u003Cspan class=\u0022cit-reflinks-full-text\u0022\u003E\u003Cspan class=\u0022free-full-text\u0022\u003EFREE \u003C\/span\u003EFull Text\u003C\/span\u003E\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022ref-label ref-label-empty\u0022\u003E\u003C\/span\u003E\u003Ca class=\u0022rev-xref-ref\u0022 href=\u0022#xref-ref-52-1\u0022 title=\u0022View reference in text\u0022 id=\u0022ref-52\u0022\u003E\u21b5\u003C\/a\u003E\u003Cdiv class=\u0022cit ref-cit ref-journal\u0022 id=\u0022cit-5.9.1815.52\u0022 data-doi=\u002210.1038\/nrg1960\u0022\u003E\u003Cdiv class=\u0022cit-metadata\u0022\u003E\u003Col class=\u0022cit-auth-list\u0022\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EWeir\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EB. S.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EAnderson\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. D.\u003C\/span\u003E\u003C\/span\u003E, \u003C\/li\u003E\u003Cli\u003E\u003Cspan class=\u0022cit-auth\u0022\u003E\u003Cspan class=\u0022cit-name-surname\u0022\u003EHepler\u003C\/span\u003E \u003Cspan class=\u0022cit-name-given-names\u0022\u003EA. B.\u003C\/span\u003E\u003C\/span\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003Ccite\u003E, \u003Cspan class=\u0022cit-pub-date\u0022\u003E2006\u003C\/span\u003E\u2003\u003Cspan class=\u0022cit-article-title\u0022\u003EGenetic relatedness analysis: modern data and new challenges.\u003C\/span\u003E \u003Cabbr class=\u0022cit-jnl-abbrev\u0022\u003ENat. Rev. Genet.\u003C\/abbr\u003E \u003Cspan class=\u0022cit-vol\u0022\u003E7\u003C\/span\u003E: \u003Cspan class=\u0022cit-fpage\u0022\u003E771\u003C\/span\u003E\u2013\u003Cspan class=\u0022cit-lpage\u0022\u003E780\u003C\/span\u003E.\u003C\/cite\u003E\u003C\/div\u003E\u003Cdiv class=\u0022cit-extra\u0022\u003E\u003Ca href=\u0022{openurl}?query=rft.jtitle%253DNature%2Breviews.%2BGenetics%26rft.stitle%253DNat%2BRev%2BGenet%26rft.aulast%253DWeir%26rft.auinit1%253DB.%2BS.%26rft.volume%253D7%26rft.issue%253D10%26rft.spage%253D771%26rft.epage%253D780%26rft.atitle%253DGenetic%2Brelatedness%2Banalysis%253A%2Bmodern%2Bdata%2Band%2Bnew%2Bchallenges.%26rft_id%253Dinfo%253Adoi%252F10.1038%252Fnrg1960%26rft_id%253Dinfo%253Apmid%252F16983373%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-openurl cit-ref-sprinkles-open-url\u0022\u003E\u003Cspan\u003EOpenUrl\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=10.1038\/nrg1960\u0026amp;link_type=DOI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-doi cit-ref-sprinkles-crossref\u0022\u003E\u003Cspan\u003ECrossRef\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=16983373\u0026amp;link_type=MED\u0026amp;atom=%2Fggg%2F5%2F9%2F1815.atom\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-medline\u0022\u003E\u003Cspan\u003EPubMed\u003C\/span\u003E\u003C\/a\u003E\u003Ca href=\u0022\/lookup\/external-ref?access_num=000241158700013\u0026amp;link_type=ISI\u0022 class=\u0022cit-ref-sprinkles cit-ref-sprinkles-newisilink cit-ref-sprinkles-webofscience\u0022\u003E\u003Cspan\u003EWeb of Science\u003C\/span\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/div\u003E\u003C\/li\u003E\u003C\/ol\u003E\u003C\/div\u003E\u003Cspan class=\u0022highwire-journal-article-marker-end\u0022\u003E\u003C\/span\u003E\u003C\/div\u003E\u003Cspan id=\u0022related-urls\u0022\u003E\u003C\/span\u003E\u003C\/div\u003E\u003Ca href=\u0022https:\/\/www.g3journal.org\/content\/5\/9\/1815.abstract\u0022 class=\u0022hw-link hw-link-article-abstract\u0022 data-icon-position=\u0022\u0022 data-hide-link-title=\u00220\u0022\u003EView Abstract\u003C\/a\u003E\u003C\/div\u003E \u003C\/div\u003E\n\n \n \u003C\/div\u003E\n\u003C\/div\u003E\n \u003C\/div\u003E\n\u003C\/div\u003E\n\u003C\/div\u003E\u003Cscript type=\u0022text\/javascript\u0022 src=\u0022https:\/\/www.g3journal.org\/sites\/default\/files\/js\/js_8GIykOophmDZWQSVemuR9p9M6vwIgWI3Rnd13-Cgx2E.js\u0022\u003E\u003C\/script\u003E\n\u003C\/body\u003E\u003C\/html\u003E"}
|
__label__pos
| 0.88586 |
Coordinate generalizzate
Da Wikipedia, l'enciclopedia libera.
(Reindirizzamento da Coordinate lagrangiane)
bussola Disambiguazione – Se stai cercando altri significati, vedi Coordinate euleriane e lagrangiane.
In meccanica lagrangiana un sistema di coordinate generalizzate (o lagrangiane) è un sistema di coordinate, di numero pari o superiore ai gradi di libertà del sistema, che determina univocamente lo stato del sistema.
Definizione[modifica | modifica wikitesto]
Dato un sistema meccanico con I gradi di libertà e un qualunque sistema di coordinate, per esempio cartesiane, nel quale lo stato del sistema è indicato dal vettore \bar x=(x_d), con m\ge n, è possibile esprimere ogni variabile x_d in funzione del vettore \bar r=(r_i). Ogni r_i è detta variabile generalizzata:
\begin{cases} x_1 = \phi (r_1, \dots, r_I)\\
x_2 = \phi (r_1, \dots , r_I) \\
\dots \; \; \dots \\
x_D = \phi (r_1, \dots , r_I)
\end{cases}
dove \bar r = (r_i) \in A \subset \mathbb{R}^n con A aperto, e \bar \phi : A \longrightarrow \mathbb{R}^m è una funzione regolare. Queste devono costituire necessariamente un insieme di generatori dello spazio vettoriale I-dimensionale degli stati del sistema, mentre non è necessario che siano linearmente indipendenti. Ciò non è vero ad esempio in presenza di vincoli che legano tra di loro alcune tra le x_i. Le coordinate generalizzate possono quindi anche essere rappresentate da grandezze diverse da posizioni o angoli, per esempio dall'energia meccanica o dal volume del sistema.
Esempi[modifica | modifica wikitesto]
Un sistema di N particelle nello spazio D-dimensionale può avere fino a N D gradi di libertà, e quindi coordinate generalizzate (una per ogni dimensione del moto di ciascuna particella). Un sistema di N corpi rigidi può avere fino a 6N coordinate generalizzate nello spazio tridimensionale, includendo 3 assi di rotazione per ogni corpo. Il numero di gradi di libertà effettivi si riduce in seguito all'introduzione di vincoli tra le posizioni delle particelle (vincoli olonomi) e le velocità (vincoli anolonomi). Ad esempio un sistema formato da due particelle puntiformi nello spazio 3D ha 6 gradi di libertà (3 per ogni coordinata cartesiana di ciascuna particella), ma con l'introduzione di un vincolo, come la condizione che le particelle rimangano a distanza fissata l'una dall'altra, riduce a 5 i gradi di libertà (6 coordinate - 1 vincolo). Una scelta conveniente delle variabili lagrangiane consiste in questo caso nell'usarne tre per localizzare il centro di massa del sistema e le rimanenti due per determinare l'orientazione nello spazio della retta che congiunge le due particelle: in questo modo abbiamo 5 coordinate indipendenti tra loro.
Un corpo costretto a spostarsi lungo un vincolo unidimensionale (es. una curva regolare \phi(t), \phi:\mathbb{R} \longrightarrow \mathbb{R}^3) ha solo un grado di libertà, e la coordinata generalizzata usata il più delle volte per descriverne il moto è l'ascissa curvilinea q=t, cioè la variabile che parametrizza la curva. Da notare che un moto nelle tre dimensioni è stato ridotto ad una dimensione.
Analogamente un corpo vincolato ad una superficie ha due gradi di libertà, anche se il suo moto è ancora agganciato alle tre dimensioni. Se la superficie è una sfera, una buona scelta di coordinate è \lbrace r_1,r_2\rbrace = \lbrace \theta,\phi \rbrace , dove \theta e \phi sono le coordinate di angolo provenienti dalle coordinate sferiche. La coordinata r è stata soppressa in quanto una particella che si muove su una sfera mantiene una distanza costante dal centro della sfera.
Un doppio pendolo costretto a muoversi su un piano può essere descritto, in un sistema di assi cartesiani (x,y), con l'asse y verticale discendente, da quattro coordinate cartesiane \lbrace x_1,y_1,x_2,y_2\rbrace, ma il sistema ha solo due gradi di libertà, ed un sistema più efficiente potrebbe essere quello di considerare come variabili lagrangiane l'angolo che ciascun pendolo forma con la verticale. Ponendo \lbrace r_1,r_2\rbrace = \lbrace\theta_1,\theta_2 \rbrace otteniamo le seguenti relazioni:
\lbrace x_1, y_1 \rbrace = \lbrace l_1\sin\theta_1, l_1\cos\theta_1 \rbrace
\lbrace x_2, y_2 \rbrace = \lbrace l_1\sin\theta_1 + l_2\sin\theta_2 , l_1\cos\theta_1 + l_2\cos\theta_2 \rbrace
dove l_1 è la lunghezza del pendolo vincolato all'origine e l_2 è la lunghezza del pendolo vincolato all'estremità libera dell'altro.
Velocità generalizzata[modifica | modifica wikitesto]
Exquisite-kfind.png Per approfondire, vedi spazio delle fasi.
Ogni coordinata generalizzata r_i è associata ad una velocità generalizzata \dot r_i, definita come:
\dot r_i \stackrel{\mathrm{\Delta}}{=}{dr_i \over dt}
Nell'ipotesi che le coordinate sono linearmente indipendenti fra loro, esse dipendono solo dal tempo:
\dot r_i={\partial r_i \over \partial t}
Sia dato un sistema di N particelle in D dimensioni, quindi con al massimo ND gradi di libertà. L'n-esima particella ha come coordinata d-esima (X_{nd}), e quindi le posizioni del sistema sono rappresentabili come una matrice X \in R^{N \times D}. Si può passare ad un sistema di riferimento formato da ND coordinate generalizzate se esistono le D+1 equazioni di trasformazione tra le D coordinate cartesiane e le generalizzate:
x_d = x_d \left (r_n, t \right )
Queste equazioni possono infatti essere derivate nel tempo, ottenendo le velocità:
\dot x_d \stackrel{\mathrm{\Delta}}{=} \frac {d}{dt} x_d \left (r_n, t \right )=\sum_{i=1}^{ND}\frac{\partial x_d}{\partial r_i}{\partial r_i \over \partial t}+\frac{\partial x_d}{\partial t} = \sum_{i=1}^{ND}\frac{\partial x_d}{\partial r_i}\dot r_i+\frac{\partial x_d}{\partial t}
e quindi il vettore D-dimensionale velocità è dato da:
\dot {\bar x}_{(\dot {\bar r})} = \nabla \bar x \cdot \dot {\bar r} + \frac{\partial \bar x}{\partial t}
Quantità di moto generalizzata[modifica | modifica wikitesto]
La quantità di moto generalizzata è definita come grandezza corrispondente alle quantità di moto newtoniane:
q_i \stackrel{\mathrm{\Delta}}{=} \sum_{n = 1}^N p_n \frac{\partial \bar x_n}{\partial r_i} = \sum_{n = 1}^N m_n \dot {\bar x}_n \frac{\partial \dot {\bar x}_n}{\partial \dot r_i} = \frac{\partial {\sum_{n = 1}^N \frac{1}{2}m_n \dot {\bar x}_n^2}}{\partial \dot r_i}
Risulta che:
q_i = \frac{\partial T}{\partial \dot r_i}=\sum_{j = 1}^I H_{ij} T_{(\bar 0)} \dot r_j + \nabla_i T_{(\bar 0)}
Quest'ultima equivalenza può essere comprovata utilizzando la dimostrazione delle equazioni di Lagrange. La quantità di moto generalizzata vale dunque:
\bar q_{(\dot {\bar r})} = \bar H T_{(\bar 0)} \cdot \dot {\bar r} + \nabla T_{(\bar 0)}
Si tratta di una forma lineare dell'energia cinetica nelle velocità generalizzate. Per un sistema olonomo, in particolare, risulta:
\bar q_{(\dot {\bar r})} = \bar H T_{(\bar 0)} \cdot \dot {\bar r}
Si deve porre attenzione nel legare quantità di moto generalizzate e forze generalizzate, in quanto le quantità di moto lagrangiane sono in base alle equazioni di Lagrange del I tipo:
q_i = \int F_i - \frac{\partial T}{\partial r_i} dt = p_i - \int \frac{\partial T}{\partial r_i} dt
e differiscono quindi per il secondo termine - \int\frac{\partial T}{\partial r_i} dt dal momento coniugato p_i = \int F_i dt cui si arriverebbe tentando di generalizzare la definizione newtoniana di forza come derivata totale temporale della quantità di moto, cioè il secondo principio della dinamica.
In coordinate cartesiane, la quantità di moto generalizzata ritorna chiaramente la quantità di moto semplice, mentre in coordinate sferiche diventa il momento angolare. In generale però non ne è sempre possibile una interpretazione intuitiva.
Energia cinetica in coordinate generalizzate[modifica | modifica wikitesto]
L'energia cinetica di N particelle è data in meccanica newtoniana D-dimensionale come:
T : \R^{N D} \to \R
T_{(\dot {\bar x})} \stackrel{\mathrm{\Delta}}{=} \frac {1}{2} \sum_{n=1}^{N} m_n \dot {\bar x}_n \cdot \dot {\bar x}_n
Esprimendo gli N vettori posizione newtoniani \bar x_{(\bar r)} (delle particelle rispetto ai D assi cartesiani) in funzione delle I coordinate lagrangiane r_i:
T_{(\dot {\bar r})}=\frac {1}{2} \sum_{n=1}^{N}m_n \left(\frac{\partial \bar x_n}{\partial t} + \sum_{i=1}^{I}\frac{\partial \bar x_n}{\partial r_i}\dot r_i\right)\cdot \left(\frac{\partial \bar x_n}{\partial t} + \sum_{j=1}^{I}\frac{\partial \bar x_n}{\partial r_j}\dot r_j\right) .
Svolgendo e raccogliendo nelle velocità generalizzate \dot r_i:
T_{(\dot {\bar r})}= \frac{1}{2} \sum_{n = 1}^N {m_n} (\frac{\partial \bar x_n}{\partial t})^2+ \sum_{i=1}^{I}\sum_{n = 1}^N {m_n} \frac{(\partial \bar x_n)^2}{\partial r_i \partial t} \dot r_i + \frac{1}{2}\sum_{i, j=1}^{I} \sum_{n = 1}^N {m_n} \frac{(\partial \bar x_n)^2}{\partial r_i \partial r_j} \dot r_i \dot r_j
se :\quad T_{(\bar 0)} \stackrel{\mathrm{\Delta}}{=} \quad \frac{1}{2}\sum_{n = 1}^N {m_n} (\frac{\partial \bar x_n}{\partial t})^2,
\quad \nabla_i T_{(\bar 0)} \stackrel{\mathrm{\Delta}}{=} \quad \frac{\partial}{\partial r_i} \sum_{n = 1}^N m_n \bar x_n \frac{\partial \bar x_n}{\partial t} = \sum_{n = 1}^N {m_n} \frac{(\partial \bar x_n)^2}{\partial r_i \partial t}, \, per sistemi classici in cui la massa non dipende dalle coordinate generalizzate: \nabla m_n = \bar 0, \,
\quad \bar \bar H_{ij} T_{(\bar 0)} \stackrel{\mathrm{\Delta}}{=} \quad \frac{{\partial}^2}{\partial r_i \partial r_j} \sum_{n = 1}^N m_n (\bar x_n)^2 = \sum_{n = 1}^N {m_n} \frac{(\partial \bar x_n)^2}{\partial r_i \partial r_j}, \, per sistemi classici in cui la massa non dipende dalle coordinate generalizzate: \bar \bar H m_n = \bar 0.
Quindi riassumendo vettorialmente l'identità scalare:
T_{(\dot {\bar r})}= T_{(\bar 0)} + \sum_{i=1}^{I}\nabla_i T_{(\bar 0)} \dot r_i + \frac{1}{2}\sum_{i, j=1}^{I} H_{ij} T_{(\bar 0)} \dot r_i \dot r_j
si ottiene infine:
T_{(\dot {\bar r})}= T_{(\bar 0)} + \nabla T_{(\bar 0)} \cdot \dot {\bar r} + \frac{1}{2} \dot {\bar r} \cdot \bar \bar H T_{(\bar 0)} \cdot \dot {\bar r}
T : \R^I \to \R
L'energia cinetica in coordinate lagrangiane è in conclusione una serie di Taylor in I variabili del second'ordine nel vettore velocità \dot {\bar r}, definita positiva poiché lo è l'hessiana H che vi compare. Inoltre i due termini lineare \nabla T_{(\bar 0)} e costante T_{(\bar 0)} dipendono in generale dal tempo: nel caso di un sistema olonomo l'energia cinetica si riduce a
T|_{(\frac{\partial \bar x_n}{\partial t} = 0)} = \frac{1}{2} \dot {\bar r} \cdot \bar \bar H_{\dot {\bar r}}T_{(\bar 0)} \cdot \dot {\bar r} = \frac{1}{2} \bar p \cdot \dot {\bar r}
È importante ricordare che le coordinate lagrangiane rispetto a cui si determina l'energia cinetica hanno l'ulteriore vantaggio di non dovere necessariamente essere inerziali, a differenza di quelle cartesiane.
Forza generalizzata[modifica | modifica wikitesto]
Le forze generalizzate sono definite come in numero di I grandezze scalari, con I il grado di libertà del sistema:
F_i \stackrel{\mathrm{\Delta}}{=} \frac{\partial W}{\partial r_i} = \sum_{n = 1}^N \bar F_n \cdot \frac{\partial \bar x_n}{\partial r_i},
Dove W è il lavoro della risultante attiva F agente sul sistema. Si tratta quindi in termini newtoniani per variabili lunghezza e angolo rispettivamente delle grandezze forza e momento meccanico prese lungo la variabile, nel caso più generale di una combinazione delle due.
Nel caso di vincoli bilaterali permettono di ignorare nell'analisi del sistema le reazioni vincolari (di risultante R), anche per sistemi scleronomi: dato uno spostamento virtuale \delta x_n, ottenuto considerando solo gli spostamenti ammissibili con i vincoli considerati come fissi all'istante di riferimento, il lavoro virtuale agente sull'n-esima particella del sistema vale:
\delta W_n=(\bar F_n+\bar R_n)\cdot \bar \delta \bar x_n
Se i vincoli del sistema sono bilaterali, per il principio delle reazioni vincolari i lavori virtuali vincolari sono nulli, e cioè le reazioni sono ortogonali agli spostamenti virtuali:
\delta W_{i}=F_i\cdot \delta \bar x_i
Esprimendo \delta \bar x_n in funzione delle coordinate generalizzate r_i, e ricordando che \frac{\partial \bar x_n}{\partial t}=0 per definizione di spostamento virtuale:
\delta W_{n}=\sum_{i=1}^I \bar F_n\cdot \frac{\partial \bar x_n}{\partial r_i}\delta r_i=\sum_{i=1}^I F_{n,i} \cdot \delta r_i
Il lavoro virtuale sulla particella sottoposta a vincoli bilaterali è cioè interamente calcolabile tramite le forze generalizzate agenti su di essa. A livello ingegneristico dove è necessario risalire allo sforzo che dovrebbe essere fatto da tutte le forze non vincolari se il sistema subisse uno spostamento virtuale \delta r_h, oppure alle sollecitazioni esterne imposte realmente dai vincoli, l'approccio Lagrangiano risulta quindi particolarmente utile.
In base alle equazioni di Lagrange del I tipo e in forma di Nielsen si può legare la forza generalizzata all'energia cinetica del sistema: F_i = \dot p_i = {\partial{T}\over \partial{\dot r_i}} - 2 {\partial{T}\over \partial r_i}, Si noti ancora che la forza generalizzata differisce in generale per il secondo termine - \frac{\partial T}{\partial r_i} dalla derivata temporale della quantità di moto \dot q_i, cui si arriverebbe erroneamente inducendo una generalizzazione da una definizione di forza basata sul secondo principio della dinamica, valida solo per la dinamica newtoniana.
Bibliografia[modifica | modifica wikitesto]
• Wells, D.A., Schaum's Outline of Lagrangian Dynamics; McGraw-Hill, Inc. New York, 1967.
Voci correlate[modifica | modifica wikitesto]
Collegamenti esterni[modifica | modifica wikitesto]
Meccanica Portale Meccanica: accedi alle voci di Wikipedia che trattano di Meccanica
|
__label__pos
| 0.95494 |
Skip to main content
Theory and Modern Applications
Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function
Abstract
A new family of p-Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help of the Gauss hypergeometric function. Motivated by that paper and in the light of the recent interests in finding degenerate versions, we construct the generalized degenerate Bernoulli numbers and polynomials by means of the Gauss hypergeometric function. In addition, we construct the degenerate type Eulerian numbers as a degenerate version of Eulerian numbers. For the generalized degenerate Bernoulli numbers, we express them in terms of the degenerate Stirling numbers of the second kind, of the degenerate type Eulerian numbers, of the degenerate p-Stirling numbers of the second kind and of an integral on the unit interval. As to the generalized degenerate Bernoulli polynomials, we represent them in terms of the degenerate Stirling polynomials of the second kind.
1 Introduction
We have witnessed in recent years that many interesting arithmetic and combinatorial results were obtained in studying degenerate versions of some special polynomials and numbers (see [713] and the references therein), which was initiated by Carlitz when he introduced the degenerate Stirling, Bernoulli and Euler numbers in [3]. The studies have been done with various different tools such as combinatorial methods, generating functions, umbral calculus, p-adic analysis, differential equations, special functions, probability theory and analytic number theory. It should be noted that studying degenerate versions can be done not only for polynomials but also for transcendental functions. Indeed, the degenerate gamma functions were introduced as a degenerate version of ordinary gamma functions in [9]. The degenerate special polynomials and numbers have potential to find diverse applications in many areas just as ‘ordinary’ special polynomials and numbers play very important role in science and engineering as well as in mathematics. Indeed, it was shown in [10, 11] that the expressions of the probability distributions of appropriate random variables can be represented in terms of both the degenerate λ-Stirling polynomials of the second kind and the r-truncated degenerate λ-Stirling polynomials of the second kind.
In [14], Rahmani introduced a new family of p-Bernoulli numbers and polynomials by means of the Gauss hypergeometric function which reduce to the classical Bernoulli numbers and polynomials for \(p=0\). Motivated by that paper and as a degenerate version of those numbers and polynomials, in this paper we introduce the generalized degenerate Bernoulli numbers and polynomials again in terms of the Gauss hypergeometric function which reduce to the Carlitz degenerate Bernoulli numbers and polynomials for \(p=0\). In addition, we introduce the degenerate type Eulerian numbers as a degenerate version of Eulerian numbers. The aim of this paper is to study the generalized degenerate Bernoulli numbers and polynomials and to show their connections to other special numbers and polynomials. Among other things, for the generalized degenerate Bernoulli numbers we express them in terms of the degenerate Stirling numbers of the second kind, of the degenerate type Eulerian numbers, of the degenerate p-Stirling numbers of the second kind and of an integral on the unit interval. As to the generalized degenerate Bernoulli polynomials, we represent them in terms of the degenerate Stirling polynomials of the second kind. For the rest of this section, we recall the necessary facts that are needed throughout this paper.
For any \(\lambda \in \mathbb{R}\), the degenerate exponential functions are defined by
$$ e_{\lambda }^{x}(t)=\sum_{n=0}^{\infty }(x)_{n,\lambda } \frac{t^{n}}{n!}, e_{\lambda }(t)=e_{\lambda }^{1}(t)\quad ( \text{see [6, 9]}), $$
(1)
where \((x)_{0,\lambda }=1, (x)_{n,\lambda }=x(x-\lambda )\cdots (x-(n-1) \lambda )\) \((n\ge 1)\). Note that \(\lim_{\lambda \rightarrow 0}e^{x}_{\lambda }(t)=e^{xt} \).
Let \(\log _{\lambda }(t)\) be the compositional inverse function of \(e_{\lambda }(t)\) with \(\log _{\lambda } (e_{\lambda }(t) )=e_{\lambda } (\log _{ \lambda }(t) )=t\). Then we have
$$ \log _{\lambda }(1+t)=\sum_{n=1}^{\infty } \lambda ^{n-1}(1)_{n,1/ \lambda }\frac{t^{n}}{n!} \quad(\text{see [7]}). $$
(2)
In [7], the degenerate Stirling numbers of the first kind are defined by
$$ (x)_{n}=\sum_{l=0}^{n}S_{1,\lambda }(n,l) (x)_{l,\lambda } \quad(n\ge 0), $$
(3)
where \((x)_{0}=1, (x)_{n}=x(x-1)(x-2)\cdots (x-n+1)\) \((n\ge 1)\).
As the inversion formula of (3), the degenerate Stirling numbers of the second kind are defined by
$$ (x)_{n,\lambda }=\sum_{k=0}^{n}S_{2,\lambda }(n,k) (x)_{k} \quad(n\ge 0)\ (\text{see [7]}). $$
(4)
From (3) and (4), we note that
$$ \frac{1}{k!} \bigl(\log _{\lambda }(1+t) \bigr)^{k}=\sum _{n=k}^{\infty }S_{1, \lambda }(n,k) \frac{t^{n}}{n!}, $$
(5)
and
$$ \frac{1}{k!} \bigl(e_{\lambda }(t)-1 \bigr)^{k}=\sum _{n=k}^{\infty }S_{2, \lambda }(n,k) \frac{t^{n}}{n!} \quad(k\ge 0)\ (\text{see [7]}). $$
(6)
It is well known that the Gauss hypergeometric function is given by
F 1 2 ( a , b c | x ) = k = 0 a k b k c k x k k ! (see [1, 2, 12]),
(7)
where \(\langle a\rangle _{0}=1, \langle a\rangle _{k}=a(a+1)\cdots (a+k-1), (k\ge 1)\).
The Euler transformation formula is given by
F 1 2 ( a , b c | x ) = ( 1 x ) c a b 2 F 1 ( c a , c b c | x ) (see [1, 2]).
(8)
The Eulerian number n k is the number of permutation \(\{1,2,3,\dots,n\}\) having k permutation ascents. The Eulerian numbers are given explicitly by the finite sum
n k = j = 0 k + 1 ( 1 ) j ( n + 1 j ) ( k j + 1 ) n (n,k0,nk)
(9)
and
k = 0 n n k =n!(see [4, 5]).
(10)
For \(n,m\ge 0\), we have
n m = k = 0 n m S 2 (n,k) ( n k m ) ( 1 ) n k m k!(see [5])
(11)
and
x n = k = 0 n n k ( x + k n ) (see [4, 5]).
(12)
Recently, the degenerate Stirling polynomials of the second kind were defined by
$$ \frac{1}{k!} \bigl(e_{\lambda }(t)-1 \bigr)^{k}e_{\lambda }^{x}(t)= \sum_{n=k}^{ \infty }S_{2,\lambda }(n,k|x) \frac{t^{n}}{n!} (k\ge 0)\quad (\text{see [8]}). $$
(13)
Thus, by (13), we get
$$\begin{aligned} S_{2,\lambda }(n,k|x) &= \sum_{l=k}^{n} \binom{n}{l}S_{2,\lambda }(l,k) (x)_{n-l, \lambda } \quad(\text{see [8]}) \\ &= \sum_{l=0}^{n}\binom{n}{l}S_{2,\lambda }(l,k) (x)_{n-l,\lambda } \quad(n\ge 0). \end{aligned}$$
(14)
For \(x=0\), \(S_{2,\lambda }(n,k)=S_{2,\lambda }(n,k|0)\) \((n,k\ge 0, n\ge k)\), are called the degenerate Stirling numbers of the second kind.
Carlitz introduced the degenerate Bernoulli polynomials given by
$$ \frac{t}{e_{\lambda }(t)-1}e_{\lambda }^{x}(t)=\sum _{n=0}^{\infty } \beta _{n,\lambda }(x)\frac{t^{n}}{n!}\quad (\text{see [3]}). $$
(15)
When \(x=0\), \(\beta _{n,\lambda }=\beta _{n,\lambda }(0)\) \((n\ge 0)\), are called the degenerate Bernolli numbers.
2 Generalized degenerate Bernoulli numbers
By (1) and (2), we get
$$\begin{aligned} \frac{t}{e_{\lambda }(t)-1} &= \frac{1}{e_{\lambda }(t)-1}\sum_{n=1}^{ \infty } \lambda ^{n-1}(1)_{n,1/\lambda }\frac{1}{n!} \bigl(e_{\lambda }(t)-1 \bigr)^{n} \\ &= \sum_{k=0}^{\infty }\frac{\lambda ^{k}(1)_{k+1,1/\lambda }}{k+1} \cdot \frac{1}{k!} \bigl(e_{\lambda }(t)-1 \bigr)^{k} \\ &= \sum_{k=0}^{\infty }\frac{\lambda ^{k}(1)_{k+1,1/\lambda }}{k+1} \sum _{n=k}^{\infty }S_{2,\lambda }(n,k) \frac{t^{n}}{n!} \\ &= \sum_{n=0}^{\infty } \Biggl(\sum _{k=0}^{n} \frac{\lambda ^{k}(1)_{k+1,1/\lambda }}{k+1}S_{2,\lambda }(n,k) \Biggr) \frac{t^{n}}{n!}. \end{aligned}$$
(16)
Therefore, by (15) and (16), we obtain the following theorem.
Theorem 1
For \(n\ge 0\), we have
$$\beta _{n,\lambda }=\sum_{k=0}^{n} \frac{\lambda ^{k}(1)_{k+1,1/\lambda }}{k+1}S_{2,\lambda }(n,k). $$
Replacing t by \(\log _{\lambda }(1+t)\) in (15), we get
$$\begin{aligned} \frac{\log _{\lambda }(1+t)}{e_{\lambda }(\log _{\lambda }(1+t))-1} &= \sum_{k=0}^{\infty }\beta _{k,\lambda }\frac{1}{k!} \bigl(\log _{ \lambda }(1+t) \bigr)^{k} \\ &= \sum_{k=0}^{\infty }\beta _{k,\lambda }\sum _{n=k}^{\infty }S_{1, \lambda }(n,k) \frac{t^{n}}{n!} \\ &= \sum_{n=0}^{\infty } \Biggl(\sum _{k=0}^{n}S_{1,\lambda }(n,k)\beta _{k, \lambda } \Biggr)\frac{t^{n}}{n!}. \end{aligned}$$
(17)
On the other hand, by (2), we get
$$\begin{aligned} \frac{\log _{\lambda }(1+t)}{e_{\lambda }(\log _{\lambda }(1+t))-1} &= \frac{1}{t}\log _{\lambda }(1+t) = \frac{1}{t}\sum_{n=1}^{\infty } \lambda ^{n-1}(1)_{n,1/\lambda }\frac{t^{n}}{n!} \\ &= \sum_{n=0}^{\infty }\frac{\lambda ^{n}(1)_{n+1,1/\lambda }}{n+1} \frac{t^{n}}{n!}. \end{aligned}$$
(18)
Therefore, by (17) and (18), we obtain the following theorem.
Theorem 2
For \(n\ge 0\), we have
$$\sum_{k=0}^{n}S_{1,\lambda }(n,k)\beta _{k,\lambda }=\frac{1}{n+1} \lambda ^{n}(1)_{n+1,1/\lambda }. $$
From (15) and (16), we note that
n = 0 β n , λ t n n ! = 1 e λ ( t ) 1 n = 1 λ n 1 ( 1 ) n , 1 / λ 1 n ! ( e λ ( t ) 1 ) n = n = 0 ( 1 ) n ( 1 ) n + 1 , 1 / λ λ n n ! ( n + 1 ) ! ( 1 e λ ( t ) ) n n ! = n = 0 1 λ n 1 n 2 n ( 1 e λ ( t ) ) n n ! = 2 F 1 ( 1 λ , 1 2 | 1 e λ ( t ) ) .
(19)
In view of (19), we may consider the generalized degenerate Bernoulli numbers given in terms of Gauss hypergeometric function by
F 1 2 ( 1 λ , 1 p + 2 | 1 e λ ( t ) ) = n = 0 β n , λ ( p ) t n n ! ,
(20)
where \(p\in \mathbb{Z}\) with \(p\ge -1\). When \(p=0\), \(\beta _{n,\lambda }^{(0)}=\beta _{n,\lambda }, (n\ge 0)\).
Let us take \(p=-1\) in (20). Then we have
n = 0 β n , λ ( 1 ) t n n ! = 2 F 1 ( 1 λ , 1 1 | 1 e λ ( t ) ) = n = 0 ( λ 1 ) n n ! ( e λ ( t ) 1 ) n = n = 0 ( λ 1 n ) ( e λ ( t ) 1 ) n = e λ λ 1 ( t ) = n = 0 ( λ 1 ) n , λ t n n ! .
(21)
By comparing the coefficients on both sides of (21), we get
$$ \beta _{n,\lambda }^{(-1)}=(\lambda -1)_{n,\lambda } \quad(n\ge 0). $$
(22)
From (20), we note that
n = 0 β n , λ ( p ) t n n ! = 2 F 1 ( 1 λ , 1 p + 2 | 1 e λ ( t ) ) = k = 0 1 λ k 1 k p + 2 k ( 1 e λ ( t ) ) k k ! = ( p + 1 ) ! k = 0 λ k ( 1 ) k + 1 , 1 / λ k ! ( p + k + 1 ) ! 1 k ! ( e λ ( t ) 1 ) k = ( p + 1 ) ! k = 0 λ k ( 1 ) k + 1 , 1 / λ k ! ( p + k + 1 ) ! n = k S 2 , λ ( n , k ) t n n ! = n = 0 ( k = 0 n λ k ( 1 ) k + 1 , 1 / λ ( p + k + 1 p + 1 ) S 2 , λ ( n , k ) ) t n n ! .
(23)
Therefore, by comparing the coefficients on both sides of (23), we obtain the following theorem.
Theorem 3
For \(n\ge 0\) and \(p\ge -1\), we have
β n , λ ( p ) = k = 0 n λ k ( 1 ) k + 1 , 1 / λ ( p + k + 1 p + 1 ) S 2 , λ (n,k).
From (6), we get
$$\begin{aligned} \sum_{n=k}^{\infty }S_{2,\lambda }(n,k) \frac{t^{n}}{n!} &= \frac{1}{k!} \bigl(e_{\lambda }(t)-1 \bigr)^{k} = \frac{1}{k!}\sum_{l=0}^{k} \binom{k}{l}(-1)^{k-l}e_{\lambda }^{l}(t) \\ &= \sum_{n=0}^{\infty } \Biggl(\frac{1}{k!} \sum_{l=0}^{k}\binom{k}{l}(-1)^{k-l}(l)_{n, \lambda } \Biggr)\frac{t^{n}}{n!}. \end{aligned}$$
(24)
By (24), we get
$$ \sum_{l=0}^{k}\binom{k}{l}(-1)^{k-l}(l)_{n,\lambda }= \textstyle\begin{cases} k!S_{2,\lambda }(n,k) & \text{if $n\ge k$}, \\ 0 & \text{otherwise.} \end{cases} $$
(25)
Let be a difference operator with \(\triangle f(x)=f(x+1)-f(x)\). Then we have
$$\triangle ^{n}f(x)=\sum_{k=0}^{n} \binom{n}{k}(-1)^{n-k}f(x+k). $$
From (25), we have
$$ k!S_{2,\lambda }(n,k)=\triangle ^{k}(0)_{n,\lambda } \quad(n,k\ge 0, n \ge k). $$
(26)
In the light of (11), we may consider the degenerate type Eulerian numbers given by
( 1 ) n m n m λ = k = 0 n m λ k ( 1 ) k + 1 , 1 / λ ( n k m ) k ( 0 ) n , λ k ! .
(27)
By (26) and (27), we get
( 1 ) n m n m λ = k = 0 n m λ k ( 1 ) k + 1 , 1 / λ ( n k m ) S 2 , λ (n,k).
(28)
We observe that
k = 0 n λ k ( 1 ) k + 1 , 1 / λ S 2 , λ ( n , k ) ( t + 1 ) n k = k = 0 n λ k ( 1 ) k + 1 , 1 / λ S 2 , λ ( n , k ) m = 0 n k ( n k m ) t m = m = 0 n ( k = 0 n m λ k ( 1 ) k + 1 , 1 / λ S 2 , λ ( n , k ) ( n k m ) ) t m = m = 0 n ( 1 ) n m n m λ t m .
(29)
From (29) and Theorem 3, we note that
β n , λ ( p ) = k = 0 n λ k ( 1 ) k + 1 , 1 / λ ( p + k + 1 k ) 1 S 2 , λ ( n , k ) = ( p + 1 ) k = 0 n λ k ( 1 ) k + 1 , 1 / λ S 2 , λ ( n , k ) 0 1 t p ( 1 t ) k d t = ( p + 1 ) 0 1 k = 0 n λ k ( 1 t ) n t p ( 1 ) k + 1 , 1 / λ S 2 , λ ( n , k ) ( 1 + t 1 t ) n k d t = ( p + 1 ) 0 1 ( 1 t ) n t p k = 0 n n k λ ( 1 ) n k ( t 1 t ) k d t = ( p + 1 ) k = 0 n n k λ ( 1 ) n k 0 1 ( 1 t ) n k t p + k d t = ( p + 1 ) k = 0 n n k λ ( 1 ) n k ( n k ) ! ( p + k ) ! ( p + n + 1 ) ! = p + 1 n + p + 1 k = 0 n n k λ ( 1 ) n k ( p + n p + k ) 1 .
(30)
Therefore, by (30), we obtain the following theorem.
Theorem 4
For \(n,p\ge 0\), we have
β n , λ ( p ) = p + 1 n + p + 1 k = 0 n n k λ ( 1 ) n k ( p + n p + k ) 1 .
Let r be a positive integer. The unsigned r-Stirling number of the first kind \({n \brack k}_{r}\) is the number of permutations of the set \([n]=\{1,2,3,\dots,n\}\) with exactly k disjoint cycles in such a way that the numbers \(1,2,3,\dots,r\) are in distinct cycles, while the r-Stirling number of the second kind \({n \brace k}_{r}\) counts the number of partitions of the set \([n]\) into k non-empty disjoint subsets in such a way that the numbers \(1,2,3,\dots,r\) are in distinct subsets. In [13], Kim et al. introduced the unsigned degenerate r-Stirling numbers of the first kind \({n \brack k}_{r,\lambda }\) as a degenerate version of \({n \brack k}_{r}\) and the degenerate r-Stirling number of the second kind \({n \brace k}_{r,\lambda }\) as a degenerate version of \({n \brace k}_{r}\). It is well known that the degenerate r-Stirling numbers of the second kind are given by
$$ (x+r)_{n,\lambda }=\sum_{k=0}^{n}{n+r \brace k+r}_{r,\lambda }(x)_{k}\quad (n \ge 1). $$
(31)
From (31), we note that
$$ \frac{1}{k!} \bigl(e_{\lambda }(t)-1 \bigr)^{k}e_{\lambda }^{r}(t)= \sum_{n=k}^{ \infty }{n+r \brace k+r}_{r,\lambda }\frac{t^{n}}{n!}\quad (k\ge 0, r \ge 1). $$
(32)
By the Euler transformation formula in (8) and (32), we get
n = 0 β n , λ ( p ) t n n ! = F 1 2 ( 1 λ , 1 p + 2 | 1 e λ ( t ) ) = e λ p + λ ( t ) k = 0 p + 1 + λ k p + 1 k p + 2 k ( 1 e λ ( t ) ) k k ! = p + 1 1 p + 1 , 1 / λ k = 0 λ k 1 p + k + 1 , 1 / λ p + k + 1 ( 1 ) k k ! ( e λ ( t ) 1 ) k e λ p + λ ( t ) = p + 1 1 p + 1 , 1 / λ k = 0 λ k 1 p + k + 1 , 1 / λ p + k + 1 ( 1 ) k m = k { m + p k + p } p , λ t m m ! ( 1 + λ t ) = m = 0 p + 1 1 p + 1 , 1 / λ k = 0 m λ k 1 p + k + 1 , 1 / λ p + k + 1 ( 1 ) k { m + p k + p } p , λ t m m ! ( 1 + λ t ) = n = 0 { p + 1 1 p + 1 , 1 / λ k = 0 n λ k 1 p + k + 1 , 1 / λ p + k + 1 ( 1 ) k { n + p k + p } p , λ } t n n ! + n = 1 { n ( p + 1 ) 1 p + 1 , 1 / λ k = 0 n 1 λ k + 1 1 p + k + 1 , 1 / λ p + k + 1 ( 1 ) k { n + p 1 k + p } p , λ } t n n ! ,
(33)
where \(\langle x\rangle _{0,\lambda }=1, \langle x\rangle _{n,\lambda }=x(x+ \lambda )\cdots (x+(n-1)\lambda ) (n\ge 1)\). Therefore, we obtain the following theorem.
Theorem 5
For \(n\ge 1\) and \(p\ge 0\), we have
$$\begin{aligned} \beta _{n,\lambda }^{(p)}={}&\frac{p+1}{\langle 1\rangle _{p+1,1/\lambda }} \sum _{k=0}^{n} \frac{\lambda ^{k}\langle 1\rangle _{p+k+1,1/\lambda }}{p+k+1}(-1)^{k}{n+p \brace k+p}_{p,\lambda } \\ &{} +n\lambda \frac{(p+1)}{\langle 1\rangle _{p+1,1/\lambda }} \sum_{k=0}^{n-1} \frac{\lambda ^{k}\langle 1\rangle _{p+k+1,1/\lambda }}{p+k+1}(-1)^{k}{n+p-1 \brace k+p}_{p,\lambda }. \end{aligned}$$
Note that
$$\lim_{\lambda \rightarrow 0}\beta _{n,\lambda }^{(p)}= \frac{p+1}{p!} \sum_{k=0}^{n}(-1)^{k} \frac{(p+k)!}{p+k+1}{n+p \brace k+p}_{p, \lambda }. $$
From Theorem 3, we have
n = 0 β n , λ ( p ) t n n ! = n = 0 ( k = 0 n λ k ( 1 ) k + 1 , 1 / λ ( p + k + 1 p + 1 ) S 2 , λ ( n , k ) ) t n n ! = k = 0 λ k ( 1 ) k + 1 , 1 / λ ( p + k + 1 p + 1 ) 1 k ! ( e λ ( t ) 1 ) k = ( p + 1 ) k = 0 p ! k ! ( k + p + 1 ) ! λ k ( 1 ) k + 1 , 1 / λ 1 k ! ( e λ ( t ) 1 ) k = ( p + 1 ) k = 0 ( 1 ) k λ k ( 1 ) k + 1 , 1 / λ k ! ( 1 e λ ( t ) ) k 0 1 ( 1 x ) p x k d x = ( p + 1 ) k = 0 ( 1 ) k ( λ 1 k ) ( 1 e λ ( t ) ) k 0 1 ( 1 x ) p x k d x = ( p + 1 ) 0 1 ( 1 x ) p ( 1 x ( 1 e λ ( t ) ) ) λ 1 d x .
(34)
Therefore, we obtain the following theorem.
Theorem 6
For \(p\ge 0\), we have
$$\sum_{n=0}^{\infty }\beta _{n,\lambda }^{(p)} \frac{t^{n}}{n!}=(p+1) \int _{0}^{1}(1-x)^{p} \bigl(1-x \bigl(1-e_{\lambda }(t)\bigr) \bigr)^{\lambda -1}\,dx. $$
3 Generalized degenerate Bernoulli polynomials
In this section, we consider the generalized degenerate Bernoulli polynomials which are derived from the Gauss hypergeometric function. In the light of (20), we define the generalized degenerate Bernoulli polynomials by
n = 0 β n , λ ( p ) (x) t n n ! = 2 F 1 ( 1 λ , 1 p + 2 | 1 e λ ( t ) ) e λ x (t).
(35)
When \(x=0\), \(\beta _{n,\lambda }^{(p)}(0)=\beta _{n,\lambda }^{(p)}\) \((n\ge 0)\). Thus, by (35), we get
n = 0 β n , λ ( p ) ( x ) t n n ! = 2 F 1 ( 1 λ , 1 p + 2 | 1 e λ ( t ) ) e λ x ( t ) = l = 0 β l , λ ( p ) t l l ! m = 0 ( x ) m , λ t m m ! = n = 0 ( l = 0 n ( n l ) β l , λ ( p ) ( x ) n l , λ ) t n n ! .
(36)
Therefore, by comparing the coefficients on both sides of (36), we obtain the following theorem.
Theorem 7
For \(n\ge 0\), we have
$$\beta _{n,\lambda }^{(p)}(x)=\sum_{l=0}^{n} \binom{n}{l}\beta _{l, \lambda }^{(p)}(x)_{n-l,\lambda }. $$
From (35), we note that
n = 1 d d x β n , λ ( p ) ( x ) t n n ! = 2 F 1 ( 1 λ , 1 p + 2 | 1 e λ ( t ) ) d d x e λ x ( t ) = 1 λ log ( 1 + λ t ) 2 F 1 ( 1 λ , 1 p + 2 | 1 e λ ( t ) ) e λ x ( t ) = 1 λ l = 1 ( 1 ) l 1 λ l l t l m = 0 β m , λ ( p ) ( x ) t m m ! = n = 1 ( l = 1 n ( λ ) l 1 l n ! β n l , λ ( p ) ( x ) ( n l ) ! ) t n n ! .
Thus, we have
$$\frac{d}{dx}\beta _{n,\lambda }^{(p)}(x)= \sum _{l=1}^{n}(-\lambda )^{l-1}(l-1)! \binom{n}{l}\beta _{n-l,\lambda }^{(p)}(x). $$
Proposition 8
For \(n\ge 1\), we have
$$\frac{d}{dx}\beta _{n,\lambda }^{(p)}(x)= \sum _{l=1}^{n}(-\lambda )^{l-1}(l-1)! \binom{n}{l}\beta _{n-l,\lambda }^{(p)}(x). $$
By (13), we easily get
$$\begin{aligned} \sum_{n=k}^{\infty }S_{2,\lambda }(n,k|x) \frac{t^{n}}{n!} &= \frac{1}{k!} \bigl(e_{\lambda }(t)-1 \bigr)^{k}e_{\lambda }^{x}(t) \\ &= \frac{1}{k!}\sum_{l=0}^{k} \binom{k}{l}(-1)^{k-l}e_{\lambda }^{l+x}(t) \\ &= \sum_{n=0}^{\infty } \Biggl(\frac{1}{k!} \sum_{l=0}^{k}(-1)^{k-l}(l+x)_{n, \lambda } \Biggr)\frac{t^{n}}{n!}. \end{aligned}$$
Thus we have
$$ \frac{1}{k!}\sum_{l=0}^{k} \binom{k}{l}(-1)^{k-l}(l+x)_{n,\lambda }= \textstyle\begin{cases} S_{2,\lambda }(n,k|x), & \text{if $n\ge k$,} \\ 0, & \text{otherwise.} \end{cases} $$
(37)
From (37), we note that
$$S_{2,\lambda }(n,k|x)=\frac{1}{k!}\triangle ^{k}(x)_{n,\lambda }\quad (n \ge k). $$
Lemma 9
For \(n,k\ge 0\) with \(n\ge k\), we have
$$S_{2,\lambda }(n,k|x)=\frac{1}{k!}\triangle ^{k}(x)_{n,\lambda }\quad (n \ge k). $$
Now, we observe that
n = 0 β n , λ ( p ) ( x ) t n n ! = k = 0 ( p + 1 ) ! k ! ( p + k + 1 ) ! λ k ( 1 ) k + 1 , 1 / λ 1 k ! ( e λ ( t ) 1 ) k e λ x ( t ) = k = 0 ( 1 ) k + 1 , 1 / λ λ k ( p + k + 1 p + 1 ) n = k S 2 , λ ( n , k | x ) t n n ! = n = 0 ( k = 0 n ( 1 ) k + 1 , 1 / λ λ k ( p + k + 1 p + 1 ) S 2 , λ ( n , k | x ) ) t n n ! .
(38)
Therefore, by (38), we obtain the following theorem.
Theorem 10
For \(n\ge 0\), we have
β n , λ ( p ) (x)= k = 0 n ( 1 ) k + 1 , 1 / λ λ k ( p + k + 1 p + 1 ) S 2 , λ (n,k|x).
Remark 11
Let p be a nonnegative integer. Then, by Theorem 7 and (35), we easily get
$$\begin{aligned} & \beta _{n,\lambda }^{(p)}(x+y)=\sum_{k=0}^{n} \binom{n}{k}\beta _{k, \lambda }^{(p)}(x) (y)_{n-k,\lambda } \quad(n \ge 0), \\ & \beta _{n,\lambda }^{(p)}(x+1)-\beta _{n,\lambda }^{(p)}(x) = \sum_{k=0}^{n-1}\binom{n}{k}\beta _{k,\lambda }^{(p)}(x) (1)_{n-k, \lambda } \quad(n \ge 1), \\ & \beta _{n,\lambda }^{(p)}(mx) = \sum_{k=0}^{n} \binom{n}{k}\beta _{k, \lambda }^{(p)}(x) (m-1)^{n-k}(x)_{n-k,\lambda /m-1}\quad (n \ge 0, m \ge 2). \end{aligned}$$
4 Conclusion
This work was motivated by Rahmani’s paper [14] in which a new family of p-Bernoulli numbers and polynomials was constructed by means of the Gauss hypergeometric function. This family of numbers and polynomials generalizes the classical Bernoulli numbers and polynomials, in the sense that they reduce to the classical Bernoulli numbers and polynomials for \(p=0\). In the light of the regained recent interests in them, we were interested in finding a degenerate version of those numbers and polynomials. Indeed, the generalized degenerate Bernoulli numbers and polynomials, which reduce to the Carlitz degenerate Bernoulli numbers and polynomials for \(p=0\), were constucted in terms of the Gauss hypergeometric function. Moreover, the degenerate type Eulerian numbers were introduced as a degenerate version of Eulerian numbers.
In this paper, we expressed the generalized degenerate Bernoulli numbers in terms of the degenerate Stirling numbers of the second kind, of the degenerate type Eulerian numbers, of the degenerate p-Stirling numbers of the second kind and of an integral on the unit interval. In addition, we represented the generalized degenerate Bernoulli polynomials in terms of the degenerate Stirling polynomials of the second kind.
It is one of our future projects to continue pursuing this line of research. Namely, by studying degenerate versions of some special polynomials and numbers, we want to find their applications in mathematics, science and engineering.
Availability of data and materials
Not applicable.
References
1. Andrews, G.E., Askey, R., Roy, R.: Special Functions. Cambridge University Press, Cambridge (1999)
Book Google Scholar
2. Bailey, W.N.: Generalized Hypergeometric Series. Cambridge Tracts in Mathematics and Mathematical Physics, vol. 32. Stechert-Hafner, New York (1964)
Google Scholar
3. Carlitz, L.: Degenerate Stirling, Bernoulli and Eulerian numbers. Util. Math. 15, 51–88 (1979)
MathSciNet MATH Google Scholar
4. Comtet, L.: Advanced Combinatorics. Reidel, Dordrecht (1974)
Book Google Scholar
5. Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete Mathematics: A Foundation for Computer Science, 2nd edn. Addison-Wesley, Reading (1994)
MATH Google Scholar
6. Jang, L.-C., Kim, D.S., Kim, T., Lee, H.: Some identities involving derangement polynomials and numbers and moments of gamma random variables. J. Funct. Spaces 2020, Article ID 6624006 (2020)
MathSciNet MATH Google Scholar
7. Kim, D.S., Kim, T.: A note on a new type of degenerate Bernoulli numbers. Russ. J. Math. Phys. 27(2), 227–235 (2020)
Article MathSciNet Google Scholar
8. Kim, T.: A note on degenerate Stirling polynomials of the second kind. Proc. Jangjeon Math. Soc. 20(3), 319–331 (2017)
MathSciNet MATH Google Scholar
9. Kim, T., Kim, D.S.: Note on the degenerate gamma function. Russ. J. Math. Phys. 27(3), 352–358 (2020)
Article MathSciNet Google Scholar
10. Kim, T., Kim, D.S., Kim, H.Y., Kwon, J.: Degenerate Stirling polynomials of the second kind and some applications. Symmetry 11(8), 1046 (2019)
Article Google Scholar
11. Kim, T., Kim, D.S., Kim, H.Y., Kwon, J.: Erratum Kim, T. et al. Degenerate Stirling polynomials of the second kind and some applications. Symmetry 11(8), 1046 (2019). Symmetry 11(12), 1530 (2019)
Article Google Scholar
12. Kim, T., Kim, D.S., Lee, H., Kwon, J.: Degenerate binomial coefficients and degenerate hypergeometric functions. Adv. Differ. Equ. 2020, Article ID 115 (2020)
Article MathSciNet Google Scholar
13. Kim, T., Kim, D.S., Lee, H., Park, J.-W.: A note on degenerate r-Stirling numbers. J. Inequal. Appl. 2020, Article ID 225 (2020)
Article MathSciNet Google Scholar
14. Rahmani, M.: On p-Bernoulli numbers and polynomials. J. Number Theory 157, 350–366 (2015)
Article MathSciNet Google Scholar
Download references
Acknowledgements
The authors would like to thank the reviewers for their valuable comments and suggestions and Jangjeon Institute for Mathematical Science for the support of this research.
Funding
The first author has been conducted by the Research Grant of Kwangwoon University in 2021.
Author information
Authors and Affiliations
Authors
Contributions
TK and DSK conceived of the framework and structured the whole paper; DSK and TK wrote the paper; HL typed; LCJ, and HYK checked the results of the paper; DSK and TK completed the revision of the paper. All authors have read and approved the final version of the manuscript.
Corresponding author
Correspondence to Lee-Chae Jang.
Ethics declarations
Competing interests
The authors declare that they have no competing interests.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Reprints and Permissions
About this article
Check for updates. Verify currency and authenticity via CrossMark
Cite this article
Kim, T., Kim, D.S., Jang, LC. et al. Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function. Adv Differ Equ 2021, 175 (2021). https://doi.org/10.1186/s13662-021-03337-5
Download citation
• Received:
• Accepted:
• Published:
• DOI: https://doi.org/10.1186/s13662-021-03337-5
MSC
• 11B68
• 11B73
• 11B83
• 33C05
Keywords
• Generalized degenerate Bernoulli numbers
• Generalized degenerate Bernoulli polynomials
• Degenerate type Eulerian numbers
|
__label__pos
| 0.996902 |
Setting up Jupyter notebook with Tensorflow, Keras and Pytorch for Deep Learning
I was trying to set up my Jupyter notebook to work on some deep learning problem (some image classification on MNIST and imagenet dataset) on my laptop (Ubuntu 16.04 LTS). Previously I have used a little bit of Keras (which runs on top of Tensorflow) on a small dataset, but I did not use that with Jupyter. For that purpose I installed Tensorflow and Keras independently and used them in a Python script. However, it was not working from my Jupyter notebook. I googled for the solution, but found nothing concrete. I tried to activate the tensorflow environment and run jupyter notebook from their but in vein. I guess the reason is, I have downloaded different packages in different times and that might make some compatibility issues. Therefore, I decided to create a BRAND NEW conda environment for my deep learning endeavor. This is how it goes:
Continue reading “Setting up Jupyter notebook with Tensorflow, Keras and Pytorch for Deep Learning”
Using baseplot for Ploting Geographical Coordinates
Basemap is a great tool for creating maps using python in a simple way. It’s a matplotlib extension, so it has got all its features to create data visualizations, and adds the geographical projections and some datasets to be able to plot coast lines, countries, and so on directly from the library [1].
Continue reading “Using baseplot for Ploting Geographical Coordinates”
Copy File from Cloud HDFS to Local Computer
While I work with big data technologies like Spark and a large dataset I like to work on the university cloud, where everything is faster. However, for different reasons sometimes I have to move to local computer (my laptop). This time the reason is, I need to use a package of Python matplotlib, named baseplot, which is not installed on the cloud. However, the data I need to work on is on the cloud HDFS. Therefore, I need to copy the data from HDFS to my local laptop. This can be done in two simple steps:
Step 1: copy data from HDFS to remote local (not HDFS)
Step 2: copy data from remote local to local (my laptop)
Continue reading “Copy File from Cloud HDFS to Local Computer”
Data Science Interview Questions
In this post I am going to make a compilation of interview questions for data science role. A big part of them are questions that I faced during my interviews. I have also gathered questions from different websites and which I found interesting. So, lets get started.
What do you know about bias-variance/bias-variance tradeoff?
In statistics and machine learning, the bias–variance tradeoff (or dilemma) is the problem of simultaneously minimizing two sources of error that prevent supervised learning algorithms from generalizing beyond their training set [Wikipedia]:
• The bias is an error from erroneous assumptions in the learning algorithm. High bias can cause an algorithm to miss the relevant relations between features and target outputs (underfitting). Bias are the simplifying assumptions made by a model to make the target function easier to learn. Examples of low-bias machine learning algorithms include: Decision Trees, k-Nearest Neighbors and Support Vector Machines. Examples of high-bias machine learning algorithms include: Linear Regression, Linear Discriminant Analysis and Logistic Regression [2].
• The variance is an error from sensitivity to small fluctuations in the training set. High variance can cause an algorithm to model the random noise in the training data, rather than the intended outputs (overfitting). Variance is the amount that the estimate of the target function will change if different training data was used. Low variance suggests small changes to the estimate of the target function with changes to the training dataset. High variance suggests large changes to the estimate of the target function with changes to the training dataset. Generally, nonparametric machine learning algorithms that have a lot of flexibility have a high variance. For example, decision trees have a high variance, that is even higher if the trees are not pruned before use. Examples of low-variance machine learning algorithms include: Linear Regression, Linear Discriminant Analysis and Logistic Regression. Examples of high-variance machine learning algorithms include: Decision Trees, k-Nearest Neighbors and Support Vector Machines [2].
Continue reading “Data Science Interview Questions”
Printing Jupyter Notebook to other File Format
As a data scientist, I frequently use Jupyter notebook. For writing some report one might need to print out (on paper) the full notebook. There is a print preview option in the current version of Jupyter notebook, but no print option.
I tried to use CTRL + P command on the print preview page, but the output was horrible (like when we try to print an webpage). I googled and found a better way of doing that.
I am running Jupyter notebook on Ubuntu 16.04. The steps are very simple:
(1) Open terminal
(2) Change directory (where the notebook is located)
(3) Use command: ipython nbconvert –to pdf A1.ipynb (A1.ipynb is my notebook)
shanto@shanto:~$ cd ~/Desktop/BigData/706/Assignments/
shanto@shanto:~/Desktop/BigData/706/Assignments$ ls
A1.ipynb
shanto@shanto:~/Desktop/BigData/706/Assignments$ jupyter nbconvert --to pdf A1.ipynb
[NbConvertApp] Converting notebook A1.ipynb to pdf
[NbConvertApp] Writing 25564 bytes to notebook.tex
[NbConvertApp] Building PDF
[NbConvertApp] Running xelatex 3 times: ['xelatex', 'notebook.tex']
[NbConvertApp] Running bibtex 1 time: ['bibtex', 'notebook']
[NbConvertApp] WARNING | bibtex had problems, most likely because there were no citations
[NbConvertApp] PDF successfully created
[NbConvertApp] Writing 23494 bytes to A1.pdf
shanto@shanto:~/Desktop/BigData/706/Assignments$
The figure shows a snap of the generated *.pdf file. The file is reasonably neat with a good formating.
If we change the –to pdf part to –to whateverFormat then the same command can be used to convert the notebook to other formats. Conversion to a few other format is shown below.
shanto@shanto:~/Desktop/BigData/706/Assignments$ jupyter nbconvert --to script A1.ipynb
[NbConvertApp] Converting notebook A1.ipynb to script
[NbConvertApp] Writing 2077 bytes to A1.py
shanto@shanto:~/Desktop/BigData/706/Assignments$ # convert to latex
shanto@shanto:~/Desktop/BigData/706/Assignments$ jupyter nbconvert --to latex A1.ipynb
[NbConvertApp] Converting notebook A1.ipynb to latex
[NbConvertApp] Writing 25564 bytes to A1.tex
shanto@shanto:~/Desktop/BigData/706/Assignments$
Running Spark on Local Machine
Apache Spark is a fast and general-purpose cluster computing system. To get maximum potential out of it, Spark should be running on a distributed computing system. However, one might not have access to any distributed system all the time. Specially, for learning purpose one might want tor run spark on his/her own computer. This is actually a very easy task to do. There is a handful of way to do this. I would show, what I have done to run Spark on my laptop.
Continue reading “Running Spark on Local Machine”
Find Similarity Using Jaccard Similarity
We read the file using Pandas.
import pandas as pd
import numpy as np
rawData = pd.read_csv('data-Assignment2.txt', sep=",", header=None)
We need to find the signature matrix. For that we need to make a permutation of the rows of the whole matrix. We can do that using pandas like this.
permuteData = rawData.sample(frac=1)
Just as a note we can use frac less than one if we want to do a random subsample. We can also shuffle in-place and use this.
df = df.sample(frac=1).reset_index(drop=True) # in place shuffle, drop index column
We can test if it works by using a random matrix created by Pandas.
# create a random matrix with 0 and 1, like our example matrix
df = pd.DataFrame(np.random.randint(0,2,size=(100, 4)), columns=list('ABCD'))
# now we can do a shuffle like this
df = df.sample(frac=1)
The before and after is shown by the following figure:
a = []
b = []
for k in range(3):
for j in range(4):
a.append(j)
b.append(a)
a = []
print(b)
# OUTPUT: [[0, 1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3]]
*.csv File Preprocessing Using Pandas
For any machine learning or data mining purpose, the first job is to pre-process the data so that we can us the data for the original purpose. In lots of cases we have the raw data in *csv format, which we need to import and preprocess using the language we are using for the particular job. Python is one of the most popular language for this purpose. For this article I will use Python and one very popular library named pandas to show how we can use pandas for read, import and preprocess a *.csv file.
We have a *csv file which we want to pre-process. This is a file with a large number of columns, so it is not a good idea to display it here. I am showing a part of it.
Continue reading “*.csv File Preprocessing Using Pandas”
Understanding MapReduce in My Way : Starting with Word Count
Word Count problem is known as the ‘Hello World’ for MapReduce. In this article I will explain, how I understand different bits of MapReduce in my way. The code provided in this article is trivial and is available in lots of places including the official MapReduce website. My concern would be to focus on how it really works.
Continue reading “Understanding MapReduce in My Way : Starting with Word Count”
|
__label__pos
| 0.856457 |
KidsMD Health Topics
Our Health Topics
Unicameral Bone Cyst
• Overview
What is a unicameral bone cyst?
A unicameral bone cyst, otherwise known as a simple bone cyst, is a fluid-filled cavity in the bone, lined by compressed fibrous tissue. It usually occurs in the long bones of a growing child, especially the upper part of the humerus (50 - 60% of the time) or the upper part of the femur (25-30 % of the time). Other bones, however, can be affected.
These cysts usually affect children primarily between the ages of 5 to 15, but can affect older children or adults. In older children and adults, they tend to occur in flat bones (such as the pelvis, jaw, skull or rib cage) or in the large heel bone (calcaneus)
Unicameral bone cysts are considered benign. They do not metastasize (spread) beyond the bone. Some heal spontaneously, while others enlarge. More invasive cysts can grow to fill most of the bone's metaphysis (the transitional zone where the shaft of the bone joins the end of the bone) and cause what is known as a pathological fracture. A more invasive cyst could also destroy the bone's growth plate, leading to shortening of the bone. Shortening in the upper arm (humerus) usually does not cause a functional problem, but it may produce a cosmetic problem if it occurs in early childhood.
These cysts are sometimes classified as either "active" or "latent".
An active cyst is adjacent to the growth plate and tends to enlarge, causing the problems mentioned above.
A latent cyst is one that is more apt to heal with treatment because the growth plate has migrated away from the cyst.
What causes a unicameral bone cyst?
The cause of a unicameral bone cyst remains unknown. Theories have been proposed but none have been definitively proven. One of these theories is that the cysts result from a disorder of the growth plate. Another is that the cysts result from problems with circulation that are caused by a developmental anomaly in the veins of the affected bone. The role trauma plays in the development of these cysts is unknown. Some speculate that repeated trauma puts the bone at risk for developing a bone cyst. This, however, has not been proven.
What are the symptoms of a unicameral bone cyst?
Unless there has been a fracture, bone cysts are without symptoms. They may occasionally be discovered by chance on x-rays obtained for other reasons. There is no mass or tenderness unless there is a fracture. There may be an abnormal angulation of the limb secondary to the fracture or shortening of the limb if the adjacent growth plate is involved.
Keep in mind that each child experiences symptoms differently. The symptoms of a unicameral bone cyst may resemble other conditions or medical problems. Always consult your child's physician for a diagnosis.
How is a unicameral bone cyst diagnosed?
In addition to a performing a complete physical examination and taking your child's medical history, the doctor will likely take a simple x-ray of the affected area, which can be used alone to diagnose a unicameral bone cyst. The following diagnostic tests are usually not required, except if the cyst is found in an unusual location, such as the pelvis:
• magnetic resonance imaging (MRI) - a diagnostic procedure that uses a combination of large magnets, radiofrequencies, and a computer to produce detailed images of organs and structures within the body. This test is done to help document the extent of the cyst, how aggressive it is, and distinguish it from other types of bone cysts.
• computerized tomography scan (also called a CT or CAT scan) - a diagnostic imaging procedure that uses a combination of x-rays and computer technology to produce cross-sectional images (often called slices), both horizontally and vertically, of the body. A CT scan shows detailed images of any part of the body, including the bones, muscles, fat, and organs. CT scans are more detailed than general x-rays. This test can also help document the extent of the cyst, and distinguish it from other bone cysts.
• bone scans - a nuclear imaging method to evaluate any degenerative and/or arthritic changes in the joints; to detect bone diseases and tumors; to determine the cause of bone pain or inflammation. This test is to rule out other cysts (which are quite unusual)
Treatment for a unicameral bone cyst
Specific treatment for a unicameral bone cyst will be determined by your child's physician based on:
• your child's age, overall health, and medical history
• extent of the disease
• your child's tolerance for specific medications, procedures, or therapies
• how your child's physician expects the disease may progress
• your opinion or preference
Treatment is aimed primarily at preventing recurrent fractures. If it is decided that the bone is relatively strong, observation may be recommended. If the child's activities are such that fracture is unlikely (especially in the humerus) observation may be recommended.
The decision to treat is sometimes difficult and the risks of the surgery must be compared to the likelihood of fracture without treatment. There is no right answer for everyone. If treatment is opted for, it will likely involve one or a combination of the following surgical procedures performed by a pediatric orthopaedic surgeon:
• Curettage/Bone Grafting: Curettage describes a surgical scraping of the cyst with a special instrument called a curette that has a scoop, loop or ring at its tip. For this procedure, surgeons make an incision in the bone to create a window. The fluid in the cyst is aspirated and the lining tissue is completely curetted. The remaining cavity is then packed with donor bone tissue (allograft), bone chips taken from another bone (autograft), or other materials depending on the preference of the surgeon.
• Steroid Injection: Injection of the steroid methylprednisone acetate into these cysts can help heal the cyst, sometimes without any other therapy. The steroid's healing ability is not fully understood, although it is believed that steroids can reduce the levels of prostaglandin, a type of fatty acid found in the cyst fluid. Prostaglandin is believed to reduce the cyst's ability to reabsorb into the bone.
For this procedure, spinal or bone marrow biopsy needles are placed into the cyst and the fluid is aspirated. The cyst is injected with radiographic contrast, which helps doctors determine whether the cyst can be filled. Then, the steroid is injected and the needles are removed. The cyst will likely be reinjected at regular intervals every several months, until there is adequate healing, which may take 6-12 months. Overall, the results of steroid injection are similar to curettage and the procedure is much easier on the child, so it is usually preferred to curettage as the first treatment. The risks of this treatment are minimal and generally restricted to the risk of general anesthesia, infection, fracture, and recurrence or persistence of the cyst. There is one case report of air getting into the blood stream. This is a potentially dangerous complication, but it is very unlikely to occur.
• Bone marrow injection: Some evidence suggests that bone marrow aspirated from the pelvis above the hip through a small needle and injected in the cyst will help the healing. This is sometimes used in conjunction with demineralized bone gel to stimulate bone formation. The demineralized bone is from donor (allograft) bones. The calcium is removed in these preparations, but the bone proteins that stimulate bone formation remain, and it is believed that this may stimulate healing. The preparation is tested for transmissible diseases such as AIDS (HIV), hepatitis and bacteria and is believed to be very safe. Whether or not this approach is better or inferior to simple steroid injection is unknown.
What is the long-term outlook for a child with a unicameral bone cyst?
Prognosis for a unicameral bone cyst is generally good. Most of these cysts do heal with proper treatment and if left alone, most heal spontaneously by the time the skeleton ceases to grow. Recurrence can, however, occur. Continuous follow-up care is essential for the successful treatment of this kind of bone cyst. A schedule of follow-up care should be determined by your child's physician and other members of your care team to monitor ongoing response to treatment and possible late effects of treatment.
»
Boston Children's Hospital
300 Longwood Avenue
Fegan 2
Boston MA 02115
617-355-6021
ADDITIONAL SERVICES THAT TREAT THIS CONDITION
+
[ visit the site ]
Boston Children's Hospital
300 Longwood Ave
Fegan 2
Boston MA 02115
617-355-6021
fax: 617-730-0456
Request an Appointment
If this is a medical emergency, please dial 9-1-1. This form should not be used in an emergency.
Patient Information
Date of Birth:
Contact Information
Appointment Details
Send RequestIf you do not see the specialty you are looking for, please call us at: 617-355-6000.International visitors should call International Health Services at +1-617-355-5209.
Please complete all required fieldsThis department is currently not accepting appointment requests onlineThis department is currently not accepting appointment requests online
Thank you.
Your request has been successfully submitted
You will be contacted within 1 business day.
If you have questions or would like more information, please call:
617-355-6000 +1-617-355-6000
close
Find a Doctor
Search by Clinician's Last Name or Specialty:
Select by Location:
Search by First Letter of Clinician's Last Name: *ABCDEFGHIJKLMNOPQRSTUVWXYZ
More optionsSearch
Condition & Treatments
Search for a Condition or Treatment:
Show Items Starting With: *ABCDEFGHIJKLMNOPQRSTUVWXYZ
View allSearch
Visitor Information
The future of pediatrics will be forged by thinking differently, breaking paradigms and joining together in a shared vision of tackling the toughest challenges before us.”
- Sandra L. Fenwick, President and CEO
Close
|
__label__pos
| 0.931442 |
How HGH Declines With Age And How To Fix It With Injections?
HGH is the hormone that makes humans grow taller and stronger. It is produced by the pituitary gland, with an average annual production of three to five billion micrograms per day during adulthood. However, levels of this hormone are generally much lower or zero at all in people beyond their early 30’s.
By age 60, HGH levels have dropped considerably and may remain low for many years after that point. Researchers do not yet know what causes this hormonal change. Still, they speculate that it might be related to increased body fat and lower activity levels due to the natural ageing process. Whatever the cause, it is fixed when you buy HGH for sale here and use them effectively in your treatment.
Science Behind Declining Level of HGH with Age
Ageing is a natural process that happens to all living beings and represents a general decline in capabilities and a dramatic change in the body’s structure and function. Ageing also includes the physical changes associated with it. Human growth hormone (HGH) is an important part of successful ageing.
Normally, physical activities and exercising become minimal with increasing age. This increases fat levels in our bodies. With no hormonal output, the body will rely on fat, sometimes referred to as ‘insulin resistance. This can lead to many health problems, including diabetes, heart disease, and cardiovascular health.
HGH’s ability to influence human ageing is crucially important because the hormone is the only known physiologic process that has ever been shown capable of naturally increasing life expectancy. Successful ageing should be defined as how well a person ages without being hampered by the critically low level of HGH.
Injections to Boost HGH Levels
The feeling of boundless enthusiasm and vitality is missed badly while growing old. That’s because the hormone levels start declining with age, affecting your health, happiness, wellbeing and more. This feeling of loss of energy and fitness is rather a horrible one.
Although HGH levels are commonly low in humans with passing age, this level can be increased now with HGH injections. This is because these injections directly contact our body’s biological system and account for the low HGH levels in our body.
HGH aids in the production of our body’s protein. You can buy HGH injections that cause your body to produce more proteins for growth hormones used in the different areas of your body. Many think that HGH is a drug that can help them lose weight, but this is not the case. This hormone is only used by your body when you need it.
HGH is short for human growth hormone, a substance produced in the pituitary gland. This tiny endocrine organ is located at the base of your brain and releases hormones that regulate growth in children and adolescents. Unfortunately, as we age, our HGH levels start to decline. That’s why many people experience less energy, loss of muscle mass and increased body fat as they get older.
Similar Posts
Leave a Reply
Your email address will not be published. Required fields are marked *
|
__label__pos
| 0.820019 |
Is it OK to lose weight during pregnancy if you are overweight?
Is it safe to lose weight while pregnant if overweight?
If you are obese (usually defined as having a BMI of 30 or above) and pregnant, do not try to lose weight during your pregnancy. It will not reduce the chance of complications and may not be safe. The best way to protect you and your baby’s health is to go to all your antenatal appointments.
Can you lose a baby from being overweight?
Having a high BMI during pregnancy increases the risk of various pregnancy complications, including: The risk of miscarriage, stillbirth and recurrent miscarriage. Gestational diabetes.
Is it weird to lose weight while pregnant?
“It’s not uncommon for women in their first trimester to lose a little bit of weight due to bad nausea and vomiting that precludes them from eating in a normal way,” says Henderson. A loss of appetite because of the morning sickness is a common cause of pregnancy weight loss too.
How can I avoid getting fat during pregnancy?
How to avoid gaining too much weight during pregnancy
1. Start pregnancy at a healthy weight if possible.
2. Eat balanced meals and refuel often.
3. Drink up (water, that is)
4. Make your cravings constructive.
5. Choose complex carbs.
6. Start a simple walking routine.
7. If you’re already moving, don’t stop.
8. Make weight a regular discussion.
IT IS INTERESTING: Your question: Can having an Orgasim cause miscarriage in first trimester?
What is considered a plus size pregnancy?
And what exactly is a “plus-size pregnancy”? There’s no official definition of “plus size.” However, according to the Centers for Disease Control and Prevention (CDC) , women with a body mass index (BMI) of 25.0 to 29.9 are considered to be overweight, and those with a BMI of 30.0 or above have obesity.
When should I worry about weight loss during pregnancy?
Sometimes, it is nothing to worry about, especially if the weight loss is short-lived and followed by the recommended weight gain. However, losing weight during pregnancy is cause for concern if the weight loss is substantial, long-lasting, or occurs after the first trimester.
Does being obese affect pregnancy?
How can obesity affect a pregnancy? Obesity increases the risk of the following problems during pregnancy: Birth defects—Babies born to women who are obese have an increased risk of having birth defects, such as heart defects and neural tube defects (NTDs)
Does being overweight make it harder to get pregnant?
In most cases, being overweight does not affect your ability to get pregnant. However, being obese (rather than overweight) can decrease your chances of getting pregnant. That’s because weight can have an effect on your hormones and can prevent your ovaries from releasing an egg (ovulation).
Do you burn more calories when pregnant?
Yes, you burn more calories when you are pregnant because of the increase in weight and body surface area. At baseline, your body has to burn calories just to keep your heart pumping, brain functioning, blood flowing, and muscles working.
IT IS INTERESTING: Is it OK to gain 40 pounds when pregnant?
Can you lose 50lbs while pregnant?
The authors of a 2015 meta-analysis reviewed six studies and concluded that, in general, doctors should not recommend weight loss for women with obesity during pregnancy. They suggest that losing weight at this time can increase the risk of complications to the baby.
Can you lose weight while pregnant if you exercise?
You’ll gain less fat weight during your pregnancy if you continue to exercise (assuming you exercised before becoming pregnant). But don’t expect or try to lose weight by exercising while you’re pregnant. For most women, the goal is to maintain their fitness level throughout pregnancy.
What causes weight gain during pregnancy?
Women gain more weight in the final months of pregnancy than they do in the first few months. This isn’t only due to the weight of the growing baby. Much of the weight gained is extra fluid (water) in the body. This is needed for things like the baby’s circulation, the placenta and the amniotic fluid.
What month of pregnancy do you gain weight?
In general, you should gain about 2 to 4 pounds during the first 3 months you‘re pregnant and 1 pound a week during the rest of your pregnancy.
|
__label__pos
| 0.99998 |
Search Results
You are looking at 1 - 10 of 16 items for
• Author: Alejandro Pérez-Castilla x
• Refine by Access: All Content x
Clear All Modify Search
Restricted access
Changes in the Load–Velocity Profile Following Power- and Strength-Oriented Resistance-Training Programs
Alejandro Pérez-Castilla and Amador García-Ramos
Objective: To compare the short-term effect of power- and strength-oriented resistance-training programs on the individualized load–velocity profiles obtained during the squat (SQ) and bench-press (BP) exercises. Methods: Thirty physically active men (age = 23.4 [3.5] y; SQ 1-repetition maximum [1RM] = 126.5 [26.7] kg; BP 1RM = 81.6 [16.7] kg) were randomly assigned to a power- (exercises: countermovement jump and BP throw; sets per exercise: 4–6; repetitions per set: 5–6; load: 40% 1RM) or strength-training group (exercises: SQ and BP; sets per exercise: 4–6; repetitions per set: 2–8; load: 70%–90% 1RM). The training program lasted 4 wk (2 sessions/wk). The individualized load–velocity profiles (ie, velocity associated with the 30%–60%–90% 1RM) were assessed before and after training through an incremental loading test during the SQ and BP exercises. Results: The power-training group moderately increased the velocity associated with the full spectrum of % 1RM for the SQ (effect size [ES] range: 0.70 to 0.93) and with the 30% 1RM for the BP (ES: 0.67), while the strength-training group reported trivial/small changes across the load–velocity spectrum for both the SQ (ES range: 0.00 to 0.35) and BP (ES range: −0.06 to −0.33). The power-training group showed a higher increase in the mean velocity associated with all % 1RM compared with the strength-training group for both the SQ (ES range: 0.54 to 0.63) and BP (ES range: 0.25 to 0.53). Conclusions: The individualized load–velocity profile (ie, velocity associated with different % 1RM) of lower-body and upper-body exercises can be modified after a 4-wk resistance-training program.
Restricted access
Sensitivity of the iLOAD® Application for Monitoring Changes in Barbell Velocity Following Power- and Strength-Oriented Resistance Training Programs
Alejandro Pérez-Castilla, Daniel Boullosa, and Amador García-Ramos
Objective: To evaluate the sensitivity of the iLOAD® application to detect the changes in mean barbell velocity of complete sets following power- and strength-oriented resistance training (RT) programs. Methods: Twenty men were randomly assigned to a power training group (countermovement jump and bench press throw at 40% of the 1-repetition maximum [1RM]) or strength training group (back squat and bench press at 70% to 90% of 1RM). Single sets of 10 repetitions at 25% and 70% of 1RM during the back squat and bench press exercises were assessed before and after the 4-week RT programs simultaneously with the iLOAD® application and a linear velocity transducer. Results: The power training group showed a greater increment in velocity performance at the 25% of 1RM (effect size range = 0.66–1.53) and the 70% of 1RM (effect size range = 0.11–0.30). The percent change in mean velocity after the RT programs highly correlated between the iLOAD® application and the linear velocity transducer for the back squat (r range = .85–.88) and bench press (r range = .87–.93). However, the iLOAD® application revealed a 2% greater increase in mean velocity after training compared to the linear velocity transducer. Conclusions: The iLOAD® application is a cost-effective, portable, and easy-to-use tool which can be used to detect changes in mean barbell velocity after power- and strength-oriented RT programs.
Restricted access
Lifting Velocity as a Predictor of the Maximum Number of Repetitions That Can Be Performed to Failure During the Prone Bench Pull Exercise
Sergio Miras-Moreno, Alejandro Pérez-Castilla, and Amador García-Ramos
Objective: To explore (1) the goodness of fit of generalized and individualized relationships between the maximum number of repetitions performed to failure (RTF) and the fastest mean velocity and peak velocity of the sets (RTF–velocity relationships), (2) the between-sessions reliability of mean velocity and peak velocity values associated with different RTFs, and (3) whether the errors in the prediction of the RTF under fatigued and nonfatigued conditions differ between generalized and individualized RTF–velocity relationships. Methods: Twenty-three sport-science students performed 4 testing sessions with the prone bench pull exercise in a Smith machine: a 1-repetition-maximum [1RM] session, 2 identical sessions consisting of singles sets of RTF against 4 randomized loads (60%–70%–80%–90%1RM), and 1 session consisting of 4 sets of RTF against the 75%1RM. Results: Individualized RTF–velocity relationships presented a higher goodness of fit (r 2 = .96–.97 vs .67–.70) and accuracy (absolute errors = 2.1–2.9 repetitions vs 2.8–4.3 repetitions) in the prediction of the RTF than generalized RTF–velocity relationships. The reliability of the velocity values associated with different RTFs was generally high (average within-subject coefficient of variation = 4.01% for mean velocity and 3.98% for peak velocity). The error in the prediction of the RTF increased by ~1 repetition under fatigue (ie, set 1 vs sets 2–4). Conclusions: Individualized RTF–velocity relationships can be used with acceptable precision and reliability to prescribe the loads associated with a given RTF during the match a specific XRM during the prone bench pull exercise, but a lower accuracy is expected in a fatigued state.
Restricted access
Selective Changes in the Mechanical Capacities of Lower-Body Muscles After Cycle-Ergometer Sprint Training Against Heavy and Light Resistances
Amador García-Ramos, Alejandro Torrejón, Alejandro Pérez-Castilla, Antonio J. Morales-Artacho, and Slobodan Jaric
Purpose: To explore the feasibility of the linear force–velocity (F–V) modeling approach to detect selective changes of F–V parameters (ie, maximum force [F 0], maximum velocity [V 0], F–V slope [a], and maximum power [P 0]) after a sprint-training program. Methods: Twenty-seven men were randomly assigned to a heavy-load group (HLG), light-load group (LLG), or control group (CG). The training sessions (6 wk × 2 sessions/wk) comprised performing 8 maximal-effort sprints against either heavy (HLG) or light (LLG) resistances in leg cycle-ergometer exercise. Pre- and posttest consisted of the same task performed against 4 different resistances that enabled the determination of the F–V parameters through the application of the multiple-point method (4 resistances used for the F–V modeling) and the recently proposed 2-point method (only the 2 most distinctive resistances used). Results: Both the multiple-point and the 2-point methods revealed high reliability (all coefficients of variation <5% and intraclass correlation coefficients >.80) while also being able to detect the group-specific training-related changes. Large increments of F 0, a, and P 0 were observed in HLG compared with LLG and CG (effect size [ES] = 1.29–2.02). Moderate increments of V 0 were observed in LLG compared with HLG and CG (ES = 0.87–1.15). Conclusions: Short-term sprint training on a leg cycle ergometer induces specific changes in F–V parameters that can be accurately monitored by applying just 2 distinctive resistances during routine testing.
Restricted access
Optimal Resistive Forces for Maximizing the Reliability of Leg Muscles’ Capacities Tested on a Cycle Ergometer
Amador García-Ramos, Alejandro Torrejón, Antonio J. Morales-Artacho, Alejandro Pérez-Castilla, and Slobodan Jaric
This study determined the optimal resistive forces for testing muscle capacities through the standard cycle ergometer test (1 resistive force applied) and a recently developed 2-point method (2 resistive forces used for force-velocity modelling). Twenty-six men were tested twice on maximal sprints performed on a leg cycle ergometer against 5 flywheel resistive forces (R1–R5). The reliability of the cadence and maximum power measured against the 5 individual resistive forces, as well as the reliability of the force-velocity relationship parameters obtained from the selected 2-point methods (R1–R2, R1–R3, R1–R4, and R1–R5), were compared. The reliability of outcomes obtained from individual resistive forces was high except for R5. As a consequence, the combination of R1 (≈175 rpm) and R4 (≈110 rpm) provided the most reliable 2-point method (CV: 1.46%–4.04%; ICC: 0.89–0.96). Although the reliability of power capacity was similar for the R1–R4 2-point method (CV: 3.18%; ICC: 0.96) and the standard test (CV: 3.31%; ICC: 0.95), the 2-point method should be recommended because it also reveals maximum force and velocity capacities. Finally, we conclude that the 2-point method in cycling should be based on 2 distant resistive forces, but avoiding cadences below 110 rpm.
Restricted access
Influence of Coaching Condition on the Magnitude and Reliability of Drop Jump Height in Men and Women
Alejandro Pérez-Castilla, F. Javier Rojas, John F.T. Fernandes, Federico Gómez-Martínez, and Amador García-Ramos
This study examined the effect of different coaching conditions on the magnitude and reliability of drop jump height in men and women. Nineteen collegiate sport sciences students (10 men) performed two sets of 10 drop jumps under four different coaching conditions: neutral, augmented feedback, external focus of attention, and a combination of augmented feedback and external focus of attention. The augmented feedback condition revealed a significantly higher jump height than the neutral condition (p = .002), while no significant differences were observed for the remaining conditions (p ≥ .38). The external focus of attention condition was more reliable than the neutral and augmented feedback conditions (coefficient of variationratio ≥ 1.15), while no differences were observed between the remaining conditions. These results suggest that both the magnitude and reliability of the drop jump height performance are influenced by the coaching condition.
Restricted access
Precision of 7 Commercially Available Devices for Predicting Bench-Press 1-Repetition Maximum From the Individual Load–Velocity Relationship
Alejandro Pérez-Castilla, Antonio Piepoli, Gabriel Garrido-Blanca, Gabriel Delgado-García, Carlos Balsalobre-Fernández, and Amador García-Ramos
Objective: To compare the accuracy of different devices to predict the bench-press 1-repetition maximum (1RM) from the individual load–velocity relationship modeled through the multiple- and 2-point methods. Methods: Eleven men performed an incremental test on a Smith machine against 5 loads (45–55–65–75–85%1RM), followed by 1RM attempts. The mean velocity was simultaneously measured by 1 linear velocity transducer (T-Force), 2 linear position transducers (Chronojump and Speed4Lift), 1 camera-based optoelectronic system (Velowin), 2 inertial measurement units (PUSH Band and Beast Sensor), and 1 smartphone application (My Lift). The velocity recorded at the 5 loads (45–55–65–75–85%1RM), or only at the 2 most distant loads (45–85%1RM), was considered for the multiple- and 2-point methods, respectively. Results: An acceptable and comparable accuracy in the estimation of the 1RM was observed for the T-Force, Chronojump, Speed4Lift, Velowin, and My Lift when using both the multiple- and 2-point methods (effect size ≤ 0.40; Pearson correlation coefficient [r] ≥ .94; standard error of the estimate [SEE] ≤ 4.46 kg), whereas the accuracy of the PUSH (effect size = 0.70–0.83; r = .93–.94; SEE = 4.45–4.80 kg), and especially the Beast Sensor (effect size = 0.36–0.84; r = .50–.68; SEE = 9.44–11.2 kg), was lower. Conclusions: These results highlight that the accuracy of 1RM prediction methods based on movement velocity is device dependent, with the inertial measurement units providing the least accurate estimate of the 1RM.
Restricted access
Reliability of the Load–Velocity Relationship Obtained Through Linear and Polynomial Regression Models to Predict the 1-Repetition Maximum Load
Francisco Luis Pestaña-Melero, G. Gregory Haff, Francisco Javier Rojas, Alejandro Pérez-Castilla, and Amador García-Ramos
This study aimed to compare the between-session reliability of the load–velocity relationship between (1) linear versus polynomial regression models, (2) concentric-only versus eccentric–concentric bench press variants, as well as (3) the within-participants versus the between-participants variability of the velocity attained at each percentage of the 1-repetition maximum. The load–velocity relationship of 30 men (age: 21.2 [3.8] y; height: 1.78 [0.07] m, body mass: 72.3 [7.3] kg; bench press 1-repetition maximum: 78.8 [13.2] kg) were evaluated by means of linear and polynomial regression models in the concentric-only and eccentric–concentric bench press variants in a Smith machine. Two sessions were performed with each bench press variant. The main findings were: (1) first-order polynomials (coefficient of variation: 4.39%–4.70%) provided the load–velocity relationship with higher reliability than the second-order polynomials (coefficient of variation: 4.68%–5.04%); (2) the reliability of the load–velocity relationship did not differ between the concentric-only and eccentric–concentric bench press variants; and (3) the within-participants variability of the velocity attained at each percentage of the 1-repetition maximum was markedly lower than the between-participants variability. Taken together, these results highlight that, regardless of the bench press variant considered, the individual determination of the load–velocity relationship by a linear regression model could be recommended to monitor and prescribe the relative load in the Smith machine bench press exercise.
Restricted access
Differences in the Load–Velocity Profile Between 4 Bench-Press Variants
Amador García-Ramos, Francisco Luis Pestaña-Melero, Alejandro Pérez-Castilla, Francisco Javier Rojas, and Guy Gregory Haff
Purpose: To compare the load–velocity relationship between 4 variants of the bench-press (BP) exercise. Methods: The full load–velocity relationship of 30 men was evaluated by means of an incremental loading test starting at 17 kg and progressing to the individual 1-repetition maximum (1RM) in 4 BP variants: concentric-only BP, concentric-only BP throw (BPT), eccentric-concentric BP, and eccentric-concentric BPT. Results: A strong and fairly linear relationship between mean velocity (MV) and %1RM was observed for the 4 BP variants (r 2 > .96 for pooled data and r 2 > .98 for individual data). The MV associated with each %1RM was significantly higher in the eccentric-concentric technique than in the concentric-only technique. The only significant difference between the BP and BPT variants was the higher MV with the light to moderate loads (20–70%1RM) in the BPT using the concentric-only technique. MV was significantly and positively correlated between the 4 BP variants (r = .44–.76), which suggests that the subjects with higher velocities for each %1RM in 1 BP variant also tend to have higher velocities for each %1RM in the 3 other BP variants. Conclusions: These results highlight the need for obtaining specific equations for each BP variant and the existence of individual load–velocity profiles.
Restricted access
Validity of a Linear Velocity Transducer for Testing Maximum Vertical Jumps
Alejandro Pérez-Castilla, Belén Feriche, Slobodan Jaric, Paulino Padial, and Amador García-Ramos
This study aimed to examine the validity of mechanical variables obtained by a linear velocity transducer from the unconstrained and constrained squat jump (SJ). Twenty-three men were tested on the unconstrained SJ and the SJ constrained by a Smith machine. Maximum values of force, velocity, and power were simultaneously recorded both by a linear velocity transducer attached to a bar of mass of 17, 30, 45, 60, and 75 kg and by a force plate. Linear velocity transducer generally overestimated the outcomes measured as compared to the force plate, particularly in unconstrained SJ. Bland-Altman plots revealed that heteroscedasticity of errors was mainly observed for velocity variables (r 2 = .26–.58) where the differences were negatively associated with the load magnitude. However, exceptionally high correlations were observed between the same outcomes recorded with the 2 methods in both unconstrained (median r = .89 [.71–.95]) and constrained SJ (r = .90 [.65–.95]). Although the systematic and proportional bias needs to be acknowledged, the high correlations between the variables obtained by 2 methods suggest that the linear velocity transducer could provide valid values of the force, velocity, and power outputs from both unconstrained and constrained SJ.
|
__label__pos
| 0.795134 |
Posted on
Write a Python program WSDpy that implements the Naive Bayes algorithm for word
Write a Python program WSD.py that implements the Naive Bayes algorithm for word sensedisambiguation, as discussed in class. Specifically, your program will have to assign a giventarget word with its correct sense in a number of test examples. You are not to use externallibraries such as pandas, scikit-learn, or NLTK.Please implement the Naive Bayes algorithm and cross-validation yourself, do notuse scikit-learn (or other machine learning library).You will train and test your program on a datase
Read More
|
__label__pos
| 0.989415 |
Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Screen reader users: click this link for accessible mode. Accessible mode has the same essential features but works better with your reader.
Patents
1. Advanced Patent Search
Publication numberUS3507376 A
Publication typeGrant
Publication dateApr 21, 1970
Filing dateNov 16, 1967
Priority dateNov 16, 1967
Also published asDE1809195A1
Publication numberUS 3507376 A, US 3507376A, US-A-3507376, US3507376 A, US3507376A
InventorsHaig Kafafian
Original AssigneeHaig Kafafian
Export CitationBiBTeX, EndNote, RefMan
External Links: USPTO, USPTO Assignment, Espacenet
Communication system for the handicapped
US 3507376 A
Abstract available in
Images(4)
Previous page
Next page
Claims available in
Description (OCR text may contain errors)
H. KAFAFIAN A ril 21, 1970 COMMUNICATION SYSTEM FOR THE HANDICAPPED Filed Nov. 16. 1967 4 Sheets-Sheet'l INVENTOR fin/e KnFAF/AN ATTORNEYS April 21, 1970 H. KAFAFIAN COMMUNICATION SYSTEM FOR THE HANIHCAPPED 4 Sheets-Sheet 5 Filed NOV. 16, 1967 A ril 21, 1970 H. KAFAFIAN 5 COMMUNICATION SYSTEM FOR THE HANDICAPPED Filed Nov. 16, 1967 4 Sheets-Sheet 4 5' INVENTOR. j I A I Hfl/G KAFHFMN A T TOR NF) Y5 United States Patent Office 3,507,376 Patented Apr. 21, 1970 Int. Cl. B41j 5/10 US. Cl. 19719 Claims ABSTRACT OF THE DISCLOSURE The present invention relates to an improved method and apparatus for operating typewriting, Braille or other program-controlled machines, which are particularly suited for use by handicapped persons since the manual operation of a conventional keyboard is not required. According to one embodiment of the invention the op erator is provided with an arrangement of contacts'or other means fixed upon his finger tips and electrically connected to a master character selector. The contacts may be activated by moving the appropriate fingers adjacent to a flat conductive plate located in a console on or remote from the machine in order to complete the electrical circuits necessary for the selection of a predetermined key and operation of the machine. In a second embodiment, the electrical contacts are fixed in the fingers of gloves worn by the operator. In that embodiment the thumb of each glove acts as a conductive plate and the operator need only place the respective finger contacts against the thumb in order to complete the desired electrical circuits.
In either of these embodiments the finger contacts may be replaced by pressure actuated switches mounted on the fingers or installed in the glove fingers. Such switches need not be touched to a conductive plate but may be operated by merely pressing the finger against any hard surface.
In all of the above embodiments a dual input matrix circuit is used as a master character selector; with the x input circuits being controlled by the right hand contacts and the y inputs being controlled by the left hand contacts, for example. A dual input code or machine language is used whereby each individual character is selected by closing a unique combination of one contact of the x input circuits and one contact of the y input circuits.
In another embodiment of the invention, the same dual input code is used but the finger contacts are replaced by two small groupings of keys. For example, a left grouping of seven keys controls the y input circuits and a right grouping of seven keys controls the x input circuits of the character selector. The two key groupings are mounted near each other so that they may beeasily spanned and depressed by one hand of an operator or by an individual wearing prosthetic and/or orthotic/ prosthetic devices. Alternatively, the two groups of keys may be mounted, respectively, on the right and left sides of a wheelchair.
BACKGROUND OF THE INVENTION anism or keyboard which accepts the program; a memory in the form of key bars or other mechanisms which store functions in the machine; and an output or visual readout which may take the form of a picture, typed words and characters, Braille characters, three dimensiona1 impressions, punched tape, magnetic tape or palpable vibrations.
Many of the common program-controlled machines such as typewriters, business machines, and computers for example include keyboards as the man-machine interface or input mechanism. These keyboards, conventionally include a large plurality of keys, each of which represents one function, character, or symbol in the upper case position and other functions, characters, or symbols in the lower case position and require that the operator strike the key and depress it in order to print the character or carry out the desired function. Thus, the ordinary programming of a key-board mechanism is accomplished by the operators selection of one finger at a time and direction of that finger to a specific letter or function key. Then the preselected key is struck and depressed in order to accomplish the desired function. In order to achieve continuous operation of a keyboard at a satisfactory speed, the location of each of the keys must be mentally realized by the operator, and the operators hands must be coordinately moved to new 10- cations in order to reach the appropriate keys. Certain limitations are present in such a conventional keyboard even with respect to a physically able operator. For Braille machine operation use of as many as six fingers at a time are necessary to obtain the desired character or symbol. Thus, extensive training and practice is necessary for an operator to attain superior typewriter or Braille keyboard operating proficiency and even then the ability of an experienced keyboard operator to adjust to or transfer between modified arrangements of keys or functions is usually nil. Also, the fact that a typewriter operator continually performs a sequential, single, digitto-key procedure withoutarm or hand-support eventually leads to fatigue.
A language-structure problem also presents obstacles for keyboard operators. Thus, some linguists and others knowledgeable of language structure are aware of inherent inadequacies in the conventional typewriter keyboard layout. For example, although ED, ING, THE and AND, appear frequently in the English language as sequential groups of letters, the locations of these letters are widely spaced on the. keyboard. In the French language the most frequently used digraphs are ES, EN, LE and DE. Again the. keys for these letters are not in an ideal location for rapid vtyping. In either of these languages typing speed is affected when fingers must be manipulated to widely spaced positions. In addition, the probability of introducing errors is increased when the series of characters to be sequentially programmed are at remote locations on the keyboard. These unnatural finger stretches .deserve special attention when standard keyboards are considered. However, with Braille machines,
where simultaneous finger manipulations of up to six fingers at one time are used, the difficulty in attaining rapid programming by blind persons, who might therefore also have poorer manual dexterity, is even more serious. In addition most of the other factors mentioned above cause vastly more severe constraintsfor disabled machine operators than for physically able operators.
For example, a significant restriction for the blind in typing is the difficulty in merely learning and teaching the positions of the keys and the-use of the conventional keyboard. In fact the difficulties of the blind in this respect are compounded since they are compelled to learn one programming method for typewriters and another, completely different keyboard and programming method, for Braille machines.
Another problem is the obvious futility of even a sighted person, handicapped by a debilitating condition such as cerebral palsy or multiple sclerosis, in trying to exercise the manual dexterity demanded by a typewriter keyboard comprised of about fifty haphazardly-positioned keys. Thus, the involuntary muscular contractions associated with these disabling conditions usually preclude the satisfactory manipulation of an intricate keyboard. Likewise, an amputee with the aid of his prosthesis may be entirely unable to sequentially strike and depress the keys of a conventional keyboard one at a time. A further inherent constricting factor to the teaching and learning of conventional keyboard use by all handicapped persons is the adverse psychological effect and frustration associated with their usually slow progress in learning to perform movements in accordance with the complex machine language and key placement;
A number of systems employing other than conventional keyboards have been devised in the prior art in attempts to overcome some of the above factors and enable high speed typing or permit disabled persons to satisfactorily operate programmed machines. For example some typing systems, such as that described in US. Patent No. 2,613,797 to Hogg utilize an expanded lever and key system which overlays the ordinary keyboard and permits the operator to use a closed fist or other portion of the hand in the writing operation. Another system designed for use by invalids, described in US. Patent No. 2,924,321, includes a light beam and photocell arrangement which may be controlled by the operator to select a particular letter to be printed by the remotely located machine. Yet another approach to typing is described in US. Patent No. 3,022,878 to Seibel et al. which discloses a machine control system designed especially for aerospace applications wherein the operator is equipped with a three-position transducer for each finger and is required to perform only small movements of his fingers in order to actuate the controls of the machine.
It should be apparent that each of the systems mentioned above is nevertheless subject'to certain of the objections mentioned above with respect to conventional keyboard systems. In particular it is apparent that the Seibel et a1. system demands high manual dexterity and would not be suitable for use by those with debilitating conditions and/or people who do not have fingers.
SUMMARY OF THE INVENTION The present invention provides a simplified apparatus for controlling typewriters, Braille or other programcontrolled machines which overcomes the above-mentioned disadvantages in the use of conventional keyboard machines. It is one object of this invention to provide a machine input apparatus which may be located remote from the machine itself, if necessary, and which may be operated by a person wearing prosthetic and/ or orthotic/ prosthetic devices or by an amputee. It is a further object of the invention to provide a control system which utilizes a unique machine language compatible with the operation of a dual input master character selector; which language is easily and rapidly learned and may be implemented by handicapped persons on the interface apparatus provided.
In one embodiment of the invention for persons with fingers but who may be blind, for example, electrical contacts are fixed on the finger tips of both hands of the operator by means of plastic clasps and a pair ofcorresponding fiat conductive plates are provided to which the operator may touch the contacts. An electrical conductor is provided from each finger contact to a master character selector circuit and the conductive plates are energized by a suitable low voltage direct current source whereby input signals to the master character selector may be generated by the operator merely by touching one of the contacts to the corresponding conductiye plate. The contacts of the left hand are utilized as the y inputs and the contacts of the right hand as the x inputs to a dual input master character selector.
A unique dual input code or machine language is used with the system whereby any desired control operation such as the actuation of an appropriate key operating solenoid on an electric typewriter may be initiated by touching one predetermined contact of a y input and one predetermined contact of an x input to the corresponding left and right conductive plates. More than one electrical contact may be provided on each finger, for example one contact may be located at the point of each finger tip and a second contact on the ball of each finger tip whereby they may be easily manipulated even by a handicapped person. This arrangement permits a satisfactory number of unique character combinations in the dual input machine language to handle the operation of all the keys on a conventional typewriter keyboard, as well as Braille and other program-controlled machines.
In a second embodiment of the invention, the electrical contacts are fixed in the fingers of gloves worn by the operator. In that embodiment, the conductive plates are eliminated and the thumb contacts of the gloves are connected to a suitable source of voltage so that the operator need only place the respective finger contacts against the thumb contacts of the gloves in order to complete the desired electrical circuits.
In a third embodiment of the invention the finger or glove contacts are replaced by pressure actuated switches. Such switches need not be touched to a conductive plate, but may instead be operated merely by pressing the finger carrying any particular switch against a hard surface so as to apply the necessary light operating pressure upon that switch.
In a fourth embodiment of the invention, the same dual input code is also used but the finger contacts are replaced by two small groupings of keys. For example, a left grouping of seven keys controls the y input circuits and a right grouping of seven keys controls the x input circuits. The two key groupings are mounted near each other. so that they may be easily spanned and operated by one hand of an operator or an individual wearing prosthetic and/or orthotic/prosthetic devices.
Alternatively the two groups of keys described above may be separated and mounted, respectively, near the right and left arm rests of a wheelchair so that an invalid sitting therein may easily operate said keys.
It should be noted that other types of responsive devices can be employed in place of the contacts, pressure switches or key groupings in order to adapt the present invention for use by an invalid capable of limited response. Such arrangements might include the use of photo responsive cells or electrical circuits actuated by muscular contractions and/or electrical outputs from the central nervous system.
Likewise it is not necessary for an operator to use all ten fingers in order to provide a sufficient number of dual input combinations to control all the keys on a typewriter, for example. Thus, combinations of dual inputs controlled by fingers on one hand may be used, with or without combinations of inputs controlled by other body members such as arms and legs, for example, in order to achieve the necessary number of input combinations.
In addition, the y and x inputs to the selection circuit need not be exclusively controlled by the left and right hands, respectively. On the contrary, the arrangements of keys or contacts may be designed so that certain x or y inputs are located in the same grouping or under controlof one hand.
BRIEF DESCRIPTION OF THE DRAWINGS The novel features of the invention are set forth in the appended claims. The invention itself, both as to its construction and manner of o eration together with additional objects and advantages thereof, will be best understood from the following description of a preferred embodiment when read in conjunction with the accompanying drawing in which:
FIG. 1 is a diagrammatic view showing the present invention adapted for use as a control system for a typewriter;
FIG. 2 is a sectional view of the bottom of the type writer showing electrically responsive control mechanisms for operating the typewriter keys;
FIG. 3 is a partial top section of FIG. 2 showing the horizontal orientation of the key operating solenoids;
FIG. 4 is a diagram showing one preferred embodiment of the invention including a schematic diagram of the master character selector circuit and the electrical contacts fastened to plastic clasps worn by the operator;
FIG. 5 is a schematic diagram of an alternative embodiment of the invention shown in FIG. 4, wherein a separate conductive plate is provided for each hand of the operator;
FIG. 6 is a diagrammatic view of a glove having electrical contacts mounted in the fingers which may be used in another embodiment of the invention;
FIG. 7 is a schematic diagram of yet another alternative embodiment of the invention wherein the finger contacts are replaced by keys;
FIG. 8 is a chart showing a dual input machine language designed to operate the keys on a typewriter; and
FIG. 9 is a detailed view of a plastic clasp, including two electrical contacts, which may be worn on the finger of the machine operator.
DESCRIPTION OF THE PREFERRED "EMBODIMENTS Referring now to FIG. 1, a typewriting machine 1 is shown supported on one end of a console 2. The console also acts as a support for large flat metallic plate 4 mounted within a suitable frame 5 which can be fastened to the console by screws or bolts 7 if desired. An electrically responsive mechanism and apparatus for operating the keys of the typewriter is contained within a housing 8 attached to the underside of the typewriter; while a master character selection circuit electrically connected therewith is confined within housing 9 shown conveniently attached to the bottom of the console beneath the conductive plate.
The operator of the machine may be seated in front of the console in any position where his hands comfortably reach the conductive plate. In order to operate the machine the operators hands are equipped with electrical contacts mounted on plastic finger clasps in a manner generally indicated in FIGS. 4 and 5. To cause any character on the typewriter to be printed, the operator need only touch one predetermined contact of the left hand and one predetermined contact of the right hand to any portion of the conductive plate in a manner which will be explained hereinafter.
FIG. 2 shows an end section of the details of the key operating mechanism mounted beneath the typewriter keyboard. As shown, each typewriter key 20 is connected by means of a rod 21 to an end 24 of an L-shaped link 23. The plurality of links are pivotably mounted on an axle 26 supported beneath the typewriter by braces 28. Thus, any typewriter key will be depressed to print a character when its corresponding link is caused to pivot or rotate in a clockwise direction. The other end 25 of each pivotable link is connected by means of one of the rods 30 to one of a plurality of corresponding solenoids 32, which may be called motor devices, fixedly arranged in four spaced banks angularly offset with respect to each other as shown.
Each solenoid includes an outer housing 35, a cylindrical armature 33 and a coil 34 surrounding the armature and wound so that the armature will be moved a small distance away from axle 26 when the solenoid coil is energized and returned to its original position when the coil is deenergized. The coil of each solenoid is connected, by conductors not shown, in circuit with the master character selector whereby the coils and therefore the typewriter keys may be selectively actuated by the operator.
FIG. 3 shows a partial section of a top view of one upper and one lower bank of the key operating solenoids 32. As shown the solenoids of the upper bank are horizontally offset with respect to the solenoids of the lower bank in order to provide operating clearance for the rods 30.
It should be understood that, while only a single row of typewriter keys are shown in FIG. 2, the mechanism described may be easily adapted to handle multiple rows of keys merely by adding the necessary number of additional solenoids and key linkages.
It should also be understood that while a particular mechanism has been described herein for operating typewriter keys the present invention is not limited to the embodiment shown. Rather, any electrically responsive mechanism for operating typewriter keys or corresponding input elements of any other program-controlled mechanism would be suitable for use in the system of the present invention.
FIG. 4 shows a diagrammatic view of one preferred embodiment of the invention which includes a schematic of the dual input master character selection circuit utilized in the invention. In the upper part of the figure a large conductive plate 40 is shown which corresponds to the plate 4 shown mounted on the console in FIG. 1. The operators hands are shown in dotted outline over the plate and plastic clasps are fixed upon the fingers of each hand. Referring briefly to FIG. 9, each plastic clasp 10 includes a split expansible ring portion 11 designed to hold the clasp firmly, but comfortably, about the tip of one of the operators fingers; as well as a nose portion 13 upon the exterior of which two electrical contacts 15, 16 are attached. A separate electrical conductor is connected to each of the electrical contacts, which are oriented on the clasp so that one contact 15 may be addressed to the conductive plate by laying the finger on the plate in a flat position and the second contact 16 may be addressed to the plate by touching the tip of the finger to the plate. The inner portion of the clasp may be lined with a suitable material to act as padding and insulate the wearer from the electrical contacts'although this is not essential.
Referring back to FIG. 4 it should be apparent that four fingers of each hand of the operator are provided with plastic clasps. Of these the thumb clasp includes but a single electrical contact while each of the other fingers has two electrical contacts; making a total of seven contacts on each hand, all of which may be easily manipulated even by a handicapped person to touch the board conductive plate. The seven conductors from each hand may be gathered and bound into a separate flexible cable which is connected into the master character selector in a manner which does not unduly interfere with the movement of the operators hands.
As shown, the conductors from the left hand contacts are connected as the y input circuits 4147 and the seven conductors of the right hand are connected as the x input circuits 51-57 of the master character selection circuit 60.
For convenience the master character selector circuit is shown as including 49 coils which in actuality are the coils of the key operating solenoids shown in FIG. 3. Although these coils are schematically shown in electrical circuit with the diodes of the character selector circuit, it should be realized that they are physically confined in a housing beneath the typewirter. By the same token, a number of dual input circuits other than seven may be used in which case the number of elements in the master selector would vary. For example, eight y and eight x inputs have been used in one embodiment of the invention designed to operate a Braille machine.
In the preferred embodiment of the invention shown in FIG. 4 the coils correspond to the 49 keys or operators necessary to control the keys on a conventional typewriter in accordance with the machine language chart shown in FIG. 8 For convenience these coils are shown in FIG. 4 as being arranged in seven horizontal rows and seven vertical columns. Connected to the upper terminal of each coil is a solid state diode poled to permit current flow in one direction through the coil and block current flow in the opposite direction. The lower ends of the coils in each row are connected in common through a conductor to one of the x inputs 5157. The x inputs are connected, respectively, to the positive terminals of batteries 51a57a used to energize the solenoid coils. It should be apparent that any other suitable source of power could be used in place of the batteries shown. The negative terminals of the batteries are connected, respectively, through conductors 71-77 to the seven electrical contacts 71a77a controlled by the operators right hand. The upper or cathode terminals of all of the diodes in any respective column are connected through a common conductor to a corresponding one of the y input terminals 41-47. The y input terminals are connected, respectively, through conductors 61-67 to the seven electrical contacts 61a67a controlled by the operators left hand.
It should be apparent that any predetermined solenoid may be energized by simultaneously touching one appropriate contact controlled by the left hand and one appropriate contact controlled by the right hand to the conductive plate. For example should the thumb contact of the left hand and the tip contact of the middle finger of the right hand both be touched to the conductive plate a circuit would be completed from the positive terminal of battery 53a to x input 53 and then through coil 70, diode 69 to y input 47. The circuit may then be traced on through conductor 67 to contact 67a on the thumb of the operators left hand, through plate 40 to contact 73a on the tip of the middle finger of the operators right hand and on to completion along line 73 to the negative terminal of battery 53a. Note that all the possible circuits through the other coils of the same row which are connected to the battery 53a are open circuited at this time. Consequently only the solenoid associated with coil 70 will be operated by the operation described above.
In the preferred embodiment disclosed herein a battery voltage of 28 volts is used to energize the solenoids and thereby cause the selected key to be operated. However, through the choice of other equally suitable solenoids a lower battery voltage or any other suitable source of power may be employed. It should be noted that, although the finger clasps may be padded for comfortable wear and insulated from the electrical contacts, the current fiow in the circuits of the system is so slight as to present no problems should the conductive plate be touched by the operator.
In the event the operator, in trying to print a selected character, accidentally touches two contacts on one hand to the plate it should be apparent that two solenoid coils may be simultaneously energized in which case an error may occur in the desired output of the machine. However, this has not been found to be a serious drawback in the operation of the disclosed embodiment in view of the ease with which the contacts may be maniplated. Moreover, though the details are not disclosed herein, well known logic or voting circuits exist which may be easily embodied in the circuitry of the character selector in order to minimize output errors due to these mistakes on the part of the operator. In addition, time delay circuits may be easily added to the character selector to eliminate the need for the preselected contact on each hand to be simultaneously touched to the plate.
In addition it is not necessary that the x inputs be controlled exclusively by the right hand and the y inputs be controlled exclusively by the left hand. On the contrary, various combinations of x and 1 inputs may be placed under the control of either the right or the left hand merely by making appropriate connections.
It is believed to be a highly significant aspect of the invention that the dual input character selection circuit makes possible the use of the vastly simplified machine language shown in the chart of FIG. 8. In the chart, the various characters (letters and numbers) and operators (back space, tab, etc.) are set forth in the 49 center squares, while the various possible finger positions of the left and right hand of the operator are shown on either side of the bottom of the chart. It should now be apparent that to type the letter H, the flat contact of the index finger of the left hand and the flat contact of the middle finger of the right hand are used. Likewise the letter K may be printed by use of the flat contact of the ring finger of the left hand and the fiat contact of the middle finger of the right hand. As with a conventional typewriter keyboard all the keys are operable in a natural and shift position in order to print both upper and lower case letters. In order to print upper case letters with the present apparatus, the shift lock lever is first operated, then the desired upper case letter is printed, after which the shift unlock lever is operated. Alternatively the function of the shift lock and shift unlock circuits may be delegated to a separate circuit controlled by a shift bar mounted for convenient actuation by the operator. Thus, FIG. 1 shows a bar 6 which the operator may easily depress with his wrist or the base of his hand, without pausing appreciably in typing operations, in order to selectively print upper case letters or symbols.
An alternative embodiment of the invention is shown in FIG. 5 to include separate conductive plates 40a and 40b for each of the operators hands. In practice the two conductive plates may be mounted side by side on the console or, as is also the case where a single plate is used, in any other convenient location remote from the machine to be operated. The dual plate arrangement shown in FIG. 5 includes the same general arrangement of finger contacts and basically the same selector circuit as were used in the previously described embodiment. However, by dividing the plate, a single battery or power source may be used to service all the solenoids in conjunction with the selector circuit. Thus, by connecting the battery 58 between the two conductive plates, as shown, an energized circuit will be completed through any desired solenoid as the operator touches the appropriate two finger contacts to the respective conductive plates. In this manner the batteries 51a-57a are replaced by a single battery. In FIG. 5 spark suppression diodes 59 are connected in parallel with each coil to reduce sparks at the contacts in the circuits. These spark suppression diodes may be employed, as well, with any of the other embodiments of the invention.
In another alternative embodiment of the invention, the operator wears a glove-like apparatus, as is shown in FIG. 6, on each hand. The use of this type of glove eliminates the need for a conductive plate, since the thumb of the glove acts as a conductive plate and the operator need only touch an appropriate finger contact on each hand to the thurnb of the glove on that hand in order to control the machine. Thus, FIG. 6 shows a right-hand glove which includes two electrical contacts on each of the index, middle and ring fingers and a single contact mounted at the base of the index finger to comprise a total of seven finger contacts.
As before, each of the contacts is connected via one of the separate electrical conductors 71b-77b to an input of a selector circuit, not shown, of the same type used in the embodiment of FIG. 5. A similar glove is used on the left hand of the operator to control the y inputs to the selector circuit. The thumb of each glove includes a larger contact which is also insulated from the wearer and attached to a separate electrical conductor. Each of the contacts shown is located so as to be easily touched to one of the thumb contacts. It should be apparent that the thumb contact of the right hand will be connected to the positive terminal of a battery, not shown, and the thumb contact of the left hand connected to the negative terminal of the battery in which case the gloved hand embodiment will function as a machine control system using the same machine language as the other embodiments.
Yet another alternative embodiment of the invention is shown in FIG. 7 where 14 key controlled switches are used to control the machine instead of an arrangement of finger contacts. The switches are of a conventional type having two terminals which are bridged by a conductive bar when the key is depressed in order to complete an electrical circuit through the switch. The keys are shown arranged into two groups of seven each, conveniently mounted upstanding from a keyboard where they may be operated by both hands of an operator. However, it should be noted that the arrangement of the keys is sutficiently compact to be spanned by a single hand of the operator whereby one-handed operation is quite possible. It should also be apparent that the offset orientation of the keys enables their convenient operation by a person wearing prosthetic and/or orthotic/ prosthetic devices. In this regard it should be noted that the wearer of artificial arms may have difficulty in maintaining control through a wide angle of movement. Consequently the rather compact dual input arrangement of fourteen keys described above is significantly easier for an armless person to operate with his prosthesis than a conventional typewriter keyboard where approximately 49 keys are spaced over a large area.
As in the other embodiments the y inputs of the master selector are controlled by the seven left keys 8187- and the x inputs by the seven right keys 91-97 whereby the same character selector and machine language may be used. For example, the three upper keys 81, 83, 85 of the left hand group of FIG. 7 may be seen to correspond respectively to the tip positions of the ring, middle and index fingers of the left hand as shown in FIG. 8. Likewise the lower three small keys 82, 84, 86 correspond respectively to the fiat positions of the ring, middle and index fingers of the same hand. The remaining large key 87 is equivalent to the thumb contact of the left hand. As shown, the upper terminals of the left hand keys are commonly connected to one terminal of a battery 88 and the upper terminals of the right hand keys are commonly connected to the other battery terminal. Therefore, it should be apparent that the simultaneous depression of one key of the left hand group and one key from the right hand group can again energize a unique solenoid.
Although any of the above embodiments may be efficiently used by non-handicapped individuals, it 1s with respect to the handicapped that the present invention takes on the most significance. Thus it should be apparent that the embodiments of FIGS. 4 and 5 are particularly adapted for use by the blind and those affiicted with debilitating diseases which impair the free and coordinate movement of their fingers. In the case of the blind the ease with which the machine language of the present invention may be learned and the ease with which a blind operator may carry out the necessary physical movements of the present invention where he is relieved of the necessity of continuously reorienting his hands to a keyboard result in a mode of machine control vastly improved over any other available system for operating a conventional typewriter keyboard or Braille machine. For example, it requires considerably less time to achieve satisfactory typing skill using the present system, than is usually required to operate a conventional Braille machine. At the same time, the absence of any necessity for timed coordinated movements to an exact location by the fingers of the operator obviously results in a machine control system which is more desirable for the victims of cerebral palsy than a conventional keyboard. Alternatively the key groupings shown in conjunction with FIG. 7 might be separated and mounted, respectively, near the right and left arm rests on a wheelchair so that a disabled person confined therein might easily operate said keys without arm and/or wrist movements. Likewise a suitable arrangement of keys could be designed for use by a person con fined in some other special environment such as an oxygen tent.
The embodiment described in conjunction with FIG. 6 also has special significance when used by a blind person since it eliminates even the necessity for locating a conductive plate. It should also be clear that the embodiment of FIG. 7 will enable the wearers of prosthetic and/ or orthotic/ prosthetic devices to operate program-controlled machines whereas they are completely helpless to operate a conventional keyboard.
In addition to the embodiments described herein, it should be further apparent that the apparatus of the present invention might be easily adapted for operation by other body parts whereby amputees or other severely disabled persons may also have access to the communication media of program-controlled machines.
What is claimed is:
1. Apparatus for man-machine communication comprising:
a dual input interface for the direct input of signals by an operator,
said interface including two spaced input sections, each comprising a plurality of individual input means, the input means of one section being positioned and adapted to be selectively actuated by a movement of one portion of the operators body, and the input means of the second section being positioned and adapted to be selectively actuated by a second portion of the operators body;
a signal output means assembly disposed at a point remote from said input means, said output means comprising a plurality of individual output elements each adapted to signal a different letter of an entire alphabet,
each of said input means incorporating a single switch;
a source of electric power, and circuit means establishing an electrical connection between said dual input interface and said signal output means remote therefrom, each of said switches controlling a single circuit only of said circuit means,
said circuit means being arranged to connect each of said output elements to one and only one of the input means of each input section, through the respective switches thereof, said circuit means being further arranged to require that the actuation of each output means requires the actuation of one input means of each input section, said circuit means being still further arranged so that the actuation of any two or more input means of a single input section without the actuation of any input means of the other input section will not operate any of the output means,
whereby the simultaneous bilateral movement of two portions of the operators body efl ects selective operation of a single output element to signal a single desired letter of the alphabet.
2. The apparatus of claim 1 wherein said circuit means comprises a detachable interconnection whereby different interfaces may be selectively coupled to a single signal output means assembly.
3. A control apparatus comprising:
a multiplicity of electrically operable motor devices, each arranged to actuate a corresponding movable device;
said motor devices being arranged to define a matrix of rows and columns of motor devices;
a first plurality of contacts respectively connected to each of said rows and a second plurality of contacts respectively connected to each of said columns;
a source of electric power;
further contact means arranged to be engaged with a selected contact of each of said first and second plurality of contacts to complete a circuit, including said source of electric power and that motor device common to the row and column connected to said selected contacts; and
means for mounting said first and second plurality of contacts on the fingers of an operators hands, said further contact means being positioned so as to be readily engageable by said first and second plurality of contacts on the fingers of the operators hands.
4. Control apparatus as defined in claim 3 wherein said further contact means comprises at least one conductive metal plate adapted to be engaged by said contacts on the operators fingers.
5. Control apparatus as defined in claim 3 wherein said motor devices are solenoids and wherein each movable device is a typewriter key.
6. Control apparatus as defined in claim 3 wherein said further contact means comprises a single conductive plate adapted to be engaged by at least one contact of each of said first and second pluralities, said source of electric power being connected in series with contacts of one of said plurality of contacts and their corresponding motor devices.
7. Control apparatus as defined in claim 3 wherein said further contact means comprises two conductive plates each positioned to be engaged by a corresponding one of said first or second plurality of contacts, said source of electric power being connected between and in series with said plates.
8. Control apparatus as defined in claim 3 wherein said first and second pluralities of contacts are mounted on the fingers of gloves adapted to be worn by an operator.
9. Control apparatus as defined in claim 3 wherein said contacts of said first and second pluralities of contacts are mounted on resilient clips each adapted to gri and be held on a finger tip.
10. Control apparatus as defined in claim 3 wherein said further contact means comprises a conductive plate and means for mounting the same on the thumb of an operators hand in position to be easily engaged by any contact on a finger of that hand.
References Cited UNITED STATES PATENTS 2,031,017 2/1936 Tenis.
2,912,090 11/1959 Holmes.
1,904,784 4/1933 Garrity et al. 19719 XR 2,566,971 9/1951 Watson 197--19 2,613,797 10/1952 Hogg 19719 2,981,395 4/1961 Gibson 197-19 3,022,878 2/1962 Seibel et al. 19719 3,158,318 11/1964 Beason et al. 235146 3,166,856 1/1965 Uttal 35-6 3,234,664 2/1966 Yaeger 356 XR 3,241,115 3/1966 Maling 197--1XR 3,280,267 10/1966 Feucht 340-166 XR 3,308,439 3/1967 Tink et al. 340-1725 3,375,497 3/1968 Jones et al. 340-176XR EDGAR S. B-URR, Primary Examiner US. Cl. X.R.
Patent Citations
Cited PatentFiling datePublication dateApplicantTitle
US1904784 *Dec 22, 1931Apr 18, 1933 Electbic automatic becobding scale
US2031017 *Dec 18, 1931Feb 18, 1936Robert TevisKeyboard
US2566971 *Jun 4, 1948Sep 4, 1951IbmRemote control apparatus for typewriting machines
US2613797 *Jun 30, 1950Oct 14, 1952Hogg Reuben TTypewriter operating apparatus
US2912090 *Dec 16, 1957Nov 10, 1959Holmes Jr LawrenceRemote control system for stenographic machines
US2981395 *Jul 9, 1957Apr 25, 1961Gibson Charles HOperator mechanism for the control of the automatic operation of a series of successive individually selected operational steps in business, calculating and similar machines
US3022878 *Jan 11, 1960Feb 27, 1962IbmCommunication device
US3158318 *Sep 12, 1963Nov 24, 1964The National Cash Register CompanyDetent controlling mechanism
US3166856 *Feb 9, 1962Jan 26, 1965IbmEducational device
US3234664 *Sep 5, 1963Feb 15, 1966Honeywell IncTraining apparatus
US3241115 *May 28, 1962Mar 15, 1966Maling Reginald GeorgeControl systems for use by partially or totally paralyzed persons
US3280267 *Mar 8, 1963Oct 18, 1966Siemens AgCross-wire control circuit arrangement for communication systems
US3308439 *Jan 2, 1964Mar 7, 1967Ncr CoOn-line system
US3375497 *Apr 27, 1964Mar 26, 1968Ncr CoMatrix control circuitry using gate controlled unidirectional signalling devices
Referenced by
Citing PatentFiling datePublication dateApplicantTitle
US3705424 *Mar 29, 1971Dec 5, 1972Richard P Harvey JrElectrical switching apparatus utilizing conductivity of the human skin
US3781802 *Mar 27, 1972Dec 25, 1973H KafafianMethod of communication and/or testing of the handicapped
US3824354 *Mar 17, 1972Jul 16, 1974Anderson NOperator means associated with multiple switch array and signal to function correlator means
US3835468 *Jun 29, 1972Sep 10, 1974Dos Santos ARational alphabetic system
US4008793 *Sep 7, 1972Feb 22, 1977Vittorino TerracinaTypewriting machine
US4138197 *Jul 22, 1977Feb 6, 1979National Controls, Inc.Key actuator
US4194085 *Sep 14, 1978Mar 18, 1980Scelzi Joseph IFinger keyer for code transmission
US4274753 *Oct 2, 1978Jun 23, 1981Brown David LNon-oral communication device
US4408192 *Aug 8, 1980Oct 4, 1983Ward Geoffrey AMethod and device for use by disabled persons in communicating
US4517424 *Jun 12, 1984May 14, 1985Inro FranceHand-secured pushbutton control device
US4655621 *Aug 21, 1984Apr 7, 1987Richard HoldenCombinatorial keyboards which encode characters and a space
US4661005 *Jan 16, 1984Apr 28, 1987Creative AssociatesSpittable keyboard for word processing, typing and other information input systems
US5200988 *Mar 11, 1991Apr 6, 1993Fon-Ex, Inc.Method and means for telecommunications by deaf persons utilizing a small hand held communications device
US5220652 *Jun 22, 1989Jun 15, 1993Rowley Blair AComputer application programs data input interface for handicapped persons responsive to multiple push buttons for selecting data stored in binary tree
US5581484 *Jun 27, 1994Dec 3, 1996Prince; Kevin R.Finger mounted computer input device
US5993089 *Feb 3, 1997Nov 30, 1999Burrell, Iv; James William8-bit binary code for use as an 8-dot braille arrangement and data entry system and method for 8-key chordic binary keyboards
US6943776Feb 25, 2002Sep 13, 2005Herman EhrenburgComputer-compatible, visualizably presented, intuitive and self-explanatory manual input system
US8884790 *Mar 3, 2011Nov 11, 2014Twitch Technologies LlcMatrix keyboarding system
US9342241 *Nov 10, 2014May 17, 2016Twitch Technologies LlcMatrix keyboarding system
US20030067444 *Feb 25, 2002Apr 10, 2003Herman EhrenburgVisualizable-presented, computer-compatible, color-coded manual input system
US20110187637 *Jan 29, 2010Aug 4, 2011David Scott NicholsTactile Input Apparatus
US20110215954 *Mar 3, 2011Sep 8, 2011John Dennis PageMatrix Keyboarding System
US20150109151 *Nov 10, 2014Apr 23, 2015Twitch Technologies LlcMatrix keyboarding system
EP0050565A1 *Oct 15, 1981Apr 28, 1982Inro FranceHand-held keyboard
WO1981000478A1 *Aug 8, 1980Feb 19, 1981G WardCommunication
WO1982001345A1 *Oct 15, 1981Apr 29, 1982Kroczynski PatriceHand-bound keyboard
Classifications
U.S. Classification400/87, 400/477, 341/21, 178/101, 400/474, 340/4.12
International ClassificationA61F4/00, G06F3/09, B41J7/00
Cooperative ClassificationB41J7/005, A61F4/00, G06F3/09
European ClassificationG06F3/09, B41J7/00B, A61F4/00
|
__label__pos
| 0.573149 |
Free cookie consent management tool by TermsFeed Policy Generator
Changeset 13399
Ignore:
Timestamp:
11/25/15 17:14:14 (9 years ago)
Author:
bburlacu
Message:
#1772: Fix compilation errors caused by changes in the Visualization branch.
File:
1 edited
Legend:
Unmodified
Added
Removed
• branches/HeuristicLab.EvolutionTracking/HeuristicLab.EvolutionTracking.Views/3.4/GenealogyGraphChart.cs
r13061 r13399
4343 private Dictionary<Tuple<VisualGenealogyGraphNode, VisualGenealogyGraphNode>, VisualGenealogyGraphArc> arcMap;
4444
45 #region chart modes
45 #region chart options
4646 public bool SimpleLineages { get; set; }
4747 public bool LockGenealogy { get; set; }
4848 public bool TraceFragments { get; set; }
49 #endregion
50
51 #region chart modes
52 public Dictionary<string, ChartMode> ChartMode { get; private set; }
4953 #endregion
5054
8084 }
8185
82 // public bool UpdateEnabled {
83 // get { return Chart.UpdateEnabled; }
84 // set { Chart.UpdateEnabled = value; }
85 // }
86
87 // public void EnforceUpdate() {
88 // Chart.EnforceUpdate();
89 // }
90
9186 private Visualization.Rectangle TargetRectangle { get; set; }
9287 protected VisualGenealogyGraphNode SelectedVisualNode { get; set; }
112107 public GenealogyGraphChart() {
113108 InitializeComponent();
109
110 ChartMode = new Dictionary<string, ChartMode> {
111 { "Select", new SelectChartMode(this) },
112 { "ZoomIn", new ZoomInChartMode(this) },
113 { "ZoomOut", new ZoomOutChartMode(this) },
114 { "Pan", new PanChartMode(this) }
115 };
114116
115117 defaultBrush = new SolidBrush(Color.Transparent);
189191 switch (e.Button) {
190192 case MouseButtons.Left:
191 Mode = ChartMode.Select;
193 Mode = ChartMode["Select"];
192194 Cursor = Cursors.Default;
193195 break;
194196 case MouseButtons.Middle:
195 Mode = ChartMode.Move;
197 Mode = ChartMode["Pan"];
196198 Cursor = Cursors.Hand;
197199 break;
203205 protected override void PictureBoxOnMouseUp(object sender, MouseEventArgs e) {
204206 Cursor = Cursors.Default;
205 if (Mode == ChartMode.Move) {
206 Mode = ChartMode.Select;
207 return;
208 }
209 if (Mode != ChartMode.Select) {
210 base.PictureBoxOnMouseUp(sender, e);
211 return;
212 }
207
213208 var primitive = Chart.GetAllPrimitives(e.Location).FirstOrDefault(p => p is VisualGenealogyGraphNode);
214209 if (primitive == null) {
Note: See TracChangeset for help on using the changeset viewer.
|
__label__pos
| 0.989793 |
使用netty实现文件上传服务器
使用netty实现文件上传服务器
代码实现根据官网提供的example https://github.com/netty/nett...
以及netty官网的api文档 https://netty.io/4.1/api/inde...
项目地址 https://github.com/1433365571...
1 编写 server 启动类
package server;
import io.netty.bootstrap.ServerBootstrap;
import io.netty.channel.Channel;
import io.netty.channel.EventLoopGroup;
import io.netty.channel.nio.NioEventLoopGroup;
import io.netty.channel.socket.nio.NioServerSocketChannel;
import io.netty.handler.logging.LogLevel;
import io.netty.handler.logging.LoggingHandler;
import io.netty.handler.ssl.SslContext;
import io.netty.handler.ssl.SslContextBuilder;
import io.netty.handler.ssl.util.SelfSignedCertificate;
public final class HttpUploadServer {
static final boolean SSL = System.getProperty("ssl") != null;
static final int PORT = Integer.parseInt(System.getProperty("port", SSL ? "8443" : "8080"));
public static void main(String[] args) throws Exception {
// Configure SSL.
final SslContext sslCtx;
if (SSL) {
SelfSignedCertificate ssc = new SelfSignedCertificate();
sslCtx = SslContextBuilder.forServer(ssc.certificate(), ssc.privateKey()).build();
} else {
sslCtx = null;
}
EventLoopGroup bossGroup = new NioEventLoopGroup(1);
EventLoopGroup workerGroup = new NioEventLoopGroup();
try {
ServerBootstrap b = new ServerBootstrap();
b.group(bossGroup, workerGroup);
b.channel(NioServerSocketChannel.class);
b.handler(new LoggingHandler(LogLevel.INFO));
b.childHandler(new HttpUploadServerInitializer(sslCtx));
Channel ch = b.bind(PORT).sync().channel();
System.err.println("Open your web browser and navigate to " +
(SSL ? "https" : "http") + "://127.0.0.1:" + PORT + '/');
ch.closeFuture().sync();
} finally {
bossGroup.shutdownGracefully();
workerGroup.shutdownGracefully();
}
}
}
2 绑定handler
/*
* Copyright 2012 The Netty Project
*
* The Netty Project licenses this file to you under the Apache License,
* version 2.0 (the "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at:
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* License for the specific language governing permissions and limitations
* under the License.
*/
package server;
import io.netty.channel.ChannelInitializer;
import io.netty.channel.ChannelPipeline;
import io.netty.channel.socket.SocketChannel;
import io.netty.handler.codec.http.HttpContentCompressor;
import io.netty.handler.codec.http.HttpRequestDecoder;
import io.netty.handler.codec.http.HttpResponseEncoder;
import io.netty.handler.ssl.SslContext;
public class HttpUploadServerInitializer extends ChannelInitializer<SocketChannel> {
private final SslContext sslCtx;
public HttpUploadServerInitializer(SslContext sslCtx) {
this.sslCtx = sslCtx;
}
@Override
public void initChannel(SocketChannel ch) {
ChannelPipeline pipeline = ch.pipeline();
if (sslCtx != null) {
pipeline.addLast(sslCtx.newHandler(ch.alloc()));
}
pipeline.addLast(new HttpRequestDecoder());
pipeline.addLast(new HttpResponseEncoder());
// Remove the following line if you don't want automatic content compression.
pipeline.addLast(new HttpContentCompressor());
// pipeline.addLast("http-aggregator",
// new HttpObjectAggregator(65536));// 目的是将多个消息转换为单一的request或者response对象
pipeline.addLast(new HttpUploadServerHandler());
}
}
3 上传处理的handler
package server;
import io.netty.buffer.ByteBuf;
import io.netty.buffer.Unpooled;
import io.netty.channel.ChannelHandlerContext;
import io.netty.channel.SimpleChannelInboundHandler;
import io.netty.handler.codec.http.*;
import io.netty.handler.codec.http.multipart.*;
import io.netty.util.CharsetUtil;
import java.io.File;
import java.io.IOException;
import java.net.URI;
public class HttpUploadServerHandler extends SimpleChannelInboundHandler<HttpObject> {
private HttpRequest request;
private static final String uploadUrl = "/up";
private static final String fromFileUrl = "/post_multipart";
private static final HttpDataFactory factory =
new DefaultHttpDataFactory(DefaultHttpDataFactory.MINSIZE); // Disk if size exceed
private HttpPostRequestDecoder decoder;
static {
DiskFileUpload.deleteOnExitTemporaryFile = true; // should delete file
// on exit (in normal
// exit)
DiskFileUpload.baseDirectory = null; // system temp directory
DiskAttribute.deleteOnExitTemporaryFile = true; // should delete file on
// exit (in normal exit)
DiskAttribute.baseDirectory = null; // system temp directory
}
@Override
public void channelInactive(ChannelHandlerContext ctx) {
if (decoder != null) {
decoder.cleanFiles();
}
}
protected void channelRead0(ChannelHandlerContext ctx, HttpObject msg) throws Exception {
if (msg instanceof HttpRequest) {
this.request = (HttpRequest) msg;
URI uri = new URI(request.uri());
System.out.println(uri);
urlRoute(ctx, uri.getPath());
}
if (decoder != null) {
if (msg instanceof HttpContent) {
// 接收一个新的请求体
decoder.offer((HttpContent) msg);
// 将内存中的数据序列化本地
readHttpDataChunkByChunk();
}
if (msg instanceof LastHttpContent) {
System.out.println("LastHttpContent");
reset();
writeResponse(ctx, "<h1>上传成功</h1>");
}
}
}
// url路由
private void urlRoute(ChannelHandlerContext ctx, String uri) {
StringBuilder urlResponse = new StringBuilder();
// 访问文件上传页面
if (uri.startsWith(uploadUrl)) {
urlResponse.append(getUploadResponse());
} else if (uri.startsWith(fromFileUrl)) {
decoder = new HttpPostRequestDecoder(factory, request);
return;
} else {
urlResponse.append(getHomeResponse());
}
writeResponse(ctx, urlResponse.toString());
}
private void writeResponse(ChannelHandlerContext ctx, String context) {
ByteBuf buf = Unpooled.copiedBuffer(context, CharsetUtil.UTF_8);
FullHttpResponse response = new DefaultFullHttpResponse(
HttpVersion.HTTP_1_1, HttpResponseStatus.OK, buf);
response.headers().set(HttpHeaderNames.CONTENT_TYPE, "text/html;charset=utf-8");
//设置短连接 addListener 写完马上关闭连接
ctx.channel().writeAndFlush(response).addListener(ChannelFutureListener.CLOSE);
}
private String getHomeResponse() {
return " <h1> welcome home </h1> ";
}
private String getUploadResponse() {
return "<!DOCTYPE html>\n" +
"<html lang=\"en\">\n" +
"<head>\n" +
" <meta charset=\"UTF-8\">\n" +
" <title>Title</title>\n" +
"</head>\n" +
"<body>\n" +
"\n" +
"<form action=\"http://127.0.0.1:8080/post_multipart\" enctype=\"multipart/form-data\" method=\"POST\">\n" +
"\n" +
"\n" +
" <input type=\"file\" name=" +
" " +
"" +
"\"YOU_KEY\">\n" +
"\n" +
" <input type=\"submit\" name=\"send\">\n" +
"\n" +
"</form>\n" +
"\n" +
"</body>\n" +
"</html>";
}
private void readHttpDataChunkByChunk() throws IOException {
while (decoder.hasNext()) {
InterfaceHttpData data = decoder.next();
if (data != null) {
if (data.getHttpDataType() == InterfaceHttpData.HttpDataType.FileUpload) {
FileUpload fileUpload = (FileUpload) data;
if (fileUpload.isCompleted()) {
fileUpload.isInMemory();// tells if the file is in Memory
// or on File
fileUpload.renameTo(new File(PathUtil.getFileBasePath() + fileUpload.getFilename())); // enable to move into another
// File dest
decoder.removeHttpDataFromClean(fileUpload); //remove
}
}
}
}
}
private void reset() {
request = null;
// destroy the decoder to release all resources
decoder.destroy();
decoder = null;
}
}
4 环境文件
package server;
import java.io.File;
public class PathUtil {
private static final ClassLoader classLoader = PathUtil.class.getClassLoader();
public static String getFileBasePath() {
String os = System.getProperty("os.name");
String basePath;
if (os.toLowerCase().startsWith("win")) {
basePath = "D:/warehouse/";
} else {
basePath = "/root/upload_source";
}
basePath = basePath.replace("/", File.separator);
return basePath;
}
public static String getSourcePath(String name) {
return classLoader.getResource(name).getPath();
}
}
5 pom文件
<?xml version="1.0" encoding="UTF-8"?>
<project xmlns="http://maven.apache.org/POM/4.0.0"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
<modelVersion>4.0.0</modelVersion>
<groupId>nettyHttpUploadServer</groupId>
<artifactId>http.upload</artifactId>
<version>1.0-SNAPSHOT</version>
<properties>
<project.build.sourceEncoding>UTF-8</project.build.sourceEncoding>
</properties>
<dependencies>
<!-- https://mvnrepository.com/artifact/io.netty/netty-all -->
<dependency>
<groupId>io.netty</groupId>
<artifactId>netty-all</artifactId>
<version>4.1.10.Final</version>
</dependency>
</dependencies>
<!-- <build>-->
<!-- <plugins>-->
<!-- <plugin>-->
<!-- <groupId>org.apache.maven.plugins</groupId>-->
<!-- <artifactId>maven-jar-plugin</artifactId>-->
<!-- <configuration>-->
<!-- <archive>-->
<!-- <manifest>-->
<!-- <addClasspath>true</addClasspath>-->
<!-- <mainClass>server.HttpUploadServer</mainClass>-->
<!-- </manifest>-->
<!-- </archive>-->
<!-- </configuration>-->
<!-- </plugin>-->
<!-- </plugins>-->
<!-- </build>-->
<build>
<plugins>
<plugin>
<artifactId>maven-assembly-plugin</artifactId>
<version>3.0.0</version>
<configuration>
<archive>
<manifest>
<mainClass>server.HttpUploadServer</mainClass>
</manifest>
</archive>
<descriptorRefs>
<descriptorRef>jar-with-dependencies</descriptorRef>
</descriptorRefs>
</configuration>
<executions>
<execution>
<id>make-assembly</id>
<phase>package</phase>
<goals>
<goal>single</goal>
</goals>
</execution>
</executions>
</plugin>
<plugin>
<groupId>org.apache.maven.plugins</groupId>
<artifactId>maven-jar-plugin</artifactId>
<configuration>
<archive>
<manifest>
<mainClass>server.HttpUploadServer</mainClass>
</manifest>
</archive>
</configuration>
</plugin>
<plugin>
<groupId>com.jolira</groupId>
<artifactId>onejar-maven-plugin</artifactId>
<version>1.4.4</version>
<executions>
<execution>
<goals>
<goal>one-jar</goal>
</goals>
</execution>
</executions>
</plugin>
<plugin>
<groupId>org.apache.maven.plugins</groupId>
<artifactId>maven-compiler-plugin</artifactId>
<configuration>
<source>1.8</source>
<target>1.8</target>
</configuration>
</plugin>
</plugins>
</build>
</project>
6 代码说明
• ChannelHandlerContext 控制数据处理管道 ChannelPipeline 执行流程
• HttpObject 消息处理的接口
• HttpRequest 封装http请求头请求协议等
• DefaultFullHttpResponse 构造http响应
• httpcontext netty会将请求体分块处理此文章解释较详细，直接处理完整的请求体可以请将HttpObjectAggregator放在ChannelPipelineHttpObjectDecoder之后
图片描述
• LastHttpContent 标识Http请求结束
• HttpDataFactory 上传文件的处理方式
• HttpPostRequestDecoder post请求体的解析类
7 访问 http://127.0.0.1:8080/up 上传文件
0 声望
1 粉丝
0 条评论
推荐阅读
【小白必学】文件上传的漏洞介绍及常见防御方法
在文件上传的功能处，若服务端脚本语言未对上传的文件进行严格验证和过滤，导致恶意用户上传恶意的脚本文件时，就有可能获取执行服务端命令的能力，这就是文件上传漏洞。
代码熬夜敲阅读 1k
一分钟学会、三分钟上手、五分钟应用，快速上手开源责任链框架详解 | 京东云技术团队
责任链模式是开发过程中常用的一种设计模式，在SpringMVC、Netty等许多框架中均有实现。我们日常的开发中如果要使用责任链模式，通常需要自己来实现，但自己临时实现的责任链既不通用，也很容易产生框架与业务代...
京东云开发者阅读 891
封面图
《跟闪电侠学Netty》阅读笔记 - 开篇入门Netty
和 《Netty In Action》 不同，这本书直接从Netty入门程序代码开始引入Netty框架，前半部分教你如何用Netty搭建简易的通讯系统，整体难度比较低，后半部分直接从服务端源码、客户端源码、ChannelPipeline开始介绍...
Xander阅读 639
Netty入门
进程通过将一个或多个fd传递给select或poll系统调用，阻塞在select操作上，select/poll是顺序扫描fd是否就绪，需要扫描所有的客户端是否就绪epoll使用基于事件驱动方式替代顺序扫描，当有fd就绪时，立即回调函数r...
journey1阅读 412
uniapp实现文件选择上传，支持App/小程序/H5
lsj-upload插件地址：[链接]不清楚使用方式可点击右侧导入示例项目运行完整示例此次更新2.0与1.0使用方式略有差异，已使用1.0的同学自行斟酌是否更新到2.0版本！！！使用插件有任何问题欢迎加入QQ讨论群：群1：70...
shanjunLi阅读 376
长连接Netty服务内存泄漏，看我如何一步步捉“虫”解决 | 京东云技术团队
老板说： 长连接吗? 我说：是的！ 老板说：该来的还是要来的，最终还是来了，快，赶紧先把服务重启下！ 我说：已经重启了！ 老板说： 这问题必须给我解决了！ 我说：必须的！
京东云开发者阅读 210
封面图
Netty服务端开发及性能优化 | 京东云技术团队
Netty是一个异步基于事件驱动的高性能网络通信框架，可以看做是对NIO和BIO的封装，并提供了简单易用的API、Handler和工具类等，用以快速开发高性能、高可靠性的网络服务端和客户端程序。
京东云开发者阅读 204
封面图
0 声望
1 粉丝
宣传栏
|
__label__pos
| 0.670458 |
wont charge past 90%
Discussion in 'Android Tech Support' started by LOUISSSSS, Aug 19, 2010.
1. LOUISSSSS
LOUISSSSS Member
Joined:
Mar 31, 2010
Messages:
64
Likes Received:
0
Trophy Points:
6
Ratings:
+0
Won't charge past 90%. I just updated to 2.2 and my phone has been at 90% charge for w hours. How do I get it to fully charge?
2. dmacleo
dmacleo Premium Member Rescue Squad Premium Member
Joined:
Jan 12, 2010
Messages:
1,479
Likes Received:
0
Trophy Points:
36
Location:
Etna,ME
Ratings:
+0
I'd drain and let it die then recharge on approved AC charger.
had this happen once.
3. hookbill
hookbill Premium Member Premium Member
Joined:
Nov 30, 2009
Messages:
19,502
Likes Received:
7
Trophy Points:
168
Location:
N.E. Ohio
Ratings:
+7
There has got to be an app running that's keeping it from reaching maximum charge. Does it feel hot?
4. LOUISSSSS
LOUISSSSS Member
Joined:
Mar 31, 2010
Messages:
64
Likes Received:
0
Trophy Points:
6
Ratings:
+0
looks like it wasn't the battery, was the program (battery time)
i had it when i was using 2.1, then i upgraded to 2.2 and it didn't go to 100%. I just reinstalled it and looks like i'm getting the correct reading again
I found out that i was getting incorrect reading by looking at the "locked" screen when i'm charging. It shoes the phone's reading on the screen.
5. LOUISSSSS
LOUISSSSS Member
Joined:
Mar 31, 2010
Messages:
64
Likes Received:
0
Trophy Points:
6
Ratings:
+0
update. My problem is not fixed. I still can't charge past 90%. The phone has been charging w/ original charger sitting there idling for over 2 hours and its still maxing out at 90%. How do i go about this???
how can i find out which app is sucking up the battery while running in the backgroud to keep it from reaching 100%. The battery successfully charged from 60% -> 90% though...
6. jstafford1
jstafford1 DF Super Moderator Rescue Squad
Joined:
Nov 15, 2009
Messages:
9,863
Likes Received:
631
Trophy Points:
228
Location:
Hebron, Oh.
Ratings:
+677
Twitter:
jstaff79
Try uninstalling battery time then reboot.
7. Jonny Kansas
Jonny Kansas DF Super Moderator Staff Member Rescue Squad
Joined:
Jan 21, 2010
Messages:
7,922
Likes Received:
2,038
Trophy Points:
393
Location:
Michigan's Upper Peninsula
Ratings:
+2,395
Current Phone Model:
Note 4
Twitter:
jonny_ks
Thread moved to appropriate sub-forum.
8. Tallica
Tallica Premium Member Rescue Squad Premium Member
Joined:
Mar 17, 2010
Messages:
3,259
Likes Received:
1
Trophy Points:
101
Location:
Middleboro, MA
Ratings:
+1
settings>about phone>battery use
9. Vivien
Vivien New Member
Joined:
Aug 22, 2011
Messages:
1
Likes Received:
0
Trophy Points:
1
Ratings:
+0
I have the Motorola Atrix and am experiencing the same problem. After updating my phone it can not charge past 80% (as displayed on the lock screen). However if I turn off my phone and turn on again it shows it fully charged. I believe that the update has caused some glitch in displaying the correct percentage of battery. Does anyone have anone have any knowledge on this issue? Thanks!
10. SacramentoDJ
SacramentoDJ New Member
Joined:
Aug 24, 2011
Messages:
1
Likes Received:
0
Trophy Points:
1
Ratings:
+0
Turn the power off and you will notice...
the charge is at 100%...it is probably a bug in the software...It wasn't happening with the earlier version of the OS for me...only after the Gingerbread update...
11. Brhad56
Brhad56 New Member
Joined:
Dec 11, 2011
Messages:
1
Likes Received:
0
Trophy Points:
1
Ratings:
+0
90% Charging Solution
I had the same problem, where my ATRIX would not charge past 90%. Based upon reading the android hackers posts for solutions to this problem I found one that worked for me.
1) Let your battery fall to 0%. (Play a game or something till it shuts itself down)
2) Pull out battery
3) wait 30 seconds put it back in
4) Charge phone from wall mount.DO NOT TURN PHONE ON
5) DO NOT TURN PHONE BACK ON , let it charge while off. Don't press button to check status or anything, just give it enough time fully charge. 5 hours should work.
6) After 5+ hours haveshould elapsed, leaving phone still plugged in, pull out battery
7) After Motorola logo pops up, unplug phone.
8) Put battery back in.
9) Turn on phone. It should now say 100%
Seems there is a battery statistic file that your trying to fix. I read about rooting your phone and running battery calibration tools but my phone isn't rooted and I built this solution trying to reproduce the phone receiving a fresh new battery. I honestly don't know if all the steps are required, but its what I did and it worked for me. Good luck.
Search tags for this page
android phone only charges to 90
,
my phone stops charging at 80
,
phone only charges to 90
,
phone stops charging at 80
,
phone stops charging at 80%
,
phone wont charge over 90
,
phone wont charge past 80
,
phone wont charge past 90
,
why does my phone only charge to 90
,
why isn't my motorola atrix charging
|
__label__pos
| 0.900402 |
Medical Definition of Pyogenic granuloma
Reviewed on 3/29/2021
Pyogenic granuloma: a small, vascular benign tumor of the skin or mucous membranes. They appear as a small reddish bump that grows rapidly at first and then remains a constant size. The size rarely exceeds 1 cm in diameter. Pyogenic granulomas usually develop on the arms, hands, or face. They occur in people of all ages, but those most commonly affected are in the second and third decades of life. Their exact cause is unknown. They bleed easily because they are rich in blood vessels. Surgery is the preferred treatment because they do not resolve on their own and tend to bleed heavily. They may recur if not completely excised.
Pyogenic granuloma is also known as lobular capillary hemangioma. The name "pyogenic" suggests an infectious process, but an infection is not believed to be the cause.
CONTINUE SCROLLING OR CLICK HERE
SLIDESHOW
Rosacea, Acne, Shingles, Covid-19 Rashes: Common Adult Skin Diseases See Slideshow
Health Solutions From Our Sponsors
References
MedlinePlus.com. Pyogenic granuloma.
|
__label__pos
| 0.786832 |
jQuery Plugin: Table of Contents with Smooth Scrolling
Hey guys, have you noticed that pretty box on WordPress codex that gives us a preview about what we can see on a page? So, I haven’t seen too many blogs use this kind of feature and it is really useful for our readers, since they can just skip to the content that they are interested in and avoid wasting time. Wikipedia has a table of contents that makes it easier for readers to skip around, right?
I’m not the very first to do something like this with jQuery. But our goal in here is to develop a complete jQuery plugin, from start to finish, with options, and that is easy to customize. And, of course, something that I hope is useful to you
So, let’s rock!
STOC – Smooth Table of Contents jQuery plugin
Since there are a lot of “tocs” around the web, our plugin will be called STOC and the main features are:
• Automatically adds the table of contents to target element
• You can select to search just a part of you page
• You can select what is the first heading we will have to search (h1, h2…)
• You can select the “depth” of the search
• SubItems are made of sublists inside parent item
• You can select which text will display before the table (title)
• You can select whether ol or ul to you listing
• You can enable / disable smooth scrolling
Here is how it should look in our demo:
Here’s a running Demo. You can also download all files here.
Planning and planning – Before code, let’s think about it
The main idea is to have a jQuery plugin that generates a table of content inside the target element. To have this working we need some basic customization with these options:
• Where to search – If the table is generated based on entire page, just a section content
• Depth of H’s – How many “levels” of titles we will have in our search
• Start tag – Which level of heading will be the first on set (h1, h2, h3)
• Title if the box – What to display as box’s title
• List type – whether to have ordered or unordered list
The hardest thing when we are doing something just for fun is to define the scope. Actually it is hard too when we have a “real” project, but when it comes to pet projects it is harder because you just can’t measure accurately what will bring you the expected revenue (fun).
So, what do I do in these cases is list anything that I could do on it, and just cut down what will take too much time and will not be so good to do.
In this case, for example I listed these features:
• Customizable via options – I think this one was essential, so I just kept it
• Smooth scrolling - This one I didn’t see in any other plugin / snippet. It would be good to have, so I kept it.
• Accordion for hierarchy - I found this idea really cool, but useless, I drop it.
• Preview of the text on hover - I’ve stolen this idea of one site but actually didn’t find it useful also, so I drop it.
So what I’ve done here is to define which of the cool features had big potential to be a waste of time. Even if I had more time to code I would never use them, just because they haven’t the expected benefit (fun x time).
Now that we now what we want to do, let’s start to code.
Basic plugin structure with options
First we need to create our file. The standard for jQuery plugins files names is jQuery.PLUGINNAME.js so, our file will be jquery.stoc.js.
We also have all our options defined above, so we need now to save a variable for each one of them, so our user can send his own parameters.
Here is our commented code:
/*
This line creates our function "wrapped" by jQuery container, so we won't have any problem with others libraries
*/
(function($){
/*
Here the standard is $.fn.PLUGINNAME. so when we call $(element).stoc() jquery will run this code
Pay attention that we pass options to our funcion, so when user defines it we can extend our plugin
*/
$.fn.stoc = function(options) {
//Our default options
var defaults = {
search: "body", //where we will search for titles
depth: 6, //how many hN should we search
start: 1, //which hN will be the first (and after it we go just deeper)
stocTitle: "<h2>Contents</h2>", //what to display before our box
listType: "ul", //could be ul or ol
smoothScroll: 1
};
//let's extend our plugin with default or user options when defined
var options = $.extend(defaults, options);
return this.each(function() {
//our functions here
alert("I'm a beta tester alert box!");
});
};
})(jQuery);
Let’s try a simple demo to see it working. Create this HTML in same folder as our plugin:
<!DOCTYPE HTML PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml"><head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Smooth Table Of Contents jQuery plugin - DEMO</title>
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.4/jquery.min.js"></script>
<script type="text/javascript" src="jquery.stoc.js"></script>
<script type="text/javascript">
$(function(){
$("#items").stoc();
});
</script>
<style type="text/css">
body {
background: #fafafa url(handmadepaper.png); //via subtlepatterns
}
#container {
position: relative;
top: 50px;
width: 960px;
margin: 0 auto;
padding-bottom: 20px;
}
#container p, #container h1, #container h2, #container h3, #container h4, #container h5 {
font-family: "arial";
padding: 10px 20px 0;
margin: 0
}
#items {
float: right;
width: 260px;
padding-bottom: 10px;
margin:0 0 10px 20px;
/* rgba with ie compatibility */
background-color: transparent;
background-color: rgba(255,255,255,0.4);
filter:progid:DXImageTransform.Microsoft.gradient(startColorstr=#20ffffff,endColorstr=#20ffffff);
-ms-filter: "progid:DXImageTransform.Microsoft.gradient(startColorstr=#20ffffff,endColorstr=#20ffffff)";
}
#items ul {
margin: 0 0 0 20px;
padding: 0 0 5px;
list-style-type: none;
}
#items ul ul {
font-size: 90%;
}
#items ul a {
font-family: "arial";
text-decoration: none;
color: #c10000;
}
#items ul a:hover { color: #ff0000 }
</style>
</head>
<body id="page-1">
<div id="container">
<div id="items">
</div>
<h1>1 - Phasellus vulputate</h1>
<p>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Maecenas metus est, egestas vel aliquet at, pellentesque nec lorem. Pellentesque molestie bibendum eros, eu suscipit nisi volutpat fringilla. Vivamus fringilla nisl ut ante commodo porta. Morbi ipsum nunc, sollicitudin ac pretium pretium, iaculis vel enim. Nulla cursus porta orci, sed vulputate magna feugiat et. Aliquam nibh massa, pharetra tincidunt vehicula ac, pellentesque vitae nibh. In lobortis semper eros fermentum pretium. Sed posuere, urna eget ornare luctus, mi lectus lacinia leo, sit amet faucibus orci ipsum sit amet ipsum. Maecenas sapien neque, ultrices a lacinia sit amet, fermentum non enim. Integer at venenatis orci. In hac habitasse platea dictumst.</p>
[... lot of more lipsum text with h's here]
</div>
</body>
</html>
If you create this file, when you load it you should see our pretty beta tester alert. So our plugin is being called (make sure that you add jquery before it, as I’ve done including api.googleapis…). if you want to overwrite any option defined before, you just have to pass it as .stoc({ OPTIONNAME: VALUE }) instead of just .stoc(). For example, to define our search just in #container, add .stoc({ search: "#container" }).
How should we select our headings?
Now we have to prepare our plugin to get all h’s that we have to (based in our options). What we can do is get all the headings we have to, and when we loop through each one of them we will discover which level it is. I think it is easier than trying to get the whole hierarchy for each “tree” of headings.
Since our current object can change as we run our code, we have also to “cache” our current object so we will always now which object we are modifying. Our code now will be:
return this.each(function() {
//"cache" our target and search objects
obj = $(this); //target
src = $(options.search); //search
//let's declare some variables. We need this var declaration to create them as local variables (not global)
var appHTML = "", tagNumber = 0, txt = "", id = "", before = "", after = "", previous = options.start, start = options.start, depth = options.depth, i = 0, srcTags = "h" + options.start, cacheHN = "";
//which tags we will search
while ( depth > 1) {
start++; //we will just get our start level and numbers higher than it
srcTags = srcTags + ", h" + start;
depth--; //since went one level up, our depth will go one level down
}
});
If you alert you srcTags you will see something like this “h1, h2, h3, h4, h5, h6″. This is what we will pass to jQuery as the elements that we want to search for.
Building our table
We have all our elements, what we have to do is run a function on each one of them with the wonderful each() jQuery function.
Inside each element, we need to:
• Know which level the current element is (tagNumber)
• Set one id to this element, if it doesn’t have one
• Get the elements text
• Test if is its level is lower, higher or equal than previous element and open / close ul’s based on this
• If element number is higher than previous means that we went down one level (e.g. from h2 to h3)
• If element number is equals to previous means that we stay on same level (e.g. h4)
• If element number is lower than previous means that we went up, but we don’t know how many levels (e.g. from h4 to h1)
• Append element HTML to our target item
We also have to correct the last item because if it is not top-level it will let some uls open, and we don’t want it :D
Our commented code now will be:
/* our setup stuff here */
/*inside our return function */
//which tags we will search
while ( depth > 1) {
start++; //we will just get our start level and numbers higher than it
srcTags = srcTags + ", h" + start;
depth--; //since went one level up, our depth will go one level down
}
src.find(srcTags).each(function() {
//we will cache our current H element
cacheHN = $(this);
//if we are on h1, 2, 3...
tagNumber = ( cacheHN.get(0).tagName ).substr(1);
//sets the needed id to the element
id = cacheHN.attr('id');
if (id == "") { //if it doesn't have only, of course
id = "h" + tagNumber + "_" + i;
cacheHN.attr('id', id);
}
//our current text
txt = cacheHN.text();
switch(true) { //with switch(true) we can do comparisons in each case
case (tagNumber > previous) : //it means that we went down one level (e.g. from h2 to h3)
appHTML = appHTML + "<" + options.listType +"><li>"+ before +"<a href=\"#"+ id + "\">" + txt + "</a>";
previous = tagNumber;
break;
case (tagNumber == previous) : //it means that stay on the same level (e.g. h3 and stay on it)
appHTML = appHTML + "</li><li>"+ before +"<a href=\"#"+ id + "\">" + txt + "</a>";
break;
case (tagNumber < previous) : //it means that we went up but we don't know how much levels (e.g. from h3 to h2)
while(tagNumber != previous) {
appHTML = appHTML + "</" + options.listType +"></li>";
previous--;
}
appHTML = appHTML + "<li>"+ before +"<a href=\"#"+ id + "\">" + txt + "</a></li>";
break;
}
i++;
});
//corrects our last item, because it may have some opened ul's
while(tagNumber != options.start) {
appHTML = appHTML + "</" + options.listType +">";
tagNumber--;
}
//append our html to our object
appHTML = options.stocTitle + "<"+ options.listType + ">" + appHTML + "</" + options.listType + ">";
obj.append(appHTML);
How to Make our STOC smoother
I’ve stolen CSS trick’s smooth scroll code, but I hope they don’t mind :D
What we have to do here is just put this (compressed) function to load when our smooth scroll in on (if the user doesn’t set it as 0).
/*all code above in here*/
//append our html to our object
appHTML = options.stocTitle + "<"+ options.listType + ">" + appHTML + "</" + options.listType + ">";
obj.append(appHTML);
//our pretty smooth scrolling here
// acctually I've just compressed the code so you guys will think that I'm the man . Source: http://css-tricks.com/snippets/jquery/smooth-scrolling/
if (options.smoothScroll == 1) {
$(window).load(function(){
function filterPath(string){return string.replace(/^\//,'').replace(/(index|default).[a-zA-Z]{3,4}$/,'').replace(/\/$/,'')}var locationPath=filterPath(location.pathname);var scrollElem=scrollableElement('html','body');obj.find('a[href*=#]').each(function(){var thisPath=filterPath(this.pathname)||locationPath;if(locationPath==thisPath&&(location.hostname==this.hostname||!this.hostname)&&this.hash.replace(/#/,'')){var $target=$(this.hash),target=this.hash;if(target){var targetOffset=$target.offset().top;$(this).click(function(event){event.preventDefault();$(scrollElem).animate({scrollTop:targetOffset},400,function(){location.hash=target})})}}});function scrollableElement(els){for(var i=0,argLength=arguments.length;i<argLength;i++){var el=arguments[i],$scrollElement=$(el);if($scrollElement.scrollTop()>0){return el}else{$scrollElement.scrollTop(1);var isScrollable=$scrollElement.scrollTop()>0;$scrollElement.scrollTop(0);if(isScrollable){return el}}}return[]}
});
}
Our final result is this:
(function($){
$.fn.stoc = function(options) {
//Our default options
var defaults = {
search: "body", //where we will search for titles
depth: 6, //how many hN should we search
start: 1, //which hN will be the first (and after it we go just deeper)
stocTitle: "<h2>Contents</h2>", //what to display before our box
listType: "ul", //could be ul or ol
smoothScroll: 1
};
//let's extend our plugin with default or user options when defined
var options = $.extend(defaults, options);
return this.each(function() {
//"cache" our target and search objects
obj = $(this); //target
src = $(options.search); //search
//let's declare some variables. We need this var declaration to create them as local variables (not global)
var appHTML = "", tagNumber = 0, txt = "", id = "", before = "", after = "", previous = options.start, start = options.start, depth = options.depth, i = 0, srcTags = "h" + options.start, cacheHN = "";
//which tags we will search
while ( depth > 1) {
start++; //we will just get our start level and numbers higher than it
srcTags = srcTags + ", h" + start;
depth--; //since went one level up, our depth will go one level down
}
src.find(srcTags).each(function() {
//we will cache our current H element
cacheHN = $(this);
//if we are on h1, 2, 3...
tagNumber = ( cacheHN.get(0).tagName ).substr(1);
//sets the needed id to the element
id = cacheHN.attr('id');
if (id == "") { //if it doesn't have only, of course
id = "h" + tagNumber + "_" + i;
cacheHN.attr('id', id);
}
//our current text
txt = cacheHN.text();
switch(true) { //with switch(true) we can do comparisons in each case
case (tagNumber > previous) : //it means that we went down one level (e.g. from h2 to h3)
appHTML = appHTML + "<" + options.listType +"><li>"+ before +"<a href=\"#"+ id + "\">" + txt + "</a>";
previous = tagNumber;
break;
case (tagNumber == previous) : //it means that stay on the same level (e.g. h3 and stay on it)
appHTML = appHTML + "</li><li>"+ before +"<a href=\"#"+ id + "\">" + txt + "</a>";
break;
case (tagNumber < previous) : //it means that we went up but we don't know how much levels (e.g. from h3 to h2)
while(tagNumber != previous) {
appHTML = appHTML + "</" + options.listType +"></li>";
previous--;
}
appHTML = appHTML + "<li>"+ before +"<a href=\"#"+ id + "\">" + txt + "</a></li>";
break;
}
i++;
});
//corrects our last item, because it may have some opened ul's
while(tagNumber != options.start) {
appHTML = appHTML + "</" + options.listType +">";
tagNumber--;
}
//append our html to our object
appHTML = options.stocTitle + "<"+ options.listType + ">" + appHTML + "</" + options.listType + ">";
obj.append(appHTML);
//our pretty smooth scrolling here
// acctually I've just compressed the code so you guys will think that I'm the man . Source: http://css-tricks.com/snippets/jquery/smooth-scrolling/
if (options.smoothScroll == 1) {
$(window).load(function(){
function filterPath(string){return string.replace(/^\//,'').replace(/(index|default).[a-zA-Z]{3,4}$/,'').replace(/\/$/,'')}var locationPath=filterPath(location.pathname);var scrollElem=scrollableElement('html','body');obj.find('a[href*=#]').each(function(){var thisPath=filterPath(this.pathname)||locationPath;if(locationPath==thisPath&&(location.hostname==this.hostname||!this.hostname)&&this.hash.replace(/#/,'')){var $target=$(this.hash),target=this.hash;if(target){var targetOffset=$target.offset().top;$(this).click(function(event){event.preventDefault();$(scrollElem).animate({scrollTop:targetOffset},400,function(){location.hash=target})})}}});function scrollableElement(els){for(var i=0,argLength=arguments.length;i<argLength;i++){var el=arguments[i],$scrollElement=$(el);if($scrollElement.scrollTop()>0){return el}else{$scrollElement.scrollTop(1);var isScrollable=$scrollElement.scrollTop()>0;$scrollElement.scrollTop(0);if(isScrollable){return el}}}return[]}
});
}
});
};
})(jQuery);
Are you hungry yet?
What about you help me with some improvements on this plugin? Do you have any tip? Anything that you can think of a better way to do?
Do you have any other features in mind? Or even another plugin idea that you’d like to see a tutorial on?
Share your thoughts with us! :D
Rochester Oliveira
I'm a web designer and entrepreneur from Itajubá (MG), Brasil. I love writing about obscure topics and doing some cool stuff. And also I do some FREE stuff, check it out: http://www.roch.com.br/
15 Smart Tools To Help You Build Your Freelance Business
Discover the awesome tools we use in making our clients comfortable and happy in learning new things every day.
Download Now
Comments
1. says
Hey,
I fixed a bug in your plugin where it went to an infinite loop at this line:
while(tagNumber != options.start) {
appHTML = appHTML + “”;
tagNumber–;
}
The tagnumber went under 0 so this loop never stopped and made the browsers to crash. You can find the fix here:
https://gist.github.com/2719592
2. Diego says
sorry.
Here is the code
case (tagNumber < previous) : //it means that we went up but we don't know how much levels (e.g. from h3 to h2)
appHTML = appHTML + "";
while(tagNumber != previous) {
appHTML = appHTML + "";
previous--;
}
appHTML = appHTML + ""+ before +"" + txt + "";
break;
• Diego says
Here i go again…
case (tagNumber < previous) : //it means that we went up but we don't know how much levels (e.g. from h3 to h2)
appHTML = appHTML + "”;
while(tagNumber != previous) {
appHTML = appHTML + “”;
previous–;
}
appHTML = appHTML + “”+ before +”lessThan a h ref=\”#”+ id + “\”>” + txt + “Lessthan/a>”;
break;
3. Robin says
Any chance of fixing this for the latest version of JQuery? The link come back as undefined and smooth scroll doesn’t work.
4. says
Great plugin!
The best part about it is that there is nothing you have to hardcode. So, as long as there are H1s on the page, you are good to go :)
Thank you so much!
5. Alex C says
Documented how to use your amazing plugin with SharePoint. Thanks again for this great article and the code :)
• says
Hi Alex,
I’ve read it, and you won’t believe how glad I am. You really improved it, and your article is pretty well explained.
Thanks A LOT!
[]’s
Rochester
6. Alex C says
For some reason, on SharePoint 2010, it was appending “#undefined” to all the table of contents items. So I modified the JS to this:
if (id == "" || typeof id === "undefined") { //if it doesn't have only, of course
id = "h" + tagNumber + "_" + i;
cacheHN.attr('id', id);
}
It now works! Just in case anyone else runs into this issue.
7. Alex C says
Amazing stuff! Thanks for sharing this. I was looking to add this to a SharePoint publishing page and thought of creating from scratch until I came across this. Very nice. Thank you for creating this :)
8. says
Thanks for sharing, it’s a very useful technique. I just want to add that a scroll to top will be a nice feature. But there’s so many options to implement this… it’s not a problem.
I spent several years making internal manuals in various companies, and online classes too, it’s like making a mini-site with huge individual pages. I found that a non-fix vertical menu on a left sidebar was the more practical and intuitive way to implement a table of content. You want your reader focused on its reading, so the wiki format isn’t, in my feel, the best way to help somebody to learn and memorize something new. If you sum to this some tool-tips and modal windows, and your table of content, you have a fantastic and powerful tool for teaching.
Once again, thanks for sharing this.
• says
Hey egiova,
As Abdelhadi said below it would be really helpful. It is pretty easy to add it, is just append some code (like this “top” link) while you are in each() loop.
I agree with you, this must to be the best way to wiki-like sites, and I think it is really helpful for tutorials or roundups, so readers can go and read just what they want to learn (like if you are in a jquery plugins roundup and just want to see the sliders)..
Thank you, again!
[]’s
9. Julian says
nice code,and good description to develop own jquery plugins. very
usefull, thanks!
10. Abdelhadi Touil says
Very nice plugin; thanks very much for sharing.
I think it’ll be better if it adds automatically a “top” link ine the of each section. What do you think?
(Sorry for my bad English)
• says
Hey Abdelhadi, It is a good idea, and pretty simple do do, since our smooth scrolling can apply to this link also..
Thank you for the insight!
[]’s
• says
Hey wesley, I think we missed it. MIT is ok to me, since you can do anything you want with this code and it has no warranty.
Thank you for pointing it out, next time I’ll include this in our .zip !
[]’s
|
__label__pos
| 0.52194 |
Publications
Publications in peer reviewed journals
34 Publications found
• Acidobacteria are active and abundant members of diverse atmospheric H2-oxidizing communities detected in temperate soils
Giguere AT, Eichorst SA, Meier D, Herbold CW, Richter A, Greening C, Woebken D
2020 - ISME J, in press
Abstract:
Significant rates of atmospheric H2 consumption have been observed in temperate soils due to the activity of high-affinity enzymes, such as the group 1h [NiFe]-hydrogenase. We designed broadly inclusive primers targeting the large subunit gene (hhyL) of group 1h [NiFe]-hydrogenases for long-read sequencing to explore its taxonomic distribution across soils. This approach revealed a diverse collection of microorganisms harboring hhyL, including previously unknown groups and taxonomically not assignable sequences. Acidobacterial group 1h [NiFe]-hydrogenases genes were abundant and expressed in temperate soils. To support the participation of acidobacteria in H2 consumption, we studied two representative mesophilic soil acidobacteria, which expressed group 1h [NiFe]-hydrogenases and consumed atmospheric H2 during carbon starvation. This is the first time mesophilic acidobacteria, which are abundant in ubiquitous temperate soils, have been shown to oxidize H2 down to below atmospheric concentrations. As this physiology allows bacteria to survive periods of carbon starvation, it could explain the success of soil acidobacteria. With our long-read sequencing approach of group 1h [NiFe]-hydrogenases genes, we show that the ability to oxidize atmospheric levels of His more widely distributed among soil bacteria than previously recognized and could represent a common mechanism enabling bacteria to persist during periods of carbon deprivation.
• Genomic and kinetic analysis of novel Nitrospinae enriched by cell sorting
Mueller AJ, Jung MY, Strachan CR, Herbold CW, Kirkegaard RH, Wagner M, Daims H
2020 - ISME J., in press
Abstract:
Chemolithoautotrophic nitrite-oxidizing bacteria (NOB) are key players in global nitrogen and carbon cycling. Members of the phylum Nitrospinae are the most abundant, known NOB in the oceans. To date, only two closely affiliated Nitrospinae species have been isolated, which are only distantly related to the environmentally abundant uncultured Nitrospinae clades. Here, we applied live cell sorting, activity screening, and subcultivation on marine nitrite-oxidizing enrichments to obtain novel marine Nitrospinae. Two binary cultures were obtained, each containing one Nitrospinae strain and one alphaproteobacterial heterotroph. The Nitrospinae strains represent two new genera, and one strain is more closely related to environmentally abundant Nitrospinae than previously cultured NOB. With an apparent half-saturation constant of 8.7±2.5 µM, this strain has the highest affinity for nitrite among characterized marine NOB, while the other strain (16.2±1.6 µM) and Nitrospina gracilis (20.1±2.1 µM) displayed slightly lower nitrite affinities. The new strains and N. gracilis share core metabolic pathways for nitrite oxidation and CO2 fixation but differ remarkably in their genomic repertoires of terminal oxidases, use of organic N sources, alternative energy metabolisms, osmotic stress and phage defense. The new strains, tentatively named “Candidatus Nitrohelix vancouverensis” and “Candidatus Nitronauta litoralis”, shed light on the niche differentiation and potential ecological roles of Nitrospinae.
• Environmental and intestinal phylum Firmicutes bacteria metabolize the plant sugar sulfoquinovose via a 6-deoxy-6-sulfofructose transaldolase pathway
Frommeyer B, Fiedler AW, Oehler SR, Hanson BT, Loy A, Franchini P, Spiteller D, Schleheck D
2020 - iScience, In press
Abstract:
Bacterial degradation of the sugar sulfoquinovose (SQ, 6-deoxy-6-sulfoglucose) produced by plants, algae and cyanobacteria, is an important component of the biogeochemical carbon and sulfur cycles. Here, we reveal a third biochemical pathway for primary SQ degradation in an aerobic Bacillus aryabhattaistrain. An isomerase converts SQ to 6-deoxy-6-sulfofructose (SF). A novel transaldolase enzyme cleaves the SF to 3-sulfolactaldehyde (SLA), while the non-sulfonated C3-(glycerone)-moiety is transferred to an acceptor molecule, glyceraldehyde phosphate (GAP), yielding fructose-6-phosphate (F6P). Intestinal anaerobic bacteria such as Enterococcus gilvus, Clostridium symbiosum and Eubacterium rectale strains also express transaldolase-pathway gene clusters during fermentative growth with SQ. The now three known biochemical strategies for SQ catabolism reflect adaptations to the aerobic or anaerobic life-style of the different bacteria. The occurrence of these pathways in intestinal (family) Enterobacteriaceae and (phylum) Firmicutes strains further highlights a potential importance of metabolism of green-diet SQ by gut microbial communities to, ultimately, hydrogen sulfide.
• Anaerobic bacterial degradation of protein and lipid macromolecules in subarctic marine sediment
Pelikan C, Wasmund K, Glombitza C, Hausmann H, Herbold CW, Flieder M, Loy A
2020 - ISME J, In press
Abstract:
Microorganisms in marine sediments play major roles in marine biogeochemical cycles by mineralizing substantial quantities of organic matter from decaying cells. Proteins and lipids are abundant components of necromass, yet the taxonomic identities of microorganisms that actively degrade them remain poorly resolved. Here, we revealed identities, trophic interactions and genomic features of bacteria that degraded 13C-labelled proteins and lipids in cold anoxic microcosms containing sulfidic subarctic marine sediment. Supplemented proteins and lipids were rapidly fermented to various volatile fatty acids within five days. DNA-stable isotope probing (SIP) suggested Psychrilyobacter atlanticus was an important primary degrader of proteins, and Psychromonas members were important primary degraders of both proteins and lipids. Closely related Psychromonas populations, as represented by distinct 16S rRNA gene variants, differentially utilized either proteins or lipids. DNA-SIP also showed 13C-labeling of various Deltaproteobacteria within ten days, indicating trophic transfer of carbon to putative sulfate-reducers. Metagenome-assembled genomes revealed the primary hydrolyzers encoded secreted peptidases or lipases, and enzymes for catabolism of protein or lipid degradation products. Psychromonas species are prevalent in diverse marine sediments, suggesting they are important players in organic carbon processing in situ. Together, this study provides new insights into the identities, functions and genomes of bacteria that actively degrade abundant necromass macromolecules in the seafloor.
• Proposal to reclassify the proteobacterial classes Deltaproteobacteria and Oligoflexia, and the phylum Thermodesulfobacteria into four phyla reflecting major functional capabilities
Waite DW, Chuvochina M, Pelikan C, Parks DH, Yilmaz P, Wagner M, Loy A, Naganuma T, Nakai R, Whitman WB, Hahn MW, Kuever J, Hugenholtz P
2020 - Int J Syst Evol Microbiol, in press
Abstract:
The class Deltaproteobacteria comprises an ecologically and metabolically diverse group of bacteria best known for dissimilatory sulphate reduction and predatory behaviour. Although this lineage is the fourth described class of the phylum Proteobacteria, it rarely affiliates with other proteobacterial classes and is frequently not recovered as a monophyletic unit in phylogenetic analyses. Indeed, one branch of the class Deltaproteobacteria encompassing Bdellovibrio-like predators was recently reclas- sified into a separate proteobacterial class, the Oligoflexia. Here we systematically explore the phylogeny of taxa currently assigned to these classes using 120 conserved single-copy marker genes as well as rRNA genes. The overwhelming majority of markers reject the inclusion of the classes Deltaproteobacteria and Oligoflexia in the phylum Proteobacteria. Instead, the great majority of currently recognized members of the class Deltaproteobacteria are better classified into four novel phylum-level lineages. We propose the names Desulfobacterota phyl. nov. and Myxococcota phyl. nov. for two of these phyla, based on the oldest validly published names in each lineage, and retain the placeholder name SAR324 for the third phylum pending formal description of type material. Members of the class Oligoflexia represent a separate phylum for which we propose the name Bdellovibrionota phyl. nov. based on priority in the literature and general recognition of the genus Bdellovibrio. Desulfobacterota phyl. nov. includes the taxa previously classified in the phylum Thermodesulfobacteria, and these reclassifications imply that the ability of sulphate reduction was vertically inherited in the phylum Thermodesulfobacteria rather than laterally acquired as previously inferred. Our analysis also indicates the independent acquisition of predatory behaviour in the phyla Myxococcota and Bdellovibrionota, which is consistent with their distinct modes of action. This work represents a stable reclassification of one of the most taxonomically challenging areas of the bacterial tree and provides a robust framework for future ecological and systematic studies.
• Rational design of a microbial consortium of mucosal sugar utilizers reduces Clostridiodes difficile colonization.
Pereira FC, Wasmund K, Cobankovic I, Jehmlich N, Herbold CW, Lee KS, Sziranyi B, Vesely C, Decker T, Stocker R, Warth B, von Bergen M, Wagner M, Berry D
2020 - Nat Commun, 1: 5104
Abstract:
Many intestinal pathogens, including Clostridioides difficile, use mucus-derived sugars as crucial nutrients in the gut. Commensals that compete with pathogens for such nutrients are therefore ecological gatekeepers in healthy guts, and are attractive candidates for therapeutic interventions. Nevertheless, there is a poor understanding of which commensals use mucin-derived sugars in situ as well as their potential to impede pathogen colonization. Here, we identify mouse gut commensals that utilize mucus-derived monosaccharides within complex communities using single-cell stable isotope probing, Raman-activated cell sorting and mini-metagenomics. Sequencing of cell-sorted fractions reveals members of the underexplored family Muribaculaceae as major mucin monosaccharide foragers, followed by members of Lachnospiraceae, Rikenellaceae, and Bacteroidaceae families. Using this information, we assembled a five-member consortium of sialic acid and N-acetylglucosamine utilizers that impedes C. difficile's access to these mucosal sugars and impairs pathogen colonization in antibiotic-treated mice. Our findings underscore the value of targeted approaches to identify organisms utilizing key nutrients and to rationally design effective probiotic mixtures.
• A refined set of rRNA-targeted oligonucleotide probes for in situ detection and quantification of ammonia-oxidizing bacteria
Lukumbuzya M, Kristensen JM, Kitzinger K, Pommerening-Roser A, Nielsen PH, Wagner M, Daims H, Pjevac P
2020 - Water Res., 186: 116372
ammonia oxidizing bacteria FISH picture
Abstract:
Ammonia-oxidizing bacteria (AOB) of the betaproteobacterial genera Nitrosomonas and Nitrosospira are key nitrifying microorganisms in many natural and engineered ecosystems. Since many AOB remain uncultured, fluorescence in situ hybridization (FISH) with rRNA-targeted oligonucleotide probes has been one of the most widely used approaches to study the community composition, abundance, and other features of AOB directly in environmental samples. However, the established and widely used AOB-specific 16S rRNA-targeted FISH probes were designed up to two decades ago, based on much smaller rRNA gene sequence datasets than available today. Several of these probes cover their target AOB lineages incompletely and suffer from a weak target specificity, which causes cross-hybridization of probes that should detect different AOB lineages. Here, a set of new highly specific 16S rRNA-targeted oligonucleotide probes was developed and experimentally evaluated that complements the existing probes and enables the specific detection and differentiation of the known, major phylogenetic clusters of betaproteobacterial AOB. The new probes were successfully applied to visualize and quantify AOB in activated sludge and biofilm samples from seven pilot- and full-scale wastewater treatment systems. Based on its improved target group coverage and specificity, the refined probe set will facilitate future in situ analyses of AOB.
• Flow-through stable isotope probing (Flow-SIP) minimizes cross-feeding in complex microbial communities.
Mooshammer M, Kitzinger K, Schintlmeister A, Ahmerkamp S, Nielsen JL, Nielsen PH, Wagner M
2020 - ISME J, in press
Abstract:
Stable isotope probing (SIP) is a key tool for identifying the microorganisms catalyzing the turnover of specific substrates in the environment and to quantify their relative contributions to biogeochemical processes. However, SIP-based studies are subject to the uncertainties posed by cross-feeding, where microorganisms release isotopically labeled products, which are then used by other microorganisms, instead of incorporating the added tracer directly. Here, we introduce a SIP approach that has the potential to strongly reduce cross-feeding in complex microbial communities. In this approach, the microbial cells are exposed on a membrane filter to a continuous flow of medium containing isotopically labeled substrate. Thereby, metabolites and degradation products are constantly removed, preventing consumption of these secondary substrates. A nanoSIMS-based proof-of-concept experiment using nitrifiers in activated sludge and C-bicarbonate as an activity tracer showed that Flow-SIP significantly reduces cross-feeding and thus allows distinguishing primary consumers from other members of microbial food webs.
• Woeseiales transcriptional response to shallow burial in Arctic fjord surface sediment
Buongiorno J, Sipes K, Wasmund K, Loy A, Lloyd K
2020 - PLoS One, 15: e0234839
Abstract:
Distinct lineages of Gammaproteobacteria clade Woeseiales are globally distributed in marine sediments, based on metagenomic and 16S rRNA gene analysis. Yet little is known about why they are dominant or their ecological role in Arctic fjord sediments, where glacial retreat is rapidly imposing change. This study combined 16S rRNA gene analysis, metagenome-assembled genomes (MAGs), and genome-resolved metatranscriptomics uncovered the in situ abundance and transcriptional activity of Woeseiales with burial in four shallow sediment sites of Kongsfjorden and Van Keulenfjorden of Svalbard (79°N). We present five novel Woeseiales MAGs and show transcriptional evidence for metabolic plasticity during burial, including sulfur oxidation with reverse dissimilatory sulfite reductase (dsrAB) down to 4 cm depth and nitrite reduction down to 6 cm depth. A single stress protein, spore protein SP21 (hspA), had a tenfold higher mRNA abundance than any other transcript, and was a hundredfold higher on average than other transcripts. At three out of the four sites, SP21 transcript abundance increased with depth, while total mRNA abundance and richness decreased, indicating a shift in investment from metabolism and other cellular processes to build-up of spore protein SP21. The SP21 gene in MAGs was often flanked by genes involved in membrane-associated stress response. The ability of Woeseiales to shift from sulfur oxidation to nitrite reduction with burial into marine sediments with decreasing access to overlying oxic bottom waters, as well as enter into a dormant state dominated by SP21, may account for its ubiquity and high abundance in marine sediments worldwide, including those of the rapidly shifting Arctic.
• It Takes a Village: Discovering and Isolating the Nitrifiers.
2020 - Front Microbiol, 1900
Abstract:
It has been almost 150 years since Jean-Jacques Schloesing and Achille Müntz discovered that the process of nitrification, the oxidation of ammonium to nitrate, is a biological process carried out by microorganisms. In the following 15 years, numerous researchers independently contributed paradigm shifting discoveries that formed the foundation of nitrification and nitrification-related research. One of them was Sergei Winogradsky, whose major accomplishments include the discovery of both lithotrophy (in sulfur-oxidizing bacteria) and chemoautotrophy (in nitrifying bacteria). However, Winogradsky often receives most of the credit for many other foundational nitrification discoveries made by his contemporaries. This accumulation of credit over time is at least in part due to the increased attention, Winogradsky receives in the scientific literature and textbooks as a "founder of microbiology" and "the founder of microbial ecology." Here, some light is shed on several other researchers who are often overlooked, but whose work was instrumental to the emerging field of nitrification and to the work of Winogradsky himself. Specifically, the discovery of the biological process of nitrification by Schloesing and Müntz, the isolation of the first nitrifier by Grace and Percy Frankland, and the observation that nitrification is carried out by two distinct groups of microorganisms by Robert Warington are highlighted. Finally, the more recent discoveries of the chemolithoautotrophic ammonia-oxidizing archaea and complete ammonia oxidizers are put into this historical context.
• Dietary Supplementation with Sugar Beet Fructooligosaccharides and Garlic Residues Promotes Growth of Beneficial Bacteria and Increases Weight Gain in Neonatal Lambs.
Quijada NM, Bodas R, Lorenzo JM, Schmitz-Esser S, Rodríguez-Lázaro D, Hernández M
2020 - Biomolecules, 8: in press
Abstract:
The proper development of the early gastrointestinal tract (GIT) microbiota is critical for newborn ruminants. This microbiota is susceptible to modification by diverse external factors (such as diet) that can lead to long-lasting results when occurring in young ruminants. Dietary supplementation with prebiotics, ingredients nondigestible and nonabsorbable by the host that stimulate the growth of beneficial GIT bacteria, has been applied worldwide as a potential approach in order to improve ruminant health and production yields. However, how prebiotics affect the GIT microbiota during ruminants' early life is still poorly understood. We investigated the effect of milk supplementation with a combination of two well-known prebiotics, fructooligosaccharides (FOS) from sugar beet and garlic residues (all together named as "additive"), exerted on preweaned lamb growth and the composition of their fecal microbiota, by using 16S rRNA gene amplicon high-throughput sequencing. The results showed a significant increase in the mean daily weight gain of lambs fed with the additive. Lamb fecal microbiota was also influenced by the additive intake, as additive-diet lambs showed lower bacterial diversity and were significantly more abundant in , , and . These bacteria have been previously reported to confer beneficial properties to the ruminant, including promotion of growth and health status, and our results showed that they were strongly linked to the additive intake and the increased weight gain of lambs. This study points out the combination of FOS from sugar beet and garlic residues as a potential prebiotic to be used in young ruminants' nutrition in order to improve production yields.
• Molecular causes of an evolutionary shift along the parasitism-mutualism continuum in a bacterial symbiont.
Herrera P, Schuster L, Wentrup C, König L, Kempinger T, Na H, Schwarz J, Köstlbacher S, Wascher F, Zojer M, Rattei T, Horn M
2020 - Proc. Natl. Acad. Sci. U.S.A., in press
Abstract:
Symbiosis with microbes is a ubiquitous phenomenon with a massive impact on all living organisms, shaping the world around us today. Theoretical and experimental studies show that vertical transmission of symbionts leads to the evolution of mutualistic traits, whereas horizontal transmission facilitates the emergence of parasitic features. However, these studies focused on phenotypic data, and we know little about underlying molecular changes at the genomic level. Here, we combined an experimental evolution approach with infection assays, genome resequencing, and global gene expression analysis to study the effect of transmission mode on an obligate intracellular bacterial symbiont. We show that a dramatic shift in the frequency of genetic variants, coupled with major changes in gene expression, allow the symbiont to alter its position in the parasitism-mutualism continuum depending on the mode of between-host transmission. We found that increased parasitism in horizontally transmitted chlamydiae residing in amoebae was a result of processes occurring at the infectious stage of the symbiont's developmental cycle. Specifically, genes involved in energy production required for extracellular survival and the type III secretion system-the symbiont's primary virulence mechanism-were significantly up-regulated. Our results identify the genomic and transcriptional dynamics sufficient to favor parasitic or mutualistic strategies.
• Composition and activity of nitrifier communities in soil are unresponsive to elevated temperature and CO, but strongly affected by drought.
Séneca J, Pjevac P, Canarini A, Herbold CW, Zioutis C, Dietrich M, Simon E, Prommer J, Bahn M, Pötsch EM, Wagner M, Wanek W, Richter A
2020 - ISME J, in press
soil nitrifier response to climate change
Abstract:
Nitrification is a fundamental process in terrestrial nitrogen cycling. However, detailed information on how climate change affects the structure of nitrifier communities is lacking, specifically from experiments in which multiple climate change factors are manipulated simultaneously. Consequently, our ability to predict how soil nitrogen (N) cycling will change in a future climate is limited. We conducted a field experiment in a managed grassland and simultaneously tested the effects of elevated atmospheric CO, temperature, and drought on the abundance of active ammonia-oxidizing bacteria (AOB) and archaea (AOA), comammox (CMX) Nitrospira, and nitrite-oxidizing bacteria (NOB), and on gross mineralization and nitrification rates. We found that N transformation processes, as well as gene and transcript abundances, and nitrifier community composition were remarkably resistant to individual and interactive effects of elevated CO and temperature. During drought however, process rates were increased or at least maintained. At the same time, the abundance of active AOB increased probably due to higher NH availability. Both, AOA and comammox Nitrospira decreased in response to drought and the active community composition of AOA and NOB was also significantly affected. In summary, our findings suggest that warming and elevated CO have only minor effects on nitrifier communities and soil biogeochemical variables in managed grasslands, whereas drought favors AOB and increases nitrification rates. This highlights the overriding importance of drought as a global change driver impacting on soil microbial community structure and its consequences for N cycling.
• Exploring the upper pH limits of nitrite oxidation: diversity, ecophysiology, and adaptive traits of haloalkalitolerant Nitrospira
Daebeler A, Kitzinger K, Koch H, Herbold CW, Steinberger M, Schwarz J, Zechmeister T, Karst S, Albertsen M, Nielsen PH, Wagner M, Daims H
2020 - ISME J, in press
Ca. N. alkalitolerans
Abstract:
Nitrite-oxidizing bacteria of the genus Nitrospira are key players of the biogeochemical nitrogen cycle. However, little is known about their occurrence and survival strategies in extreme pH environments. Here, we report on the discovery of physiologically versatile, haloalkalitolerant Nitrospira that drive nitrite oxidation at exceptionally high pH. Nitrospiradistribution, diversity, and ecophysiology were studied in hypo- and subsaline (1.3-12.8 g salt/l), highly alkaline (pH 8.9-10.3) lakes by amplicon sequencing, metagenomics, and cultivation-based approaches. Surprisingly, not only were Nitrospira populations detected, but they were also considerably diverse with presence of members of Nitrospira lineages I, II and IV. Furthermore, the ability of Nitrospira enrichment cultures to oxidize nitrite at neutral to highly alkaline pH of 10.5 was demonstrated. Metagenomic analysis of a newly enriched Nitrospira lineage IV species, “Candidatus Nitrospira alkalitolerans”, revealed numerous adaptive features of this organism to its extreme environment. Among them were a sodium-dependent N-type ATPase and NADH:quinone oxidoreductase next to the proton-driven forms usually found in Nitrospira. Other functions aid in pH and cation homeostasis and osmotic stress defense. “Ca. Nitrospira alkalitolerans” also possesses group 2a and 3b [NiFe] hydrogenases, suggesting it can use hydrogen as alternative energy source. These results reveal how Nitrospira cope with strongly fluctuating pH and salinity conditions and expand our knowledge of nitrogen cycling in extreme habitats.
• Gut microbiota and undigested food constituents modify toxin composition and suppress the genotoxicity of a naturally occurring mixture of Alternaria toxins in vitro.
Crudo F, Aichinger G, Mihajlovic J, Dellafiora L, Varga E, Puntscher H, Warth B, Dall'Asta C, Berry D, Marko D
2020 - Arch. Toxicol., in press
Abstract:
Molds of the genus Alternaria produce several mycotoxins, some of which may pose a threat for health due to their genotoxicity. Due to the lack of adequate toxicological and occurrence data, they are currently not regulated. Interactions between mycotoxins, gut microbiota and food constituents might occur after food ingestion, modifying the bioavailability and, therefore, overall toxicity of mycotoxins. The present work aimed to investigate the impact of in vitro short-term fecal incubation on the in vitro DNA-damaging effects exerted by 5 µg/mL of an Alternaria alternata extract, containing, among others, 15 nM alternariol, 12 nM alternariol monomethyl ether, 241 nM altertoxin II and 301 nM stemphyltoxin III, all of which are known as genotoxic. The involvement of microorganisms, undigested food constituents and soluble substances of human fecal samples in modifying the composition and the genotoxicity of the extract was investigated through the application of LC-MS/MS analysis and comet assays in HT-29 cells. Results showed that the potential of the mycotoxins to induce DNA strand breaks was almost completely quenched, even before anaerobic incubation, by contact with the different fractions of the fecal samples, while the potency to induce formamidopyrimidine DNA glycosylase (FPG)-sensitive sites was only slightly reduced. These effects were in line with a reduction of mycotoxin concentrations found in samples analyzed by LC-MS/MS. Although a direct correlation between the metabolic activity of the gut microbiota and modifications in mycotoxin contents was not clearly observed, adsorptive phenomena to bacterial cells and to undigested food constituents might explain the observed modifications.
• Microbiome definition re-visited: old concepts and new challenges.
Berg G, Rybakova D, Fischer D, Cernava T, Vergès MC, Charles T, Chen X, Cocolin L, Eversole K, Corral GH, Kazou M, Kinkel L, Lange L, Lima N, Loy A, Macklin JA, Maguin E, Mauchline T, McClure R, Mitter B, Ryan M, Sarand I, Smidt H, Schelkle B, Roume H, Kiran GS, Selvin J, Souza RSC, van Overbeek L, Singh BK, Wagner M, Walsh A, Sessitsch A, Schloter M
2020 - Microbiome, 1: 103
Abstract:
The field of microbiome research has evolved rapidly over the past few decades and has become a topic of great scientific and public interest. As a result of this rapid growth in interest covering different fields, we are lacking a clear commonly agreed definition of the term "microbiome." Moreover, a consensus on best practices in microbiome research is missing. Recently, a panel of international experts discussed the current gaps in the frame of the European-funded MicrobiomeSupport project. The meeting brought together about 40 leaders from diverse microbiome areas, while more than a hundred experts from all over the world took part in an online survey accompanying the workshop. This article excerpts the outcomes of the workshop and the corresponding online survey embedded in a short historical introduction and future outlook. We propose a definition of microbiome based on the compact, clear, and comprehensive description of the term provided by Whipps et al. in 1988, amended with a set of novel recommendations considering the latest technological developments and research findings. We clearly separate the terms microbiome and microbiota and provide a comprehensive discussion considering the composition of microbiota, the heterogeneity and dynamics of microbiomes in time and space, the stability and resilience of microbial networks, the definition of core microbiomes, and functionally relevant keystone species as well as co-evolutionary principles of microbe-host and inter-species interactions within the microbiome. These broad definitions together with the suggested unifying concepts will help to improve standardization of microbiome studies in the future, and could be the starting point for an integrated assessment of data resulting in a more rapid transfer of knowledge from basic science into practice. Furthermore, microbiome standards are important for solving new challenges associated with anthropogenic-driven changes in the field of planetary health, for which the understanding of microbiomes might play a key role. Video Abstract.
• Chlamydiae in the Environment.
Collingro A, Köstlbacher S, Horn M
2020 - Trends Microbiol., in press
Abstract:
Chlamydiae have been known for more than a century as major pathogens of humans. Yet they are also found ubiquitously in the environment where they thrive within protists and in an unmatched wide range of animals. This review summarizes recent advances in understanding chlamydial diversity and distribution in nature. Studying these environmental chlamydiae provides a novel perspective on basic chlamydial biology and evolution. A picture is beginning to emerge with chlamydiae representing one of the evolutionarily most ancient and successful groups of obligate intracellular bacteria.
• Roadmap for naming uncultivated Archaea and Bacteria.
Murray AE, Freudenstein J, Gribaldo S, Hatzenpichler R, Hugenholtz P, Kämpfer P, Konstantinidis KT, Lane CE, Papke RT, Parks DH, Rosselló-Móra R, Stott MB, Sutcliffe IC, Thrash JC, Venter SN, Whitman WB, Acinas SG, Amann RI, Anantharaman K, Armengaud J, Baker BJ, Barco RA, Bode HB, Boyd ES, Brady CL, Carini P, Chain PSG, Colman DR, DeAngelis KM, de Los Rios MA, Estrada-de los Santos P, Dunlap CA, Eisen JA, Emerson D, Ettema TJG, Eveillard D, Girguis PR, Hentschel U, Hollibaugh JT, Hug LA, Inskeep WP, Ivanova EP, Klenk HP, Li WJ, Lloyd KG, Löffler FE, Makhalanyane TP, Moser DP, Nunoura T, Palmer M, Parro V, Pedrós-Alió C, Probst AJ, Smits THM, Steen AD, Steenkamp ET, Spang A, Stewart FJ, Tiedje JM, Vandamme P, Wagner M, Wang FP, Hedlund BP, Reysenbach AL
2020 - Nat Microbiol, 8: 987-994
Roadmap for naming uncultured microbes
Abstract:
The assembly of single-amplified genomes (SAGs) and metagenome-assembled genomes (MAGs) has led to a surge in genome-based discoveries of members affiliated with Archaea and Bacteria, bringing with it a need to develop guidelines for nomenclature of uncultivated microorganisms. The International Code of Nomenclature of Prokaryotes (ICNP) only recognizes cultures as 'type material', thereby preventing the naming of uncultivated organisms. In this Consensus Statement, we propose two potential paths to solve this nomenclatural conundrum. One option is the adoption of previously proposed modifications to the ICNP to recognize DNA sequences as acceptable type material; the other option creates a nomenclatural code for uncultivated Archaea and Bacteria that could eventually be merged with the ICNP in the future. Regardless of the path taken, we believe that action is needed now within the scientific community to develop consistent rules for nomenclature of uncultivated taxa in order to provide clarity and stability, and to effectively communicate microbial diversity.
• The role of metal contamination in shaping microbial communities in heavily polluted marine sediments
Di Cesare A, Pjevac P, Eckert E, Curkov N, Miko Šparica M, Corno G, Orlić S
2020 - Environ. Pollut., 265: 114823
Abstract:
Microorganisms in coastal sediments are fundamental for ecosystem functioning, and regulate processes relevant in global biogeochemical cycles. Still, our understanding of the effects anthropogenic perturbation and pollution can have on microbial communities in marine sediments is limited. We surveyed the microbial diversity, and the occurrence and abundance of metal and antibiotic resistance genes is sediments collected from the Pula Bay (Croatia), one of the most significantly polluted sites along the Croatian coast. With a collection of 14 samples from the bay area, we were able to generate a detailed status quo picture of a site that only recently started a cleaning and remediation process (closing of sewage pipes and reduction of industrial activity). The concentrations of heavy metals in Pula Bay sediments are significantly higher than in pristine sediments from the Adriatic Sea, and in some cases, manifold exceed international sediment quality guidelines. While the sedimentary concentrations of heavy metals did significantly influence the abundance of the tested metal resistance genes, no strong effect of heavy metal pollution on the overall microbial community composition was observed. Like in many other marine sediments, Gammaproteobacteria, Bacteroidota and Desulfobacterota dominated the microbial community composition in most samples, and community assembly was primarily driven by water column depth and nutrient (carbon and nitrogen) availability, regardless of the degree of heavy metal pollution.
• Verrucomicrobia use hundreds of enzymes to digest the algal polysaccharide fucoidan.
Sichert A, Corzett CH, Schechter MS, Unfried F, Markert S, Becher D, Fernandez-Guerra A, Liebeke M, Schweder T, Polz MF, Hehemann JH
2020 - Nat Microbiol, 8: 1026-1039
Abstract:
Brown algae are important players in the global carbon cycle by fixing carbon dioxide into 1 Gt of biomass annually, yet the fate of fucoidan-their major cell wall polysaccharide-remains poorly understood. Microbial degradation of fucoidans is slower than that of other polysaccharides, suggesting that fucoidans are more recalcitrant and may sequester carbon in the ocean. This may be due to the complex, branched and highly sulfated structure of fucoidans, which also varies among species of brown algae. Here, we show that 'Lentimonas' sp. CC4, belonging to the Verrucomicrobia, acquired a remarkably complex machinery for the degradation of six different fucoidans. The strain accumulated 284 putative fucoidanases, including glycoside hydrolases, sulfatases and carbohydrate esterases, which are primarily located on a 0.89-megabase pair plasmid. Proteomics reveals that these enzymes assemble into substrate-specific pathways requiring about 100 enzymes per fucoidan from different species of brown algae. These enzymes depolymerize fucoidan into fucose, which is metabolized in a proteome-costly bacterial microcompartment that spatially constrains the metabolism of the toxic intermediate lactaldehyde. Marine metagenomes and microbial genomes show that Verrucomicrobia including 'Lentimonas' are abundant and highly specialized degraders of fucoidans and other complex polysaccharides. Overall, the complexity of the pathways underscores why fucoidans are probably recalcitrant and more slowly degraded, since only highly specialized organisms can effectively degrade them in the ocean.
• Crypt residing bacteria and proximal colonic carcinogenesis in a mouse model of Lynch syndrome.
Lang M, Baumgartner M, Rożalska A, Frick A, Riva A, Jarek M, Berry D, Gasche C
2020 - Int. J. Cancer, 8: 2316-2326
Abstract:
Colorectal cancer is a multifactorial disease involving inherited DNA mutations, environmental factors, gut inflammation and intestinal microbiota. Certain germline mutations within the DNA mismatch repair system are associated with Lynch syndrome tumors including right-sided colorectal cancer with mucinous phenotype and presence of an inflammatory infiltrate. Such tumors are more often associated with bacterial biofilms, which may contribute to disease onset and progression. Inflammatory bowel diseases are also associated with colorectal cancer and intestinal dysbiosis. Herein we addressed the question, whether inflammation can aggravate colorectal cancer development under mismatch repair deficiency. MSH2 mice were crossed into the IL-10 background to study the importance of inflammation and mucosal bacteria as a driver of tumorigenesis in a Lynch syndrome mouse model. An increase in large bowel tumorigenesis was found in double knockout mice both under conventional housing and under specific pathogen-free conditions. This increase was mostly due to the development of proximal tumors, a hotspot for tumorigenesis in Lynch syndrome, and was associated with a higher degree of inflammation. Additionally, bacterial invasion into the mucus of tumor crypts was observed in the proximal tumors. Inflammation shifted fecal and mucosal microbiota composition and was associated with enrichment in Escherichia-Shigella as well as Akkermansia, Bacteroides and Parabacteroides genera in fecal samples. Tumor-bearing double knockout mice showed a similar enrichment for Escherichia-Shigella and Parabacteroides. Lactobacilli, Lachnospiraceae and Muribaculaceae family members were depleted upon inflammation. In summary, chronic inflammation aggravates colonic tumorigenesis under mismatch repair deficiency and is associated with a shift in microbiota composition.
• Energetic Basis of Microbial Growth and Persistence in Desert Ecosystems.
Leung PM, Bay SK, Meier DV, Chiri E, Cowan DA, Gillor O, Woebken D, Greening C
2020 - mSystems, 2: in press
Abstract:
Microbial life is surprisingly abundant and diverse in global desert ecosystems. In these environments, microorganisms endure a multitude of physicochemical stresses, including low water potential, carbon and nitrogen starvation, and extreme temperatures. In this review, we summarize our current understanding of the energetic mechanisms and trophic dynamics that underpin microbial function in desert ecosystems. Accumulating evidence suggests that dormancy is a common strategy that facilitates microbial survival in response to water and carbon limitation. Whereas photoautotrophs are restricted to specific niches in extreme deserts, metabolically versatile heterotrophs persist even in the hyper-arid topsoils of the Atacama Desert and Antarctica. At least three distinct strategies appear to allow such microorganisms to conserve energy in these oligotrophic environments: degradation of organic energy reserves, rhodopsin- and bacteriochlorophyll-dependent light harvesting, and oxidation of the atmospheric trace gases hydrogen and carbon monoxide. In turn, these principles are relevant for understanding the composition, functionality, and resilience of desert ecosystems, as well as predicting responses to the growing problem of desertification.
• Activity and metabolic versatility of complete ammonia oxidizers in full-scale wastewater treatment systems.
Yang Y, Daims H, Liu Y, Herbold CW, Pjevac P, Lin JG, Li M, Gu JD
2020 - mBio, 11: e03175-19
Abstract:
The recent discovery of complete ammonia oxidizers (comammox) contradicts the paradigm that chemolithoautotrophic nitrification is always catalyzed by two different microorganisms. However, our knowledge of the survival strategies of comammox in complex ecosystems, such as full-scale wastewater treatment plants (WWTPs), remains limited. Analyses of genomes and transcriptomes of four comammox organisms from two full-scale WWTPs revealed that comammox were active and showed a surprisingly high metabolic versatility. A gene cluster for the utilization of urea and a gene encoding cyanase suggest that comammox may use diverse organic nitrogen compounds in addition to free ammonia as the substrates. The comammox organisms also encoded the genomic potential for multiple alternative energy metabolisms, including respiration with hydrogen, formate, and sulfite as electron donors. Pathways for the biosynthesis and degradation of polyphosphate, glycogen, and polyhydroxyalkanoates as intracellular storage compounds likely help comammox survive unfavorable conditions and facilitate switches between lifestyles in fluctuating environments. One of the comammox strains acquired from the anaerobic tank encoded and transcribed genes involved in homoacetate fermentation or in the utilization of exogenous acetate, both pathways being unexpected in a nitrifying bacterium. Surprisingly, this strain also encoded a respiratory nitrate reductase which has not yet been found in any other genome and might confer a selective advantage to this strain over other strains in anoxic conditions. The discovery of comammox in the genus changes our perception of nitrification. However, genomes of comammox organisms have not been acquired from full-scale WWTPs, and very little is known about their survival strategies and potential metabolisms in complex wastewater treatment systems. Here, four comammox metagenome-assembled genomes and metatranscriptomic data sets were retrieved from two full-scale WWTPs. Their impressive and-among nitrifiers-unsurpassed ecophysiological versatility could make comammox an interesting target for optimizing nitrification in current and future bioreactor configurations.
• Raman-based sorting of microbial cells to link functions to their genes.
Lee KS, Wagner M, Stocker R
2020 - Microb Cell, 3: 62-65
Abstract:
In our recent work, we developed an optofluidic platform that allows a direct link to be made between the phenotypes (functions) and the genotypes (genes) of microbial cells within natural communities. By combining stable isotope probing, optical tweezers, Raman microspectroscopy, and microfluidics, the platform performs automated Raman-based sorting of taxa from within a complex community in terms of their functional properties. In comparison with manual sorting approaches, our method provides high throughput (up to 500 cells per hour) and very high sorting accuracy (98.3 ± 1.7%), and significantly reduces the human labour required. The system provides an efficient manner to untangle the contributions of individual members within environmental and host-associated microbiomes. In this News and Thoughts, we provide an overview of our platform, describe potential applications, suggest ways in which the system could be improved, and discuss future directions in which Raman-based analysis of microbial populations might be developed.
• Complementary Metagenomic Approaches Improve Reconstruction of Microbial Diversity in a Forest Soil.
Alteio LV, Schulz F, Seshadri R, Varghese N, Rodriguez-Reillo W, Ryan E, Goudeau D, Eichorst SA, Malmstrom RR, Bowers RM, Katz LA, Blanchard JL, Woyke T
2020 - mSystems, 2: in press
Abstract:
Soil ecosystems harbor diverse microorganisms and yet remain only partially characterized as neither single-cell sequencing nor whole-community sequencing offers a complete picture of these complex communities. Thus, the genetic and metabolic potential of this "uncultivated majority" remains underexplored. To address these challenges, we applied a pooled-cell-sorting-based mini-metagenomics approach and compared the results to bulk metagenomics. Informatic binning of these data produced 200 mini-metagenome assembled genomes (sorted-MAGs) and 29 bulk metagenome assembled genomes (MAGs). The sorted and bulk MAGs increased the known phylogenetic diversity of soil taxa by 7.2% with respect to the Joint Genome Institute IMG/M database and showed clade-specific sequence recruitment patterns across diverse terrestrial soil metagenomes. Additionally, sorted-MAGs expanded the rare biosphere not captured through MAGs from bulk sequences, exemplified through phylogenetic and functional analyses of members of the phylum Analysis of 67 sorted-MAGs showed conserved patterns of carbon metabolism across four clades. These results indicate that mini-metagenomics enables genome-resolved investigation of predicted metabolism and demonstrates the utility of combining metagenomics methods to tap into the diversity of heterogeneous microbial assemblages. Microbial ecologists have historically used cultivation-based approaches as well as amplicon sequencing and shotgun metagenomics to characterize microbial diversity in soil. However, challenges persist in the study of microbial diversity, including the recalcitrance of the majority of microorganisms to laboratory cultivation and limited sequence assembly from highly complex samples. The uncultivated majority thus remains a reservoir of untapped genetic diversity. To address some of the challenges associated with bulk metagenomics as well as low throughput of single-cell genomics, we applied flow cytometry-enabled mini-metagenomics to capture expanded microbial diversity from forest soil and compare it to soil bulk metagenomics. Our resulting data from this pooled-cell sorting approach combined with bulk metagenomics revealed increased phylogenetic diversity through novel soil taxa and rare biosphere members. In-depth analysis of genomes within the highly represented phylum provided insights into conserved and clade-specific patterns of carbon metabolism.
• Using Colonization Assays and Comparative Genomics To Discover Symbiosis Behaviors and Factors in Vibrio fischeri.
Bongrand C, Moriano-Gutierrez S, Arevalo P, McFall-Ngai M, Visick KL, Polz M, Ruby EG
2020 - mBio, 2: in press
Abstract:
The luminous marine Gram-negative bacterium () is the natural light organ symbiont of several squid species, including the Hawaiian bobtail squid, , and the Japanese bobtail squid, Work with has shown how the bacteria establish their niche in the light organ of the newly hatched host. Two types of strains have been distinguished based upon their behavior in cocolonization competition assays in juvenile , i.e., (i) niche-sharing or (ii) niche-dominant behavior. This study aimed to determine whether these behaviors are observed with other strains or whether they are specific to those isolated from light organs. Cocolonization competition assays between strains isolated from the congeneric squid or from other marine animals revealed the same sharing or dominant behaviors. In addition, whole-genome sequencing of these strains showed that the dominant behavior is polyphyletic and not associated with the presence or absence of a single gene or genes. Comparative genomics of 44 squid light organ isolates from around the globe led to the identification of symbiosis-specific candidates in the genomes of these strains. Colonization assays using genetic derivatives with deletions of these candidates established the importance of two such genes in colonization. This study has allowed us to expand the concept of distinct colonization behaviors to strains isolated from a number of squid and fish hosts. There is an increasing recognition of the importance of strain differences in the ecology of a symbiotic bacterial species and, in particular, how these differences underlie crucial interactions with their host. Nevertheless, little is known about the genetic bases for these differences, how they manifest themselves in specific behaviors, and their distribution among symbionts of different host species. In this study, we sequenced the genomes of isolated from the tissues of squids and fishes and applied comparative genomics approaches to look for patterns between symbiont lineages and host colonization behavior. In addition, we identified the only two genes that were exclusively present in all strains isolated from the light organs of sepiolid squid species. Mutational studies of these genes indicated that they both played a role in colonization of the squid light organ, emphasizing the value of applying a comparative genomics approach in the study of symbioses.
• The Signal and the Noise: Characteristics of Antisense RNA in Complex Microbial Communities.
Michaelsen TY, Brandt J, Singleton CM, Kirkegaard RH, Wiesinger J, Segata N, Albertsen M
2020 - mSystems, 1: in press
Abstract:
High-throughput sequencing has allowed unprecedented insight into the composition and function of complex microbial communities. With metatranscriptomics, it is possible to interrogate the transcriptomes of multiple organisms simultaneously to get an overview of the gene expression of the entire community. Studies have successfully used metatranscriptomics to identify and describe relationships between gene expression levels and community characteristics. However, metatranscriptomic data sets contain a rich suite of additional information that is just beginning to be explored. Here, we focus on antisense expression in metatranscriptomics, discuss the different computational strategies for handling it, and highlight the strengths but also potentially detrimental effects on downstream analysis and interpretation. We also analyzed the antisense transcriptomes of multiple genomes and metagenome-assembled genomes (MAGs) from five different data sets and found high variability in the levels of antisense transcription for individual species, which were consistent across samples. Importantly, we challenged the conceptual framework that antisense transcription is primarily the product of transcriptional noise and found mixed support, suggesting that the total observed antisense RNA in complex communities arises from the combined effect of unknown biological and technical factors. Antisense transcription can be highly informative, including technical details about data quality and novel insight into the biology of complex microbial communities. This study systematically evaluated the global patterns of microbial antisense expression across various environments and provides a bird's-eye view of general patterns observed across data sets, which can provide guidelines in our understanding of antisense expression as well as interpretation of metatranscriptomic data in general. This analysis highlights that in some environments, antisense expression from microbial communities can dominate over regular gene expression. We explored some potential drivers of antisense transcription, but more importantly, this study serves as a starting point, highlighting topics for future research and providing guidelines to include antisense expression in generic bioinformatic pipelines for metatranscriptomic data.
• Diarrhoeal events can trigger long-term Clostridium difficile colonization with recurrent blooms.
VanInsberghe D, Elsherbini JA, Varian B, Poutahidis T, Erdman S, Polz MF
2020 - Nat Microbiol, 4: 642-650
Abstract:
Although Clostridium difficile is widely considered an antibiotic- and hospital-associated pathogen, recent evidence indicates that this is an insufficient depiction of the risks and reservoirs. A common thread that links all major risk factors of infection is their association with gastrointestinal disturbances, but this relationship to C. difficile colonization has never been tested directly. Here, we show that disturbances caused by diarrhoeal events trigger susceptibility to C. difficile colonization. Using survey data of the human gut microbiome, we detected C. difficile colonization and blooms in people recovering from food poisoning and Vibrio cholerae infections. Carriers remained colonized for year-long time scales and experienced highly variable patterns of C. difficile abundance, where increased shedding over short periods of 1-2 d interrupted week-long periods in which C. difficile was undetectable. Given that short shedding events were often linked to gastrointestinal disturbances, our results help explain why C. difficile is frequently detected as a co-infecting pathogen in patients with diarrhoea. To directly test the impact of diarrhoea on susceptibility to colonization, we developed a mouse model of variable disturbance intensity, which allowed us to monitor colonization in the absence of disease. As mice exposed to avirulent C. difficile spores ingested increasing quantities of laxatives, more individuals experienced C. difficile blooms. Our results indicate that the likelihood of colonization is highest in the days immediately following acute disturbances, suggesting that this could be an important window during which transmission could be interrupted and the incidence of infection lowered.
• Single cell analyses reveal contrasting life strategies of the two main nitrifiers in the ocean.
Kitzinger K, Marchant HK, Bristow LA, Herbold CW, Padilla CC, Kidane AT, Littmann S, Daims H, Pjevac P, Stewart FJ, Wagner M, Kuypers MMM
2020 - Nat Commun, 1: 767
Nitrospina AOA in situ growth rates
Abstract:
Nitrification, the oxidation of ammonia via nitrite to nitrate, is a key process in marine nitrogen (N) cycling. Although oceanic ammonia and nitrite oxidation are balanced, ammonia-oxidizing archaea (AOA) vastly outnumber the main nitrite oxidizers, the bacterial Nitrospinae. The ecophysiological reasons for this discrepancy in abundance are unclear. Here, we compare substrate utilization and growth of Nitrospinae to AOA in the Gulf of Mexico. Based on our results, more than half of the Nitrospinae cellular N-demand is met by the organic-N compounds urea and cyanate, while AOA mainly assimilate ammonium. Nitrospinae have, under in situ conditions, around four-times higher biomass yield and five-times higher growth rates than AOA, despite their ten-fold lower abundance. Our combined results indicate that differences in mortality between Nitrospinae and AOA, rather than thermodynamics, biomass yield and cell size, determine the abundances of these main marine nitrifiers. Furthermore, there is no need to invoke yet undiscovered, abundant nitrite oxidizers to explain nitrification rates in the ocean.
• Culture-independent tracking of Vibrio cholerae lineages reveals complex spatiotemporal dynamics in a natural population.
Kirchberger PC, Orata FD, Nasreen T, Kauffman KM, Tarr CL, Case RJ, Polz MF, Boucher YF
2020 - Environ. Microbiol., in press
Abstract:
Populations of the bacterium Vibrio cholerae consist of dozens of distinct lineages, with primarily (but not exclusively) members of the pandemic generating lineage capable of causing the diarrhoeal disease cholera. Assessing the composition and temporal dynamics of such populations requires extensive isolation efforts and thus only rarely covers large geographic areas or timeframes exhaustively. We developed a culture-independent amplicon sequencing strategy based on the protein-coding gene viuB (vibriobactin utilization) to study the structure of a V. cholerae population over the course of a summer. We show that the 26 co-occurring V. cholerae lineages continuously compete for limited space on nutrient-rich particles where only a few of them can grow to large numbers. Differential abundance of lineages between locations and size-fractions associated with a particle-attached or free-swimming lifestyle could reflect adaptation to various environmental niches. In particular, a major V. cholerae lineage occasionally grows to large numbers on particles but remain undetectable using isolation-based methods, indicating selective culturability for some members of the species. We thus demonstrate that isolation-based studies may not accurately reflect the structure and complex dynamics of V. cholerae populations and provide a scalable high-throughput method for both epidemiological and ecological approaches to studying this species.
• Transcriptomic Response of Nitrosomonas europaea Transitioned from Ammonia- to Oxygen-Limited Steady-State Growth.
Sedlacek CJ, Giguere AT, Dobie MD, Mellbye BL, Ferrell RV, Woebken D, Sayavedra-Soto LA, Bottomley PJ, Daims H, Wagner M, Pjevac P
2020 - mSystems, 1: e00562-19
N. europaea electron flow
Abstract:
Ammonia-oxidizing microorganisms perform the first step of nitrification, the oxidation of ammonia to nitrite. The bacterium is the best-characterized ammonia oxidizer to date. Exposure to hypoxic conditions has a profound effect on the physiology of , e.g., by inducing nitrifier denitrification, resulting in increased nitric and nitrous oxide production. This metabolic shift is of major significance in agricultural soils, as it contributes to fertilizer loss and global climate change. Previous studies investigating the effect of oxygen limitation on have focused on the transcriptional regulation of genes involved in nitrification and nitrifier denitrification. Here, we combine steady-state cultivation with whole-genome transcriptomics to investigate the overall effect of oxygen limitation on Under oxygen-limited conditions, growth yield was reduced and ammonia-to-nitrite conversion was not stoichiometric, suggesting the production of nitrogenous gases. However, the transcription of the principal nitric oxide reductase (cNOR) did not change significantly during oxygen-limited growth, while the transcription of the nitrite reductase-encoding gene () was significantly lower. In contrast, both heme-copper-containing cytochrome oxidases encoded by were upregulated during oxygen-limited growth. Particularly striking was the significant increase in transcription of the B-type heme-copper oxidase, proposed to function as a nitric oxide reductase (sNOR) in ammonia-oxidizing bacteria. In the context of previous physiological studies, as well as the evolutionary placement of sNOR with regard to other heme-copper oxidases, these results suggest sNOR may function as a high-affinity terminal oxidase in and other ammonia-oxidizing bacteria. Nitrification is a ubiquitous microbially mediated process in the environment and an essential process in engineered systems such as wastewater and drinking water treatment plants. However, nitrification also contributes to fertilizer loss from agricultural environments, increasing the eutrophication of downstream aquatic ecosystems, and produces the greenhouse gas nitrous oxide. As ammonia-oxidizing bacteria are the most dominant ammonia-oxidizing microbes in fertilized agricultural soils, understanding their responses to a variety of environmental conditions is essential for curbing the negative environmental effects of nitrification. Notably, oxygen limitation has been reported to significantly increase nitric oxide and nitrous oxide production during nitrification. Here, we investigate the physiology of the best-characterized ammonia-oxidizing bacterium, , growing under oxygen-limited conditions.
• The role of gut microbiota, butyrate and proton pump inhibitors in amyotrophic lateral sclerosis: a systematic review.
Erber AC, Cetin H, Berry D, Schernhammer ES
2020 - Int. J. Neurosci., 7: 727-735
Abstract:
We conducted a systematic review on existing literature in humans and animals, linking the gut microbiome with amyotrophic lateral sclerosis (ALS). Additionally, we sought to explore the role of the bacterially produced metabolite butyrate as well as of proton pump inhibitors (PPIs) in these associations. Following PRISMA guidelines for systematic literature reviews, four databases (Medline, Scopus, Embase and Web of Science) were searched and screened by two independent reviewers against defined inclusion criteria. Six studies in humans and six animal studies were identified, summarized and reviewed. Overall, the evidence accrued to date is supportive of changes in the gut microbiome being associated with ALS risk, and potentially progression, though observational studies are small (describing a total of 145 patients with ALS across all published studies), and not entirely conclusive. With emerging studies beginning to apply metagenome sequencing, more clarity regarding the importance and promise of the gut microbiome in ALS can be expected. Future studies may also help establish the therapeutic potential of butyrate, and the role of PPIs in these associations.
• Archaeal nitrification is constrained by copper complexation with organic matter in municipal wastewater treatment plants.
Gwak JH, Jung MY, Hong H, Kim JG, Quan ZX, Reinfelder JR, Spasov E, Neufeld JD, Wagner M, Rhee SK
2020 - ISME J, 2: 335-346
Abstract:
Consistent with the observation that ammonia-oxidizing bacteria (AOB) outnumber ammonia-oxidizing archaea (AOA) in many eutrophic ecosystems globally, AOB typically dominate activated sludge aeration basins from municipal wastewater treatment plants (WWTPs). In this study, we demonstrate that the growth of AOA strains inoculated into sterile-filtered wastewater was inhibited significantly, in contrast to uninhibited growth of a reference AOB strain. In order to identify possible mechanisms underlying AOA-specific inhibition, we show that complex mixtures of organic compounds, such as yeast extract, were highly inhibitory to all AOA strains but not to the AOB strain. By testing individual organic compounds, we reveal strong inhibitory effects of organic compounds with high metal complexation potentials implying that the inhibitory mechanism for AOA can be explained by the reduced bioavailability of an essential metal. Our results further demonstrate that the inhibitory effect on AOA can be alleviated by copper supplementation, which we observed for pure AOA cultures in a defined medium and for AOA inoculated into nitrifying sludge. Our study offers a novel mechanistic explanation for the relatively low abundance of AOA in most WWTPs and provides a basis for modulating the composition of nitrifying communities in both engineered systems and naturally occurring environments.
• Horizontal acquisition of a patchwork Calvin cycle by symbiotic and free-living Campylobacterota (formerly Epsilonproteobacteria).
Assié A, Leisch N, Meier DV, Gruber-Vodicka H, Tegetmeyer HE, Meyerdierks A, Kleiner M, Hinzke T, Joye S, Saxton M, Dubilier N, Petersen JM
2020 - ISME J, 1: 104-122
Abstract:
Most autotrophs use the Calvin-Benson-Bassham (CBB) cycle for carbon fixation. In contrast, all currently described autotrophs from the Campylobacterota (previously Epsilonproteobacteria) use the reductive tricarboxylic acid cycle (rTCA) instead. We discovered campylobacterotal epibionts ("Candidatus Thiobarba") of deep-sea mussels that have acquired a complete CBB cycle and may have lost most key genes of the rTCA cycle. Intriguingly, the phylogenies of campylobacterotal CBB cycle genes suggest they were acquired in multiple transfers from Gammaproteobacteria closely related to sulfur-oxidizing endosymbionts associated with the mussels, as well as from Betaproteobacteria. We hypothesize that "Ca. Thiobarba" switched from the rTCA cycle to a fully functional CBB cycle during its evolution, by acquiring genes from multiple sources, including co-occurring symbionts. We also found key CBB cycle genes in free-living Campylobacterota, suggesting that the CBB cycle may be more widespread in this phylum than previously known. Metatranscriptomics and metaproteomics confirmed high expression of CBB cycle genes in mussel-associated "Ca. Thiobarba". Direct stable isotope fingerprinting showed that "Ca. Thiobarba" has typical CBB signatures, suggesting that it uses this cycle for carbon fixation. Our discovery calls into question current assumptions about the distribution of carbon fixation pathways in microbial lineages, and the interpretation of stable isotope measurements in the environment.
Book chapters and other publications
4 Publications found
• Is too much fertilizer a problem?
Sedlacek CJ, Giguere AT, Pjevac P
2020 - Frontiers for Young Minds, 8: 63
Abstract:
Fertilizers are added to crops in order to produce enough food to feed the human population. Fertilizers provide crops with nutrients like potassium, phosphorus, and nitrogen, which allow crops to grow bigger, faster, and to produce more food. Nitrogen in particular is an essential nutrient for the growth of every organismon Earth.Nitrogen is all around us and makes up about 78% of the air you breathe. However, plants and animals cannot use the nitrogen gas in the air. To grow, plants require nitrogen compounds fromthe soil,which can be produced naturally or be provided by fertilizers. However, applying excessive amounts of fertilizer leads to the release of harmful greenhouse gases into the atmosphere and the eutrophication of our waterways. Scientists are currently trying to find solutions to reduce the environmentally harmful effects of fertilizers, without reducing the amount of food we can produce when using them.
• Thinking outside the Chlamydia box
A Taylor-Brown, T Halter, A Polkinghorne, M Horn
2020 - 429-458. in Chlamydia Biology. (M Tan, JH Hegemann, C Sütterlin). Caister Academic Press
Abstract:
Chlamydiae have long been studied exclusively in the context of disease. Yet, accumulating evidence over nearly three decades shows that chlamydiae are ubiquitous in the environment, thriving as symbionts of unicellular eukaryotes such as amoeba and infecting a broad range of animal hosts. These chlamydiae share the characteristic chlamydial developmental cycle and other chlamydial hallmarks. Their discovery fundamentally changed our perspective on chlamydial diversity. Instead of a single genus, Chlamydia, including closely related pathogens, the chlamydiae comprise hundreds of families and genera. Investigating isolates and non-cultured representatives provided insights into features that are in common with or divergent from known Chlamydia species, and suggested that some of these chlamydiae may also be considered pathogens. Importantly, these studies have contributed to a better understanding of the biology of all chlamydiae, and they provide a framework for investigating the evolution of the chlamydial intracellular lifestyle and pathogenicity.
• One complete and seven draft genome sequences of subdivision 1 and 3 Acidobacteria from soil
Eichorst SA, Trojan D, Huntemann M, Clum A, Pillay M, Palaniappan K, Varghese N, Mikhailova N, Stamatis D, Reddy TBK, Daum C, Goodwin LA, Shapiro N, Ivanova N, Kyrpides N, Woyke T, Woebken D
2020 - Microbiology Resource Announcements, 9: 1-4
Abstract:
We report eight genomes from representatives of the phylum Acidobacteriasubdivisions 1 and 3, isolated from soils. The genome sizes range from 4.9 to 6.7 Mb. Genomic analysis reveals putative genes for low- and high-affinity respiratory oxygen reductases, high-affinity hydrogenases, and the capacity to use a diverse collection of carbohydrates.
• Draft genome sequences of Chlamydiales bacterium STE3 and Neochlamydia sp. AcF84, endosymbionts of Acanthamoeba spp.
Köstlbacher S, Michels S, Siegl A, Schulz F, Domman D, Jongwutiwes S, Putaporntip C, Horn M, Collingro A
2020 - Microbiol Resour Announc, 9: e00220-20
Abstract:
Chlamydiales bacterium STE3 and Neochlamydia sp. strain AcF84 are obligate intracellular symbionts of Acanthamoeba spp. isolated from the biofilm of a littoral cave wall and gills from striped tiger leaf fish, respectively. We report the draft genome sequences of these two environmental chlamydiae affiliated with the family Parachlamydiaceae.
|
__label__pos
| 0.761371 |
keylifejourneys
Click here for a special video from Key Life Journeys
Welcome | A Soul Journey | Caregiver Resources | Products | Keynotes | Blog | Articles | Testimonials
1
Join Key Life News
Get A Free Caregiver Resource!
Name:
Email:
1
Towards effective communication
Towards effective communication with those cognitively impaired by Alzheimer’s disease or other dementias.
By
Susan M. Ellis
1. Gain Attention
No information will be retained if the individual is not attentive or concentrating on the person giving instructions. Gain eye contact, call out the individual’s name, touch her and do not begin to talk until you are sure you have her attention. If hearing is a problem, never call out instructions when the back is turned, when a distance away or calling from another room. The sound will be a jumble of noise, which has no clarity.
2. Break down task into stages
Those with memory problems have difficulty retaining a multistage command such as “After you have finished shaving put on your blue shirt and gray trousers, and don’t forget to comb your hair.” With all this information the person with a dementia does not know where to begin. Recall will be confused and the individual will become frustrated, afraid of failing and may refuse to attempt the task. You must decide on the sequence needed to complete the task.
3. Give instructions one step at a time
Give only the information that is relevant at that time. Let all the clues in the conversation be geared to the fulfillment of that one step. Only when it has been completed should you move on to the next instruction.
4. Avoid ambiguity
Language is lost in dementia. It is not just the forgotten word, but the language becomes more concrete and is interpreted more literally. Ambiguity therefore leads to misinterpretation. Humour, which depends so much on a play on words, the double entendre, is not understood. The individual may be able to use long-term memory to tell a joke, but may not get it when told one. Euphemisms must be avoided. We must explain precisely what we mean. To “Make a bed” literally means to get out the hammer and nails; “do you need a washroom” does not literally mean, “do you have to pee?” The question “how many children do you have” may be met with the answer “I don’t have any children.” Whereas the correct answer may be produced by asking “how many sons/daughters do you have?”. In the mind of the concrete thinker, children are youngsters and have not grown up. Our words must be more literal, have less flowery descriptions and be to the point.
5. Limit distractions
Those with a dementia have difficulty interpreting the stimuli that bombard them. We may hear the siren from a fire truck in the distance, recognize what it is, assess that it is not coming to our house and then tune it out. For the person who is cognitively impaired that sound is of unknown origin and will distract her from the task at hand. It will occupy her thoughts and your words will be lost. The radio or TV playing in the background may not distract you, but it will certainly absorb the person who is having difficulty understanding and focusing on her environment.
6. Speak slowly and clearly
We must slow down our speech to the speed of the impaired person’s thinking. We must speak clearly to aid the hearing impaired and to ensure our words are not misinterpreted. When the mother tongue is not the one you are communicating in ensure your language is straightforward. Words from a second language are often lost and individuals may return to their mother tongue.
7. Use visual clues, gestures, demonstrations, pictures
Many who have dementia suffer from perceptual problems. That is, they have difficulty correctly interpreting the stimuli they receive from their environment. This may show itself through failing to understand verbal instructions, read warning signs, or recognize familiar objects and their use. If a blue shirt is placed on a blue bedspread, an impaired individual may not be able to differentiate the colours or textures and fail to locate the shirt. If the blue shirt is in a crowded closet, the individual may only see a jumbled mass of colour and not identify the shirt for its whole shape is not visible. He may face the closet, not recognize a shirt and say that there isn’t one there. Or in frustration will just keep putting back on the one taken off the previous evening. Sometimes understanding where the body is in space maybe impaired, dressing and undressing may become difficult. The individual may choose not to undress at all. Some will have difficulty initiating an action or plan a series of actions. Dressing and feeding will become more difficult. To compensate for these losses we must provide the individual with clues. Pictures and gestures may provide recognition when your words do not. Some may be able to mimic the action of another person while being unable to initiate the action. If you gesture with a toothbrush, he may be able to mimic the action. If you guide the spoon to his mouth, he may be able to carry on when the instruction “drink your soup” brought no response. What may be lost is the recognition of an objects use. Therefore the toothbrush may be used like a comb, the razor like a toothbrush. If this is the case we must ensure the safety of the individual and give clues, such as handing the person the correct object for the task.
8. Repeat
There are so many reasons why a person with a disease such as Alzheimer’s may have difficulty following instructions and performing tasks. Therefore it is important to repeat the information over and over again. We may become angry and wish to shout “but I’ve told you a thousand times…..” but it is important to understand that they are hearing it as if for the first time.
9. Limit Options
“What do you want for lunch?” May be met with “I don’t want lunch” since the individual cannot conjure an answer out of nowhere.
So you counter with “Would you like a ham and cheese sandwich or an egg salad sandwich?” and the reply is “I don’t know.” Most people with a dementia cannot make a decision and so often will reply “no.” If given a menu in a restaurant she will order what the person before her ordered – even if she has never liked it. So you say “But you never order liver.” Now the person with dementia is embarrassed, anxious, uncomfortable and has really lost her appetite.
Finally you say “How about an egg sandwich for your lunch, okay?” The sandwich gets eaten.
It is only by trial and error that we find out at what level the decision-making ability is. But by giving choice we can offer a sense of control and confidence. Sometimes that choice is purely agreeing with the decision we have made. We would not want to say “do you want your pills now?” because we don’t want her to say no. But we can offer the pills with apple juice or water. By providing limited options we give information that can be acted on. If we just ask, “What do you want?” we will be no further ahead.
10. Avoid confrontation
“I told you to meet me outside the post office.” “No you didn’t.” “Yes I did.” This is a conversation that is going nowhere. There will be no resolution to the argument. There will be two angry people. Projecting fault onto others is a defense mechanism all of us use. An object which has been misplaced, must have been stolen. We can protect ourselves when we can blame someone else. It is important that we do not enter the argument. Change the subject till the anxiety has lessened. It is possible to think more clearly when less anxious. Avoid having the last word.
11. Use residual skills
An individual with a dementia such as Alzheimer’s disease is loosing the ability to perform past learned skills. We must recognize the skills that remain and provide opportunity to perform them. This way he will remain stimulated, involved and retain self respect. Activities of a repetitive nature are best because sequencing is often difficult.
12. Reduce chance of failure
Learn the limits of her performance and attempt to secure an environment where he can function within those limits. Maybe she used to like to watch TV but now gets agitated when the commercials come on. Pre-recording programs with the commercials removed can lead to hours of enjoyment. We can use the memory loss to advantage by re-playing the same program at intervals. Indeed the familiarity often relaxes the individual whose memory loss makes her feel as if everything is new.
13. Avoid sensory overload
A person with a cognitive impairment will often have difficulty interpreting the sights and sounds of the world around her. Too much sensory input will cause confusion, anxiety and fear. It is as if a fuse blows and there can be what is known as a catastrophic reaction. That is behaviour which, to us, is out of proportion to the events occurring. There may be displays of aggression, running away, shouting etc. It is often possible to recognize the signs of this building, but often we fail to see the warning signs. Often we do not realize the distracting stimuli present when we demand action. We may feel we do not have time to wait for him to calm down before proceeding. But time invested in preventing a catastrophic reaction will be well spent in the long term.
14. Provide a calm familiar environment.
Maintain routines in daily schedules. Don’t make major changes like rearranging the furniture. If the individual has to be moved to a new setting, then take some familiar objects to be there when she arrives. When complex task are performed such as dressing and eating, ensure that distractions are minimal. If she must follow verbal instructions, ensure your voice is the one that will be noticed. Turn off the TV; close the door to others etc.
Caregivers, especially relatives, who have known an individual before the cognitive deficits changed him/her, have difficulty altering the way they relate. It is hard to break well-established habits. But the impaired person is in fact no longer the person from yesterday. The person before you now has new needs; severe limitations and can no longer live up to past expectations. It is the caregiver who must let the past go and learn to communicate on a new level. This cannot be achieved alone. All caregivers need emotional support. They must build around them a support system, a network of friends and professionals as they fulfill this difficult role.
1
Aspects of Caring - A Video by Sue Ellis - SME Productions
aspects_of_living_thumb.jpg
Aspects of Everday Life - a video by Sue Ellis - SME Productions
Aspects of Hope - A video by Sue Ellis - SME Productions
zrii.gif
Welcome | A Soul Journey | Caregiver Resources | Products | Keynotes | Blog | Articles | Testimonials
Copyright © 2006–2013 by Key Life Journeys. All rights reserved. Strategy & Design by Conscious Commerce
|
__label__pos
| 0.63493 |
Contributions to the hardness foundations of lattice-based cryptography
The manuscript: pdf.
Jury (November 6th, 2018 at Amphi Bio/SVT, ENS de Lyon)
President: Philippe GABORIT
Reviewers: Pierre-Alain FOUQUE
Alexander MAY
Daniele MICCIANCIO
Examiners: Caroline FONTAINE
Damien Stehlé (PhD supervisor)
Absract
Lattice-based cryptography is one of the most competitive candidates for protecting privacy, both in current applications and post quantum period. The central problem that serves as the hardness foundation of lattice-based cryptography is called the Learning with Errors (LWE). It asks to solve a noisy equation system, which is linear and over-determined modulo q. Normally, we call LWE problem as an average-case problem as all the coefficients in the equation system are randomly chosen modulo q. The LWE problem is conjectured to be hard even wtih a large scale quantum computer. It is at least as hard as standard problems defined in the lattices, such as Bounded Distance Decoding (BDD) and unique Shortest Vector Problem (uSVP). Finally, the best known algorithm for solving these problems is BKZ, which is very expensive.
In this thesis, we study the quantum hardness of LWE, the hardness relations between the underlying problems BDD and uSVP, and the practical performance of the BKZ algorithm. First, we give a strong evidence of quantum hardness of LWE. Concretely, we consider a relaxed version of the quantum version of dihedral coset problem and show an computational equivalence between LWE and this problem. Second, we tighten the hardness relation between BDD and uSVP. More precisely, We improve the reduction from BDD to uSVP by a factor √ 2 , compared to the one by Lyubashevsky and Micciancio. Third, we propose a more precise simulator for BKZ. In the last work, we propose the first probabilistic simulotor for BKZ, which can pridict the practical behavior of BKZ very precisely.
Chapter 1: Introduction.
The backgroud and motivation of this thesis, as well as a brief description of our main contributions are given in this chapter.
Chapter 2: Preliminaries.
Some necessary prerequisite definitions, concepts and results are given in this chapter.
Chapter 3: An improved reduction from BDD to uSVP.
In this chapter, we first give a brief discussion of the Lyubashevsky-Micciancio reduction from BDD1/2γ to uSVPγ. Then we give our improved reduction from BDD1/√ 2 γ to uSVPγ. We refer the reader to the link: https://eprint.iacr.org/2016/753, for a publication corresponding to this chapter.
Chapter 4: A Computational Equivalence between LWE and an Extrapolated Variant of DCP.
In this chapter, we first give a brief discussion on Regev's uSVP to DCP reduction. Then we given our results on the computational equivalence between LWE and an extrapolated version of DCP. We refer the reader to the link: https://arxiv.org/abs/1710.08223, for a publication corresponding to this chapter.
Chapter 5: A finer modelling of BKZ: understanding the head concavity.
In this chapter, we first report some experiments providing more insight on the shorter-than-expected phenomenon, which denote the phenomenon that the first few Gram-Schmidt norms in experiments are smaller than the ones in the Chen--Nguyen BKZ simulator. Then, we present a refined BKZ simulator, and experimentally show that the new simulator can predict the behavior of BKZ more accurately. Finally, we further propose a new BKZ variant by exploiting the shorter-than-expected phenomenon, which can be used to solve the SVP-120 instance of the Darmstadt lattice challenge faster.
Our BKZ experiments were run using the fplll (version 5.2.0) and fpylll (version 0.4.0dev) open-source libraries. Our simulator, coded in Python, and the BKZ variants, coded in C++ are all freely available online: https://github.com/BKZsimulator under the GNU Lesser General Public License (either version 2.1 of the License or any later version).
Some data corresponding to the figures of this chapter:
fig5.1-5.2,
fig5.3, fig5.4, fig5.5, fig5.6, fig5.7, fig5.8 (a chain of block-sizes (movie)), fig5.9, fig5.10, fig5.11, fig5.12, fig5.13, fig5.14,
fig5.15-5.16, fig5.17-5.18, fig5.19-5.20 (full GSO norms (movie), first GSO norm (movie)), fig5.21, fig5.22, fig5.23, fig5.24, fig5.25,
fig5.26 (a process of pressed-BKZ60 (movie)), fig5.27, fig5.28, fig5.29, fig5.30-5.31, fig5.32-5.33, fig5.34, fig5.35.
Homepage
|
__label__pos
| 0.787254 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.