Difference between revisions of "PHY543 spring 2021"

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* High Energy Electron Linacs: Applications to Storage Ring RF Systems and Linear Colliders, by Perry B. Wilson
 
* High Energy Electron Linacs: Applications to Storage Ring RF Systems and Linear Colliders, by Perry B. Wilson
  
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==Course Description==
 
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*Relativistic mechanics and E&D. Linear algebra.
 
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*:This will be a brief but complete rehash of relativistic mechanics, E&M and linear algebra material required for this course.
 
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*N-dimensional phase space, Canonical transformations, simplecticity, invariants
 
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*:Canonical transformations and related to it simplecticity of the phase space are important part of beam dynamics in accelerators. We will consider connections between them as well as derive all Poincare invariants (including Liouville theorem). We will use a case of a coupled N-dimensional linear oscillator system for transforming to the action and phase variables. We finish with adiabatic invariants.
 
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*Relativistic beams, Reference orbit and Accelerator Hamiltonian
 
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*:We will use least action principle to derive the most general form of accelerator Hamiltonian using curvilinear coordinate system related to the beam trajectory (orbit).
 
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*Linear beam dynamics
 
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*:This part of the course will be dedicated to detailed description of linear dynamics of particles in accelerators. You will learn about particles motion in oscillator potential with time- dependent rigidity. You will learn how to calculate matrices of arbitrary element in accelerators. We will use eigen vectors and eigen number to parameterize the particles motion and describe its stability in circular accelerators. Here you find a number of analogies with planetary motion, including oscillation of Earth’s moon. You will learn some “standards” of the accelerator physics – betatron tunes and beta-function and their importance in circular accelerators.
 
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*Longitudinal beam dynamics
 
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*:Here you will learn about one important approximation widely used in accelerator physics – “slow” longitudinal oscillations, which are have a lot of similarity with pendulum motion. If you were ever wondering why Saturn rings do not collapse into one large ball of rock under gravitational attraction – this where you will learn of the effect so-called negative mass in longitudinal motion of particles when attraction of the particles cause their separation.
 
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*Invariants of motion, Canonical transforms to the action and phase variables, emittance of the beam, perturbation methods, perturbative non-linear effects
 
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*:In this part of the course we will remove “regular and boring” oscillatory part of the particle’s motion and focus on how to include weak linear and nonlinear perturbations to the particles motion. We will solve a number of standard accelerator problems: perturbed orbit, effects of focusing errors, “weak effects” such as synchrotron radiation, resonant Hamiltonian, etc. We will re-introduce Poincare diagrams for illustration of the resonances. You will learn how non- linear resonances may affect stability of the particles and about their location on the tune diagram. You will learn about chromatic (energy dependent) effects, use of non-linear elements to compensate them, and about problems created by introducing them.
 
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*Non-linear effects, Lie algebras and symplectic maps
 
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*:This part of the course will open you the door into and complex nonlinear beam dynamics. We will introduce you to non-perturbative nonlinear dynamics and fascinating world of non-linear maps, Lie algebras and Lie operators. These are the main tools in the modern non-linear beam dynamics. You will learn about dynamic aperture of accelerators as well as how our modern tools are similar to those used in celestial mechanics.
 
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*Vlasov and Fokker-Plank equations
 
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*:This part of the course is dedicated to the developing of tools necessary for studies of collective effects in accelerators. We will introduce distribution function of the particles and its evolution equations: one following conservation of Poincare invariants and the other including stochastic processes.
 
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*Radiation effects
 
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*:You will learn how to use the tools we had developed in previous lectures (both the perturbation methods and Fokker-Plank equation) to evaluate effect of synchrotron radiation on the particle’s motion in accelerator. You will see how the effect of radiation damping and quantum excitation lead to formation of equilibrium Gaussian distribution of the particles.
 
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*Collective phenomena
 
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*:Intense beam of charged particles excite E&M fields when propagate through accelerator structures. These fields, in return, act on the particles and can cause variety of instabilities. Some of these instabilities – such as a free-electron lasers (FEL) – can be very useful as powerful coherent X-rays sources. Others (and they are majority) do impose limits on the beam intensities or limit available range of the beam parameters. You will learn techniques involved in studies of collective effects and will use them for some of instabilities, including FEL. The second part of the collective effect will focus on how we can cool hadron beams, which do not have natural cooling.
 
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*Spin dynamics
 
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*:Many particles used in accelerators have spin. Beams of such particles with preferred orientation of their spins called polarized. Large number of high energy physics experiments using colliders strongly benefit from colliding polarized beams. You will learn the main aspects of the spin dynamics in the accelerators and about various ways to keep beam polarized. One more “tunes” to worry about - spin tune.
 
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*Accelerator application
 
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*:We will finish the course with a brief discussion of accelerator application, among which are accelerators for nuclear and particle physics, X-ray light sources, accelerators for medical uses, etc. You will also learn about future accelerators at the energy and intensity frontiers as well as about new methods of particle acceleration.
 
  
 
==Grades==
 
==Grades==

Revision as of 21:09, 15 April 2021

Class meet time and dates Instructors
  • When: M, 6:05p-8:00p
  • Where: The course is taught remotely via Zoom. A Zoom meeting link was sent to registered students via email before the first lecture.
  • Prof. Sergey Belomestnykh
  • Dr. Sam Posen
  • Dr. Irina Petrushina


Course Overview

TThis graduate level course covers application of radio frequency (RF) superconductivity to contemporary particle accelerators: particle colliders, storage rings for X-ray production, pulsed and CW linear accelerators (linacs), energy recovery linacs (ERLs), etc. The course addresses both physics and engineering aspects of the field. It covers fundamentals of RF superconductivity, types of superconducting radio frequency (SRF) accelerating structures, performance-limiting phenomena, beam-cavity interaction issues specific to superconducting cavities, approaches to designing SRF systems and engineering of superconducting cavity cryomodules. The course is intended for students interested in accelerator physics and technology who want to learn about application of RF superconductivity to particle accelerators.

Course Content

  • The course includes a brief introduction of the basic concepts of microwave cavities and fundamental concepts of RF superconductivity.
  • Then it covers the beam-cavity interaction issues in accelerators: wake fields and higher-order modes (HOMs) in superconducting structures, associated bunched beam instabilities and approaches to deal with these instabilities (HOM absorbers and couplers, cavity geometry optimization, …), bunch length manipulation with SRF cavities, beam loading effects, etc.
  • Following that we discuss a systems approach and its application to SRF systems for accelerators.
  • We discuss the ways in which the superconducting material, and in particular the surface, can be modified to improve quality factor and accelerating gradient.
  • Finally, we address issues related to engineering of the SRF system components: cryostats, cavities, input couplers, HOM loads, and frequency tuners.

Learning Goals

Upon completion of this course, students are expected to understand the physics underlying RF superconductivity and its application to accelerators, as well as the advantages and limitations of SRF technology. The aim is to provide students with ideas and approaches that enable them to evaluate and solve problems related to the application of superconducting cavities to accelerators, as well actively participate in the development of SRF systems for various accelerators.

Main Texts and suggested materials

While all necessary material will be provided during lectures, we recommend the following textbook for in-depth study of the subject:

  • RF Superconductivity for Accelerators, by H. Padamsee, J. Knobloch, and T. Hays, John Wiley & Sons, 2nd edition (2008).

Other Reading Recommendations It is recommended that students re-familiarize themselves with the fundamentals of electrodynamics at the level of

  • Fields and Waves in Communication Electronics (Chapters 1 through 11) by S. Ramo, J. R. Whinnery, and T. Van Duzer, John Wiley & Sons, 3rd edition (1994)
  • Classical Electrodynamics (Chapters 1 through 8) by J. D. Jackson, John Wiley & Sons, 3rd edition (1999)

or other similar textbooks. Additional reference books:

  • Handbook of Accelerator Physics and Engineering, edited by A. W. Chao, K. H. Mess, M. Tigner, and F. Zimmermann, World Scientific, 2nd Edition (2013)
  • RF Superconductivity: Science, Technology, and Applications, by H. Padamsee, Wiley-VCH (2009)

Online resources:

  • The Physics of Electron Storage Rings: An Introduction, by M. Sands
  • Microwave Theory and Applications, by S. F. Adam
  • High Energy Electron Linacs: Applications to Storage Ring RF Systems and Linear Colliders, by Perry B. Wilson


Grades

There will be a substantial number of problems. Most of them are aiming for better understanding of material covered during classes. The final grade will be based on:

  • Homework assignments - 40% of the grade
  • Presentation of a research topic - 40% of the grade
  • Class Participation - 20% of the grade


The Rules

  • You may collaborate with your classmates on the homework's if you are contributing to the solution. You must personally write up the solution of all problems. It would be appropriate and honorable to acknowledge your collaborators by mentioning their names. These acknowledgments will not affect your grades.
  • We will greatly appreciate your homeworks being readable. Few explanatory words between equations will save us a lot of time while checking and grading your home-works. Nevertheless, your writing style will not affect your grades.
  • Do not forget that simply copying somebody's solutions does not help you and in a long run we will identify it. If we find two or more identical homeworks, they all will get reduced grades. You may ask more advanced students, other faculty, friends, etc. for help or clues, as long as you personally contribute to the solution.
  • You may (and are encouraged to) use the library and all available resources to help solve the problems. Use of Mathematica, other software tools and spreadsheets are encouraged. Cite your source, if you found the solution somewhere.
  • You should return homework before the deadline. Homework returned after the deadline could be accepted with reduced grading - 15% per day. Otherwise, it will be unfair for your classmates who are doing their job on time. Therefore, you should be on time to keep your grade high. Exceptions are exceptions and do not count on them (if your dog eats your homework on a regular basis - feed it with something healthy, eating homework is bad for your pet and for you grade).

Presentation on a Research Project

  • This presentation will be in place of the final exam. You will pick an accelerator project of your interest from a list provided by the instructors. We allow presentations on papers directly related to your research if they are linked to accelerator physics, but you will have to get it approved by the instructors. The presentations will be in a PowerPoint or equivalent a form.
  • We will grade your presentations on: adequate understanding (good physics), adequate preparation (clear way of presentation, Visual Aids - pictures and figures), adequate references (where you find materials).
  • The research project should be fun and we encourage you to choose an original topic and an original way of presentation. Nevertheless, any topic prepared and presented properly will have high grade.
  • Suggested topics for Projects, by Prof. Litvinenko

Lecture Notes



  • Final Exam, December 16
  • Part 1: Lead Prof. Jing
  • 3:00 pm Xiangdong Li, Free electron lasers
  • 3:30 pm Jiayang Yan, Laser-Plasma Accelerators
  • 4:00 pm Nikhil Bachhawat, e+e- colliders
  • Part 2: Lead Prof. Wang
  • 4:45 pm Kristina Finnelli - Industrial applications of accelerators
  • 5:15 pm Nikhil Kumar - Medical application of accelerators
  • 5:45 pm Ian Schwartz - Accelerators in Food Processing



Home Works

Recitation sessions

  • Session 1, September 29, 2020, HWs 1-3 by Prof. Jing
  • Session 2, October 13, 2020, HWs 4-8 by Prof. Jing
  • Session 3, October 27, 2020, HWs 9-12 by Prof. Jing
  • Session 4, November 10, 2020, HWs 13-15 by Prof. Jing
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