PHY554 Fall 2023
Class meet time and dates  Instructors 



Contents
Teaches, Students, Topics
Course Overview
The graduate/senior undergraduate level course focuses on the fundamental physics and key concepts of modern particle accelerators. The course is intended for graduate students and advanced undergraduate students who want to familiarize themselves with principles of accelerating charged particles and gain knowledge about contemporary particle accelerators and their applications.
It will cover the following contents:
 History of accelerators and basic principles (eg. centre of mass energy, luminosity, accelerating gradient, etc)
 Radio Frequency cavities, linacs, SRF accelerators;
 Magnets, Transverse motion, Strong focusing, simple lattices; Nonlinearities and resonances;
 Circulating beams, Longitutdinal dynamics, Synchrotron radiation; principles of beam cooling,
 Applications of accelerators: light sources, medical uses
Students will be evaluated based on the following performances: final presentation on specific research paper (40%), homework assignments (40%) and class participation (20%).
Learning Goals
Students who have completed this course should
 Understand how various types of accelerators work and understand differences between them.
 Have a general understanding of transverse and longitudinal beam dynamics in accelerators.
 Have a general understanding of accelerating structures.
 Understand major applications of accelerators and the recent new concepts.
Textbook and suggested materials
Textbook is to be decided from the following:
 Accelerator Physics, by S. Y. Lee
 An Introduction to the Physics of High Energy Accelerators, by D. A. Edwards and M. J. Syphers
 Introduction To The Physics Of Particle Accelerators, by Mario Conte and William W Mackay
 Particle Accelerator Physics, by Helmut Wiedemann
 The Physics of Particle Accelerators: An Introduction, by Klaus Wille and Jason McFall
10+ S.Y. Lee's and EdwardsSyphers' books are available in BNL library.
Course Description
 Introduction to accelerator physics
You will have a glance into the history of accelerators and will learn about a variety of accelerators from electrostatic TVtubes to gigantic atom and nuclear smashers. Basic figures of merit will be introduced (center of mass energy, luminosity, accelerating gradient, etc.) You will learn general principles behing linear accelerators and circular accelerators, their relative advantages and disadvantages.
 Radio frequency cavities, linacs, superconducting RF accelerators
This part of the course will be dedicated to physics and technology of accelerating structures. You will learn basic principles of using radio frequency electromagnetic fields to accelerate particles to very high energies. Different types of accelerating structures will be introduced. You will also learn about brand new direction in linear accelerators – socalled energy recovery linacs. As many modern accelerators are based on superconducting RF (SRF) technlogy, you will learn fundamentals of the SRF accelerators and their advantages over conventional (normal conductoing) RF accelerators.
 Linear transverse beam dynamics
This part of the course will be dedicated to detailed description of linear dynamics of particles in accelerators. You will learn about similarity of particles motion to an oscillator with timedependent rigidity, matrix optics of various elements in accelerators, equation for beam envelopes and stability of periodic (circular) motion of the particles. 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 betafunction and their importance in circular accelerators.
 Nonlinear transverse beam dynamics
This lecture will open door in fascinating and neverending elegance and complexity on nonlinear beam dynamics. You will learn about nonlinear resonances, which may affect stability of the particles and about their location on the tune diagram. You will learn about chromatic (energy dependent) effects, use of nonlinear elements to compensate them, and about problems created by introducing them. Some of traditional perturbation theory methods will be introduced during this lecture.
 Longitudinal beam dynamics
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 socalled negative mass in longitudinal motion of particles. You will also learn about socalled synchrotron oscillations, which are have a lot of similarity with pendulum motion. One more “tunes” to remember about  synchrotron tune.
 Radiation effects
Charged particles going around an accelerator do radiate when their trajectory is bent – hence, there is entire range of topics arising from this fact. It goes from such effect as radiation damping of the particle oscillations, quantum excitation of such oscillation to the use of this extraordinary radiation as cuttingedge research tool. We will look both into positive (usefulness of synchrotron and FEL radiation) and negative (limiting the energy of electron storage rings) aspects of this natural phenomenon.
 Accelerator applications
We will devote this part of the course to the discussion of variety of accelerator application, among which are accelerators for nuclear and particle physics, Xray light sources, accelerators for medical uses, etc. You will also learn about future accelerators at the energy and intensity forntiers as well as about new methods of particle acceleration.
Lecture Notes
 PHY554 Lecture 1, Modern Accelerators, by Prof. V.N. Litvinenko
 PHY554 Lectures 2 and 3, History of Accelerators, by Prof. V.N. Litvinenko
 PHY554 Lecture 4, Transverse (Betatron) Motion, by Dr. Kai Shih
 PHY554 Lecture 5, Floquet Theorem, Phase space, by Dr. Kai Shih
 PHY554 Lecture 6, Emittance, Closed orbit, by Dr. Kai Shih
 PHY554 Lecture 7, Offmomentum particles, dispersion function, by Prof. Y. Jing
 PHY554 Lecture 8, Quadrupole field errors, by Prof. Y. Jing
 PHY554 Lecture 9, Introduction to RF accelerators, by Dr. Jun Ma
 PHY554 Lecture 10, Fundamentals of RF accelerators, by Dr. Jun Ma
 PHY554 Lecture 11, Superconducting RF accelerators and ERLs, by Dr. Jun Ma
 PHY554 Lecture 12, Synchrotron Radiation, by Prof. G. Wang
 PHY554 Lecture 13, Synchrotron Radiation Source, by Prof. G. Wang
 PHY554 Lecture 14, Longitudinal beam dynamics, by Prof. Y. Jing
 PHY554 Lecture 1516, Electron storage rings, by Prof. Y. Jing
 PHY554 Lecture 17, Chromaticities, its correction and simplectic integration, by Prof. Y. Jing
 PHY554 Lecture 18, Nonlinear Dynamics, by Prof. Y. Jing
 PHY554 Lecture 19, Collective Effects I: Wakefield and Impedances, by Prof. G. Wang
 PHY554 Lecture 20, Collective Effects II: Examples of Collective Instabilities, by Prof. G. Wang
 PHY554 Lecture 21, Free Electron Lasers I: Low Gain Regime
 PHY554 Lecture 22, Free Electron Lasers II: High Gain Regime
 PHY554 Lecture 23, Hadron Cooling
 PHY554 Lectures 24, Advanced Acceleration Methods
 PHY554 Lectures 25 and 26, Applications of Accelerators
 Final exams, Session 1, Parts 1,2,3,4  December 13
 Final exams, Session 2, Parts 1,2,3,4  December 18
Refreshment Classes (Physics Room D103):
 Matrix calculus, by Dr. Jun Ma, Friday, September 15,
 Special relativity, by Dr. Kai Shih, Tuesday, September 21
 Hamiltonian mechanics, by Prof. Gang Wang, Friday, September 22
 Linear Betatron Oscillation, by Dr. Kai Shih, Monday, September 25
 Complex analysis, by Dr. Jun Ma, Thursday, September 28
HomeReading:
 Least Action Principle, Geometry of Special Relativity, Particles in E&M fields, by Prof. Litvinenko
 Matrix calculus refresher, by Prof. V.N. Litvinenko
 Derivations for Lecture 12, Synchrotron Radiation, by Prof. G. Wang
 for PHY554 Lecture 13, Longitudinal beam dynamics animations, by Prof. V.N. Litvinenko
 matlab script to test stochastic cooling, change the file name to SC_test.m, by Prof. G. Wang
 Vector calculus, by Dr. Jun Ma
Home Works (will be replaced with new edition for Fall 2023)
 Homework 1 due September 13, 2023 Solution
 Homework 2 due September 25, 2023 Solution
 Homework 3 due October 11, 2023 Solution
 Homework 4 due October 18, 2023 Solution
 Homework 5 due October 25, 2023 Solution
 Homework 6 due November 8, 2023 Solution
 Homework 7 due November 15, 2023 Solution
 Homework 8 due November 27, 2023 Solution
 Homework 9 due December 4, 2023
2021 Fall HWs
 Homework 2
 Homework 3
 Homework 4
 Homework 5
 Homework 6
 Homework 7
 Homework 9
 Homework 12
 Homework 13
 Homework 14
 Homework 15
 Homework 16
Students will be evaluated based on the following performances: final presentation on specific research paper (40%), homework assignments (40%) and class participation (20%).