Difference between revisions of "PHY554 Fall 2024"

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; Non-linearities 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: homework assignments (40%), class participation (20%), mid-term exam (20%) and final presentation on specific research paper (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 Edwards-Syphers' books are available in BNL library and electronic copies are available upon requests.

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 TV-tubes 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 – so-called 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 time-dependent 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 beta-function and their importance in circular accelerators.

• Nonlinear transverse beam dynamics
  This lecture will open door in fascinating and never-ending elegance and complexity on nonlinear beam dynamics. You will learn about non-linear 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 non-linear 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 so-called negative mass in longitudinal motion of particles. You will also learn about so-called 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 cutting-edge 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, X-ray 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. Y. Jing
• PHY554 Lecturs 2 and 3, History of Accelerators, by Prof. V. N. Litvinenko
• PHY554 Lecture 4, Transverse motion, by Prof. Y. Jing
• PHY554 Lecture 5, Floquet Theorem, by Prof. Y. Jing
• PHY554 Lecture 6, Beam Emittance, Dipole Field Error, by Prof. Y. Jing
• PHY554 Lecture 7, Off-momentum particles, dispersion function, by Prof. Y. Jing
• PHY554 Lecture 8, Quadrupole Field Error, by Prof. Y. Jing
• PHY554 Lecture 9, Synchrotron Radiation, by Prof. G. Wang
• PHY554 Lecture 10, Synchrotron Radiation Sources, by Prof. G. Wang
• PHY554 Lecture 11, Introduction to RF accelerators, by Dr. Jun Ma
• PHY554 Lecture 12, Fundamentals of RF accelerators, by Dr. Jun Ma
• PHY554 Lecture 13, Longitudinal Dynamics, by Prof. Y. Jing
• PHY554 Lecture 14-15, Electron storage rings, by Prof. Y. Jing

Home-Reading:

• Least Action Principle, Geometry of Special Relativity, Particles in E&M fields, by Prof. Litvinenko
• Matrix calculus
• Complex analysis
• Vector calculus

Homework

• Homework 1, August 28: due September 11 Solutions
• Homework 2, September 11: due September 18 Solutions
• Homework 3, September 23: due September 30 Solutions
• Homework 4, October 2: due October 9 Solutions
• Homework 5, October 7: due October 16 Solutions
• Homework 6, October 28: due November 4

List of suggested projects

Exam

• Mid-term, Oct 23 8:30 pm: due Oct 24 24:00 pm Solutions

Mid-term course review:

• Transverse and Longitudinal Dynamics
• RF cavities