U.S. Particle Accelerator School
U.S. Particle Accelerator School
Education in Beam Physics and Accelerator Technology

Accelerator Physics

Sponsoring University:

Michigan State University

Course Name:

Accelerator Physics


Steven Lund, MSU/USPAS; Yue Hao, Michigan State University/FRIB

Purpose and Audience
The purpose of this course is give a theoretical foundation to the physics and technology of charged particle accelerators. This course is suitable for graduate students from physics and engineering who are interested in accelerators as part of their research or career goals, or scientists and engineers who want more detail on the physics of accelerator systems. 

Required: Undergrad Electricity and Magnetism: level Griffiths, Intro to Electrodynamics (including special relativity)
Required: Undergrad Classical Mechanics: level Taylor, Classical Mechanic (including Hamiltonian formulation of dynamics)
Recommend: Undergrad Accelerator Physics: level USPAS Fundamentals of Accelerator Physics
Recommend: Graduate Electricity and Magnetism: level Jackson, Classical Electrodynamics
Recommend: Graduate Classical Mechanics: level Goldstein, Classical Mechanics

It is the responsibility of the student to ensure that they meet the course prerequisites or have equivalent experience.

On successful completion of this course, students should attain a basic understanding of the physics of charged particle accelerators. Emphasis is on theoretical and analytical methods of describing the focusing and acceleration of charged particle beams. Some aspects of numerical and experimental methods will also be covered. Topics are systematically covered to provide a foundation to designing a diversity of linear and circular machines. Example applications are highlighted to attain a better understanding of accelerator systems used in a plethora of fields such as high energy and nuclear physics, light sources for materials science, medical technology, and industrial applications.

Instructional Method
Daily lectures will begin in morning sessions and will continue through the afternoon. Daily problem sets will be assigned that will be expected to be completed outside of scheduled class sessions. Problem sets will generally be due the morning of the next lecture session. Afternoon recitation sections will review problems turned in and will engage the students on material covered in lecture. Afternoon computer exercises employing cloud based computing resources will be applied to illustrate concepts covered. A comprehensive final take home exam will be given on the second Thursday. The final will be open note and will be due the morning of the final Friday lectures. Students are encouraged to work together on homeworks while turning in their own solutions. Independent work is required on the final. Lecturers and graders will be available for questions during evening homework sessions. 

Course Content
This course provides a systematic introduction to the physics of charged particle beam accelerators. Topics include: particle sources and injectors, field calculations of magnetic and electric focusing and bending optics, particle equations of motion, multipole descriptions of applied focusing and bending fields, thin-lens and quadrupole focusing, edge focusing, solenoid focusing and beam canonical angular momentum, phase amplitude methods and Hill’s equation to describe linear focusing, phase advance in periodic focusing lattices, the Courant-Snyder invariant and beam emittance, symplectic dynamics, dispersive and chromatic effects, momentum compaction in rings, acceleration induced effects on beam emittance, resonance effects, longitudinal particle acceleration with emphasis on RF technology, RF cavities and traveling wave structures, Panofsky’s equation describing longitudinal RF focusing, longitudinal beam dynamics in linacs and  rings, synchrotron radiation, electron storage rings, undulator radiation, free electron lasers, hadron beam cooling, and space-charge effects, and new acceleration techniques. Concepts are illustrated by brief application sketches applying to a variety of linear and circular architecture machines including synchrotrons, electron storage rings, and light sources.

Reading Requirements
Extensive class notes will be provided that will serve as the primary reference. Students should bring a laptop or tablet with a web browser to read notes and better participate on cloud based computer exercises. Students are encouraged to open a free github server account (https://github.com/) in advance to expedite setup of the computer exercises. In some cases paper copies of notes may be provided for note taking.  Notes will be archived and updated on the course web site:
The course is based on the MSU course “Accelerator Physics,” last taught in Spring 2018: 

A supplemental text will be provided by the USPAS: "Particle Accelerator Physics" Fourth Edition, Helmut Wiedemann, Springer 2015.

Credit Requirements
Students will be evaluated based on performance: homework assignments (80 % of course grade), and final exam (20 % of course grade).

Michigan State University course number: PHY 963 - 301 - Accelerator Physics
Indiana University course number: Physics 570, Introduction to Accelerator Physics
MIT course number: 8.790, Accelerator Physics