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

Accelerator Physics

Sponsoring University:

UC Davis Continuing and Professional Education

Course Name:

Accelerator Physics
This class is full. Please contact uspas@fnal.gov to have your name added to the waiting list.


Steven Lund, Michigan State University and USPAS; Yue Hao and Kyung (Kilean) Hwang, Michigan State University
TA: Anthony Tran, Michigan State University

Purpose and Audience
The purpose of this course is give a broad 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. 




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 developed to provide a foundation toward understanding 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 variable-duration afternoon sessions that will continue lectures, recitation sections to review problems, and simulation exercises. 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 take-home final exam will be given on the second Thursday and will be due at the start of the final day’s lectures. The final will be open note. 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 notes, problems sets, and the final exam will be distributed via the course web site.

Course Website
To be posted closer to date of course.

Course Content
This course provides a systematic introduction to the physics of charged particle beam accelerators. Topics include:

  • Particle sources and injectors
  • Magnetic and electric focusing and bending optics and multipole field expansions
  • Particle equations of motion
  • 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 and multi-bend achromats
  • Undulator radiation
  • Free electron lasers
  • Hadron beam cooling; space-charge effects
  • Advanced 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. Various topics are further highlighted in simulation labs using cloud-based computer resources.  

Reading Requirements
Extensive class notes will be provided that will serve as the primary reference. Students must 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. Notes will be archived and updated on the course web site.

The course will be similar and updated from USPAS Accelerator Physics, taught in Summer 2021: https://people.nscl.msu.edu/~lund/uspas/ap_2021/.  Students wishing to prepare in advance can review materials from this course. 

A supplemental text will be provided by the USPAS:  ┬áSY Lee, Accelerator Physics, Fourth Edition, (World Scientific, 2019).

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

USPAS Computer Requirements
There will be no Computer Lab and all participants are required to bring their own portable computer to access online course notes and computer resources. This can be a laptop or a tablet with a sufficiently large screen and keyboard. Windows, Mac, and Linux-based systems that are wifi capable and have a standard web browser and mouse are all acceptable. You should have privileges for software installs. If you are unable to bring a computer, please contact uspas@fnal.gov ASAP to request a laptop loan. Very limited IT support and spare loaner laptops will be available during the session.

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