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

Beam Cooling in Particle Accelerators

Sponsoring University:


Course Name:

Beam Cooling in Particle Accelerators


Sergei Nagaitsev, Fermilab

Purpose and Audience
The purpose of this course is to introduce the students to beam cooling in accelerators. It is designed for graduate students pursuing accelerator physics as a career or having interest in learning this subject of accelerator physics.

Classical mechanics, electrodynamics, and physical or engineering mathematics, all at entrance graduate level, and the USPAS course “Accelerator Physics” (graduate level) or “Accelerator Fundamentals” with a strong math background or equivalent.

It is the responsibility of the student to ensure that he or she meets the course prerequisites or has equivalent experience.

Upon completion of this course, the students are expected to understand the basic principles that underline the physics of beam cooling in particle accelerators. They will have learned the notion of the phase-space density and how the increase in the phase-space density is considered “beam cooling”, under certain conditions.  Several practical examples of cooling will be presented: stochastic, electron, Doppler laser cooling, etc. Applying this knowledge, they will then have developed an insight into the mechanisms of both beam diffusion and beam cooling as well as applications to modern accelerators and colliders.

Instructional Method
This course includes a series of lectures and exercise sessions.  Homework problems will be assigned daily which will be graded and answers provided in the exercise session the following day. There will be an open-book final exam at the conclusion of the course.

Course Content
The course will start with a description of Hamiltonian and non-Hamiltonian processes in particle accelerators, the Liouville’s theorem will be introduced. Examples of beam diffusion processes will be discussed.  Various cooling methods and their applications will be considered.

Reading Requirements

Suggested Reading
 “Accelerator Physics” 4th edition by S.Y. Lee, (World Scientific Pub. Co, NY, 2018), section 2.7.

Credit Requirements
Students will be evaluated based on the following performances: Final exam (50%), Homework assignments and class participation (50%).

TBD course number:
Indiana University course number:
Physics 671, Advanced Topics in Accelerator Physics
Michigan State University course number: PHY 963, "U.S. Particle Accelerator School"
MIT course number: 8.790, "Accelerator Physics"