U.S. Particle Accelerator School

Wakefields and Collective Beam Instabilities


Northern Illinois University and UT-Battelle

Course Name:

Wakefields and Collective Beam Instabilities


Gennady Stupakov and Panagiotis Baxevanis, SLAC National Accelerator Lab

Purpose and Audience
This course will instruct students in the topic of the physics of collective instabilities in modern particle accelerators.  It is designed for graduate students pursuing accelerator physics as a career or having interest in learning this subject of accelerator physics.  The course is also appropriate for scientists and engineers working in accelerator-related fields who wish to broaden their background.

A general understanding of classical physics and electromagnetism; the USPAS undergraduate-level course "Accelerator Fundamentals" or equivalent; entry-level experience to run computer simulations.    

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

On completion of this course, the students are expected to understand the basic physical principles that determine the physics of collective instabilities. They will learn the frequently used terminologies such as wakefields and impedances. Applying this knowledge, they will develop an insight into the mechanisms of the various collective instabilities that play a role of limiting beam intensities in linear as well as circular accelerators.

Instructional Method
This course includes a series of lectures and exercise sessions.  Homework problems will be assigned daily which will be completed overnight by the students and then graded and answers provided in the exercise session in the following day. Computer classes will be arranged in some of the afternoons. There will be an open-book exam at the conclusion of the course.

Course Content
Electromagnetic forces in relativistic beams. Space charge force. Definition and general properties of wakefields and impedances. Transverse and longitudinal wakefields in axisymmetric and non-axisymmetric geometries. Broadband and narrowband impedance. Causality, and the Panofsky-Wenzel formula. Example of wakefields in accelerators: resistive wall long-range and short-range wakefields, cavity wakefield, collimators and steps, wakes for very short bunches. Computer codes for calculation of wakefields. Coherent synchrotron radiation (CSR) wake. Transverse and longitudinal instabilities. Single-bunch and multi-bunch instabilities.  Vlasov equation and the Haissinski equilibrium. Transverse mode coupling instability.  Beam break-up in linear accelerators, and BNS damping.

Reading Requirements
Reading materials will be supplied in electronic form and posted on the website.

Credit Requirements
Students will be evaluated based on the following performances: homework assignments and class participation (60% of final grade), final exam (40% of final grade).

Northern Illinois University 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"