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

Wakefields and Collective Beam Instabilities


Northern Illinois University

Course Name:

Wakefields and Collective Beam Instabilities


Gennady Stupakov, SLAC; Ryan Lindberg, Argonne National Lab; Boris Podobedov, Brookhaven National 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 dynamics and electromagnetism is required at the senior undergraduate level; the USPAS undergraduate-level course Fundamentals of Accelerator Physics and Technology with Simulations and Measurements Lab or equivalent experience; and experience to run computer simulations are all required. Graduate-level experience with Classical Electrodynamics is recommended.   

It is the responsibility of the student to ensure that they meet the course prerequisites or have 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. Loss factor and kick factor. Example of wakefields in accelerators: resistive wall long-range and short-range wakefields, cavity wakefield, collimators and steps, wakes for very short bunches. Coherent synchrotron radiation (CSR) wake. Computer codes for calculation of wakefields. Vlasov equation. Kapchinsky-Vladimirsky distribution. Plasma oscillations in relativistic beams. Beam break-up in linear accelerators, and BNS damping. Transverse multi-bunch instabilities in circular accelerators. Beam loading and Robinson instability. Longitudinal instability of coasting beam and Keil-Schnell stability criterium. Landau damping. Haissinski equilibrium and microwave instability. Transverse mode-coupling instability. Simulations of beam instabilities with computer codes. Feedbacks. Electron cloud and ion instabilities.

Reading Requirements
Reading materials will be supplied in electronic form and posted on the website. The textbook Beam Dynamics in High Energy Particle Accelerators by Andrzej Wolski (Imperial College Press 2014) will be provided by the USPAS.

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

Northern Illinois University course number: PHYS 790D Special Topics in Physics - Beam Physics
Indiana University course number: Physics 571 Special Topics in Physics of Beams
Michigan State University course number: PHY 963 "U.S. Particle Accelerator School"
MIT course number: 8.790 Accelerator Physics