U.S. Particle Accelerator School

The Plasma Physics of Beams course

Sponsoring University:

Michigan State University


The Plasma Physics of Beams


Patrick L. Colestock, Los Alamos National Lab

Purpose and Audience
This course is intended for accelerator physicists with a basic knowledge of collective effects in beams, but no previous familiarity with the physics or mathematical techniques of plasma physics. It is appropriate for the experimentalist who would like to broaden his/her understanding of nonlinear physical phenomena that may be occurring during typical beam operations, and for the accelerator theorist who would like to become familiar with the analytical techniques developed in the field of plasma physics to describe nonlinear processes. Emphasis will be on developing physical intuition regarding nonlinear phenomena, and on making a close connection between the physical effects and the mathematical analysis.

The student should have a basic understanding of electromagnetics, complex variable analysis and collective effects in beams. All topics will be reviewed from a basic level during the lectures.

The objective of the course will be to make the student familiar with the range of nonlinear phenomena that have been studied in plasma physics and to show the close physical correspondence between a plasma and a particle beam. The mathematical techniques of plasma physics will be applied, leading to new results for particle beams such as solitons, weak turbulence and echoes.

Instructional Method:
The course will consist of lectures in the morning, followed by afternoon problem-solving and discussion sessions. Grading will be based on completion of the problem sets and on one open-book written exam given on the final day of the class.

Course Syllabus:

1. The Vlasov equation: its interpretation and solution methods.
2. Linear waves and kinetic processes in beams – a review.
3. Weakly nonlinear waves – parametric coupling.
4. Echoes as nonlinear beam probes.
5. Strong nonlinearities – solitons
6. Turbulence - both weak and strong

Reading Assignments:
Reading for the course will be based on course notes provided by the instructor.

Credit Requirements:
70% of the grade will be based on the completion of homework assignments and 30% on the final exam.