U.S. Particle Accelerator School

Computational Methods in Beam Dynamics course

Sponsoring University:

University of California, Berkeley


Computational Methods in Beam Dynamics


Robert Ryne, LBNL

Purpose and Audience
The development of modern particle beam accelerators depends heavily on the use of computer simulation codes. Such codes, used in concert with theory and experiment, are crucial for the design, analysis, and optimization of particle accelerators. This course provides an introduction to the numerical and computational methods commonly used for such simulations as well as a discussion on the underlying physics involved. Emphasis will be placed on modeling charged particle beam dynamics in accelerators. The primary audience will be students and working accelerator physicists who are involved in, or expect to be involved in, the design of particle accelerators.

The students will be assumed to have a basic knowledge of accelerator physics and some experience with scientific programming.

Upon completion of this course, the student is expected to have a basic working knowledge of, and hands-on experience in, the numerical and computational techniques for simulating charged particle beam dynamics in accelerators. The student will also have an understanding of the theoretical formalism underlying the various physical models presented in the course. The student will furthermore be able to modify and extend the computer codes presented in the course to serve his/her research purposes.

Instructional Method
Every morning and afternoon, the students will receive approximately 1-1.5 hours of lecture, followed by 2-2.5 hours of hands-on computer exercises. The course will use a combination of illustrative codes (small codes that the students will make modifications to and experiment with), and production beam dynamics codes. The students will also learn through interaction with the instructor and teaching assistants during the performance of homework assignments.

Course Content
Topics will include Hamilton's equations, numerical integration, single-particle magnetic optics, multi-particle dynamics, envelope equations, Poisson solvers, and particle-in-cell (PIC) simulation. Starting on the first day with simple trajectory calculations involving idealized beamlines, the students will use and develop increasingly complex codes for modeling more realistic systems. By the end of the week, the students will have gained familiarity with the algorithms commonly used in PIC codes, and they will perform PIC simulations of beams with space charge. Throughout the course we will avoid the treatment of codes as "black boxes," and instead pay close attention to the physics in the codes and the numerical algorithms used in the codes.

Reading Requirement
Course notes on “Computational Methods in Accelerator Physics” (by R. D. Ryne, approx. 100 pages) will be the primary source of reading material. Included in the notes are exercises for the students that will be used for homework assignments. Students will also read and perform computer lab assignements (approx 5 pages each), which will be assigned daily.

Credit Requirements
Students will be evaluated based on performance. Lab reports (50% of final grade), assignments (25% of final grade), and final exam (25% of final grade).