U.S. Particle Accelerator School

Computational Methods in Electromagnetism course

Sponsoring University:

Cornell University


Computational Methods in Electromagnetism


Kwok Ko and Zenghai Li, SLAC

Purpose and Audience
This course studies the electromagnetic effects arising in particle accelerators and their impact on the design and performance of these machines through numerical computations. The material is aimed at graduate students in physics, engineering or mathematical sciences with strong interest in computational accelerator physics, particularly in the area of electromagnetic modeling. The course provides the knowledge, skills and tools for workers in accelerator technology to aid in designing and analyzing accelerating cavities and beamline components.

Electromagnetism and Accelerator Physics, background in mathematics and experience with computers.

This multi-disciplinary course serves to lay a broad foundation in accelerator simulation and to develop the modeling expertise that is necessary for a possible career in computational accelerator physics. Students will be exposed to the underlying principles of electromagnetism in accelerators, the numerical methods for solving Maxwell equations in various regimes, the basics of scientific computing for best practice in simulation, and the modeling techniques and codes used in design and analysis exercises pertaining to real machines.

Instructional Method
The daily instruction will consist of two lectures during the morning session covering material from textbooks and handout notes. The afternoon laboratory session will focus on computer simulations to provide hands-on experience in working with modeling software and applying them to solve real-world problems encountered in accelerator R&D. Two instructors will be on hand to help with computer exercises. There will be daily problem sets and a take home final exam.

Course Content
The course will cover topics in electromagnetism that include statics, eddy currents and high frequency RF as well as space charge and wakefield effects. Numerical methods in the time and frequency domain based on finite difference and finite element discretization for treating Maxwell equations in these areas will be presented. Algorithms for solving the resulting linear systems or eigen-systems will be discussed, and different time-stepping schemes (explicit versus implicit) compared. Elements of an EM code package from meshing to solver to post-processing will be described. Using standard commercial and SLAC software, the students will be introduced to a range of computational techniques for designing and analyzing accelerator components such as those considered for linear colliders, storage rings and light sources. They will learn how to compute wakefields and impedances, and will study particle simulation. Advanced topics including parallel computing, adaptive refinement, and shape optimization to deal with complex designs under stringent accuracy requirement will be explored.

Reading Requirements
(to be provided by the USPAS) "Numerical Techniques in Electromagnetics" by Matthew N.O. Sadiku, CRC Press; 2nd edition ( July 12, 2000).

Credit Requirements
Student’s course grade will be based on problem sets (40 %), computer lab performance (30 %), and a final exam (30%).