U.S. Particle Accelerator School

Computational Methods in Beam Physics course

Sponsoring University:

The University of Texas at Austin


Computational Methods in Beam Physics


Martin Berz and Kyoko Makino, Michigan State University

The course will provide an introduction to the two dominating computational tasks in beam physics, the computation and analysis of paticle motion as well as the computation of the fields that govern the motion. Particle motion will be addressed within the framework of transfer maps. Beginning with the linear theory we discuss transfer matrices, beam ellipses, lattice functions, and basic building blocks of accelerators and beamlines. The nonlinear theory will be treated within the differential algebraic framework, and will cover nonlinear aberrations, parameter dependent fixed points, tune shifts, resonances, various symplectic representations, and tracking.

Field computation will be discussed both from the perspective of multipole expansions as well via 3D and 4D field solvers. The local view of multipole expansions will cover both the so-called main fields and the intricate nonlinear phenomena that can result in fringe fields, and will be based on fixed point problems of differential algebraic operators. The global view of field solution will cover the divided difference- and low- and high-order finite elements approaches as well as some aspects of mesh generation.

Participants will spend about half of their time with hands-on computational work on a PC cluster running Windows NT. Problems are both based on existing dynamics and field codes, including COSY INFINITY, as well as the development and testing of small modules for various tasks within a FORTRAN environment.