U.S. Particle Accelerator School

Accelerator Mathematics course

Sponsoring University:

University of Maryland
(This session has been cancelled)


Accelerator Mathematics


Richard Talman and Elizabeth Young, Cornell University

This course will introduce and develop practical methods for calculating accelerator phenomena. Using idealized models, computational programs will be developed rather than employing "canned" accelerator codes. The emphasis will be on beam dynamics, not the calculation of EM fields. Topics in week one include: analysis of beam signals, time domain, frequency domain, Fourier, Laplace, and z-transforms, transfer functions, reconciling observations and mathematics; map description of orbits; magnetic deflections; lattice functions; lattice design; Fourier diagnosis of field imperfection; and practical diagnostics using beam signals. While the more advanced material in week two includes: nonlinearity; resonance; chaotic particle motion; stochasticity, electron beam statistics; z-transform analysis of instability and feedback; symplecticity; and compensation of lattices for errors. The Computation Laboratory for this course will have daily sessions and utilize Mathematica although similar programs such as Maple, Matlab or even programmable calculators can be used by students more familiar with them. In addition to the computer-based problems, a certain amount of non-computational problem solving will also be required. Students will be permitted to emphasize either computation or traditional problem solving. Prerequisites: undergraduate course in mathematics and college physics. This course may be taken by those at the junior or senior undergraduate level.