U.S. Particle Accelerator School

Introduction to Beam Optics course

Sponsoring University:

University of Washington, Seattle


Introduction to Beam Optics


Martin Berz, Michigan State University

The course will begin with basic concepts of linear beam optics based on matrix methods. Several elementary systems will be introduced, including imaging systems, -I transforms, achromats, and energy and mass spectrometers. We will introduce FODO cells and other examples useful in periodic systems and study some of their basic characteristics such as tunes, invariant ellipses, fixed points and chromaticities. We will proceed with methods for the calculation of higher order terms for the analysis of nonlinear effects, including perturbation integrals, differential algebraic methods, Lie factorizations, and normal form methods. These will be applied (1) to the computation and correction of aberrations of single pass systems, and (2) to the analysis and correction of nonlinear effects in repetitive systems such as amplitude tune shifts, resonances, and long-term stability estimates. Problem sets covering all the concepts of the course will be provided, many of which require computer use. We will introduce basic concepts and techniques of beam optics computation, and use the program COSY INFINITY to solve the computational problems.