Using Lie Algebra methods to analytically study non-perturbative effects in beam lines

摘要

Non-perturbative effects can arise in beam lines from strong chromatic and nonlinear elements or from large lattice errors. We present a general approach using Lie algebra methods which provides analytic treatment of beam lines with strong elements or large errors. In addition to affording insight into lattice design and performance, these techniques can answer a broad spectrum of tolerance questions without use of numerical simulations. We give several detailed examples.