Mathematical and Numerical Methods for Non-linear Beam Dynamics

TL;DR

This paper introduces mathematical and numerical techniques for analyzing and mitigating non-linear effects in particle beam dynamics, emphasizing systematic tools for improved accelerator performance.

Contribution

It provides a comprehensive overview of modern mathematical and numerical methods specifically designed for non-linear beam dynamics analysis.

Findings

Systematic approaches to non-linear beam effects

Application of numerical methods for beam stability

Tools for suppressing detrimental non-linear effects

Abstract

One of the most severe limitations in particle accelerators and beam transport are non-linear effects. Techniques to study and possibly suppress some of these detrimental effects exist, the most popular are based on particle tracking and its analysis. This lecture is an introduction to the topic, shows some of the problems and presents several contemporary tools to treat them using a systematic and consistent approach.