Detecting chaos in particle accelerators through the frequency map analysis method

TL;DR

This paper discusses how frequency map analysis can detect chaos in particle accelerators caused by non-linear effects, aiding in stability improvements through simulations and experiments.

Contribution

It demonstrates the effectiveness of frequency map analysis in identifying chaotic beam motion and guiding corrections in particle accelerators.

Findings

Frequency map analysis detects chaotic motion effectively.

The method guides correction of non-linear effects.

Applications shown in simulations and experimental data.

Abstract

The motion of beams in particle accelerators is dominated by a plethora of non-linear effects which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.