Efficient algorithms for dynamic aperture and momentum acceptance calculation

TL;DR

This paper introduces innovative algorithms for faster calculation of dynamic aperture and momentum acceptance in circular accelerators, significantly improving computational efficiency while maintaining accuracy.

Contribution

It presents a raster graphics-inspired flood-fill algorithm for dynamic aperture and a new Fast Touschek Tracking method for momentum acceptance, both offering substantial speed improvements.

Findings

Speed-up factors of up to 100x in calculations

Limited accuracy loss with new momentum acceptance method

Validated with modern accelerator simulation codes

Abstract

New algorithms useful for the calculation of dynamic aperture and momentum acceptance in circular accelerators are developed and presented. The flood-fill tool from raster graphics inspired us to efficiently compute dynamic apertures by minimizing required trackings on stable initial coordinates, leading to several factors of speed-up with respect to standard algorithms. A novel technique for momentum acceptance calculations, Fast Touschek Tracking, is developed. Thorough benchmarking using modern accelerator codes shows that the new technique can provide one or two orders of magnitude faster computation of local momentum acceptances with only limited loss of accuracy.