Fast dynamic aperture optimization with reversal integration

TL;DR

This paper introduces a rapid method for optimizing the dynamic aperture of storage rings by utilizing reversal integration to detect chaos, significantly improving the efficiency of the optimization process.

Contribution

The paper presents a novel chaos indicator based on reversal integration differences, enabling faster dynamic aperture optimization in storage rings.

Findings

The chaos indicator correlates with particle stability.

Optimization using the indicator accelerates convergence.

Validated on multiple storage ring models.

Abstract

A fast method for dynamic aperture (DA) optimization of storage rings has been developed through the use of reversal integration. While chaotic dynamical systems have exact time-reversal symmetry, numerical forward integration differs from its reversal due to scaled cumulative round-off errors. The difference, intrinsically associated with the Lyapunov exponent, is a generic indicator of chaos because it represents the sensitivity of chaotic motion to an initial condition. A chaos indicator of the charged particle motion is then obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. "backward integrations." The indicator was confirmed to be observable through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. The DA of the National Synchrotron Light Source II storage ring, and another test diffraction-limited light source ring, were optimized using this method for the purpose of demonstration.