Fast chaos indicator from auto-differentiation for dynamic aperture optimization

TL;DR

This paper introduces a fast chaos indicator based on auto-differentiation and tangent map norms, enabling efficient dynamic aperture optimization in particle accelerators.

Contribution

It proposes using the tangent map norm from differentiable tracking as a computationally efficient chaos indicator, reducing the cost of dynamic aperture optimization.

Findings

The tangent map norm effectively indicates chaotic behavior.

Few-turn tangent maps suffice for chaos detection.

Application to ALS-U lattice shows improved optimization efficiency.

Abstract

Automatic differentiation provides an efficient means of computing derivatives of complex functions with machine precision, thereby enabling differentiable simulation. In this work, we propose the use of the norm of the tangent map, obtained from differentiable tracking of particle trajectories, as a computationally efficient indicator of chaotic behavior in phase space. In many cases, a one-turn or few-turn tangent map is sufficient for this purpose, significantly reducing the computational cost associated with dynamic aperture optimization. As an illustrative application, the proposed indicator is employed in the dynamic aperture optimization of an ALS-U lattice design.