Improving beam stability in particle accelerator models by using Hamiltonian control

TL;DR

This paper introduces a Hamiltonian control method for particle accelerator models, significantly enhancing beam stability by enlarging the dynamical aperture and reducing chaos in a 4D symplectic map with sextupole nonlinearity.

Contribution

A novel Hamiltonian control approach tailored for 4D symplectic maps in particle accelerators, improving orbital regularity and stability.

Findings

Controlled system exhibits up to 1.7 times larger dynamical aperture.

Hamiltonian control reduces chaotic behavior in the model.

Enhanced beam stability demonstrated through SALI chaos indicator.

Abstract

We derive a Hamiltonian control theory which can be applied to a 4D symplectic map that models a ring particle accelerator composed of elements with sextupole nonlinearity. The controlled system is designed to exhibit a more regular orbital behavior than the uncontrolled one. Using the Smaller Alignement Index (SALI) chaos indicator, we are able to show that the controlled system has a dynamical aperture up to 1.7 times larger than the original mode