Finding stability domains and escape rates in kicked Hamiltonians

TL;DR

This paper analyzes the stability and escape rates of particles in kicked Hamiltonian systems, using effective Hamiltonians, perturbation theories, and noise modeling to estimate stable regions and particle loss in storage rings.

Contribution

It introduces analytical methods to estimate stability domains and escape rates in chaotic kicked Hamiltonian systems, incorporating noise and damping effects.

Findings

Derived analytical escape rate estimates in the small damping regime.

Compared perturbation theories and variational methods for stability estimation.

Validated analytical results with numerical simulations.

Abstract

We use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the resonances, the dynamics typically has a finite region in phase space where it is stable. Inherent noise in the system leads to particle loss from this stable region. The competition of this noise with radiation damping, which increases stability, determines the escape rate. Determining this `aperture' and finding escape rates is therefore an important physical problem. We compare the results of two different perturbation theories and a variational method to estimate this stable region. Including noise, we derive analytical estimates for the steady-state populations (and the resulting beam emittance), for the escape rate in the small damping regime, and compare them with numerical simulations.