Phase space focusing in dissipative driven elliptical billiards

TL;DR

This paper investigates how dissipation and harmonic driving in elliptical billiards interact to suppress Fermi acceleration, create dynamical attractors, and enable control over particle states, offering a new method for particle preparation.

Contribution

It introduces a novel analysis of dissipative and driven elliptical billiards, demonstrating control over attractors and phase space focusing for particle state manipulation.

Findings

Dissipation and driving balance to prevent Fermi acceleration.

Dynamical attractors focus the ensemble in phase space.

Control over attractor position via parameters.

Abstract

We study the interplay of dissipation and harmonic driving in the elliptical billiard. These two competing processes balance each other, which leads to a destruction of Fermi acceleration and thus to a saturation of the ensemble averaged velocity. In particular, the emergence of dynamical attractors sharply focuses the ensemble onto certain parts of phase space. The population of individual attractors can be controlled by adding small hyperbolic elements to certain parts of the boundary of the billiard. Furthermore, the position of the attractors in momentum space can be adjusted by tuning parameters like the dissipation constant or the driving amplitude and frequency. Thus, the dissipative, driven elliptical billiard represents a powerful tool for particle preparation.