In-flight dissipation as a mechanism to suppress Fermi acceleration

TL;DR

This paper investigates how in-flight dissipation via drag force suppresses Fermi acceleration in a time-dependent elliptical billiard, showing a phase transition from unlimited to limited energy growth.

Contribution

It introduces a dissipative model with in-flight drag force and demonstrates its effect on suppressing Fermi acceleration, extending previous studies on damping effects.

Findings

Dissipation causes a phase transition from unlimited to limited energy growth.

Average velocity behavior can be described using scaling arguments.

In-flight dissipation effectively suppresses Fermi acceleration.

Abstract

Some dynamical properties of time-dependent driven elliptical-shaped billiard are studied. It was shown that for the conservative time-dependent dynamics the model exhibits the Fermi acceleration [Phys. Rev. Lett. 100, 014103 (2008)]. On the other hand, it was observed that damping coefficients upon collisions suppress such phenomenon [Phys. Rev. Lett. 104, 224101 (2010)]. Here, we consider a dissipative model under the presence of in-flight dissipation due to a drag force which is assumed to be proportional to the square of the particle's velocity. Our results reinforce that dissipation leads to a phase transition from unlimited to limited energy growth. The behaviour of the average velocity is described using scaling arguments.