Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard

TL;DR

This paper investigates how energy decays and Fermi acceleration is suppressed in a dissipative stadium-like billiard system, using scaling arguments to analyze long-term particle dynamics and attractors.

Contribution

It introduces a nonlinear mapping model for a dissipative stadium billiard and demonstrates how dissipation prevents unlimited energy growth, supporting the idea that Fermi acceleration is not structurally stable.

Findings

Energy decays over time due to dissipation.

Different initial conditions lead to various attractors.

Fermi acceleration is suppressed in the dissipative regime.

Abstract

The behavior of the average energy for an ensemble of non-interacting particles is studied using scaling arguments in a dissipative time-dependent stadium-like billiard. The dynamics of the system is described by a four dimensional nonlinear mapping. The dissipation is introduced via inelastic collisions between the particles and the moving boundary. For different combinations of initial velocities and damping coefficients, the long time dynamics of the particles leads them to reach different states of final energy and to visit different attractors, which change as the dissipation is varied. The decay of the average energy of the particles, which is observed for a large range of restitution coefficients and different initial velocities, is described using scaling arguments. Since this system exhibits unlimited energy growth in the absence of dissipation, our results for the dissipative case give support to the principle that Fermi acceleration seem not to be a structurally stable phenomenon.