Deceleration mechanism of Fermi acceleration in a time-dependent stadium billiard

TL;DR

This paper investigates how particles in a time-dependent stadium billiard can experience deceleration due to sticky orbits, which act as a natural brake on Fermi acceleration, depending on initial velocities.

Contribution

It introduces a deceleration mechanism in a stadium billiard system, showing how sticky orbits can limit Fermi acceleration without dissipation.

Findings

Particles with initial velocity above critical exhibit Fermi acceleration.

Particles below critical velocity are temporarily trapped in stability islands.

Sticky orbits can serve as a natural deceleration mechanism.

Abstract

The dynamics of a time-dependent stadium-like billiard are studied by a four dimensional nonlinear mapping. We have shown that even without any dissipation, the particle experiences a decrease on its velocity. Such condition is related with a critical resonance velocity, where if the initial velocity has a higher value than the resonant one, we can observe Fermi acceleration, however, if the initial velocity has a initial value smaller than the critical one, the particle is temporarily trapped surrounding the stability islands, in a stickiness regime. We believe that this sticky orbits can act as deceleration mechanism for Fermi Acceleration.