Fermi acceleration in time-dependent rectangular billiards due to multiple passages through resonances

TL;DR

This paper investigates how a slowly rotating rectangular billiard with moving boundaries can cause particles to undergo resonance phenomena, leading to the breakdown of adiabatic invariance and unlimited acceleration.

Contribution

It introduces a canonical perturbation theory approach to describe resonance phenomena and particle acceleration in time-dependent billiards with moving boundaries.

Findings

Resonance conditions can be satisfied during slow boundary evolution.

Scattering on a resonance and capture into a resonance occur in the system.

These phenomena result in the destruction of adiabatic invariance and unlimited particle acceleration.

Abstract

We consider a slowly rotating rectangular billiard with moving boundaries and use the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be satisfied. Correspondingly, phenomena of scattering on a resonance and capture into a resonance happen in the system. These phenomena lead to destruction of adiabatic invariance and to unlimited acceleration of the particle.