Robust Exponential Acceleration in Time-Dependent Billiards

TLDR

The acceleration mechanism has a natural thermodynamical interpretation and applies to a hot dilute gas of repelling particles. The study constructs a class of nonrelativistic particle accelerators that enable the majority of particles to gain energy exponentially. The accelerators are realized as ergodic billiards with a piston that moves and is removed adiabatically in a periodic cycle. The exponential energy growth is robust to chaotic‑preserving deformations, analytically controllable, and confirmed by numerical simulations.

Abstract

A class of nonrelativistic particle accelerators in which the majority of particles gain energy at an exponential rate is constructed. The class includes ergodic billiards with a piston that moves adiabatically and is removed adiabatically in a periodic fashion. The phenomenon is robust: deformations that keep the chaotic character of the billiard retain the exponential energy growth. The growth rate is found analytically and is, thus, controllable. Numerical simulations corroborate the analytic predictions with good precision. The acceleration mechanism has a natural thermodynamical interpretation and is applied to a hot dilute gas of repelling particles.