Free particle scattering off two oscillating disks

TL;DR

This paper studies the classical scattering dynamics of particles off two oscillating disks, revealing complex energy exchange, chaotic behavior, and stochastic cooling effects, with implications for understanding non-conservative scattering systems.

Contribution

It introduces a detailed analysis of energy and velocity distributions in a non-conservative, oscillating disk scattering system, highlighting novel stochastic cooling phenomena.

Findings

Energy of exiting particles shows non-monotonic gaps at certain velocities.

High-energy exit velocities follow a Gaussian distribution with consistent mean and variance.

Irregular initial velocities lead to Gaussian distributions with reduced mean and variance, demonstrating stochastic cooling.

Abstract

We investigate the two-dimensional classical dynamics of the scattering of point particles by two periodically oscillating disks. The dynamics exhibits regular and chaotic scattering properties, as a function of the initial conditions and parameter values of the system. The energy is not conserved since the particles can gain and loose energy from the collisions with the disks. We find that for incident particles whose velocity is on the order of the oscillating disk velocity, the energy of the exiting particles displays non-monotonic gaps of allowed energies, and the distribution of exiting particle velocities shows significant fluctuations in the low energy regime. We also considered the case when the initial velocity distribution is Gaussian, and found that for high energies the exit velocity distribution is Gaussian with the same mean and variance. When the initial particle velocities are in the irregular regime the exit velocity distribution is Gaussian but with a smaller mean and variance. The latter result can be understood as an example of stochastic cooling. In the intermediate regime the exit velocity distribution differs significantly from Gaussian. A comparison of the results presented in this paper to previous chaotic static scattering problems is also discussed.