Dissipation effects in the ratchetlike Fermi acceleration

TL;DR

This paper investigates how dissipation influences Fermi acceleration driven by asymmetric AC pulses, revealing that dissipation causes velocity saturation and diminishes control over particle dynamics, with specific power-law decay behaviors.

Contribution

It demonstrates the significant impact of dissipation on Fermi acceleration modes and quantifies how dissipation parameters affect velocity saturation and control.

Findings

Saturation time decays as a power law with dissipation parameter.

Mean velocity at saturation decreases with dissipation, following specific power laws.

Dissipation limits the controllability of particle acceleration modes.

Abstract

Ac driven asymmetric pulses can be used to control the Fermi acceleration between three different motions, ${\bf A:}$ the {\it accelerated} mode; ${\bf D:}$ the {\it decelerated} mode and ${\bf H:}$ the {\it hyperaccelerated} mode. In this work we show that dissipation strongly affects the particles velocity, reducing the possibility for an accurate control of the dynamics. The saturation time, where the mean velocity starts to be constant due to dissipation, decays with a power law $\sim\gamma^{-\beta}$, where $\gamma$ is the dissipation parameter and $\beta$ is close to 1. The value of the saturated mean velocity also decays with a power law with exponent $\beta\sim0.6$ for the case ${\bf H}$, and $\beta\sim0.3$ for the case ${\bf A}$. In the case ${\bf D}$ this velocity is almost constant for small dissipations.