Out-of-equilibrium mean-field dynamics of a model for wave-particle interaction

TL;DR

This paper studies the out-of-equilibrium mean-field dynamics of a wave-particle interaction model, revealing a transition between regimes and applying violent relaxation theory to predict laser saturation behavior.

Contribution

It introduces a novel analysis of wave-particle interactions, identifying a dynamical transition and applying violent relaxation theory to predict system regimes.

Findings

Identified a transition separating macroscopic regimes.

Violent relaxation theory predicts saturated regimes below the transition.

Transition explained as a switch between metastable states.

Abstract

The out-of-equilibrium mean-field dynamics of a model for wave-particle interaction is investigated. Such a model can be regarded as a general formulation for all those applications where the complex interplay between particles and fields is known to be central, e.g., electrostatic instabilities in plasma physics, particle acceleration and free-electron lasers (FELs). The latter case is here assumed as a paradigmatic example. A transition separating different macroscopic regimes is numerically identified and interpreted by making use of the so-called violent relaxation theory. In the context of free-electron lasers, such a theory is showed to be effective in predicting the saturated regime for energies below the transition. The transition is explained as a dynamical switch between two metastable regimes, and is related to the properties of a stationary point of an entropic functional.