Short-time dynamics in presence of wave-particles interactions: a perturbative approach

TL;DR

This paper develops a perturbative analytical approach to study the short-time dynamics of wave-particle interactions in a Free Electron Laser, providing explicit formulas that match numerical simulations.

Contribution

It introduces a novel perturbative method for deriving analytical expressions of macroscopic observables in wave-particle systems.

Findings

Analytical expressions agree with numerical simulations.

The approach effectively describes early-time dynamics.

Applicable to waterbag distributions in FEL models.

Abstract

The self-consistent interaction between a beam of charged particles and a wave is considered, within a Vlasov picture. The model is discussed with reference to the case of a Free Electron Laser. Starting with a spatially bunched waterbag distribution, we derive, via perturbative methods, closed analytical expressions for the time evolution of the main macroscopic observables. Predictions of the theory are shown to agree with direct numerical simulations.