Hydrodynamic Approach to the Free Electron Laser Instability

TL;DR

This paper derives a hydrodynamic model from the Vlasov-Maxwell system for free electron laser instability, showing it is equivalent to the kinetic description and accurately predicts small signal gain.

Contribution

It introduces an exact relativistic hydrodynamic closure for water bag distributions, bridging kinetic and fluid models for free electron laser analysis.

Findings

Hydrodynamic equations are fully equivalent to Vlasov-Maxwell equations.

The fluid model accurately predicts small signal gain features.

Results agree well with previous kinetic-based studies.

Abstract

Starting from the Vlasov-Maxwell system, an exact relativistic hydrodynamic closure for a special type water bag distributions satisfying the Vlasov equation has been derived. It has been shown that the hydrodynamic equations are fully equivalent to the original Vlasov-Maxwell equations. The linear stability of the exact hydrodynamic closure has been studied as well. It has been shown that all basic features of the small signal gain can be derived from the fluid dynamic description developed here. Satisfactory agreement with previously reported results has been also found.