Long time behavior of the Vlasov-Maxwell-Fokker-Planck system with a strong external magnetic field

TL;DR

This paper analyzes the long-term behavior of the Vlasov-Maxwell-Fokker-Planck system under a strong magnetic field, deriving and rigorously justifying a reduced model in lower dimensions using the modulated energy method.

Contribution

It introduces a formally derived asymptotic model for plasma confinement and provides a rigorous mathematical justification for it in a simplified setting.

Findings

The reduced model is well-posed as a dynamical system.

Rigorous justification of the asymptotic model is achieved.

The modulated energy method is effectively applied.

Abstract

The subject matter of this paper concerns the magnetic confinement of plasma. We investigate the long time behavior of the Vlasov-Maxwell-Fokker-Planck system under the effect of a strong external magnetic field. We first formally derive an asymptotically reduced model. In three space dimensions, a constraint occurs along the parallel direction to the magnetic field. To eliminate the corresponding Lagrange multiplier, we then study the Vlasov-Maxwell-Fokker-Planck system in two spatial dimensions and three velocity dimensions. In this setting, we show that the obtained asymptotic model defines a well-posed dynamical system, and we provide a rigorous mathematical justification of the formally derived system. Our proofs rely on the modulated energy method.