On massless electron limit for a multispecies kinetic system with external magnetic field

TL;DR

This paper rigorously derives a new anisotropic drift-diffusion model for electrons in a plasma as their mass tends to zero, accounting for magnetic field effects and electron-ion interactions.

Contribution

It introduces a novel kinetic-to-fluid limit for a multispecies plasma with magnetic field, incorporating Fokker-Planck collisions and anisotropic diffusion effects.

Findings

Convergence to an anisotropic drift-diffusion equation for electrons.

Handling of magnetic field effects and regularity issues in the limit.

Application of advanced mathematical methods for kinetic-fluid transition.

Abstract

We consider a three-dimensional kinetic model for a two species plasma consisting of electrons and ions confined by an external nonconstant magnetic field. Then we derive a kinetic-fluid model when the mass ratio $m_e/m_i$ tends to zero. Each species initially obeys a Vlasov-type equation and the electrostatic coupling follows from a Poisson equation. In our modeling, ions are assumed non-collisional while a Fokker-Planck collision operator is taken into account in the electron equation. As the mass ratio tends to zero we show convergence to a new system where the macroscopic electron density satisfies an anisotropic drift-diffusion equation. To achieve this task, we overcome some specific technical issues of our model such as the strong effect of the magnetic field on electrons and the lack of regularity at the limit. With methods usually adapted to diffusion limit of collisional kinetic equations and including renormalized solutions, relative entropy dissipation and velocity averages, we establish the rigorous derivation of the limit model.