Finite Larmor radius approximation for the Fokker-Planck-Landau equation

TL;DR

This paper derives a finite Larmor radius approximation for the Fokker-Planck-Landau equation, accounting for collisions, and demonstrates that the resulting collision operator preserves key physical properties in plasma physics.

Contribution

It introduces a new collision operator for the gyroaveraged Fokker-Planck-Landau equation that maintains essential physical properties.

Findings

The averaged collision kernel conserves mass, momentum, and energy.

The operator dissipates entropy, aligning with physical expectations.

The approximation applies to various collision kernels.

Abstract

The subject matter of this paper concerns the derivation of the finite Larmor radius approximation, when collisions are taken into account. Several studies are performed, corresponding to different collision kernels. The main motivation consists in computing the gyroaverage of the Fokker-Planck-Landau operator, which plays a major role in plasma physics. We show that the new collision operator enjoys the usual physical properties; the averaged kernel balances the mass, momentum, kinetic energy and dissipates the entropy.