The three-dimensional Finite Larmor Radius Approximation

TL;DR

This paper rigorously derives the three-dimensional gyrokinetic limit of the Vlasov-Poisson system for plasmas with a large magnetic field, incorporating quasineutrality and electron thermodynamics, using averaging techniques.

Contribution

It extends the finite Larmor radius approximation to a three-dimensional setting with rigorous mathematical proof of the asymptotic limit.

Findings

Established the gyrokinetic limit in 3D plasma models

Validated the use of averaging lemmas in this context

Provided a rigorous mathematical framework for the approximation

Abstract

Following Fr\'enod and Sonnendr\"ucker, we consider the finite Larmor radius regime for a plasma submitted to a large magnetic field and take into account both the quasineutrality and the local thermodynamic equilibrium of the electrons. We then rigorously establish the asymptotic gyrokinetic limit of the rescaled and modified Vlasov-Poisson system in a three-dimensional setting with the help of an averaging lemma.