Two-dimensional Finite Larmor Radius approximation in canonical gyrokinetic coordinates

TL;DR

This paper develops new mathematical results on approximating the 2D Vlasov-Poisson system with a strong magnetic field using finite Larmor radius models, employing two-scale convergence techniques.

Contribution

It introduces a novel approach to analyze the approximation using canonical gyrokinetic coordinates and extends previous work with new convergence proofs.

Findings

Established two-scale convergence results for the model

Extended previous theoretical frameworks with new proofs

Provided a detailed mathematical analysis of the approximation

Abstract

In this paper, we present some new results about the approximation of the Vlasov-Poisson system with a strong external magnetic field by the 2D finite Larmor radius model. The proofs within the present work are built by using two-scale convergence tools, and can be viewed as a new slant on previous works of Fr\'enod and Sonnendr\"ucker and Bostan on the 2D finite Larmor Radius model. In a first part, we recall the physical and mathematical contexts. We also recall two main results from previous papers of Fr\'enod and Sonnendr\"ucker and Bostan. Then, we introduce a set of variables which are so-called canonical gyrokinetic coordinates, and we write the Vlasov equation in these new variables. Then, we establish some two-scale convergence and weak-* convergence results.