Two-dimensional Finite Larmor Radius approximation in canonical gyrokinetic coordinates

Details Two-dimensional Finite Larmor Radius approximation in canonical gyrokinetic coordinates Two-dimensional Finite Larmor Radius approximation in canonical gyrokinetic coordinates

2010-11-03

arxiv.org/abs/1011.0826v1

Journal of Pure and Applied Mathematics: Advances and Applications 4, 2 (2010) 135-166

Mathematics

Numerical Analysis

Scientific paper

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.

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