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Journal Articles Journal of Pure and Applied Mathematics: Advances and Applications Year : 2010

Two-dimensional Finite Larmor Radius approximation in canonical gyrokinetic coordinates

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 Frénod & Sonnendrücker 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 Frénod & Sonnendrücker 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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Dates and versions

hal-00531361 , version 1 (02-11-2010)

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Emmanuel Frénod, Alexandre Mouton. Two-dimensional Finite Larmor Radius approximation in canonical gyrokinetic coordinates. Journal of Pure and Applied Mathematics: Advances and Applications, 2010, 4 (2), pp.135-166. ⟨hal-00531361⟩
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