Two-dimensional Finite Larmor Radius approximation in canonical gyrokinetic coordinates

Emmanuel Frénod (1, 2) , Alexandre Mouton (2, 3)

1 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (UMR 3192)
2 CALVI - Scientific computation and visualization
3 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Homogenization; Two-scale convergence; Vlasov-Poisson models; Finite Larmor radius; Plasma physics

Domaines: Analyse numérique [math.NA]; Physique des plasmas [physics.plasm-ph]; Equations aux dérivées partielles [math.AP]

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⟩