The Vlasov–Poisson system with strong external magnetic field. Finite Larmor radius regime

Article type: Research Article

Authors: Bostan, Mihai

Affiliations: Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France. E-mail: mbostan@univ-fcomte.fr

Abstract: We study here the finite Larmor radius regime for the Vlasov–Poisson equations with strong external magnetic field. The derivation of the limit model follows by formal expansion in power series with respect to a small parameter. If we replace the particle distribution by the center distribution of the Larmor circles the limit of these densities satisfies a transport equation, whose velocity is given by the gyro-average of the electric field. We justify rigorously the convergence towards the above model and we investigate the well-posedness of it.

Keywords: Vlasov–Maxwell equations, finite Larmor radius regime, gyro-average

DOI: 10.3233/ASY-2008-0908

Journal: Asymptotic Analysis, vol. 61, no. 2, pp. 91-123, 2009