Affiliations: LMAM, Université de Bretagne Sud, Centre Universitaire de Vannes, 1 rue de la loi, F‐56000 Vannes, France E‐mail: Emmanuel.Frenod@univ‐ubs.fr | CNRS, Institut Elie Cartan, Université Henri Poincaré – Nancy 1, B.P. 239, F‐54506 Vandœuvre‐lès‐Nancy Cedex, France E‐mail: Eric.Sonnendrucker@iecn.u‐nancy.fr
Note: [] Corresponding author.
Abstract: Motivated by the difficulty arising in the numerical simulation of the movement of charged particles in presence of a large external magnetic field, which adds an additional time scale and thus imposes to use a much smaller time step, we perform in this paper a homogenization of the Vlasov equation and the Vlasov–Poisson system which yield approximate equations describing the mean behavior of the particles. The convergence proof is based on the two‐scale convergence tools introduced by N’Guetseng and Allaire. We also consider the case where, in addition to the magnetic field, a large external electric field orthogonal to the magnetic field and of the same magnitude is applied.
