Homogenization of the Vlasov equation and of the Vlasov-Poisson system with a strong external magnetic field

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.