Homogenization of the Vlasov Equation and of the Vlasov - Poisson System with a Strong External Magnetic Field

Emmanuel Frénod (1) , Eric Sonnendrücker (2)

1 LMAM - Laboratoire de Mathématiques et Applications des Mathématiques, EA 3885
2 NUMATH - Mathematical Analysis and Numerical Simulation of Non-Linear Models

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 of 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.

Mots clés: Vlasov-Poisson equations; kinetic equations; homogenization; gyrokinetic approximation; multiple time scales; two scale convergence

Domaines: Autre [cs.OH]

Emmanuel Frénod, Eric Sonnendrücker. Homogenization of the Vlasov Equation and of the Vlasov - Poisson System with a Strong External Magnetic Field. Asymptotic Analysis, 1998, 18 (3-4), pp.193--214. ⟨inria-00073462v2⟩