Asymptotic Behavior for the Vlasov--Poisson Equations with Strong External Magnetic Field. Straight Magnetic Field Lines

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

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 ...

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

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 beh...

Long Time Behavior of the Two-Dimensional Vlasov Equation with a Strong External Magnetic Field

Poisson-Vlasov in a strong magnetic field: A stochastic solution approach

Stochastic solutions are obtained for the Maxwell-Vlasov equation in the approximation where magnetic field fluctuations are neglected and the electrostatic potential is used to compute the electric field. This is a reasonable approximation for plasmas in a strong external magnetic field. Both Fourier and configuration space solutions are constructed. PACS: 52.25Dg, 02.50Ey

Multiscale Particle-in-Cell methods and comparisons for the long-time two-dimensional Vlasov-Poisson equation with strong magnetic field

We applied different kinds of multiscale methods to numerically study the long-time Vlasov-Poisson equation with a strong magnetic field. The multiscale methods include an asymptotic preserving Runge-Kutta scheme, an exponential time discretization scheme, stroboscopic averaging method and a uniformly accurate two-scale formulation. We briefly review these methods and then adapt them to solve t...