Modeling, analysis, computation and application of kinetic equations

Asymptotically stable particle-in-cell methods for the Vlasov-Poisson system with a strong external magnetic field

Francis Filbet

Paul Sabatier University, Toulouse III

We are interested in the numerical resolution of the Vlasov-Poisson system with a strong external magnetic field by Particle-In-Cell (PIC) methods. In this regime, classical PIC methods are subject to stability constraints on the time and space steps related to the small Larmor radius and plasma frequency. Here, we propose an asymptotic-preserving PIC scheme which is not subjected to these limitations. Our approach is based on first and higher order semiimplicit numerical schemes already validated on dissipative systems. Additionally, when the magnitude of the external magnetic field becomes large, this method provides a consistent PIC discretization of the guiding-center equation, that is, incompressible Euler equation in vorticity form. We propose several numerical experiments which provide a solid validation of the method and its underlying concepts.