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

Abstract

This paper deals with the numerical resolution of the Vlasov-Poissonsystem with a strong external magnetic field by Particle-In-Cell(PIC) methods. In this regime, classical PIC methods are subject tostability constraints on the time and space steps related to the smallLarmor radius and plasma frequency. Here, we propose anasymptotic-preserving PIC scheme which is not subjected to theselimitations. Our approach is based on first and higher order semi-implicit numericalschemes already validated on dissipative systems. Additionally, when the magnitude of the external magneticfield becomes large, this method provides a consistent PICdiscretization of the guiding-center equation, that is, incompressibleEuler equation in vorticity form. We propose several numerical experiments which provide a solid validation of the method and its underlying concepts.