A modified Crank-Nicolson scheme for the Vlasov-Poisson system with a strong external magnetic field

Abstract

We propose and study a Particle-In-Cell (PIC) method based on the Crank-Nicolson time discretization for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic field with fixed direction, where we focus on the motion of particles in the plane orthogonal to the magnetic field. In this regime, the time step can be subject to stability constraints related to the smallness of Larmor radius and plasma frequency [21]. To avoid this limitation, our approach is based on numerical schemes [9, 10, 12], providing a consistent PIC discretization of the guiding-center system taking into account variations of the magnetic field. We carry out some theoretical proofs and perform several numerical experiments to validate the method and its underlying concepts.