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

TL;DR

This paper introduces a modified Crank-Nicolson Particle-In-Cell method for the Vlasov-Poisson system with a strong magnetic field, improving stability and accuracy in plasma simulations.

Contribution

It develops a novel PIC scheme based on Crank-Nicolson discretization that accounts for magnetic field variations, extending previous methods to more complex plasma regimes.

Findings

The method is stable under small Larmor radius conditions.

Numerical experiments validate the accuracy of the scheme.

The approach effectively captures guiding-center dynamics.

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.