Convergence analysis of a Crank-Nicolson scheme for strongly magnetized plasmas

TL;DR

This paper analyzes the convergence of an asymptotic preserving particle scheme for the Vlasov equation in strongly magnetized plasmas, enabling stable large-scale simulations even with coarse discretizations.

Contribution

It provides a rigorous convergence analysis of a novel implicit-explicit scheme that relaxes stability constraints in plasma simulations with strong magnetic fields.

Findings

Error bounds explicitly depend on discretization and stiffness parameters.

Numerical tests confirm sharpness of theoretical error estimates.

Scheme effectively captures large-scale plasma dynamics in strong magnetic fields.

Abstract

The present paper is devoted to the convergence analysis of an asymptotic preserving particle scheme designed to serve as a particle pusher in a Particle-In-Cell (PIC) method for the Vlasov equation with a strong inhomogeneous magnetic field. The asymptotic preserving scheme that we study removes classical strong restrictive stability constraints on discretization steps while capturing the large-scale dynamics, even when the discretization is too coarse to capture fastest scales. Our error bounds are explicit regarding the discretization and stiffness parameters and match sharply numerical tests. The present analysis is expected to be representative of the general analysis of a class of schemes, developed by the authors, conceived as implicit-explicit schemes on augmented formulations.