Abstract
This paper deals with 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 semi-implicit numerical schemes already validated on dissipative systems [S. Boscarino, F. Filbet, and G. Russo, J. Sci. Comput., 2016, doi:10.1007/s10915-016-0168-y]. 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, an incompressible Euler equation in vorticity form. We propose several numerical experiments which provide a solid validation of the method and its underlying concepts.
Highlights
This paper deals with the numerical resolution of the Vlasov-Poisson system with a strong external magnetic field by Particle-In-Cell (PIC) methods
We consider a plasma constituted of a large number of charged particles, which is described by the Vlasov equation coupled with the Maxwell or Poisson equations to compute the self-consistent fields
We will consider an intermediate model where the magnetic field is given, 1 B(t, x) = ε Bext(t, x⊥), with ε > 0 and we focus on the long time behavior of the plasma in the orthogonal plane to the external magnetic field, that is the two dimensional Vlasov-Poisson system with an external strong magnetic field
Summary
The numerical resolution of the Vlasov equation and related models is usually performed by Particle-In-Cell (PIC) methods which approximate the plasma by a finite number of particles. Trajectories of these particles are computed from characteristic curves (1.4) corresponding to the the Vlasov equation (1.3), whereas self-consistent fields are computed on a mesh of the physical space. The Vlasov equation is discretized in phase space using either semi-Lagrangian [17, 18, 32, 36], finite difference [39] or discontinuous Galerkin [4, 26] schemes These direct methods are very costly, several variants of particle methods have been developed over the past decades.
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