Long time behaviour of an exponential integrator for a Vlasov-Poisson system with strong magnetic field

Emmanuel Frenod (1, 2) , Sever Adrian Hirstoaga (1) , Mathieu Lutz (1, 3) , Eric Sonnendrücker (4)

1 TONUS - TOkamaks and NUmerical Simulations
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
3 IRMA - Institut de Recherche Mathématique Avancée
4 IPP - Max-Planck-Institut für Plasmaphysik [Garching]

With the aim of solving in a four dimensional phase space a multi-scale Vlasov-Poisson system, we propose in a Particle-In-Cell framework a robust time-stepping method that works uniformly when the small parameter vanishes. As an exponential integrator, the scheme is able to use large time steps with respect to the typical size of the solution's fast oscillations. In addition, we show numerically that the method has accurate long time behaviour and that it is asymptotic preserving with respect to the limiting Guiding Center system.

Mots clés: Particle-In-Cell method; exponential integrators; asymptotic preserving scheme; Vlasov-Poisson system; guiding center model

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Modélisation et simulation; Physique des plasmas [physics.plasm-ph]

Emmanuel Frenod, Sever Adrian Hirstoaga, Mathieu Lutz, Eric Sonnendrücker. Long time behaviour of an exponential integrator for a Vlasov-Poisson system with strong magnetic field. 2014. ⟨hal-00974028v1⟩