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Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field

Published online by Cambridge University Press:  30 July 2015

Emmanuel Frénod
Université Bretagne-Sud, UMR 6205, LMBA, F-56000 Vannes, France Inria Nancy-Grand Est, TONUS Project & IRMA (UMR CNRS 7501), Université de Strasbourg, France
Sever A. Hirstoaga*
Inria Nancy-Grand Est, TONUS Project & IRMA (UMR CNRS 7501), Université de Strasbourg, France
Mathieu Lutz
IRMA (UMR CNRS 7501) Université de Strasbourg, 7 rue René Descartes, F-67084 Strasbourg & Inria Nancy-Grand Est, TONUS Project, France
Eric Sonnendrücker
Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany & TU Munich, Zentrum Mathematik - M16, Boltzmannstr. 3, 85747 Garching, Germany
*Corresponding author. Email addresses: (E. Frénod), (S. A. Hirstoaga), (M. Lutz), (E. Sonnendrücker)
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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.

Research Article
Copyright © Global-Science Press 2015 

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